EPA/600/R-99/011

February 1999

THREE-DIMENSIONAL NAPL FATE AND TRANSPORT MODEL

by

Gary A. Pope, Kamy Sepehrnoori, Mukul M. Sharma,

Daene C. McKinney, Gerald E. Speitel, Jr., and Richard E. Jackson*

Center for Petroleum and Geosystems Engineering

The University of Texas at Austin

Austin, Texas 78712

and

*Duke Engineering and Services, Inc.

9111 Research Blvd.

Austin, Texas 78758

Cooperative Agreement CR-821897

Project Officer

Jong Soo Cho

Subsurface Protection and Remediation Division

National Risk Management Research Laboratory

Ada, Oklahoma 74820

NATIONAL RISK MANAGEMENT RESEARCH LABORATORY

OFFICE OF RESEARCH AND DEVELOPMENT

U.S. ENVIRONMENTAL PROTECTION AGENCY

CINCINNATI, OH 45268
ii

 Notice

The U. S. Environmental Protection Agency through its Office of Research and Development partially

funded and collaborated in the research described here under assistance agreement number CR-821897 to

The University of Texas at Austin. It has been subjected to the Agency's peer and administrative review

and has been approved for publication as an EPA document. Mention of trade names or commercial

products does not constitute endorsement or recommendation for use.

When available, the software described in this document is supplied on "as-is" basis without guarantee or

warranty of any kind, express or implied. Neither the United States Government (United States

Environmental Protection Agency, Office of Research and Development, National Risk Management

Research Laboratory), The University of Texas at Austin, nor any of the authors accept any liability

resulting from use of this software.
iii

Foreword

The U. S. Environmental Protection Agency is charged by Congress with protecting the Nation's land, air,

and water resources. Under a mandate of national environmental laws, the Agency strives to formulate and

implement actions leading to a compatible balance between activities and the ability of natural systems to

support and nurture life. To meet these mandates, EPA's research program is providing data and technical

support for solving environmental problems today and building a science knowledge base necessary to

manage our ecological resources wisely, understand how pollutants affect our health, and prevent or reduce

environmental risks in the future.

The National Risk Management Research Laboratory is the Agency's center for investigation of

technological and management approaches for reducing risks from threats to human health and the

environment. The focus of the Laboratory's research program is on methods for the prevention and control

of pollution to air, land, water, and subsurface resources; protection of water quality in public water

systems; remediation of contaminated sites and ground water; and prevention and control of indoor air

pollution. The goal of this research effort is to catalyze development and implementation of innovative,

cost-effective environmental technologies; develop scientific and engineering information needed by EPA

to support regulatory and policy decisions; and provide technical support and information transfer to ensure

effective implementation of environmental regulations and strategies.

Simulation models are needed for analyzing and predicting the fate and transport of nonaqueous phase

liquids (NAPLs) in the subsurface environment and to assess the effectiveness of remedial actions at NAPL

contaminated sites. There are a number of crucial questions concerning the physical, chemical, and

biological processes affecting the fate and transport of NAPLs that can only be addressed by modeling the

processes under realistic conditions taking into account aquifer heterogeneities, compositional phenomena,

geochemistry, microbiology, and other complications. This report describes the development, testing and

validation of a comprehensive flow and transport simulator (UTCHEM) that can model fate and transport

of NAPLs as well as processes for their remediation. Illustrations of both surfactant remediation and

bioremediation of contaminated aquifers are given.

Clinton W. Hall, Director

Subsurface Protection and Remediation Division

National Risk Management Research Laboratory
iv

 Abstract

We have added several new and significant capabilities to UTCHEM to make it into a general-purpose

NAPL simulator. The simulator is now capable of modeling transient and steady-state three-dimensional

flow and mass transport in the groundwater (saturated) and vadose (unsaturated) zones of aquifers. The

model allows for: changes in fluid properties as a site is remediated; heterogeneous aquifer properties; the

flow and transport of remedial fluids whose density, viscosity and temperature are variable, including

surfactants, cosolvents and other enhancement agents; the dissolution and/or mobilization of NAPLs by

nondilute remedial fluids; and chemical and microbiological transformations. Appropriate physical,

chemical and biological process models important in describing the fate and transport of NAPLs in

contaminated aquifers have been incorporated into the simulator, such as multiple organic NAPL phase,

nonequilibrium interphase mass transfer, sorption, microbiological and geochemical reactions, and the

temperature dependence of pertinent chemical and physical properties. The biodegradation model includes

inhibition, sequential use of electron acceptors, and cometabolism and can be used to model a very general

class of bioremediation processes. The model can be used to simulate the actual field operation of

remediation activities such as surfactant remediation or bioremediation as well as laboratory experiments

with large-scale aquifer models.

A systematic evaluation was undertaken to assess the applicability and accuracy of all physical and

chemical models of the various pertinent phenomena such as capillary pressure, relative permeability,

adsorption, nonequilibrium mass transfer, dispersion, and phase behavior. The microbiological model

suitable for very general bioremediation simulations was added to UTCHEM and tested with data from the

literature with good agreement. Comparisons to analytical solutions were made and numerical dispersion

control and accuracy testing were performed. The model was tested against experimental and field data.

The FORTRAN source code has been delivered to EPA along with sample input and output files.

This report contains 12 sections. Section 1 gives an overview of the project objectives and

accomplishments. Sections 2 through 12 describe the formulation of UTCHEM. Appendix A contains the

user’s guide for UTCHEM, Appendix B contains the user’s guide for UTCHEM local grid refinement.

Appendix C presents the discretized flow equations.

This report was submitted in fulfillment of CR-821897 by The University of Texas at Austin under partial

sponsorship of the U.S. Environmental Protection Agency. This report covers a period from September

1994 to September 1996 and work was completed as of September 1996.
v

Contents

Notice ......................................................................................................................................................... ii

Foreword.................................................................................................................................................... iii

Abstract.......................................................................................................................................................iv

Figures..................................................................................................................................................... viii

Tables .........................................................................................................................................................ix

Section 1 Project Summary .........................................................................................................................1

1.1 Introduction ......................................................................................................................................1

1.2 Model Development..........................................................................................................................2

1.2.1 Microbiological Population Modeling.....................................................................................3

1.2.2 Numerical Enhancements to the Model...................................................................................4

1.2.3 New Relative-Permeability and Capillary-Pressure Models ....................................................5

1.2.4 New Organic and Tracer Components ....................................................................................6

1.3 Model Evaluation..............................................................................................................................8

1.4 Conclusions ......................................................................................................................................9

Section 2 UTCHEM Model Formulation...................................................................................................15

2.1 Introduction ....................................................................................................................................15

2.2 Model Formulation .........................................................................................................................17

2.2.1 General Description..............................................................................................................17

2.2.2 Mass Conservation Equations...............................................................................................18

2.2.3 Energy Conservation Equation..............................................................................................19

2.2.4 Pressure Equation .................................................................................................................19

2.2.5 Non Equilibrium Dissolution of Nonaqueous Phase Liquids.................................................20

2.2.6 Well Models.........................................................................................................................21

2.2.7 Fluid and Soil Properties.......................................................................................................21

2.2.8 Adsorption............................................................................................................................21

2.2.9 Cation Exchange...................................................................................................................23

2.2.10Phase Behavior.....................................................................................................................24

2.2.11Phase Saturations..................................................................................................................27

2.2.12Interfacial Tension................................................................................................................27

2.2.13Density .................................................................................................................................28

2.2.14Capillary Pressure.................................................................................................................28

2.2.15Relative Permeability............................................................................................................31

2.2.16Trapping Number .................................................................................................................32

2.2.17Viscosity...............................................................................................................................34

2.2.18Polymer Permeability Reduction...........................................................................................35

2.2.19Polymer Inaccessible Pore Volume.......................................................................................36

2.3 Numerical Methods.........................................................................................................................36

2.3.1 Temporal Discretization........................................................................................................36

2.3.2 Spatial Discretization............................................................................................................36

2.4 Model Verification and Validation..................................................................................................37

2.5 Summary and Conclusions..............................................................................................................38

2.6 Nomenclature .................................................................................................................................38

Section 3 Hysteretic Relative Permeability and Capillary Pressure Models................................................46

3.1 Introduction ....................................................................................................................................46

3.2 Oil Phase Entrapment .....................................................................................................................46

3.2.1 Kalurachchi and Parker.........................................................................................................47
vi

3.2.2 Parker and Lenhard...............................................................................................................47

3.3 Capillary Pressure...........................................................................................................................48

3.3.1 Two-Phase Flow...................................................................................................................48

3.3.2 Three Phase Oil/Water/Air Flow...........................................................................................48

3.4 Relative Permeability......................................................................................................................48

3.5 Capillary Number Dependent Hysteretic Model..............................................................................48

Section 4 UTCHEM Tracer Options..........................................................................................................51

4.1 Introduction ....................................................................................................................................51

4.2 Non-Partitioning Tracer..................................................................................................................51

4.3 Partitioning Tracer..........................................................................................................................51

4.3.1 Water/Oil..............................................................................................................................51

4.3.2 Gas/Oil .................................................................................................................................52

4.4 Radioactive Decay ..........................................................................................................................53

4.5 Adsorption......................................................................................................................................53

4.6 Reaction..........................................................................................................................................53

4.7 Capacitance.....................................................................................................................................54

Section 5 Dual Porosity Model..................................................................................................................56

5.1 Introduction ....................................................................................................................................56

5.2 Capacitance Model..........................................................................................................................56

5.3 Subgridding ....................................................................................................................................58

5.4 Implementation...............................................................................................................................59

5.5 Results............................................................................................................................................60

5.6 Conclusions ....................................................................................................................................61

5.7 Nomenclature .................................................................................................................................61

Section 6 UTCHEM Model of Gel Treatment ...........................................................................................69

6.1 Introduction ....................................................................................................................................69

6.2 Gel Conformance Treatments .........................................................................................................69

6.3 Gel Viscosity ..................................................................................................................................71

6.4 Gel Adsorption ...............................................................................................................................71

6.5 Gel Permeability Reduction ............................................................................................................71

6.5.1 Chromium Retention ............................................................................................................71

6.5.2 Cation Exchange...................................................................................................................72

6.5.3 Adsorption............................................................................................................................72

6.5.4 Precipitation .........................................................................................................................72

6.5.5 Polymer/Chromium Chloride Gel .........................................................................................72

6.5.6 Polymer/Chromium malonate Gel.........................................................................................73

6.5.7 Silicate Gel...........................................................................................................................74

6.6 Temperature Effects........................................................................................................................75

Section 7 Multiple Organic Components ...................................................................................................76

7.1 Introduction ....................................................................................................................................76

7.2 Mass Transfer for Nonaqueous Phase Liquid ..................................................................................76

7.2.1 No Surfactant or Surfactant Concentration Below CMC .......................................................76

7.2.2 Surfactant Concentration Above CMC..................................................................................77

7.3 Physical Properties for NAPL Mixture............................................................................................79

7.4 NAPL Mixture Viscosity ................................................................................................................81

7.5 Density of NAPL Mixtures.............................................................................................................81

7.6 Adsorption of Organic Species........................................................................................................81

7.7 Nomenclature .................................................................................................................................81

Section 8 EQBATCH Program Description...............................................................................................83

8.1 Introduction ....................................................................................................................................83

8.2 User's Guide ...................................................................................................................................83

Section 9 Microbiological Population Modeling......................................................................................105

9.1 Introduction ..................................................................................................................................105

9.2 Model Description and Features....................................................................................................105

9.3 Biodegradation Equations and Solution Procedure........................................................................106

9.4 Example Simulations....................................................................................................................109

9.4.1 LNAPL Simulation Example ..............................................................................................110

9.4.2 DNAPL Simulation Example..............................................................................................110
vii

Section 10 Well Models ..........................................................................................................................117

10.1 Introduction ..................................................................................................................................117

10.2 Vertical Wells with Cartesian or Curvilinear Grid Options............................................................117

10.2.1Well Constraints for Injection Wells...................................................................................118

10.2.2Well Constraints for Production Wells................................................................................119

10.3 Vertical Wells with Radial Grid Option ........................................................................................120

10.3.1Rate Constraint Injector......................................................................................................120

10.3.2Rate Constraint Producer....................................................................................................120

10.3.3External Boundary..............................................................................................................120

10.4 Horizontal Well with Cartesian or Curvilinear Grid Options.........................................................121

10.4.1Productivity Index for Horizontal Wells .............................................................................121

Section 11 Effect of Alcohol on Phase Behavior .....................................................................................124

11.1 Introduction ..................................................................................................................................124

11.2 Alcohol Partitionaing....................................................................................................................124

11.3 Effective Salinity ..........................................................................................................................127

114 Flash Calculations.........................................................................................................................128

11.4.1For Type II(-) Phase Bahavior ............................................................................................131

11.4.2For Type II(+) Phase Bahavior ...........................................................................................131

11.4.3For Type III Phase Behavior...............................................................................................135

Section 12 Organic Dissolution Model in UTCHEM...............................................................................139

12.1 Introduction ..................................................................................................................................139

12.2 Saturated Zone (Gas Phase Is Not Present) ...................................................................................139

12.2.1Organic Solubility ..............................................................................................................140

12.2.2Phase Saturations................................................................................................................141

12.3 Vadose Zone.................................................................................................................................143

12.4 Nomenclature ...............................................................................................................................144

Appendix A UTCHEM 6.1 User's Guide .................................................................................................146

A.1 Introduction ..................................................................................................................................146

A.2 Operation of the Simulator............................................................................................................147

A.3 Input Data Description..................................................................................................................152

A.4 Output Files..................................................................................................................................225

A.5 Geochemistry Option (IREACT>1) ..............................................................................................229

A.6 Main Program Flow Outline .........................................................................................................232

A.7 Phases and Species in UTCHEM ..................................................................................................234

A.8 Time-Step Selection......................................................................................................................236

A.9 Description of work.job File .........................................................................................................238

Appendix B UTCHEM Local Grid Refinement User's Guide ..................................................................239

B.1 Introduction ..................................................................................................................................239

B.2 Local Grid Refinement Specifications...........................................................................................240

B.3 Operation of the Simulator............................................................................................................244

B.4 Input Data Description..................................................................................................................245

B.5 Nomenclature ...............................................................................................................................299

B.6 Output Files and Reactions ...........................................................................................................303

Appendix C Discretized Flow Equations .................................................................................................318

References................................................................................................................................................322
viii

Figures

1.1 Comparison of substrate profiles calculated by UTCHEM simulator to those predicted by

the model of Molz et al. (1986). ..........................................................................................................9

1.2 a) Definition of zone and interface and b) coarse-fine and fine-fine interfaces. ..................................10

1.3 Comparison between analytical solutions and third-order finite-difference solutions in

UTCHEM..........................................................................................................................................11

1.4 Simulated and laboratory PCE recovery from the 2-D column...........................................................12

1.5 Tracer concentrations produced at extraction well SB-1 during Hill AFB Phase I test. ......................12

1.6 Surfactant concentrations produced at extraction well SB-1 during Hill AFB Phase I test..................13

2.1 Schematic representation of Type II(-). .............................................................................................43

2.2 Schematic representation of high-salinity Type II(+). ........................................................................43

2.3 Schematic representation of Type III. ................................................................................................43

2.4 Correspondence between (a) ternary diagram and (b) hand plot.........................................................43

2.5 Coordinate transformation for the two-phase calculations in Type III. ...............................................44

2.6 Measured and simulated PCE saturation at the location of Core 3 prior to surfactant

flooding (after Freeze et al., 1994).....................................................................................................44

2.7 Measured and simulated PCE saturation at the location of Core 6 at the end of surfactant

flooding (after Freeze et al., 1994).....................................................................................................45

3.1 Capillary pressure curves as a function of effective water saturation..................................................50

5.1 Comparison of capacitance model (UTCHEM) to equivalent dual porosity model

(UTDUAL) results.............................................................................................................................63

5.2 Schematic of matrix block subgrids. ..................................................................................................63

5.3 Comparison of capacitance model vs. subgrid model in UTCHEM....................................................64

5.4 Subgrid refinement studies with UTCHEM, Km = 3.243x10-2 ft2/day.............................................64

5.5 Comparison of UTCHEM and UTDUAL subgridding.......................................................................65

5.6 2D subgrid refinement studies with UTCHEM. .................................................................................65

5.7 Comparison of execution time with different numbers of subgrids, 1D case. .....................................66

5.8 Comparison of execution time with different numbers of subgrids, 2D case. .....................................66

5.9 Comparison of simulated results vs. analytical solution (Tang et al., 1981) for radionuclide

concentration in the fracture. .............................................................................................................67

5.10 Comparison of simulated results vs. analytical solution (Tang et al., 1981) and SWIFT II

(Reeves et al., 1986) for radionuclide concentration in the matrix. ....................................................67

9.1 Modeling domain size and discretization. ........................................................................................112

9.2 NAPL saturation history in the vicinity of a hypothetical gasoline spill. ..........................................112

9.3 Comparison of benzene and toluene concentrations in the aqueous phase 500 days after a

gasoline spill....................................................................................................................................113

9.4 Concentrations of benzene without biodegradation, benzene with biodegradation, toluene,

oxygen, and nitrate in upper 1.2 m of aquifer along aquifer center line at 500 days. ........................114

9.5 Plan view of TCE, a hypothetical TCE tracer, methane and oxygen concentrations in the

upper 1.2 m of a confined aquifer 170 days after a TCE spill...........................................................114

11.1 Schematic representations of a) Type II(-), b) Type II(+), and c) Type III. ......................................137

11.2 Effect of alcohol on the maximum height of binodal curve..............................................................138

11.3 Coordinate transformation for Type III............................................................................................138
ix

Tables

1.1 List of Elements and Reactive Species...............................................................................................14

1.2 Physical Property Data Used in the 2-D Simulations..........................................................................14

2.1 Physical Property Input Parameters for the Test Cell Simulation .......................................................45

3.1 Notation Used in Section 3 ................................................................................................................50

5.1 Equivalence Between Capacitance and Dual Porosity Models............................................................68

5.2 Input Data for the Comparisons of Capacitance Model in UTCHEM to Dual Porosity

Model in UTDUAL ...........................................................................................................................68

8.1 Water Analysis for Makeup and Formation Water.............................................................................88

8.2 Example List of Elements and Reactive Species................................................................................88

8.3 List of Reactions for the Example Run ..............................................................................................89

8.4 Stoichiometric Coefficient of Ith Element in Jth Fluid Species (for the AR Array)............................91

8.5 Stoichiometric Coefficient of Ith Element in Jth Solid Species (for the BR Array) ............................91

8.6 Stoichiometric Coefficient of Ith Element in Jth Sorbed Species (for the DR Array) .........................91

8.7 Stoichiometric Coefficient of Ith Element in Jth Surfactant Associated Cation (for the ER

Array)................................................................................................................................................92

8.8 Exponent of Jth Independent Fluid Species (for BB Array) ...............................................................92

8.9 Exponent of Jth Independent Species in the Ith Solid (for EXSLD Array).........................................93

8.10 Charge of Ith Fluid Species (for CHARGE Array).............................................................................93

8.11 Equilibrium Constants for Ith Fluid Species (for EQK Array) ...........................................................93

8.12 Charge of Jth Sorbed Species (for SCHARG Array)..........................................................................93

8.13 Exchange Equilibrium Constants for Jth Exchange (for EXK Array).................................................93

8.14 Exponent of Kth Independent Species in Jth Equilibrium Relation (for EXEX Array).......................94

8.15 Valence Difference Between Cation Involved In Exchange (for REDU Array)..................................94

8.16 Solubility Product of Ith Solid (for SPK Array).................................................................................94

8.17 Charge of Ith Surfactant Associated Cation (for CHACAT Array).....................................................94

8.18 Equilibrium Constant for Ith Exchange (for ACATK Array) .............................................................94

8.19 Exponent of Jth Independent Species in Ith Cation Exchange on Surfactant (for EXACAT

Array)................................................................................................................................................94

8.20 Sample Input Data for EQBATCH Program......................................................................................95

8.21 Sample Output of EQBATCH Program.............................................................................................97

8.22 Sample UTCHEM Input File Generated From EQBATCH Program ...............................................102

9.1 Flow Parameters for All Simulations...............................................................................................115

9.2 Parameters for LNAPL Simulation Example ...................................................................................115

9.3 Parameters for DNAPL Simulation Example...................................................................................116
1

Section 1

Project Summary

1.1 Introduction

Pioneering research conducted at The University of Texas at Austin has provided a scientific and engineering

basis for modeling the enhanced recovery of oil and the enhanced remediation of aquifers through the

development and application of compositional simulators. This research has resulted in the development and

application of a 3-D, multicomponent, multiphase, compositional model of chemical flooding processes,

UTCHEM, which accounts for complex phase behavior, chemical and physical transformations and

heterogeneous porous media properties, and uses advanced concepts in high-order numerical accuracy and

dispersion control and vector and parallel processing. The simulator was originally developed by Pope and

Nelson in 1978 to simulate the enhanced recovery of oil using surfactant and polymer processes. Thus, the

complex phase behavior of micellar fluids as a function of surfactant, alcohol, oil, and aqueous components

was developed early and has been extensively verified against enhanced oil recovery experiments.

Generalizations by Bhuyan et al. in 1990 have extended the model to include other chemical processes and a

variety of geochemical reactions between the aqueous and solid phases. The nonequilibrium dissolution of

organic components from a nonaqueous phase liquid (NAPL) into a flowing aqueous or microemulsion phase

is modeled using a linear mass-transfer model. In this simulator, the flow and mass-transport equations are

solved for any number of user-specified chemical components (water, organic contaminants, surfactant,

alcohols, polymer, chloride, calcium, other electrolytes, microbiological species, electron acceptors, etc.).

These components can form up to four fluid phases (air, water, oil, microemulsion) and any number of solid

minerals depending on the overall composition. The microemulsion forms only above the critical micelle

concentration (CMC) of the surfactant and is a thermodynamically stable mixture of water, surfactant and

one or more organic components. All of these features taken together, but especially the transport and flow

of multiple phases with multiple species and multiple chemical and biological reactions make UTCHEM

unique. A description of UTCHEM model formulation is given in Delshad et al. [1996].

The objective of this research was to develop, validate and apply a three-dimensional, multiphase,

multicomponent model capable of simulating the fate and transport of NAPLs in the saturated and

unsaturated zones of confined and unconfined aquifers undergoing enhanced remediation. The model is

capable of simulating multiple solids and fluid phases (water/air/NAPL) under realistic aquifer conditions and

transformations of both inorganic and microbiological species. The specific objectives of this research were:

• Develop a three-dimensional simulation model capable of evaluating aquifer remediation methods

using enhanced dissolution and/or mobilization of NAPLs trapped at residual saturation in aquifers.

The simulator is capable of modeling transient and steady-state, three-dimensional flow and mass

transport in the groundwater (saturated) and vadose (unsaturated) zones of aquifers. The simulator
Section 1 – Project Summary

2

allows for changes in fluid properties as a site is remediated; heterogeneous aquifer properties; the

flow and transport of remedial fluids whose density, viscosity and temperature are variable, including

surfactants, cosolvents, microbes, and other enhancement agents; the dissolution of NAPLs by

nondilute remedial fluids; and chemical and microbiological transformations. Nondilute components

such as surfactant can and typically do cause large changes in phase volumes, phase velocities, and

phase properties that cannot be accurately modeled by assuming these components are at very low

concentrations so that they follow the conventional advection-reaction-dispersion equation used in

almost all groundwater models. Rather, more general mass-balance equations and constitutive

equations such as those used here must be solved. The resulting set of equations are highly nonlinear

and more difficult to solve than those in conventional models, but provide a vastly more general and

accurate description of the processes that actually occur in aquifers undergoing remediation, the

migration of NAPLs in the subsurface, and the natural attenuation processes of NAPLs in the

subsurface. Many of these processes such as the migration of the NAPLs during and after a spill or

disposal operation involve the flow of two or more phases, which requires the modeling of relative

permeability and other effects related to multiphase flow.

• Incorporate appropriate physical, chemical, and biological process models important in describing the

fate and transport of contaminants in aquifers, such as nonequilibrium interphase mass transfer,

sorption, decay processes, microbiological and geochemical reactions, capillary pressure and relative

permeability.

• Incorporate numerical-dispersion-minimization techniques and efficient solution algorithms into the

model.

• Evaluate the model through a series of tests including comparison with analytical solutions,

experimental data, and results from other models. Present a theoretical analysis and demonstration of

the numerical dispersion control and minimization techniques employed in the model.

• Demonstrate the stability and robustness of the model with sensitivity analysis simulations using

various aquifer conditions (surface spill conditions, initial saturation distributions) and heterogeneities

(spatial variations of permeability and porosity).

• Evaluate this new model by comparison with data from actual field operations of remediation, in

particular, surfactant-enhanced remediation at the Canadian Forces Borden site and other large-scale

model aquifer or field operations such as the one recently completed at the Air Force Base in Utah.

• Provide copies of the UTCHEM source code and the user's guide to U.S. EPA personnel.

1.2 Model Development

During the past three years, we have added several new and significant capabilities to UTCHEM to make it

into a general-purpose NAPL simulator. These new features are discussed below. The simulator is now

capable of modeling transient and steady-state three-dimensional flow and mass transport in the groundwater

(saturated) and vadose (unsaturated) zones of aquifers. The model allows for changes in fluid properties as a

site is remediated; heterogeneous aquifer properties; the flow and transport of remedial fluids whose density,

viscosity and temperature are variable, including surfactants, cosolvents and other enhancement agents; the

dissolution and/or mobilization of NAPLs by nondilute remedial fluids; and chemical and microbiological

transformations. Appropriate physical, chemical and biological process models important in describing the

fate and transport of NAPLs in contaminated aquifers have been incorporated into the simulator, such as
Section 1 – Project Summary

3

multiple organic NAPL phase, nonequilibrium interphase mass transfer, sorption, microbiological and

geochemical reactions, and the temperature dependence of pertinent chemical and physical properties. The

biodegradation model includes inhibition, sequential use of electron acceptors, and cometabolism and can be

used to model a very general class of bioremediation processes. The model can be used to simulate the

actual field operation of remediation activities such as surfactant remediation or bioremediation as well as

laboratory experiments with large-scale aquifer models.

1.2.1 Microbiological Population Modeling

Biodegradation capabilities have been added to a three-dimensional, multiphase, multicomponent porous

media flow model. The model simulates the transport and biodegradation of light nonaqueous phase liquids

(LNAPLs) and dense nonaqueous phase liquids (DNAPLs). The biodegradation model describes biological

transformation of the organic contaminants originating from NAPL sources and can accommodate multiple

substrates, electron acceptors, and biological species.

Here we give a brief description of the model assumptions and the capabilities. For more detailed

information on model formulation, method of solution, and example simulations to demonstrate its capability,

please refer to de Blanc et al. [1996a,b]. UTCHEM simulates the biodegradation of chemical compounds

that can serve as substrates (carbon and/or energy sources) for microorganisms. The model simulates the

destruction of substrates, the consumption of electron acceptors (e.g., oxygen, nitrate, etc.), and the growth

of biomass. Substrates can be biodegraded by free-floating microorganisms in the aqueous phase or by

attached biomass present as microcolonies in the manner of Molz et al. [1986]. Multiple substrates, electron

acceptors and biological species are accommodated by the model. Important assumptions for the

biodegradation model are:

1. Biodegradation reactions occur only in the aqueous phase.

2. Microcolonies are fully penetrated; i.e., there is no internal resistance to mass transport within the

attached biomass.

3. Biomass is initially uniformly distributed throughout the porous medium.

4. Biomass is prevented from decaying below a lower limit by metabolism of naturally occurring organic

matter unless cometabolic reactions act to reduce the active biomass concentrations below natural

levels.

5. The area available for transport of organic constituents into attached biomass is directly proportional

to the quantity of biomass present.

6. The number of cells per microcolony, biomass density, and microcolony volume are constant, so that

mass per microcolony is also constant.

The biodegradation model includes the following features:

• Monod, first-order, or instantaneous biodegradation kinetics.

• Formation of biodegradation by-products.
Section 1 – Project Summary

4

• External mass-transfer resistances to microcolonies (mass-transfer resistances can be ignored by the

user if desired).

• Inhibition of biodegradation by electron acceptors and/or toxic substrates.

• Nutrient limitations to biodegradation reactions.

• First-order abiotic decay reactions.

• Enzyme competition between multiple substrates.

• Modeling of cometabolism with transformation capacities and reducing power limitations using the

model of Chang and Alvarez-Cohen [1995].

• Biodegradation reactions in both the vadose and saturated zones.

The biodegradation model equations describe the transport of substrate and electron acceptor from the

aqueous phase into attached biomass, the loss of substrate and electron acceptor through biodegradation

reactions, and the resulting growth of the free-floating or attached biomass. The flow and biodegradation

system is solved through operator splitting, in which the solution to the flow equations is used as the initial

conditions for the biodegradation reactions. This approach is convenient because modifications can be made

to the system of biodegradation equations without having to reformulate the partial differential equations that

describe advection and dispersion.

The biodegradation equations comprise a system of ordinary differential equations that must be solved at

each gridblock and each timestep after the advection and dispersion terms are calculated. Because the mass

transfer terms can make the system of equations stiff, the system is solved using a Gear's method routine

published by Kahaner et al. [1989]. The characteristics and numerical solution of this system of equations

are discussed by de Blanc et al. [1996b].

To validate the model, one-dimensional, single-phase simulation based on the example given in Molz et al.

[1986] has been run. The UTCHEM simulation results have been compared to biodegradation model

solutions published by Molz et al. In this simulation, a single substrate is biodegraded by attached biomass

using oxygen as the electron acceptor. The reactor is 100 cm long with initial colony density of 1.0x105

colonies per cm3 of porous medium. Pore velocity is 25 cm/day. The initial substrate and oxygen

concentrations are constant throughout the reactor at 5 mg/L. At the boundary x = 0 and time zero, the

substrate concentration is increased instantaneously to 15 mg/L. At the same boundary, the oxygen

concentration is maintained at 5 mg/L. Substrate profiles generated by the two models are shown in Fig. 1.1.

The simulation results are very similar to the data of Molz et al., indicating that the UTCHEM

biodegradation model is functioning properly. The model predictions are not exactly the same because of

slightly different assumptions about endogenous decay and slightly different flow conditions.

1.2.2 Numerical Enhancements to the Model

We present a summary of the local grid-refinement method and implementation in UTCHEM. The

formulation and simulation examples are given in UTCHEM-LGR User's manual.

The aquifer is initially defined by a coarse grid (called a base grid) with NXCxNYCxNZC standard cells

(gridblocks). Subject to memory limitations, any number and any combination of the base grid cells can be

refined by a single local-level NXFxNYFxNZF that is of fixed resolution for all refined cells. The refined base
Section 1 – Project Summary

5

grid cells are called zones. The resulting grid is comprised of coarse base cells and fine-zone regions. When

a coarse base cell or a fine zone is adjacent to a refined base cell or zone, this gives rise to a coarse-fine

interface or fine-fine interface, respectively. With respect to a given zone, the interfaces act as interior

domain boundaries. An example is presented in Fig. 1.2, where the definition of zone and interface are

illustrated in Fig. 1.2a.

The implementation strategy attempts to treat each zone as a separate domain subject to interior domain

boundary conditions and is in that sense based on domain decomposition, pictorially illustrated in Fig. 1.2b.

Computations in the interior of each local fine zone are effectively performed in isolation from other regions

of the flow domain (giving rise to an inner loop) subject to appropriate interface and exterior boundary

conditions that are imposed in an outer loop over the local domains and serve to connect the various local

domains together.

Local grid refinement (LGR) has been implemented for the Cartesian option with a higher-order scheme or

two-point upstream weighting for the concentration equations, although single-point upstream weighting is

also maintained as an option. While the current code allows static (fixed) local cell refinement, where each

coarse cell selected for refinement remains refined and the grid does not change throughout the computation,

the implementation will allow future extension to dynamic local refinement.

Some recent examples of use of this kind of local refinement in reservoir simulation can be found in Espedal

et al. [1990] and Deimbacher and Heinemann [1993]. However, with the exception of Edwards [1992a,b]

and Edwards and Christie [1993] where a higher-order (in space and time) total-variation-diminishing type

scheme is employed, all other adaptive methods in reservoir simulation to date have employed first-order

upstream differencing for discretization of the advective terms in the flow equations. The new method and

development reported here have led to the first simulator to include local grid refinement with a higher-order

scheme and a full tensor diffusion operator in three dimensions.

Most of the current code development, in terms of new subroutines, is concerned with treatment of the

domain interface conditions for the concentration equations and pressure equation, which enable the zones to

link together and complete the global flow-domain solution definition. Aspects that have critical impact on

this logic deal with identification of the junction type at an interface. For example, a coarse cell that has been

refined can have a neighboring cell that is either refined or coarse or a physical boundary, and appropriate

internal or external boundary conditions (Neumann/Dirichlet) must be imposed. In addition, the coarse-fine

and/or fine-fine zone configurations that underlie the higher-order scheme for concentrations must be

identified. While the pressure equation involves nearest-neighbor and nearest-interface-neighbor information,

the higher-order scheme stencil support relies on neighbor and neighbor-of-neighbor information. In addition

the full tensor diffusion operator relies on nearest neighbor and diagonal neighbor information, adding

another level of complexity to the implementation.

Zone interior calculations can be performed in isolation and, subject to appropriate boundary interface

conditions, the solution procedure can simplistically be visualized as a sequence of calls to the simulator for

each domain, followed by calls to boundary-coupling routines that "seal" the isolated local zones together,

forming the global domain. However, in practice, the implementation is far more involved.

In addition to the nontrivial interface routines directly concerned with solving the flow equations, further

interface logic is required for the calculation of any nonlocal variable that is a function of more than a single

cell. The code has to be sifted for such cases. Examples include determination of the maximum flow rate

required for calculating the maximum timestep, testing for negative saturations and pressures, and material-
Section 1 – Project Summary

6

balance calculations, and all involve tests and/or calculations over all domain cells; more complex examples

arise with physical models such as capillary number, which involves further interface routines to handle the

spatial derivatives. Definition of physical boundary conditions such as injection/production wells and

inflow/outflow boundaries both involve summations over a range of cells, and appropriate interface tests and

calculations must be built into the code to ensure that a given boundary condition extends over the desired

region of the flow domain.

A cell-centered finite-volume formulation is employed in constructing discretizations of the flow equations

applicable on grids with embedded local refinement. In a cell-centered formulation, the flow domain is

represented by a grid of quadrilateral cells. All flow variables including saturations, concentrations and

pressures are defined at the cell centers, and the flow equations are integrated over each cell using the Gauss

flux theorem.

This is the first simulator to offer LGR with a higher-order scheme and full tensor diffusion in three

dimensions applicable to a variety of problems of practical importance. The initial three-dimensional results

were very encouraging. Successful adaptivity requires that the key coarse grid cells (containing flow

variables with steep gradients) be refined. Static refinement is best suited to problems where crucial flow

gradients are known a priori to be contained in certain regions of the domain.

1.2.3 New Relative-Permeability and Capillary-Pressure Models

A new multiphase capillary-pressure and relative-permeability function has been implemented in UTCHEM.

As the result of this task, UTCHEM has now the option of either Brooks-Corey or van Genuchten capillarypressure functions. The two-phase gas-water, water-oil, or microemulsion-oil and three-phase oil-water-gas

capillary pressure-saturation functions are determined using the generalization of Parker et al. [1987] to the

two-phase flow model of van Genuchten [1980]. The new two- and three-phase relative permeabilities are

also based on the generalization of Parker and Lenhard to the two-phase flow model of van Genuchten.

Both capillary-pressure and relative-permeability functions account for hysteresis due to arbitrary changes in

saturation path by incorporating an oil-phase-entrapment model. The hysteresis modeling in UTCHEM is

based on the work by Kalurachchi and Parker [1992]. The assumptions made in developing and applying this

model are:

• The model applies only to strongly water-wet media where the wettability in descending order is for

water (or microemulsion), oil, and gas phases. Oil will be used in this report to mean any nonaqueous

phase liquid (NAPL).

• The model applies to three-phase air-water-oil flow in the vadose zone and two-phase oil-water or

oil-microemulsion flow in the saturated zone.

• To avoid numerical oscillations with changes from two phases (air-water) to three phases (air-wateroil), once a location is classified as a three-phase node, it will not revert back to two phases (airwater).

• Gas entrapment is neglected for the three-phase case. Therefore, oil entrapment in three-phase airwater-oil flow can be inferred directly from that in a two-phase oil-water system.

• Water relative permeability is unaffected by oil entrapment.

• There is no oil entrapment on the main drainage curve.
Section 1 – Project Summary

7

• There is no oil entrapment when water saturation is at its residual value in the vadose zone.

A detailed description on the formulation of the new hysteretic capillary-pressure and relative-permeability

models is given in Section 2.2 of this report.

1.2.4 New Organic and Tracer Components

New organic and tracer components were added to UTCHEM. We have added multiple organic components

so that we can model NAPL mixtures. Adding this capability to UTCHEM required developing a phasebehavior model for NAPL mixtures and the physical property models such as density and viscosity for each

phase. We have also added additional water tracer components and gas phase tracers.

New organic components

Nonaqueous phase liquids (NAPLs) usually consist of more than one organic species that mix and form a

single liquid. Common examples of such miscible species include TCE, TCA and PCE among many others.

When NAPLs leak to the subsurface, they can dissolve and migrate into groundwater. To model the fate and

transport of these soluble organics during remediation processes such as pump-and-treat, bioremediation and

surfactant remediation, it is important to determine the migration of the individual soluble organics. The

dissolution can be either a local equilibrium or a rate-limited (nonequilibrium) mass-transfer process. We

have added the capability of multiple organic components to UTCHEM to model these NAPL mixtures. The

multiple organic dissolution can be either local-equilibrium partitioning or a rate-limited mass transfer. We

also developed and incorporated in UTCHEM a phase-behavior model for a mixture of NAPL mixtures,

surfactant, and water. The physical-property models developed and implemented for a NAPL mixtures in

UTCHEM were density, viscosity, and adsorption. A more detailed description of the model is given in

Section 2.6 of this report.

Three recent papers by Baran et al. [1994a,b,c] show that the phase behavior of surfactants with both pure

chlorocarbons and mixtures of chlorocarbons is similar to classical phase behavior with hydrocarbons. The

phase behavior changes from microemulsion in equilibrium with excess oil (Winsor Type I or Type II(-)) to

microemulsion in equilibrium with excess aqueous and organic phase (Winsor Type III), and to

microemulsion in equilibrium with excess water (Winsor Type II or Type II(+)) as salinity increases. The

lower and upper limits of effective salinity are the effective salinities at which three phases form or disappear.

The optimal salinity is defined as the midpoint of these two salinity limits .

Hand's equation (Pope and Nelson, 1978) is used in UTCHEM to describe the phase envelope and binodal

curve. For organic mixtures, the upper and lower limits of effective salinity, the height of binodal curve at

lower, optimal, and upper salinities are functions of organic species concentrations. These parameters are

modeled as functions of the equivalent alkane carbon number (EACN) of the mixture, which is a function of

organic species concentrations. EACN for an alkane is the number of carbons in the alkane chain of the

hydrocarbon; for example, it is equal to 6 for hexane. EACN for a nonalkane is obtained by measuring the

optimal salinity for a binary mixture of an alkane and a nonalkane with known molar fractions. The measured

optimal salinity is used to determine EACN for the binary mixture. For example, the EACN data listed in the

Baran et al. papers are built into the UTCHEM database: PCE (EACN = 2.90), CCl4 (EACN = -0.06), TCE

(EACN = -3.81), p-xylene (EACN = 2), toluene (EACN = 1), 1,2-C6H4Cl2 (EACN = -4.89), 1,2-C2H4Cl2

(EACN = -12.10), CHCl3 (EACN = -13.67), CH2Cl2 (EACN = -13.79), and 1,1,2,2-C2H2Cl4

(EACN = -22.15).
Section 1 – Project Summary

8

New tracer components

The number of oil/water tracers in UTCHEM was previously limited to three. Modifications to the model

have been completed to allow the simulation of any number of tracer components.

Gas tracers have been added to UTCHEM. The gas-phase tracers are either chemical nonreacting or

radioactive components. The gas tracer can partition only between gas and organic phases with a constant

partition coefficient. Radioactive decay is applied to radioactive tracers with a constant decay coefficient.

The gas tracers can also adsorb on the soil surface using a linear adsorption model and a constant retardation

factor.

Enhancements of Geochemical Option

The geochemical option in UTCHEM has been extended to allow the modeling of any aqueous and solid

reactive species. In the original UTCHEM model, the component numbering in the transport calculations

was fixed in the source code and each reaction option had specific geochemical components and species.

Thus, the geochemical option in UTCHEM was limited only to those specific species and reactions. This

restriction was removed by implementing a dynamic component-numbering scheme for geochemical

components. The component numbers are increased according to the user-specified elements. Component

partitioning between phases and the adsorbed and solid concentrations in the mass-balance calculations are

not, however, included for all the new species.

To test and illustrate the UTCHEM capability in modeling a complex geochemical process, an application to

an acid mine-tailing contamination problem was simulated. A total of 51 aqueous species and 7 solid species

were simulated (Table 1.1). New components such as chromium, lead, and sulfate were included that were

not available in the original UTCHEM model. The aquifer and site conditions for this example were similar

to the conditions at the Nordic site near Elliot Lake, northern Ontario (Walter et al., 1994). The initial and

injected component concentrations were similar to those used in the simulation by Walter et al. Initial

concentrations for UTCHEM simulation were determined by equilibrating the water and mineral phases using

batch equilibrium calculations. The UTCHEM results showed a very similar trend to those presented by

Walter et al. The results were not expected to be identical since the conditions were different; i.e., species

such as K, Mn, and Fe were not included in the UTCHEM simulation.

1.3 Model Evaluation

The numerical accuracy of the UTCHEM model has been evaluated through a series of tests including

comparisons with analytical solutions and experimental data.

The numerical accuracy of UTCHEM model was evaluated by comparison with analytical solutions for

problems such as the 1-D water tracer, 2-D tracer, and polymerflood examples given in Fig. 1.3 (Liu et al.,

1994) and by comparison with 2-D laboratory column data of Pennell et al. [1996]. The experiment involved

a 2-D horizontal sandpack contaminated with tetrachloroethylene (PCE). A mixture of surfactant solution

was injected under both mobilization and solubilization conditions for PCE removal from the column. The

UTCHEM model with the recently added trapping number (Jin, 1995; Delshad et al., 1996) was used to

model this experiment.

The column was packed with 40-270 mesh Ottawa sand with a permeability of 16.3 darcies and porosity of

0.3509. Table 1.2 gives the physical properties. The surfactant solution was a 4% 1:1 mixture of sodium

dihexyl sulfosuccinate and sodium dioctyl sulfosuccinate (Aerosol AY/OT) in 500 mg/L CaCl2. The

measured phase behavior and fluid properties such as viscosity, density, and desaturation data were used to

obtain the UTCHEM input parameters. The injection rate was at 4.95 cc/min (0.0488 ft3/day). Pennell et al.
Section 1 – Project Summary

9

observed that the injected surfactant solution appeared to preferentially flow along the top of the soil column,

while mobilized PCE migrated downward through the soil column because of buoyancy forces. It took about

3 pore volumes of surfactant solution to completely displace the mobilized bank of PCE formed near the

column outlet. To model the results of the laboratory data, 2-D simulations with 22 gridblocks in the

horizontal direction and 10 gridblocks in the vertical direction were performed. Figure 1.4 compares the

laboratory and simulated free-product PCE recovery as a function of surfactant solution throughput. This

favorable comparison indicates that UTCHEM can successfully model the vertical migration and mobilization

of PCE.

The model was also evaluated by comparison with data from actual field operations of remediation, in

particular, surfactant enhanced aquifer remediation (SEAR) at the Canadian Forces Borden site and a fieldscale tracer and SEAR tests at the Operational Unit 2 site at Hill Air Force Base in Utah. The UTCHEM

simulator was used to model the surfactant-enhanced remediation of PCE in a test cell at the Borden site in

Allison, Ontario (Freeze et al., 1994). UTCHEM was able to closely reproduce the PCE recovery and the

PCE distribution. The second sets of simulations were performed to design pre- and post-surfactant flushing

partitioning interwell tracer tests and to design the surfactant flood for the Operational Unit 2 (OU2) site at

Hill AFB, Utah. A multitude of simulation cases were performed to develop the recommended designs for

the tests. These simulations have also allowed us to study the effect of design variables such as injection and

extraction wells, number of wells, and well pattern. Figures 1.5 and 1.6 show a favorable comparison of the

field and UTCHEM predictions of effluent tracer and surfactant concentrations. The field design, results,

and UTCHEM predictions are given in Brown et al. [1996] and Brown [1999]. The stability and robustness

of the simulation results were evaluated with sensitivity analysis to various aquifer conditions, for example,

initial saturation distribution, permeability and porosity distributions, and injection/extraction strategies

(Brown, 1999).

More examples of UTCHEM large-scale simulations are given in a report prepared by INTERA (Butler and

Jin, 1996). INTERA's particular role in this project was to apply UTCHEM to typical NAPL problems that

INTERA encountered during its work at various hazardous waste sites in North America. UTCHEM was

used to study the distribution, volume, and remediation of DNAPL in an alluvial aquifer. The model was

used to design both a partitioning interwell tracer test (PITT) and a subsequent surfactant flood at the

Portsmouth Gaseous Diffusion Plant in southern Ohio. The analysis of an actual PITT conducted at

Portsmouth in July 1996 is also included in the report.

1.4 Conclusions

As the result of this three-year research contract, we have developed a mathematical model capable of

simulating the performance of three-dimensional, multicomponent, multiphase flow of NAPLs in subsurface

environments including saturated and unsaturated conditions. A systematic evaluation was undertaken to

assess the applicability and accuracy of all physical and chemical models of the various pertinent phenomena

such as capillary pressure, relative permeability, adsorption, nonequilibrium mass transfer, dispersion, and

phase behavior. A biological component was added to UTCHEM. Comparisons to analytical solutions were

made and numerical dispersion control and accuracy testing were performed. The model was tested against

experimental and field data. The model will be delivered to U.S. EPA along with user manuals and sample

outputs. The model is in the form of a FORTRAN source code that has been optimized for a vector

computer.
Section 1 – Project Summary

10

0 . 0 0 0

0 . 0 0 2

0 . 0 0 4

0 . 0 0 6

0 . 0 0 8

0 . 0 1 0

0 . 0 1 2

0 . 0 1 4

0 . 0 1 6

0 2 0 4 0 6 0 8 0 1 0 0

d i s t a n c e i n c o l u m n ( c m )

1 d a y

2 d a y s

tr a c e r a f t e r 4 d a y s

3 d a y s

4 d a y s

S o l i d l i n e s - U T C H E M m o d e l

S y m b o l s - D a t a f r o m M o lze t a l. ( 1 9 8 6 )

Figure 1.1. Comparison of substrate profiles calculated by UTCHEM simulator to those predicted

by the model of Molz et al. [1986].

ZONE

Coarse-Fine Interface

Window

Composite Grid

h-Adaptive Grid

Window

Patch

Adaptive Grid Refinement Notation 

Figure 1.2a. Definition of zone and interface.
Section 1 – Project Summary

11

Decomposition of Domain 

Figure 1.2b. Coarse-fine and fine-fine interfaces.
Section 1 – Project Summary

12

-0.2

0.00.20.40.60.81.01.21.4

0.25 0.50 0.75 1.00

Analytical Solution

Nu

merical Solution

Nu

m

ber of Grid

blocks: 100

Courant Nu

m

ber: 0.05

Base of the Triangle: 0.2

noit ul oS

Distance

t = 0.25 t = 0.5

C

o

n

vectio

n-Diffusio

n

E

qu

atio

n

0.00.20.40.60.81.01.2

0.0 0.2 0.4 0.6 0.8 1.0

Nu

m

ber of Grid

blocks : 100

Courant Nu

m

ber: 0.1

noit art necno Cre myl oPro noit arut aSret a W

Normalized

Distance

Water Saturation

P

oly

merflo

o

d

Polymer

Concentration

0.10.20.30.40.50.60.7

0.0 0.2 0.4 0.6 0.8 1.0

Nu

m

ber of Grid

blocks: 200

Courant Nu

m

ber: 0.05

Pore Volu

mes Injected: 0.2

noit arut aSret a W

Normalized

Distance

B

uckley-Leverett Pro

blem

0.000.050.100.15

0.5 1.0

1.5

Grids: 30x30Courant Nu

m

ber: 0.4

Peclet N

u

mber: 500

Slug SIze: 2%

PV

noit art necno Crecar Tt neulff Edezil a mro N

Pore Volu

mes Injected

T

w

o-Dimensio

n

al Tracer Flo

w

Fig

ure 1.3. C

o

m

p

aris

o

n

b

etw

e

e

n

a

n

alytic

al s

olutio

n

s

a

n

d third-ord

er finite-differe

n

c

e

s

olutio

n

s in

U

T

C

H

E

M.
Section 1 – Project Summary

13

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.5 1.0 1.5 2.0 2.5

Free product PCE

(column experiment)

Solubilized PCE

(simulated)

Pore volumes injected

Free product PCE 

(simulated)

Total PCE (simulated)

Figure 1.4. Simulated and laboratory PCE recovery from the 2-D column.
Section 1 – Project Summary

14

0

100

200

300

400

0 1 2 3 4 5 6

UTCHEM 2-propanol

Field 2-propanol, K=0

UTCHEM 1-pentanol

Field 1-pentanol, K=3.9

C

o

n

c

e

ntratio

n, m

g/l

Days

Figure 1.5. Tracer concentrations produced at extraction well SB-1 during

Hill AFB Phase I test.

0.0

0.2

0.4

0.6

0.8

1.0

0 20 40 60 80 100 120 140

Time (hrs)

UTCHEM

Field

Figure 1.6. Surfactant concentrations produced at extraction well SB-1

during Hill AFB Phase I test.
Section 1 – Project Summary

15
Section 1 – Project Summary

16

Table 1.1. List of Elements and Reactive Species

ELEMENTS AQUEOUS SPECIES SOLID SPECIES

Cr

H

Pb

Mg

Ca

Na

Al

Si

Cl

CO3

SO4

O

Cr(OH)2+, H+, Pb2+, Mg2+,

Ca2+, Na+, Al3+, H4SiO4,

Cl-

, CO3

2-, SO42-, H2O, OH-

,

H3SiO4

-

, MgOH+, MgCO3 (Aq.),

MgHCO3

+

, MgSO4 (Aq.), CaOH+,

CaHCO3

+, CaCO3 (Aq.), CaSO4 (Aq.),

NaCO3

-

, NaHCO3 (Aq.), NaSO4

-

,

AlOH 2+, Al(OH)2

+

, AlSO4

+

,

Al(SO4)2

-

, PbCl+, PbCl2 (Aq.),

PbCl3

-

, PbCl4

2-

, Pb(CO3)2

2-

,

PbOH+, Pb2OH3+

, PbSO4 (Aq.),

PbCO3 (Aq.), Pb(SO4)2

2-

, PbHCO3

+

,

HCO3

-

, H2CO3 (Aq.), HSO4

-

, Cr3+,

Cr(OH)2+, CrCl2+, CrCl2

+

, CrSO4

+

,

CrOHSO4 (Aq.), Cr2(OH)2SO4

2+

,

Cr2(OH)2(SO4)2 (Aq.)

CALCITE (CaCO3)

GIBBSITE (Al(OH)3)

GYPSUM (CaSO4)

SiO2

CERRUSITE (PbCO3)

ANGLESITE (PbSO4)

Cr(OH)3

Table 1.2. Physical Property Data Used in the 2-D Simulations

Permeability, darcies 16.3

Porosity, fraction 0.3509

Residual water saturation 0.30

Residual PCE saturation 0.1242

Initial water saturation 0.8758

Water viscosity, cp 1.0

PCE viscosity, cp 0.89

Water density, g/cc 1.0

PCE density, g/cc 1.63

Surfactant density, g/cc 1.15

Initial/injected chloride conc., meq/L 0.009

Initial/injected calcium conc., meq/mL 0.009
15

Section 2

UTCHEM Model Formulation

This chapter is an expanded version of the paper by Delshad et al. [1996] where we describe a threedimensional, multicomponent, multiphase compositional finite difference simulator for application to the

analysis of contaminant transport and surfactant enhanced aquifer remediation (SEAR) of nonaqueous

phase liquid (NAPL) pollutants. The simulator can model capillary pressures, three-phase relative

permeabilities (water/gas/organic phases or water/organic/microemulsion phases), dispersion, diffusion,

adsorption, chemical reactions, nonequilibrium mass transfer between phases and other related phenomena.

The finite-difference method uses second- and third-order approximations for all of the time and space

derivatives and a flux limiter that makes the method total variation diminishing (TVD). Mixtures of

surfactant, alcohol, water and NAPL can form many types of micellar and microemulsion phases with a

complex and important dependence on many variables of which the dilute aqueous solution typically

assumed in SEAR models is just one example. The phase behavior model is central to our approach and

allows for the full range of the commonly observed micellar and microemulsion behavior pertinent to

SEAR. The other surfactant related properties such as adsorption, interfacial tension, capillary pressure,

capillary number and microemulsion viscosity are all dependent on an accurate phase behavior model. This

has proven to be a highly successful approach for surfactant enhanced oil recovery modeling, so it was

adapted to SEAR modeling. However, there are many significant differences between petroleum and

environmental applications of surfactants, so many new features have been added to model contaminant

transport and remediation and these are described and illustrated for the first time here.

2.1 Introduction

Many nonaqueous phase liquids (NAPLs) are used in large quantities by many industries throughout the

world. Due to their wide usage, organic liquids are among the most common type of soil and groundwater

pollutants. Of the organic chemical contaminants which have been detected in groundwaters, dense

nonaqueous phase liquids (DNAPLs) such as chlorinated solvents are among the most frequently and

serious types encountered. DNAPLs are heavier than water, typically volatile, and only slightly soluble in

water. Many conventional remediation techniques such as pump-and-treat, vapor extraction, and in-situ

biorestoration have proven to be unsuccessful or of limited success in remediating soil and groundwater

contaminated by DNAPL due to low solubility, high interfacial tension, and the sinking tendency below the

water table of most DNAPLs. Surfactant enhanced aquifer remediation is actively under research and

development as a promising technology that avoids at least some of the problems and limitations of many

other remediation methods.

Surfactants have been studied and evaluated for many years in the petroleum industry for enhanced oil

recovery from petroleum reservoirs (Nelson and Pope, 1978). Surfactants are injected to create low

interfacial tension to reduce capillary forces and thus mobilize trapped oil. Solubilization and mobilization
Section 2 – UTCHEM Model Formulation

16

are the two mechanisms by which surfactants can enhance the removal of NAPLs from saturated zones.

Surfactants can also be used to increase the solubility without generating ultra-low interfacial tension or

mobilizing the trapped oil. Enhanced solubility is the main mechanism for recovery of entrapped organic

residuals in surfactant enhanced aquifer remediation (Fountain, 1992; Fountain and Hodge, 1992; Powers et

al., 1991; West and Harwell, 1992; Wunderlich et al., 1992; Brown et al., 1994; Pennell et al., 1994). For

example, the solubility of perchloroethylene (PCE) is increased 300 fold by the addition of a 4% blend of

sodium diamyl and dioctyl sulfosuccinates (Abriola et al., 1993). SEAR can also be based on mobilization

of the residual DNAPL, which has a greater potential to increase the remediation but is riskier because of

the movement of free-phase DNAPL.

The objective of SEAR modeling is to aid in the scaleup and optimization of the design of SEAR, to assess

the performance of the method at both the laboratory and field scales with respect to both risk and

effectiveness, to improve our understanding of process mechanisms, and to explore alternative strategies

and approaches to remediation. To the extent that these modeling objectives are met, risk will be reduced

and fewer mistakes will be made, the performance and cost effectiveness of the method will be improved,

and the number of field trials will be minimized. The model should have the capability of modeling

advection, dispersion, and the mass transfer of species (surfactant, water, organic contaminants, air) in the

aquifer under various pumping and injection strategies. Most multiphase compositional models reported in

the environmental engineering literature (Abriola and Pinder, 1985a,b; Baehr and Corapcioglu, 1987; Faust

et al., 1989; Letniowski and Forsyth, 1990; Sleep and Sykes, 1990; Mayer and Miller; 1990; Kalurachchi

and Parker, 1990; Sleep and Sykes, 1993) are limited in their applicability in one way or another (1-or 2-

dimensional modeling, single species, equilibrium mass transfer, inadequate numerical accuracy, and lack

of modeling miscibility which occurs during surfactant flooding). The only SEAR models reported in the

literature are for single phase flow and are those of Wilson [1989], Wilson and Clarke [1991] and Abriola

et al. [1993] with simplified surfactant phase behavior and properties. None of these models account for

the effects of surfactant on interfacial tension (IFT), surfactant phase behavior, capillary number, or

surfactant adsorption. This paper describes the formulation and application of a general purpose chemical

compositional simulator, The University of Texas Chemical Flooding simulator (UTCHEM), for use in

SEAR studies, that does not have these common limitations.

Enhanced oil recovery processes such as polymer flooding or surfactant/polymer flooding have utilized

polymer to reduce fluid mobility to improve the sweep efficiency of the reservoir, i.e., to increase the

volume of the permeable medium contacted at any given time (Lake, 1989; Sorbie, 1991). Sweep

efficiency is reduced by streamline pattern effects, gravity effects, viscous fingering, channeling (caused by

contrasts in the permeability) and flow barriers. Polymers could be used in the SEAR process to improve

the sweep efficiency just as they have been in enhanced oil recovery and this may reduce the cost, risk and

time required to remediate the aquifer. Under some conditions, polymers can also reduce the dispersion

and adsorption of the surfactant and this is another potential benefit of using them. Polymer concentrations

on the order of 500 mg/L are likely to be adequate for SEAR applications, so the additional cost of the

polymer is small compared to the potential reduction in surfactant costs assuming that fewer pore volumes

of surfactant will be needed as a result of the polymer.

UTCHEM can be used to simulate a wide range of displacement processes at both the field and laboratory

scales. The model is a multiphase, multicomponent, three-dimensional finite-difference simulator. The

model was originally developed to model surfactant enhanced oil recovery but modified for applications

involving the use of surfactant for enhanced remediation of aquifers contaminated by NAPLs. The balance

equations are the mass conservation equations, an overall balance that determines the pressure for up to four

fluid phases, and an energy balance equation to determine the temperature. The number of components is
Section 2 – UTCHEM Model Formulation

17

variable depending on the application, but would include at least surfactant, oil and water for SEAR

modeling. When electrolytes, tracers, co-solvents, polymer, and other commonly needed components are

included, the number of components may be on the order of twenty or more. When the geochemical option

is used, a large number of additional aqueous components and solid phases may be used.

A significant portion of the research effort on chemical flooding simulation at The University of Texas at

Austin has been directed toward the development and implementation of accurate physical and chemical

property models in UTCHEM. Heterogeneity and variation in relative permeability and capillary pressure

are allowed throughout the porous medium, since for example each gridblock can have a different

permeability and porosity.

Surfactant phase behavior modeling is based in part on the Hand representation of the ternary phase

diagram (Hand, 1939). A pseudophase theory (Prouvost et al., 1984b; Prouvost et al., 1985) reduces the

water, oil, surfactant, and co-surfactant fluid mixtures to a pseudoternary composition space. The major

physical phenomena modeled are density, viscosity, velocity-dependent dispersion, molecular diffusion,

adsorption, interfacial tension, relative permeability, capillary pressure, capillary trapping, cation exchange,

and polymer and gel properties such as permeability reduction, inaccessible pore volume, and nonNewtonian rheology. The phase mobilization is modeled through entrapped phase saturation and relative

permeability dependence on trapping number.

The reaction chemistry includes aqueous electrolyte chemistry, precipitation/dissolution of minerals, ion

exchange reactions with the matrix (the geochemical option), reactions of acidic components of oil with the

bases in the aqueous solution (Bhuyan, 1989; Bhuyan et al., 1990 and 1991) and polymer reactions with

crosslinking agents to form gel (Garver et al., 1989; Kim, 1995).

Nonequilibrium mass transfer of an organic component from the oleic phase to the surfactant-rich

microemulsion phase is modeled using a linear mass transfer model similar to that given by Powers et al.

[1991]. Even in the absence of surfactant, the model allows for a small dissolution of oil in the aqueous

phase. Nonequilibrium mass transfer of tracer components is modeled by a generalized Coats-Smith model

(Smith et al., 1988).

The model includes options for multiple wells completed either horizontally or vertically. Aquifer

boundaries are modeled as constant-potential surfaces or as closed surfaces.

A dual-porosity formulation to model transport in fractured media has recently been added to the simulator

(Liang, 1997). We have recently incorporated a biodegradation model in UTCHEM. Multiple organic

compounds can be degraded by multiple microbial species using multiple electron acceptors (de Blanc,

1998; Delshad et al., 1994).

The resulting flow equations are solved using a block-centered finite-difference scheme. The solution

method is implicit in pressure and explicit in concentration (IMPES type). One- and two-point upstream

and third-order spatial discretization are available as options in the code. To increase the stability and

robustness of the second-and third-order methods, a flux limiter that is total-variation-diminishing (TVD)

has been added (Liu, 1993; Liu et al., 1994). The third-order method gives the most accurate solution.
Section 2 – UTCHEM Model Formulation

18

2.2 Model Formulation

2.2.1 General Description

In this section, a brief description of the model formulation is given. Additional features needed only for

enhanced oil recovery can be found in Datta Gupta et al., [1986], Bhuyan et al., [1990], and Saad [1989].

The balance equations are as follows:

1. The mass balance equation for each species.

2. The aqueous phase pressure is obtained by an overall mass balance on volume-occupying

components (water, oil, surfactant, co-solvent, and air). The other phase pressures are computed by

adding the capillary pressure between phases.

3. The energy balance equation.

Four phases are modeled. The phases are a single component gas phase (l=4) and up to three liquid phases:

aqueous (l=1), oleic (l=2), and microemulsion (l=3), depending on the relative amounts and effective

electrolyte concentration (salinity) of the phase environment. Any number of water, oil, or gas tracers can

be modeled. The tracers can partition, adsorb, and decay if they are radioactive. UTCHEM can model

partitioning interwell tracer tests (PITT) for the detection and estimation of contaminants and for the

remediation performance assessment in both saturated and vadose zones (Jin et al., 1995).

The flow equations allow for compressibility of soil and fluids, dispersion and molecular diffusion,

chemical reactions, and phase behavior and are complemented by constitutive relations.

2.2.2 Mass Conservation Equations

The assumptions imposed when developing the flow equations are local thermodynamic equilibrium except

for tracers and dissolution of organic component, immobile solid phases, slightly compressible soil and

fluids, Fickian dispersion, ideal mixing, and Darcy's law. The boundary conditions are no flow and no

dispersive flux across the impermeable boundaries.

The continuity of mass for component κ in association with Darcy's law is expressed in terms of overall

volume of component κ per unit pore volume (C  ̃ 

κ

) as

 

∂

∂t

φC  ̃ ( κ ρκ )+

r 

∇ ⋅ ρκ Cκl

r 

u l−  ̃ 

r 

D ( κl)

l=1

np

∑

 

 

 

 

 

 

 

 = Rκ (2.1)

where the overall volume of component κ per unit pore volume is the sum over all phases including the

adsorbed phases:

 

C  ̃ 

κ = 1− C ˆ κ

κ =1

ncv

∑

 

 

  

 

 

  SlCκl

l=1

np

∑ + C ˆ 

κ

 for κ = 1,..., nc (2.2)

ncv is the total number of volume-occupying components. These components are water, oil, surfactant, and

air. np is the number of phases; C ˆ 

κ

 is the adsorbed concentration of species κ; and ρκ is the density of pure

component κ at a reference phase pressure PR relative to its density at reference pressure PR0, usually taken

at the surface condition of 1 atm. We assume ideal mixing and small and constant compressibilities Cκ

o

.
Section 2 – UTCHEM Model Formulation

19

ρκ = 1 + Cκ

o

PRPR0

( ) (2.3)

The dispersive flux is assumed to have a Fickian form:

 

 ̃ 

r 

D κl,x = φSl

r 

r 

K κl ⋅

r 

∇ Cκl

(2.4)

The dispersion tensor 

 

r 

r 

K κl including molecular diffusion (Dkl) are calculated as follows (Bear, 1979):

 

r 

r 

K κlij ≡

Dκl

τ

δij +

αTl

φSl

r 

u lδij +

(αLl − αTl)

φSl

uli ulj

r 

u l

(2.5)

where αLl and αTl are phase l longitudinal and transverse dispersivities; τ is the tortuosity factor with the

definition of being a value greater than one; uli and ulj are the components of Darcy flux of phase l in

directions i and j; and δij is the Kronecker delta function. The magnitude of vector flux for each phase is

computed as

 

r 

u l

= uxl

( )

2

+(uyl )

2

+ uzl

( )

2

(2.6)

The phase flux from Darcy's law is

 

r 

u l = −

krl

r 

r 

k 

μl

⋅

r 

∇ Pl − γl

r ( ∇ h) (2.7)

where 

r r 

k is the intrinsic permeability tensor and h is the vertical depth. Relative permeability (krl),

viscosity (μl), and specific weight (γl) for phase l are defined in the following sections.

The source terms Rκ are a combination of all rate terms for a particular component and may be expressed as

 

Rκ = φ Slrκl

l=1

np

∑ + (1 − φ)rκs + Qκ (2.8)

where Qκ is the injection/production rate for component κ per bulk volume. rκl and rκs are the reaction

rates for component κ in phase l and solid phase s respectively.

Analogous equations apply for the fluxes in the y- and z-directions.

2.2.3 Energy Conservation Equation

The energy balance equation is derived by assuming that energy is a function of temperature only and

energy flux in the aquifer or reservoir occurs by advection and heat conduction only.

 

∂

∂t

(1 − φ)ρsC vs + φ ρl

SlCvl

l=1

np

∑

 

 

 

 

 

 

 

 T +

r 

∇ ⋅ ρlCpl

ul

l=1

np

∑ T − λT

r 

∇ T

 

 

  

 

 

  = q H − QL

(2.9)
Section 2 – UTCHEM Model Formulation

20

where T is the reservoir temperature; Cvs and Cvl are the soil and phase l heat capacities at constant

volume; Cpl is the phase l heat capacity at constant pressure; and λT is the thermal conductivity (all

assumed constant). qH is the enthalpy source term per bulk volume. QL is the heat loss to overburden and

underburden formations or soil computed using the Vinsome and Westerveld [1980] heat loss method.

2.2.4 Pressure Equation

The pressure equation is developed by summing the mass balance equations over all volume-occupying

components, substituting Darcy's law for the phase flux terms, using the definition of capillary pressure,

and noting that 

 

Cκl

κ =1

ncv

∑ = 1. The pressure equation in terms of the reference phase pressure (phase 1) is

 

φCt

∂P1

∂t

+

r 

∇ ⋅

r 

r 

k ⋅ λrTc

r 

∇ P1 = −

r 

∇ ⋅

r 

r 

k ⋅ λrlc

r 

∇ h

l=1

np

∑ +

r 

∇ 

r 

r 

k ⋅ λrlc

r 

∇ Pcl1

l=1

np

∑ + Qκ

κ =1

ncv

∑ (2.10)

where 

 

λrlc =

k rl

μ l

ρκ

κ =1

ncv

∑ Cκl

 and total relative mobility with the correction for fluid compressibility is

 

λrTc = λrlc

l=1

np

∑ .

The total compressibility, Ct

, is the volume-weighted sum of the rock or soil matrix (Cr) and component

compressibilities (Cκ

o

):

Ct = Cr + Cκ

o

κ =1

ncv

∑ C  ̃ 

κ (2.11)

where φ = φR 1 + Cr

PR − PR0 [ ( )].

2.2.5 Nonequilibrium Dissolution of Nonaqueous Phase Liquids

Mathematical models of multiphase flow in subsurface environments generally employ a local equilibrium

assumption; that is, it is assumed that the concentration of water leaving a region of residual NAPL has

dissolved concentrations of the organic phase at the solubility level. However, field data frequently indicate

that contaminant concentrations in groundwater are lower than their corresponding equilibrium values

(Mackay et al, 1985; Mercer and Cohen, 1990). Experimental investigations indicate that the dissolution

process is mass-transfer limited when (1) NAPL is distributed nonuniformly due to aquifer heterogeneity,

(2) water velocity is high and (3) NAPL saturation is low (Powers et al., 1991; Guarnaccia et al., 1992;

Powers et al., 1992). UTCHEM has the capability of modeling a nonequilibrium mass transfer relationship

between NAPL and water or microemulsion phases. The NAPL dissolution rate is assumed to be

represented by a linear driving force model similar to the one proposed by Abriola et al., [1992], Powers et

al., [1991], Mayer and Miller, [1990], and Powers et al., [1992]. The species mass transfer rate at the

interface between the two phases (

 

Rκl

I

) is modeled as

 

Rκl

I

= −Mκ Cκl − Cκl

eq ( ) for l = 1 or 3 (2.12)
Section 2 – UTCHEM Model Formulation

21

where Mκ is the mass transfer coefficient for species κ across the boundary layer and Cκl and 

 

Cκl

eq are the

mass concentrations of κ in the bulk aqueous solution and at equilibrium, respectively. Equation 2.12 can

be written in terms of volumetric concentration of organic species (κ=2) as

 

∂(SlC2lφ)

∂t

=

r 

∇ ⋅ C2l

r 

u l −  ̃ 

r 

D ( 2l )+ M2 C2l

eq ( − C2l ) for l = 1 or 3 (2.13)

where C2l is the volumetric concentration of organic species in the aqueous phase and 

 

C2l

eq is the

equilibrium concentration. The time derivative was discretized using a backward finite difference

approximation.

The equilibrium concentration for pure NAPL in water or aqueous phase with surfactant concentration

below the critical micelle concentration (CMC) is an input solubility limit which is small for many of the

NAPLs of interest to contaminant hydrogeologists. In the presence of surfactant, however, the equilibrium

concentrations are calculated for surfactant/NAPL/water phase behavior using Hand's equation. The

nonequilibrium concentration of NAPL in water and phase saturations are then computed using the previous

time step saturations and concentrations and the new time step equilibrium concentrations. The mass

transfer coefficient is assumed to be a constant although it may be a function of groundwater velocity,

composition, saturation, and porous medium properties (Pennell et al., 1993).

2.2.6 Well Models

Injection and production wells are considered source and sink terms in the flow equations. Wells can be

completed vertically in several layers of the aquifer or horizontally with any length and can be controlled

according to pressure or rate constraints. The well models used are based on formulations by Peaceman

[1983] and Babu and Odeh [1989]. The aquifer boundaries are treated as either constant-potential or closed

surfaces.

2.2.7 Fluid and Soil Properties

Geologic heterogeneities are probably the key factor which reduce the effectiveness of chemical enhanced

recovery processes because their success depends on the delivery of injected chemical and water into the

subsurface to contact the organic liquids. Heterogeneities result in a complex distribution of DNAPL in

residual zones and pools. To capture some of the geologic features, reservoir properties such as formation

permeability, porosity, residual phase saturation, phase relative permeability, and phase capillary pressure

are allowed to vary spatially in UTCHEM. Phase trapping functions and adsorption of both surfactant and

polymer are modeled as a function of permeability.

Many of the properties of anionic surfactants and polymers depend on the electrolyte concentrations in the

water. Divalent cations such as calcium and magnesium ions are particularly important and can make

significant differences in adsorption and other properties even at the low concentrations typically found in

ground water. Furthermore, it cannot be assumed that these concentrations do not change since processes

such as cation exchange and mineral dissolution occur during surfactant remediation. In this paper, we

describe these electrolyte effects in terms of salinity or effective salinity (defined below) and these terms as

used in this context refer to any electrolyte concentrations of interest, but especially to those of interest to

surfactant remediation of aquifers containing ground water at low electrolyte concentrations. The same

term and the same models are used to describe high salinities typical of oil reservoirs, but it should not be

inferred that these electrolyte effects are only significant at high salinities. In fact, cation exchange between

the water and clays and between the water and micelles (when anionic surfactant above its critical micellar
Section 2 – UTCHEM Model Formulation

22

concentration is present) is more important at low salinities typical of potable water than it is at high

salinities such as sea water or high salinity oil reservoirs.

The description of properties in this paper assumes that alcohols, polymer/cross-linker, and components for

high-pH flooding are absent. These property models are described in Saad [1989], Bhuyan et al. [1990],

and Kim [1995].

2.2.8 Adsorption

Surfactant

Surfactant adsorption can be an important mechanism for a SEAR process since it causes retardation and

consumption of surfactant. The remaining adsorbed surfactant after flushing with water at the end of the

remediation process may also be important even for food grade surfactants and even though the mass

concentration in the porous media at this time is likely to be very low on the order of the CMC. Some

additional time will be required for this remaining surfactant to biodegrade and this will depend on the

surfactant concentration among other variables. Surfactant adsorption has been the subject of extensive

study for many decades and is now very well understood, especially for the types of surfactants and porous

media of interest to SEAR. Rouse et al. [1993] and Adeel and Luthy [1994] are examples of recent studies

done to compare the adsorption of different types of surfactant on soils. Somasundaran and Hanna [1977]

and Scamehorn et al. [1982] are examples among the hundreds of studies done to evaluate the adsorption of

surfactants on porous media in the context of surfactant enhanced oil recovery. These studies show that

surfactant adsorption isotherms are very complex in general. This is especially true when the surfactant is

not isomerically pure and the substrate is not a pure mineral. However, we and others have found that for

many if not most conditions of interest to us the general tendency is for the surfactant isotherm to reach a

plateau at some sufficiently large surfactant concentration. For pure surfactants, this concentration is in fact

the CMC, which is often 100 times or more below the injected surfactant concentration. Thus, the complex

detailed shape of the isotherm below the CMC has little practical impact on the transport and effectiveness

of the surfactant and for this reason it has been found that a Langmuir-type isotherm can be used to capture

the essential features of the adsorption isotherm for this purpose. Camilleri et al. [1987a] illustrate this by

simulating an oil recovery experiment and Saad et al. [1989] by successfully simulating a surfactant field

project using this approach. We also used a Langmuir-type adsorption isotherm for the simulation of the

surfactant remediation of the Borden cell test illustrated below.

UTCHEM uses a Langmuir-type isotherm to describe the adsorption level of surfactant which takes into

account the salinity, surfactant concentration, and soil permeability (Hirasaki and Pope, 1974). The

adsorption is irreversible with concentration and reversible with salinity. The adsorbed concentration of

surfactant (κ = 3) is given by

ˆ C κ = min C  ̃ 

κ ,

aκ C  ̃ 

κ − C ˆ ( κ )

1+ bκ C  ̃ κ − C ˆ ( κ )

 

 

  

 

 

  κ = 3 or 4 (2.14)

The concentrations are normalized by the water concentration in the adsorption calculations. The minimum

is taken to guarantee that the adsorption is no greater than the total surfactant concentration. Adsorption

increases linearly with effective salinity and decreases as the permeability increases as follows:

a3 = (a 31 + a32 CSE )k

− 0.5

(2.15)
Section 2 – UTCHEM Model Formulation

23

where CSE is the effective salinity described later. The value of a3/b3 represents the maximum level of

adsorbed surfactant and b3 controls the curvature of the isotherm. The adsorption model parameters a31,

a32, and b3 are found by matching laboratory surfactant adsorption data.

Polymer

The retention of polymer molecules in permeable media is due to both adsorption onto solid surfaces and

trapping within small pores. The polymer retention similar to that of surfactant slows down the polymer

velocity and depletes the polymer slug. Polymer adsorption is modeled as a function of permeability,

salinity, and polymer concentration (Eq. 2.14 for κ = 4). The parameter a4 is defined as

a 4 = a 41 + a 42CSEP ( )k

− 0.5

(2.16)

The effective salinity for polymer (CSEP) is

CSEP =

C51 + (βP −1)C61

C11

(2.17)

where C51, C61, and C11 are the anion, calcium, and water concentrations in the aqueous phase and βP is

measured in the laboratory and is an input parameter to the model.

Organic

Organic sorption can be an important parameter in assessments of the fate and transport of DNAPLs in

soils. The magnitude of sorbed organics is described in terms of a partition coefficient with respect to the

organic fraction, Koc (Karickhoff, 1984). The higher Koc, the greater is its tendency to sorb into organic

carbon in the subsurface. A linear sorption isotherm is used to model the organic sorption:

C ˆ 

2 = foc Koc C21 (2.18)

where C ˆ 2 is the adsorbed organic, foc is the fraction of organic carbon in the soil, and C21 is the organic

concentration in the water phase. Koc is defined as the ratio of the amount of organic adsorbed per unit

weight of organic carbon in the soil to the concentration of the organic in solution at equilibrium.

2.2.9 Cation Exchange

Cation exchange occurs when there is an incompatibility in the electrolyte composition of injected fluids

and the initial fluids saturating the soil. Cation exchange affects the transport of ions in solution and

therefore may have a significant effect on the optimum salinity and the surfactant phase behavior (Pope et

al., 1978; Fountain, 1992) and surfactant adsorption. The type and concentration of cations involved in the

exchange process can also affect the hydraulic conductivity (Fetter, 1993). We use a cation exchange

model based on Hirasaki's model [1982]. Cations exist in the form of free ions, adsorbed on clay surfaces,

and associated with either surfactant micelles or adsorbed surfactant. The mass action equations for the

exchange of calcium (κ=6) and sodium (κ=12) on clay and surfactant describe the cation exchange model as

C12

s

( )

2

C6

s

= β

s

C3

m

C12

f

( )

2

C6

f

(2.19)
Section 2 – UTCHEM Model Formulation

24

C12

c

( )

2

C6

c

= β

cQv

C12

f

( )

2

C6

f

(2.20)

where the superscripts f, c, and s denote free cation, adsorbed cation on clay, and adsorbed cation on

micelles, respectively. The simulator input parameters are Qv, the cation exchange capacity of the mineral,

βc and βs, the ion exchange constants for clay and surfactant, and C3

m , the concentration of surfactant in

meq/ml. The electrical neutrality and mass balances needed to close the system of ion exchange equations

are

C5 = C12

f

+ C6

f

(2.21)

C6 = C6

f

+ C6

s

+ C6

c

(2.22)

C3 = C6

s

+ C12

s

(2.23)

Qv = C6

c

+ C12

c

(2.24)

C5 − C6 = C12

f

+ C12

s

+ C12

c

(2.25)

where Cκ

f

 is the fluid concentration for species κ normalized by water concentration All concentrations in

ion exchange equations are expressed in meq/ml of water. The molar volume concentration of surfactant is

computed as

C3

m

=

1000C3

C1 M3

(2.26)

where M3 is the equivalent weight of the surfactant.

The cation exchange equations are solved for the six unknowns C6

c

, C12

c

,C6

f

,C12

f

, C6

s

, andC12

s

 using

Newton-Raphson method.

2.2.10 Phase Behavior

The surfactant/oil/water phase behavior is based on Winsor [1954], Reed and Healy [1977], Nelson and

Pope [1978], Prouvost et al. [1985], and others. Surfactant phase behavior considers up to five volumetric

components (oil, water, surfactant, and two alcohols) which form three pseudocomponents in a solution. In

the absence of alcohols (the formulation described in this paper), only three components are modeled. The

volumetric concentrations of these three components are used as the coordinates on a ternary diagram.

Salinity and divalent cation concentrations have a strong influence on phase behavior. At low salinity, an

excess oil phase that is essentially pure oil and a microemulsion phase that contains water plus electrolytes,

surfactant, and some solubilized oil exist. The tie lines (distribution curves) at low salinity have negative

slope (Fig. 2.1). This type of phase environment is called Winsor Type I, or alternatively Type II(−) in

some of the literature. If the surfactant concentration is below CMC, the two phases are an aqueous phase

containing all the surfactant, electrolytes, and dissolved oil at the water solubility limit and a pure excess oil

phase. For high salinity, an excess water phase and a microemulsion phase containing most of the

surfactant and oil, and some solubilized water exist. This type of phase environment is called Winsor Type
Section 2 – UTCHEM Model Formulation

25

II, or alternatively Type II(+) (Fig. 2.2). An overall composition at intermediate salinity separates into

three phases. These phases are excess oil and water phases and a microemulsion phase whose composition

is represented by an invariant point. This phase environment is called Winsor Type III, or just Type III

(Fig. 2.3).

Other variables besides electrolyte concentrations, e.g. alcohol type and concentration, the equivalent

alkane carbon number of the oil or solvent and changes in temperature or pressure also cause a phase

environment shift from one type of phase behavior to another type. Three papers by Baran et al. [1994

a,b,c] show that the phase behavior of surfactants with both pure chlorocarbons such as trichloroethylene

(TCE) and mixtures of chlorocarbons such as TCE and carbon tetrachloride is essentially identical in form

to the classical behavior with hydrocarbons, so we are justified in using the same approach for these

contaminants as we have used for hydrocarbons.

The surfactant/oil/water phase behavior can be represented as a function of effective salinity once the

binodal curve and tie lines are described. The phase behavior model in UTCHEM uses Hand's rule (Hand,

1939) and is based on the work by Pope and Nelson [1978], Prouvost et al. [1984b; 1985; 1986], Satoh

[1984], and Camilleri et al. [1987a,b,c].

Effective Salinity

The effective salinity increases with the divalent cations bound to micelles (Glover et al., 1979; Hirasaki,

1982; Camilleri et al., 1987a,b,c) and decreases as the temperature increases for anionic surfactants and

increases as the temperature increases for nonionic surfactants.

CSE = C51 1 −β6

f6

s

( )

−1

1 +β T T − Tref [ ( )]

−1

(2.27)

where C51 is the aqueous phase anion concentration; β6 is a positive constant; f

6

s

is the fraction of the total

divalent cations bound to surfactant micelles as f

6

s

=

C6

s

C3

m

; and βΤ is the temperature coefficient.

The effective salinities at which the three equilibrium phases form or disappear are called lower and

upper limits of effective salinity (CSEL and CSEU).

Binodal Curve

The formulation of the binodal curve using Hand's rule (Hand, 1939) is assumed to be the same in all phase

environments. Hand's rule is based on the empirical observation that equilibrium phase concentration ratios

are straight lines on a log-log scale. Figures 2.4a and 2.4b show the ternary diagram for a Type II(−)

environment with equilibrium phases numbered 2 and 3 and the corresponding Hand plot. The binodal

curve is computed from

 

C3l

C2l

= A

C3l

C1l

 

  

 

  

B

l = 1,2, or 3 (2.28)

where A and B are empirical parameters. For a symmetric binodal curve where B = −1, which is the

current formulation used in UTCHEM, all phase concentrations are calculated explicitly in terms of oil

concentration C2l (recalling 

 

Cκl

κ=1

3

∑ = 1).
Section 2 – UTCHEM Model Formulation

26

 

C3l =

1

2

−AC2l + AC2l

( )

2

+ 4AC2l

1 − C2l

( )

 

  

 

  for l = 1, 2, or 3 (2.29)

Parameter A is related to the height of the binodal curve as follows

Am =

2C3max,m

1 − C3max,m

 

  

 

  

2

 m = 0, 1, and 2 (2.30a)

where m = 0, 1, and 2 are corresponding to low, optimal, and high salinities. The height of binodal curve is

specified as a linear function of temperature:

C3max,m = HBNC,m + HBNT,m T − Tref ( ) m = 0, 1, and 2 (2.30b)

where HBNC,m and HBNT,m are input parameters. Am is linearly interpolated as

A = (A0 − A1) 1−

CSE

CSEOP

 

  

 

  + A1

for CSE ≤ CSEOP

A = (A2 − A1)

CSE

CSEOP

−1

 

  

 

  + A1

forCSE > CSEOP

(2.31)

where CSEOP is the optimum effective salinity and the arithmetic average of CSEL and CSEU. The heights

of the binodal curve at three reference salinities are input to the simulator and are estimated based on phase

behavior laboratory experiments.

Tie lines for two-phases

For both Type II(−) and Type II(+) phase behavior, there are only two phases below the binodal curve. Tie

lines are the lines joining the composition of the equilibrium phases and are given by

 

C3l

C2l

= E

C33

C13

 

  

 

  

F

(2.32)

where l=1 for Type II(+) and l=2 for Type II(−). In the absence of available data for tie lines, F is

calculated from F = −1/B. For a symmetric binodal curve (B=−1), F is equal to 1. Since the plait point is

on both the binodal curve and tie line, we have

E =

C1P

C2P

=

1− C2P − C3P

C2P

(2.33)

Applying the binodal curve equation to the plait point and substituting C3P (Eq. 2.29) in Eq. 2.33, we have

E =

1 − C2P −

1

2

−AC2P + (AC2P )

2

+ 4AC2P(1 − C2P )

 

  

 

  

C2P

(2.34)

where C2P is the oil concentration at the plait point and is an input parameter for Type II(−) and Type II(+)

phase environments.
Section 2 – UTCHEM Model Formulation

27

Tie lines for Type III

The phase composition calculation for the three-phase region of Type III is simple due to the assumption

that the excess oleic and aqueous phases are pure. The microemulsion phase composition is defined by the

coordinates of the invariant point. The coordinates of the invariant point (M) are calculated as a function of

effective salinity:

C2M =

CSE − CCSEL

CSEU − CCSEL

(2.35)

C3M is computed by substituting C2M in Eq. 2.29 and noting that C1M = 1− C2M −C3M.

The phase composition calculations for lobes II(−) and II(+) are analogous. The plait point must vary from

zero to the II(+) value, C2PL

*

or zero to II(−) value, C2PR

*

. Here, we only consider the II(−) lobe. The

plait point is calculated by interpolation on effective salinity:

C2PR = C2PR

*

+

CSE − CSEL

CSEU − CSEL

1− C2PR

*

( ) (2.36)

In order to apply Hand's equation, we transform the concentrations as shown in Fig. 2.5. The transformed

concentrations are

 

C ′ 1l = C1lsec θ

C ′ 3l = C3l − C2ltanθ

C ′ 2l =1 − C 1′ l − C ′ 3l

 for l = 2 or 3 (2.37)

The angle θ is

tan θ =

C3M

C1M

sec θ =

C1M

2 + C3M2

C1M

(2.38)

Parameter E of the tie line equation is now calculated in terms of untransformed coordinates of the plait

point as

E =

C ′ 1P

C ′ 2P

=

1− (sec θ − tanθ)C2PR − C3PR

C2PR sec θ

(2.39)

where C3PR is given by Eq. 2.29 and C1PR = 1− C2PR − C3PR.

2.2.11 Phase Saturations

The phase saturations in the saturated zone in the presence of surfactant are calculated from the phase

concentrations, overall component concentration, and saturation constraints once the phase environment and

phase compositions are known. The overall component concentration and saturation constraints are
Section 2 – UTCHEM Model Formulation

28

 

Cκ = SlCκl

κ=1

3

∑ l = 1,2,or 3 (2.40)

 

Sl

l =1

3

∑ = 1 (2.41)

The phase saturations in the vadose zone (phase 3 is absent) are computed from the overall component

concentration and the saturation constraint by

S2 =

C2 − C21

1− C21

,S1 =

C1

1 − C11

,S4 = 1− S1 − S2

(2.42)

where C21 is the concentration of dissolved organic species in the water phase.

2.2.12 Interfacial Tension

The two models for calculating microemulsion/oil (σ23) and microemulsion/water (σ13) interfacial tension

(IFT) are based on Healy and Reed [1974] and Huh [1979]. The IFTs for water and oil (σow) and water

and air (σaw) are assumed to be known constants.

Healy et al.

The first IFT model is based on Hirasaki's modification (Hirasaki, 1981) of the model of Healy and Reed

[1974]. Once the phase compositions have been determined, the interfacial tensions between

microemulsion and the excess phases (σ13, σ23) are calculated as functions of solubilization parameters:

 

log10 σl3 = log10 Fl + Gl2 +

Gl1

1 + Gl3Rl3

 for Rl3 ≥ 1

log10 σl3 = log10 Fl + (1 − Rl3)log10 σow +Rl3 Gl2 +

Gl1

1 + Gl3

 

  

 

  for Rl3 < 1

 

 

  

 

  

 for l=1,2 (2.43)

where Gl1

, Gl2, and Gl3 are input parameters. R l3

is the solubilization ratio (

 

Cl3

C33

). The correction factor

introduced by Hirasaki, Fl, ensures that the IFT at the plait point is zero and is

 

Fl =

1− e

− conl

1− e

− 2

 for l = 1, 2 (2.44)

where

 

con l = Cκl − Cκ 3

( )

2

κ =1

3

∑ (2.45)

and in the absence of surfactant or the surfactant concentration below CMC, the IFTs equal σow.

Chun-Huh

The interfacial tension is related to solubilization ratio in Chun-Huh's equation as
Section 2 – UTCHEM Model Formulation

29

 

σl3 =

c

R l3

2

 for l = 1 or 2 (2.46)

where c is typically equal to about 0.3. We introduced Hirasaki's correction factor Fl (Eq. 2.44) and

modified Huh's equation so that it reduces to the water-oil IFT (σow) as the surfactant concentration

approaches zero.

 

σl3 = σow e

−a Rl3 +

c Fl

Rl3

2

1 − e

−a Rl3

3  

     for l = 1 or 2

(2.47)

where a is a constant equal to about 10.

2.2.13 Density

Phase specific weights (γl = gρl) are modeled as a function of pressure and composition as follows:

 

γ l = C1lγ1l + C2lγ 2l + C3lγ 3l + 0.02533C5l − 0.001299C6l + C8lγ8l for l = 1,..., np (2.48)

where 

 

γ kl= γ kR 1 + Ck

o

Pl− PR0 [ ( )]. γkR is the component κ specific weight at a reference pressure and is

an input parameter. The numerical constants account for the weight of dissolved ions and have units of

psi/ft per meq/ml of ions.

We have recently modified the density calculation for the microemulsion phase (l = 3) to use an apparent

oil component specific weight in the microemulsion phase (γ23R) instead of the oil component specific

weight (γ2R).

2.2.14 Capillary Pressure

Both the Parker et al. [1987] generalization of the van Genuchten [1980] model and the Brooks and Corey

[1966] model are options used to calculate the capillary pressure. Hysteresis in capillary pressure is taken

into account in a very simplistic fashion discussed below, but a full hysteretic and trapping number

dependent model that is more complete is also available (Delshad et al., 1994).

Brooks-Corey

Capillary pressure in Brooks and Corey capillary pressure-saturation relationship (Brooks and Corey, 1966)

is scaled for interfacial tension, permeability, and porosity (Leverett, 1941). The organic spill event in the

unsaturated (vadose) zone is assumed to be in the imbibition direction (total liquid saturation increasing).

The organic spill event in the saturated zone is taken to be in the first drainage direction (wetting phase,

water, saturation decreasing) for the entire spill process. The water flushing or surfactant injection process

is assumed to be in the imbibition direction for the entire injection period.

Vadose Zone

Implicit assumptions in the capillary pressure formulation in the vadose zone where up to three phases exist

are that the direction of descending wettability is water, organic, and air and that the water phase is always

present.
Section 2 – UTCHEM Model Formulation

30

 

Pb

Pc1l

 

  

 

  

λi

= 1 − Sn1 for l = 2 or 4 (2.49)

where the maximum capillary pressure Pb is scaled by soil permeability and porosity and is equal to

 

Cpci

σ1l

σ12

φ

k

, which then gives

 

Pc1l

= Cpci

φ

k

σ1l

σ12

1 − Sn1

( )

−1 λi

 for l = 2 or 4 (2.50)

where Cpci and EPCi

 = -1/λi are positive input parameters. The normalized saturations are defined as

 

Snl =

Sl − Slr

1 − S1r − S2r − S4 r

(2.51)

The entrapped organic saturation for three-phase (air/organic/water) flow (S2r) is based on a function by

Fayers and Matthews [1982] which uses the two-phase entrapped saturation values:

S2r = S2r1 1 −

S4

1 − S1r − S2r 4

 

 

  

 

 + S2 r4

S4

1 − S1r − S2r 4

 

 

  

 

 (2.52)

where S2r1 and S2r4 are the entrapped organic saturations to flowing water and air phases, respectively.

Saturated Zone

The capillary pressure in the saturated zone where up to three phases (water, organic, microemulsion) exist

according to the surfactant phase behavior is calculated as follows.

Two-phase organic-water

The drainage capillary pressure is modeled using the Brooks-Corey function:

Pb

Pc12

 

 

  

  

λd

= Sn1(2.53)

where λd is a measure of pore size distribution of the medium, the entry pressure Pb equals Cpcd

φ

k

 and

the normalized water saturation is defined as

Sn1 =

S1 − S1r

1 − S1r

(2.54)

where Cpcd and EPCd = -1/λd are input parameters. The UTCHEM input parameter EPCd must be a

negative value.

Two-phase water/microemulsion or organic/microemulsion

The imbibition capillary pressure using a Corey-type function is
Section 2 – UTCHEM Model Formulation

31

 

Pbl

Pcl3

 

 

  

  

λi

= 1 − S

nl

'

(2.55)

For l = 1, l

' = 1 while for l = 2, l' = 3. Pbl equals 

 

Cpci

σl3

σ12

φ

k

. The normalized saturations are defined

as

Sn1 =

S1 − S1r

1 − S1r − S3r

(2.56)

Sn3 =

S3 − S3r

1 − S2r − S3r

(2.57)

Three-phase water/organic/microemulsion

Pb1

Pc13

 

 

  

  

λi

= 1 − Sn1(2.58)

Pb2

Pc23

 

 

  

  

λi

= 1 −

S2 − S2r

S1 − S ( 1r )+ S3 − S ( 3r )

(2.59)

where 

Sn1 =

S1 − S1r

1 − S1r − S2 r − S3r and Pbl equals 

Cpci

σl3

σ12

φ

k

.

The residual saturations (Slr) in Brooks and Corey's model are either a constant and input to the simulator

or computed as a function of trapping number discussed later.

van Genuchten

The three-phase capillary pressure-saturation function determined using the generalization of Parker et al.

[1987] to the two-phase flow model of van Genuchten [1980] is represented by

 

S l= 1 + α h

*

( )

n  

 

 

 

−m

h

* > 0

S l = 1 h

* ≤ 0

(2.60)

where 

 

S l =

Sl − S1r

1 − S1r

is the effective saturation, 

 

h

*

= βll ′ PCll ′ is the scaled capillary pressure; 

 

βll ′ is the

scaling coefficient for fluid pair of l and l ′ ; α (UTCHEM parameter of CPC) and n (UTCHEM parameter

of EPC) are the model parameters, and m = 1−1/n. A significant difference between the van Genuchten and

Brooks Corey models is the discontinuity in the slope of the capillary pressure curve at the entry pressure in

the latter model whereas Eq. 2.60 is both continuous and has a continuous slope. The implementation of

this model in the simulator includes scaling α with soil permeability and porosity similar to that described

in Brooks-Corey model.
Section 2 – UTCHEM Model Formulation

32

2.2.15 Relative Permeability

Multiphase relative permeabilities are modeled based on either Corey-type functions (Brooks and Corey,

1966; Delshad and Pope, 1989) or Parker et al. [1987] extension of van Genuchten two-phase flow equation

to three-phase flow. Hysteresis in the Corey-type relative permeability model discussed below is accounted

for by assuming the flow in the saturated zone is on the drainage curve for the spill event and the

remediation of the saturated zone is an imbibition process. However, a full hysteretic relative permeability

model that is trapping number dependent is also available (Delshad et al., 1994).

Corey-Type

Multiphase imbibition and drainage relative permeabilities in both the vadose and saturated zones are

modeled using Corey-type functions that are a function of trapping number.

Vadose Zone

The organic phase movement in a three-phase porous medium consisting of water/organic/air is assumed to

be in the imbibition direction during the organic spill in the vadose zone. We also assume that water and

air relative permeabilities are unique functions of their respective saturations only. Organic phase relative

permeability, however, is assumed to be a function of two saturations (Delshad and Pope, 1989). These

assumptions are consistent with relative permeability measurements (Corey et al., 1956; Saraf and Fatt,

1967; Schneider and Owens, 1970; Saraf et al., 1982; Fayers and Matthews, 1982; Oak, 1990; Oak, et al.,

1990).

 

krl = krl

o

Snl

( )

nl

 for l = 1, 2, or 4 (2.61)

where the normalized saturations are defined as

 

Snl =

Sl − Slr

1 − S1r − S2rl − S4r

 for l = 1, or 4 (2.62)

Sn2 =

S2 − S2r

1 − S1r − S2r − S4r

(2.63)

where 

 

krl

o

, nl, and Slr are the relative permeability endpoint, exponent, and entrapped saturation for phase

l. The trapped organic saturation for three-phase flow (S2r) is calculated from Eq. 2.52. These equations

reduce to two-phase flow relative permeabilities in the absence of the third phase.

Saturated Zone

The organic phase movement during the spill event in the saturated zone where up to two fluid phases

(water and organic) exist is assumed to be in the drainage direction. The organic movement during the

remediation process, e.g., water flushing or surfactant injection, however, is assumed to be in the imbibition

direction for the entire injection period.

Organic spill process

The relative permeabilities for water and organic fluid phases are

kr1 = kr1

o

Sn1( )

n1

(2.64)

kr 2 = kr 2

o

1 − Sn1( )

n2

(2.65)
Section 2 – UTCHEM Model Formulation

33

where the normalized water saturation is Sn1 =

S1 − S1r

1 − S1r

.

Remediation process

There are up to three liquid phases present according to the surfactant/water/ organic phase behavior during

a SEAR process in the saturated zone. The relative permeabilities are assumed to be unique functions of

their respective saturations only. The latter assumption is supported by experimental data measured at The

University of Texas at Austin for a mixture of petroleum sulfonate, n-decane, isobutyl alcohol, and water

(Delshad et al., 1987; Delshad, 1990). The relative permeability is defined by

 

krl = krl

o

Snl

( )

nl

 for l = 1, 2, or 3 (2.66)

where the normalized saturations are defined as

 

Snl =

Sl − Slr

1 − Slr

l=1

3

∑

 for l = 1, 2, or 3 (2.67)

The relative permeabilities reduce to water/organic, water/microemulsion, or organic/microemulsion two

phase flow functions. The residual saturations, relative permeability endpoints, and exponents are either

constants and input parameters or functions of trapping number as discussed in the next section.

Parker et al.

Parker et al. [1987] extended the two-phase relative permeability-saturation expression derived by van

Genuchten to three-phase water/oil/air flow using scaled variables as follows:

kr1 = S 1

1/ 2

1 − 1 − S 1

1/m

( )

 m

 

 

 

2

(2.68)

kr 2 = S t − S ( 1)

1/ 2

1 − S 1

1/m

( )

m

− 1 − S t

1/m

( )

 m

 

 

 

2

(2.69)

kr 4 = (S 4 )

1/ 2

1 − S t

1/m

( )

2m

(2.70)

where St is the total liquid saturation. The assumptions in deriving the above relative permeability

functions are that water or gas relative permeability is a function of its own saturation only whereas oil

relative permeability is a function of both water and oil saturations.

2.2.16 Trapping Number

One of the possible mechanisms for SEAR is the mobilization of trapped organic phase due to reduced

interfacial tension resulting from the injection of surfactants into the aquifer (Tuck et al., 1988; Cherry et

al., 1990; Pennell et al., 1994; Brown et al., 1994). Buoyancy forces can also affect the mobilization of a

trapped organic phase and can be expressed by the Bond number (Morrow and Songkran, 1982). The Bond

and capillary numbers for the trapping and mobilization of a nonwetting phase are usually treated as two

separate dimensionless groups, one to represent gravity/capillary forces (Bond number) and the other to

represent viscous/capillary forces (capillary number). One of several classical definitions of capillary

number (Brownell and Katz, 1949; Stegemeier, 1977; Chatzis and Morrow, 1981; Lake, 1989) is as follows
Section 2 – UTCHEM Model Formulation

34

 

Ncl

=

r r 

k ⋅

r 

∇ Φl'

σ

ll'

 for l = 1,..., np (2.71)

where l and l' are the displaced and displacing fluids and the gradient of the flow potential is given by

 

∇Φl' = ∇Pl' − g

l'

ρ ∇h .

Bond number can be defined as

 

NBl=

k g (ρl − ρl' )

σll'

 for l = 1,..., np (2.72)

where k is the permeability and g is the gravitational force constant.

We have recently developed a new dimensionless number called the trapping number which includes both

gravity and viscous forces. The dependence of residual saturations on interfacial tension is modeled in

UTCHEM as a function of the trapping number. This is a new formulation that we found necessary to

adequately model the combined effect of viscous and buoyancy forces in three dimensions. Buoyancy

forces are much less important under enhanced oil recovery conditions than under typical SEAR conditions

and so had not until now been carefully considered under three-dimensional surfactant flooding field

conditions as a result.

The trapping number is derived by applying a force balance on the trapped NAPL globule. The forces

controlling the movement of the blob are the viscous force due to the hydraulic gradient, the trapping force

due to capillary pressure and the gravity force, which can act as either a driving or trapping force depending

on the direction of the flow. The condition for mobilizing a trapped blob of length L is as follows

Hydraulic force + Buoyancy force • Capillary force (2.72a)

Substituting the definition for each of these forces we have

ΔL ∇Φw − gΔρ ≥ ΔPc(2.72b)

The trapping number is defined by the left-hand side of Eq. 2.72b as

 

NTl =

−

r 

r 

k ⋅

r 

∇ Φl' −

r 

r 

k ⋅ g (ρ

l'

− ρl

)

r [ ∇ h]

σ

ll'

(2.72c)

For one-dimensional vertical flow, the viscous and buoyancy forces add directly and a trapping number can

be defined as 

 

NTl

= Ncl+ NBl

. For two-dimensional flow a trapping number is defined as

 

NTl

= cl

2 N + 2 Ncl NBl sin θ + Bl2 N for l = 1,..., np (2.73)

where θ is the angle between the local flow vector and the horizontal (counter clockwise). The

derivation of trapping number for three-dimensional heterogeneous, anisotropic porous media is given by

Jin [1995].
Section 2 – UTCHEM Model Formulation

35

Residual saturations are then computed as a function of trapping number as

 

Slr = min Sl, Slr

high +

Slr

low − Slr

high

1 + Tl NT l

 

 

 

 

 

 for l = 1,..., np (2.74)

where Tl is a positive input parameter based on the experimental observation of the relation between

residual saturations and trapping number. 

 

Slr

low and 

 

Slr

high are the input residual saturations for phase l at

low and high trapping numbers. This correlation was derived based on the experimental data for n-decane

(Delshad, 1990) and have recently been successfully applied to residual PCE as a function of trapping

number measured by Abriola et al. [1994; 1995].

The endpoints and exponents of both the relative permeability curves and capillary pressure curves change

as the residual saturations change at high trapping numbers because of detrapping (Morrow and Chatzis,

1981; Morrow et al., 1985; Fulcher et al., 1985; Delshad et al., 1986). The endpoints and exponents in

relative permeability functions are computed as a linear interpolation (Delshad et al., 1986) between the

given input values at low and high trapping numbers 

 

k rl

o

low

, krl

o

high

,n l

low

, nl

 high

     :

 

krl

o

= krl

o

low

+

Sl'r

low − Sl' r

Sl'r

low − Sl' r

high krl

o

high

− krl

o  low

   for l = 1,..., np (2.75)

 

nl = nl

low

+

Sl' r

low

− Sl' r

Sl'r

low

− Sl' r

high nl

high

− nl

low ( )for l = 1,..., np (2.76)

The above correlations have successfully been tested against experimental data (Delshad et al., 1986).

2.2.17 Viscosity

Liquid phase viscosities are modeled in terms of pure component viscosities and the phase concentrations of

the organic, water and surfactant:

 

μl = C1lμw e

α1 C2l ( +C3l )

+ C2lμo

e

α2 C1l ( +C3l )

+ C3lα3

e

α4C1l+ α5

( C2l )

 for l = 1, 2, or 3 (2.77)

where the α parameters are determined by matching laboratory microemulsion viscosities at several

compositions. In the absence of surfactant and polymer, water and oil phase viscosities reduce to pure

water and oil viscosities (μw, μo). When polymer is present, μw is replaced by μp defined below.

The following exponential relationship is used to compute viscosities as a function of temperature (T).

μκ = μκ,ref exp bκ

1

T

−

1

Tref

 

  

 

  

 

  

 

  for κ = water, oil, or air (2.78)

where μκ,ref is the viscosity at a reference temperature of Tref and bκ is an input parameter.

Air viscosity is computed as a linear function of pressure by

μ4 = μa 0 + μaS PR − PR0( ) (2.79)
Section 2 – UTCHEM Model Formulation

36

where μa0, the air viscosity at a reference pressure of PR0 and μaS, the slope of air viscosity vs. pressure,

are input parameters.

The viscosity of a polymer solution depends on the concentration of polymer and on salinity. The FloryHuggins equation (Flory, 1953) was modified to account for variation in salinity as

 

μp

0

= μw 1+ Ap1 C4l + Ap2 C

4l

2

+ Ap3C

4l

3

( )CSEP

S  p

     for l = 1 or 3 (2.80)

where C4l is the polymer concentration in the water or microemulsion phase, μw is the water viscosity, AP1,

AP2, and AP3 are constants. The factor CSEP

Sp

allows for dependence of polymer viscosity on salinity and

hardness. The effective salinity for polymer is given by Eq. 2.17 and Sp is the slope of 

μp

0 − μw

μw

 

 

  

 

 

  vs.

CSEP on a log-log plot.

The reduction in polymer solution viscosity as a function of shear rate (γ Ý) is modeled by Meter's equation

(Meter and Bird, 1964):

μp = μw +

μp

0 − μw

1 +

Ý γ 

Ý γ 1 2

 

 

 

 

  

Pα−1

(2.81)

where Ý γ 1 2

 is the shear rate at which viscosity is the average of μp

0

 and μw and Pα is an empirical

coefficient. When the above equation is applied to flow in permeable media, μp is usually called apparent

viscosity and the shear rate is an equivalent shear rate Ý γ eq . The in-situ shear rate for phase l is modeled by

the modified Blake-Kozeny capillary bundle equation for multiphase flow (Lin, 1981; Sorbie, 1991) as

 

Ý γ eq =

Ý γ c

ul

k krl φSl

(2.82)

where Ý γ c

 is equal to 3.97C sec-1 and C is the shear rate coefficient used to account for non-ideal effects

such as slip at the pore walls (Wreath et al., 1990; Sorbie, 1991). The appropriate average permeability k 

is given by

 

k =

1

kx

uxl

ul

 

 

  

  

2

+

1

ky

uyl

ul

 

 

  

  

2

+

1

kz

uzl

ul

 

 

  

  

2  

 

 

 

 

 

−1

(2.83)

2.2.18 Polymer Permeability Reduction

Polymer solutions reduce both the mobility of the displacing fluid and the effective permeability of the

porous medium. The permeability reduction is measured by a permeability reduction factor, Rk, defined as
Section 2 – UTCHEM Model Formulation

37

Rk =

effective permeabilityof water

effective permeability of polymer

(2.84)

The change in mobility due to the combined effect of increased viscosity and reduced permeability is

called resistance factor, RF, calculated by

RF = Rk

μp

μw

(2.85)

The effect of permeability reduction lasts even after the polymer solution has passed through the porous

medium and is called the residual resistance factor, RRF, defined as

RRF =

mobility before polymersolution

mobility after polymersolutio

(2.86)

The permeability reduction factor in UTCHEM is modeled as

 

Rk = 1 +

(Rk max − 1)brk C4l

1 + brk C4l

where

R k max = 1−

crk Ap1CSEP

S  p

     

1

3

kxky

φ

 

 

  

 

 

  

1

2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

− 4

(2.87)

and l refers to the phase with the highest polymer concentration, brk and Crk are the input parameters.

The effect of permeability reduction is assumed to be irreversible i.e., it does not decrease as polymer

concentration decreases and thus RRF = Rk. The viscosity of the phase that contains the polymer is

multiplied by the value of the Rk to account for the mobility reduction in the simulator.

2.2.19 Polymer Inaccessible Pore Volume

The reduction in porosity due to inaccessible or excluded pores to the large size polymer molecules

is called inaccessible pore volume. The resulting effect is a faster polymer velocity than the velocity of

water. This effect is modeled by multiplying the porosity in the conservation equation for polymer by the

input parameter of effective pore volume.

2.3 Numerical Methods

The pressure equation and species conservation equations are discretized spatially and temporally as

described below. The discretized equations are given in Appendix C.
Section 2 – UTCHEM Model Formulation

38

2.3.1 Temporal Discretization

The temporal discretization in UTCHEM is implicit in pressure, explicit in concentration (IMPES-like).

The solution of the pressure equation using the Jacobi conjugate gradient method is then followed by a back

substitution into the explicit mass conservation equation for each component. The temporal accuracy for

the conservation equation is increased by using a time-correction technique that is second-order in time

(Liu, 1993; Liu et al., 1994).

2.3.2 Spatial Discretization

Either one-point upstream, two-point upstream, or a third-order spatial discretization of the

advective terms is used (see Appendix C). It is well-known that lower-order upwind schemes cause

smearing of the saturation and concentration profiles by increasing numerical dispersion. There have been

a number of discretization methods developed to minimize these effects associated with multiphase flow

and transport simulation (Todd et al., 1972; Leonard, 1979; Taggart and Pinczewski, 1987; Bell et al.,

1989; Le Veque, 1990; Datta Gupta et al., 1991; Blunt and Rubin, 1992; Dawson, 1993; Arbogast and

Wheeler, 1995). We use a scheme that is approximately third-order in space to minimize numerical

dispersion and grid-orientation effects. In order to obtain oscillation-free, high-resolution, high-order

results, Harten [1983] developed the total-variation-diminishing scheme (TVD) that includes a limiting

procedure. The limiter is a flux limiter with constraints on the gradient of the flux function (Sweby, 1984;

Datta Gupta et al., 1991; Liu et al., 1994). The limiter function developed by Liu [1993], which varies as a

function of timestep and gridblock size, was implemented in the simulator.

2.4 Model Verification and Validation

UTCHEM has extensively been verified by comparing problems such as one-dimensional two-phase flow

with the Buckley-Leverett solution (Buckley and Leverett, 1942), one-dimensional miscible water/tracer

flow against the analytical solution of the convection-diffusion equation, two-dimensional ideal tracer flow

with the analytical solution given by Abbaszadeh-Dehghani and Brigham [1984], and two-dimensional

nonlinear Burgers equation (Schiesser, 1991) by Liu [1993]. Excellent agreement between the numerical

and analytical solutions were obtained when the TVD third-order scheme was used. The model has also

been validated by comparisons with laboratory surfactant floods (Camilleri et al., 1987a), field data from

the Big Muddy surfactant pilot (Saad et al., 1989), and a multiwell waterflood tracer field project (Allison

et al., 1991). Pickens et al. [1993] have compared UTCHEM results with a tetrachloroethylene (PCE)

infiltration experiment in a sandpack with four types of sands performed by Kueper [1989] and Kueper and

Frind [1991]. They concluded that the simulator can accurately predict the vertical and lateral distribution

of DNAPL in a heterogeneous medium.

The model has recently been used to model the surfactant-enhanced remediation of PCE in a test cell at

Canadian Forces Base Borden in Allison, Ontario (Freeze et al., 1994). The model was 3 m by 3 m by 4 m

deep test cell described as layered with soil properties estimated from the field data. The detailed

description of the test cell is given by Kueper et al. [1993]. PCE in the amount of 231 L was first injected

to the center of the test cell. The remediation process involved the following steps:

1. Direct pumping of free-phase for about two weeks where 47 L of PCE was recovered,

2. Pump and treat for about two months where additional 12 L of free-phase and dissolved PCE was

removed, and

3. Surfactant flushing to solubilize additional PCE for about seven months. The surfactant solution

was 1 wt% nonyl phenol ethoxylate (NP 100) and 1 wt% phosphate ester of the nonyl phenol
Section 2 – UTCHEM Model Formulation

39

ethoxylate (Rexophos 25-97). A total of 130,000 L of surfactant solution was recirculated through

the test cell. Additional 62 L of PCE was recovered as a result of enhanced solubility by the

surfactant solution. The surfactant-enhanced solubility of PCE was measured to be about 11,700

mg/L as compared to an aqueous solubility of about 200 mg/L.

The measured and simulated vertical distributions of PCE before and after the surfactant injection are

shown in Figs. 2.6 and 2.7 and show good agreement. Here we discuss the features of UTCHEM model

that were used in this application and the input parameters for the physical property models since Freeze et

al. did not discuss these in their paper. The assumptions made based on the test cell conditions were 1)

isothermal simulations, 2) insignificant electrolyte concentration, incompressible fluids and soil,

equilibrium PCE dissolution, and no mobilization of PCE. The species considered in the simulation were

water, PCE, and surfactant and the resulting phases were water, PCE, and microemulsion. The phase

behavior parameters were chosen such that either residual PCE/microemulsion, residual PCE/water, or

single phase microemulsion are present. Due to lack of any phase behavior measurements for this

surfactant mixture, the phase behavior parameters (C2P, Hbnc70 in Eq. 2.30b) were adjusted such that the

simulated solubility is similar to the measured value of 11700 mg/L. Table 2.1 gives the input parameters

for the physical properties. The test cell was simulated using 12 and 9 gridblocks in the x and y directions

and 14 vertical layers. The porosity was constant equal to 0.39 and the hydraulic conductivity in the range

of 0.003 to 0.01 cm/s. The ratio of vertical to horizontal permeability was 1. Longitudinal and transverse

dispersivities for all three phases were assumed to be 0.03 and 0.01 m, respectively. The 201-day

simulation of surfactant flooding took 22 minutes on a DEC 3000/500 alpha workstation.

UTCHEM was able to closely reproduce both the PCE recovery and the vertical distribution of PCE over

the period of 201 days. The favorable comparison of UTCHEM results with the field test results

demonstrates the utility of the model in predicting SEAR processes at the field scale.

2.5 Summary and Conclusions

We have presented the description of a three-dimensional, multicomponent, multiphase compositional

model, UTCHEM, for simulating the contamination of aquifers by organic species and the remediation of

aquifers by surfactant injection. UTCHEM has the capability of simulating both enhanced dissolution and

separate phase removal of NAPLs from both saturated and vadose zones. The simulator has been verified

with several analytical solutions and validated by comparisons with both laboratory and field experiments.

The model uses a block-centered finite-difference discretization. The solution method is analogous to the

implicit in pressure and explicit in concentration method. Either one-, two-point upstream, or third-order

spatial weighting schemes is used. A flux limiter that is total-variation-diminishing has also been added to

the third-order scheme to increase stability and robustness.

UTCHEM accounts for effects of surfactants on interfacial tension, surfactant phase behavior, capillary

trapping, and surfactant adsorption. Multiphase capillary pressures, relative permeabilities, physical

dispersion, molecular diffusion, cation exchange, and partitioning of NAPLs to the aqueous phase which

accounts for nonequilibrium effects are some of the important physical properties features in the simulator.

UTCHEM can be used to design the most efficient surfactant remediation strategies taking into account

realistic soil and fluid properties. Due to its capability, several important variables that can significantly

affect the outcome of any SEAR program such as mobilization vs. solubilization, mobility control by

adding polymer, nonequilibrium interphase mass transfer, temperature gradient, and electrolyte

concentrations where the soil/water interactions are important; e.g., fresh water in the presence of clay can

be studied before implementing a field project.
Section 2 – UTCHEM Model Formulation

40

2.6 Nomenclature

a3 Surfactant adsorption parameter

a31 Surfactant adsorption parameter, (L2)

0.5

a32 Surfactant adsorption parameter, (L2)

0.5 (Eq/L3)-1

b3 Surfactant adsorption parameter

a4 Polymer adsorption parameter

a41 Polymer adsorption parameter, (L2)

0.5

a42 Polymer adsorption parameter, (L2)

0.5 (Eq/L3)-1

b4 Polymer adsorption parameter, L3/wt% polymer

brk Permeability reduction factor parameter, L3/wt% polymer

Ci,κ Total concentration of species κ in gridblock i, L3/L3 PV

CSE Effective salinity for phase behavior and surfactant adsorption, Eq/L3

CSEL Salinity for Type II(–)/III phase boundary or lower effective salinity limit, Eq/L3

CSEP Effective salinity for polymer, Eq/L3

CSEU Salinity for Type III/II(+) phase boundary or upper effective salinity limit, Eq/L3

C6

o Concentration of free calcium cations, L3/L3

C9

o Concentration of free sodium cations, L3/L3

Cκ Overall concentration of species κ in the mobile phases, L3/L3

Cκ

eq Equilibrium concentration of species κ, L3/L3

Cκ

o Compressibility of species κ, (mL-1t

-2)-1

ˆ C κ Adsorbed concentration of species κ, L3/L3 PV

 ̃ C κ Overall concentration of species κ in the mobile and stationary phases, L3/L3 PV

Cκl Concentration of species κ in phase l, L3/L3

Cpl Constant pressure heat capacity of phase l, QT-1m-1

Cr Rock compressibility, (mL-1t

-2)-1

CT Total compressibility, (mL-1t

-2)-1

Cvl Volumetric heat capacity of phase l, QT-1m-1

Cvs Volumetric heat capacity of soil, QT-1m-1

crk Permeability reduction factor parameter, L(wt%)1/3

Da Damkohler number

Dκl Diffusion coefficient of species κ in phase l, L2t

-1

foc Organic carbon fraction in soil

f κ

s Amount of species κ associated with surfactant, L3/L3

g Gravitational constant, Lt-2

h Depth, L

K Dispersion coefficient, L2t

-1

k Average permeability, L2
Section 2 – UTCHEM Model Formulation

41

 

r 

r 

K Permeability tensor, L2

k Soil permeability, L2

ka Apparent permeability used in capillary pressure calculations, L2

Koc Amount of organic adsorbed per unit weight of organic carbon in soil, (mL-3)

-1

krl Relative permeability of phase l

 

k

rl

o

Endpoint relative permeability of phase l

 

krl

o

high

, 

 

krl

o

low

Endpoint relative permeability of phase l at high and low capillary numbers

kx, ky, kz Absolute permeability in the x, y and z directions, L2

L Length of the core, or reservoir length, L

Mκ Mass transfer coefficient for species κ, t-1

npc Capillary pressure exponent

nl Relative permeability exponent for phase l (dimensionless)

 

nl

high

, 

 

nl

low Relative permeability exponent for phase l at high and low capillary numbers

NBl Bond number of phase l

Ncl Capillary number of phase l

NTl Trapping number of phase l

PCll' Capillary pressure between phases l and l', mL-1t

-2

Pl Pressure of phase l, mL-1t

-2

PR Reference pressure, mL-1t

-2

Qκ Source/sink for species κ, L3/T

QL Heat loss, Qt-1L-2

Qv Cation exchange capacity of clay, Eq./L3

qH Enthalpy source per bulk volume, Qt-1L-3

RF Polymer resistance factor

Rk Polymer permeability reduction factor

RRF Polymer residual resistance factor

Rl3 Solubilization ratio for phase l, L3/L3

Rκ Total source/sink for species κ, mL-3t

-1

 

Rκl

I Mass exchange rate at interface for species κ in phase l, mL-3t

-1

rκ l Reaction rate for species κ in phase l, mL-3t

-1

rκ s Reaction rate for species κ in solid phase, mL-3t

-1

Snl Normalized mobile saturation of phase l used in relative permeability and capillary

pressure calculations

Sl Saturation of phase l, L3/L3 PV

Slr Residual saturation of phase l, L3/L3 PV

 

Slr

high

, 

 

Slr

low Residual saturation of phase l at high and low capillary numbers L3/L3 PV

t Time, t
Section 2 – UTCHEM Model Formulation

42

Δt

n, Δtn+1 Time-step size at nth and n+1th time level, t

T Temperature, T

Tl Trapping parameter for phase l 

 

r 

u l Darcy flux, Lt-1

•xi, •yi, •zi Size of gridblock i in the x, y, and z directions, L

Greek Symbols

α1-α5 Microemulsion phase viscosity parameters

αL, αT Longitudinal and Transverse dispersivity, L

βC Cation exchange constant for clay

βS Cation exchange constant for surfactant

β6 Effective salinity parameter for calcium

γκ Specific weight of species κ, mL-2t

-2

γ Ý Shear rate, t-1

γκR Specific weight of species κ at reference pressure, mL-2t

-2

μo Oil viscosity, ML-1T-1

μP Polymer viscosity, ML-1T-1

μp

0

Polymer viscosity at zero shear rate, mL-1t

-1

μw Water viscosity, mL-1t

-1

μl Viscosity of phase l, mL-1t

-1

μa,ref Viscosity of air at reference pressure, mL-1t

-1

μa,s Slope of air viscosity function

λd Drainage Capillary pressure exponent

λiImbibition Capillary pressure exponent

λl Relative mobility of phase l, (mL-1t

-1)-1

λrT Total relative mobility, (mL-1t

-1)-1

λT Thermal conductivity, Qt-1T-1L

ρg Rock density, m/L3

ρs Soil density, m/L3

ρl Density of phase l, m/L3

σaw Interfacial tension between air and water, mt2

σwo Interfacial tension between oil and water, mt2

σll'Interfacial tension between phases l and l', mt2

φ Porosity, fraction

φi Porosity of gridblock i, fraction

Φ Potential, mL-1t

-2

τ Τortuosity factor
Section 2 – UTCHEM Model Formulation

43

Subscripts

κ species number

1 - Water

2 - Oil

3 - Surfactant

4 - Polymer

5 - Chloride

6 - Calcium

7 - Alcohol

8 - air

9-κ - Tracer components

l Phase number

1 - Aqueous

2 - Oleic

3 - Microemulsion

4 - Air

r Residual

s solid

Superscripts

C Cation

f Free

S Surfactant
Section 2 – UTCHEM Model Formulation

44

two-phase

Surfactant

single-phase

water oil

P

R

Figure 2.1. Schematic representation

of Type II (-).

two-phase

Surfactant

single-phase

water oil

P

L

Figure 2.2. Schematic representation

of high-salinity Type II (+).

two-phase

Surfactant

single-phase

water oil

PL

PR

invariant point

three-phase

Figure 2.3. Schematic representation

of Type III.

Surfactant

phase 3

A

water

B

oil

P

phase 2

Ternary diagram

log scale

log scale

A C32 C32

C22 C12

vs.

B

C

P

C33 C33

C23 C13

vs.

C

33 C32

C

13 C22

vs.

Hand plot

Figure 2.4. Correspondence between (a) ternary diagram and (b) Hand plot.
Section 2 – UTCHEM Model Formulation

45

C1

0

Right lobe θ

C1'

M

P

C3

C

3

'

Figure 2.5. Coordinate transformation for the

two-phase calculations in Type III.

196.25

196.75

197.25

197.75

198.25

198.75

0.0 5.0 10.0 15.0 20.0 25.0

Measured

Simulated

PCE saturation, percent

Ele

v

atio

n, m

asl

Figure 2.6. Measured and simulated PCE saturation at the

location of Core 3 prior to surfactant flooding (after Freeze et

al., 1994).
Section 2 – UTCHEM Model Formulation

46

196.25

196.75

197.25

197.75

198.25

198.75

0.0 2.0 4.0 6.0 8.0 10.0

Simulated

Measured

Ele

v

atio

n, m

asl

PCE saturation, percent

Figure 2.7. Measured and simulated PCE saturation at the

location of Core 6 at the end of surfactant flooding (after

Freeze et al., 1994).

Table 2.1. Physical Property Input Parameters for the Test Cell Simulation

Property Value References and Comments

Density

Pure water, g/cc

Pure PCE, g/cc

Surfactant, g/cc

1

1.6249

1.15

Viscosity

Pure water (μw), cp

Pure PCE (μo), cp

Microemulsion (max. value)

α1 - α5 parameter values

1

0.89

4

3.4, 1.0, 3.0, 1.0,

1.0

Eq. 2.77; Parameters were estimated

based on the measured data for a

different surfactant mixture (Pennell et

al., 1994)

Interfacial tension

PCE/water (σow), dyne/cm

PCE/microemulsion (minimum value),

dyne/cm

G21, G22, G23 (Healy and Reed 1974)

45

0.02

13, -14.5, 0.01

Eq. 2.43; parameters are based on the

measured data for a different surfactant

mixture (Pennell et al., 1994)

PCE solubility

Max. in water, mg/L

Max. in surfactant, mg/L

200

11,700

West and Harwell [1992]

Fountain [1992]

Surfactant adsorption

Max. value, mg/g soil

Parameter values: a31, a32, b3

0.311

1.1, 0.0, 1000

Eq. 2.15; but assuming surfactant

adsorption is independent of

permeability

Capillary pressure (Corey function)

Imbibition: Cpci, λi 2.7, -0.454

Eq. 2.55; based on Kueper [1989]

Relative permeability (Corey function)

Water (Imbibition):S1r, n1, kr1

o

PCE: S2r, n2, kr 2

o

Microemulsion: S3r, n3, kr 3

o

0.306, 2.2, 0.556

0.0, 2.2, 0.309

0.306, 2.2, 0.556

Eq. 2.66; based on Kueper [1989]
Section 2 – UTCHEM Model Formulation

47
46

Section 3

Hysteretic Relative Permeability and

Capillary Pressure Models

3.1 Introduction

A new multiphase capillary pressure and relative permeability function has been implemented in

UTCHEM. Both capillary pressure and relative permeability functions account for hysteresis due to

arbitrary changes in saturation path by incorporating an oil phase entrapment model. The hysteresis

modeling in UTCHEM is based on the work by Kalurachchi and Parker [1992]. The assumptions made in

developing and applying this model are

• The model applies only to strongly water-wet media where the wettability in descending order is for

water (or microemulsion), oil, and gas phases. Oil will be used in this report to mean any nonaqueous phase liquid (NAPL).

• The model applies to three-phase air-water-oil flow in the vadose zone and two-phase oil-water or

oil-microemulsion flow in the saturated zone

• To avoid numerical oscillations with changes from two phases (air-water) to three phases (air-wateroil), once a location is classified as a three-phase node, it will not revert back to two phases (airwater).

• Gas entrapment is neglected for the three-phase case. Therefore, oil entrapment in a three-phase airwater-oil can be inferred directly from that in a two-phase oil-water system.

• Water relative permeability is unaffected by oil entrapment e.g. krw = f (Sw ).

• There is no oil entrapment on the main drainage curve.

• There is no oil entrapment when water saturation is at its residual value in the vadose zone.

We use the notation adapted from Parker et al. [1987] shown in Table 3.1.

3.2 Oil Phase Entrapment

On any scanning curve (e.g. point A on Fig. 3.1), effective residual oil saturation is estimated from Land's

equation (Land, 1968), where the residual nonwetting phase saturation after imbibition is related

empirically to the initial nonwetting saturation (1 − S w

min) as
Section 3 - Hysteretic Relative Permeability and Capillary Pressure Models

47

S or

A =

1 − S w

min

1 + R 1 − S w

min ( )

where R =

1

S or

max

− 1

(3.1)

The trapped oil saturation at nonzero capillary pressure is calculated from the following relationships.

3.2.1 Kalurachchi and Parker

To estimate trapped oil saturation at nonzero capillary pressure, Kalurachchi and Parker estimated the

trapped oil saturation as the difference between residual oil saturation for the actual scanning curve and that

for a curve with a reversal point equal to the free (continuous) oil saturation on the actual path. This is

exactly the same idea as proposed by Stegemeier in 1977 and described in Lake [1989]. For example,

consider point B on the scanning curve on Fig. 3.1 with apparent water saturation of S w = S w + S ot. Points

B and C have the same capillary pressure, therefore the difference between the x coordinates of points B

and C is the disconnected nonwetting phase saturation ( S ot ). Using Land's relation for the residual oil

saturation for the scanning path starting from point A ( S or

A

) and that starting from point C ( S or

C

) we have

S or

A

=

1− S w

min

1+ R 1− S w

min ( )

(3.2)

S or

C

=

1− S w

1+ R(1− S w )

(3.3)

and

S ot = S or

A

− S or

C

S ot =

min 1 − S w

min

1 + R 1 − S w

min ( )

−

1 − S w

1 + R(1 − S w )

 

 

 

 

 

 

 

 , S o

 

 

 

 

 

 

 

 when S w > S w

min

0.0 otherwise

 

 

  

 

 

 

(3.4)

Equation 3.4 is a conditional quadratic equation that can be solved for S ot since S w = S w + S ot. Once S ot

is computed, capillary pressures and relative permeabilities are computed from the equations discussed

below.

3.2.2 Parker and Lenhard

The trapped oil saturation is calculated by linear interpolation since the effective trapped oil saturation

along any scanning curve (e.g., the curve with reversal point of A in Fig. 3.1) varies from zero at the

reversal point of S w

min to S orA

 at S w = 1 as
Section 3 - Hysteretic Relative Permeability and Capillary Pressure Models

48

S ot = min S or

A S w − S w

min

1 − S w

min

 

 

 

 

  , S o

 

 

 

 

  (3.5)

where S or

A

 is calculated from Eq. 3.2.

3.3 Capillary Pressure

The two-phase air-water, water-oil or microemulsion-oil and three-phase oil-water-air capillary pressuresaturation function determined using the generalization of Parker et al. [1987] to the two-phase flow model

of van Genuchten [1980] is represented as follows.

3.3.1 Two-Phase Flow

 

S w = 1 + αβll ′ Pcll ′ ( )

n

[ ]

−m

(3.6)

where 

 

βll ′ is the scaling coefficient for fluid pair l and l ′ ; α and n are the adjustable parameters, and

m = 1−1/n. The implementation of this model in the simulator includes scaling with intrinsic permeability

(k) and porosity (φ) where α is replaced by α

k

φ

. β is approximated by the ratio of water-air interfacial

tension (σaw) to the interfacial tension of the fluid pair. Here and elsewhere the subscript w applies to

either water or microemulsion for the case of two-phase flow with oil.

 

βll ′ = σaw / σll ′ 

3.3.2 Three-Phase Oil/Water/Air Flow

S w = 1 + αβow P ( cow )

n

[ ]

− m

(3.7)

S t = 1 + αβao Pcao ( )

n

[ ]

−m

(3.8)

3.4 Relative Permeability

The two- and three-phase relative permeabilities are based on the generalization of Parker and Lenhard to

the two-phase flow model of van Genuchten.

krw = S w

1/ 2

1 − 1 − S w

1/m

( )

 m

 

 

 

2

(3.9)

kro = S t − S w

 

   

1/ 2

1 − S w

 1/m

   

m

− 1 − S t

1/m

( )

 m

  

 

  

2

(3.10)

kra = 1 − S ( t)

1/2

1 − S t

1/m

( )

2m

(3.11)
Section 3 - Hysteretic Relative Permeability and Capillary Pressure Models

49

3.5 Capillary Number Dependent Hysteretic Model

An important new extension of these models is the inclusion of their dependence on interfacial tension via

the trapping number. The capillary number traditionally used by both the groundwater and oil reservoir

literatures has been generalized by Jin [1995] and is now called the trapping number. We assume that 1)

the capillary pressure parameters n and m are independent of trapping number and 2) the residual oil

saturation (Sor

max ) and residual water (or microemulsion) saturation (Swr) are functions of trapping number.

We compute the residual water and residual oil saturations as a function of trapping number as follows:

 

Slr = min Sl, Slr

high +

Slr

low − Slr

high

1 + Tl NTl

 

 

  

 

 where l = w (or microemulsion), oil (3.12)

where the 

 

Slr

high and 

 

Slr

low are the phase l residual saturations at high and low trapping numbers, Tl is the

adjustable parameter. This correlation was derived based on the experimental data for n-decane (Delshad,

1990) and have recently been successfully applied to residual PCE as a function of trapping number

measured by Pennell et al. [1996]. The trapping number NTl is computed as

 

NTl =

−

r 

r 

k ⋅

r 

∇ Φl' −

r 

r 

k ⋅ g (ρ

l'

− ρl

)

r [ ∇ h]

σ

ll'

(3.13)

where h is the vertical depth (positive downward), ρl and 

 

ρl'are the displaced and displacing fluid

densities, and the gradient of the flow potential is given by 

 

r 

∇ Φl' =

r 

∇ Pl' − g

l '

ρ

r 

∇ h .

We then substitute the water (or microemulsion) and oil residual saturations calculated from Eq. 3.13 for

Swr and Sor

max in the calculations of entrapped oil phase saturations (Sot), capillary pressure, and relative

permeabilities described above. This extension makes the hysteretic model suitable for remediation

processes that involve changes in interfacial tension; e.g., co-solvent, surfactant, etc. (Delshad et al., 1996).

The reduction in interfacial tension due to the presence of surfactant or co-solvent in the above equations is

calculated from a modified Huh's equation (Huh, 1979) where the interfacial tension is related to the

solubilization ratio (Delshad et al., 1996). The interfacial tension for oil-water in the absence of surfactant

or co-solvent or water-air fluid pairs is assumed to be a constant.
Section 3 - Hysteretic Relative Permeability and Capillary Pressure Models

50

Effective water saturation

Main drainage

Main imbibition

Sw

min

A

B C

Sor

max

Sor

A

Sor

C

Figure 3.1. Capillary pressure curves as a function of effective water saturation.

Table 3.1. Notation Used in Section 3

Water and oil saturations: Sw, So

Residual water saturation: Swr

Effective water saturation : S w =

Sw − Swr

1 − Swr

Effective total liquid saturation: S t =

Sw + So − Swr

1 − Swr

Effective oil saturation: S o =

So

1 − Swr

Apparent water saturation: S w = S w + S ot

Residual and trapped oil saturation: Residual oil saturation corresponds to the trapped oil

saturation at zero capillary pressure, S or = S ot(@ Pc = 0. 0)

Minimum effective water saturation

(corresponds to the reversal from drainage

to imbibition):

S w

min

Maximum effective residual oil saturation

(corresponds to main imbibition curve): S or

max

=

Sor

max

1 − Swr
51

Section 4

UTCHEM Tracer Options

4.1 Introduction

Any number of tracers can be modeled in UTCHEM. These tracers can be water tracer, oil tracer,

partitioning oil/water tracer, gas tracer, and partitioning gas/oil tracer. There are up to two reacting tracers

allowed. Reacting tracers are considered only for water/oil tracers and tracer components 2 and 3 are

reacting and product tracers for the first reacting tracer. Tracer components 4 and 5 are reacting and

product tracers for the second reacting tracer. The assumptions made in the modeling of tracers are:

1. Tracers do not occupy volume

2. Tracers have no effect on the physical properties

The overall tracer concentrations are computed from the species conservation equations which include a

reaction term for the reacting tracer. The tracer phase concentrations are calculated according to the tracer

type: water, oil, gas, or partitioning.

UTCHEM can model single-well tracer test (Descant, 1989), partitioning interwell tracer tests (Allison et

al., 1991; Jin et al., 1995), and single-well wettability tracer test (Ferreira et al., 1992).

4.2 Non-Partitioning Tracer

The tracer phase composition for a non-partitioning tracer is proportional to the ratio of the total tracer

concentration to the total concentration of water, oil, or gas depending on the tracer type as

 

CTl

= Cκl

CT

Cκ

 T = water, oil, or gas tracer (4.1)

4.3 Partitioning Tracer

4.3.1 Water/Oil

The tracer partitioning coefficient for a water/oil tracer is defined on the basis of water or oil

pseudocomponent concentration as

KT =

CT2

CT1

(4.2)

where CT1

and CT2

 are the tracer concentrations in the water and oil pseudocomponents. The tracer phase

compositions are then computed from the tracer material balance equation as
Section 4 - UTCHEM Tracer Options

52

 

CTl= C1lCT1+ C2lCT2

where

CT1

=

CT

C1 + C2KT

CT2

= KT

CT

C1 + C2KT

(4.3)

where C1, C2 are the overall concentrations for water and oil species.

The partitioning coefficient of tracer i as a function of reservoir salinity is modeled using a linear

relationship as

KTi

= KTi,Sref (1 + TKSi(C51 − C51,ref )) (4.4)

where C51 is the concentration of anions in aqueous phase and C51,ref is the electrolytes concentration in

chloride equivalent (eq/l) at a reference condition (initial electrolyte concentrations). TKSi is a constant

input parameter in (eq/l)-1 and KTi,Sref is the partitioning coefficient at the reference salinity of C51,ref in

eq/l.

UTCHEM also has the capability of modeling tracer partitioning coefficients as a function of reservoir

temperature. Partitioning coefficient for tracer i as a function of temperature is given by a linear function

as:

KTi

= KTi,Tref 1 + TKi T − Tref ( ( )) for tracer i (4.5)

where the temperatures are in •F and KTi, Tref is the partitioning coefficient of tracer i at reference

temperature, Tref. TKi is a constant input parameter in (°F)-1.

4.3.2 Gas/Oil

The partitioning coefficient for a gas/oil tracer is defined as

KT =

CT2

CT8

(4.6)

and the phase concentration for the tracer is computed using the tracer material balance equation as

 

CTl= C8lCT8+ C2lCT2

where

CT8

=

CT

C8 + C2KT

CT2

= KT

CT

C8 + C2KT

 l = 2 and 4 (4.7)

where C8, C2 are the overall concentrations for gas and oil species.
Section 4 - UTCHEM Tracer Options

53

UTCHEM has the capability of modeling gas/oil tracer partitioning coefficients as a function of reservoir

temperature. Partitioning coefficient for tracers as a function of temperature is given by a linear function

as:

KTi

= KTi

,ref 1 + TKi T − Tref [ ( )]

 

for tracer i (4.8)

where the temperatures are in •F and KTi

,ref is the partitioning coefficient of tracer i at reference

temperature (Tref) and TKi is a constant input parameter in (•F)-1.

4.4 Radioactive Decay

Radioactive decay can be used for any type of tracer (oil, water, gas) as

dCT

dt

= −λCT(4.9)

where λ is a constant input radioactive decay coefficient in (days)-1. The above equation is solved for

decayed tracer concentration once the overall tracer concentration (CT

) is solved for as

CT

( )

decay = CT (1 − λΔt) (4.10)

where Δt is the time step size in days.

4.5 Adsorption

The tracer adsorption for any type of tracer is assumed to be linear and can be modeled using an input

retardation factor parameter (Ds) as

 

Ds =

C T

CTl

=

(1 − φ)ρr

aT

φρlCTl

 l = 1 or 4 (4.11)

where aT is the mass of adsorbed tracer divided by the mass of rock. ρr and ρl are the rock and water ( l =

1) or gas phase (l = 4) densities. C T

 is the adsorbed tracer concentration. The adsorption is applied to

total tracer flux (convective and dispersive ) and modeled as

 

Vt

( )

ret.

=

u

φSl

1

1 + Ds

 

 

  

  (4.12)

where u is the Darcy flux in ft/d and φ is the porosity.

4.6 Reaction

Hydrolysis of an ester to form an alcohol is assumed to be irreversible and of first order. The reaction of an

acetate as an example is:

1 CH3COO[CnH2n+1] + 1 H2O --------> 1 CnH2n+1[OH] + 1 C2H4O2

Acetate Water Alcohol Acetic Acid
Section 4 - UTCHEM Tracer Options

54

where 1 mole of acetate (e.g., component 10) generates one mole of product alcohol (e.g. . component 11).

The reaction is modeled as

∂C10

∂t

= −KhC10

and

∂C11

∂t

= KhC10

(4.13)

where Kh is an input reaction rate in day-1. UTCHEM has the capability of modeling the tracer reaction

rate as a function of reservoir temperature. The rate of hydrolysis of tracer as a function of reservoir

temperature is given by:

Khi

= Khi

,ref exp HKi

1

T

−

1

Tref

 

 

  

   

  

 

  

 

for tracer i (4.14)

where the temperature is in •K and Khi

,ref is the rate of tracer hydrolysis at reference temperature (Tref)

and HKi

 is a constant input parameter in (•K)-1.

4.7 Capacitance

The capacitance model is based on a generalized Coats-Smith model (Smith et al., 1988) and is applied to

water/oil tracer components and gas tracer components (κ). The model is unsteady state, therefore the

flowing and dendritic saturations can change in each time step. The phase saturations and phase

composition from the overall species concentration and phase flash are the flowing saturation (

 

Sl

f

) and

phase concentrations (

 

Cκl

f

) in the capacitance model in UTCHEM. The mass transfer between the flowing

and dendritic fraction is given by

 

∂

∂t

Sl

dCκld

( )= Mκl Cκl

f

− Cκl

d

( ) (4.15)

The dendritic saturation is calculated from:

 

Sl

d

= 1 − Fl( )Sl(4.16)

where Fl is the flowing fraction for phase l defined as

 

Fl =

Sl

f

Sl

= Fl0 + Fl1 − Fl 0( )f

l

(4.17)

where the flowing fraction (Fl) is assumed to be a linear function of fractional flow (fl). The intercepts of

the flowing fraction line versus fractional flow at the residual saturation of nonwetting phase (f1 = 0.0) and

wetting phase (f1 = 1.0) are Fl0 and Fl1 and are input parameters. The product of dendritic saturation (

 

Sl

d

)

and dendritic phase composition (

 

Cκl

d

) is
Section 4 - UTCHEM Tracer Options

55

 

Cκl

d

Sl

d

( )

n+1

= Cκl

d

S ( l )

n

+ ΔtMκ Cκl

f

− Cκl

d

( )

n

(4.18)

where Mκ is the input mass transfer coefficient in (day)-1 and the dendritic phase composition (

 

Cκl

d

) is

calculated from

 

Cκl

d

=

Cκl

d Sld

Sl

d

(4.19)

The flowing phase saturations are then determined from

 

Sl

f

= Fl

Sl

(4.20)

and the total flowing tracer concentrations are computed as

 

Cκ

f Cκf

S

f

( )

l=1

np

∑ = Cκ − Cκl

d

Sl

d

( )

l =1

np

∑ (4.21)
56

Section 5

Dual Porosity Model

5.1 Introduction

In most naturally fractured reservoirs, fractures tend to be developed in a way that makes the fractures

interconnected and the bulk reservoir rock isolated into blocks. Fractured reservoirs can thus be considered

as blocks of porous rock matrix surrounded by a network of communicating channels (fractures). The rock

matrix generally has high bulk volume and high porosity, but very low permeability. In contrast, the

fractures occupy very small volume, but have high permeability. The dual porosity model assumes that

there are two flow systems coexisting in a fractured reservoir − an interconnected fracture system and a

disjoint matrix system. In the dual porosity model, continuity equations are solved for the two systems

using conventional methods, while the mass transfer between the two systems is calculated by so-called

transfer functions that characterize flow between matrix blocks and fractures. By dividing the matrix

system into subgrids at each fracture node, transient flow of fluid in the matrix and between matrix and

fractures can be studied. For simplicity, matrix blocks are often assumed to be regularly shaped. In this

implementation, we use parallelepiped matrix blocks to handle vertical fractures and slabs for horizontal

fractures.

This section presents results of a project to implement dual porosity behavior for tracer studies in

UTCHEM, a chemical flood simulator developed at the University of Texas at Austin. Two approaches

were implemented. In the first, a capacitance model already existing in UTCHEM was made to mimic dual

porosity behavior by setting capacitance parameters to equivalent dual porosity parameters. This approach

is equivalent to a dual porosity model with no subgridding. The second approach involved adapting a

subgridding approach developed by J. Chen [1993] for counter current imbibition in fractured reservoirs.

Test runs and comparisons with the SWIFT II simulator (Reeves et al., 1986) are also made.

5.2 Capacitance Model

Dispersion into matrix blocks from surrounding fractures is typically calculated by assuming that the tracer

concentration in the fractures is uniform within a given volume of reservoir rock. This assumption results

in the following equation for diffusion of a single tracer in a single fluid phase:

∂ φ

m C m

( )

∂t

= φ

mKmSA

∂C

m

∂n

 

  

 

  

f

(5.1)

where

φm = matrix porosity, fraction
Section 5 - Dual Porosity Model

57

C m

= average tracer concentration in matrix block, m/L3

Km = tracer diffusion coefficient in matrix, L2/t

SA = matrix block surface area per unit bulk volume of reservoir, L-1

∂C

m

∂n

 

  

 

  

f = tracer concentration gradient normal to matrix block surface, m/L4

If transient behavior is ignored, Eq. 5.1 may be approximated by

∂ C m

( )

∂t

= σK

m Cf

− C m

( ) (5.2)

where s is a shape factor to account for matrix block geometry and number of matrix blocks per unit

reservoir volume, and Cf

 is the tracer concentration in the fracture. Note that the shape factor has units of

L-2. Kazemi et al. [1976] recommended a shape factor for cubic matrix blocks of

σ =

4nN

L

2

(5.3)

where n is the number of matrix blocks per unit bulk volume of reservoir and N is the "dimensionality" of

the fracture set. A good discussion of shape factors can be found in M. M. Chen [1993].

UTCHEM includes a "capacitance" model that treats diffusive transfer in a similar manner. In the

capacitance model a fluid phase is divided into two fractions: a flowing fraction (which is analogous to the

fracture system in a dual porosity model) and a dendritic fraction (which is analogous to the matrix

system). Since matrix and fracture porosities are both based on total reservoir bulk volume, the flowing

fraction, F, and the dendritic fraction, 1−F, are equivalent to:

F =

φ

f

φ

m + φf

=

S

f

S

(5.4)

1 − F =

φ

m

φ

m + φf

=

S

d

S

(5.5)

For single phase flow, of course, S = 1. Total porosity is simply

φ = φ

m + φf

(5.6)

In the capacitance model, mass transfer from the flowing to dendritic fractions is calculated by

∂ (1− F)C

d

[ ]

∂t

= M C

f

− C

d

( ) (5.7)

or for a fixed dendritic fraction:
Section 5 - Dual Porosity Model

58

∂ C

d

( )

∂t

=

M

1− F

C

f

− C

d

( ) (5.8)

where C

d

is the tracer concentration in the dendritic fraction, C

f

is the tracer concentration in the flowing

fraction, and M is the capacitance mass transfer coefficient. The capacitance model can thus be made to

calculate dual porosity behavior using the equivalents given in Table 5.1.

Figure 5.1 shows comparisons of capacitance runs in UTCHEM compared to UTDUAL, a dual porosity

simulator developed at the University of Texas at Austin. Although UTDUAL has the capability of

subgridding matrix blocks (which would yield more accurate results), these comparisons were made with

no subgridding. For these comparisons, UTDUAL was modified slightly to account for tracer diffusion in a

manner similar to counter current water imbibition. Data used to generate Fig. 5.1 are given in Table 5.2.

Note the high degree of agreement. In fact, for a mass transfer coefficient of 10-5 sec-1, the two curves are

indistinguishable on the graph.

5.3 Subgridding

Due to the relatively low permeability in matrix blocks, viscous convection of phases is very slow and is

ignored in this formulation. Molecular diffusion of tracer becomes the dominant process flow within the

matrix. The equation for tracer diffusion into the matrix can be simplified into the following equation:

 

∂

∂t

φ

m

C

m

( )= ∇⋅ φ

m v 

K m ⋅ ∇C

m

( )− λφm

C

m (5.9)

where λ is the radioactive decay constant of the tracer.

Parallelepiped matrix blocks are assumed for the subgridding. In the horizontal direction (j-index) the

matrix is subdivided into Nsub concentric grids. In the vertical direction (k-index), the matrix is sliced into

Msub slabs. Figure 5.2 shows the discretization of a single matrix block. The advantage of subgridding the

matrix this way is that many types of fracture systems can be described. By setting Msub=1 and the vertical

diffusion coefficient to zero, a vertical fracture network can be simulated. If Nsub=1 and the horizontal

diffusion coefficient is equal to zero, then horizontal fractures can be simulated. A combination of

subgridding in these two directions can be used to simulate a 3D fracture system. When Msub=1 and

Nsub=1, the system reduces to the capacitance (no subgridding) model.

The volume fraction of each subgrid is an input value with the property:

fjk

j=1

Nsub

∑ = 1

 

k = 1,...,Msub (5.10)

The volume fraction of the jth ring and kth layer subgrid is:

fjk =

(LxjkLyjk − Lxj−1kLyj−1k)hk

Vbk

m

(5.11)
Section 5 - Dual Porosity Model

59

where Vbk

m

 is the bulk volume of the kth layer of the matrix, Lxjk and Lyjk are the outer dimensions of the

subgrid, h k

 is the thickness of the kth layer, and Nsub is the number of the subgrids in the horizontal

direction (Fig. 5.2).

From Eqs. 5.10 and 5.11, the outer dimensions for each subgrid are calculated by:

Lxjk = Lx

f

ik

i=1

j

∑

 

 

  

 

 

  

1

2

 

j = 1,...,Nsub; k = 1,...,Msub (5.12)

Lyjk = Ly

f

ik

i=1

j

∑

 

 

  

 

 

  

1

2

 

j = 1,...,Nsub; k = 1,...,Msub (5.13)

where Lx

 and Ly are the dimensions of the matrix block.

The dimensions of a matrix block can be different than the dimensions of a gridblock. The mass transfer

rate is simply calculated by multiplying the mass transfer rate of one representative matrix block by the

number of matrix blocks per gridblock.

Using one-point upstream weighting, the finite-difference form of Eq. 5.9 becomes

φ

m Cm

( )

n +1

− C

m

( )

 n

  

 

  =

Δt

ΔVjk

m

TV

jk−

1

2

C

m

( )

jk−1

n

+ TH

j−

1

2

k

C

m

( )

j−1k

n

+ TCjk C

m

( )

jk

 n

  

+TH

j+

1

2

k

C

m

( )

j+1k

n

+ TV

jk+

1

2

C

m

( )

jk+1

n

− ΔVjk

m

λφm C

m

( )

jk

n  

  

(5.14)

where ΔVjk

m

 is the volume of the jth ring and the kth layer, and TV and TH are the transmissibilities in the

vertical and horizontal directions, respectively:

TH j+

1

2

k

=

Lyjkhk Kxy

m

Lx j+1k− Lx jk

+

Lxjkhk Kxy

m

Ly j+1k− Ly jk

(5.15)

TVjk+

1

2

=

f

jk LxLyKz

m

h jk+1 + h jk

(5.16)

and TC is calculated by:

TCjk = −(TVjk−

1

2

+ TH j−

1

2

k

+ THj+

1

2

k

+ TVjk+

1

2

)

(5.17)

The boundary condition is

C jk

m = Cf

j = Nsub; k = 1,...,Msub (sides)

j = 1,...,Nsub; k = 1 and k = Msub (top and bottom) (5.18)
Section 5 - Dual Porosity Model

60

5.4 Implementation

In this implementation the original 3D compositional code, UTCHEM, solves the pressure distributions and

tracer concentrations in the fracture system. After solving the fracture system equations, the tracer

concentration at each node is used as the boundary condition for the matrix at the same node. Only a single

tracer in single phase flow is handled.

An additional subroutine, TDIFFU, is added to UTCHEM to do the matrix calculations. The methodology

used for this implementation is described by J. Chen [1993] and Chen et al. [1994]. In this routine, the

equations developed above are used to solve the tracer concentration distribution in the subgridded matrix

system. Concentrations in the fracture are modified to account for mass transfer between the matrix and

fracture.

Several other subroutines are also modified. Subroutine INOUT is extended to read in the parameters used

to describe the subgridding system. The initial values of the matrix tracer concentration are also read in this

routine. Subroutine TIME0 is modified to set the initial tracer concentrations in the matrix system.

Calculations of the horizontal and vertical transmissibilities of the subgrids are added to the TRAN1

routine. Some output commands are added to subroutine OUTDT1. And, of course, the MAIN program is

also modified to handle the new calculations. The distribution of tracer concentrations within the matrix are

written to output file CAPP.

In order to minimize the code changes to the whole system, the control flag for the dual porosity option is

the variable ICAP, which is also used to flag use of the capacitance model. A value of 2 is used to

represent that the dual porosity model with subgridding is used.

5.5 Results

Several test runs were made with this implementation. The first test is a comparison of the capacitance

model with the case of only one subgrid. A 1D linear reservoir 1000 ft long with 10 ft width and depth is

simulated. Gridblock size is 10x10x10 ft3. Matrix blocks are also 10x10x10 ft3. There are thus 100

gridblocks in the x−direction. Fracture and matrix porosities are 0.01 and 0.19, respectively. Permeability

in the fractures is 1000 md and longitudinal dispersivity is 1.0 ft. Fluid injection rate is 0.5 ft3

/day. Figure

5.3 shows results for mass transfer coefficients of 10-5, 10-8 and 10-9 sec-1. Results show that the dual

porosity model reduces to the capacitance model when there is no subgridding.

The second comparison is between UTCHEM and UTDUAL (J. Chen, 1993). The reservoir and fluid

conditions are the same as the first set of runs, except that a diffusion coefficient (Km) of 4.32x10-3 ft2

/day

was used. The subgrid numbers compared are 1, 2, 4, and 8. One more run with 16 subgrids was run on

UTDUAL which showed that the curve converges with only 8 subgrids. Figure 5.4 shows the results.

Figure 5.5 shows agreement between UTCHEM and UTDUAL. The pore volumes reported in these figures

refer to the total (fracture + matrix) pore volumes. The UTCHEM output files, however, give the fracture

pore volumes only.

The third case run was a 2D case. The reservoir is 100x100x10 ft3

and with grid number of 10x10x1. Each

grid size is 10x10x10 ft3

. Fluid is injected in one corner and produced from an opposite corner, simulating

a quarter of a five-spot pattern. All other properties are the same as the second set of runs. The number of

matrix subgrids ranges from 1 to 8. Figure 5.6 shows the result. Note that the solid line is the overlap of

the two curves of the capacitance model and the dual porosity model with one subgrid.
Section 5 - Dual Porosity Model

61

It is expected that increasing the number of subgrids will increase computing time. However, the amount

of additional time required for additional subgridding is very small in this implementation. Figures 5.7 and

5.8 show CPU times for the runs made above. Note that only slightly more time was needed, even with 8

subgrids.

The last comparison is with SWIFT II (Reeves et al., 1986), a code developed for contaminant transport

studies. The case simulated is the transport of a decaying radionuclide in a fractured porous medium. A

thin fracture is situated within a saturated porous rock matrix. Both the fracture and matrix are semiinfinite in extent. The radionuclide is convected and dispersed through the fracture with constant velocity

and is diffused into the rock matrix. The fracture aperture is 10-4 m, matrix porosity is 0.01, matrix

tortuosity is 0.1, fracture dispersivity is 0.5 m, molecular diffusion coefficient in water is 1.6x10-5 cm2

/sec,

radionuclide decay constant is 0.0561 yr-1, and fracture velocity is 0.01 m/day. Note that the value of the

dispersivity in UTCHEM (Km) is equivalent to the product of tortuosity times the molecular diffusion

coefficient in water used by SWIFT II. A constant tracer concentration boundary condition on the source

side of the system is required to match an analytical solution to this problem (Tang et al., 1981). UTCHEM

was modified slightly to handle this boundary condition. Variable gridblocks are used in both fracture and

matrix. A 10,000-day period was simulated. Figure 5.9 shows the radionuclide concentration in the

fracture. Note that the simulated results and the analytical solution by Tang et al. match very well. Figure

5.10 shows the radionuclide concentration in the matrix 1.5 m from the injection point at 10,000 days. The

result also matches the analytical solution. This problem is described in detail in the SWIFT II manual

(Reeves et al., 1986).

5.6 Conclusions

From the above test runs and comparisons with other simulators, the following conclusions are made:

1. A dual porosity formulation to model tracer flow in fractured reservoirs has been implemented in

the UTCHEM chemical flooding simulator. Good matches are obtained compared with other

simulators.

2. Different fracture systems can be modeled by the simulator. These include vertical fractures,

horizontal fractures, and combinations of the two.

3. Computer time required to refine the matrix system does not appreciably increase for reasonable

numbers of subgrids.

4. The dual porosity model reduces to the capacitance model when the number of subgrids is equal to

one.

5.7 Nomenclature

Cd = tracer concentration in dendritic fraction, m/L3

Cf = tracer concentration in flowing fraction or fracture system, m/L3

C

m = matrix block tracer concentration, m/L3

C m

= average tracer concentration in matrix block, m/L3

fjk = volume fraction of subgrid j, k, dimensionless
Section 5 - Dual Porosity Model

62

F = flowing fraction 

S

f

S

 

  

 

  , dimensionless

1−F = dendritic fraction 

S

d

S

 

  

 

  , dimensionless

hk = thickness of kth layer, L

K

m = tracer diffusion coefficient in matrix, L2/t

Kxy

m

= tracer diffusion coefficient in matrix in horizontal direction, L2/t

Kz

m

= tracer diffusion coefficient in matrix in vertical direction, L2/t

Lx, Ly = matrix dimensions, L

Lxjk, Lyjk = subgrid dimensions in x and y directions, L

M = capacitance mass transfer coefficient, t-1

Msub = number of subgrids in vertical direction (layers)

n = number of matrix blocks per unit bulk volume of reservoir

N = dimensionality of fracture set

Nsub = number of subgrids in horizontal direction (rings)

SA = matrix block surface area per unit bulk volume of reservoir, L-1

Sd = dendritic saturation, dimensionless

Sf = flowing saturation, dimensionless

TC = sum of transmissibilities in the vertical and horizontal directions, L3/t

TH = transmissibility in the horizontal direction, L3/t

TV = transmissibility in the vertical direction, L3/t

t = time, t

Vbk

m

= bulk volume of layer k of the matrix, L-3

ΔVjk

m

= volume of the jth ring and the kth layer of matrix subgrids, L-3

φ = total porosity, fraction

φ

f

= fracture porosity, fraction

φ

m = matrix porosity, fraction

λ = radioactive decay constant, t-1

σ = shape factor, L-2

∂C

m

∂n

 

  

 

  

f

= tracer concentration gradient normal to matrix block surface, m/L4
Section 5 - Dual Porosity Model

63

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Dim

e

nsio

nless e

fflu

e

nt c

o

n

c

e

ntr

atio

n

Pore volumes injected

M = 10-9 sec

-1

M = 10-8 sec

-1

Capacitance Model

Dual Porosity Model

M=10-5 sec

-1

Figure 5.1. Comparison of capacitance model (UTCHEM) to equivalent dual

porosity model (UTDUAL) results.

Lyj

Lxj

j=1 2 Nsub

hk

Ly

Lx

Msub

k=1

2

Figure 5.2. Schematic of matrix block subgrids.
Section 5 - Dual Porosity Model

64

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Dim

e

nsio

nless e

fflu

e

nt c

o

n

c

e

ntratio

n

Pore volumes injected

M = 10-9 sec

-1

M = 10-8 sec

-1

Capacitance

1 Subgrid

M=10-5 sec

-1

Figure 5.3. Comparison of capacitance model vs. subgrid model in UTCHEM.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Dim

e

nsio

nless e

fflu

e

nt c

o

n

c

e

ntratio

n

Pore volumes injected

1 subgrid

2 subgrids

4 subgrids

8 subgrids

Figure 5.4. Subgrid refinement studies with UTCHEM, Km = 3.243x10-2 ft2/day.
Section 5 - Dual Porosity Model

65

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Dim

e

nsio

nless e

fflu

e

nt c

o

n

c

e

ntr

atio

n

Pore volumes injected

8 subgrids UTDUAL

8 subgrids UTCHEM

Figure 5.5. Comparison of UTCHEM and UTDUAL subgridding.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Dim

e

nsio

nless e

fflu

e

nt c

o

n

c

e

ntratio

n

Pore volumes injected

Capacitance

1 subgrid

2 subgrids

4 subgrids

8 subgrids

Figure 5.6. 2D subgrid refinement studies with UTCHEM.
Section 5 - Dual Porosity Model

66

â

Ö

Ö

Ö

Ö

80

90

100

110

120

130

0 1 2 3 4 5 6 7 8 9

Number of subgrids

â Capacitance

Ö Subgrids

Figure 5.7. Comparison of execution time with different numbers of

subgrids, 1D case.

â

Ö

Ö

Ö

Ö

150

160

170

180

190

200

210

220

230

0 1 2 3 4 5 6 7 8 9

Number of subgrids

â Capacitance

Ö Subgrids

Figure 5.8. Comparison of execution time with different numbers of

subgrids, 2D case.
Section 5 - Dual Porosity Model

67

Ö Ö Ö Ö Ö Ö Ö Ö Ö

Ö

Ö

Ö

Ö

Ö

Ö

ÖÖ

Ö

â â â â â â â

â

â

â

â

â

â

â

â

â

Ç Ç Ç Ç Ç

Ç

Ç

Ç

Ç

Ç

Ç

Ç

Ç

Ç

ÇÇ

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6 7 8 9 10

Distance down fracture

Ö UTCHEM 100 days

â UTCHEM 1,000 days

Ç UTCHEM 10,000 days

Analytical 100 days

Analytical 1,000 days

Analytical 10,000 days

Figure 5.9. Comparison of simulated results vs. analytical solution (Tang et al.,

1981) for radionuclide concentration in the fracture.

N

N

N

N

N

N

N

N

N

N

N N

O

O

O

O

O

O

O

O

O

O

0 O

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 0.2 0.4 0.6 0.8 1 1.2

Distance into matrix (m)

N SWIFT II

O UTCHEM

Analytical

t = 10,000 days

x = 1.5 m

Figure 5.10. Comparison of simulated results vs. analytical solution (Tang et al.,

1981) and SWIFT II (Reeves et al., 1986) for radionuclide concentration in the

matrix.
Section 5 - Dual Porosity Model

68

Table 5.1. Equivalence Between Capacitance and Dual Porosity Models

Capacitance Model Dual Porosity Model

Porosity (φ) φ

m + φf

Flowing fraction (F)

φ

f

φ

m + φf

Dendritic fraction (1− F)

φ

m

φ

m + φf

Flowing fraction tracer concentration (C

f

) C

f

Dendritic fraction tracer concentration

(C

d

)

C m

Mass transfer coefficient (M) σK

m φ

m

φ

m + φf

Table 5.2. Input Data for the Comparisons of Capacitance

Model in UTCHEM to Dual Porosity Model in UTDUAL

System size 100x10x10 ft

Fluid injection rate 0.5 ft3/day

Capacitance Model

Total porosity

Flowing fraction

Dendritic fraction

Mass transfer

coefficient

0.20

0.05

0.95

10-5

10-8

10-9

sec-1

sec-1

sec-1

Dual Porosity Model

Fracture porosity

Matrix porosity

Shape factor

Matrix block size

Diffusion coefficient

0.01

0.19

0.08

10x10x10

10.8

1.08x10-2

1.08x10-3

ft-2

ft

ft2/day

ft2/day

ft2/day
69

Section 6

UTCHEM Model of Gel Treatment

6.1 Introduction

This section is based on the dissertation entitled "A Simulation Study of Gel Conformance Treatments" by

H. Kim, The University of Texas at Austin, Ph.D., May 1995.

6.2 Gel Conformance Treatments

The operational aspect of a gel treatment includes the following :

• Zonal isolation

• Types of gel treatments

• Shut-in time

• Gel injection rate

• Amount of gelant

The types of gel treatments are 1) simultaneous injection of polymer and crosslinker into the reservoir,

2) alternate injection of polymer and crosslinker slugs, and 3) injection of pre-gelled fluid into the reservoir.

The type of gel treatment selected influences the placement of the gel in the reservoir. In this study, the

simultaneous mode of injection of polymer and crosslinker was modeled.

The shut-in time allowed after injection, before the well is put back on production, is critical to the success

of a gel job. If the gel does not reach most of its strength, its efficacy in plugging the high-permeability

layer will suffer.

The injection rate determines the rate of shearing of the polymer and gel as well as the injection pressure.

The injection rate should be such that the wellbore pressure does not exceed the fracture pressure of the

rock matrix.

The amount of gelants injected determines the depth of penetration of the gel into the formation. The

amount injected must ensure adequate plugging of the high-permeability, watered-out zone.

Zonal isolation is used to selectively treat the problem zone. In some wells, improper well completion or

casing damage may lead to mechanical difficulties in achieving zonal isolation. In this work, gel treatments

were simulated with and without zonal isolation to demonstrate the effectiveness of zonal isolation.
Section 6 - UTCHEM Model of Gel Treatment

70

The polymer-gel system chosen for a particular treatment will depend on its compatibility with the reservoir

and operational conditions. The properties considered when choosing a particular system are

• Viscosity

• Gelation time

• Permeability reduction

• Thermal and mechanical stability

• Mechanical strength

• Safety

Viscosity of the gel and polymer determines the wellbore pressure during injection. Very high viscosities

may cause the wellbore pressure to exceed the fracture pressure of the reservoir.

Gelation time depends on the kinetics of gel formation and influences the injection rate and shut-in time

used during the treatment. Ideally, the gelation time should allow proper placement of the gel before full

gel strength develops.

The permeability reduction caused by the gel in the porous medium is an indicator of its ability to modify

the flow patterns in the reservoir. In near-wellbore treatments, the gel should be able to plug the high

water-cut zones.

The ultimate mechanical strength developed by a gel is a measure of the pressure it can withstand before

breaking down. The gel should have enough mechanical strength to remain in place when subjected to

normal drawdown during production.

Safety of the gel, polymer and crosslinker may ultimately determine its usage. Gel components need to be

safe for handling and storage and should pose no risk to the environment. The application of some toxic

gels may be limited or restricted by the environmental concerns in certain locations. Studies of

environmentally benign gels that do not use any toxic materials as a gel component are active.

It is important to characterize the reservoir in which the gel is ultimately going to be placed. Some reservoir

characteristics that have a significant impact on gel treatment success are

• Permeability contrast

• Vertical communication

• Rock properties such as clay content

• Salinity

• Temperature

The permeability contrast between the layers influences the relative depth of penetration in the layers. A

high permeability contrast mitigates the damage done to the oil-producing low-permeability zone.
Section 6 - UTCHEM Model of Gel Treatment

71

Crossflow between the layers leads to mixing of fluids between the layers. This can cause some penetration

of low-permeability layers even during selective treatments. During post-gel treatment production,

crossflow may cause the water to bypass the plugged zone and be produced.

The clay content and the cation exchange capacity of the clays can have a significant impact on crosslinker

propagation. Experiments indicate that a significant portion of injected cations like chromium may be

retained on the clays and hence are not available for gelation. Salinity influences polymer and gel

viscosities, while the temperature of the reservoir affects the rate of gelation and the stability of the gel for

an extended period of time.

The gel properties modeled in UTCHEM include

• effect of gel on aqueous-phase viscosity,

• gel retention on matrix, and

• aqueous phase permeability reduction.

6.3 Gel Viscosity

The viscosity of an aqueous solution containing gel is modeled using the Flory-Huggins equation with

additional terms for gel (Thurston et al., 1987).

μ1 = μw 1+ Ap1 C4,1 +Ap2 C4,1

2

+ Ap3C4,1

3

( )CSEP

SP + Ag1C15,1 + Ag2 C15,1

2

[ ]

(6.1)

6.4 Gel Adsorption

Gel retention modeling is done using a "Langmuir-type" isotherm to correlate adsorbed concentration with

the aqueous-phase concentrations.

C ˆ 15 =

a15C15,1

1 + b15C15,1

(6.2)

6.5 Gel Permeability Reduction

The effect of gel on aqueous-phase permeability reduction is taken into account through a residual

resistance factor commonly used for polymer flooding.

RRF = 1 +

( RRF max − 1 ) Agk C15,1

1 + Bgk C15,1

(6.3a)

where the maximum residual resistance factor is calculated by

RRF max = 1−

crg Ap1 CSEP

S  p

   

  

1

3

kx ky

φ

 

 

  

 

 

  

1

2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

− 4

(6.3b)
Section 6 - UTCHEM Model of Gel Treatment

72

The parameter crg is an input parameter which depends on the gel type. The permeability reduction for

silicate gel (KGOPT=3) is independent of the silicate viscosity and the maximum residual resistance factor

(RRFmax) is equal to 10.

6.5.1 Chromium Retention

The following equilibria have been implemented in UTCHEM to simulate the exchange between

chromium, sodium and hydrogen on the clays.

6.5.2 Cation Exchange

6.5.2.1 Chromium-Sodium Exchange

3 Na

+

+ Cr

3+

= 3 Na

+

+ Cr

3+

K14,9 =

C ˆ 

14 C9,1

3

C ˆ 9

3C14,1

(6.4)

6.5.2.2 Hydrogen-Sodium Exchange

Na+ + H

+

 = Na+ + H

+

K16,9 =

C ˆ 16 C9,1

C ˆ 9 C16,1

(6.5)

6.5.3 Adsorption

As an alternative to cation exchange, the retention of chromium has also been modeled as a "Langmuirtype" isotherm in UTCHEM.

C ˆ 

14 =

a14C14,1

1 + b14C14,1

(6.6)

6.5.4 Precipitation

Chromium precipitation is modeled using geochemical reaction equilibria in UTCHEM. Cr(III) precipitates

in the form of chromium hydroxide complex.

Cr3+ + H2O = Cr(OH)2+ + H

+

(6.7)

Cr3+ + 2 H2O = Cr(OH)2

+

 + 2 H

+

(6.8)

Cr(OH)3

↓ = Cr3+ + 3 OH-(6.9)

Gel reactions are implemented in the source term as gel kinetic equations and the mass-conservation

equation is solved with reacted amount of each gel component.

Polymer molecules are crosslinked by Cr(III), which is known to be one of the most widely used

crosslinkers. Three types of gel reactions and kinetics are implemented in UTCHEM. The kinetics of

polymer/chromium chloride gel were modified, and gel reactions of polymer/chromium malonate gel and

silicate were modeled.
Section 6 - UTCHEM Model of Gel Treatment

73

6.5.5 Polymer/Chromium Chloride Gel

Two sets of reactions and kinetics for polymer/chromium chloride gel are implemented in UTCHEM. The

first is in-situ gelation of polymer with sodium dichromate with reducing agent thiourea, and the second is

the gelation of Cr(III) with polymer to form gel.

The kinetics for the reaction between polymer and chromium have been generalized to allow for any

exponent (Hunt, 1987). The gel is formed by fast reaction of trivalent chromium (Cr(III)) and polymer.

There is an option for the slow delaying reaction between Cr(VI) and thiourea. The sodium dichromate

(Na2Cr2O7) and thiourea (CS(NH2))2 are treated like tracers in the sense that they do not occupy any

volume. The Cr(III) for the gelation process can be generated in situ by redox reaction between Cr(VI) and

thiourea.

Cr2O7

2 −

+ 6CS(NH2

)2 + 8H

+   

k 

1 → 2Cr3+

+ 3 CS(NH2

) [ 2 ]2

+ 7H2O

The gel reaction is highly dependent on pH (Lockhart, 1992; Seright and Martin, 1991). For more realistic

simulations of gel reactions, pH was implemented in the gel kinetic equation as hydrogen ion concentration.

6.5.6 Polymer/Chromium Malonate Gel

The components of polymer/chromium chloride gel are as follows:

1. Polymer – Hydrolyzed polyacrylamide (HPAM) and HE-100 (acrylamido-3-propane sulfonic acid

co-polymer) were used. HE-100/chromium malonate is reported to have a longer gelation time than

HPAM/chromium malonate (Lockhart, 1992).

2. Crosslinker – Chromium malonate, Cr ( HOOC - CH2 - COOH )3. Among various complexes of

chromium, chromium malonate has the longest gelation time and stability at high temperature

(Lockhart, 1992).

3. Ligand (delaying) – Malonate ion (uncomplexed), ( HOOC - CH - COOH )-

. The uncomplexed

malonate ion as a delaying ligand is an optional component that gives a longer gelation time.

6.5.6.1 Kinetics

Case I ( polymer and crosslinker only )

The kinetics for this gel are the same as the kinetics of chromium chloride gel except with different

exponents:

[ polymer ] + n [ Cr(III) ] = [ gel ] ,

d [ Cr (III) ]

dt = - k [ Cr (III) ]X14 [ polymer ] X4

H

+ X16

 

,

d [ gel ]

dt = - 1

n

 

d [ Cr (III) ]

dt 

,

where the possible values for exponents from Lockhart [1992] are

X4 2.6
Section 6 - UTCHEM Model of Gel Treatment

74

X14 0.6

X16 1.0

Case II (polymer, crosslinker, and malonate ion )

When the malonate ion is used as a delaying ligand, the gelation kinetics are different, with zero-order

reaction for chromium :

d [ Cr (III) ]

dt = - k [ polymer ] X4

[ malonate ]X13 H

+ X16

 

,

d [ gel ]

dt = - 1

n

 

d [ Cr (III) ]

dt

where some possible values for exponents from Lockhart [19912] are

X4 2.6

X13 0.3

X16 1.0

The uncomplexed malonate ion slowly decomposes to acetate and carbon dioxide, and this is a first-order

reaction:

( HOOC - CH - COOH )- -----> CH3COO- + CO2

First-order reaction :

d [ malonate ]

dt = - 0.037347 [ malonate ]

6.5.7 Silicate Gel

UTCHEM was modified to simulate the gel reaction of the silicate gel. Polymer and chromium were

replaced with silicate (SiO2) and hydroxyl ion (OH-

), respectively. The gelation was limited to occur only

for pH > 7 (Bennett et al., 1988; Iler, 1979) to eliminate complex behavior of gel reaction rate at pH < 7,

and the aqueous-phase permeability-reduction factor was independent of silicate viscosity.

Silicate gel is formed by polymerization when appropriate conditions are established. The exact

mechanism of gelation is not clear yet; several authors (Iler, 1979; Jurinak et al., 1989) explain the general

mechanism of gelations of various types of gels.

The general process of gelation is as follows (Jurinak et al., 1989):

• condensation of monomer and dimer silicate species to form higher-order oligomers,

• intramolecular condensation of silanol groups within polymers leading to ring closure and eventual

particle formation, and

• aggregation of individual particles to form chains and microgel.
Section 6 - UTCHEM Model of Gel Treatment

75

The rate of gelation (Kristensen et al., 1993) is a function of

• silicate concentration

• pH

• ionic strength

• temperature

The basic equations that govern polymerization of silicate (Iler, 1979) are as follows:

SiO2 + 2 H2O = Si(OH)4 (6.10)

- SiOH + HOSi - = - SiOSi - + H2O (6.11)

In general form,

n SiO2 + z OH- = SinOy(OH)(nx-z)

z- + (y-2) H2O 

, (6.12)

where

n = degree of polymerization

x = ratio of OH:Si

x = 4.85 n

- 1/3 - 7.8 n- 2/3 + 4.2 n- 1

y = 4 n - n x

2

 + z

z = number of charges on polymer

Equation 6.12 can be written in simplified form as

[SiO2] + m [OH-

] = [silicate gel] , (6.13)

where m is the stoichiometric ratio.

From Eq. 6.13, the gelation kinetics equation can be derived.

d[SiO2 ]

dt

= −k[SiO2 ]

X4 OH−

[ ]

X14

(6.14)

where

X4 = gelation kinetics exponent for silicate

X14 = gelation kinetics exponent for hydroxyl ion

d [ gel ]

dt = - 

d [ SiO2 ]

dt

where some possible values for exponents (Kristensen et al., 1993) are
Section 6 - UTCHEM Model of Gel Treatment

76

X4 3.8

X14 -2.5

6.6 Temperature Effects

The reaction constants for gel (k) and the delaying reaction of sodium dichromate and thiourea (k1) are

calculated as a function of temperature if the temperature variation is modeled in the simulations as below.

k1 = k1ref exp kT1

1

T

−

1

Tref

 

 

  

   

  

 

  

where the temperature T and Tref are in 0R. The input parameters are Tref , KT1, and k1ref for the

dichromate reaction.

k = kref exp kT2

1

T

−

1

Tref

 

 

  

   

  

 

  

where the input parameters are Tref , KT2, and kref for the gel reaction.
76

Section 7

Multiple Organic Components

We have added multiple organic components so that we can model NAPL mixtures. Adding this capability

to UTCHEM required developing a phase behavior model for NAPL mixtures and the physical property

models such as density and viscosity for each phase.

7.1 Introduction

Nonaqueous phase liquids (NAPLs) usually consist of more than one organic species that mix and form a

single liquid. Common examples of such miscible species include TCE, TCA and PCE among many

others. When NAPLs leak to the subsurface, they can dissolve and migrate into groundwater. To model

the fate and transport of these soluble organics during remediation processes such as pump-and-treat,

bioremediation and surfactant remediation, it is important to determine the migration of the individual

soluble organics. The dissolution can be either a local equilibrium or a rate-limited (non-equilibrium) mass

transfer process. We have added the capability of multiple organic components to UTCHEM to model

these NAPL mixtures. The multiple organic dissolution can be either at local equilibrium partitioning or a

rate-limited mass transfer. We also present the phase behavior model developed for a mixture of NAPL

mixtures, surfactant, and water. The physical property models to calculate the density, viscosity, and

adsorption of the organic species and NAPL mixtures are also included.

7.2 Mass Transfer for Nonaqueous Phase Liquid

When a NAPL component dissolves in water, its concentration in ground water can reach its solubility

(equilibrium mass transfer) but often is much lower than the solubility due to a rate-limited mass transfer.

UTCHEM allows for both equilibrium and nonequilibrium mass transfer for a multiple organic NAPL. The

mass transfer is modeled for the cases with or without surfactant.

7.2.1 No Surfactant or Surfactant Concentration Below CMC

7.2.1.1 Equilibrium Mass Transfer

For the equilibrium case, a constant partition coefficient between water and NAPL is assumed for each

organic species:

Kk

o

=

Ck1

o

Ck2

o

 k=1,2,3,...,no(7.1)

The overall fluid concentrations for water (C1), surfactant (C3), and each organic components (Ck

o

) are

solved from the species mass conservation equation. The overall fluid phase concentration is the

summation of phase concentrations over all the phases:
Section 7 - Multiple Organic Components

77

Ck = Ck1S1

 k=1,3 (7.2)

and

Ck

o

= Ck1

o

S1

+ Ck2

o

S2

 k=1,2,3,..., no(7.3)

The definitions of overall phase concentrations (Eqs. 7.2 and 7.3), the constraints that phase concentrations

sum up to one (C31 + Ck1

o

+ C11

k=1

no

∑ = 1 and Ck2

o

k=1

no

∑ = 1), and the known partition coefficients for organic

components (Eq. 7.1) are used to solve the phase concentrations and saturations. These equations are

solved by reformulating C31 and Ck

o

 in terms of C11 and using Newton's method to solve

f C11 ( )= C31 + Ck1

0

+ C11

k=1

no

∑ −1 = 0. A phase stability rule is used to determine the number of phases. If

Ck

o

Kk

o

k=1

no

∑ >1, the fluid is two phases. Otherwise, it is a single phase.

7.2.1.2 Nonequilibrium Mass Transfer

For nonequilibrium mass transfer, a linear driving force rate, as proposed by Powers et al. [1992] is used.

The mass transfer rate between NAPL and water interface for each NAPL component is a mass transfer

coefficient times the driving force that is the difference between the equilibrium and phase concentrations.

The mass transfer coefficient is currently modeled as a constant. The computational procedure for nonequilibrium mass transfer requires the calculation of the equilibrium organic concentrations, Ck1

oeq, first.

Then we solve for the phase concentrations and saturations for the nonequilibrium case. It is similar to the

equilibrium case, except that the mass balance equation for the organic in the water phase is used instead of

constant partition coefficient of the equilibrium case. The organic species mass balance equations in the

water phase are given by:

 

∂φ 1− C ˆ 

n

n=1

nc

∑

 

 

  

 

 

  

1 + c

k

a P [ ( 1 − PRa )]S1C k1o

∂t

+

v 

∇ ⋅ 1 + c

k

a

[ (P1 − PRa )]

= Rk1

o + Qk1o + Mko Ck1

oeq

− Ck1

o

( ) k =1, 2, 3,...,no

Ck1

o v 

u 1

v v 

D k1

o

( ) (7.4)

7.2.2 Surfactant Concentration Above CMC

7.2.2.1 Equilibrium Mass Transfer

When the surfactant concentration is greater than the CMC, micelles form. When organic species are

solubilized into these micelles under certain conditions, a microemulsion forms. Organic species dissolve

by two mechanisms: (1) organic components dissolve into water according to their equilibrium solubilities

in water and (2) the organic mixture solubilized by the micelles has the same composition as the NAPL. To

model both mechanisms, each organic component is divided into two parts, one associated with water,

Ck

ow , and the other associated with the micelles, Ckoo

.
Section 7 - Multiple Organic Components

78

The organic dispersed into water follows the constant partition coefficient as described above. The

remainder of the organic is assumed to follow the same microemulsion as used for a single component (as

given in Appendix C and based upon Hand's equation). The calculations of phase compositions are divided

into two parts. First, assume the surfactant is not present and calculate phase equilibrium concentrations as

before. This calculation gives the overall concentration of each organic components associated with water,

Ck

ow

= C1

Ck1

ow

1 − Ck1

ow

k =1

no

∑

.

Hand's equation is then used to calculate the phase concentrations and saturations using the normalized total

concentrations as

C1N =

C1

1 − Ck

ow − CMC

k=1

no

∑

(7.5)

C2N =

Ck

o

− Ck

ow

k=1

no

∑

k=1

no

∑

1− Ck

ow − CMC

k=1

no

∑

(7.6)

C3N =

C3− CMC

1 − Ck

ow − CMC

k=1

no

∑

(7.7)

The phase concentrations and saturations for the normalized concentrations are calculated from Hand's

equations.

 

CkN = CklN SlN

l =1

3

∑ k=1,2,3 (7.8)

For the Type II(-) phase environment with corner plait point, C12N=0, C22N=1, C32N=0, and S1N=0. The

phase concentrations in terms of the original concentrations are calculated from the following equations:

 

C1l = C1lN 1 − Ck

ow

− CMC

k =1

no

∑

 

 

  

 

 

  (7.9)

 

Ckl

o

= Ck2

ooC2lN 1 − Ckow

− CMC

k =1

no

∑

 

 

  

 

 

  + Ck

ow k = 1,2,...,no (7.10)

 

C3l = C3lN 1 − Ck

ow

− CMC

k =1

no

∑

 

 

  

 

 

  + CMC (7.11)
Section 7 - Multiple Organic Components

79

and the saturation is unaffected by the normalization.

7.2.2.2 Nonequilibrium Mass Transfer

Once the equilibrium saturations and concentrations are known, the organic species mass balance equations

in the aqueous phase (Eq. 7.12) are used to calculate the nonequilibrium saturations and concentrations. A

single mass transfer coefficient is assumed for all organic components.

 

∂φ 1− C ˆ 

n

n=1

nc

∑

 

 

  

 

 

  

1 + c

k

a P [ ( 1 − PRa )]S1C k1o

∂t

+

v 

∇ ⋅ 1 + c

k

a

[ (P1 − PRa )]

= Rk1

o + Qk1o + M2

Ck1

oeq

− Ck1

o

( ) k = 1,2,3,..., no

Ck1

o v 

u 1

v v 

D k1

o

( ) (7.12)

where the equilibrium concentrations and saturations are already known from the phase behavior

calculations.

7.3 Physical Properties for NAPL Mixture

Phase behavior, adsorption, viscosity, and density are the physical property relations modeled for the NAPL

mixtures.

7.3.1 Phase behavior

Three recent papers by Baran et al. [1994a,b,c] show that the phase behavior of surfactants with both pure

chlorocarbons and mixtures of chlorocarbons is similar to classical phase behavior with hydrocarbons. The

phase behavior changes from microemulsion in equilibrium with excess oil (Winsor Type I or Type II(-)) to

microemulsion in equilibrium with excess aqueous and organic phase (Winsor Type III), and to

microemulsion in equilibrium with excess water (Winsor Type II or Type II(+)) as salinity increases. The

lower (CSEL) and upper (CSEU) limits of effective salinity are the effective salinity which three phases form

or disappear. The optimal salinity (CSEOP) is defined as the midpoint of these two salinity limits (Salager

et al. 1979).

Hand's equation (Pope and Nelson, 1978) is used in UTCHEM to describe the phase envelope, binodal

curve. The concentrations at binodal curve are described by the following equation:

 

C3l

C2 l

= A

C3l

C1l

 

 

  

  

B

 l = 1, 2, 3 (7.13)

where parameter A and B are empirical parameters. Parameter A is related to the height of the binodal

curve and B is assumed to be -1 in UTCHEM for a symmetric binodal curve. Parameter A is a function of

salinity and is linearly interpolated with the values of A at low (m=0), optimal (m=1) and high (m=2)

salinities as following:

A = A0 − A1

( ) 1 −

CSE

CSEOP

 

 

 

 + A1

 CSE • CSEOP (7.14)

and
Section 7 - Multiple Organic Components

80

A = A2 − A1

)

CSE

CSEOP

−1

 

  

 

  + A1

 CSE > CSEOP (7.15)

Parameter A in terms of the height of binodal curve is described as

Am =

2C3max,m

1 − C3max,m

 

  

 

  

2

 m=0,1,2 (7.16)

For organic mixtures, the upper and lower limits of effective salinity for Type III region, the height of

binodal curve at lower, optimal, and upper salinities are functions of organic species concentrations. These

parameters are modeled as functions of the equivalent alkane carbon number (EACN) of the mixture, which

is a function of organic species concentrations.

E ACN = E ACN, k

o

xk

o

k =1

no

∑ (7.17)

where x k

o

 is the molar fraction for organic components only, xk

o

k=1

no

∑ =1. EACN for an alkane is the number

of carbons in the alkane chain of the hydrocarbon, for example it is equal to 6 for hexane. EACN for a

nonalkane is obtained by measuring the optimal salinity for a binary mixture of an alkane and a nonalkane

with known molar fractions. The measured optimal salinity is used to determine EACN for the binary

mixture from Salager's equation. Then EACN for the nonalkane is calculated from Equation (7.17). The

EACN data listed in the Baran et al. papers are built into the UTCHEM database: C2Cl4 (PCE,

EACN = 2.90), CCl4 (EACN = -0.06), C2HCl3 (TCE, EACN = -3.81), p-xylene (EACN = 2), toluene

(EACN = 1), 1,2-C6H4Cl2 (DCB, EACN = -4.89), 1,2-C2H4Cl2 (EACN = -12.10), CHCl3 (EACN = -13.67),

CH2Cl2 (DCE, EACN = -13.79), and 1,1,2,2-C2H2Cl4 (EACN = -22.15).

The natural log of the optimal salinity is a linear function of EACN (Salager et al., 1979; Baran et al.,

1994a,b.c)

ln CSEOP = sse(EACN - Emin) (7.18)

The slope sse is about 0.16 for the optimal salinity with the unit of wt.% per liter. The difference of the

upper and lower effective salinities for the three-phase region is assumed as a linear function of EACN

CSEU − CSEL

CSEOP

= sdsE ACN + bds (7.19)

where

CSEOP =

CSEU + CSEL

2

(7.20)

CSEOP, CSEL, and CSEU can be solved using Eqs. 7.18-7.20.
Section 7 - Multiple Organic Components

81

The solubilization parameter is usually reported by experimentalists doing surfactant phase behavior

measurements rather than the height of the binodal curve. The solubilization parameter is defined as the oil

concentration divided by the surfactant concentration in the microemulsion phase as σ =

C2,max

C3,max

. Thus,

parameter A can be expressed in terms of the solubilization parameter:

Am = (σm)

-2 m = 0,1,2 (7.21)

The solubilization parameter is a linear function of EACN as

σm = sσ,m EACN + bσ,m m = 0,1,2 (7.22)

In UTCHEM, coefficients sse, Emin, sds, bds, sσ,m, and bσ,m are not input data. Instead, data for two

measured samples including concentrations and component names, the optimal salinity, the difference of

the lower and upper salinity limits, and the solubilization parameters at three salinities are specified since

these are what are typically measured and reported (see Baran et al., 1994a,b.c for examples). UTCHEM

calculates the coefficients based on the input values for the two specified compositions and E ACN, k

o

 values

in the UTCHEM database, or those entered by the user as needed.

7.4 NAPL Mixture Viscosity

Microemulsion viscosities are modeled as:

 

μl = C1lμ1e

α1 C2l +C3l( )

+ C2lμ2le

α2 C1l +C3l( )

+ C3lα3e

α4(C1l +α5C3l )

(7.23)

where C2l is the total organic concentration, 

 

C2l = Ckl

o

k=1

no

∑ , and μ2l is the organic mixture viscosity.

Grumberg and Nissan’s correlation is used to calculate the NAPL viscosity as a function of organic species

concentration.

 

lnμ2l = x kl

o

k=1

no

∑ lnμk

o

(7.24)

7.5 Density of NAPL Mixtures

Hydrostatic pressure gradients for the microemulsion (γ=ρg) are calculated as:

 

γ l = C1lγ1l + C2lγ2l + C3lγ3l + 0. 02535C5l − 0. 001299C6l + C8lγ 8l(7.25)

For a NAPL mixture, the overall organic hydrostatic pressure gradient is obtained by assuming ideal mixing

 

C2l

γ 2l = Ck

o

γ

kl

o

k=1

no

∑ (7.26)

UTCHEM allows two different hydrostatic pressure gradients for the organic species, one for the

microemulsion phase and the other for the organic phase.
Section 7 - Multiple Organic Components

82

7.6 Adsorption of Organic Species

The organic adsorption is modeled as a linear adsorption isotherm. A constant partition coefficient with

respect to the organic fraction is used for each organic component as

 

ˆ C k

o

= focKoc, k

o

Ckl

o

 l is the water-rich phase (7.27)

7.7 Nomenclature

ck = Compressibility of species k

Ck

, Ck

o

= Overall fluid concentration of species k and organic species k

Ckll

, 

 

Ckll

o

= Concentration of species k and organic species k in phase l

C ˆ 

k

, C ˆ 

k

o

= Adsorbed concentration of species k and organic species k

CSE = Effective salinity

CSEL = Lower effective salinity

CSEOP = Optimal effective salinity

CSEU = Upper effective salinity

 

v v 

D kl = Dispersion flux of species k in phase l

foc = Organic carbon fraction in soil

Koc, k

o

= Adsorption of organic species k per unit weight of organic carbon in soil

no = Total number of organic species

PR = Reference pressure

Qk

, Qk

o

= Source/sink term for species k and organic species k

Rk = Reaction rates for species

t = Time

 

v 

u l

= Darcy flux of phase l

φ = Porosity
83

Section 8

EQBATCH Program Description

8.1 Introduction

EQBATCH is a preprocessor batch program to calculate the equilibrium concentrations for all the flow and

solid species based on the chemical reactions considered in UTCHEM simulations. In this program, it is

assumed that all the flow species dissolve in a single phase, water. The initial pH of the formation or

makeup water can be matched by using EQBATCH with suitable input data. Also, the output of

EQBATCH can be used as the input data of UTCHEM for the geochemical options (IREACT = 2-4). In

this section, a detailed description for preparation of input data for EQBATCH is presented. To specify the

reactions considered in the simulations, elements and chemical species need to be identified. Based on the

information of the formation and makeup water analyses and the rock constituents, the key elements and

chemical species can be decided. The example shown in this section is based on the water analysis results

listed in Table 8.1. The elements such as hydrogen, sodium, calcium, magnesium, carbonate, and chlorine,

are considered since these chemicals are the primary ions contained in the formation and makeup water.

The pseudo-element (oleic acid, A) is taken into account as an element when the mechanism of in situ

generated surfactant is considered. From these elements, the expected chemical species involved in fluid

reactions, clay adsorptions, cation exchange, and solid dissolution/precipitation reactions can be specified

(Table 8.2). There are 7 elements, 18 fluid species, 4 solid species, 4 clay adsorbed cations, and 3

surfactant cation exchangers considered in this example. To represent the interactions among these

chemical species, the reaction equilibrium relations are required (Table 8.3). Tables 8.4-8.19 give the

example input data for different sections of the input file. A sample input file for EQBATCH is given in

Table 8.20 and the output file for this example is given in Table 8.21. The EQBATCH program also writes

the output data in a format similar to the geochemistry input data of UTCHEM (Section 3.5 of the

UTCHEM user's guide, lines 3.5.4 through 3.5.41) so it can be directly pasted into the UTCHEM input file

(Table 8.22).

8.2 User's Guide

A detailed user's guide for the EQBATCH program is presented as follows:

1. TITLE

A title line is required.

2. IREACT, ICHARGE, IMG

IREACT - Flag indicating the components to be considered

Possible values:

2 - Without acidic crude

3 - With acidic crude (insitu surfactant generation)
Section 8 - EQBATCH Program Description

84

4- Gel option without acidic crude

ICHRGE - Flag indicating whether an oxygen mass balance or a charge balance will be used.

Possible Values:

0 - Oxygen balance used

1 - Charge balance in solution used

Note: If solid SiO2 is considered, the oxygen balance must be used

IMG - Flag indicating whether magnesium ions participate in cation exchange reactions or not.

Possible Values:

0 - Magnesium ions are considered.

1 - Magnesium ions are not considered.

3. NELET, NFLD, NSLD, NSORB, NACAT

NELET - Total number of elements less non reacting element.

NFLD - Total number of fluid species.

NSLD - Total number of solid species.

NSORB - Total number of sorbed species.

NACAT - Total number of surfactant associated cations.

4. NIAQ, NEX, NSLEL, NSURF1 (This line is read only if IMODE > 2)

NIAQ - Total number of independent fluid species.

NEX - Total number of insoluble exchangers.

NSLEL - Total number of elements comprising the solid species.

NSURF1 - Position number corresponding to the in situ generated surfactant anion in the fluid

species array FLDSPS.

Note: NSURF1 is automatically set to 0 by the program if IMODE = 2 or 4.

5. NH, NNA, NCA, NMG, NCARB

NH - Position number corresponding to the hydrogen element in the element array ELEMNT.

NNA - Position number corresponding to the sodium element in the element array ELEMNT.

NCA - Position number corresponding to the calcium element in the element array ELEMNT.

NMG - Position number corresponding to the magnesium element in the element array ELEMNT.

NCARB - Position number corresponding to the carbonate pseudo-element in the element array

ELEMNT.

Note: If any of these elements is not considered, the position no. must be set equal to 0.

6. NALU, NSILI, NOXY

NALU - Position number corresponding to the aluminum element in the element array ELEMNT.

NSILI - Position number corresponding to the silicon element in the element array ELEMNT.

NOXY - Position number corresponding to the oxygen element in the element array ELEMNT.

7. NACD (This line is read only if IREACT = 3)

NACD - Position number corresponding to the petroleum acid pseudo-element in the element array

ELEMNT.

8a. NCR, NHFD, NCRFD (This line is read only if IREACT = 4)

NCR - Position number corresponding to the chromium in the element array ELEMNT.
Section 8 - EQBATCH Program Description

85

NHFD - Position number corresponding to the hydrogen ion element in the fluid species array

FLDSPS.

NCRFD - Position number corresponding to CR(III) ion in the fluid species array FLDSPS.

8b. ELEMNT(I), ELCRG(I), for I = 1, NELET

ELEMNT(I) - Name of the Ith element.

ELCRG(I) - Charge for the Ith element.

Note: The name of each element may not exceed 32 characters and each name must be on

a separate line of the input file.

9. FLDSPS(I), for I = 1, NFLD

FLDSPS(I) - Name of the Ith fluid species.

Note: The name of each fluid species may not exceed 32 characters and each name must

be on a separate line of the input file. If IREACT=3, the last fluid species must be HAw (petroleum

acid in water).

10. SLDSPS(I), for I = 1, NSLD (This line is read only if NSLD > 0)

SLDSPS(I) - Name of the Ith solid species.

Note: The name of each solid may not exceed 32 characters and each name must be on a

separate line of the input file.

11. SORBSP(I), for I = 1, NSORB (This line is read only if NSORB > 0)

SORBSP(I) - Name of the Ith adsorbed cation.

Note: The name of each adsorbed cation may not exceed 32 characters and each name

must be on a separate line of the input file.

12. ACATSP(I), for I = 1, NACAT (This line is read only if NACAT > 0)

ACATSP(I) - Name of the Ith surfactant adsorbed cation.

Note: The name of each surfactant adsorbed cation may not exceed 32 characters and

each name must be on a separate line of the input file.

13. NSORBX(I), for I = 1, NEX (This line is read only if NSORB > 0)

NSORBX(I) - Number of cations for Ith exchanger.

14. AR(I,J), for J = 1, NFLD, for I = 1, NELET << or >>

AR(I,J), for J = 1, NFLD, for I = 1, NELET-1

AR(I,J) - Stoichiometric coefficient of Ith element in Jth fluid species.

Note: If ICHRGE = 0, then NFLD × NELET values are required by the program. If ICHRGE = 1,

then NFLD × (NELET-1) values are required by the program.

15. BR(I,J), for J = 1, NSLD, for I = 1, NELET << or >>

BR(I,J), for J = 1, NSLD, for I = 1, NELET-1 (This line is read only if NSLD > 0)

BR(I,J) - Stoichiometric coefficient of Ith element in Jth solid species.

Note:If ICHRGE = 0, then NSLD × NELET values are required by the program. If ICHRGE = 1,

then NSLD × (NELET-1) values are required by the program.

16. DR(I,J), for J = 1, NSORB, for I = 1, NELET << or >>
Section 8 - EQBATCH Program Description

86

DR(I,J), for J = 1, NSORB, for I = 1, NELET-1 (This line is read only if NSORB > 1)

DR(I,J) - Stoichiometric coefficient of Ith element in Jth sorbed species.

Note: If ICHRGE = 0, then NSORB × NELET values are required by the program. If

ICHRGE = 1, then NSORB × (NELET-1) values are required by the program.

17. ER(I,J), for J = 1, NACAT, for I = 1, NELET << or >>

ER(I,J), for J = 1, NACAT, for I = 1, NELET-1 (This line is read only if NACAT > 1)

ER(I,J) - Stoichiometric coefficient of Ith element in Jth surfactant associated cation.

Note: If ICHRGE = 0, then NACAT × NELET values are required by the program. If

ICHRGE = 1, then NACAT × (NELET-1) values are required by the program.

18. BB(I,J), for J = 1, NIAQ+NSORB+NACAT, for I = 1, NFLD+NSORB+NACAT

BB(I,J) - Exponent of the Jth independent fluid species concentration when the Ith fluid species is

expressed in terms of independent species concentrations.

19. EXSLD(I,J), for J = 1, NIAQ, for I = 1, NSLD (This line is read only if NSLD > 0)

EXSLD(I,J) - Exponent of the Jth independent fluid species concentration in the solubility product

definition of the Ith solid.

20. CHARGE(I), for I = 1, NFLD

CHARGE(I) - Charge of the Ith fluid species.

21. EQK(I), for I = 1, NFLD

EQK(I) - Equilibrium constant for Ith fluid species when expressed in independent species

concentrations only.

22. SCHARG(I,J), for J = 1, NSORBX(I), for I = 1, NEX (This line is read only if NSORB > 0)

SCHARG(I,J) - Charge of the Jth sorbed species on the Ith exchanger.

23. EXK(I,J), for J = 1, NSORBX(I)-1, for I = 1, NEX (This line is read only if NEX > 0)

EXK(I,J) - Exchange equilibrium constant for Jth exchange equilibrium of the Ith insoluble

exchanger.

24. EXEX(I,J,K), for K = 1, NIAQ+NSORB+NACAT, for J = 1, NSORBX(I)-1, for I = 1, NEX

(This line is read only if and NEX > 0)

EXEX(I,J,K) - Exponent of Kth independent species in Jth equilibrium relation of the Ith exchanger

25. REDUC(I,J), for J = 1, NSORBX(I)-1, for I = 1, NEX (This line is read only if NEX > 0)

REDUC(I,J) - Valence difference of the two cations involved in the exchange reaction J on

exchanger I.

Note: This value is positive if the higher valence cation bulk concentration has a positive

exponent in EXEX(I,J) definition and is negative otherwise.

26. EXCAI(I), for I = 1, NEX (This line is read only if NEX >0)

EXCAI(I) - Exchange capacity of Ith insoluble exchanger.

Units: meq/ml pore volume
Section 8 - EQBATCH Program Description

87

27. SPK(I), for I = 1, NSLD (This line is read only if NSLD > 0)

SPK(I) - Solubility product of Ith solid defined in terms of independent fluid species concentrations

only.

28. CHACAT(I), for I = 1, NACAT (This line is read only if NACAT > 0)

CHACAT(I) - Charge of Ith surfactant associated cation.

29. ACATK(I), for I = 1, NACAT-1 (This line is read only if NACAT > 0)

ACATK(I) - Equilibrium constant for Ith exchange equilibrium for cation exchanges on surfactant.

30. EXACAT(I,J) for J = 1, NIAQ+NSORB+NACAT, for I = 1, NACAT-1 (This line is read only if

NACAT > 0)

EXACAT(I,J) - Exponent of Jth independent species in Ith equilibrium for cation exchange on

surfactant.

31. C5I, CSURF

C5I - Initial concentration of chloride ion.

Units: meq/ml

CSURF- Initial concentration of surfactant.

Units: vol. fraction

32. CELAQI(J), for J = 1, NELET-1

CELAQI(J) - Initial concentrations of NELET-1 elements.

Units: equivalents/liter

33. CSLDI(I), for I = 1, NSLD (This line is read only if NSLD > 0)

CSLDI(I) - Initial concentration of I

th solid.

Units: moles/liter pore volume

34. CSORBI(I), for I = 1, NSORB (This line is read only if NSORB > 0)

CSORBI(I) - Initial concentration of Ith adsorbed cation.

Units: moles/liter pore volume

35. CAQI(J), for J = 1, NIND

CAQI(J) - Initial guesses for Jth independent species concentration, adsorbed species, and surfactant

associated species.

Units: moles/liter water

36. S

S - Initial water saturation in core flooding or reservoir condition.

Units: fraction

37. EQWPS (This line is read only if IREACT= 3)

EQWPS - Equivalent weight of petroleum acid.
Section 8 - EQBATCH Program Description

88

Table 8.1. Water Analysis for Makeup and Formation Water

Ions Formation water Makeup water

Na+, mg/l 2,398.90 52.9

Mg2+, mg/l 36.46 11.54

Ca2+, mg/l 54.2 67.13

Cl-, mg/l 2091 39.00

HCO3

-

, mg/l 2623 152.55

CO2-

3

, mg/l 240 6.00

SO2-

4

, mg/l — 134.56

pH 8.1 7.95

Table 8.2. Example List of Elements and Reactive Species

Elements or pseudo-element: Hydrogen (reactive), Sodium, Calcium, Magnesium,

Carbonate, A (from acid HA), Chlorine,

Independent aqueous or oleic species: H+, Na+,Ca2+, Mg2+,CO2-

3

, HAo, H2O

Dependent aqueous or oleic species: Ca(OH)+, Mg(OH)+, Ca(HCO3)

+, HAw, Mg(HCO3)+, OH-

,

HCO3

, A-, H2CO3, CaCOo

3

 , MgCOo

3

 

Solid species: CaCO3 (Calcite), Ca(OH)2 (Calcium hydroxide), MgCO3

(Magnesite), Mg(OH)2 (Magnesium hydroxide)

Adsorbed cations: __

H + , 

__

Na + , 

__

Ca 2+, 

__

Mg 2+

Adsorbed cations on micelles: =

Na + , 

=

Ca 2+, 

=Mg 2+
Section 8 - EQBATCH Program Description

89

Table 8.3. List of Reactions for the Example Run

Partitioning of HA Partition Coefficient

HAo

KD∅♦

 HAw KD

 = 

[ HAw ] water

[ HAo ] oil

Aqueous Reactions Equilibrium Constant

H2

O 

K

eq

1∅♦

 H

+

 + OH- K

eq

1

 = [ H ]

+

 [ OH ]

-

 

HAw

 + OH- K

eq

2∅♦

 A

-

 + H2

O K

eq

2

 = 

[ A ]

-

[ H ]

+

[ ]

HAw

H

+

 + CO2-

3

K

eq

3 ∅♦

 HCO

-

3 K

eq

3

 = 







 HCO

-

3

[ H ]

+







CO 

2-

3

Ca2+ + H2

O 

K

eq

4∅♦

 Ca(OH)+ + H+

K

eq

4

 = 

[ Ca(OH) ]

+

[ H ]

+

[ Ca ]

2+

Mg2+ + H2

O 

K

eq

5∅♦

 Mg(OH)+ + H+

K

eq

5

 = 

[ Mg(OH) ]

+

[ H ]

+

[ Mg ]

2+

Ca2+ + H+

+ CO2-

3

K

eq

6∅♦

 Ca(HCO3

)

+

K

eq

6

 = 







Ca(HCO 

3

)

+

[ Ca ]

2+ 





CO 

2-

3

[ H ]

+

Mg2+ + H+

+ CO2-

3

K

eq

7∅♦

 Mg(HCO3

)

+

K

eq

7

 = 





 Mg(HCO 

3

)

+

[ Mg ]

2+ 





CO 

2-

3

[ H ]

+

2H+

+ CO2-

3

K

eq

8∅♦

 H2

CO3

K

eq

8

 = 

[ ]

H2

CO3







CO 

2-

3

[ H ]

+ 2

Ca2+ + CO2-

3

K

eq

9∅♦

 CaCOo

3 K

eq

9

 = 







CaCO 

o

3

[ Ca ]

2+ 





CO 

2-

3

Mg2+ + CO2-

3

K

eq

10 ∅♦

 MgCOo

3 K

eq

10 = 





 MgCO 

o

3

[ Mg ]

2+ 





CO 

2-

3
Section 8 - EQBATCH Program Description

90

Table 8.3. List of Reactions for the Example Run (cont.)

Dissolution Reactions Solubility Product

CaCO3

K

sp

1 ∅♦

 Ca2+ + CO2-

3

 

K

sp

1

 = [ Ca ]

2+ 





CO 

2-

3

MgCO3

K

sp

2 ∅♦

 Mg2+ + CO2-

3

 

K

sp

2

 = [ Mg ]

2+ 





CO 

2-

3

Ca(OH)2

K

sp

3 ∅♦

 Ca2+ + 2OH- K

sp

3

 = [ Ca ]

2+ [ H ]+ -2

Mg(OH)2

K

sp

4 ∅♦

 Mg2+ + 2OH- K

sp

4

 = [ Mg ]

2+ [ H ]+ -2

Exchange Reactions (On Matrix) Exchange Equilibrium Constant

2

__

Na + + Ca2+ 

K

ex

1 ∅♦

 2Na+ + 

__

Ca 2+

K

ex

1

 = 







__ 

Ca2+ [ Na ]

+ 2

[ Ca ]

2+ 





__ 

Na+

2

2

__

Na + + Mg2+ 

K

ex

2 ∅♦

 2Na+ + 

__

Mg 2+

K

ex

2

 = 







__ 

Mg2+ [ Na ]

+ 2

[ Mg ]

2+ 





__ 

Na+

2

_

H + + Na+

 + OH- K

ex

3 ∅♦

 

__

Na + + H2O

K

ex

3

 = 

[ Na ]

+







__ 

H

+







__ 

Na+

[ H ]

+

Exchange Reactions (On Micelle) Exchange Equilibrium Constant

2

=

Na + + Ca2+ 

K

exm

1 ∅♦

 2Na+ + 

=

Ca 2+

K

exm

1

 = 







= 

Ca2+ [ Na ]

+ 2







= 

Na+ 2

[ Ca ]

2+

where Kexm

1

= β

exm

1

{[A-] +[S-]}

2

=

Na + + Mg2+ 

K

exm

2 ∅♦

 2Na+ + 

=Mg 2+

K

exm

2

 = 







=  Mg2+ [ Na ]

+ 2







= 

Na+ 2

[ Mg ]

2+

where Kexm

2

= β

exm

2

{[A-] +[S-]}
Section 8 - EQBATCH Program Description

91

Table 8.4. Stoichiometric Coefficient of Ith Element in Jth

Fluid Species (for the AR Array)

Ca Mg CO3 Na H A

1 H+ 0 0 0 0 1 0

2 Na+ 0 0 0 1 0 0

3 Ca2+ 1 0 0 0 0 0

4 Mg2+ 0 1 0 0 0 0

5 CO32- 0 0 1 0 0 0

6 HAo0 0 0 0 1 1

7 H2O 0 0 0 0 2 0

8 Ca(OH)+ 1 0 0 0 1 0

9 Mg(OH)+ 0 1 0 0 1 0

10 Ca(HCO3

)

+ 1 0 1 0 1 0

11 Mg(HCO3

)

+ 0 1 1 0 1 0

12 A- 0 0 0 0 0 1

13 OH- 0 0 0 0 1 0

14 HCO3- 0 0 1 0 1 0

15 H2CO30 0 1 0 2 0

16 CaCO31 0 1 0 0 0

17 MgCO30 1 1 0 0 0

18 HAw 0 0 0 0 1 1

Note: The transposition of this table is the form required for

EQBATCH Program

Table 8.5. Stoichiometric Coefficient of Ith

Element in Jth Solid Species (for the BR

Array)

CaCO3 MgCO3 Ca(OH)2 Mg(OH)2

Ca 1 0 1 0

Mg 0 1 0 1

CO31 1 0 0

Na 0 0 0 0

H 0 0 2 2

A 0 0 0 0

Table 8.6. Stoichiometric Coefficient of Ith

Element in Jth Sorbed Species (for the DR

Array)

H+ Na+ Ca2+ Mg2+

Ca 0 0 1 0

Mg 0 0 0 1

CO30 0 0 0

Na 0 1 0 0

H 1 0 0 0

A 0 0 0 0
Section 8 - EQBATCH Program Description

92

Table. 8.7. Stoichiometric Coefficient of Ith

Element in Jth Surfactant Associated Cation

(for the ER Array)

Na+ Ca2+ Mg2+

Ca 0 1 0

Mg 0 0 1

CO30 0 0

Na 1 0 0

H 0 0 0

A 0 0 0

Table 8.8. Exponent of Jth Independent Fluid Species (for BB Array)

H

+ Na+ Ca2+ Mg2+ CO32- HAo H2O H+ Na+ Ca2+ Mg2+ Na+ Ca2+ Mg2+

1 H

+

1

2 Na+1

3 Ca2+ 1

4 Mg2+ 1

5 CO3

2- 1

6 HAo1

7 H2O 1

8 Ca(OH)+-1 1

9 Mg(OH)+-1 1

10 Ca(HCO3)

+

1 1 1

11 Mg(HCO3)

+

1 1 1

12 A

-

-1 1

13 OH--1

14 HCO3

-

1 1

15 H2CO32 1

16 CaCO31 1

17 MgCO31 1

18 HAw 1

19 H

+

s 1

20 Na+s 1

21 Ca2+s 1

22 Mg2+s 1

23 Na+1

24 Ca2+ 1

25 Mg2+sa 1

Sorbed Species Surfactant Assoc. Cation

Note: The blank cells in the above table need to be filled with zero for the input data for EQBATCH program.
Section 8 - EQBATCH Program Description

93

Table 8.9. Exponent of Jth Independent Species in the Ith Solid (for EXSLD Array)

H+ Na+ Ca2+ Mg2+ CO3

2- HAo H2O

CaCO30 0 1 0 1 0 0

MgCO30 0 0 1 1 0 0

Ca(OH)2-2 0 1 0 0 0 0

Mg(OH)2-2 0 0 1 0 0 0

Table 8.10. Charge of Ith Fluid Species

(for CHARGE Array)

Fluid species Charge

1 H+ 1

2 Na+ 1

3 Ca2+ 2

4 Mg2+ 2

5 CO3

2- -2

6 HAo0

7 H2O 0

8 Ca(OH)+ 1

9 Mg(OH)+ 1

10 Ca(HCO3

)

+ 1

11 Mg(HCO3

)

+ 1

12 A- -1

13 OH- -1

14 HCO3

- -1

15 H2CO30

16 CaCO30

17 MgCO30

18 HAw 0

Table 8.11. Equilibrium Constants for Ith

Fluid Species (for EQK Array)

Fluid species Equilibrium Constants

1 H+ 1

2 Na+ 1

3 Ca2+ 1

4 Mg2+ 1

5 CO3

2- 1

6 HAo1

7 H2O 1

8 Ca(OH)+ 0.12050E-12

9 Mg(OH)+ 0.38871E-11

10 Ca(HCO3

)

+ 0.14124E+12

11 Mg(HCO3

)

+ 0.58345E+12

12 A- 0.85480E-14

13 OH- 0.10093E-13

14 HCO3- 0.21380E+11

15 H2CO30.39811E+17

16 CaCO30.15849E+04

17 MgCO30.47863E+04

18 HAw 0.85480E-04

Table 8.12. Charge of Jth Sorbed Species

(for SCHARG Array)

Adsorbed species Charge

H+(sorbed) 1

Na+(sorbed) 1

Ca2+(sorbed) 2

Mg2+(sorbed) 2

Table 8.13. Exchange Equilibrium Constants

for Jth Exchange (for EXK Array)

Adsorbed Equilibrium Constants

Kex1 0.2623E+03

Kex2 0.1509E+03

Kex3 0.1460E+08
Section 8 - EQBATCH Program Description

94

Table8.14. Exponent of Kth Independent Species in Jth Equilibrium Relation (for EXEX Array)

H

+ Na+ Ca2+ Mg2+ CO3

2 − HAo H2O H

+ Na+ Ca2+ Mg2+ Na+ Ca2+ Mg2+

0 2 -1 0 0 0 0 0 -2 1 0 0 0 0

0 2 0 -1 0 0 0 0 -2 0 1 0 0 0

-1 1 0 0 0 0 0 1 -1 0 0 0 0 0

Sorbed Species Surfactant Assoc. Cation

Table 8.15. Valence Difference Between

Cation Involved In Exchange (for REDU

Array)

Ca2+ Mg2+ Na+

Na+ -1

Na+ -1

H+ 0

Table 8.16. Solubility Product of Ith Solid (for SPK Array)

CaCO3 MgCO3 Ca(OH)2 Mg(OH)

0.4953E-09 0.00007 4.7315E+22 5.6104E+16

Table 8.17. Charge of Ith Surfactant

Associated Cation (for CHACAT Array)

Na+ Ca2+ Mg2+

1 2 2

Table 8.18. Equilibrium Constant for Ith

Exchange (for ACATK Array)

Na+ Ca2+

2.5 2.94

Table 8.19. Exponent of Jth Independent Species in Ith Cation Exchange on Surfactant (for

EXACAT Array)

H

+ Na+ Ca2+ Mg2+ CO3

2 −

HAo H2O H

+ Na+ Ca2+ Mg2+ Na+ Ca2+ Mg2+

0 2 -1 0 0 0 0 0 0 0 0 -2 1 0

0 2 0 -1 0 0 0 0 0 0 0 -2 0 1

Sorbed Species Surfactant Assoc. Cation
Section 8 - EQBATCH Program Description

95

Table 8.20. Sample Input Data for EQBATCH Program

R1 (* TITLE *)

3 1 1 (* IREACT ICHARGE IMG *)

7 18 4 4 3 (* NNELET NFLD NSLD NSORB NACAT *)

7 1 4 12 (* NIAQ NEX NSLWL NSURF1 *)

5 4 1 2 3 (* NH NNA NCA NMG NCARB *)

0 0 0 (* NALU NSILI NOXYG *)

6 (* NACD *)

CALCIUM 2

MAGNESIUM 2

CARBON (AS CARBOBATES) -2

SODIUM 1

HYDROGEN (REACTIVE) 1

ACID (PETROLEUM) -1

CHLORINE -1

HYDROGEN ION

SODIUM ION

CALCIUM ION

MAGENSIUM ION

CARBONATE ION

PETROLEUM ACID IN OIL

WATER

CALCIUM MONOHYDROXIDE ION

MAGNESIUM MONOHYROXIDE ION

CA (HC03) +

MG (HCO3) +

PETRLEUM ACID ANION

HYDROXIDE ION

BICARBONATE ION

DISSOLVED CARBON MONOHYDROXIDE

AQUEOUS CALCIUM CARBONATE

AQUEOUS MAGNESIUM CARBONATE

PETROLEUM ACID IN OIL (* FLDSPS *)

CALCIUM CARBONATE(SOLID)

MAGNESIUM CARBONATE (SOLID)

CALCIUM HYDROXIDE (SOLID)

MAGNESIUM HYDROXIDE(SOLID) (* SLDSPS *)

SORBED HYDROGEN ION

SORBED SODIUM ION

SORBED CALCIUM ION

SORBED MAGNESIUM ION (* SORBSPS *)

SURF. ASSOCIATED SODIUM ION

SURF. ASSOCIATED CALCIUM ION

SURF. ASSOCIATED MAGNESIUM ION (* ACATSPC *)

4 (* NSORBX *)

0. 0. 1. 0. 0. 0. 0. 1. 0. 1. 0. 0. 0. 0. 0. 1. 0. 0.

0. 0. 0. 1. 0. 0. 0. 0. 1. 0. 1. 0. 0. 0. 0. 0. 1. 0.

0. 0. 0. 0. 1. 0. 0. 0. 0. 1. 1. 0. 0. 1. 1. 1. 1. 0.

0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.

1. 0. 0. 0. 0. 1. 2. 1. 1. 1. 1. 0. 1. 1. 2. 0. 0. 1.

0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 1. (* AR *)

1.0 0.0 1.0 0.0

0.0 1.0 0.0 1.0

1.0 1.0 0.0 0.0

0.0 0.0 0.0 0.0

0.0 0.0 2.0 2.0

0.0 0.0 0.0 0.0 (* BR *)

0.0 0.0 1.0 0.0

0.0 0.0 0.0 1.0

0.0 0.0 0.0 0.0

0.0 1.0 0.0 0.0

1.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 (* DR *)

0.0 1.0 0.0

0.0 0.0 1.0

0.0 0.0 0.0
Section 8 - EQBATCH Program Description

96

1.0 0.0 0.0

0.0 0.0 0.0

0.0 0.0 0.0 (* ER *)

1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.

0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.

Table 8.20. Sample Input Data for EQBATCH Program (cont.)

0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0.

-1. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.

-1. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.

1. 0. 1. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0.

1. 0. 0. 1. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0.

-1. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0.

-1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.

1. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0.

2. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 1. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 1. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0.

0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. (* BB *)

0. 0. 1. 0. 1. 0. 0.

0. 0. 0. 1. 1. 0. 0.

-2. 0. 1. 0. 0. 0. 0.

-2. 0. 0. 1. 0. 0. 0. (* EXSLD *)

1. 1. 2. 2. -2. 0. 0. 1. 1. 1. 1. -1. -1. -1. 0. 0. 0. 0. (* CHAEGE *)

1. 1. 1. 1. 1. 1. 1. 0.1205e-12 0.38871e-11 0.14125e+12

0.58345e+12 0.959e-12 0.10093e-13 0.2138e+11 0.3981e+17

0.15849e+04 0.47863e+04 0.959-04 (* KEQ *)

1. 1. 2. 2. (* SCHARGE *)

0.793+01 0.52+01 0.27+07 (* KEX *)

0. 2. -1. 0. 0. 0. 0. 0. -2. 1. 0. 0. 0. 0.

0. 2. 0. -1. 0. 0. 0. 0. -2. 0. 1. 0. 0. 0.

-1. 1. 0. 0. 0. 0. 0. 1. -1. 0. 0. 0. 0. 0. (* EXEX *)

-1. -1. 0. (* REDUC *)

0.3403 (* EXCAI *)

0.474851e-09 0.00007 0.47315e+23 0.56045e+17 (* KSP *)

1. 2. 2. (* CHACAT *)

2.5 2.94 (* KACAT *)

0. 2. -1. 0. 0. 0. 0. 0. 0. 0. 0. -2. 1. 0.0

0. 2. 0. -1. 0. 0. 0. 0. 0. 0. 0. -2. 0. 1. (* EXACAT *)

0.059 0.0 (*C50, Csurf*)

0.00135 0.0015 0.047 0.1043 111.043 0.019 (*CELFLT 1,NELEMENT-1*)

2.00 0.0 0.0000 0.0 (*CSLD(I), I=1,NSLD*)

 0.05 0.25 0.01 0.002 (* CSORBI *)

0.1200077231590e-05 0.01 0.1e-04

0.4616423363603e-05 0.3092684582095e-08 0.5399766653843e-03

55.49999314650 1.0e-06 1.0e-02 1.0e-03 1.0e-04

1.0e-06 1.0e-08 1.0e-08 (*CIND*)

0.602 (*S1*)

500 (*EQW*)
Section 8 - EQBATCH Program Description

97

Table 8.21. Sample Output of EQBATCH Program

R1

 REACTIVE SYSTEM DESCRIPTION

 TOTAL NO. OF ELEMENTS LESS ONE = 7

 TOTAL NO. OF FLUID SPECIES = 18

 TOTAL NO. OF SOLID SPECIES = 4

 TOTAL NO. OF ADSORBED SPECIES = 4

 NO. OF CATIONS ASSOC. WITH SURF.= 3

 TOTAL NO. OF IND. FLUID SPECIES = 7

 TOTAL NO. OF EXCHANGER = 1

 ELEMENT NO. NAME CHARGE

 1 CALCIUM 2

 2 MAGNESIUM 2

 3 CARBON (AS CARBOBATES) -2

 4 SODIUM 1

 5 HYDROGEN (REACTIVE) 1

 6 ACID (PETROLEUM) -1

 7 CHLORINE -1

 FLUID SPECIES NO. NAME

 (INDEPENDENT)

 1 HYDROGEN ION

 2 SODIUM ION

 3 CALCIUM ION

 4 MAGENSIUM ION

 5 CARBONATE ION

 6 PETROLEUM ACID IN OIL

 7 WATER

 (DEPENDENT)

 8 CALCIUM MONOHYDROXIDE ION

 9 MAGNESIUM MONOHYROXIDE ION

 10 CA (HC03) +

 11 MG (HCO3) +

 12 PETRLEUM ACID ANION

 13 HYDROXIDE ION

 14 BICARBONATE ION

 15 DISSOLVED CARBON MONOHYDROXIDE

 16 AQUEOUS CALCIUM CARBONATE

 17 AQUEOUS MAGNESIUM CARBONATE

 18 PETROLEUM ACID IN OIL

 SOLID SPECIES NO. NAME

 1 CALCIUM CARBONATE(SOLID)

 2 MAGNESIUM CARBONATE (SOLID)

 3 CALCIUM HYDROXIDE (SOLID)

 4 MAGNESIUM HYDROXIDE(SOLID)

 SORBED SPECIES NO. NAME

 1 SORBED HYDROGEN ION

 2 SORBED SODIUM ION

 3 SORBED CALCIUM ION

 4 SORBED MAGNESIUM ION

 ASSOC. CATION NO. NAME

 1 SURF. ASSOCIATED SODIUM ION
Section 8 - EQBATCH Program Description

98

 2 SURF. ASSOCIATED CALCIUM ION

 3 SURF. ASSOCIATED MAGNESIUM ION

Table 8.21. Sample Output of EQBATCH Program (cont.)

 NO. OF MOLES OF ELEMENT I IN ONE MOLE OF

 FLUID SPECIES J

 J= 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

22 23 24 25

 I= 1 0. 0. 1. 0. 0. 0. 0. 1. 0. 1. 0. 0. 0. 0. 0. 1. 0. 0.

 I= 2 0. 0. 0. 1. 0. 0. 0. 0. 1. 0. 1. 0. 0. 0. 0. 0. 1. 0.

 I= 3 0. 0. 0. 0. 1. 0. 0. 0. 0. 1. 1. 0. 0. 1. 1. 1. 1. 0.

 I= 4 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.

 I= 5 1. 0. 0. 0. 0. 1. 2. 1. 1. 1. 1. 0. 1. 1. 2. 0. 0. 1.

 I= 6 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 1.

 NO. OF MOLES OF ELEMENT I IN ONE MOLE OF

 SOLID SPECIES K

 K= 1 2 3 4 5 6 7 8 9 10

 I= 1 1. 0. 1. 0.

 I= 2 0. 1. 0. 1.

 I= 3 1. 1. 0. 0.

 I= 4 0. 0. 0. 0.

 I= 5 0. 0. 2. 2.

 I= 6 0. 0. 0. 0.

 NO. OF MOLES OF ELEMENT I IN ONE MOLE OF

 ADSORBED SPECIES K

 K= 1 2 3 4 5

 I= 1 0. 0. 1. 0.

 I= 2 0. 0. 0. 1.

 I= 3 0. 0. 0. 0.

 I= 4 0. 1. 0. 0.

 I= 5 1. 0. 0. 0.

 I= 6 0. 0. 0. 0.

 NO. OF MOLES OF ELEMENT I IN ONE MOLE OF

 SURF. ASS. SPECIES K

 K= 1 2 3 4 5

 I= 1 0. 1. 0.

 I= 2 0. 0. 1.

 I= 3 0. 0. 0.

 I= 4 1. 0. 0.

 I= 5 0. 0. 0.

 I= 6 0. 0. 0.

 EXPONENT OF THE IND. SPECIES CONC. J

 FOR FLUID SPECIES I

 J= 1 2 3 4 5 6 7 8 9 10

 I= 1 1. 0. 0. 0. 0. 0. 0.

 I= 2 0. 1. 0. 0. 0. 0. 0.

 I= 3 0. 0. 1. 0. 0. 0. 0.

 I= 4 0. 0. 0. 1. 0. 0. 0.
Section 8 - EQBATCH Program Description

99

 I= 5 0. 0. 0. 0. 1. 0. 0.

 I= 6 0. 0. 0. 0. 0. 1. 0.

 I= 7 0. 0. 0. 0. 0. 0. 1.

 I= 8 -1. 0. 1. 0. 0. 0. 0.

 I= 9 -1. 0. 0. 1. 0. 0. 0.

 I=10 1. 0. 1. 0. 1. 0. 0.

 I=11 1. 0. 0. 1. 1. 0. 0.

 I=12 -1. 0. 0. 0. 0. 1. 0.

 I=13 -1. 0. 0. 0. 0. 0. 0.

 I=14 1. 0. 0. 0. 1. 0. 0.

Table 8.21. Sample Output of EQBATCH Program (cont.)

 I=15 2. 0. 0. 0. 1. 0. 0.

 I=16 0. 0. 1. 0. 1. 0. 0.

 I=17 0. 0. 0. 1. 1. 0. 0.

 I=18 0. 0. 0. 0. 0. 1. 0.

FLUID SPECIES NO. CHARGE

 1 1.0

 2 1.0

 3 2.0

 4 2.0

 5 -2.0

 6 0.0

 7 0.0

 8 0.0

 9 1.0

 10 1.0

 11 1.0

 12 -1.0

 13 -1.0

 14 -1.0

 15 0.0

 16 0.0

 17 0.0

 18 0.0

 ADSORBED SPECIES NO. CHARGE

 1 1.0

 2 1.0

 3 2.0

 4 2.0

 ASSOC. CATION(SURF) CHARGE

 1 1.0

 2 2.0

 3 2.0

 EXPONENT OF IND. FLUID SPECIES J IN THE

 SOLUBILITY PRODUCT DEFINITION OF SOLID I

 J= 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

 I= 1 0. 0. 1. 0. 1. 0. 0.

 I= 2 0. 0. 0. 1. 1. 0. 0.

 I= 3 -2. 0. 1. 0. 0. 0. 0.

 I= 4 -2. 0. 0. 1. 0. 0. 0.

 FLUID SPECIES NO. EQUILM. CONSATNT
Section 8 - EQBATCH Program Description

100

 1 0.10000E+01

 2 0.10000E+01

 3 0.10000E+01

 4 0.10000E+01

 5 0.10000E+01

 6 0.10000E+01

 7 0.10000E+01

 8 0.12050E-12

 9 0.38871E-11

 10 0.14125E+12

 11 0.58345E+12

 12 0.95900E-12

 13 0.10093E-13

 14 0.21380E+11

 15 0.39810E+17

Table 8.21. Sample Output of EQBATCH Program (cont.)

 16 0.15849E+04

 17 0.47863E+04

 18 0.95900E-04

 EXCHANGE EQUILIBRIUM CONSTANT FOR EQUILM. J

 OF THE EXCHANGER I

 J= 1 2 3 4 5

 I= 1 0.7930E+01 0.5200E+01 0.2700E+07

 EXCHANGER NO. EXCHANGE CAPACITY

 1 0.34030E+00

 EXPONENT OF THE IND. SPECIES CONC. K IN

 THE EXCHANGE EQUILIBRIUM J ON EXCHANGER I

 I= 1

 K= 1 2 3 4 5 6 7 8 9 10 11 12 13 14

15 16 17 18

 J=1 0.0 2.0 -1.0 0.0 0.0 0.0 0.0 0.0 -2.0 1.0 0.0 0.0 0.0 0.0

 J=2 0.0 2.0 0.0 -1.0 0.0 0.0 0.0 0.0 -2.0 0.0 1.0 0.0 0.0 0.0

 J=3 -1.0 1.0 0.0 0.0 0.0 0.0 0.0 1.0 -1.0 0.0 0.0 0.0 0.0 0.0

 SOLID NUMBER SOLUBILITY PRODUCT

 1 0.47485E-09

 2 0.70000E-04

 3 0.47315E+23

 4 0.56045E+17

EXCHANGE EQLM. (I) ON SURF. BETAS(I)

 1 0.25000E+01

 2 0.29400E+01

 EXPONENT OF THE IND. SPECIES CONC. K IN

 THE EXCHANGE EQUILIBRIUM J ON SURFACTANT

 K= 1 2 3 4 5 6 7 8 9 10 11 12 13 14

15 16 17 18

 J=1 0.0 2.0 -1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -2.0 1.0 0.0

 J=2 0.0 2.0 0.0 -1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -2.0 0.0 1.0
Section 8 - EQBATCH Program Description

101

 INITIAL AQ. ELEMENTAL CONCS.(MOLES/L)

 1 2 3 4 5 6 7 8

9 10

 .13500E-02 .15000E-02 .47000E-01 .10430E+00 .11104E+03 .19000E-01

 INITIAL CHLORIDE CONC.(EQ/LITER) = 0.5900E-01

 INITIAL SURFACTANT CONC.(EQ/LITER) = 0.0000E+00

 INITIAL SOLID CONCS.(MOLES/LITRE PV)

 1 2 3 4 5 6 7 8

9 10

 .20000E+01 .00000E+00 .00000E+00 .00000E+00

 INITIAL ADSORED IONS(MOLES/LITRE PV)

 1 2 3 4 5 6 7 8

9 10

Table 8.21. Sample Output of EQBATCH Program (cont.)

 .50000E-01 .25000E+00 .10000E-01 .20000E-02

 INITIAL GUESSES OF INDEPENDENT CONCENTRATIONS

 1.200077231590000E-006 1.000000000000000E-002 1.000000000000000E-005

 4.616423363603000E-006 3.092684582095000E-009 5.399766653843000E-004

 55.4999931465000 1.000000000000000E-006 1.000000000000000E-002

 1.000000000000000E-003 1.000000000000000E-004 1.000000000000000E-006

 1.000000000000000E-008 1.000000000000000E-008

 END OF REACTION MODULE INPUT DATA

 RESIDUALS AT THE END OF 18 ITERATIONS IDAMP = 1

0.000E+00 0.000E+00 -.555E-16 0.142E-13 0.000E+00 0.000E+00 0.000E+00 0.999E-15

0.666E-15 0.000E+00 0.000E+00 -.486E-16 -.245E-12 0.000E+00

FLUID SPECIES CONCENTRATIONS

0.7849769316806E-08 0.7529549105585E-01 0.2274287723632E-05 0.5387616767727E-04

0.2087910843759E-03 0.1899585758862E-01 0.5548234868752E+02 0.3491206679296E-10

0.2667875232078E-07 0.5265052518920E-06 0.5151920872179E-04 0.2320708633881E-05

0.1285770268228E-05 0.3504100430504E-01 0.5121744571970E-03 0.7525913499000E-06

0.5384043523296E-04 0.1821702742749E-05

 SOLID SPECIES CONCENTRATIONS

0.2011131391413E+01 0.0000000000000E+00 0.0000000000000E+00 0.0000000000000E+00

 SORBED SPECIES CONCENTRATIONS

0.7318622640939E-01 0.2600025853849E+00 0.2150482869699E-03 0.3340545815905E-02

 SURF. ASSOCIATED CATION CONCS.

0.1900192355929E-01 0.6880963477427E-08 0.1916937102421E-06

 ELEMENT NO. OLD TOTAL NEW TOTAL ERROR

 1 0.2011350000000E+01 0.2011350000000E+01 0.0000000000000E+00

 2 0.3500000000000E-02 0.3500000000000E-02 0.0000000000000E+00

 3 0.2047000000000E+01 0.2047000000000E+01 0.0000000000000E+00

 4 0.3543000000000E+00 0.3543000000000E+00 0.2220446049250E-15
Section 8 - EQBATCH Program Description

102

 5 0.1110930000000E+03 0.1110930000000E+03 -0.1110223024625E-15

 6 0.1900000000000E-01 0.1900000000000E-01 0.0000000000000E+00

 ISOLN= 14

 COMPUTATION TIME= 0.00000E+00

 INITIAL CONDITIONS FOR UTCHEM

 C1I,C2I,C50,C60,C12I,C13I,C14I,C15I

 0.999997928798602 0.985633815850358 5.900000000000000E-002

 7.120600401936443E-006 9.429741461513917E-002 111.019813773591

 3.189083681891565E-004 7.173721717434252E-002

 A- + HA(WATER) = 4.142411376630453E-006 HA(OIL) = 2.915115922082504E-002

 VOLUMES FRACTIONS OF WATER,OIL AND ACID

 0.601998753136758 0.392282258708443 5.718988154799202E-003

 EQUIV. OF ACID/LITRE TOTAL VOL 1.143797630959840E-002

 EQK( 12) EQK( 18) 6.249160552927827E-013

 6.249160552927826E-005

 CSLDI(I),I=1,NSLD UNIT=MOLES/LITER PV

 1.21069859002472 0.000000000000000E+000 0.000000000000000E+000

 0.000000000000000E+000

 CSORBI(I),I=1,NSORB UNIT=MOLES/LITER PV

 4.405801704523635E-002 0.156521232214020 1.294588006200680E-004

 2.011004415971278E-003

 EXCHANGE CAPACITY(MEQ/ML PV)= 0.204860175692439
Section 8 - EQBATCH Program Description

103

Table 8.22. Sample UTCHEM Input File Generated From EQBATCH Program

 FOLLOWING LINES OF DATA FORMATED FOR UTCHEM

 7 18 4 4 3 1

 7 1 4 12

 5 4 1 2 3

 6

 CALCIUM 2

 MAGNESIUM 2

 CARBON (AS CARBOBATES) -2

 SODIUM 1

 HYDROGEN (REACTIVE) -1

 ACID (PETROLEUM) -1

 CHLORINE

 HYDROGEN ION

 SODIUM ION

 CALCIUM ION

 MAGENSIUM ION

 CARBONATE ION

 PETROLEUM ACID IN OIL

 WATER

 CALCIUM MONOHYDROXIDE ION

 MAGNESIUM MONOHYROXIDE ION

 CA (HC03) +

 MG (HCO3) +

 PETRLEUM ACID ANION

 HYDROXIDE ION

 BICARBONATE ION

 DISSOLVED CARBON MONOHYDROXIDE

 AQUEOUS CALCIUM CARBONATE

 AQUEOUS MAGNESIUM CARBONATE

 PETROLEUM ACID IN OIL

 CALCIUM CARBONATE(SOLID)

 MAGNESIUM CARBONATE (SOLID)

 CALCIUM HYDROXIDE (SOLID)

 MAGNESIUM HYDROXIDE(SOLID) (*

 SORBED HYDROGEN ION

 SORBED SODIUM ION

 SORBED CALCIUM ION

 SORBED MAGNESIUM ION (*

 SURF. ASSOCIATED SODIUM ION

 SURF. ASSOCIATED CALCIUM ION

 SURF. ASSOCIATED MAGNESIUM ION

 4

 0. 0. 1. 0. 0. 0. 0. 1. 0. 1. 0. 0. 0. 0. 0.

 1. 0. 0.

 0. 0. 0. 1. 0. 0. 0. 0. 1. 0. 1. 0. 0. 0. 0.

 0. 1. 0.

 0. 0. 0. 0. 1. 0. 0. 0. 0. 1. 1. 0. 0. 1. 1.

 1. 1. 0.

0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.

 0. 0. 0.

 1. 0. 0. 0. 0. 1. 2. 1. 1. 1. 1. 0. 1. 1. 2.

 0. 0. 1.

 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 1. 0. 0. 0.

 0. 0. 1.

 1. 0. 1. 0.

 0. 1. 0. 1.

 1. 1. 0. 0.

 0. 0. 0. 0.

 0. 0. 2. 2.

 0. 0. 0. 0.

 0. 0. 1. 0.

 0. 0. 0. 1.

 0. 0. 0. 0.

 0. 1. 0. 0.
Section 8 - EQBATCH Program Description

104

 1. 0. 0. 0.

 0. 0. 0. 0.

 0. 1. 0.

 0. 0. 1.

 0. 0. 0.

Table 8.22. Sample UTCHEM Input File Generated From EQBATCH Program (cont.)

 1. 0. 0.

 0. 0. 0.

 0. 0. 0.

 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

 0.0 0.0

 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

 0.0 0.0

 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

 0.0 0.0

 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

 0.0 0.0

 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

 0.0 0.0

 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0

 0.0 0.0

 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0

 0.0 0.0

-1.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

 0.0 0.0

-1.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

 0.0 0.0

 1.0 0.0 1.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

 0.0 0.0

 1.0 0.0 0.0 1.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

 0.0 0.0

-1.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0

 0.0 0.0

-1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0

1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

 0.0 0.0

 2.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

 0.0 0.0

 0.0 0.0 1.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

 0.0 0.0

 0.0 0.0 0.0 1.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

 0.0 0.0

 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0

 0.0 0.0

 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0

 0.0 0.0

 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0

 0.0 0.0

 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0

 0.0 0.0

 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0

 0.0 0.0

 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0

 0.0 0.0

 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

 1.0 0.0

 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

 0.0 1.0

 0.0 0.0 1.0 0.0 1.0 0.0 0.0

 0.0 0.0 0.0 1.0 1.0 0.0 0.0

-2.0 0.0 1.0 0.0 0.0 0.0 0.0

-2.0 0.0 0.0 1.0 0.0 0.0 0.0

 1.0 1.0 2.0 2.0 -2.0 0.0 0.0 1.0 1.0 1.0 1.0 -1.0

-1.0 -1.0 0.0 0.0 0.0 0.0

 1.0 1.0 2.0 2.0
Section 8 - EQBATCH Program Description

105

0.1000000000000E+01 0.1000000000000E+01 0.1000000000000E+01

0.1000000000000E+01 0.1000000000000E+01 0.1000000000000E+01

0.1000000000000E+01 0.1205000000000E-12 0.3887100000000E-11

0.1412500000000E+12 0.5834500000000E+12 0.6249160552928E-12

0.1009300000000E-13 0.2138000000000E+11 0.3981000000000E+17

0.1584900000000E+04 0.4786300000000E+04 0.6249160552928E-04

0.7930000000000E+01 0.5200000000000E+01 0.2700000000000E+07

 0.0 2.0 -1.0 0.0 0.0 0.0 0.0 0.0 -2.0 1.0 0.0 0.0

 0.0 0.0

 0.0 2.0 0.0 -1.0 0.0 0.0 0.0 0.0 -2.0 0.0 1.0 0.0

 0.0 0.0

Table 8.22. Sample UTCHEM Input File Generated From EQBATCH Program (cont.)

-1.0 1.0 0.0 0.0 0.0 0.0 0.0 1.0 -1.0 0.0 0.0 0.0

 0.0 0.0

-1.0 -1.0 0.0

0.2048601756924E+00

0.4748510000000E-09 0.7000000000000E-04 0.4731500000000E+23

0.5604500000000E+17

1.0 2.0 2.0

0.2500000000000E+01 0.2940000000000E+01

 0.0 2.0 -1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -2.0

 1.0 0.0

 0.0 2.0 0.0 -1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -2.0

 0.0 1.0

0.1900192355929E-01 0.6880963477427E-08 0.1916937102421E-06

0.5900000000000E-01 0.7120600401936E-05

0.9429741461514E-01 0.1110198137736E+03 0.3189083681892E-03

0.7173721717434E-01 0.4142411376630E-05

0.2915115922083E-01

0.7849769316806E-08 0.7529549105585E-01 0.2274287723632E-05

0.5387616767727E-04 0.2087910843759E-03 0.1899585758862E-01

0.5548234868752E+02

0.1210698590025E+01 0.0000000000000E+00 0.0000000000000E+00

0.0000000000000E+00

0.4405801704524E-01 0.1565212322140E+00 0.1294588006201E-03

0.2011004415971E-02

0.9999979287986E+00 0.9856338158504E+00

0.1000000000000E-07 0.5000000000000E+03
105

Section 9

A 3-D NAPL Flow and Biodegradation Model

Biodegradation capabilities have been added to a three-dimensional, multi-phase, multi-component porous

media flow model. The model simulates the transport and biodegradation of lighter-than-water nonaqueous

phase liquids (LNAPLs) and denser-than-water nonaqueous phase liquids (DNAPLs). The biodegradation

model describes biological transformation of the organic contaminants originating from NAPL sources, and

can accommodate multiple substrates, electron acceptors, and biological species. The biodegradation model

includes inhibition, sequential use of electron acceptors, and cometabolism. Example simulations illustrate

the model capabilities.

9.1 Introduction

The University of Texas is completing improvements to a multi-phase flow simulator called UTCHEM.

Advanced biodegradation capabilities have recently been incorporated into UTCHEM that allow both the

flow of nonaqueous phase liquids (NAPLs) and the fate of organic NAPL constituents to be described

within the same model. This paper describes the biodegradation model components, discusses the

biodegradation model equations and features, and provides two example UTCHEM simulations that

demonstrate some of the capabilities of the combined NAPL flow and biodegradation model.

9.2 Model Description and Features

UTCHEM is a multi-phase, multi-component, three-dimensional, numerical model that simulates the fate

and transport of both dissolved and nonaqueous phase organic contaminants in porous media. The model

describes flow of the NAPL resulting from capillary, gravity and pressure forces. Dispersion of organic

constituents in each phase is also modeled. The model can be used to simulate spills of either lighter-thanwater NAPLs (LNAPLs) or denser-than-water NAPLs (DNAPLs). The transfer of organic contaminants

from the NAPL to the aqueous phase is described through either equilibrium partitioning or a linear driving

force nonequilibrium mass transfer model. Adsorption of organic constituents is modeled through

equilibrium partitioning. An arbitrary number of injection and pumping wells can be specified so that

bioremediation schemes can be modeled and optimized. The full development of the UTCHEM flow

model is described in detail by Delshad et al. [1996] and Datta Gupta et al. [1986].

UTCHEM simulates the biodegradation of chemical compounds that can serve as substrates (carbon and/or

energy sources) for microorganisms. The model simulates the destruction of substrates, the consumption of

electron acceptors (e.g., oxygen, nitrate, etc.), and the growth of biomass. Substrates can be biodegraded

by free-floating microorganisms in the aqueous phase or by attached biomass present as microcolonies in

the manner of Molz et al. (1986). Multiple substrates, electron acceptors and biological species are

accommodated by the model. Important assumptions for the biodegradation model are:
Section 9 - A 3-D NAPL Flow and Biodegradation Model

106

1. Biodegradation reactions occur only in the aqueous phase.

2. Microcolonies are fully penetrated; i.e., there is no internal resistance to mass transport within the

attached biomass.

3. Biomass is initially uniformly distributed throughout the porous medium.

4. Biomass is prevented from decaying below a lower limit by metabolism of naturally occurring

organic matter unless cometabolic reactions act to reduce the active biomass concentrations below

natural levels.

5. The area available for transport of organic constituents into attached biomass is directly proportional

to the quantity of biomass present.

6. The number of cells per microcolony, biomass density, and microcolony volume are constant, so

that mass per microcolony is also constant.

The biodegradation model includes the following features:

• Monod, first-order, or instantaneous biodegradation kinetics.

• Formation of biodegradation by-products.

• External mass transfer resistances to microcolonies (mass transfer resistances can be ignored by the

user if desired).

• Inhibition of biodegradation by electron acceptors and/or toxic substrates.

• Nutrient limitations to biodegradation reactions.

• First-order abiotic decay reactions.

• Enzyme competition between multiple substrates.

• Modeling of cometabolism with transformation capacities and reducing power limitations using the

model of Chang and Alvarez-Cohen [1995].

• Biodegradation reactions in both the vadose and saturated zones.

9.3 Biodegradation Equations and Solution Procedure

The biodegradation model equations describe the transport of substrate and electron acceptor from the

aqueous phase into attached biomass, the loss of substrate and electron acceptor through biodegradation

reactions, and the resulting growth of the free-floating or attached biomass. The flow and biodegradation

system is solved through operator splitting, in which the solution to the flow equations is used as the initial

conditions for the biodegradation reactions. This approach is convenient because modifications can be

made to the system of biodegradation equations without having to reformulate the partial differential

equations that describe advection and dispersion.

The biodegradation equations comprise a system of ordinary differential equations that must be solved at

each gridblock and each time step after the advection and dispersion terms are calculated. Because the mass

transfer terms can make the system of equations stiff, the system is solved using a Gear's method routine
Section 9 - A 3-D NAPL Flow and Biodegradation Model

107

published by Kahaner et al. [1989]. The characteristics and numerical solution of this system of equations

is discussed by de Blanc et al. [1996b].

For a simple system of a single substrate, electron acceptor and biological species, the system of

biodegradation equations is:

dS

dt

= −

βκX 

mc

(S − S )−

μmaxX

Y

S

Ks + S

 

  

 

  A

Ka + A

 

  

 

  − kabioS (9.1)

dS 

dt

= −

βκ

Vc

(S − S )−

μ maxρx

Y

S 

Ks + S 

 

  

 

  A 

Ka + A 

 

  

 

  − kabioS (9.2)

dA

dt

= −

βκX 

mc

(A − A )−

μ maxXE

Y

S

Ks + S

 

  

 

  A

Ka + A

 

  

 

  (9.3)

dA 

dt

= −

βκ

Vc

(A − A )−

μmaxρxE

Y

S 

Ks + S 

 

  

 

  A 

Ka + A 

 

  

 

  (9.4)

dX

dt

= μmaxX

S

Ks + S

 

  

 

  A

Ka + A

 

  

 

  − bX (9.5)

dX 

dt

= μ maxX 

S 

Ks + S 

 

  

 

  A 

Ka + A 

 

  

 

  − bX (9.6)

where:

S = aqueous phase substrate concentration (ML-3)

S = substrate concentration in attached biomass (ML-3)

A = aqueous phase electron acceptor concentration (ML-3)

A = electron acceptor concentration in attached biomass (ML-3)

X = aqueous phase concentration of unattached biomass (ML-3)

X = attached biomass concentration; mass of attached cells per volume of aqueous phase

(ML-3)

E = mass of electron acceptor consumed per mass of substrate biodegraded

β = surface area of a single microcolony (L2)

k = mass transfer coefficient (LT-1)

μmax = maximum specific growth rate (T-1)

ρx = biomass density; mass of cells per volume of biomass (ML-3)

Vc = volume of a single microcolony (L3)

mc = mass of cells in a single microcolony; mc = rxVc (M)

Y = yield coefficient; mass of cells produced per mass of substrate biodegraded
Section 9 - A 3-D NAPL Flow and Biodegradation Model

108

Ks = substrate half-saturation coefficient (ML-3)

Ka = electron acceptor half-saturation coefficient (ML-3)

b = endogenous decay coefficient (T-1)

kabio = first-order abiotic rate constant (T-1)

t = time (T)

These equations are similar to the system of equations solved by Molz et al. [1986] and Chen et al. [1992].

Equation 9.1 includes three mechanisms for loss of substrate from the aqueous phase: diffusion of substrate

across a stagnant liquid layer into attached biomass; biodegradation of substrate by unattached

microorganisms in the aqueous phase; and abiotic loss of the substrate through first-order reactions. The

biodegradation reactions are limited by both the substrate and electron acceptor concentrations through the

Monod terms.

Equation 9.2 describes the loss of substrate within attached biomass and is written for a single microcolony

(Molz et al., 1986). This equation describes the diffusion of substrate into attached biomass,

biodegradation of the substrate within the biomass, and abiotic decay of the substrate.

Equations 9.3 and 9.4 describe the loss of the electron acceptor. These equations are of the same form as

Eqs. 9.1 and 9.2 in that they describe diffusion across a liquid film and loss in biodegradation reactions.

The biodegradation rate expressions are multiplied by the factor E, the mass of electron acceptor consumed

per mass of substrate biodegraded. Equations 9.5 and 9.6 describe the growth and decay of unattached and

attached biomass, respectively. The relationship between the attached biomass concentration X appearing

in Eqs. 9.1, 9.3 and 9.6 to the biomass density, microcolony volume and microcolony mass is

X =

Ccρbmc

nφ

(9.7)

where Cc is the number of cells per mass of solid, ρb is the bulk density, n is the number of cells per

microcolony (a constant), and φ is the porosity. Since the biomass density, number of cells per

microcolony, porosity, and mass per microcolony are assumed to be constant, changes in X actually

correspond to changes in Cc, or alternately, to Cc/n, the number of microcolonies (Molz et al., 1986). The

area available for transport of species from the aqueous phase to the biomass is directly proportional to X 

because the surface area per microcolony is constant.

If external mass transport is ignored, then the system of six equations is reduced to three equations

consisting of Eq. 9.6 and a single equation each for loss of the substrate and electron acceptor:

dS

dt

= −

μmaxX 

Y

S

Ks + S

 

  

 

  A

Ka + A

 

  

 

  − k abioS (9.8)

dA

dt

= −

μmaxX E

Y

S

Ks + S

 

  

 

  A

Ka + A

 

  

 

  (9.9)

where X is the concentration of attached biomass and all other concentrations are aqueous phase

concentrations.
Section 9 - A 3-D NAPL Flow and Biodegradation Model

109

When biodegradation reactions that involve more than one substrate are being modeled, equations of the

same form as Eqs. 9.1 and 9.2 (or 9.8) are solved for each additional substrate. Similarly, equations of the

form of Eqs. 9.3 and 9.4 (or 9.9) are solved for each additional electron acceptor. Substrates can be

biodegraded by microorganisms using more than one electron acceptor, and each electron acceptor can be

used for biodegradation of multiple substrates.

When substrate competition is considered, the half-saturation coefficient of each Monod term is modified in

the following manner (Bailey and Ollis, 1986):

S1

Ks,1 1+

S2

Ks,2

 

  

 

  + S1

where:

S1, S2 = concentration of substrates 1 and 2, respectively (ML-3)

Ks,1, Ks,2 = half-saturation coefficients of substrates 1 and 2, respectively (ML-3)

If sequential electron acceptor utilization occurs (e.g., oxygen consumption followed by consumption of

nitrate), then the biodegradation rate expressions in the equations for substrate loss, electron acceptor

consumption and biomass growth are multiplied by an inhibition factor of the form (Widdowson et al.,

1988):

I

I + Cihb

 

  

 

  

where I is an experimentally determined inhibition constant. The inhibition factor approaches 0 as the

concentration of the inhibiting substance Cihb increases. For nitrate respiration, for example, this term

keeps denitrification rates very small until oxygen is nearly exhausted.

When cometabolic reactions are considered, the equations describing the loss of cometabolite and attached

biomass growth are, in the case of no mass transfer resistances (Chang and Alvarez-Cohen, 1995):

dC

dt

= −kcX 

C

Kc + C

 

  

 

  A

Ka + A

 

  

 

  R

Kr + R

 

     (9.10)

dX 

dt

= −

μmax,sX 

Y

S

Ks + S

 

  

 

  A

Ka + A

 

  

 

  R

Kr + R

 

     −

kcX 

Tc

C

Kc + C

 

  

 

  A

Ka + A

 

  

 

  R

Kr + R

 

     − bX (9.11)

where kc is the maximum specific cometabolite biodegradation rate (ML-3T-1), C is the aqueous phase

cometabolite concentration, R is the reducing power (NAD(P)H) concentration within the cells, Kr

 is the

NAD(P)H half-saturation constant, Kc is the cometabolite half-saturation coefficient, μmax,s is the

maximum specific growth rate on growth substrate, and Tc is the transformation capacity, defined as the

maximum possible mass of substrate biodegraded per mass of biomass. The second expression in Eq. 9.11

describes the deactivation of biomass through cometabolism reactions, which can produce toxic by-products

that damage cells (Chang and Alvarez-Cohen, 1995). When reducing power limitations are considered, an
Section 9 - A 3-D NAPL Flow and Biodegradation Model

110

equation is also needed to describe the production of NAD(P)H by the growth substrate and the

consumption of NAD(P)H by the cometabolite:

dR

dt

= −kcErcX 

C

Kc + C

 

  

 

  A

Ka + A

 

  

 

  R

Kr + R

 

     +

μmaxErpX 

Y

S

Ks + S

 

  

 

  A

Ka + A

 

  

 

  R

Kr + R

 

     (9.12)

where Erc is the mass of NAD(P)H consumed per mass of cometabolite biodegraded, and Erp is the mass of

NAD(P)H produced per mass of growth substrate biodegraded.

9.4 Example Simulations

The multi-phase flow and biodegradation capabilities of the model are demonstrated through the simulation

of hypothetical LNAPL and DNAPL spills. In these simulations, the modeling domain consists of a

homogeneous, initially uncontaminated, confined aquifer that is 125 m long by 54 m wide by 6 m thick (see

Fig. 9.1). The domain is simulated with 25 gridblocks in the x direction, 11 gridblocks in the y direction,

and 5 gridblocks in the z direction. Groundwater is flowing in the positive x direction (left to right in all

figures) with an average velocity of 0.1 m/day. Other flow and physiochemical parameters are listed in

Table 9.1. The spills are modeled by injecting NAPL into the center of gridblock (x = 5, y = 6, z = 1),

which is approximately 22 meters from the left boundary. All chemical species are assumed to be nonadsorbing. There is no air phase in these simulations; the top boundary is a no-flow boundary.

For both of these examples, local equilibrium is assumed between the NAPL and the aqueous phase, so that

the concentration of organic constituents in the aqueous phase is calculated by the partitioning relationship:

Ci,aq = Ci,solxi,NAPL (9.13)

where Ci,aq is the aqueous phase concentration of component i, Ci,sol is the aqueous phase solubility of

component i, and xi,NAPL is the volume fraction of component i in the NAPL.

9.4.1 LNAPL Simulation Example

Sequential use of electron acceptors and equilibrium partitioning of multiple components into the aqueous

phase are illustrated with an example LNAPL simulation. The LNAPL example simulates a leak of 3.8 m3

of gasoline containing approximately 1% by volume of benzene and 6% by volume of toluene into a

shallow, confined aquifer. The leak is assumed to occur over a four-day period. The groundwater initially

contains 8 mg/L oxygen and 10 mg/L nitrate. Parameters used for this simulation are listed in Table 9.2.

Figure 9.2 shows the NAPL saturation history in a vertical slice down the center of the aquifer in the x-z

plane. As seen in Fig. 9.2, the NAPL moves little once the NAPL lens is established. The NAPL lens

gradually decreases in size as the organic constituents dissolve into the flowing groundwater.

As the benzene and toluene partition out of the gasoline into the aqueous phase, they become available to

microorganisms as substrates. For simplicity, a single population of microorganisms capable of

biodegrading the benzene and toluene is assumed to exist in the aquifer. This biological species

biodegrades both benzene and toluene aerobically and biodegrades toluene anaerobically with nitrate as the

electron acceptor. Abiotic decay and biodegradation by free-floating microorganisms are assumed to be

negligible (kabio and X are 0). Biodegradation kinetic parameters used for the simulation were obtained

from Chen et al. [1992].
Section 9 - A 3-D NAPL Flow and Biodegradation Model

111

Figure 9.3 compares the concentration of benzene in the aqueous phase at 500 days to the concentration of

benzene that would exist if no biodegradation reactions were occurring. This figure shows that significant

biodegradation of dissolved benzene has occurred. The toluene plume is also shown in Fig. 9.3. Although

the toluene solubility is three times less than the benzene solubility, the maximum toluene concentration in

the aqueous phase is higher than the maximum benzene concentration because its concentration in the

gasoline is six times the benzene concentration of the gasoline. Toluene concentrations are nearly as low as

benzene concentrations at the fringes of the plume because toluene is biodegraded both aerobically and

anaerobically, where oxygen is exhausted, but the benzene is not.

The concentrations of benzene, toluene, oxygen and nitrate at 500 days are compared in Fig. 9.4. Oxygen

immediately downgradient of the spill is practically exhausted. Nitrate is also nearly exhausted from the

area immediately downgradient of the spill because sufficient time has elapsed since oxygen depletion to

allow denitrification to occur. However, at the forward edge of the plume, relatively high nitrate

concentrations still exist in areas where oxygen has been depleted, but not exhausted.

9.4.2 DNAPL Simulation Example

Different model capabilities are illustrated with a DNAPL simulation in which trichloroethylene (TCE) is

biodegraded through cometabolism. In this simulation, 0.028 m3 of TCE are spilled in a single day. The

cometabolic process is illustrated by injecting water containing methane through five injection wells located

approximately 24 meters downgradient of the spill. The injected water contains 20 mg/L methane and 8

mg/L oxygen. The water injection rate is 1.4 m3 per day per well. The groundwater is assumed to contain

8 mg/L oxygen. Parameters used for the DNAPL simulation example are listed in Table 9.3.

A population of methanotrophic microorganisms, capable of biodegrading TCE aerobically through

cometabolism, is assumed to exist in the aquifer. The methanotrophs use methane as the primary substrate

and oxygen as the electron acceptor. TCE biodegradation is assumed to reduce the active biomass and

consume reducing power of the methanotrophs, so that TCE biodegradation both reduces the active biomass

concentration and reduces the active biomass's biodegradation effectiveness. Once biomass has become

deactivated, it does not become active again. Biodegradation rate parameters were obtained from Chang

and Alvarez-Cohen [1995]. External mass transport of chemical species from the aqueous phase to the

biomass was ignored for this example.

The effect of the methane injection wells is illustrated in Fig. 9.5, where concentrations of TCE, a

hypothetical TCE tracer, oxygen and methane are shown at 170 days. The TCE tracer is simply TCE that is

not allowed to biodegrade in the model so that the effects of biodegradation can be seen. Concentration

contours of the different constituents are shown in the top 1.2-m layer of the aquifer. Oxygen is depleted

downgradient of the plume, but only a small fraction of the oxygen is consumed upgradient of the methane

injection wells. Most of the oxygen upgradient of the wells remains because the high TCE concentrations

deactivate the biomass and consume reducing power, preventing the TCE from biodegrading. Even with a

small TCE spill, TCE concentrations in the aquifer are so high that most biomass immediately

downgradient of the spill is rapidly deactivated. Significant TCE biodegradation occurs only where

appreciable methane is present to regenerate the microorganism's reducing power and where TCE

concentrations are low. These effects can be seen in Fig. 9.5. The high concentration contours of the TCE

and TCE tracer are nearly the same, but biodegradation of the TCE causes a slight retardation in the

progress of the TCE plume at low concentrations.
Section 9 - A 3-D NAPL Flow and Biodegradation Model

112

X

Y

Z

54 m, ny = 11

6 m, nz = 5

125 m, nx = 25

spill

location

direction of groundwater flow

Figure 9.1. Modeling domain size and discretization.

d

e

pth (m)

4 days 0

3

0 38

distance in direction of

groundwater flow (m)

0.0 0.15 0.3

Oil saturation

d

e

pth (m)

44 days

0

3

0 38

300 days 0

3

0 38

d

e

pth (m) d

e

pth (m)

500 days

0

3

0 distance in direction of 38

groundwater flow (m)

spill

source

Figure 9.2. NAPL saturation history in the vicinity of a hypothetical

gasoline spill. The figure shows a vertical section along the x axis in the

center of the aquifer. This gasoline spill is simulated by injecting 3.8 m3 of

gasoline at a depth 0.6 m below the top of the confined aquifer.
Section 9 - A 3-D NAPL Flow and Biodegradation Model

113

0

d

e

pth (m)

6

0 30.5 61 91.5 122

20

15

10 5 1

Toluene concentration - with biodegradatio n

10 5

1

0

d

e

pth (m)

6

0 30.5 61 91.5 122

20

15 10 5 1

Toluene concentration - no biodegradatio n

10 5

1

0

d

e

pth (m)

6

0 30.5 61 91.5 122

10

5 1

1

Benzene concentration - with biodegradati

n

0

d

e

pth (m)

6

0 30.5 61 91.5 122

10

5 15

1

Benzene concentration - no biodegradatio n

distance in direction of groundwater flow (m)

0 15 30

Concentration (mg/L)

Figure 9.3. Comparison of benzene and toluene concentrations in the

aqueous phase 500 days after a gasoline spill. The figure shows a vertical

section along the x axis in the center of the aquifer. Gasoline was injected

at the location of the white circle. Concentrations of benzene and toluene

are compared for the assumptions of no biodegradation and

biodegradation of the two compounds.
Section 9 - A 3-D NAPL Flow and Biodegradation Model

114

0

5

1 0

1 5

2 0

2 5

3 0

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0

dist anc e in direc t io n of gro undw at er f low ( m )

oxy gen

t oluene

benzene

n it r at e

benz ene( no

bio degradat ion)

concentration(mg/L)

Figure 9.4. Concentrations of benzene without

biodegradation, benzene with biodegradation,

toluene, oxygen, and nitrate in upper 1.2 m of

aquifer along aquifer center line at 500 days.

10

-5

10

-3

10 1 -1

10

0 30.5 61 91.5 122

TCE tracer

10

-5

10

-3

10

-1

10 1

0 30.5 61 91.5 122

TCE

10

-3

10

-1 1

10

-3

10

-1 1

0 30.5 61 91.5 122

Methane

0 30.5 61 91.5 122

Oxygen

distance in direction of groundwater flow (m) distance in direction of groundwater flow (m)

TCE Source Methane injection well

5 1 10

-3

1 5

Figure 9.5. Plan view of TCE, a hypothetical TCE tracer, methane and oxygen

concentrations in the upper 1.2 m of a confined aquifer 170 days after a TCE

spill. All concentrations are mg/L. Groundwater is flowing from left to right at 0.1

m/d. Shading is present for visualization purposes only and does not correspond

to specific chemical concentrations. Assumptions are: TCE solubility = 1,100

mg/L; initial oxygen concentration = 8 mg/L; methane concentration in injected

water = 20 mg/L. Biodegradation rate parameters are from Chang and AlvarezCohen [1995].
Section 9 - A 3-D NAPL Flow and Biodegradation Model

115

Table 9.1. Flow Parameters for All Simulations

average velocity, v (m/d) 0.1

porosity, φ 0.38

bulk soil density, ρb (g/cm3) 1.64

longitudinal dispersivity, αL (m) 5

transverse dispersivity, αT (m) 0.625

initial oxygen concentration, Ao (mg/L) 8.0

initial nitrate concentration, An (mg/L) 10.0

Table 9.2. Parameters for LNAPL Simulation Example

Simulation parameters

Spill volume (m3) 3.8

Spill duration (d) 4

Physiochemical parameters

Density of gasoline (g/cm3) 0.87

Density of benzene (g/cm3) 0.87

Density of toluene (g/cm3) 0.86

Solubility of benzene (mg/L) 1,778

Solubility of toluene (mg/L) 500

Initial benzene concentration in NAPL (volume %) 1.1

Initial toluene concentration in NAPL (volume %) 6.1

Mass transfer coefficient for benzene, κb (m2/d) 4.60 X 10-1

Mass transfer coefficient for toluene, κt

 (m2/d) 4.26 X10-1

Mass transfer coefficient for oxygen, κo (m2/d) 7.92 X 10-1

Mass transfer coefficient for nitrate, κn (m2/d) 6.52 X 10-1

Microbial parameters (from Chen et al., 1992)

Initial cell concentration, Cc (cells/g soil) 3.8 X 105

Colony population density, n (cells/microcolony) 100

Biomass density, ρx (g/cm3) 1.0

Microcolony surface area, β (m2/microcolony) 1.19 X 10-10

Microcolony volume, Vc (m3/microcolony) 1.0 X 10-16

Initial attached biomass concentration, X (mg/L) 1.64

Maximum specific growth rate on benzene, μmax,b (d-1)

4.15

Maximum specific growth rate on toluene, μmax,t (d-1)

4.95

Yield coefficient for benzene, Yb (g cells/g benzene) 0.5

Yield coefficient for toluene, Yt (g cells/g toluene) 0.5

Half-saturation coef. of benzene for oxygen respiration, Ks

bo

(mg/L)

12.2
Section 9 - A 3-D NAPL Flow and Biodegradation Model

116

Half-saturation coef. of toluene for oxygen respiration, Ks

to

(mg/L)

17.4
Section 9 - A 3-D NAPL Flow and Biodegradation Model

117

Table 9.2. Parameters for LNAPL Simulation Example

Half-saturation coef. of toluene for nitrate respiration, Ks

tn (mg/L) 17.4

Half-saturation coef. of oxygen for benzene biodeg., Ka

bo (mg/L) 0.1

Half-saturation coef. of oxygen for toluene biodeg., Ka

to (mg/L) 0.01

Half-saturation coef.of nitrate for toluene biodeg., Ka

tn (mg/L) 2.6

Endogenous decay coefficient, b (d-1)

0.1

Table 9.3. Parameters for DNAPL Simulation Example

Simulation parameters

Spill volume (m3) 0.028

Spill duration (d) 1

Physiochemical parameters

Density of NAPL (g/cm3) 1.46

Density of TCE (g/cm3) 1.46

Solubility of TCE (mg/L) 1,100

Initial TCE concentration in NAPL (volume %) 50

Microbial parameters

Initial biomass concentration, X (mg/L) 4.31

Maximum biodegradation rate of TCE, kc (mg TCE/mg cells-d) 4.2

Maximum specific growth rate for methane, μmax,m (d-1)

0.31

Yield coefficient for methane, Y (mg cells/mg methane) 0.33

TCE transformation capacity, Tc (mg TCE/mg cells) 0.1

Half-saturation coefficient for TCE, Kc (mg/L) 7.0

Half-saturation coefficient for methane, Ks (mg/L) 1.1

Half-saturation coefficient for reducing power, Kr (mmol of e-/L) 0.54

Reducing power production coefficient, Erp

(mmol e- produced/mg methane biodegraded)

0.5

Reducing power consumption coefficient, Erc

(mmol e- consumed/ mg TCE biodegraded)

0.15

Initial reducing power concentration in cells, (mmol e-/mg cells) 0.0005
117

Section 10

Well Models

10.1 Introduction

In this section, the well models in the UTCHEM simulator are described. The options available are:

• An arbitrary number of producers in any gridblock can be specified (Cartesian grid option only).

• Skin factor (S) and completion interval can be specified.

• Both the injection wells and the producers can be shut in or opened at anytime during the

simulation. The well type can also be changed during the simulation (e.g., an injector changed to a

producer).

• Each injection well can inject multiple slugs with different component concentrations.

• Wells can be completed in any direction parallel to the axes (Cartesian and Curvilinear grid options

only).

10.2 Vertical Wells with Cartesian or Curvilinear Grid Options

Two basic well conditions of constant flow rate or constant flowing bottomhole pressure are implemented.

Application of Darcy's law to a wellblock (i,j,k) results in:

 

Q = Ql

l =1

np

∑ = PI l

l=1

np

∑ Pwf − Pl

( ) (10.1)

where Pl = P1 + Pc1l and PI is the productivity index. For two-dimensional areal (x-y) and threedimensional simulation, the PI is given by:

 

PI l =

2π kxk y Δz

(0.15802) ln ro

rw

+ S

 

  

 

  

λrl (10.2)

and for one-dimensional and cross-sectional (x-z) simulation by:

 

PI l =

kxΔyΔz

0.15802 Δx

2

λrl(10.3)
Section 10 - Well Models

118

where the constant in the above equations is the unit conversion factors where the permeability is in Darcy

and gridblock size in ft and 

 

λrl =

krl

μl

 in cp-1 to result PI in (psi)-1.

The equivalent radius, ro

, is calculated using Peaceman's model (Peaceman, 1983):

ro

= 0.28

kx

ky

 

 

  

 

 

  

1 / 2

Δy

2

+

k y

k x

 

  

 

  

1/ 2

Δx

2

 

 

 

 

 

 

 

 

1/ 2

kx

ky

 

 

  

 

 

  

1/ 4

+

k y

k x

 

   

  

1/ 4

(10.4)

The well bottomhole following pressure in any layer k, Pwf,k

 is given by:

(Pwf )k = (Pwf )k−1 + γ k

 k = 2,..., nbz (10.5)

where nbz is the number of layers perforated and

γ k = γ k

Δz k

2

+ γ k−1

Δz k−1

2

(10.6)

γk are calculated from:

 

γ

k

=

γ l

PI l

l=1

np

∑

PI l

l=1

np

∑

(10.7)

For the producer wellblock, specific weights of the produced fluids, γl

, are used in the above calculations

while for the injection wells, the specific weights of the injected phases are calculated using:

 

γ l = (Cinj ( )k,l )

k=1

nc

∑ γ k (10.8)

10.2.1 Well Constraints for Injection Wells

10.2.1.1 Rate Constraint

When the phase injection rates, Qinj,l

, are specified, the positive injection rates are allocated to the

individual layer k that is perforated according to:
Section 10 - Well Models

119

 

Ql= Qinj,l

PI l

l=1

np

∑

PIl

l=1

np

∑

k=1

nbz

∑

(10.9)

The total injection rate for the ijk block is given by:

 

Q = Ql

l =l

np

∑ (10.10)

The above term is then added to the constant vector of the pressure equation at the ijk block. In Eq. 10.9, it

is assumed that the potential gradient between the wellbore and the gridblock pressure is the same for all the

layers in the reservoir model. Nolen and Berry [1972] have shown that including the potential differences

in Eq. 10.9 may result in stability problems. Equation 10.9 may give erroneous results in the case of large

vertical heterogeneity and especially when noncommunicating layers exist. However, in the absence of a

very low permeability zone or small crossflow, the above formulation does not produce a significant error.

10.2.1.2 Pressure Constraint

When bottomhole injection pressure for the first perforated layer, (Pwf)

ij,k=1, is specified, Eq. 10.1 is used.

The term 

 

PI l

l =1

np

∑ Pwf − Pc1l

( ) in Eq. 10.1 is added to the constant vector of the pressure equation for block

ijk and term 

 

PI l

l =1

np

∑ to the (P1

)

n+1 term (diagonal element in the pressure matrix).

After the pressure equation is solved, Eq. 10.1 is used to obtain the total injection rate at the end of the time

step, Q . The injected phase cuts for each layer are the same as the total injected cuts:

Ql Q

Qinj,

Qinj,l

l =1

np

∑

(10.11)

the phase injection rates, 

 

Qinj,l , specified as input values, are treated as phase cuts.

10.2.2 Well Constraints for Production Wells

10.2.2.1 Rate Constraint

When the total production rate, input as a negative value (Qprod) is specified, the withdrawal rate for each

layer k is calculated using:
Section 10 - Well Models

120

 

Q = Qprod

PIl

l=1

np

∑

PI l

l=1

np

∑

k=1

nbz

∑

(10.12)

and the produced phase cuts are then calculated using:

 

Ql = Q

λrl

λrl

l =1

np

∑

(10.13)

10.2.2.2 Pressure Constraint

When bottomhole pressure for a producer is specified, Eq. 10.1 is used to calculate the total production rate

(Q) in the same manner as was described above for the injection well on pressure constraint. The produced

phase cuts are then obtained from:

 

Ql = Q

PI l

PI l

l =1

np

∑

(10.14)

10.3 Vertical Wells with Radial Grid Option

The boundary conditions for the radial option are

• no vertical flow at the upper and lower boundaries

• a rate constraint well at the center of the reservoir,

• a constant pressure outer boundary that is treated the same as a pressure constraint injector/producer

well.

The phase productivity index in the gridblock ijk for the injection or production well is calculated as

 

PI l =

k xΔz

Δx

2

λrl(10.15)

10.3.1 Rate Constraint Injector

Equations 10.9 and 10.10 are used to calculate the rate allocation to each layer.

10.3.2 Rate Constraint Producer

Equations 10.12 and 10.13 are used to calculate the rate withdrawal from each layer.

10.3.3 External Boundary

The amount of fluid that crosses each layer k from the last gridblock at the open boundary is calculated by
Section 10 - Well Models

121

 

Q = P

l =1

np

∑ I

l

P1

( )

e

− P1( ) ( i= nr ) (10.16)

where the outer boundary aqueous phase pressure (P1)e is maintained at the initial pressure for the duration

of the simulation as:

P1

( )

e,k

= P1

( )

e, k−1

+ γ k for k = 2,..., nbz (10.17a)

where γ k

 is calculated from Eqs. 10.6 and 10.7. The phase productivity index is calculated as:

 

PI l = 6.3266 2πkxΔz

ln

r

e

r

i

λrl (10.17b)

where the permeability and radius of the outermost gridblock (i = nr) are used. The calculation is implicit

similar to that for the pressure constrained wells discussed above. Once the pressure is known, total rate for

each layer is calculated from Eq. 10.16. The phase cuts for the fluids crossing the boundary are calculated

from Eq. 10.14.

10.4 Horizontal Well with Cartesian or Curvilinear Grid Options

Horizontal wells use the same well model equations as vertical wells. Only parameters related to the

direction of the wellbore were modified. When the wellbore is parallel to the z direction, the calculation of

the productivity index uses the gridblock height, •z, the permeability in the x direction, kx

, and the

permeability in the y direction, ky

:

 

PI l =

2π kxky Δz

0.15802 ln ro

rw

 

  

 

  + S

 

  

 

  

λrl (10.18)

where the constant 0.15802 is a unit conversion factor. kx

 and ky are in Darcy, •z, ro, and rw are in ft, and

 

λrl = krl

/ μl

 is in cp

−1

. The equivalent wellblock radius, ro, is based on Peaceman [1983] and uses

wellblock properties in the x and y directions such as the dimensions •x and •y and the permeability values

kx

 and ky:

ro = 0.28

kx

ky

 

 

  

 

 

  

1/ 2

Δy

2

+

ky

kx

 

     

1 / 2

Δx

2

 

 

 

 

 

 

 

 

1/ 2

k x

k y

 

 

  

 

 

  

1/ 4

+

ky

kx

 

     

1 / 4

(10.19)

10.4.1 Productivity Index for Horizontal Wells

The productivity index calculations were generalized for horizontal wells parallel to either the x direction or

the y direction by taking into account the pertinent directional properties. When the wellbore is parallel to
Section 10 - Well Models

122

the x direction, the productivity index calculation uses •x as the wellblock dimension parallel to the

wellbore. Since the wellbore is perpendicular to the y and z directions, the productivity index calculation

uses the permeability in the y direction and the permeability in the z direction:

 

PI l =

2 π kykz Δx

0.15802 ln ro

rw

 

  

 

  + S

 

  

 

  

λrl (10.20)

When the wellbore is parallel to the y direction, the productivity index calculation uses •y as the wellblock

dimension parallel to the wellbore. Since the wellbore is perpendicular to the x and z directions, the

productivity index calculation uses the permeability in the x direction and the permeability in the z

direction:

 

PI l=

2 π kxkz Δy

0.15802 ln ro

rw

 

  

 

  + S

 

  

 

  

λrl

(10.21)

10.4.1.1 Equivalent Wellblock Radius for Horizontal Wells (Peaceman, 1983)

The calculations of the equivalent wellblock radius were also generalized for horizontal wells by taking into

account reservoir properties perpendicular to the direction of the wellbore. In case the wellbore is parallel

to the x direction, the equivalent wellblock radius, based on Peaceman [1983], uses wellblock properties in

the y and z directions such as the dimensions •y and •z and the permeability values ky and kz:

ro = 0.28

ky

kz

 

     

0.5

Δz

2 +

kz

k y

 

 

  

 

 

  

0.5

Δy

2

 

 

 

 

 

 

 

 

0.5

ky

k z

 

     

0.25

+

kz

ky

 

 

  

 

 

  

0.25 (10.22)

In case the wellbore is parallel to the y direction, the equivalent wellblock radius uses wellblock properties

in the x and z directions such as the dimensions •x and •z and the permeability values kx and kz:

ro = 0.28

kx

kz

 

     

0.5

Δz

2

+

kz

k x

 

     

0.5

Δx

2

 

 

 

 

 

 

 

 

0.5

kx

k z

 

  

 

  

0.25

+

k z

kx

 

  

 

  

0.25 (10.23)

10.4.1.2 Equivalent Wellblock Radius (Babu et al., 1991)

In addition to Peaceman's formulation [1983], a formulation of the equivalent wellblock radius based on the

paper by Babu et al. [1991] was implemented in the simulator (Dakhlia et al, 1995). As published, the

gridblock sizes were assumed uniform and the equations depended on gridblock numbering. However,

numerical reservoir simulation is often carried out with non-uniform gridblock sizes. The equations were

therefore rearranged so that gridblock sizes were no longer required to be uniform and the equations no
Section 10 - Well Models

123

longer depended on the gridblock numbering. h

Δz

 was substituted for nz and a

Δx

 was substituted for nx. In

case an integer was needed, such as in the summation limits, the FORTRAN function NINT was used to

calculate the nearest integer to the argument. Therefore, NINT( h

Δz

) was substituted for nz in the

summation limit used in Sxz. In addition, 2xw

Δx

 was substituted for ν and 2zw

Δz

 was substituted for λ. 

 As a

result, the applicability of the formulation was extended to non-uniform grids. The assumption for these

substitutions was that away from the wellbore, the effect of a coarse and non-uniform grid was equivalent

to the effect of a fine and uniform grid on the pressure behavior near the wellbore.

The resulting formulation is given below for a wellbore parallel to the y direction. In case the wellbore was

parallel to either the x or z direction, the pertinent directional variables were modified accordingly.

ln

ro

h

 

   

  =

πa

6h

a

Δx

 

     

2

kz

k x

 

 

 

 

 

 

 

 

 

 

 

 

+ 0.25ln k x

kz

 

  

 

  − ln sin

πz w

h

 

   

   

  

 

  −1.84 − BE − Sxz (10.24)

where the boundary term, BE, is computed by

BE = ln 1− E1

( )+ 0.5 ln 1 − 2 cos

2πz w

h

 

     E1 + E1

2

 

  

 

  (10.25)

and

E1 = exp −

2π min(xw ,a − xw )

h

k z

kx

 

  

 

  (10.26)

and the summation term, Sxz, is

Sxz =

π

h

Δz

 

     

cos2 πnz w

h

 

  

 

  1+ xn

−

2xw

Δx

 

      

 

 

 

 

 

 

 1 + xn

−2

a − xw

Δx

 

      

 

 

 

 

 

 

 

sin πn

2

h

Δz

 

     

 

 

 

 

 

 

 

 

 

 

1+ αn

2

1 − xn

−

2a

Δx

 

      

 

 

 

 

 

 

 

n =1

NINT h

Δz

 

     −1

∑ (27)

with α, αn, and xn defined as

α =

Δx

Δz

kz

kx

(10.28)
Section 10 - Well Models

124

αn = αsin πn

2

h

Δz

 

     

 

 

 

 

 

 

 

 

 

 (10.29)

xn = αn + 1 + αn

 2

 

 

 

2

(10.30)

For symmetry purposes, the wellbore location (xw, zw) was temporarily adjusted so that

xw = min(xw, a- xw) (10.31)

and

zw = min(zw, a- zw) (10.32)
124

Section 11

Effect of Alcohol on Phase Behavior

11.1 Introduction

This section is based on the Ph.D. dissertation by Saad [1989]. The phase behavior calculation for a

mixture of water, oil, and surfactant is discussed in Section 2. The effect of alcohol on the phase behavior

is discussed here. The presence of alcohol affects the effective salinities and causes a shift in the phase

boundaries. The effect of alcohol on the solubility is accounted for by shifting the maximum height of

binodal curve. The amount of alcohol that partitions in the excess phase(s) is modeled either by constant

partitioning coefficients as in Hirasaki's model (Hirasaki, 1982) or as a function of total composition with

the concept of pseudocomponent and pseudophase as in Provoust's model (Prouvost et al., 1984a,b, 1985).

Following is a discussion of the UTCHEM phase behavior model in the presence of alcohol (Pope and

Nelson, 1978; Prouvost et al., 1984a,b, 1985; Camilleri et al., 1987c; Saad, 1989).

The phase behavior is modeled as a tetrahedric diagram at a fixed salinity. Four pseudocomponents are

surfactant, alcohol, oil, and water represented in a tetrahedric diagram. Tielines and binodal curves are

located on the ternaries sliced through tetrahedrons. The pseudophases are (1) the aqueous consists of water

and alcohol(s), (2) oleic consists of oil and alcohol(s), and (3) microemulsion consists of surfactant and

alcohol(s). Similar to the no alcohol mixture, the phase behavior parameters such as binodal curve, plait

point and invariant point are calculated as a function of effective salinity using Hand's rule (Hand, 1939).

11.2 Alcohol Partitioning

The two options available in UTCHEM to calculate the alcohol partitioning are based on the models of

Hirasaki and Prouvost. Hirasaki's model assumes a constant partition coefficient whereas experimental

results show that alcohol partition coefficients vary with total composition. Prouvost extended the

pseudophase model to calculate variable alcohol partition coefficients and to be applicable to two alcohols.

The following intensive composition parameters are defined in the model:

λ j =

Cκ

1

C1

(11.1)

γ j =

Cκ

2

C2

(11.2)

σ j =

Cκ

3

C3

(11.3)
Section 11 - Effect of Alcohol on Phase Behavior

125

where for κ = 7, the value of subscript j = 1 and for κ =8, j =2. C1

, C2, and C3 are the overall water, oil,

and surfactant volume fractions, respectively. Superscripts 1, 2, and 3 represent the association of alcohol

with aqueous, oleic, and microemulsion pseudophases. Therefore, C7

1

 is the volume of alcohol 7

(component 7 in UTCHEM) in the aqueous phase, and C8

1

 is the volume of alcohol 8 (component 8) in the

aqueous phase. The partition coefficients used in Hirasaki's model can be defined using the above

parameters:

Kκ

2

=

γ j

λj

(11.4)

Kκ

3

=

σj

λj

(11.5)

where for κ = 7, the value of subscript j = 1 and for κ = 8 , j =2. In Prouvost's model, monomeric alcohol

reactions are considered. The following thermodynamic constants are used in the model:

kw1 = partition coefficient of monomeric alcohol 7 between aqueous and oleic pseudophases

km1 = partition coefficient of monomeric alcohol 7 between interfacial and oleic pseudophases

k1 = self-association constant of monomeric alcohol 7 in oleic pseudophase

a = ratio of molar volume of monomeric alcohol 7 to equivalent molar volume of surfactant

kw2, km2, k2

, and b are similar constants for alcohol 8.

The above parameters are input to the simulator. A material balance gives the following relationships:

Cκ =

AjC1

Dj + γ jC2

+

BjC3

Ej

 

for κ = 7, j = 1 ; κ = 8, j = 2 (11.6)

where

A1 = γ1

kw11 + γ1 + γ21 + k [ ( 2)]

B1 = aγ1km11 + γ1 + γ 21 + k [ ( 2 )]

D1 = 1 + γ 2 + γ11 + k [ ( 1)] 1 + γ1 + γ 21 + k [ ( 2 − kw2 )]− γ1kw11 + γ1 + γ21 + k { [ ( 2 )]}

E1 = 1 + γ 2 + γ11 + k1 [ ( )] 1 + γ1 + γ 21 + k2 − km2 [ ( )]− γ1km11 + γ1 + γ 21 + k2 { [ ( )]}

(11.7)

A2 = γ2

kw21 + γ2 + γ11 + k [ ( 1)]

B2 = bγ 2km21 + γ 2 + γ11 + k [ ( 1)]

D2 = 1 + γ1 + γ21 + k [ ( 2 )] 1 + γ 2 + γ11 + k [ ( 1 − kw1 )]− γ 2kw21 + γ 2 + γ11 + k { [ ( 1)]}

E2 = 1 + γ1 + γ21 + k2 [ ( )] 1 + γ 2 + γ11 + k1 − km1 [ ( )]− γ2km21 + γ2 + γ11 + k1 { [ ( )]}

(11.8)
Section 11 - Effect of Alcohol on Phase Behavior

126

C7

 and C8 are the overall volume fractions of alcohol 7 and alcohol 8 in the gridblock and are known values

from the solution of species conservation equations. Knowing C7

 and C8, Eqs. 11.7 and 11.8 are solved for

γ1 and γ2 using the Newton Raphson iteration method, and then the other four intensive parameters are

calculated:

λj =

Aj

Dj

 for j = 1, 2 (11.9)

σ j =

Bj

Ej

 for j = 1 , 2 (11.10)

Once λj

, γj, and σj are determined, alcohol partition coefficients Kκ

2

, and Kκ

3

 are calculated using Eqs.

11.4 and 11.5. When only a single alcohol is used, Eq. 11.6 reduces to the following cubic equation:

A' γ

3

 + B' γ

2

 + C' γ + D' = 0 (11.11)

where

A' = (1 + k - km) (1 + k - kw) (11.12)

B' = k w(1+ k − km )

C1

C2

+ ak m(1+ k − km )

C3

C2

− (1 + k − km )(1 + k − k w )

C1

C2

+ 2 + 2k − km − k w (11.13)

C' = kw

C1

C2

+ ak m

C3

C2

− (2 + 2k − km − k w )

C1

C2

+1 (11.14)

D' =

C7

C2

(11.15)

Then the partition coefficients are calculated using:

K7

2

=

1+ γ(1 + k − k w )

k w

(11.16)

K7

3

=

a km[1+ g(1 + k − kw )]

k w[1 + g(1 + k − km )]

(11.17)

For two alcohols, the overall alcohol volumes are related to the overall volumes of water (C1

), oil (C2), and

surfactant (C3

) pseudocomponents by:

Cκ

 = λj C1 + γj C2 + σj C3 for κ = 7, j = 1 ; κ = 8, j = 2 (11.18)

The above equations, can be written in terms of the alcohol partition coefficients as:

Cκ

 = λj C1 + λj Kκ

2

 C2 + λj Kκ

3

 C3 for κ = 7, j = 1 ; κ = 8, j = 2 (11.19)

From above equations the parameters λj

 are defined as:
Section 11 - Effect of Alcohol on Phase Behavior

127

λ j =

Cκ

C1 + Kκ

2C2 + Kκ3C3

 for j = 1, 2 (11.20)

λj is then used in calculating the pseudocomponents that are the apexes of the pseudoternary diagram.

CP1= (water volume) + (alcohol volumes associated with water) = C1

 (1 + λ1 + λ2 ) (11.21)

CP2 = (oil volume) + (alcohol volumes associated with oil)

 = C2

(1+ γ1 + γ 2) = C2(1 + γ1K7

2

+ λ2K8

2

) (11.22)

CP3 = (water volume) + (alcohol volumes associated with water)

 = C3

(1 + σ1 + σ2) = C3(1+ γ1K7

3

+ λ2K8

3

) (11.23)

The calculation of the pseudocomponent volumes is summarized below:

1. Using Newton Raphson iteration, calculate γ1

 and γ2 from Eqs. 11.3 and 11.4.

2. Calculate λj

and σj using Eqs. 11.9 and 11.10.

3. a) Calculate Kκ

2

 and Kκ

3

using Eqs. 11.4 and 11.5. If there is only one alcohol, use Eq. 11.11 to

calculate γ. Then calculate the partition coefficients using Eqs. 11.16 and 11.17.

b) If constant partition coefficient option is used, Kκ

2

 and Kκ

3

 are input parameters.

c) Calculate λj

 using Eq. 11.20.

4. Calculate the volume of the pseudocomponents, CP1, CP2, and CP3, using Eqs. 11.21-11.23.

Above calculations are made in Subroutines ALCPTN and TWOALC.

11.3 Effective Salinity

Hirasaki [1982] introduced a model to account for the change in optimal salinity with respect to changes in

the concentration of alcohol and calcium. Camilleri et al. [1987c] extended Hirasaki's model to entire

salinity space to define an effective salinity for the case with one alcohol:

CSE =

C51

(1 − β

6

f

6

S

)(1− βκfκ

S

)

(11.24)

CSE is the effective salinity, and β6

 and βκ are the slope parameters for calcium and alcohol dilution

effects. f

6

S

 is the fraction of calcium cations associated with surfactant micelles and is given in Section 2.

fκ

S

is defined as:

fκ

S

=

total volume of alcohol associated with surfactant

total volume of surfactant pseudocomponent

=

σ

1+ σ

(11.25)

β6 and βκ are determined by matching an experimental salinity requirement diagram such as those reported

by Nelson [1982] or equivalent diagrams (Satoh, 1984). For formulations containing only one alcohol,
Section 11 - Effect of Alcohol on Phase Behavior

128

CSEL and CSEU are constant for a fixed chemical formulation and are determined using Eq. 11.24. If there

is no calcium present, Eq. 11.24 represents a group of straight lines which pass through the fixed point (0, -

1/βκ

). If calcium is present, then it represents a group of planes which pass through the three fixed points

(0, -1/βκ

, 0), (0, 0, 1/βκ), and (0, -1/βκ, 1/β6). Due to the fact that Eq. 11.24 is nonlinear, these planes are

not flat . The calculated effective salinity becomes negative when f6

S

 > 1/β6 or βκ is negative and fκ

S

 >

1/|βκ

|.

Since different alcohols give different salinity limits, the following effective salinity is defined for the case

when there are two alcohols present:

CSE =

C51

(1 − β6f

6

S

)(1+ β7f7

S

+ β8

f

8

S

)

(11.26)

where the effective salinity limits are not constant in this case and are calculated by:

CSEL

CSEL7 β7f7

S

+ CSEL8 β8f

8

S

β7f7

S + β8

f

8

S

(11.27)

CSEU

CSEU7 β7f7

S

+ CSEU8 β8f

8

S

β7f7

S + β8

f

8

S

(11.28)

CSEL7, CSEL8, CSEU7, and CSEU8 are effective salinity limits for alcohol 7 and 8. CSEL7 and CSEU7 are

determined when alcohol 7 is the only alcohol present and are calculated using Eq. 11.24. Similar

independent calculations are made for alcohol 8. For the two alcohol case, f7

S

 and f8

S

 are defined as:

fκ

S

=

total volume of alcohol k associated with surfactant

total volume of surfactant pseudocomponent

 =

σ1

1 + σ1 + σ2

=

λ jKκ

3

1+ λ1K7

3

+ λ2K8

3

 for κ = 7, j = 1 ; κ = 8, j = 2 (11.29)

Kκ

3

 and λj are calculated as outlined in the previous section.

Once effective salinity is calculated, the phase environment (Fig. 11.1) for each gridblock is determined

according to:

CSE < CSEL Type II(-)

CSEL • CSE • CSEU Type III

CSE > CSEU Type II(+)

Effective salinity is calculated in Subroutine CSECAL.
Section 11 - Effect of Alcohol on Phase Behavior

129

11.4 Flash Calculations

A binodal curve is an intercept of a binodal surface and a pseudoternary plane. The original simulator

introduced by Pope and Nelson [1978] could treat nonsymmetric binodal curves; however, the present

simulator can treat only a symmetric binodal curve. The effects of alcohol on the height of the binodal

curve was included which can increase as the total chemical increases. The following linear relationship

between the height of the binodal curve (C3max) and fκ

S

 is used for the case with one alcohol (Fig. 11.2):

C3max,κm = mκm fκ

S

 + Cκm for m = 0, 1, 2; κ = 7 (11.30)

where m = 0 means at zero salinity, 1 means at optimal salinity, and 2 means at two times the optimal

salinity. mκm is the slope for maximum height of binodal curve vs. fraction of alcohol (alcohol 7 or

alcohol 8 for the two alcohol case) associated with the surfactant pseudocomponent at salinity m. Cκm is

the intercept of maximum height of the binodal curve at zero fraction of alcohol (alcohol 7 or alcohol 8 for

the two alcohol case) associated with the surfactant pseudocomponent at salinity m. Parameters mκm and

Cκm are obtained by matching the volume fraction diagrams corresponding to at least three different total

chemical (alcohol + surfactant) compositions. For the first iteration, the slope parameters are set to zero

and the intercept parameters are adjusted in order to obtain a reasonable match of the volume fraction

diagrams; then the slope parameters are obtained. Having obtained the slope parameters, the matching

procedure is repeated for further improvements. This matching is done using single alcohol experiments

independently for alcohol 7 and alcohol 8 using Eq. 11.30. The variables HBNC70, HBNC71, HBNC72 in

Fig. 11.2 are the UTCHEM input parameters for Cκm at three values of m. The variables HBNS70,

HBNS71, HBNS72 in Fig. 11.2 are the UTCHEM input parameters for mκm at three values of m.

The following equations are used for calculating the height of the binodal curve for the two alcohol case:

C3max,κm = mκm f7

S

+ f8

S

( )+ Cκm 

for κ = 7 and 8 (11.31)

C3maxm = C3max,8m + (C3max,7m − C3max,8m)

f7

S

f7

S

+ f

8

S

= m7m +

C7m

f7

S

+ f

8

S

 

 

  

 

 

  f7

S

+ m8m +

C8m

f7

S

+ f

8

S

 

 

  

 

 

  f

8

S

(11.32)

The following Hand equations are used for phase behavior calculations:

CP3

CP2

= A

CP3

CP1

 

   

  

B

(11.33)

 

CP3l

CP2l

= E

CP3l'

CP1l

 

  

 

  

F

(11.34)

Equation 11.33 defines the binodal curve for all types of phase behavior, and Eq. 11.34 defines the

distribution curve (tielines) when two phases exist (Type II(-) or Type II(+)). CP1, CP2, and CP3 represent

pseudocomponents defined by Eqs. 11.21-11.23. CP2l

, CP3l, CP1l', and CP3l' represent phase

concentrations of the pseudocomponents in the two pseudophases l and l'. Because pseudocomponent
Section 11 - Effect of Alcohol on Phase Behavior

130

concentrations are in volume fractions, they must add up to one; therefore the following constraints are

used:

CP1+ CP2 + CP3 = 1 (11.35)

CP1l+ CP2l

 + CP3l = 1 (11.36)

CP1l'+ CP2l'

 + CP3l' = 1 (11.37)

The total composition, CP1, CP2, and CP3, is known. Therefore there are five equations and six unknowns

(CPκl

 , κ = 1, 2, 3, l = 1, 2). Any phase concentration can be chosen and varied between 0 and 1 to sweep

the phase diagram. Since only symmetric binodal curves are modeled in the simulator, parameter B is equal

to -1 and parameter F is equal to 1. Parameter A in Eq. 11.33 is related to the height of the binodal curve

by:

A =

2C3max

1 − C3 max

 

  

 

  

2

(11.38)

Linear interpolation is then used to determine the A parameter for arbitrary effective salinity values. The

reason for interpolating A instead of the maximum height of the binodal curve, C3max, is that, at high

salinity, C3max exceeds unity, which means the binodal curve is outside the ternary diagram. To avoid this

problem, the interpolation is done on A. The following linear interpolation equations are used:

A = (A0 − A1

) 1 −

CSE

CSEOP

 

  

 

  + A1

 for CSE • CSEOP (11.39)

A = (A2 − A1

) 1 −

CSE

CSEOP

 

  

 

  + A1

 for CSE > CSEOP (11.40)

where CSEOP is the optimum effective salinity (CSEOP = 1/2 (CSEL+CSEU)).

Parameter E is calculated from the location of the plait point. From the phase distribution equation

(Eq. 11.34) and the plait point P:

CP3P

CP2P

= E

CP3P

CP1P

 

   

  

F

(11.41)

and since the plait point is also on the binodal curve:

CP3P

CP2P

= A

CP3P

C P1P

 

   

  

B

(11.42)

Also:

CP1P + CP2P + CP3P = 1 (11.43)
Section 11 - Effect of Alcohol on Phase Behavior

131

For the case when B = -1 and F = 1 (symmetric binodal curve), all phase concentrations can be calculated

explicitly. From Eq. 11.36:

CP11 = 1 - CP21 - CP31 (11.44)

Now substituting Eq. 11.44 in Eq. 11.33, CP31 can be calculated as a function of CP21:

CP31 =

1

2

−ACP21 + (ACP21)

2

+ 4ACP21(1 − CP21)

 

 

 

 (11.45)

and from Eq. 11.42:

E =

CP1P

CP2P

(11.46)

where CP2P, the oil pseudocomponent concentration at the plait point, is an input parameter in the

simulator, and

CP3P =

1

2

−ACP2P + (ACP2P

)

2

+ 4ACP2P

(1− CP2P)

 

 

 

 (11.47)

Then from Eq. 11.36:

CP1P = 1 - CP2P - CP3P (11.48)

knowing CP1P, parameter E can be calculated from Eq. 11.46. Having calculated CP31 and CP11 from Eqs.

11.44 and 11.45, CP22 is calculated from the following:

CP22 =

A

h

2 + Ah + A

(11.49)

where

h = E

CP31

CP11

(11.50)

Then CP32 is calculated from

CP32 = h CP22 (11.51)

and

CP12 = 1 - CP22 - CP32 (11.52)

The above calculations are performed when there are only two phases present, for Type II(-) or Type II(+)

phase behavior. The only difference between the two cases is that for Type II(-) phase behavior CP2PR

*

and for Type II(+) phase behavior CP2PL

*

, are used for CP2P in the above equations. The distribution of the

three pseudocomponents in the two phases for Type II(-) and Type II(+) phase behavior are summarized

below:
Section 11 - Effect of Alcohol on Phase Behavior

132

11.4.1 For Type II(-) Phase Behavior, CSE < CSEL

Known values for this case are C3max0, C3max1, C3max2, CSE, CSEL, CSEU, CP2PR

*

 and overall

concentration of the pseudocomponents, CP1, CP2, and, CP3.

1. Calculate parameter A from Eq. 11.39.

2. Using CP2PR

*

 calculate CP3PR

*

 and CP1PR

*

using Eqs. 11.47-11.48.

3. Calculate parameter E using Eq. 11.46 and CP1PR

*

 and CP2PR

*

.

4. Vary the value of CP21 from 0 to CP2PR

*

, calculate CP11 and CP31 using Eqs. 11.44-11.45.

5. Calculate h from Eq. 11.50.

6. Calculate CP22, CP32, and CP12 using Eqs. 11.49-11.52.

7. If (CP32 - CP3) (CP21 - CP2) - (CP31 - CP3) (CP22 - CP2) • ε , where ε is a sufficiently small number

(10-4), then stop; otherwise increment CP21 using the half interval method and go to step 4.

11.4.2 For Type II(+) Phase Behavior, CSE > CSEU

Known values for this case are C3max0, C3max1, C3max2, CSEL, CSE, CSEU, CP2PL

*

 and overall

concentration of the pseudocomponents, CP1, CP2, and .CP3.

1. Calculate parameter A from Eq. 11.40.

2. Using CP2PL

*

 calculate CP3PL

*

 and CP1PL

*

from Eqs. 11.47-11.48.

3. Calculate parameter E using Eq. 11.46 and CP1PL

*

 and CP2PL

*

.

4-7. Steps 4-7 as in the Type II(-) described above.

For Type III phase behavior, the tie lines for the left (Type II(+)) and the right (Type (-)) lobes are

calculated separately. Because of the symmetric binodal curve assumption, the binodal curve is calculated

in the same manner as in the Type II(-) and Type II(+) cases. The invariant point M is calculated as

follows:

a =

CSE − CSEL

CSEU − CSEL

(11.53)

where

a − CP2M

CP3M

 = Cos 60° (11.54)

Therefore, CP3M = 2(a - CP2M).
Section 11 - Effect of Alcohol on Phase Behavior

133

Since the invariant point M is on the binodal curve, Eq. 11.33 can be used to calculate CP3M as a function

of CP2M using Eq. 11.45:

CP3M =

1

2

−ACP2M + (ACP2M )

2

+ 4ACP2M(1 − CP2M )

 

 

 

 (11.55)

Solving Eqs. 11.54-11.55 for CP2M, the following is obtained:

CP2M =

2a(4 − A) + A ± (2a(4 − A) + A)

2 −16a2

(4 − A)

2(4 − A)

(11.56)

The invariant point should disappear when CSE approaches CSEL (CP2M = 0, a = 0) and when CSE

approaches CSEU (CP2M = 1, a = 1). These conditions hold only for the negative sign in Eq. 11.56.

Therefore, the composition at the invariant point is determined by Eq. 11.55, Eq. 11.56 with the negative

sign, and by

CP1M = 1 - CP3M - CP2M (11.57)

The plait point for the left lobe of the Type III phase environment must vary between zero and the plait

point for the Type II(+) value, CP2PL

*

. The plait point is calculated by salinity interpolation:

CP2PL = CP2PL

*

+

CP2PL

CSEU − CSEL

(CSE − CSEU) (11.58)

In order to apply the Hand equations to the left lobe, a coordinate transformation is made (Fig. 11.3). The

Hand distribution equation in the new coordinate system is :

CP32

'

CP22

'

= E

C P31

'

CP11

'

 

  

 

  (11.59)

where

C'

P 2l

 = CP2l Sec θ (11.60)

C'

P 3l

 = CP3l - CP2l tan θ (11.61)

C'

P 1l

 = 1 - C'

P 2l

 - C'

P 3l

(11.62)

Now let

β = Sec θ = 

(CP2M)

2

+ (CP3M )

2

CP2M

(11.63)

α = tan θ = 

CP3M

CP2M

(11.64)

Because of the symmetric binodal curve assumption (F=1), E can be calculated explicitly from:
Section 11 - Effect of Alcohol on Phase Behavior

134

E =

CP1P

'

CP2P

'

1 − (β − α)CP2P − CP3P

βCP2P

(11.65)

where CP2P is equal to CP2PL calculated using Eq. 11.58, and CP3P and CP1P are calculated from Eqs. 11.47

and 11.48.

CP11 and CP31 are calculated by Eqs. 11.44-11.45. Now Eq. 11.59 can be solved as before:

CP22 =

A

h'

2 +A h' +A

(11.66)

where

h' =

b ECP31

'

CP11

'

(11.67)

and

CP32 = h' CP22 (11.68)

CP12 = 1 - CP22 - CP32 (11.69)

Therefore all phase concentrations for the two phases in the left lobe have been determined.

The calculations for the right lobe are very similar to the above calculations for the left lobe. The CP2P

value for the plait point in this case varies between 1 and the input value for the Type II(-) case, CP2PR

*

,

and is calculated by:

CP2PR = CP2PR

*

+

1 − CP2PR

*

CSEU − CSEL

 

  

 

  (CSE − CSEL) (11.70)

Then CP32 is calculated using Eq. 11.45 but as a function of CP12 instead of CP21:

CP32 =

1

2

−ACP12 + (ACP12 )

2

+ 4ACP12 (1− CP12)

 

 

 

 (11.71)

and

CP22 = 1 - CP12 - CP32 (11.72)

Now let

h' =

bCP32

'

ECP11

'

+ a (11.73)

Then
Section 11 - Effect of Alcohol on Phase Behavior

135

CP11 =

A

h'

2 +Ah' +A

(11.74)

CP31 = h' CP11 (11.75)

CP21 = 1 - CP11 - CP31 (11.76)

where

α =

CP3M

CP1M

(11.77)

β =

C P3M

2

+ CP1M

2

CP1M

(11.78)

 

CP1l

'

= β CP1l(11.79)

 

CP3l

'

 = CP3l - α CP1l(11.80)

 

CP2l

'

 = 1 - 

 

CP3l

'

 - 

 

CP1l

'

(11.81)

E =

CP1P

'

CP2P

'

=

βCP1P

1 −(β − α)CP1P − CP3P

(11.82)

CP1P

'

 and CP2P

'

 are calculated using Eqs. 11.79-11.81 and Eqs. 11.47-11.48.

When three phases exist, the water and oil pseudocomponents are assumed to contain no surfactant

pseudocomponent. This assumption is a consequence of the choice of phase behavior in the three phase

region which assumes that the two phase region below the three phase tie triangle is very small; therefore,

any composition in the three phase region will have three phases comprising of the surfactant-rich

pseudophase with the composition of the invariant point, water-rich pseudophase with the composition of

the water pseudocomponent apex, and oil-rich pseudophase with the composition of the oil

pseudocomponent apex. Therefore:

CP11 = CP22 = 1 (11.83)

CP21 = CP31 = CP12 = CP32 = 0 (11.84)

The composition of the third phase, CP13, CP23, and CP33, is calculated using Eqs. 11.55-11.57. Phase

concentrations in the single phase region are the same as the overall composition, CP13 = CP1, CP23 = CP2,

CP33 = CP3. The other phase concentrations are zero.

The distribution of the three pseudocomponents in the two or three pseudophases for Type III phase

behavior are summarized below:
Section 11 - Effect of Alcohol on Phase Behavior

136

11.4.3 For Type III Phase Behavior, CSEL •CSE • CSEU

Known values for this case are: C3max0, C3max1, C3max2, CSE, CSEL, CSEU, CP2PR

*

, CP2PL

*

and overall

concentration of the pseudocomponents, CP1, CP2, and .CP3.

1. Calculate parameter A from Eq. 11.39-11.40.

2. Calculate CP2M from Eqs. 11.56.

3. Calculate CP3M and CP1M from Eqs. 11.55-11.57.

4. If the total composition is in the three phase region:

• Calculate water and oil pseudophase concentrations from Eqs. 11.83-11.84.

• CP23 = CP2M calculated in step 2. CP33 = CP3M and CP13 = CP1M calculated in step 3.

5. If the total composition is in Type II(+) lobe of Type III:

• Calculate CP2PL from Eq. 11.58.

• Calculate a and b from Eqs. 11.63-11.64.

• Calculate CP3PL and CP1PL from Eqs. 11.47-11.48 using CP2PL.

• Calculate parameter E from Eq. 11.65.

* Using a value of CP21 from 0 to CP2PL, calculate CP11 and CP31 using Eqs. 11.44-11.45.

• Calculate CP31

'

 and CP11

'

 from Eqs. 11.61-11.62.

• Calculate h' from Eq. 11.67.

• Calculate CP22, CP32, and CP12 using Eqs. 11.66, 11.68, and 11.69.

• If (CP33 - CP3) (CP21 - CP2) - (CP31 - CP3) (CP23 - CP2) • ε , where ε is a sufficiently small

number (10-4), then stop; otherwise increment CP21 using the half interval method and go back

to step *.

6. If the total composition is in Type II(-) lobe of Type III:

• Calculate CP2PR from Eq. 11.70.

• Calculate α and β from Eqs. 11.77-11.78.

• Calculate CP3PR and CP1PR from Eqs. 11.47-11.48 using CP2PR.

• Calculate parameter E from Eq. 11.82.

** Using a value of CP12 from 0 to CP1PR, calculate CP32 and CP22 using Eqs. 11.71-11.72.
Section 11 - Effect of Alcohol on Phase Behavior

137

• Calculate CP31

'

 and CP11

'

 from Eqs. 11.79-11.80.

• Calculate h' from Eq. 11.73.

• Calculate CP11, CP31, and CP21 using Eqs. 11.74-11.76.

• If (CP32 - CP3) (CP23 - CP2) - (CP33 - CP3) (CP22 - CP2) • ε , where ε is a sufficiently small

number (10-4), then stop; otherwise increment CP12 using the half interval method and go back

to step **.

After the phase composition in the pseudoternary diagram and saturations are determined, the phase

concentrations are converted back to the pseudoquaternary diagram using Eqs. 11.21-11.23. Phase

compositions are calculated in Subroutine PHCOMP.
Section 11 - Effect of Alcohol on Phase Behavior

138

two-phase

Surfactant

single-phase

water oil

P

R

a) Type II(-)

two-phase

Surfactant

single-phase

water oil

PL

b) Type II (+)

two-phase

Surfactant

single-phase

water oil

PL

PR

invariant point

three-phase

c) Type III

Figure 11.1. Schematic representations of a) Type II(-), b) Type II(+), and c) Type III.
Section 11 - Effect of Alcohol on Phase Behavior

139

Figure 11.2. Effect of alcohol on the maximum height of binodal curve.

C1

0

Right lobe θ

C1'

M

P

C3

C3

'

Figure 11.3. Coordinate transformation for Type III.
139

Section 12

Organic Dissolution Model in UTCHEM

12.1 Introduction

Both equilibrium and rate limited nonequilibrium solubility of organic component in the aqueous phase are

modeled in UTCHEM. The rate limited mass transfer equations are used for the enhance solubility of oil in

the presence of surfactant. The current implementation in UTCHEM is for under optimum Type II(-)

surfactant formulation. However, it can be applied to the Type III phase environment. This section

discusses the formulation and the method of solution for the case of single component oil phase. The

formulation of the multiple organic oleic phase is given in Section 7.

12.2 Saturated Zone (Gas Phase Is Not Present)

The overall component concentrations for water (κ = 1), oil (κ = 2), and surfactant (κ = 3) in two-phase

flow of water/oil or microemulsion/oil from the conservation equations are

C1 = C11S1 + C12S2(12.1a)

C2 = C21S1 + C22S2(12.1b)

C3 = C31S1 + C32S2

(12.1c)

where phase 2 refers to the oil phase and phase 1 in this section refers to either water or surfactant rich

microemulsion phase.

The overall concentrations for oil, water, and surfactant are obtained solving the conservation equations as

below

 

∂ φCκ( )

∂t

+

r 

∇ ⋅

 ̃ F κ1 + ̃ F ( κ2 )= Qκ1 + Qκ 2

 for κ = 1, 2, 3 (12.2)

where the flux term is the sum of the convective and dispersive fluxes as

 

 ̃ F κ1 = Cκ1

r 

u 1 − φS1

r 

r 

K κ1

⋅

r 

∇ Cκ1

F  ̃ 

κ2 = Cκ2

r 

u 2 − φS2

r 

r 

K κ2

⋅

r 

∇ Cκ 2

 for κ = 1 or 2 (12.3)

The definitions of the dispersion tensor and the flux are given in Section 2. The nonequilibrium

concentration of oil in the aqueous phase is computed from the mass balance on oil species in the aqueous

phase and using the first order mass transfer rate equation for oil dissolution as
Section 12 - Organic Dissolution Model in UTCHEM

140

 

∂ φS1C21 ( )

∂t

+

r 

∇ ⋅

 ̃ F 21 = Q21 + M C21

eq ( − C21) (12.4)

where C21

eq is the known limit of solubility for oil in the aqueous phase. In the absence of the surfactant,

the C21

eq is the limit of solubility for the specific organic contaminant and when surfactant is present the

equilibrium solubility is calculated from the Hand's equations (Section 2). M is the mass transfer

coefficient for the dissolution of organic species in the water phase and is assumed to be a constant.

Equation 12.4 is solved either explicitly or implicitly as described below.

12.2.1 Organic Solubility

12.2.1.1 Explicit Solution

The new time level, (n+1), concentration of oil solubilized in water is

 

φS1C21 ( )

n +1

= φS1C21 ( )

n

+(Q21 −

r 

∇ ⋅

 ̃ F 21)Δt + MΔt C21

eq

− C21

n

( ) for C21

n

< C21

eq (12.5)

where the right-hand side of the equation is a known quantity. Therefore,

S1C21 ( )

n+1

=

(φS1C21)

n +1

φ

n +1

(12.6)

since the porosity is known either as a constant or is calculated based on the new time step pressure if rock

compressibility is not negligible.

12.2.1.2 Implicit Solution

 

φS1C21 ( )

n +1

= φS1C21 ( )

n

+(Q21 −

r 

∇ ⋅

 ̃ F 21)Δt + MΔt C21

eq

− C21

n+1

( ) (12.7)

where we define 

 

RHS = (φS1C21)

n

+ (Q21 −

r 

∇ ⋅

 ̃ F 21)Δt + MΔt C21

eq

− C21

n+1

( ).

Substituting for S1

n+1

from overall concentration for oil component (Eq. 12.1b) and noting that C22 = 1 for

the flow conditions of oil/water and the Type II(-) with corner plait point and the sum of the saturations is

equal to one (S1 + S2 = 1), we have

φC21

C2 − 1

C21 − 1

 

 

  

 

 

n+1

= RHS (12.8)

The above equation can then be rearranged in terms of oil concentration in the aqueous phase (C21) as

M Δt C21

2

+ bterm C21 + cterm = 0 (12.9)

where

bterm = φC2 − φ − MΔt − cterm (12.10)

 

cterm = φS1C21 ( )

n

+ Δt Q21 −

r 

∇ ⋅

 ̃ F ( 21)+ MΔtC21

eq (12.11)
Section 12 - Organic Dissolution Model in UTCHEM

141

The solution to the quadratic equation (Eq. 12.9) is

C21 =

2cterm

−bterm + (bterm)

2

− 4M Δt(cterm)

for bterm < 0

C21 =

2cterm

−bterm − (bterm)

2 − 4MΔt(cterm)

for bterm > 0

 

 

  

 

 

 

(12.12)

12.2.2 Phase Saturations

12.2.2.1 Oil/Water Phases (No Surfactant)

Substituting C12 = 0.0 and C22 = 1.0, Eqs. 12.1a and 12.1b become

C1

= C11 S1

C2

= C21 S1 + S2

(12.13)

The equilibrium saturations and concentrations are computed first as

S2

eq

=

C2 − min(C2, Kow )

1 − min(C2, Kow )

(12.14)

S1

eq

= 1. − S2

eq (12.15)

where Kow is the limit of solubility of oil in water at equilibrium in the absence of surfactant or cosolvent

and is an input parameter. The minimum in Eq. 12.14 is taken to ensure that the input solubility is not

greater than the total oil available in a gridblock.

The nonequilibrium phase saturations and concentrations are computed as described below once the

equilibrium organic concentration is solved for from Eq. 12.4.

12.2.2.1.1 Explicit Method

Since the product of water saturation times the oil concentration is known using the explicit solution (Eq.

12.6), the new time step oil saturation from Eq. 12.1b is

S2 = C2 − C21S1( )

n+ 1

 and S1 = 1 - S2 (12.16)

The overall oil concentration (C2) is computed from the oil material balance equation. The phase

compositions are then as follows

C11 =

C1

S1

C21 = min C21

eq

,

(C21S1)

n+1

S1

 

 

  

  

C22 = 1. 0

(12.17)

If the calculated nonequilibrium concentration is greater than the equilibrium value (C21 >C21

eq ), the

saturations are then set to the equilibrium values calculated from Eqs. 12.14 and 12.15.
Section 12 - Organic Dissolution Model in UTCHEM

142

12.2.2.1.2 Implicit Method

From the implicit solution of the mass balance equation for oil component in the aqueous phase, we could

obtain the nonequilibrium organic dissolution in the aqueous phase (Eq. 12.12). The phase saturations and

phase compositions are then calculated as

C21

noneq

= min(C21

eq

,C21)

S1 =

C1

1 − C21

noneq

S2 = 1− S1

 

 

  

 

 

 

(12.18)

and

C11 =

C1

S1

C12 = 0.0

C22 = 1.0

(12.19)

12.2.2.2 Oil/Aqueous Phases (Surfactant Below CMC)

The phase concentrations and saturations are calculated as above and surfactant concentration is

C31 =

C3

S1

(12.20)

12.2.2.3 Oil /Microemulsion Phases ( Type II (-) With Corner Plait Point)

For the case of corner plait point we have

C22 = 1.0, C12 = 0.0, and C32 = 0.0

and the equilibrium concentrations of surfactant, oil, and water in microemulsion phase C11

eq

, C21

eq

, C31

eq ( )

are calculated from Hand's equations described in Section 2. Substituting these in the overall component

concentrations, we have

C1

= C11S1

C2 = S2 + C21S1

C3 = C31S1

(12.21)

The equilibrium saturations are then computed as

S2

eq

=

C2 − C21

eq

1 − C21

eq

S1

eq

= 1− S2

eq

(12.22)

The nonequilibrium concentration of oil (C21 for the implicit solution or S1C21 for the explicit solution) is

computed from Eq. 12.4 using an explicit or implicit method. The following section gives the phase
Section 12 - Organic Dissolution Model in UTCHEM

143

saturations and phase compositions for both the implicit and explicit solutions of the organic mass balance

equation.

12.2.2.3.1 Explicit Solution

The phase saturations are computed using the overall oil concentration and the product of microemulsion

saturation times organic concentration in the microemulsion phase from Eq. 12.12.

S2 = C2 − (C21S1)

n+1

S1 = 1. −S2

(12.23)

The phase compositions are then computed as

C11 =

C1

S1

C21 = min C21

eq

,

(C21S1)

n+1

S1

 

 

  

 

 

  

C31 = 1. − C11 − C21

C22 = 1.0

C12 = 0.0

C32 = 0.0

(12.24)

If the calculated nonequilibrium concentration is greater than the equilibrium value (C21>C21

eq ), the

saturations are then set to the equilibrium values.

12.2.2.3.2 Implicit Method

From the implicit solution of mass balance equation for oil component in the microemulsion phase, we

could obtain the nonequilibrium organic dissolution (Eq. 12.12). The phase saturations and phase

compositions are calculated as

C21 = min(C21

eq

,C21

n+1

)

S2 =

C2 − C21

1− C21

S1 = 1 − S2

 

 

  

 

 

 

(12.25)

and

C11 =

C1

S1

C31 = 1− C11 − C21

C12 = 0.0, C22 = 1.0, C32 = 0.0

(12.26)
Section 12 - Organic Dissolution Model in UTCHEM

144

12.3 Vadose Zone

The solubility of organic species in three-phase flow of water/oil/gas in the vadose zone in the absence of

surfactant is modeled in UTCHEM. Similar to the previous section, the overall concentrations for oil,

water, and gas are obtained solving the conservation equations.

 

∂ φCκ( )

∂t

+

r 

∇ ⋅

 ̃ F κ1 + ̃ F ( κ2 )= Qκ1 + Qκ 2

 for κ = 1, 2, 8 (12.27)

The nonequilibrium concentration of oil in the aqueous phase is calculated from the mass balance on oil

species in the aqueous phase and using the first order mass transfer equation for oil solubility as

 

∂ φS1C21 ( )

∂t

+

r 

∇ ⋅

 ̃ F 21 = Q21 + M C21

eq ( − C21) (12.28)

where the flux term is defined as

 

 ̃ F 21 = C21

r 

u 1 − φS1

r 

r 

K 21 ⋅

r 

∇ C21 (12.29)

Equation 12.29 is solved explicitly to obtain the rate-limited solubility of contaminant in the aqueous phase

in the vadose zone. The new time level, (n+1), concentration of oil solubilized in water is

 

φS1C21 ( )

n +1

= φS1C21 ( )

n

+(Q21 −

r 

∇ ⋅

 ̃ F 21)Δt + MΔt C21

eq

− C21

n

( ) for C21

n

< C21

eq (12.30)

where the right-hand side of the equation is a known quantity. Therefore,

S1C21 ( )

n+1

=

φS1C21 ( )

n+1

φ

n+1

(12.31)

since the porosity is known and the new time step oil saturation from Eq. 12.1b is

S2 = C2 − C21S1( )

n +1

(12.32)

S1 = C1 − S1C21 ( )

n +1

(12.33)

and

S4 = 1 − S1 − S2(12.34)

where the overall concentrations (C1 and C2) are computed from the species conservation equations. The

phase compositions are then as follows

C11 =

C1

S1

C21 = min C21

eq

,

C21S1

( )

n+1

S1

 

 

  

 

 

  

C22 = 1.0

(12.34)
Section 12 - Organic Dissolution Model in UTCHEM

145

If the calculated nonequilibrium concentration is greater than the equilibrium value (C21>C21

eq ), the

saturations and phase concentrations are set back to those at the equilibrium.

12.4 Nomenclature

Ci,κ = Total concentration of species κ in gridblock i, L3/L3 PV

Cκ = Overall concentration of species κ in the mobile phases, L3/L3

Cκ

eq

= Equilibrium concentration of species κ, L3/L3

Cκl = Concentration of species κ in phase l, L3/L3

K = Dispersion coefficient, L2t

-1

 

r 

r 

K κl = Dispersion tensor for species in phase , L2

M = Mass transfer coefficient, t-1

Q = Source/sink for species , L3/T

S = Saturation of phase , L3/L3 PV

t = Time, t

t

n, tn+1 = Time-step size at nth and n+1th time level, t

 

r 

u l = Darcy flux, Lt-1

Greek Symbols

φ = Porosity, fraction

Subscripts

κ = species number

1 = Water

2 = Oil

3 = Surfactant

8 = air

l = Phase number

1 = Aqueous

2 = Oleic

3 = Microemulsion

4 = Air
146

Appendix A

UTCHEM 6.1 User's Guide

A.1 INTRODUCTION

UTCHEM is a three-dimensional chemical flooding simulator. The solution scheme is

analogous to IMPES, where pressure is solved for implicitly, but concentrations rather than

saturations are then solved for explicitly. Phase saturations and concentrations are then solved in a

flash routine. An energy balance equation is solved explicitly for reservoir temperature. The

energy balance equation includes heat flow between the reservoir and the over- and underburden

rocks. The major physical phenomena modeled in the simulator are:

dispersion

diffusion

dilution effects

adsorption for oil, surfactant and polymer

interfacial tension

relative permeability

capillary pressure

hysteresis in relative permeability and

capillary pressure

capillary trapping

cation exchange

phase density

compositional phase viscosity

phase behavior (pseudoquaternary)

aqueous reactions

partitioning of chemical species between

oil and water

dissolution/precipitation

cation exchange reactions involving more

than two cations

in-situ generation of surfactant from

acidic crude oil

pH dependent surfactant adsorption

organic biodegradation capability

multiple organic species

equilibrium and nonequilibrium organic

dissolution in aqueous phase

dual porosity option for simple phase

tracer flow

polymer properties: shear thinning

viscosity, inaccessible pore volume,

permeability reduction, adsorption

gel properties: viscosity, permeability

reduction, adsorption

tracer properties: partitioning,

adsorption, radioactive decay,

reaction (ester hydrolization), deadend pore (capacitance)

temperature dependent properties:

viscosity, tracer reaction, gel

reactions, Surfactant phase behavior

gas mobility reduction due to foam

See Section 2 of this report for the general formulation of the simulator.
Appendix A - UTCHEM 6.1 User's Guide

147

A.2 OPERATION OF THE SIMULATOR

The UTCHEM simulator is run on a CRAY J90 at the Texas Advanced Computing Center

affiliated with The University of Texas at Austin (UNICOS operating system), a number of DEC

Alpha systems (DEC 4000/610, 3000/500 & 3000/300X) at the Department of Petroleum and

Geosystems Engineering (OSF/1 operating system), and a DEC Alpha system (DEC 3000/500) at

the Department of Petroleum and Geosystems Engineering (OpenVMS operating system), a number

of IBM RS6000 workstations, and a WINDOWS-based PC workstation. The same code is executed

on all systems, except for the use of double precision (64-bit words) on the DEC, RS6000 and PC

machines—we differentiate between "Cray" and "double precision" versions of the code by adding a

"V" prior to the version number for the "Cray" version and a "D" prior to the version number for the

"double-precision". Several intrinsic Cray functions need to be implemented when not running on

the Cray; these routines are "commented" out in the "Cray" version. Please check the source code

for additional information about necessary changes when running on different computers.

2.1 Input and Output Files

UTCHEM requires one input file for non-restart runs. The program expects this file to be

named INPUT. For restart runs, a restart file (named INPUT2) is required in addition to the original

input data file used for the previous run. A detailed input data description is given in Section A.3 of

this appendix and the data in the restart data file is documented in Section 4.3 of this appendix. A

number of UTCHEM input example files demonstrating a variety of petroleum oil-field and

groundwater applications are available to UTCHEM users. The oil-field applications include water,

single-well tracer, interwell tracer, polymer, profile control using gel, surfactant/polymer, and high

pH alkaline/surfactant/polymer flooding. The groundwater applications include contaminant

infiltration, water flushing, partitioning interwell tracer, surfactant enhanced aquifer remediation,

and bioremediation.

We provide all users with two sample input files for testing purposes (see distribution disks

for copies of the files). The first sample input file (ex01) is for a 3D surfactant/polymer flood. In

that file, the surfactant properties are for petroleum sulfonate and the polymer properties are based

on the typical data for xanthan gum. CPU usage for the EX01 example run is about 10 minutes on a

DEC Alpha 4000/610 and about 153 seconds on a CRAY J90. The second sample input file (EX21)

is for a 2-D contamination event in the saturated zone of an aquifer. CPU usage for the EX21

example run is about 264 seconds on a DEC Alpha 4000/610 and about 52 seconds on a CRAY J90.

If you would like to receive additional sample input files, please contact Joanna L. Castillo

(joanna@mail.utexas.edu or 512-471-3229) for details.

The number of output files generated by UTCHEM varies depending upon several control

flags set by the user in the input file. The number of history plot files depends on the value of the

MXW parameter in the PARAM.INC source file. The FORTRAN unit number for the history plot

file is incremented by one for each well. For example, if MXW is equal to three, then three history

plot files would be generated corresponding to FORTRAN unit numbers 19, 20, and 21 even if the

run only has two wells. The input and output files are summarized in the following table.

Unit Number File Name Contents

1 TEMPL Analytical temp. profile, created if IENG=1 and IANAL=1

2 ECHO Echo print of the input file information

3 MESH Number of gridblocks and distances to center of gridblocks in each

direction.

4 PROFIL Formatted profile data; described in Section A.4 of this appendix
Appendix A - UTCHEM 6.1 User's Guide

148

5 INPUT Input data; described in detail in Section A.3 of this appendix

6 TTABLE Table of time steps and Courant numbers

7 RESTAR Stored restart run data; described in Section A.4 of this appendix

8 CONCP Component concentration profile plotting data, created if IPCTOT>0

9 OVERAL History of overall properties; described in Section A.4 of this

appendix

10 GFILEP Gel property profile plotting data, created if IREACT=1

11 PRESP Phase pressure profile plotting data, created if IPPRES>0

12 SATP Phase saturation profile plotting data, created if IPSAT>0

13 TRACP Phase tracer concentration profile plotting data, created if

IPTRAC>0

14 CAPP Capacitance property profile or dual porosity plotting data, created if

IPCAP>1

15 ALKP Alkaline option related profile plotting data, created if IREACT>1

16 INPUT2 Restart run data (input file created by an earlier run)

17 WARN Warning messages

18 TEMPP Temperature profile, created if IENG=1 and IPTEMP=1

19 HIST01 Well history plotting data for well #1; described in Section A.4 of

this appendix

20 HIST02 Well history plotting data for well #2

...

l HISTl Well history plotting data for last well

l+1 TRAC01 Aqueous (or gas) phase tracer concentration for the 1st tracer at

observation points, created if IPOBS>0; described in Section A.4 of

this appendix

l+2 TRAC02 Aqueous (or gas) phase tracer concentration for 2nd tracer at

observation points

...

n TRACn Aqueous (or gas) phase tracer concentration for the last tracer at

observation points

2.2 Source Code Array Dimensions

The parameters in the table below are used by the simulator to define array sizes. All

parameter values must be equal to or greater than the size of the grid dimensions specified in the

input file, unless otherwise noted. All parameters used in UTCHEM are defined in the

PARAM.INC source file. This file should be edited before compilation and linking of the source

code to define the maximum global discretization size. Example PARAM.INC source file:

 PARAMETER (NNX=96,NNY=96,NNZ=2,MXC=11,MXP=3)

 PARAMETER (MXW=2,MXWB=2,MXNT=3,MXMO=1)

 PARAMETER (MXELE=1,MXFLD=1,MXSLD=1,MXSORB=1,MXACAT=1,MXEX=1)

 PARAMETER (MHM=1,MVM=1)

 PARAMETER (MAXBIO=9,MAXBS=9,MAXMET=4)

The following table contains definitions of the parameter variables used in the PARAM.INC

file.
Appendix A - UTCHEM 6.1 User's Guide

149

Parameter Definition

NNX Number of gridblocks in X-direction (must be set equal or larger to NX in the input

file)

NNY Number of gridblocks in Y-direction (must be set equal or larger to NY in the input

file)

NNZ Number of gridblocks in Z-direction (must be set equal or larger to NZ in the input

file)

MXC Maximum number of components (cannot be less than 8)

MXP Number of phases (must be set equal to 3 when there is no gas phase and must be set

equal to 4 if gas is present)

MXW Maximum number of wells

MXWB Maximum number of well blocks

MXNT Maximum number of tracers (check if NT>0)

MXELE Maximum number of elements (check for IREACT>1)

MXFLD Maximum number of reactive fluid species (check for IREACT>1)

MXSLD Maximum number of solids (check for IREACT>1)

MXSORB Maximum number of adsorbed species (check for IREACT>1)

MXACAT Maximum number of cations associated with surfactant (check for IREACT>1)

MXEX Maximum number of insoluble exchangers (check for IREACT>1)

MVH Maximum number of subgrids in vertical direction (check for ICAP=2)

MHM Maximum number of subgrids in lateral direction (check for ICAP=2)

MAXBIO Maximum number of chemical and biological species participating in biodegradation

reactions

MAXMET Maximum number of metabolic combinations of substrate, electron acceptor, and

biological species

MAXBS Maximum number of biological species (check for IBIO=1)

MXMO Maximum number of organic components (check for NO>1)

2.3 Compilation and Execution on Workstations

The UTCHEM distribution package for workstations contains the following files:

Makefile-alpha, PARAM.INC, UTCHEMD6P1.for, ddriv2.f, DPUTIL.for,

ex01.data, and ex21.data. Make sure you place all seven files in the same directory on your

workstation. Then, follow these steps:

1. Split the UTCHEMD6P1.for and DPUTIL.for files using the UNIX "fsplit"

command.

2. To build an executable file called utchem.exe, issue the command:

make -f Makefile-alpha

Note that the example makefile included on the distribution disks assumes the use of

the f77 FORTRAN compiler. You will need to modify the Makefile-alpha file

if you wish to use another compiler (xlf on IBM RS6000 workstations, for

example).
Appendix A - UTCHEM 6.1 User's Guide

150

3. Run UTCHEM in the background using a command file (in the example below, the

file is called work.job). Note that the work.job file needs to be executable.

Use any text editor to create your job file and then issue the command:

chmod +x work.job

at the UNIX prompt to make sure the work.job file is executable. Then, submit

the job file by issuing the following command:

work.job &

 at the UNIX prompt. Example work.job file:

rm -r ex01.dir

mkdir ex01.dir

cd EX01.dir

ln -s ../ex01.data INPUT

time ../utchem.exe

mv TTABLE ex01.ttable

mv ECHO ex01.echo

mv MESH ex01.mesh

mv PROFIL ex01.prof

mv CONCP ex01.con

mv PRESP ex01.presp

#mv ALKP ex01.alkp

mv SATP ex01.satp

mv GFILEP ex01.gel

mv TEMPP ex01.temp

mv HIST01 ex01.hist01

mv HIST02 ex01.hist02

mv HIST03 ex01.hist03

mv HIST04 ex01.hist04

#mv HIST05 ex01.hist05

#mv HIST06 ex01.hist06

#mv HIST07 ex01.hist07

mv OVERAL ex01.overal

mv RESTAR ex01.rest

mv WARN ex01.warn

The work.job file needs to be modified to reflect the directory structure you create

for running UTCHEM jobs as well as the names you wish to use for input and output

files. See Section A.9 of this appendix for a description of the contents of the

work.job file.

2.4 Compilation and Execution on the CRAY J90

The UTCHEM distribution package for the Cray contains the following files: Makefilecray, PARAM.INC, UTCHEMV6P1.for, SDRIV2.f, ex01.data, and ex21.data. Make

sure you place all six files in the same directory on your Cray account. Then, follow these steps:

1. Split the UTCHEMV6P1.for file using the UNIX "fsplit" command.

2. To build an executable file called utchem.exe, issue the command:
Appendix A - UTCHEM 6.1 User's Guide

151

make -f Makefile-cray

3. Submit your job request to the Cray. A sample job file follows:

workdir="/insert_path/utchem/"

workdir1="/insert_path/utchem/ex01"

set -xS

cd $TMPDIR

ja jacct$$

rcp $workdir/ex01.data INPUT

#rcp $workdir1/ex01.rest INPUT2

rcp $workdir/utchem.exe a.out

a.out

rcp TTABLE $workdir1/ex01.ttable

rcp ECHO $workdir1/ex01.echo

rcp MESH $workdir1/ex01.mesh

rcp PROFIL $workdir1/ex01.prof

rcp SATP $workdir1/ex01.satp

rcp TEMPP $workdir1/ex01.temp

rcp PRESP $workdir1/ex01.presp

rcp CONCP $workdir1/ex01.concp

#rcp ALKP $workdir1/ex01.alkp

rcp GFILEP $workdir1/ex01.gel

rcp HIST01 $workdir1/ex01.his1

rcp HIST02 $workdir1/ex01.his2

rcp HIST03 $workdir1/ex01.his3

rcp HIST04 $workdir1/ex01.his4

rcp OVERAL $workdir1/ex01.overal

rcp RESTAR $workdir1/ex01.rest

rcp WARN $workdir1/ex01.warn

This job file assumes the code and input file reside in a directory called "utchem"

and that the output files will be placed in the "ex01" directory which is one level

below the "utchem" directory. Replace insert_path with the actual path to the

"utchem" directory.
Appendix A - UTCHEM 6.1 User's Guide

152

A.3 INPUT DATA DESCRIPTION

The UTCHEM input file consists of comment lines and data lines. All comment lines are

ignored by the UTCHEM simulator. It is important to note, however, that the number of comment

lines between data lines is fixed. The first twenty-two lines of the input file are reserved for

comment lines used to briefly describe the input file. Each data line is preceded by three comment

lines (except for the input described in Section 3.5 of this appendix). The input file is basically

divided into seven sections and each of those input sections (except Section 3.5) is preceded by an

additional seven comment lines. The user should update the comment lines as the input file is

modified in order to make using the simulator easier.

All data is free-formatted. This means that for each read statement, it is only necessary to

leave a blank space between data elements. Note that the first data element for a given read

statement must be on a new line in the input file. Subsequent data elements for that read statement

can span as many lines as necessary. Implicit type matching is used; that is, all REAL variables

begin with the letters A-H or O-Z and all integer variables begin with the letters I-N.

The following is a list of variables as they are read by UTCHEM. The variable names

appear in all-caps on a single line in the order they are read by the program (variables that are new

to the latest version of UTCHEM are printed in italicized boldface as well). Every list of variables

is followed by a description of each variable and corresponding units or possible values if

applicable. All of the variables listed in the input description will be read by the program unless

otherwise noted; therefore, a dummy value will be read by the program for variables not pertinent to

the problem being run.

3.1. Title and Reservoir Description Data

The first input section consists of the title and reservoir description data. Please remember

that there are 22 comment lines at the beginning of this section and that each data line is preceded

by three comment lines.

3.1.1 RUNNO

RUNNO - Run number.

Note: The run number can consist of any combination of alphanumeric characters on a

single line (not to exceed 80 characters). This information will be printed as the first

line of every output file.

3.1.2 TITLE

TITLE - Title and run description.

Note: The title can consist of any combination of alphanumeric characters spanning three

lines in the input file (not to exceed 80 characters per line). The title must span three

lines and any of those lines can be blank.

3.1.3 IMODE, IMES, IDISPC, ICWM, ICAP, IREACT, IBIO, ICOORD, ITREAC, ITC, IGAS, IENG

IMODE - Flag indicating if the problem to be run is a first run or a restart simulation.

Possible Values:

1 - First simulation run

2 - Restart simulation

Note: See Section A.4 of this appendix for more details on how to run restart simulations.

IMES - Flag indicating if a constant or automatic time-step is to be used.

Possible Values:
Appendix A - UTCHEM 6.1 User's Guide

153

1 - Constant time-step size is used

2 - Automatic time-step size selector based on method of relative changes for the first

three components is used

3 - Automatic time-step size selector based on method of relative changes for all the

components is used

4 - Automatic time-step size selector based on changes in dimensionless

concentration for all the components is used

Note: The automatic time-step selector is recommended. See input lines 3.7.9 through

3.7.13 and Section A.8 of this appendix for more details on the above options.

IDISPC - Flag indicating which type of numerical dispersion control is used.

Possible Values:

0 - Single point upstream method is used

2 - Two point upstream method is used

3 - Improved total variation diminishing third order method is used

Note: These methods are applied to both concentration and relative permeability.

ICWM - Flag indicating if the concentration well model is used or not.

Possible Values:

0 - Concentration well model is not used

1 - Concentration well model is used

Note: The concentration well model (ICWM=1) can only be used with vertical wells

(IDIR(M)=3).

ICAP - Flag indicating if the capacitance model is used or not.

Possible Values:

0 - Capacitance model or dual porosity option is not used

1 - Capacitance model is used

2 - Dual porosity option is used for single phase tracer flow

Note: The dual porosity option (ICAP=2) is available only if IMODE=1, IUNIT=0, and

ICOORD=1.

IREACT - Flag indicating if gel reactions or alkaline options are used or not.

Possible Values:

0 - Gel reactions are not used

1 - Gel reactions are used

2 - Geochemistry option with no acidic crude is used

3 - Geochemistry option with acidic crude is used

4 - IREACT=2 and gel reactions are used

IBIO - Flag indicating whether or not biodegradation reactions occur

Possible Values:

0 - No biodegradation reactions

1 - Biodegradation reactions occur

ICOORD - Flag indicating which coordinate system is used.

Possible Values:

1 - Cartesian coordinate system is used

2 - Radial coordinate system is used

3 - Cartesian coordinate system with variable-width gridblock is used (2-D cross

section only)

4 - Curvilinear grid definition of the X-Z cross section is used (2-D or 3-D)
Appendix A - UTCHEM 6.1 User's Guide

154

Note: For ICOORD=4, the 3-D grid consists of the 2-D cross sectional grid repeated at

specified intervals (uniform or non-uniform) in the Y direction, according to the definition

of DY1. The curvilinear grid option is not available with the temperature equation option.

ITREAC - Flag indicating if a tracer reaction is used or not.

Possible Values:

0 - Tracer reactions are not used

1 - Tracer reactions are used

ITC - Flag indicating if second-order time approximation is used or not.

Possible Values:

0 - Second-order time approximation is not used

1 - Second-order time approximation is used

Note: We recommend that second-order time approximation (ITC=1) only be used with

higher-order dispersion methods (IDISPC>1).

IGAS - Flag indicating if gas phase is considered or not.

Possible Values:

0 - Gas is not present

1 - Gas is present

2 - Gas is present and foam option is used

IENG - Flag indicating if temperature variation is considered or not.

Possible Values:

0 - Isothermal simulation

1 - Temperature equation is solved

3.1.4 NX, NY, NZ, IDXYZ, IUNIT

NX - Number of gridblocks along X-axis (ICOORD=1, 3, or 4) or number of gridblocks in radial

direction (ICOORD=2).

Note: This value should be equal to or smaller than the NNX parameter in UTCHEM.

NY - Number of gridblocks along Y-axis.

Note: This value should be equal to or smaller than the NNY parameter in UTCHEM. It

should be set equal to 1 if the user is running a 1-D problem or a 2-D cross sectional

problem. If ICOORD=2, this value is automatically set equal to 1.

NZ - Number of gridblocks along Z-axis.

Note: This value should be equal to or smaller than the NNZ parameter in UTCHEM. It

should be set equal to 1 if the user is running a 1-D problem or a 2-D areal problem.

IDXYZ - Flag indicating constant or variable grid size.

Possible Values:

0 - Constant grid size

1 - Variable grid size on a regional basis

2 - Variable grid size

Note: IDXYZ must be set equal to 2 if ICOORD=3.

IUNIT - Flag indicating English or Metric units.

Possible Values:

0 - English unit

1 - Metric unit

Note: UTCHEM must be compiled and run with the NX, NY, and NZ input values being equal to

or smaller than the NNX, NNY, and NNZ parameters in the code. All parameters used in

UTCHEM are defined in the PARAM.INC source file.
Appendix A - UTCHEM 6.1 User's Guide

155

Simulation Gridblock Sizes (Lines 3.1.5-3.1.23)

Refer to the following flowchart to help determine which input lines should be used to specify the gridblock

size input values for different options:

ICOORD

1

2

3

4

0

1

2

0

1

2

1

2

0

1

2

IDXYZ

IDXYZ

3.1. 6

3.1. 5

3.1. 7

3.1. 15

3.1. 17

3.1.9, 3.1.10, 3.1.11

3.1.16, 3.1.17, 3.1.19

3.1.12, 3.1.13, 3.1.14

3.1.20, 3.1.21, 3.1.22

3.1.9, 3.1.10, 3.1.11

3.1.16, 3.1.18, 3.1.19

IDXYZ

IDXYZ

3.1. 8

3.1.5 XCORD(I), ZCORD(I), for I=1, (NX+1)×(NZ+1) (This line is read only if ICOORD=4)

XCORD - Gridblock coordinate of Ith corner point in X-direction.

Units: feet (IUNIT=0) or m (IUNIT=1)

ZCOORD - Gridblock coordinate of Ith corner point in Z-direction.

Units: feet (IUNIT=0) or m (IUNIT=1)

Note: The coordinates of the corners (or vertices) of the 2-D X-Z cross section gridblocks are input

in pairs as follows:

XCORD(1), ZCORD(1)

 . .

 . .

 . .

XCORD(nodes), ZCORD(nodes)

where nodes = (NX+1) × (NZ+1) and is the total number of corner points defining the X-Z

cross section and Z is positive downward. The following figure illustrates the input order for

an example X-Z cross section grid:
Appendix A - UTCHEM 6.1 User's Guide

156

1 2 3

4

5

6

7

8

9

XCORD(1), ZCORD(1) XCORD(2), ZCORD(2)

XCORD(9), ZCORD(9)

Top (surface) of reservoir

Z

X

The number of gridblocks is equal to NX × NZ and the number of coordinate pairs (or

nodes) is equal to (NX+1) × (NZ+1).

Cautionary warning: The X-Z cross section grid should be constructed by the user such that

the curvilinear coordinate system is at least quasi-orthogonal. Departure from

orthogonality will lead to numerical errors in the solution.

3.1.6 DX1, DY1, DZ1 (This line is read only if IDXYZ=0 and ICOORD=1 or 3)

DX1 - Gridblock size in X direction.

Units: feet (IUNIT=0) or m (IUNIT=1)

DY1 - Gridblock size in Y direction.

Units: feet (IUNIT=0) or m (IUNIT=1)

DZ1 - Gridblock size in Z direction.

Units: feet (IUNIT=0) or m (IUNIT=1)

3.1.7 R(1), DX1, DZ1 (This line is read only if IDXYZ=0 and ICOORD=2)

R(1) - Wellbore radius.

Units: feet (IUNIT=0) or m (IUNIT=1)

DX1 - Distance between nodes in radial direction.

Units: feet (IUNIT=0) or m (IUNIT=1)

DZ1 - Gridblock size in Z direction.

Units: feet (IUNIT=0) or m (IUNIT=1)

3.1.8 DY1 (This line is read only if IDXYZ=0 and ICOORD=4)

DY1 - Gridblock size in Y direction.

Units: feet (IUNIT=0) or m (IUNIT=1)

3.1.9 II1, II2, DX1 (This line is read only if IDXYZ=1 and ICOORD=1 or 3)

II1 - First index for gridblocks with same size in X direction.

II2 - Last index for gridblocks with same size in X direction.

DX1 - Gridblock size in X direction

Units: feet (IUNIT=0) or m (IUNIT=1)

Note: This line is repeated until sizes for each of the NX gridblocks in the X direction have been

specified. The first line in the set must have II1=1 and the last line must have II2=NX.

Example: If NX=11 and the first three gridblocks in the X direction are 3 feet in size, the fourth

through ninth gridblocks in the X direction are 2 feet in size, and the last two gridblocks in
Appendix A - UTCHEM 6.1 User's Guide

157

the X direction are 2.5 feet in size, this line would need to be repeated three times to fully

describe the X direction gridblocks as follows:

1 3 3.0

4 9 2.0

10 11 2.5

3.1.10 JJ1, JJ2, DY1 (This line is read only if IDXYZ=1 and ICOORD=1 or 3)

JJ1 - First index for gridblocks with same size in Y direction.

JJ2 - Last index for gridblocks with same size in Y direction.

DY1 - Gridblock size in Y direction.

Units: feet (IUNIT=0) or m (IUNIT=1)

Note: This line is repeated until sizes for each of the NY gridblocks in the Y direction have been

specified. The first line in the set must have JJ1=1 and the last line must have JJ2=NY. See

the example for input line 3.1.9.

3.1.11 KK1, KK2, DZ1 (This line is read only if IDXYZ=1 and ICOORD=1 or 3)

KK1 - First index for gridblocks with same size in Z direction.

KK2 - Last index for gridblocks with same size in Z direction.

DZ1 - Gridblock size in Z direction.

Units: feet (IUNIT=0) or m (IUNIT=1)

Note: This line is repeated until sizes for each of the NZ gridblocks in the Z direction have been

specified. The first line in the set must have KK1=1 and the last line must have KK2=NZ.

See the example for input line 3.1.9.

3.1.12 R(1) (This line is read only if IDXYZ=1 and ICOORD=2)

R(1) - Wellbore radius.

Units: feet (IUNIT=0) or m (IUNIT=1)

3.1.13 II1, II2, DX1 (This line is read only if IDXYZ=1 and ICOORD=2)

II1 - First index for radial node distances of the same size.

II2 - Last index for radial node distances of the same size.

DX1 - Distance between nodes in radial direction.

Units: feet (IUNIT=0) or m (IUNIT=1)

Note: This line is repeated until the NX-1 distances between the NX nodes in the radial direction

have been specified. The first line in the set must have II1=1 and the last line must have

II2=NX-1.

Example: If NX=35 and the first ten gridblocks in the X direction are 1 foot in size and the rest are

2 feet in size, this line would need to be repeated twice to fully describe the radial direction

nodes as follows:

1 10 1.0

11 34 2.0

3.1.14 KK1, KK2, DZ1 (This line is read only if IDXYZ=1 and ICOORD=2)

KK1 - First index for gridblocks with same size in Z direction.

KK2 - Last index for gridblocks with same size in Z direction.

DZ1 - Gridblock size in Z direction.

Units: feet (IUNIT=0) or m (IUNIT=1)
Appendix A - UTCHEM 6.1 User's Guide

158

Note: This line is repeated until sizes for each of the NZ gridblocks in the Z direction have been

specified. The first line in the set must have KK1=1 and the last line must have KK2=NZ.

See the example for input line 3.1.9.

3.1.15 JJ1, JJ2, DY1 (This line is read only if IDXYZ=1 and ICOORD=4)

JJ1 - First index for gridblocks with same size in Y direction.

JJ2 - Last index for gridblocks with same size in Y direction.

DY1 - Gridblock size in Y direction.

Units: feet (IUNIT=0) or m (IUNIT=1)

Note: This line is repeated until sizes for each of the NY gridblocks in the Y direction have been

specified. The first line in the set must have JJ1=1 and the last line must have JJ2=NY. See

the example for input line 3.1.9.

3.1.16 DX(I), for I=1, NX (This line is read only if IDXYZ=2 and ICOORD=1 or 3)

DX(I) - Grid size of Ith block in X direction.

Units: feet (IUNIT=0) or m (IUNIT=1)

3.1.17 DY(J), for J=1, NY (This line is read only if IDXYZ=2 and ICOORD=1 or 4)

DY(J) - Grid size of Jth block in Y direction.

Units: feet (IUNIT=0) or m (IUNIT=1)

3.1.18 DY(I), for I=1, NX (This line is read only if IDXYZ=2 and ICOORD=3)

DY(I) - Thickness of Ith block.

Units: feet (IUNIT=0) or m (IUNIT=1)

3.1.19 DZ(K), for K=1, NZ (This line is read only if IDXYZ=2 and ICOORD=1 or 3)

DZ(K) - Grid size of Kth block in Z direction.

Units: feet (IUNIT=0) or m (IUNIT=1)

3.1.20 R(1) (This line is read only if IDXYZ=2 and ICOORD=2)

R(1) - Wellbore radius.

Units: feet (IUNIT=0) or m (IUNIT=1)

3.1.21 DX(I), for I=1, NX-1 (This line is read only if IDXYZ=2 and ICOORD=2)

DX(I) - Distance between the Ith node and the I+1th node in the radial direction.

Units: feet (IUNIT=0) or m (IUNIT=1)

3.1.22 DZ(K), for K=1, NZ (This line is read only if IDXYZ=2 and ICOORD=2)

DZ(K) - Grid size of Kth block in Z direction.

Units: feet (IUNIT=0) or m (IUNIT=1)

3.1.23 N, NO, NTW, NTA, NGC, NG, NOTH

N - Total number of components in the run (including tracers and reactive components).

Value must be set equal to: N=8+NO+NTW+NTA+NGC+NG+NOTH

NO - Total number of NAPL phase organic components in the run.
Appendix A - UTCHEM 6.1 User's Guide

159

Note: If IBIO=1, set NO=0 if no NAPL phase is present and all biodegrading species are

present only in the aqueous phase; otherwise, set NO to the number of organic

species.

NTW - Number of water/oil tracers.

NTA - Number of oil/gas tracers.

NGC - Number of components for geochemistry option.

NG - Number of gel components.

NOTH - Total number of other chemical and biological species that are considered in

biodegradation reactions, including products generated by biodegradation reactions,

nutrients required for biological growth, electron acceptors, and biological species.

Note: See Section A.7 of this appendix for the component numbering scheme used in UTCHEM

and Section 9 of this report for more details on the microbiological population model

options.

3.1.24 SPNAME(I), for I=1, N

SPNAME(I) - Name of Ith species.

Note: The name of each component may not exceed 8 characters and each name must be

on a separate line of the input file.

3.1.25 ITRU(I), for I=1, NTW (This line is read only if NTW>0 and ITREAC=1)

ITRU(I) - Flag indicating the units of the Ith water tracer.

Possible Values:

1 - Ith tracer units are in volume %

2 - Ith tracer units are in weight %

3.1.26 ICF(KC), for KC=1, N

ICF(KC) - Flag indicating if KCth component is included in the calculations or not.

Possible Values:

0 - The KCth component is not included in the calculations

1 - The KCth component is included in the calculations

Example: If 11 components are considered but Alcohol 2 is not present, this line would appear as

follows:

1 1 1 1 1 1 1 0 1 1 1

3.2 Output Option Data

The second input section consists of output options. Please remember that there are seven

comment lines at the beginning of this section and that each data line is preceded by three comment

lines.

3.2.1 ICUMTM, ISTOP

ICUMTM - Flag indicating if the output intervals indicated by the CUMPR1, CUMHI1, WRHPV,

WRPRF and RSTC variables on input line 3.7.8 are specified in pore volumes or days.

Possible Values:

0 - Data will be written in day intervals

1 - Data will be written in pore volume intervals

Note: The day interval output option (ICUMTM=0) is particularly useful if there is a shut

in period.
Appendix A - UTCHEM 6.1 User's Guide

160

ISTOP - Flag indicating if the maximum and injection times (variables TMAX on input line 3.3.1

and TINJ on input line 3.7.8) are specified in pore volumes or days.

Possible Values:

0 - TMAX and TINJ are specified in days

1 - TMAX and TINJ are specified in pore volumes

Note: A 3rd variable (ICOPSM) which used to control printing to UNIT 3 is no longer available

with the latest version of UTCHEM.

3.2.2 IPRFLG(KC), for KC=1, N

IPRFLG(KC) - Flag indicating if profile of KCth component should be written to UNIT 8.

Possible Values:

0 - Profile of KCth component will not be written

1 - Profile of KCth component will be written

Note: If IPCTOT=0, none of the component profiles will be written.

Example: If 11 components are present and only profiles for the oil, surfactant, and polymer

components are desired, this line would appear as follows:

0 1 1 1 0 0 0 0 0 0 0

3.2.3 IPPRES, IPSAT, IPCTOT, IPTRAC, IPCAP, IPGEL, IPALK, IPTEMP, IPOBS, IBPR

IPPRES - Flag indicating if profile of phase pressures should be written to UNIT 11.

Possible Values:

0 - Profile of phase pressures will not be written

1 - Profile of phase pressures will be written

IPSAT - Flag indicating if profile of phase saturations should be written to UNIT 12.

Possible Values:

0 - Profile of phase saturations will not be written

1 - Profile of phase saturations will be written

IPCTOT - Flag indicating if profile of component concentrations should be written to UNIT 8.

Possible Values:

0 - Profile of component concentrations will not be written

1 - Profile of component concentrations will be written

IPTRAC - Flag indicating if profile of tracer phase concentrations should be written to UNIT 13.

Possible Values:

0 - Profile of tracer phase concentrations will not be written

1 - Profile of tracer phase concentrations will be written

IPCAP - Flag indicating if profile of capacitance properties should be written to UNIT 14.

Possible Values:

0 - Profile of capacitance properties will not be written

1 - Profile of capacitance properties will be written

IPGEL - Flag indicating if profile of gel properties should be written to UNIT 10.

Possible Values:

0 - Profile of gel properties will not be written

1 - Profile of gel properties will be written

IPALK - Flag indicating if profile of properties related to the alkaline option should be written to

UNIT 15.

Possible Values:

0 - Profile of properties related to the alkaline option will not be written
Appendix A - UTCHEM 6.1 User's Guide

161

1 - Profile of properties related to the alkaline option will be written

IPTEMP - Flag indicating if profile of reservoir temperature should be written to UNIT 18.

Possible Values:

0 - Profile of temperature will not be written

1 - Profile of temperature will be written

IPOBS - Flag indicating if aqueous phase tracer concentration at observation points should be

written to the TRACxx output files.

Possible Values:

0 - Aqueous phase tracer concentrations at observation points will not be written

1 - Aqueous phase tracer concentrations at observation points will be written

IBPR - Flag indicating if chemical and biological species concentrations in the aqueous phase and

within attached biomass should be written to UNITS 4, 8, and HISTl.

Possible Values:

0 - Aqueous and intra-biomass concentrations will not be written

1 - Aqueous and intra-biomass concentrations will be written

3.2.4 IPHP, IADS, ICKL, IVEL, IVIS, IPER, ICNM, IRKF, IPHSE, ICSE

IPHP - Flag indicating if oleic and microemulsion phase pressure data should be printed.

Possible Values:

0 - Oleic and microemulsion phase pressure data will not be printed

1 - Oleic and microemulsion phase pressure data will be printed

IADS - Flag indicating if surfactant, polymer, calcium, gel, chromium, hydrogen, and sodium

adsorption data should be printed.

Possible Values:

0 - Adsorption data will not be printed

1 - Adsorption data will be printed

ICKL - Flag indicating if component concentration data in each phase should be printed.

Possible Values:

0 - Component concentration data in each phase will not be printed

1 - Component concentration data in each phase will be printed

IVEL - Flag indicating if X, Y, and Z direction phase fluxes should be printed.

Possible Values:

0 - X, Y, and Z direction phase fluxes will not be printed

1 - X, Y, and Z direction phase fluxes will be printed

IVIS - Flag indicating if phase viscosities should be printed.

Possible Values:

0 - Phase viscosities will not be printed

1 - Phase viscosities will be printed

IPER - Flag indicating if relative permeabilities should be printed.

Possible Values:

0 - Relative permeabilities will not be printed

1 - Relative permeabilities will be printed

ICNM - Flag indicating if phase capillary numbers and interfacial tensions should be printed.

Possible Values:

0 - Capillary numbers, residual saturations, and interfacial tensions will not be

printed

1 - Capillary numbers, residual saturation, and interfacial tensions will be printed
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162

IRKF - Flag indicating if permeability reduction factors should be printed.

Possible Values:

0 - Permeability reduction factors, polymer viscosities, and equivalent shear rate will

not be printed

1 - Permeability reduction factors, polymer viscosities, and equivalent shear rate will

be printed

IPHSE - Flag indicating if phase environment indexing should be printed.

Possible Values:

0 - Phase environment indexing will not be printed

1 - Phase environment indexing will be printed

Note: The indices for the phase environment are as follows:

1 - single phase

2 - two phase oil/water or oil/microemulsion or water/microemulsion

3 - three phase oil/microemulsion/water

4 - lobe II(+) of type III

5 - lobe II(-) of type III

ICSE - Flag indicating if effective salinity should be printed.

Possible Values:

0 - Effective salinity information will not be printed

1 - Effective salinity will be printed to PROFIL and history data files

Note: These flags give the option of printing a very detailed description (all flags = 1) every

CUMPR1 pore volume interval or a very limited description (all flags = 0) to UNIT 4. See

Section A.4 of this appendix for a list of the values that are written to UNIT 4 automatically.

3.2.5 NOBS (This line is read only if IPOBS=1)

NOBS - Number of tracer concentration observation points.

3.2.6 IOBS(I), JOBS(I), KOBS(I), for I=1, NOBS (This line is read only if IPOBS=1 and NOBS>0)

IOBS(I) - Index of Ith observation point in X direction.

JOBS(I) - Index of I

th observation point in Y direction.

KOBS(I) - Index of Ith observation point in Z direction.

Note: See the note for input line 3.3.6 for a description of how the gridblocks are ordered in

UTCHEM.

3.3. Reservoir Properties

The third input section consists of the reservoir properties. Please remember that there are

seven comment lines at the beginning of this section and that each data line is preceded by three

comment lines.

3.3.1 TMAX

TMAX - Total injection period (maximum simulation time).

Units: days or pore volumes (dependent on value of ISTOP flag in line 3.2.1)

3.3.2 COMPR, PSTAND

COMPR - Rock compressibility.

Units: 1/psi (IUNIT=0) or 1/kPa (IUNIT=1)

PSTAND - Reference pressure at which pore volume and fluid compressibilities are specified.
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163

Units: psi (IUNIT=0) or kPa (IUNIT=1)

Reservoir/Aquifer Properties (Lines 3.1.3-3.1.17)

3.3.3 IPOR1, IPERMX, IPERMY, IPERMZ, IMOD

IPOR1 - Flag indicating constant or variable porosity for reservoir.

Possible Values:

0 - Constant porosity for whole reservoir

1 - Constant porosity for each layer

2 - Variable porosity over reservoir

IPERMX - Flag indicating constant or variable X direction permeability (ICOORD=1 or 3) or radial

direction permeability (ICOORD=2) for reservoir.

Possible Values:

0 - Constant permeability for whole reservoir

1 - Constant permeability for each layer in the X direction (ICOORD=1 or 3) or

radial direction (ICOORD=2)

2 - Variable permeability over reservoir

IPERMY - Flag indicating constant or variable Y direction permeability for reservoir.

Possible Values:

0 - Constant permeability for whole reservoir

1 - Constant permeability for each layer in the Y direction

2 - Variable permeability over reservoir

3 - Y direction permeability is dependent on X direction permeability

IPERMZ - Flag indicating constant or variable Z direction permeability for reservoir.

Possible Values:

0 - Constant permeability for whole reservoir

1 - Constant permeability for each layer in the Z direction

2 - Variable permeability over reservoir

3 - Z direction permeability is dependent on X direction permeability

IMOD - Flag indicating whether the reservoir properties are modified or not.

Possible Values:

0 - No property is modified

1 - Allow for property modification
Appendix A - UTCHEM 6.1 User's Guide

164

Refer to the following flowchart to help determine which input lines should be used to specify the porosity

and permeability values for different options:

IPOR1

3.3.4

3.3.5

3.3.6

3.3.7

3.3.8

3.3.9

3.3.10

3.3.11

3.3.12

3.3.13

3.3.14

3.3.15

3.3.16

3.3.17

0

1

2

0

1

2

0

1

2

3

0

1

2

3

IPERMX

IPERMY

IPERMZ

(only if

ICOORD ° 2)

3.3.4 PORC1 (This line is read only if IPOR1=0)

PORC1 - Reservoir porosity.

Units: fraction

Note: All elements of the POR array will be set equal to PORC1.

3.3.5 POR(K), for K=1, NZ (This line is read only if IPOR1=1)

POR(K) - Porosity of Kth layer.

Units: fraction

Note: NZ values are actually read into a workspace array (WKSP1) and then the first set of

NX × NY elements (corresponding to layer 1) of the POR array are set equal to WKSP1(1),

the second set of NX × NY elements (corresponding to layer 2) of the POR array are set

equal to WKSP1(2), etc.

3.3.6 POR(I), for I=1, NBL (This line is read only if IPOR1=2)

POR(I) - Porosity of Ith gridblock

Units: fraction
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165

Notes:

1) The three-dimensional grid system is being read into a one-dimensional array. The

first index (column) of the three-dimensional system varies fastest, the second index

(row) varies next fastest, and the third index (layer) varies slowest. The total number

of gridblocks, NBL, is NX × NY × NZ.

Example: If you had a 4 × 3 × 2 system (4 columns—NX=4, 3 rows—NY=3, and 2

layers—NZ=2), the values would be read in the following order:

1,1,1 2,1,1 3,1,1 4,1,1

1,2,1 2,2,1 3,2,1 4,2,1

1,3,1 2,3,1 3,3,1 4,3,1

1,1,2 2,1,2 3,1,2 4,1,2

1,2,2 2,2,2 3,2,2 4,2,2

1,3,2 2,3,2 3,3,2 4,3,2

2) The transmissibilities are set to zero for gridblocks with porosity values less than or

equal to 0.01 (ICOORD=1).

3) To specify certain gridblocks as inactive, the user needs to set the porosity for the

inactive cells to a very small number (e.g. 10-6).

 3.3.7 PERMXC (This line is read only if IPERMX=0)

PERMXC - Permeability of the reservoir in the X direction or in the radial direction (ICOORD=2).

Units: millidarcies = 10-3 μm2

Note: All elements of the PERMX array will be set equal to PERMXC.

3.3.8 PERMX(K), for K=1, NZ (This line is read only if IPERMX=1)

PERMX(K) - Permeability of the Kth layer in the X direction or in the radial direction

(ICOORD=2).

Units: millidarcies = 10-3 μm2

Note: See the note for input line 3.3.5.

3.3.9 PERMX(I), for I=1, NBL (This line is read only if IPERMX=2)

PERMX(I) - Permeability of the Ith gridblock in the X direction or in the radial direction

(ICOORD=2).

Units: millidarcies = 10-3 μm2

Note: See the note and example for input line 3.3.6 for the order of the permeability values.

3.3.10 PERMYC (This line is read only if IPERMY=0 and ICOORD•2)

PERMYC - Permeability of the reservoir in the Y direction.

Units: millidarcies = 10-3 μm2

Note: All elements of the PERMY array will be set equal to PERMYC.

3.3.11 PERMY(K), for K=1, NZ (This line is read only if IPERMY=1 and ICOORD•2)

PERMY(K) - Permeability of the Kth layer in the Y direction.

Units: millidarcies = 10-3 μm2

Note: See note for input line 3.3.5.
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166

3.3.12 PERMY(I), for I=1, NBL (This line is read only if IPERMY=2 and ICOORD•2)

PERMY(I) - Permeability of the Ith gridblock.

Units: millidarcies = 10-3 μm2

Note: See the note and example for input line 3.3.6 for the order of the permeability

values.

3.3.13 FACTY (This line is read only if IPERMY=3 and ICOORD•2)

FACTY - Constant permeability multiplier for Y direction permeability.

Units: dimensionless

Note: The X direction permeabilities are multiplied by FACTY to obtain the Y direction

permeabilities.

3.3.14 PERMZC (This line is read only if IPERMZ=0)

PERMZC - Permeability of the reservoir in the Z direction.

Units: millidarcies = 10-3 μm2

Note: All elements of the PERMZ array will be set equal to PERMZC.

3.3.15 PERMZ(K), for K=1, NZ (This line is read only if IPERMZ=1)

PERMZ(K) - Permeability of the Kth layer in the Z direction.

Units: millidarcies = 10-3 μm2

Note: See note for input line 3.3.5.

3.3.16 PERMZ(I), for I=1, NBL (This line is read only if IPERMZ=2)

PERMZ(I) - Permeability of the Ith gridblock.

Units: millidarcies (10-3 μm2)

Note: See the note and example for input line 3.3.6 for the order of the permeability

values.

3.3.17 FACTZ (This line is read only if IPERMZ=3)

FACTZ - Constant permeability multiplier for Z direction permeability.

Units: dimensionless

Note: The X direction permeabilities are multiplied by FACTZ to obtain the Z direction

permeabilities.

Initial Reservoir/Aquifer Data (Lines 3.3.18-3.3.36)

3.3.18 IDEPTH, IPRESS, ISWI

IDEPTH - Flag indicating type of depth measurement of the top layer.

Possible Values:

0 - Single value for depth of the top layer is specified

1 - Depth of top gridblock (1,1,1) and the reservoir dip angles are specified

2 - Depth of each gridblock in the top layer is specified

Note: If ICOORD=2, this value is automatically set equal to 0. The depth is specified at

the middle of a gridblock.

IPRESS - Flag indicating type of reservoir initial pressure measurement.

Possible Values:

0 - Single value for reservoir initial pressure is used for all gridblocks
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1 - Initial pressure for a point at a specified depth is specified by user

2 - Initial pressure for each gridblock is specified by user

ISWI - Flag indicating type of initial water saturation measurement.

Possible Values:

0 - Single value for initial water saturation is used for all gridblocks

1 - Constant value for water saturation for each layer is specified by user

2 - Initial water saturation for each gridblock is specified by user

Refer to the following flowchart to help determine which input lines should be used to specify the initial

properties such as depth, pressure, initial water saturations, initial gas saturations when IGAS•1, and initial

organic concentrations when NO>1:

3.3.19

3.3.20

3.3.21

3.3.22

3.3.23

3.3.24

3.3.25

3.3.26

3.3.27

3.3.29

3.3.30

3.3.31

3.3.33

3.3.34

3.3.35

0

1

2

0

1

2

0

1

2

0

1

2

0

1

2

IDEPTH

ISWI

IPRESS

ISGI

(only if

IGAS=1)

ICOI

(only if

NO>1)

3.3.19 D111 (This line is read only if IDEPTH=0)

D111 - Depth of the top layer of the reservoir measured from the surface (reference plane), positive

downward.

Units: feet (IUNIT=0) or m (IUNIT=1)

Note: If IDEPTH=0 and ICOORD=4, D111 is the reference depth of the first gridblock.

3.3.20 D111, THETAX, THETAY (This line is read only if IDEPTH=1)

D111 - Depth of the first gridblock (1,1,1).

Units: feet (IUNIT=0) or m (IUNIT=1)

THETAX - Reservoir dip angle in X direction, positive downward.

Units: radians

THETAY - Reservoir dip angle in Y direction, positive downward.

Units: radians
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168

Note: If ICOORD=4, set THETAY equal to 0 (dip angle in X-Z plane).

3.3.21 EL(I), for I=1, NX × NY (This line is read only if IDEPTH=2)

EL(I) - Depth of Ith gridblock in the top layer (K=1).

Units: feet (IUNIT=0) or m (IUNIT=1)

Note: See the note and example for input line 3.3.6 for the order of the gridblock depths.

3.3.22 PRESS1 (This line is read only if IPRESS=0)

PRESS1 - Initial reservoir pressure.

Units: psi (IUNIT=0) or kPa (IUNIT=1)

3.3.23 PINIT, HINIT (This line is read only if IPRESS=1)

PINIT - Initial reservoir pressure at HINIT depth.

Units: psia (IUNIT=0) or kPa (IUNIT=1)

HINIT - Depth of the point where PINIT initial pressure is specified.

Units: feet (IUNIT=0) or m (IUNIT=1)

Note: Initial pressure is assumed to be the aqueous phase pressure.

3.3.24 P(I), for I=1, NBL (This line is read only if IPRESS=2)

P(I) - Initial pressure of each gridblock in the reservoir.

Units: psia (IUNIT=0) or kPa (IUNIT=1)

Note: See the note and example for input line 3.3.6 for the order of the initial pressure

values. This is assumed to be the aqueous phase pressure.

3.3.25 SWI (This line is read only if ISWI=0)

SWI - Initial water saturation for all gridblocks of the reservoir.

Units: fraction of pore volume

3.3.26 S(K,1), for K=1, NZ (This line is read only if ISWI=1)

S(K,1) - Initial water saturation for Kth layer.

Units: fraction of pore volume

Note: See the note for input line 3.3.5.

3.3.27 S(I,1), for I=1, NBL (This line is read only if ISWI=2)

S(I,1) - Initial water saturation for Ith block.

Units: fraction of pore volume

Note: See the note and example for input line 3.3.6 for the order of the initial water

saturation values.

3.3.28 ISGI (This line is read only if IGAS•1)

ISGI - Flag indicating type of initial gas saturation.

Possible Values:

0 - Constant initial gas saturation for whole reservoir

1 - Constant initial gas saturation for each layer

2 - Initial gas saturation for each gridblock is specified by user
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3.3.29 SGI (This line is read only if IGAS•1 and ISGI=0)

SGI - Initial gas saturation for all gridblocks of the reservoir.

Units: fraction of pore volume

3.3.30 S(K,4), for K=1, NZ (This line is read only if IGAS•1 and ISGI=1)

S(K,4) - Initial gas saturation for Kth layer.

Units: fraction of pore volume

Note: See the note for input line 3.3.5.

3.3.31 S(I,4), for I=1, NBL (This line is read only if IGAS•1 and ISGI=2)

S(I,4) - Initial gas saturation for Ith gridblock.

Units: fraction of pore volume

Note: See the note and example for input line 3.3.6 for the order of the initial gas

saturation values.

Initial Organic Concentrations (Lines 3.3.32-3.3.35) — This section is required only if the multiple

organic option is used (NO>1).

3.3.32 ICOI (This line is read only if NO>1)

ICOI - Flag indicating type of initial oil phase compositions.

Possible Values:

0 - Constant initial oil phase concentration for whole reservoir

1 - Constant initial oil phase concentration for each layer

2 - Initial oil phase concentration for each gridblock

3.3.33 COI(KO), for KO=1, NO (This line is read only if NO>1 and ICOI=0)

COI(KO) - Initial oil phase concentration for oil component KO for the reservoir.

Units: volume fraction

3.3.34 COI(K,KO), for K=1, NZ, for KO=1, NO (This line is read only if NO>1 and ICOI=1)

COI(K, KO) - Initial oil phase concentration for oil component KO at Kth layer.

Units: volume fraction

3.3.35 COI(I,KO), for I=1, NBL, for KO=1,NO (This line is read only if NO>1 and ICOI=2)

COI(I,KO) - Initial oil phase concentration for oil component KO at Ith gridblock.

Units: volume fraction

Reservoir Property Modification Data (Lines 3.3.36-3.3.46) — This section is required only if

IMOD=1.

3.3.36 IMPOR, IMKX, IMKY, IMKZ, IMSW (This line is read only if IMOD=1)

IMPOR - Flag indicating whether the porosity is modified or not.

Possible Values:

0 - No modification is considered in porosity values

1 - Allow modification in porosity

IMKX- Flag indicating whether the permeability in the X direction is modified or not.

Possible Values:
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170

0 - No modification is considered in X permeability

1 - Allow modification in X permeability

IMKY- Flag indicating whether the permeability in the Y direction is modified or not.

Possible Values:

0 - No modification is considered in Y permeability

1 - Allow modification in Y permeability

IMKZ- Flag indicating whether the permeability in the Z direction is modified or not.

Possible Values:

0 - No modification is considered in Z permeability

1 - Allow modification in Z permeability

IMSW- Flag indicating whether the initial water saturation is modified or not.

Possible Values:

0 - No modification is considered in initial water saturation values

1 - Allow modification in initial water saturation

3.3.37 NMOD0 (This line is read only if IMOD=1 and IMPOR=1)

NMOD0 - Number of regions with modified porosity.

3.3.38 IMIN, IMAX, JMIN, JMAX, KMIN, KMAX, IFACT, FACTX (This line is read only if IMOD=1

and NMOD>0)

IMIN - The first index in X direction.

IMAX - The last index in X direction.

JMIN - The first index in Y direction.

JMAX - The last index in Y direction.

KMIN - The first index in Z direction.

KMAX - The last index in Z direction.

IFACT - Flag indicating how porosity is modified.

Possible Values:

1 - Replace porosity with FACTX

2 - Multiply porosity by FACTX

3 - Add FACTX to porosity

FACTX - The constant used to modify the porosity value.

Note: See the note for input line 3.3.6 for a description of how the gridblocks are ordered in

UTCHEM. This line is repeated NMOD0 times.

3.3.39 NMOD1 (This line is read only if IMOD=1 and IMKX=1)

NMOD1 - Number of regions with modified X permeability.

3.3.40 IMIN, IMAX, JMIN, JMAX, KMIN, KMAX, IFACT, FACTX (This line is read only if IMOD=1

and NMOD1>0)

IMIN - The first index in X direction.

IMAX - The last index in X direction.

JMIN - The first index in Y direction.

JMAX - The last index in Y direction.

KMIN - The first index in Z direction.

KMAX - The last index in Z direction.

IFACT - Flag indicating how X permeability is modified.
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Possible Values:

1 - Replace X permeability with FACTX

2 - Multiply X permeability by FACTX

3 - Add FACTX to X permeability

FACTX - The constant used to modify the X permeability value.

Note: See the note for input line 3.3.6 for a description of how the gridblocks are ordered in

UTCHEM. This line is repeated NMOD1 times.

3.3.41 NMOD2 (This line is read only if IMOD=1 and IMKY=1)

NMOD2 - Number of regions with modified Y permeability.

3.3.42 IMIN, IMAX, JMIN, JMAX, KMIN, KMAX, IFACT, FACTX (This line is read only if IMOD=1

and NMOD2>0)

IMIN - The first index in direction.

IMAX - The last index in X direction.

JMIN - The first index in Y direction.

JMAX - The last index in Y direction.

KMIN - The first index in Z direction.

KMAX - The last index in Z direction.

IFACT - Flag indicating how Y permeability is modified.

Possible Values:

1 - Replace Y permeability with FACTX

2 - Multiply Y permeability by FACTX

3 - Add FACTX to Y permeability

FACTX - The constant used to modify the Y permeability value.

Note: See the note for input line 3.3.6 for a description of how the gridblocks are ordered in

UTCHEM. This line is repeated NMOD2 times.

3.3.43 NMOD3 (This line is read only if IMOD=1 and IMKZ=1)

NMOD3 - Number of regions with modified Z permeability.

3.3.44 IMIN, IMAX, JMIN, JMAX, KMIN, KMAX, IFACT, FACTX (This line is read only if IMOD=1

and NMOD3>0)

IMIN - The first index in X direction.

IMAX - The last index in X direction.

JMIN - The first index in Y direction.

JMAX - The last index in Y direction.

KMIN - The first index in Z direction.

KMAX - The last index in Z direction.

IFACT - Flag indicating how Z permeability is modified.

Possible Values:

1 - Replace Z permeability with FACTX

2 - Multiply Z permeability by FACTX

3 - Add FACTX to Z permeability

FACTX - The constant used to modify the Z permeability value.

Note: See the note for input line 3.3.6 for a description of how the gridblocks are ordered in

UTCHEM. This line is repeated NMOD3 times.
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172

3.3.45 NMOD4 (This line is read only if IMOD=1 and IMSW=1)

NMOD4 - number of regions with modified initial water saturation.

3.3.46 IMIN, IMAX, JMIN, JMAX, KMIN, KMAX, IFACT, FACTX (This line is read only if IMOD=1

and NMOD4>0)

IMIN - The first index in X direction.

IMAX - The last index in X direction.

JMIN - The first index in Y direction.

JMAX - The last index in Y direction.

KMIN - The first index in Z direction.

KMAX - The last index in Z direction.

IFACT - Flag indicating how initial water saturation is modified.

Possible Values:

1 - Replace initial water saturation with FACTX

2 - Multiply initial water saturation by FACTX

3 - Add FACTX to initial water saturation

FACTX - The constant used to modify the initial water saturation value.

Note: See the note for input line 3.3.6 for a description of how the gridblocks are ordered in

UTCHEM. This line is repeated NMOD4 times.

3.3.47 NMOD5 (This line is read only if IMOD=1, IMSW=1, and IGAS•1)

NMOD5 - number of regions with modified initial gas saturation.

3.3.48 IMIN, IMAX, JMIN, JMAX, KMIN, KMAX, IFACT, FACTX (This line is read only if IMOD=1

and NMOD5>0)

IMIN - The first index in X direction.

IMAX - The last index in X direction.

JMIN - The first index in Y direction.

JMAX - The last index in Y direction.

KMIN - The first index in Z direction.

KMAX - The last index in Z direction.

IFACT - Flag indicating how initial gas saturation is modified.

Possible Values:

1 - Replace initial gas saturation with FACTX

2 - Multiply initial gas saturation by FACTX

3 - Add FACTX to initial gas saturation

FACTX - The constant used to modify the initial gas saturation value.

Note: See the note for input line 3.3.6 for a description of how the gridblocks are ordered in

UTCHEM. This line is repeated NMOD5 times.

3.3.49 C50, C60

C50 - Initial brine salinity.

Units: meq/ml of brine

Note: This is assumed to be all the anions (in equivalents).

C60 - Initial divalent cation concentration of brine.

Units: meq/ml of brine
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Note: C50 and C60 are replaced by the input values of C5I and C6I on input line 3.5.34 when

IREACT>1.

3.4 General Physical Property Data

The fourth input section consists of the general physical property data. Please remember that

there are seven comment lines at the beginning of this section and that each data line is preceded by

three comment lines.

Surfactant/Cosolvent Phase Behavior Data (Lines 3.4.1-3.4.21)

3.4.1 C2PLC, C2PRC, EPSME, IHAND

C2PLC - Oil concentration at plait point in type II(+) region.

Units: volume fraction

C2PRC - Oil concentration at plait point in type II(-) region.

Units: volume fraction

EPSME - Critical micelle concentration (CMC)—minimum surfactant concentration for the

formation of micelles.

Units: volume fraction

IHAND - Flag to specify whether modified Hand's rule is considered or not.

Possible Values:

0 - Original Hand's rule is considered for phase behavior (default)

1 - Modified Hand's rule is considered for Phase behavior

Note: The option of IHAND=1 is available only for oil/microemulsion, Type II(-) phase

behavior, and IMASS=1.

3.4.2 IFGHBN

IFGHBN - Flag indicating type of phase behavior parameters.

Possible

0 - Input height of binodal curve (default)

1 - Input solubilization ratio (new option)

Note: The input height of binodal curve option (IFGHBN=1) is currently only available for the

multiple organic option (NO>1). The effect of temperature or alcohol on phase behavior is

not currently modeled for IFGHBN=1. See Sections 2 & 11 of this report for more details

on the input height of binodal curve option and Section 7 for more details on the input

solubilization ratio option.

Binodal Curve Input Option (Lines 3.4.3-3.4.11) — This section is required only if IFGHBN=0.

3.4.3 HBNS70, HBNC70, HBNS71, HBNC71, HBNS72, HBNC72 (This line is read only if

IFGHBN=0)

HBNS70 - Slope for maximum height of binodal curve vs. fraction of Alcohol 1 associated with

surfactant at zero salinity.

Units: volume fraction

HBNC70 - Intercept of maximum height of binodal curve at zero fraction of Alcohol 1 (associated

with surfactant at zero salinity.

Units: volume fraction
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HBNS71 - Slope for maximum height of binodal curve vs. fraction of Alcohol 1 associated with

surfactant at optimal salinity.

Units: volume fraction

HBNC71 - Intercept of maximum height of binodal curve at zero fraction of Alcohol associated

with surfactant at optimal salinity.

Units: volume fraction

HBNS72 - Slope for maximum height of binodal curve vs. fraction of Alcohol 1 associated with

surfactant at twice optimal salinity.

Units: volume fraction

HBNC72 - Intercept of maximum height of binodal curve at zero fraction of Alcohol 1 associated

with surfactant at twice optimal salinity.

Units: volume fraction

Note: If alcohol is not present, the maximum height of binodal curves at three different

salinities are the only parameters used in the phase behavior calculations.

3.4.4 HBNT70, HBNT71, HBNT72, CSET (This line is read if IFGHBN=0 and IENG=1)

HBNT70 - Slope of height of binodal curve versus temperature at zero salinity

Units: volume fraction/(•F) (IUNIT=0) or volume fraction/•C (IUNIT=1)

HBNT71 - Slope of height of binodal curve versus temperature at optimal salinity

Units: volume fraction /(•F) (IUNIT=0) or volume fraction/•C (IUNIT=1)

HBNT72 - Slope of height of binodal curve versus temperature at twice optimal salinity

Units: volume fraction /(•F) (IUNIT=0) or volume fraction/•C (IUNIT=1)

CSET - The Slope parameter, βT, for temperature dependency of the three-phase window

Units: (•F)-1 (IUNIT=0) or (•C)-1 (IUNIT=1)

3.4.5 HBNS80, HBNC80, HBNS81, HBNC81, HBNS82, HBNC82 (This line is read if IFGHBN=0)

HBNS80 - Slope for maximum height of binodal curve vs. fraction of Alcohol 2 associated with

surfactant at zero salinity.

Units: volume fraction

HBNC80 - Intercept of maximum height of binodal curve at zero fraction of Alcohol 2 associated

with surfactant at zero salinity.

Units: volume fraction

HBNS81 - Slope of maximum height of binodal curve vs. fraction of Alcohol 2 associated with

surfactant at optimal salinity.

Units: volume fraction

HBNC81 - Intercept of maximum height of binodal curve at zero fraction of Alcohol 2 associated

with surfactant at optimal salinity.

Units: volume fraction

HBNS82 - Slope for maximum height of binodal curve vs. fraction of Alcohol 2 associated with

surfactant at twice optimal salinity.

Units: volume fraction

HBNC82 - Intercept of maximum height of binodal curve at zero fraction of Alcohol 2 associated

with surfactant at twice optimal salinity.

Units: volume fraction
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3.4.6 CSEL7, CSEU7, CSEL8, CSEU8 (This line is read if IFGHBN=0)

CSEL7 - Lower effective salinity limit for type III phase region determined when Alcohol 1 and

calcium approach zero.

Units: meq/ml

CSEU7 - Upper effective salinity limit for type III phase region determined when Alcohol 1 and

calcium approach zero.

Units: meq/ml

CSEL8 - Lower effective salinity limit for type III phase region determined when Alcohol 2 and

calcium approach zero.

Units: meq/ml

CSEU8 - Upper effective salinity limit for type III phase region determined when Alcohol 2 and

calcium approach zero.

Units: meq/ml

3.4.7 BETA6, BETA7, BETA8 (This line is read if IFGHBN=0)

BETA6 - The effective salinity slope parameter for calcium.

Units: dimensionless

BETA7 - The effective salinity slope parameter for Alcohol 1.

Units: dimensionless

BETA8 - The effective salinity slope parameter for Alcohol 2.

Units: dimensionless

3.4.8 IALC, OPSK7O, OPSK7S, OPSK8O, OPSK8S (This line is read if IFGHBN=0)

IALC - Flag indicating choice of alcohol partition model to use.

Possible Values:

0 - Hirasaki's model will be used

1 - Prouvost's model will be used

OPSK7O - Alcohol partition coefficient (oil/water) for Alcohol 1.

Units: dimensionless

OPSK7S - Alcohol partition coefficient (surfactant/water) for Alcohol 1.

Units: dimensionless

OPSK8O - Alcohol partition coefficient (oil/water) for Alcohol 2.

Units: dimensionless

OPSK8S - Alcohol partition coefficient (surfactant/water) for Alcohol 2.

Units: dimensionless

Note: If IALC=0 then OPSK7O, OPSK7S, OPSK8O, and OPSK8S remain fixed. If OPSK7O,

OPSK7S, OPSK8O, and OPSK8S are equal to zero and IALC=0, then alcohol is lumped

with surfactant as a single component (total chemical). OPSK7O, OPSK7S, OPSK8O, and

OPSK8S are only used when Hirasaki's model is chosen. See Section 11 of this report for

more details on the alcohol partition models.

3.4.9 NALMAX, EPSALC (This line is read if IFGHBN=0)

NALMAX - Maximum number of iterations for alcohol partitioning for two alcohol system.

Note: The suggested value is 20 and a value of zero would result in no iterations.

EPSALC - Tolerance for convergence of iterations for two alcohol system.

Note: Suggested values are 10-3 and 10-4.
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3.4.10 AKWC7, AKWS7, AKM7, AK7, PT7 (This line is read if IFGHBN=0)

AKWC7, AKWS7 - Parameters used to determine partition coefficient of monomeric Alcohol 1

between aqueous and oleic pseudophases.

Units: dimensionless

AKM7 - Partition coefficient of monomeric Alcohol 1 between surfactant and oleic pseudophases.

Units: dimensionless

AK7 - Self-association constant of Alcohol 1 in oleic pseudophase.

Units: dimensionless

PT7 - Ratio of molar volume of Alcohol 1 to equivalent molar volume of surfactant.

Units: dimensionless

3.4.11 AKWC8, AKWS8, AKM8, AK8, PT8 (This line is read if IFGHBN=0)

AKWC8, AKWS8 - Parameters used to determine partition coefficient of monomeric Alcohol 2

between aqueous and oleic pseudophases.

Units: dimensionless

AKM8 - Partition coefficient of monomeric Alcohol 2 between surfactant and oleic pseudophases.

Units: dimensionless

AK8 - Self-association constant of Alcohol 2 in oleic pseudophase.

Units: dimensionless

PT8 - Ratio of molar volume of Alcohol 2 to equivalent molar volume of surfactant.

Units: dimensionless

Solubilization Ratio Input Option (Lines 3.4.12-3.4.21) — These lines are required only if the phase

behavior calculation is based on the solubilization ratio (IFGHBN=1).

3.4.12 IOD (This line is read if IFGHBN=1 and NO>1)

IOD - Flag indicating whether phase behavior depends on organic composition

Possible Values:

0 - Phase behavior and properties depend on organic composition

1 - Phase behavior and properties are independent of organic composition (default)

3.4.13 NCOMP (This line is read only if IFGHBN=1 and IOD=0)

NCOMP - Number of organic components in the first solubility measurement.

3.4.14 ONAME(I) for I=1, NCOMP (This line is read only if IFGHBN=1 and IOD=0)

ONAME(I) - Name of organic species in the first solubility measurement. Currently the values in

the following table can be specified.

ONAME

Value

Formula Name Molecular

Weight

Equivalent

Alkane

Carbon No.

(EACN)

DECANE C10H22 Decane 142 10

OCTANE C8H18 Octane 114 8

HEXANE C6H14 Hexane 86 6
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177

PCE C2Cl4 Tetrachloroethylene

165.8 2.9

PXYLEN P-xylene 106 2

TOLUEN Toluene 92 1

CCL4 CCl4 Carbon

tetrachloride

153.8 -0.06

TCE C2HCl3 Trichloroethylene131.4 -3.81

DCB 1,2-C6H4Cl2 1,2-dichlorobenzene146.9 -4.89

TCA CH3CCl3 1,1,1-trichloroethene133.35 -2.5

DCE 1,2-C2H4Cl2 98.9 -12.1

CHCL3 CHCl3 119.4 -13.67

CH2CL2 CH2Cl2 84.9 -13.79

C2CL4 1,1,2,2-C2H2Cl4 167.8 -22.15

3.4.15 OCOMP(I), for I=1, NCOMP (This line is read only if IFGHBN=1 and IOD=0)

OCOMP(I) - concentration of Ith organic component in the first solubility measurement.

Units: mole fraction

3.4.16 CS0, SCS0, CS1, SCS1, CS2, SCS2, DCS20 (This line is read only if IFGHBN=1)

CS0 - Effective salinity which is between the lower and optimal effective salinity limits for type III

phase region; CSEL<CS0<CSEOP.

Units: meq/ml

SCS0 - Solubility at CS0.

Units: volume fraction

CS1 - Optimal effective salinity (CSEOP).

Units: meq/ml•

SCS1 - Solubility at CS1.

Units: volume fraction

CS2 -Effective salinity which is between the optimal and the upper effective salinity limits for type

III phase region ; CSEOP<CS2<CSEU.

Units: meq/ml•

SCS2 - Solubility at CS2.

Units: volume fraction

DCS20 - The difference of the upper and the lower effective salinity limits for type III phase

region; CSEU - CSEL.

3.4.17 NCOMP (This line is read only if IFGHBN=1 and IOD=0)

NCOMP - Number of organic components in the second solubility measurement.

3.4.18 ONAME(I), for I=1, NCOMP (This line is read only if IFGHBN=1 and IOD=0)

ONAME(I) - Name of organic species in the second solubility measurement.

Note: See input line 3.4.14 for a list of available species names.
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3.4.19 OCOMP(I), for I=1, NCOMP (This line is read only if IFGHBN=1 and IOD=0)

OCOMP(I) - concentration of Ith organic component in the second solubility measurement.

Units: mole fraction

3.4.20 CS0, SCS0, CS1, SCS1, CS2, SCS2, DCS20 (This line is read only if IFGHBN=1 and IOD=0)

CS0 - Effective salinity which is between the lower and optimal effective salinity limits for type III

phase region; CSEL<CS0<CSEOP.

Units: meq/ml

SCS0 - Solubility at CS0.

Units: volume fraction

CS1 - Optimal effective salinity.

Units: meq/ml

SCS1 - Solubility at CS1.

Units: volume fraction

CS2 -Effective salinity which is between the optimal and the upper effective salinity limits for type

III phase region ; CSEOP<CS2<CSEU.

Units: meq/ml

SCS2 - Solubility at CS2.

Units: volume fraction

DCS20 - The difference of the upper and the lower effective salinity limits for type III phase

region; CSEU - CSEL.

Note: These values are the phase behavior information for the second organic mixture.

3.4.21 BETA6 (This line is read only if IFGHBN=1)

BETA6 - The effective salinity slope parameter for calcium.

Units: dimensionless

Interfacial Tension Data (Lines 3.4.22-3.4.25)

3.4.22 IFT

IFT - This flag indicates which interfacial tension correlation is used.

Possible Values:

0 - Healy and Reed's correlation will be used

1 - Huh's correlation will be used

Note: See Section 2 of this report for more details on the interfacial tension model options.

3.4.23 G11, G12, G13, G21, G22, G23 (This line is read only if IFT=0)

G11, G12, G13 - Interfacial tension parameters for water-microemulsion interface.

G21, G22, G23 - Interfacial tension parameters for oil-microemulsion interface.

Units: Dimensionless

3.4.24 CHUH, AHUH (This line is read only if IFT=1)

CHUH - Constant in modified Huh's interfacial tension correlation.

Typical Values: 0.1 - 0.35

AHUH - Constant in modified Huh's interfacial tension correlation

Typical values: 5 - 20
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179

3.4.25 XIFTW

XIFTW - log10 σwo where σwo is the interfacial tension of the water-oil interface.

Units: dynes/cm = mN/m

Organic Mass Transfer Data (Lines 3.4.26-3.4.29)

3.4.26 IMASS

IMASS - Flag indicating the choice of oil solubility in water.

Possible Values

0 - No solubility of oil in water in the absence of surfactant

1 - Allow for solubility of oil in water in the absence of surfactant or allow for

nonequilibrium transfer of oil in water

3.4.27 WSOL, CNEM2, ISOL (This line is read only if NO•1 and IMASS=1 and IGAS=0 with surfactant

being present)

WSOL - Equilibrium concentration of oil in water in the absence of surfactant.

Units: volume fraction

CNEM2 - Coefficient of nonequilibrium mass transfer of oil in aqueous phase with or without

surfactant.

Units: vol. of water/(bulk vol.-day)

Note: The input value of zero for CNEM2 represents an equilibrium mass transfer. The

nonequilibrium mass transfer (CNEM2>0) calculation is valid for type II(-) with the

plait point in the corner (C2PLC=0) and in the absence of gas phase (IGAS=0).

ISOL - Flag indicating the solution scheme for the nonequilibrium mass transfer calculations

Possible Values

0 - Implicit method is used

1 - Explicit method is used

Note: The explicit method (ISOL=1) is the only option available when gas is present

(IGAS•1).

Note: See Section 12 of this report for more details on the rate limited organic dissolution model.

3.4.28 (WSOL(KO), for KO=1, NO), CNEM2, ISOL (This line read only if NO>1, IMASS=1, and

IGAS=0 with surfactant being present)

WSOL(KO) - Water/oil equilibrium partition coefficient for oil component KO in the absence of

surfactant

Units: volume fraction

CNEM2 - Coefficient of nonequilibrium mass transfer of oil components in aqueous phase when

surfactant is present.

Units: vol. of water / (bulk vol.-day)

ISOL - Flag indicating whether the mass transfer calculation is implicit or explicit when surfactant

is present.

Possible Values:

0 - Implicit method is used

1 - Explicit method is used
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3.4.29 CNEMK(KO), for KO=1, NO (This line read only if NO>1, IMASS=1, and WSOL(KO)>0)

CNEMK(KO) - Coefficient of nonequilibrium mass transfer of oil component KO in aqueous phase

when surfactant is not present.

Units: vol. of water / (bulk vol.-day)

Note: See Section 7 of this report for more details on the rate limited multiple organic dissolution

model.

3.4.30 ITRAP, T11, T22, T33

ITRAP - Flag indicating whether residual saturations and relative permeabilities are dependent on

capillary number or not.

Possible Values:

0 - Residual saturations are not dependent on capillary number; endpoint and

exponent of relative permeability curves are constant

1 - Residual saturations and relative permeabilities are dependent on capillary

number

2 - Residual saturations and relative permeabilities are dependent on trapping

number

Note: ITRAP=2 is currently not available with the curvilinear grid option (ICOORD=4) or

when gas is present (IGAS•1)

T11 - Capillary desaturation curve parameter for aqueous phase.

T22 - Capillary desaturation curve parameter for oleic phase.

T33 - Capillary desaturation curve parameter for microemulsion phase.

Note: Options ITRAP=1 and ITRAP=2 are identical for 1-d displacement in the vertical direction

with zero capillary pressure. See Section 2 of this report for more information on the

capillary and trapping number options.

Relative Permeability Data (Lines 3.4.31-3.4.57)

3.4.31 IPERM, IHYST, IPARK

IPERM - Flag indicating which relative permeability and capillary pressure model is used.

Possible Values:

0 - Imbibition Corey

1 - First drainage Corey (only for two phase water/oil flow)

2- Parker and Lenhard's model

Note: See Section 2 of this report for more details on this option.

IHYST - Flag indicating whether the hysteresis is used with Parker and Lenhard's model

(IPERM=2)

Possible Values:

0 - Hysteretic model is not used

1 - Hysteretic model is used

Note: See Section 3 of this report for more details on this option.

IPARK - Flag indicating the model used to calculate the oil trapping for hysteretic model

Possible Values:

0 - Kalurachchi and Parker's model is used

1 - Parker and Lenhard's model is used
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181

Low Capillary Number Data (Lines 3.4.32-3.4.54)

Refer to the following flowchart to help determine which input lines should be used to specify the relative

permeability parameters for different options:

3.4.34

3.4.38-3.4.40

0

1

2

ISRW

3.4.35-3.4.37

3.4.41

3.4.45-3.4.47

0

1

2

IPRW

3.4.42-3.4.44

3.4.48

3.4.52-3.4.54

0

1

2

IEW

3.4.49-3.4.51

3.4.34

3.4.38-3.4.40

0

1

2

ISRW

3.4.35-3.4.37

0, 1

2

IPERM

3.4.32 ISRW, IPRW, IEW (This line is read only for IPERM< 2)

ISRW - Flag indicating type of residual saturation.

Possible Values:

0 - Constant residual saturation for entire reservoir

1 - Constant residual saturation for each layer

2 - Residual saturation for each gridblock

IPRW - Flag indicating type of endpoint relative permeability.

Possible Values:

0 - Constant endpoint relative permeability for entire reservoir

1 - Constant endpoint relative permeability for each layer

2 - Constant endpoint relative permeability for each gridblock

IEW - Flag indicating type of relative permeability exponent.

Possible Values:

0 - Constant relative permeability exponent for entire reservoir

1 - Constant relative permeability exponent for each layer

2 - Constant relative permeability exponent for each gridblock
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3.4.33 ISRW (This line is read only if IPERM=2)

ISRW - Flag indicating type of residual saturation.

Possible Values:

0 - Constant residual saturation for entire reservoir

1 - Constant residual saturation for each layer

2 - Residual saturation for each gridblock

3.4.34 S1RWC, S2RWC, S3RWC (This line is read only if ISRW=0)

S1RWC - Residual saturation of aqueous phase displaced by oil at low capillary number for entire

reservoir.

Units: fraction

S2RWC - Residual saturation of oleic phase displaced by water at low capillary number for entire

reservoir.

Units: fraction

S3RWC - Residual saturation of microemulsion phase displaced by water at low capillary number

for entire reservoir.

Units: fraction

3.4.35 S1RWC(K), for K=1, NZ (This line is read only if ISRW=1)

S1RWC(K) - Residual saturation of aqueous phase displaced by oil or gas at low capillary number

for Kth layer.

Units: fraction

Note: S1RWC(K) must begin a separate line in the input file for each layer.

3.4.36 S2RWC(K), for K=1, NZ (This line is read only if ISRW=1)

S2RWC(K) - Residual saturation of oleic phase displaced by water at low capillary number for Kth

layer.

Units: fraction

Note: S2RWC(K) must begin a separate line in the input file for each layer.

3.4.37 S3RWC(K), for K=1, NZ (This line is read only if ISRW=1)

S3RWC(K) - Residual saturation of microemulsion phase displaced by water or oil at low capillary

number for Kth layer.

Units: fraction

Note: S3RWC(K) must begin a separate line in the input file for each layer.

3.4.38 S1RW(I), for I=1, NBL (This line is read only if ISRW=2)

S1RW(I) - Residual saturation of aqueous phase displaced by oil or gas at low capillary number for

I

th gridblock.

Units: fraction

3.4.39 S2RW(I), for I=1, NBL (This line is read only if ISRW=2)

S2RWC(K) - Residual saturation of oleic phase displaced by water at low capillary number for Ith

gridblock.

Units: fraction
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3.4.40 S3RW(I), for I=1, NBL (This line is read only if ISRW=2)

S3RW(I) - Residual saturation of microemulsion phase displaced by water or oil at low capillary

number for Ith gridblock.

Units: fraction

Relative Permeability Endpoint and Exponent Data (Lines 3.4.41-3.4.54) — These lines are required

only if Corey function (IPERM<2) is used.

3.4.41 P1RWC, P2RWC, P3RWC (This line is read only if IPERM<2 and IPRW=0)

P1RWC - End point relative permeability of water at low capillary number for entire reservoir.

Units: dimensionless

P2RWC - End point relative permeability of oil at low capillary number for entire reservoir.

Units: dimensionless

P3RWC - End point relative permeability of microemulsion at low capillary number for entire

reservoir.

Units: dimensionless

3.4.42 P1RWC(K), for K=1, NZ (This line is read only if IPERM<2 and IPRW=1)

P1RWC(K) - Constant endpoint relative permeability of water at low capillary number for Kth

layer.

Units: dimensionless

3.4.43 P2RWC(K), for K=1, NZ (This line is read only if IPERM<2 and IPRW=1)

P2RWC(K) - Constant endpoint relative permeability of oil at low capillary number for Kth layer.

Units: dimensionless

3.4.44 P3RWC(K), for K=1, NZ (This line is read only if IPERM<2 and IPRW=1)

P3RWC(K) - Constant endpoint relative permeability of microemulsion at low capillary number for

Kth layer.

Units: dimensionless

3.4.45 P1RW(I), for I=1, NBL (This line is read only if IPERM<2 and IPRW=2)

P1RW(I) - Endpoint relative permeability of water at low capillary number for Ith gridblock.

Units: dimensionless

3.4.46 P2RW(I), for I=1, NBL (This line is read only if IPERM<2 and IPRW=2)

P2RW(I) - Endpoint relative permeability of oil at low capillary number for Ith gridblock.

Units: dimensionless

3.4.47 P3RW(I), for I=1, NBL (This line is read only if IPERM<2 and IPRW=2)

P3RW(I) - Endpoint relative permeability of microemulsion at low capillary number for Ith

gridblock.

Units: dimensionless
Appendix A - UTCHEM 6.1 User's Guide

184

3.4.48 E1WC, E2WC, E3WC (This line is read only if IPERM<2 and IEW=0)

E1WC - Phase relative permeability exponent for aqueous phase at low capillary number for entire

reservoir.

Units: dimensionless

E2WC - Phase relative permeability exponent for oleic phase at low capillary number for entire

reservoir.

Units: dimensionless

E3WC - Phase relative permeability exponent for microemulsion phase at low capillary number

system for entire reservoir.

Units: dimensionless

3.4.49 E1WC(K), for K=1, NZ (This line is read only if IPERM<2 and IEW=1)

E1WC(K) - Relative permeability exponent of aqueous phase at low capillary number for Kth layer.

Units: dimensionless

3.4.50 E2WC(K), for K=1, NZ (This line is read only if IPERM<2 and IEW=1)

E2WC(K) - Relative permeability exponent of oleic phase at low capillary number for Kth layer.

Units: dimensionless

3.4.51 E3WC(K), for K=1, NZ (This line is read only if IPERM<2 and IEW=1)

E3WC(K) - Relative permeability exponent of microemulsion phase at low capillary number for

Kth layer.

Units: dimensionless

3.4.52 E1W(I), for I=1, NBL (This line is read only if IPERM<2 and IEW=2)

E1W(I) - Relative permeability exponent of aqueous phase at low capillary number for Ith

gridblock.

Units: dimensionless

3.4.53 E2W(I), for I=1, NBL (This line is read only if IPERM<2 and IEW=2)

E2W(I) - Relative permeability exponent of oleic phase at low capillary number for Ith gridblock.

Units: dimensionless

3.4.54 E3W(I), for I=1, NBL (This line is read only if IPERM<2 and IEW=2)

E3W(I) - Relative permeability exponent of microemulsion phase at low capillary number for Ith

gridblock.

Units: dimensionless

High Capillary Number Data (Lines 3.4.55-3.4.57) — These lines are required only if ITRAP=1 or

ITRAP=2.

3.4.55 S1RC, S2RC, S3RC (This line is read only if ITRAP=1 or 2)

S1RC - Residual saturation of aqueous phase at high capillary number.

Units: fraction

S2RC - Residual saturation of oleic phase at high capillary number.

Units: fraction

S3RC - Residual saturation of microemulsion phase at high capillary number.
Appendix A - UTCHEM 6.1 User's Guide

185

Units: fraction

Note: The residual saturations at high capillary number can not be set equal to those at low

capillary number.

3.4.56 P1RC, P2RC, P3RC (This line is read only for ITRAP=1 or 2 and IPERM< 2)

P1RC - End point relative permeability of aqueous phase at high capillary number condition.

Units: dimensionless

P2RC - End point relative permeability of oleic phase at high capillary number condition.

Units: dimensionless

P3RC - End point relative permeability of microemulsion phase at high capillary number condition.

Units: dimensionless

3.4.57 E13C, E23C, E31C (This line is read only for ITRAP=1 or 2 and IPERM< 2)

E13C, E23C, E31C - Parameters used for calculating exponents for relative permeability

calculations at high capillary number.

Units: dimensionless

Viscosity Data (Lines 3.4.58-3.4.63)

3.4.58 VIS1, VIS2, TSTAND

VIS1 - Water viscosity at reference temperature.

Units: cp = mPa.s

VIS2 - Oil viscosity at reference temperature.

Units: cp = mPa.s

TSTAND - Reference temperature

Units: •F (IUNIT=0) or •C (IUNIT=1)

Note: For IENG=0, if TSTAND=0.0, the water component viscosity will be constant and

equal to the input value VIS1. If TSTAND>0.0, water component viscosity will be

calculated as a function of reservoir temperature, pressure, and local salinity for each

gridblock.

3.4.59 IOVIS (This line read only if NO>1)

IOVIS - Flag indicating whether the viscosity is a function of organic composition.

Possible Values:

0 - Viscosity does not depend on the organic species concentration.

1 - Viscosity depends on the organic species concentration.

Note: See Section 2 of this report for more information on the IOVIS=0 option and

Section 7 for more information on the IOVIS=1 option.

3.4.60 OVIS(K), for K=1, NO (This line is read only if NO>1 and IOVIS=1)

OVIS(K) - Viscosity for organic component K at reference temperature.

Units: cp = mPa.s

3.4.61 VIS4, VSLOPG (This line is read only if IGAS•1)

VIS4 - Gas viscosity at reference temperature and reference pressure.

Units: cp = mPa.s

VSLOPG - Slope of gas viscosity.
Appendix A - UTCHEM 6.1 User's Guide

186

Units: (psi)-1 (IUNIT=0) or (kPa)-1 (IUNIT=1)

3.4.62 BVI(1), BVI(2) (This line is read only if IENG=1)

BVI(1) - Parameter for calculating water viscosity as a function of reservoir temperature.

Units: (•K)-1

BVI(2) - Parameter for calculating oil viscosity as a function of reservoir temperature.

Units: (•K)-1

3.4.63 BVI(4) (This line is read only if IGAS•1 and IENG=1)

BVI(4) - Parameter for calculating gas viscosity as a function of reservoir temperature.

Units: (•K)-1

Corey Option Gas Relative Permeability Data (Lines 3.4.64-3.4.75) — These lines are required only if

IGAS•1 and IPERM=0.

Refer to the following flowchart to help determine which input lines should be used to specify the gas

relative permeability parameters for different options:

3.4.64

3.4.67-3.4.68

0

1

2

ISRW

3.4.65-3.4.66

3.4.69

3.4.71

0

1

2

IPRW

3.4.70

3.4.72

3.4.74

0

1

2

IEW

3.4.73

IPERM=0

IGAS=1

3.4.64 S2RWC4, S4RWC (This line is read only if ISRW=0)

S2RWC4 - Constant residual oil saturation to displacing gas phase for entire reservoir.

Units: fraction

S4RWC - Constant residual gas saturation for entire reservoir.

Units: fraction

3.4.65 S2RWC4(K), for K=1, NZ (This line is read only if ISRW=1)

S2RWC4(K) - Constant residual oil saturation to displacing gas phase for Kth layer.

Units: fraction
Appendix A - UTCHEM 6.1 User's Guide

187

3.4.66 S4RWC(K), for K=1, NZ (This line is read only if ISRW=1)

S4RWC(K) - Constant residual gas saturation for Kth layer.

Units: fraction

3.4.67 S2RW4(I), for I=1, NBL (This line is read only if ISRW=2)

S2RW4(I) - Constant residual oil saturation to displacing gas phase for Ith gridblock.

Units: fraction

3.4.68 S4RW(I), for I=1, NBL (This line is read only if ISRW=2)

S4RW(I) - Residual gas saturation for Ith gridblock.

Units: fraction

3.4.69 P4RWC (This line is read only if IPRW=0)

P4RWC - Constant gas endpoint relative permeability for entire reservoir.

Units: dimensionless

3.4.70 P4RWC(K), for K=1, NZ (This line is read only if IPRW=1)

P4RWC(K) - Constant gas endpoint relative permeability for Kth layer.

Units: dimensionless

3.4.71 P4RW(I), for I=1, NBL (This line is read only if IPRW=2)

P4RW(I) - Constant gas endpoint relative permeability for Ith gridblock.

Units: dimensionless

3.4.72 E4WC (This line is read only if IEW=0)

E4WC - Constant gas relative permeability exponent for entire reservoir.

Units: dimensionless

3.4.73 E4WC(K), for K=1, NZ (This line is read only if IEW=1)

E4WC(K) - Constant gas relative permeability exponent for Kth layer.

Units: dimensionless

3.4.74 E4WC(I), for I=1, NBL (This line is read only if IEW=2)

E4WC(I) - Constant gas relative permeability exponent for Ith gridblock.

Units: dimensionless

3.4.75 S4RC, P4RC, E4C, T44 (This line is read only if ITRAP=1)

S4RC - Residual gas saturations at high capillary number.

Units: fraction

P4RC - Gas endpoint relative permeability at high capillary number.

Units: dimensionless

E4C - Gas relative permeability exponent at high capillary number.

Units: dimensionless

T44 - Gas phase trapping parameter.

Units: dimensionless
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188

3.4.76 XIFTG, XIFTGW (This line is read only if IGAS•1)

XIFTG - Log of interfacial tension between gas and oil.

Units: dyne/cm = mN/m

XIFTGW - Log of interfacial tension between gas and water.

Units: dyne/cm = mN/m

Microemulsion Viscosity Data (Line 3.4.77)

3.4.77 ALPHAV(I), for I=1, 5

ALPHAV(I) - Compositional phase viscosity parameters.

Units: dimensionless

Note: All five viscosity parameters must be positive values.

Note: See Section 2 of this report for more information on the compositional viscosity model.

Polymer Property Data (Lines 3.4.78-3.4.81) — See Section 2 of this report for information on the

polymer property models.

3.4.78 AP1, AP2, AP3

AP1, AP2, AP3 - Parameters used for calculating polymer viscosity at zero shear rate as a function

of polymer and electrolyte concentrations.

Units: (wt. %)-1, (wt. %)-2, (wt. %)-3

3.4.79 BETAP, CSE1, SSLOPE

BETAP - Parameter for calculating the effective divalent salinity used to calculate polymer

viscosity.

Units: dimensionless

CSE1 - Value below which the polymer viscosity is considered to be independent of salinity.

Units: meq/ml

SSLOPE - Slope of viscosity vs. effective salinity on a log-log plot—assumed to be constant.

Units: dimensionless

Note: This value is usually large and negative for hydrolyzed polyacrylamides and small

and positive for polysaccharides.

3.4.80 GAMMAC, GAMHF, POWN

GAMMAC - Coefficient in shear rate equation below.

Units: 

day(darcy)

1 2

ft − sec

 (IUNIT=0) or 

day μm

2

( )

1 2

m − sec

 (IUNIT=1)

GAMHF - Shear rate at which polymer viscosity is one half polymer viscosity at zero shear rate.

Units: sec-1

POWN - Exponent for calculating shear rate dependence of polymer viscosity.

Units: dimensionless

3.4.81 IPOLYM, EPHI3, EPHI4, BRK, CRK

IPOLYM - Flag indicating type of polymer partitioning.

Possible Values:
Appendix A - UTCHEM 6.1 User's Guide

189

0 - All polymer exists in aqueous phase if aqueous phase exists; otherwise, it exists

completely in microemulsion phase

1 - Partitioning of polymer to water component is constant

EPHI3 - Effective porosity for surfactant—ratio of apparent porosity for surfactant to actual

porosity.

Units: dimensionless

EPHI4 - Effective porosity for polymer—ratio of apparent porosity for polymer to actual porosity.

Units: dimensionless

BRK - Parameter for calculating permeability reduction factor.

Units: volume of polymer − richphase

weight%polymer

CRK - Parameter for calculating permeability reduction factor.

Units: (darcy)1/2 (100 g/g)-1/3 = (μm2)

1/2 (100 g/g)-1/3)

Note: EPHI3 and EPHI4 are used to account for inaccessible pore volume in the case of surfactant

and polymer.

φsurfactant = φ × EPHI3

φpolymer = φ × EHPI4

The effect of permeability reduction or residual resistance is to reduce the mobility of the

polymer rich phase. This is accounted for by multiplying the viscosity of the phase by

BRK.

Component Density Data (Lines 3.4.82-3.4.88)

3.4.82 DEN1, DEN2, DEN23, DEN3, DEN7, DEN8, IDEN, IODEN

DEN1 - Specific weight or density of water (Component 1).

Units: psi/ft (IUNIT=0) or g/cm3 (IUNIT=1)

DEN2 - Specific weight or density of oil (Component 2).

Units: psi/ft (IUNIT=0) or g/cm3 (IUNIT=1)

DEN23 - Coefficient of oil in microemulsion phase density calculations.

Units: psi/ft (IUNIT=0) or g/cm3 (IUNIT=1)

DEN3 - Specific weight or density of surfactant (Component 3).

Units: psi/ft (IUNIT=0) or g/cm3 (IUNIT=1)

DEN7 - Specific weight or density of Alcohol 1 (Component 7).

Units: psi/ft (IUNIT=0) or g/cm3 (IUNIT=1)

DEN8 - Specific weight or density of Alcohol 2 (when IGAS=0) or gas (when IGAS•1)

(Component 7).

Units: psi/ft (IUNIT=0) or g/cm3 (IUNIT=1)

IDEN - Flag indicating if gravity effect should be considered.

Possible Values:

1 - Do not consider gravity effect

2 - Consider gravity effect

IODEN - Flag indicating if specific weight/density is a function of organic species concentration

for NO>1.

Possible Values:

0 - Does not depend on organic species concentration

1 - Depends on organic species concentration
Appendix A - UTCHEM 6.1 User's Guide

190

Note: See Section 2 of this report for information on the IODEN=0 option or Section 7 for

information on the IODEN=1 option.

Note: Specific weight for pure water is 0.433 psi/ft (density of 1 g/cm3). IODEN must be set to 1

if any non-aqueous phase species (those with indices < (8+NO)) participate in

biodegradation equations.

Multiple Organic Density Data (Lines 3.4.83-3.4.84) — These lines are required only if IODEN=1 and

NO>1.

3.4.83 DNOILC(K), for K=1, NO (This line is read only if IODEN=1 and NO>1)

DNOILC(K) - Specific weight or density of organic component K for oleic phase.

Units: psi/ft (IUNIT=0) or g/cm3 (IUNIT=1)

3.4.84 DNOME(K), for K=1, NO (This line is read only if IODEN=1 and NO>1)

DNOME(K) - Specific weight or density of organic component K for microemulsion phase.

Units: psi/ft (IUNIT=0) or g/cm3 (IUNIT=1)

Multiple Organic Data (Lines 3.4.85-3.4.88) — These lines are required only if NO>1. Furthermore, if

(IFGHBN=1 and IOD=0) or IOVIS=1.

3.4.85 INAME (This line is read only if NO>1 and ((IFGHBN=1 and IOD=0) or IOVIS=1)))

INAME - Flag indicating whether name of the organic components will be provided by user.

Possible Values:

0 - Name of the organic components will be provided; the molecular weight and

equivalent alkane carbon number will be obtained from the built-in database

1 - Molecular weight and equivalent alkane carbon number for each organic

components will be provided.

3.4.86 ONAME(K), for K=1, NO (This line is read only if NO>1 and ((IFGHBN=1 and IOD=0) or

IOVIS=1)) and INAME=0)

ONAME(K) - Name of organic component K. See input line 3.4.14 for a list of valid component

names.

3.4.87 OMWT(K), for K=1, NO (This line is read only if NO>1 and ((IFGHBN=1 and IOD=0) or

IOVIS=1)) and INAME=1)

OMWT(K) - Molecular weight for organic component K.

3.4.88 OEACN(K), for K=1, NO (This line is read only if NO>1 and ((IFGHBN=1 and IOD=0) or

IOVIS=1)) and INAME=1)

OEACN(K) - equivalent alkane carbon number for organic component K.

Note: See Section 7 of this report for information on the equivalent alkane carbon number.

3.4.89 ISTB

ISTB - Flag indicating the units to be used when printing injection and production rates.

Possible Values:

0 - Rates printed at bottomhole condition in ft3 or m3

1 - Rates printed at surface condition in bbls
Appendix A - UTCHEM 6.1 User's Guide

191

3.4.90 FVF(L), for L=1, MXP (This line is read only if ISTB=1 and IUNIT=0)

FVF(L) - Formation volume factor for Lth phase.

Units: SCF/ft3

Note: MXP=3 when IGAS=0 and MXP=4 when IGAS•1.

Fluid Compressibility Data (Lines 3.4.91-3.4.93)

3.4.91 COMPC(1), COMPC(2), COMPC(3), COMPC(7), COMPC(8)

COMPC(1) - Compressibility of brine (Component 1).

Units: 1/psi (IUNIT=0) or 1/kPa (IUNIT=1)

COMPC(2) - Compressibility of oil (Component 2).

Units: 1/psi (IUNIT=0) or 1/kPa (IUNIT=1)

COMPC(3) - Compressibility of surfactant (Component 3).

Units: 1/psi (IUNIT=0) or 1/kPa (IUNIT=1)

COMPC(7) - Compressibility of Alcohol 1 (Component 7).

Units: 1/psi (IUNIT=0) or 1/kPa (IUNIT=1)

COMPC(8) - Compressibility of Alcohol 2 (when IGAS=0) or gas (when IGAS•1) (Component 8).

Units: 1/psi (IUNIT=0) or 1/kPa (IUNIT=1)

Note: For incompressible fluids, values of zero should be used for the COMPC values listed

above.

3.4.92 ICOMPO (This line is read only if NO>1)

ICOMPO - Flag indicating whether each organic component has different compressibility.

Possible Values:

0 - All organic components have the same compressibility as COMPC(2)

1 - Each organic component has different compressibility

3.4.93 COMPO(K), for K=1, NO (This line is read only if NO>1 and ICOMPO=1)

COMPO(K) - Compressibility of organic component K.

Units: 1/psi (IUNIT=0) or 1/kPa (IUNIT=1)

Capillary Pressure Data (Lines 3.4.94-3.4.117) — See Section 2 of this report for capillary pressure

information.

3.4.94 ICPC, IEPC, IOW

ICPC - Flag indicating type of capillary pressure endpoint.

Possible Values:

0 - Constant capillary pressure endpoint for entire reservoir

1 - Constant capillary pressure endpoint for each layer

2 - Capillary pressure endpoint for each gridblock

IEPC - Flag indicating type of capillary pressure exponent.

Possible Values:

0 - Constant capillary pressure exponent for entire reservoir

1 - Constant capillary pressure exponent for each layer

2 - Capillary pressure exponent for each gridblock
Appendix A - UTCHEM 6.1 User's Guide

192

IOW - Flag indicating the wettability for two-phase oil/water capillary pressure calculations using

imbibition Corey function (IPERM=0).

Possible Values:

0 - The capillary pressure curve is for strongly water-wet rock (default)

1 - The capillary pressure curve is for strongly oil-wet rock

2 - The capillary pressure curve is for mixed-wet rocks

Note: IOW=1 and 2 are available only for IPERM=0.

Refer to the following flowchart to help determine which input lines should be used to specify the capillary

pressure data for different options:

3.4.107

3.4.113-3.4.117

0

1

2

3.4.108-3.4.112

3.4.95

3.4.97

0

1

2

3.4.96

3.4.101

3.4.103

0

1

2

3.4.102

3.4.98

3.4.100

0

1

2

3.4.99

3.4.104

3.4.106

0

1

2

3.4.105

ICPC

IOW=2

IOW=0, 1

ICPC

IOW=0, 1

IEPC

ICPC

IEPC

0

0, 1

2

IPERM

IOW=0
Appendix A - UTCHEM 6.1 User's Guide

193

Capillary Pressure Data for Strongly Water- or Oil-Wet Rocks (Lines 3.4.95-3.4.106) — These lines

are required only if IOW<2.

3.4.95 CPC0 (This line is read only if IOW<2 and ICPC=0 and IPERM<2)

CPC0 - Capillary pressure endpoint for entire reservoir.

Units: psi darcies (IUNIT=0) or kPa μm

2

 (IUNIT=1)

3.4.96 CPC(K), for K=1, NZ (This line is read only if IOW<2 and ICPC=1 and IPERM<2)

CPC(K) - Capillary pressure endpoint for Kth layer.

Units: psi darcies (IUNIT=0) or kPa μm

2

 (IUNIT=1)

3.4.97 CPC(I), for I=1, NBL (This line is read only if IOW<2 and ICPC=2 and IPERM<2)

CPC(I) - Capillary pressure endpoint for Ith gridblock.

Units: psi darcies (IUNIT=0) or kPa μm

2

 (IUNIT=1)

3.4.98 CPC0 (This line is read only if IOW=0 and ICPC=0 and IPERM=2)

CPC0 - van Genuchten capillary pressure parameter, α, for entire reservoir.

Units: (psi darcies)

−1

 (IUNIT=0) or μm

2

/ kPa (IUNIT=1)

3.4.99 CPC(K), for K=1, NZ (This line is read only if IOW=0 and ICPC=1 and IPERM=2)

CPC(K) - van Genuchten capillary pressure parameter, α, for Kth layer.

Units: (psi darcies)

−1

 (IUNIT=0) or μm

2

/ kPa (IUNIT=1)

3.4.100 CPC(I), for I=1, NBL (This line is read only if IOW=0 and ICPC=2 and IPERM=2)

CPC(I) - van Genuchten capillary pressure parameter, α, for Ith gridblock.

Units: (psi darcies)

−1

 (IUNIT=0) or μm

2

/ kPa (IUNIT=1)

3.4.101 EPC0 (This line is read only if IOW<2 and IEPC=0 and IPERM<2)

EPC0 - Capillary pressure exponent for entire reservoir.

Units: dimensionless

3.4.102 EPC(K), for K=1, NZ (This line is read only if IOW<2 and IEPC=1 and IPERM<2)

EPC(K) - Capillary pressure exponent for Kth layer.

Units: dimensionless

3.4.103 EPC(I), for I=1, NBL (This line is read only if IOW<2 and IEPC=2 and IPERM<2)

EPC(I) - Capillary pressure exponent for Ith gridblock.

Units: dimensionless

3.4.104 EPC0 (This line is read only if IOW=0 and IEPC=0 and IPERM=2)

EPC0 - van Genuchten capillary pressure parameter, n, for entire reservoir.

Units: dimensionless
Appendix A - UTCHEM 6.1 User's Guide

194

3.4.105 EPC(K), for K=1, NZ (This line is read only if IOW=0 and IEPC=1 and IPERM=2)

EPC(K) - van Genuchten capillary pressure parameter, n, for Kth layer.

Units: dimensionless

3.4.106 EPC(I), for I=1, NBL (This line is read only if IOW=0 and IEPC=2 and IPERM=2)

EPC(I) - van Genuchten capillary pressure parameter, n, for Ith gridblock.

Units: dimensionless

Capillary Pressure Data for Mixed-Wet Rocks (Lines 3.4.107-3.4.117) — These lines are required only

if IPERM=0 and IOW=2.

3.4.107 CPCW, EPCW, CPCO, EPCO, SSTAR (This line is read only if IPERM=0 and IOW=2 and

ICPC=0)

CPCW - Capillary pressure endpoint for entire reservoir for positive branch.

Units: psi darcies (IUNIT=0) or kPa μm

2

 (IUNIT=1)

EPCW - Capillary pressure exponent for entire reservoir for positive branch.

Units: dimensionless

CPCO - Capillary pressure endpoint for entire reservoir for negative branch.

Units: psi darcies (IUNIT=0) or kPa μm

2

 (IUNIT=1)

EPCO - Capillary pressure exponent for entire reservoir for negative branch.

Units: dimensionless

SSTAR - Water saturation where the capillary pressure is zero.

Units: dimensionless

3.4.108 CPCW(K), for K=1, NZ (This line is read only if IPERM=0 and IOW=2 and ICPC=1)

CPCW - Capillary pressure endpoint for kth layer for positive branch.

Units: psi darcies (IUNIT=0) or kPa μm

2

 (IUNIT=1)

3.4.109 EPCW(K), for K=1, NZ (This line is read only if IPERM=0 and IOW=2 and ICPC=1)

EPCW (K) - Capillary pressure exponent for entire reservoir.

Units: dimensionless

3.4.110 CPCO(K), for K=1, NZ (This line is read only if IPERM=0 and IOW=2 and ICPC=1)

CPCO (K) - Capillary pressure endpoint for Kth layer for negative branch.

Units: psi darcies (IUNIT=0) or kPa μm

2

 (IUNIT=1)

3.4.111 EPCO(K), for K=1, NZ (This line is read only if IPERM=0 and IOW=2 and ICPC=1)

EPCO (K) - Capillary pressure exponent for Kth layer for negative branch.

Units: dimensionless

3.4.112 SSTAR(K), for K=1, NZ (This line is read only if IPERM=0 and IOW=2 and ICPC=1)

SSTAR (K) - Water saturation for Kth layer where the capillary pressure is zero.

Units: dimensionless
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195

3.4.113 CPCW(I), for I=1, NBL (This line is read only if IPERM=0 and IOW=2 and ICPC=2)

CPCW (I) - Capillary pressure endpoint for Ith gridblock for positive branch.

Units: psi darcies (IUNIT=0) or kPa μm

2

 (IUNIT=1)

3.4.114 EPCW(I), for I=1, NBL (This line is read only if IPERM=0 and IOW=2 and ICPC=2)

EPCW (I) - Capillary pressure exponent for Ith gridblock for positive branch.

Units: dimensionless

3.4.115 CPCO(I), for I=1, NBL (This line is read only if IPERM=0 and IOW=2 and ICPC=2)

CPCO - Capillary pressure endpoint for Ith gridblock for negative branch.

Units: psi darcies (IUNIT=0) or kPa μm

2

 (IUNIT=1)

3.4.116 EPCO(I), for I=1, NBL (This line is read only if IPERM=0 and IOW=2 and ICPC=2)

EPCO - Capillary pressure exponent for Ith gridblock for negative branch.

Units: dimensionless

3.4.117 SSTAR(I), for I= 1, NBL (This line is read only if IPERM=0 and IOW=2 and ICPC=2)

SSTAR (I) - Water saturation in Ith gridblock where the capillary pressure is zero.

Units: dimensionless

Diffusion and Dispersion Data (Lines 3.4.118-3.4.125)

3.4.118 D(KC,1), for KC=1, N

D(KC,1) - Molecular diffusion coefficient of KCth component in aqueous phase.

Units: ft2/day (IUNIT=0) or m2/day (IUNIT=1)

3.4.119 D(KC,2), for KC=1, N

D(KC,2) - Molecular diffusion coefficient of KCth component in oleic phase.

Units: ft2/day (IUNIT=0) or m2/day (IUNIT=1)

3.4.120 D(KC,3), for KC=1, N

D(KC,3) - Molecular diffusion coefficient of KCth component in microemulsion phase.

Units: ft2/day (IUNIT=0) or m2/day (IUNIT=1)

3.4.121 D(KC,4), for KC=1, N (This line is read only if IGAS•1)

D(KC,4) - Molecular diffusion coefficient of KCth component in gas phase.

Units: ft2/day (IUNIT=0) or m2/day (IUNIT=1)

Note: The input diffusion coefficient should be divided by tortuosity (D/τ) where the

value of tortuosity is greater than one.

3.4.122 ALPHAL(1), ALPHAT(1)

ALPHAL(1) - Longitudinal dispersivity of aqueous phase.

Units: feet (IUNIT=0) or m (IUNIT=1)

ALPHAT(1) - Transverse dispersivity of aqueous phase.

Units: feet (IUNIT=0) or m (IUNIT=1)
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196

3.4.123 ALPHAL(2), ALPHAT(2)

ALPHAL(2) - Longitudinal dispersivity of oleic phase.

Units: feet (IUNIT=0) or m (IUNIT=1)

ALPHAT(2) - Transverse dispersivity of oleic phase.

Units: feet (IUNIT=0) or m (IUNIT=1)

3.4.124 ALPHAL(3), ALPHAT(3)

ALPHAL(3) - Longitudinal dispersivity of microemulsion phase.

Units: feet (IUNIT=0) or m (IUNIT=1)

ALPHAT(3) - Transverse dispersivity of microemulsion phase.

Units: feet (IUNIT=0) or m (IUNIT=1)

3.4.125 ALPHAL(4), ALPHAT(4) (This line is read only if IGAS•1)

ALPHAL(4) - Longitudinal dispersivity of gas phase.

Units: feet (IUNIT=0) or m (IUNIT=1)

ALPHAT(4) - Transverse dispersivity of gas phase.

Units: feet (IUNIT=0) or m (IUNIT=1)

Adsorption Data (Lines 3.4.126-3.4.129)

3.4.126 IADSO

IADSO - Flag to specify organic adsorption calculation.

Possible Values

0 - Organic adsorption calculation is not considered

1 - Organic adsorption calculation is considered

3.4.127 FOC, AKOC, DENS (This line is read only if IADSO=1 and NO•1)

FOC - fraction of organic carbon in soil.

Units: dimensionless

AKOC - Organic adsorption coefficient.

Units: μgadsorbed gorganiccarbon

μg ml solution

DENS - grain density

Units: lb/ft3 (IUNIT=0), g/cc (IUNIT=1)

Note: See Section 2 of this report for information on the organic adsorption model.

3.4.128 FOC, (AKOCK(K), for K=1, NO), DENS (This line is read only if IADSO=1 and NO>1)

FOC - Fraction of organic carbon in soil.

Units: dimensionless

AKOCK(K) - Organic adsorption coefficient for oil component K.

Units: μgadsorbed gorganiccarbon

μg ml solution

DENS - grain density.

Units: lb/ft3 (IUNIT=0), g/cc (IUNIT=1)

Note: See Section 7 of this report for information on the multiple organic adsorption model.
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197

3.4.129 AD31, AD32, B3D, AD41, AD42, B4D, IADK, IADS1, FADS

AD31 - Surfactant adsorption parameter.

Units: dimensionless

AD32 - Surfactant adsorption parameter.

Units: ml/meq

B3D - Surfactant adsorption parameter.

Units: volume of water

volume ofsurfactant

AD41 - Polymer adsorption parameter.

Units: dimensionless

AD42 - Polymer adsorption parameter.

Units: ml/meq

B4D - Polymer adsorption parameter.

Units: volume of water

weight%polymer

IADK - Permeability dependent adsorption flag

Possible Values:

0 - Surfactant and polymer adsorption is independent of permeability

1 - Surfactant and polymer adsorption is dependent on permeability

IADS1 - Flag to specify the competitive surfactant adsorption in the presence of polymer

Possible Values:

0 - Surfactant and polymer adsorption are independent

1 - Competitive surfactant and polymer adsorption is considered

FADS - Parameter to adjust the competitive adsorption calculation

Note: See Section 2 of this report for information on the surfactant and polymer adsorption

model.

3.4.130 QV, XKC, XKS, EQW

QV - Cation exchange capacity of clays.

Units: meq/ml of pore volume

XKC - Cation exchange constant for clays.

Units: (meq/ml)-1

XKS - Cation exchange constant for surfactant.

Units: (meq/ml)-1

EQW - Equivalent weight of surfactant.

Note: See Section 2 of this report for information on the cation exchange model.

Tracer Data (Lines 3.4.131-3.4.143) — These lines are required only if NTW+NTA>0. See Section 4 of

this report for more details on tracer modeling in UTCHEM.

3.4.131 TK(I), for I=1, NTW+NTA (This line is read only if NTW+NTA>0)

TK(I) - Tracer partitioning coefficient for Ith water/oil tracer at initial chloride concentration and

reference temperature. A value of 0.0 indicates a water or gas tracer and a value of -1.0

indicates an oil tracer.

Units: fraction
Appendix A - UTCHEM 6.1 User's Guide

198

3.4.132 TKS(I), for I=1, NTW (This line is read only if NTW>0)

TKS(I) - Parameter for calculating water/oil tracer partitioning coefficient for Ith tracer as a

function of salinity.

Units: (meq/ml)-1

3.4.133 TKT(I), for I=1, NTW+NTA (This line is read only if NTW+NTA>0 and IENG=1)

TKT(I) - Parameter for calculating tracer partitioning coefficient for Ith tracer as a function of

reservoir temperature.

Units: (•F)-1 (IUNIT=0) or (•C)-1 (IUNIT=1)

3.4.134 RDC(I), for I=1, NTW+NTA (This line is read only if NTW+NTA>0)

RDC(I) - Radioactive decay coefficient for Ith tracer. A value of 0.0 indicates a non–radioactive

tracer.

Units: 1/days

3.4.135 RET(I), for I=1, NTW+NTA (This line is read only if NTW+NTA>0)

RET(I) - Tracer adsorption parameter (adsorbed concentration/flowing concentration). A value of

0.0 indicates no retardation.

Units: dimensionless

Dead-end Pore Model Data (Lines 3.4.136-3.4.139) — These lines are required only if NTW+NTA>0

and ICAP=1.

3.4.136 FFL(1), FFH(1), CM(I,1), for I=1, NTW+NTA (This line is read only if NTW+NTA>0 and

ICAP=1)

FFL(1) - Water phase flowing fraction at fractional flow = 0.0.

Units: dimensionless

FFH(1) - Water phase flowing fraction at fractional flow = 1.0.

Units: dimensionless

CM(I,1) - Mass transfer coefficients for Ith tracer in water phase.

Units: 1/sec

3.4.137 FFL(2), FFH(2), CM(I,2), for I=1, NTW+NTA (This line is read only if NTW+NTA>0 and

ICAP=1)

FFL(2) - Oil phase flowing fraction at fractional flow = 0.0.

Units: dimensionless

FFH(2) - Oil phase flowing fraction at fractional flow = 1.0.

Units: dimensionless

CM(I,2) - Mass transfer coefficients for Ith tracer in oil phase.

Units: 1/sec

3.4.138 FFL(3), FFH(3), CM(I,3), for I=1, NTW+NTA (This line is read only if NTW+NTA>0 and

ICAP=1)

FFL(3) - Microemulsion phase flowing fraction at fractional flow = 0.0.

Units: dimensionless

FFH(3) - Microemulsion phase flowing fraction for at fractional flow = 1.0.

Units: dimensionless
Appendix A - UTCHEM 6.1 User's Guide

199

CM(I,3) - Mass transfer coefficients for Ith tracer in microemulsion phase.

Units: 1/sec

3.4.139 FFL(4), FFH(4), CM(I,4), for I=1, NTW+NTA (This line is read only if NTW+NTA>0 and

ICAP=1 and IGAS•1)

FFL(4) - Value of flowing fraction for gas phase when fractional flow = 0.0.

Units: dimensionless

FFH(4) - Value of flowing fraction for gas phase when fractional flow = 1.0.

Units: dimensionless

CM(I,4) - Mass transfer coefficients for Ith tracer in gas phase.

Units: 1/sec

Reacting Tracer Data (Lines 3.4.140-3.4.143) — The following lines are required only if NTW>0 and

ITREAC=1.

3.4.140 NRT, TAK(I), for I=1, NRT (This line is read only if NTW>0 and ITREAC=1)

NRT - Number of reacting tracers.

Possible Values: 1 or 2

TAK(I) - Rate constant for a first-order aqueous phase reaction at reference temperature for

reacting tracer I

Units: days-1

Note: First reacting tracer is tracer 2 hydrolyzes to form tracer 3. The second reacting tracer if

present is tracer 4 hydrolyzes to form tracer 5.

3.4.141 TMW(I), for I=1, NTW (This line is read only if NTW>0 and ITREAC=1)

TMW(I) - Molecular weight of the Ith tracer.

Units: The user can specify the molecular weight in any unit as long as the units are the

same for all the tracers. It is assumed that the reaction of 1 mole of primary tracer

produces 1 mole of secondary tracer. If not, use "equivalent" molecular weights.

3.4.142 TDEN(I), for I=1, NTW (This line is read only if NTW>0 and ITREAC=1)

TDEN(I) - Density of the Ith tracer.

Units: g/cm3

3.4.143 TAKT(I), for I=1, NRT (This line is read only if NTW>0 and ITREAC=1 and IENG=1)

TAKT(I) - Parameter for calculating rate constant for a first-order aqueous phase reaction as a

function of reservoir temperature for reacting tracer I.

Units: (•K)-1
Appendix A - UTCHEM 6.1 User's Guide

200

Dual Porosity Data (Lines 3.4.144-3.4.162) — This section is required for dual porosity option

(ICAP=2) only. This option works only with English unit (IUNIT=0) and the Cartesian coordinate

(ICOORD=1). See Section 5 of this report for more details on this option. The capability of dual porosity

option at this time is limited to single phase water and one tracer component. Restart capability

(IMODE=2) is not currently available for the dual porosity option.

3.4.144 NSUB, MSUB, ISUB (This line is read only if ICAP=2)

NSUB − Number of subgrids in lateral direction.

MSUB − Number of subgrids in vertical direction.

ISUB − Mode of subgridding

Possible Values:

0 - Uniform matrix block dimension

1 - Variable matrix block size dimension in each direction

2 - Variable matrix block dimension in whole reservoir

3.4.145 XL1, YL1, ZL1 (This line is read only if ICAP=2 and ISUB=0)

XL1, YL1 and ZL1 − Uniform matrix block sizes in x y, and z directions.

Units: feet

3.4.146 II1, II2, XL1 (This line is read only if ICAP=2 and ISUB=1)

II1, II2 - First and last index for gridblocks with same size in X direction.

XL1− Matrix block size in X direction.

Units: feet

3.4.147 JJ1, JJ2, YL1 (This line is read only if ICAP=2 and ISUB=1)

JJ1, JJ2 - First and last index for gridblocks with same size in Y direction.

YL1 − Matrix block size in Y direction.

Units: feet

3.4.148 KK1, KK2, ZL1 (This line is read only if ICAP=2 and ISUB=1)

KK1, KK2 - First and last index for gridblocks with same size in Z direction

ZL1 − Matrix block size in Z direction.

Units: feet

3.4.149 XL(I), for I=1, NBL (This line is read only if ICAP=2 and ISUB=2)

XL(I) - Matrix block size in X direction for Ith reservoir gridblock.

Units: feet

3.4.150 YL(I), for I=1, NBL (This line is read only if ICAP=2 and ISUB=2)

YL(I) - Matrix block size in Y direction for Ith reservoir gridblock.

Units: feet

3.4.151 ZL(I), for I=1, NBL (This line is read only if ICAP=2 and ISUB=2)

ZL(I), - Matrix block size in Z direction for Ith reservoir gridblock.

Units: feet
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201

3.4.152 VFRACM(J), for J=1, NSUB (This line is read only if ICAP=2)

VFRACM(J) − Volume fraction of Jth subgrid. These values are used to generate subgrids in the

lateral direction.

3.4.153 ZFRACM(J), for J=1, MSUB (This line is read only if ICAP=2)

ZFRACM − Thickness fraction of Jth vertical subgrid. These values are used to generate subgrids

in the vertical direction.

3.4.154 KPH, KKX, KKZ (This line is read only if ICAP=2)

KPH − Flag for matrix porosity distribution.

Possible Values:

0 - Uniform matrix porosity

1 - Variable matrix porosity

KKX − Flag for diffusion coefficient distribution in lateral direction in matrix.

Possible Values:

0 - Uniform matrix diffusion coefficient

1 - Uniform matrix diffusion coefficient in each reservoir layer

2 - Variable matrix diffusion coefficient at each reservoir node

KKZ − Flag for diffusion coefficient distribution in vertical direction in matrix.

Possible Values:

0 - Uniform matrix diffusion coefficient

1 - Uniform matrix diffusion coefficient in each reservoir layer

2 - Variable matrix diffusion coefficient at each reservoir node

3.4.155 PHIC (This line is read only if ICAP=2 and KPH=0)

PHIC − Matrix porosity.

3.4.156 PORCM(I,1,1), for I=1, NBL (This line is read only if ICAP=2 and KPH=1)

PORCM(I,1,1) − Matrix porosity of the Ith reservoir node.

3.4.157 DMC (This line is read only if ICAP=2 and KKX=0)

DMC − Matrix diffusion coefficient in lateral direction.

Units: ft2/day

3.4.158 DMX(K), for K=1, NZ (This line is read only if ICAP=2 and KKX=1)

DMX(K) − Matrix diffusion coefficient in Kth reservoir layer in lateral direction.

Units: ft2/day

3.4.159 DMX(I), for I=1, NBL (This line is read only if ICAP=2 and KKX=2)

DMX(I) − Matrix diffusion coefficient at Ith reservoir node in lateral direction.

Units: ft2/day

3.4.160 DMC (This line is read only if ICAP=2 and KKZ=0)

DMC − Matrix diffusion coefficient in vertical direction.

Units: ft2/day
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202

3.4.161 DMZ(K), for K=1, NZ (This line is read only if ICAP=2 and KKZ=1)

DMZ(K) − Matrix diffusion coefficient in Kth reservoir layer in vertical direction.

Units: ft2/day

3.4.162 DMZ(I), for I=1, NBL (This line is read only if ICAP=2 and KKZ=2)

DMZ(I) − Matrix diffusion coefficient at Ith reservoir node in vertical direction.

Units: ft2/day

Gel Reaction Data (Lines 3.4.163-3.4.167) — These lines are required only if IREACT=1 or

IREACT=4 and NG>0. Refer to Section 6 of this report for more details on this option.

3.4.163 KGOPT, AK1, AK2, SCR, X4, X13, X14, X16, WM4 (This line is read only if IREACT=1 or 4

and NG>0)

KGOPT - Flag to specify the gelation type used.

Possible Values:

1 - Polymer/chromium chloride gel

2 - Polymer/chromium malonate gel

3 - Silicate gel

AK1 - Kinetic rate coefficient for NG1 and NG2 at reference temperature (KGOPT=1).

Units: ppm-1 days-1

AK2 - Kinetic rate coefficient for gel at reference temperature .

Units: (mole/liter)1-X4-X14+X16 days-1 for KGOPT=1

(mole/liter)1-X4-X13+X16 days-1 for KGOPT=2

(mole/liter)1-X4+X14 days-1 for KGOPT=3

SCR - Stoichiometric ratio in mass between Cr3+ and polymer.

Units: dimensionless

X4 - Exponent to be used for polymer or silicate in gelation reaction.

Units: dimensionless

X13 - Exponent to be used for component (NG2) in gelation reaction for KGOPT=2.

Units: dimensionless

X14 - Exponent to be used for the third gel option component (NG3) in gelation reaction.

Units: dimensionless

X16 - Exponent to be used for hydrogen ion component (NG5) of gelation reaction.

Units: dimensionless

WM4 - Molecular weight of polymer (KGOPT=1 or 2) or silicate (KGOPT=3).

Units: g/mole

Note: The following tables define different gelation options and corresponding gel components.

For IREACT=1:

Component No. KGOPT=1 KGOPT=2 KGOPT=3

4 Polymer Polymer Silicate

NG1 Na2Cr2O7 - -

NG2 CSN2H4 Malonate ion -

NG3 Cr(III) Cr(III) OHNG4 Gel Gel Gel

NG5 Hydrogen Hydrogen -
Appendix A - UTCHEM 6.1 User's Guide

203

For IREACT=4:

Component NO. KGOPT=1 KGOPT=2

4 Polymer Polymer

NGC1 Sodium Sodium

NGC2 Hydrogen Hydrogen

NGC3 Magnesium Magnesium

NGC4 Carbonate Carbonate

NGC5 Chromium* Chromium*

NGC6 Silica Silica

NG1 Na2Cr2O7 -

NG2 CSN2H4 Malonate ion

NG3 Cr(III)** Cr(III)**

NG4 Gel Gel

Where NG and NGC are the gel option and geochemistry option species.

3.4.164 AK1T, AK2T (This line is read only if IREACT=1 or 4 and NG>0 and IENG=1)

AK1T - Parameter for calculating Kinetic rate coefficient for Cr3+ as a function of reservoir

temperature.

Units: (•K)-1

AK2T - Parameter for calculating Kinetic rate coefficient for gel as a function of reservoir

temperature.

Units: (•K)-1

3.4.165 AG1, AG2, CRG, AGK, BGK (This line is read only if IREACT=1 or 4 and NG>0)

AG1 - Flory-Huggins parameter for gel viscosity.

Units: cp ppm-1 = m = Pa.s ppm-1

AG2 - Flory-Huggins parameter for gel viscosity.

Units: cp ppm-2 = mPa.s ppm-2

CRG - Constant in the dimensionless pore radius reduction group. This constant depends on the

gel type.

Units: darcy(wt%)

1 3

 = μm

2

(wt%)

1 3

AGK, BGK - Permeability reduction parameters for Langmuir correlation with gel concentration.

Units: dimensionless

3.4.166 A15D, B15D, ICREX, A14D, B14D, CRNAK, HNAK, C160 (This line is read only if

IREACT=1 or 4 and NG>0)

A15D, B15D - Gel adsorption parameters.

Units: vol. of water / ppm gel

ICREX - Flag indicating if Cr3+ will be allowed to exchange with clays.

Possible Values:

0 - Cr3+ exchange with clays is not allowed

1 - Cr3+ exchange with clays is allowed

A14D, B14D - Chromium adsorption parameters.
Appendix A - UTCHEM 6.1 User's Guide

204

Units: vol. of water / ppm chromium

CRNAK - Chromium-sodium exchange reaction equilibrium constant.

HNAK - Hydrogen-sodium exchange reaction equilibrium constant.

C160 - Initial hydrogen ion concentration.

Units: meq/ml

Note: The input values of CRNAK, HNAK, and C160 are ignored for IREACT=4

3.4.167 IP1, IP2 (This line is read only if IREACT=1 or 4 and NG>0 and NY=1 and NZ=1)

IP1, IP2 - Gridblock locations where calculated pressure values should be printed to UNIT 19.

Note: These values are intended to be used for comparison with pressure tab data of 1-D

experiments.

Temperature Data (Lines 3.4.168-3.4.171) — These lines are required only if temperature variation is

considered in the simulation for IENG=1.

3.4.168 TEMPI (This line is read only if IENG=1)

TEMPI- Constant initial reservoir temperature.

Units: •F (IUNIT=0) or •C (IUNIT=1)

3.4.169 DENS, CRTC, CVSPR, (CVSPL(L), for L=1, MXP) (This line is read only if IENG=1)

DENS - Reservoir rock density.

Units: lb/ft3 (IUNIT=0) or g/cm3 (IUNIT=1)

CRTC - Reservoir thermal conductivity.

Units: Btu (day-ft-•F)-1 (IUNIT=0) or kJ (day-m-•K)-1 (IUNIT=1)

CVSPR - Reservoir rock heat capacity.

Units: Btu (lb-•F)-1 (IUNIT=0) or kJ (kg-•K)-1 (IUNIT=1)

CVSPL(L) - Phase L heat capacity (MXP is equal to 3 (IGAS=0) or 4 (IGAS•1)).

Units: Btu (lb-•F)-1 (IUNIT=0) or kJ (kg-•K)-1 (IUNIT=1)

3.4.170 IHLOS, IANAL (This line is read only if IENG=1)

IHLOS - Flag indicating if the heatloss calculation to overburden and underburden rock is

considered or not.

Possible Values:

0 - Heatloss is not considered

1 - Heatloss is considered

IANAL - Flag indicating if the temperature profile is calculated from analytical solution (only 1-

D).

Possible Values:

0 - Analytical solution is not considered

1 - Analytical solution is considered

3.4.171 TCONO, DENO, CVSPO, TCONU, DENU, CVSPU (This line is read only if IHLOS=1 and if

IENG=1)

TCONO - Thermal conductivity of overburden rock.

Units: Btu (day-ft-•F)-1 (IUNIT=0) or kJ (day-m-•K)-1 (IUNIT=1)

DENO - Density of overburden rock.

Units: lb/ft3 (IUNIT=0) or g/cm3 (IUNIT=1)
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205

CVSPO - Heat capacity of overburden rock.

Units: Btu (lb-•F)-1 (IUNIT=0) or kJ (kg-•K)-1 (IUNIT=1)

TCONU - Thermal conductivity of underburden rock.

Units: Btu (day-ft-•F)-1 (IUNIT=0) or kJ (day-m-•K)-1 (IUNIT=1)

DENU - Density of underburden rock.

Units: lb/ft3 (IUNIT=0) or g/cm3 (IUNIT=1)

CVSPU - Heat capacity of underburden rock.

Units: Btu (lb-•F)-1 (IUNIT=0) or kJ (kg-•K)-1 (IUNIT=1)

Foam Model Data (Lines 3.4.172 and 3.4.173) — These lines are required only if the foam option is

considered (IGAS=2).

3.4.172 RFMAX, SOSTAR, CSTAR, EPXLO, SHRTN, VELGR (This line is read only if IGAS=2)

RFMAX- Maximum foam "R" parameter.

Units: dimensionless

SOSTAR - Critical oil saturation above which foam is not generated.

Units: dimensionless

CSTAR - Critical surfactant concentration below which foam is not generated.

Units: volume fraction

EPXLO - Water saturation tolerance parameter in foam model.

Units: dimensionless

SHRTN - Gas shear thinning exponent.

Units: dimensionless

VELGR - Reference gas velocity.

Units: ft/day (IUNIT=0) or m/day (IUNIT=1)

3.4.173 SWSTAR(I), for I=1, NBL (This line is read only if IGAS=2)

SWSTAR(I)- Water saturation at critical capillary pressure for Ith gridblock.

Units: dimensionless

Note: SWSTAR(I) is assumed to be corrected for the permeability used in the simulation.

3.5 Physical Property Data for Geochemical Options

The fifth input section consists of physical property data for geochemistry option and it is

required only if IREACT>1. The data for this section is generated by a preprocessor program

(EQBATCH) and does not have the same format as the rest of the input data for UTCHEM. This

input section is read by a separate routine called GEOREAD not preceded by the usual seven

comment lines and individual data lines are not preceded by three comment lines. Section A.5 of

this appendix gives an example for the list of elements, fluid species, solid species, and adsorbed

species for geochemical options. See Section 8 of this report for information on the EQBATCH

program.

3.5.1 IRSPS, IPHAD

IRSPS - Flag indicating if the reactive species concentrations should be printed.

Possible Values:

0 - Reactive species concentrations will not be printed

1 - Independent aqueous reactive species, solid species, and sorbed species

concentrations will be printed
Appendix A - UTCHEM 6.1 User's Guide

206

2 - All aqueous species, solid species, and sorbed species concentrations will be

printed

IPHAD - Flag indicating whether surfactant adsorption is pH dependent or not.

Possible Values:

0 - Surfactant adsorption is not pH dependent

1 - Surfactant adsorption is pH dependent

3.5.2 PHC, PHT, PHT1, HPHAD (This line is read only if IPHAD>0)

PHC - Critical pH above which surfactant adsorption is pH dependent.

PHT - Extrapolated pH value at zero surfactant adsorption.

PHT1 - pH value above which surfactant adsorption is constant.

HPHAD - Fraction of the low-pH adsorption plateau retained at a pH above PHT1.

3.5.3 CSELP, CSEUP (This line is read only if IREACT=3)

CSELP - Lower optimum salinity limit for generated surfactant.

Units: meq/ml

CSEUP - Upper optimum salinity limit for generated surfactant.

Units: meq/ml

3.5.4 NELET, NFLD, NSLD, NSORB, NACAT, ICHRGE

NELET - Total number of elements less non reacting element.

NFLD - Total number of fluid species.

NSLD - Total number of solid species.

NSORB - Total number of sorbed species.

NACAT - Total number of surfactant associated cations.

ICHRGE - Flag indicating whether an oxygen balance or a charge balance will be used.

Possible Values:

0 - Oxygen balance used

1 - Charge balance in solution used

Note: If solid SiO2 is considered, the oxygen balance must be used.

3.5.5 NIAQ, NEX, NSLEL, NSURF1

NIAQ - Total number of independent fluid species.

NEX - Total number of insoluble exchangers.

NSLEL - Total number of elements comprising the solid species.

NSURF1 - Position number corresponding to the insitu generated surfactant anion in the fluid

species array FLDSPS.

Note: NSURF1 is automatically set to 0 by the program if IREACT=2.

3.5.6 NH, NNA, NCA, NMG, NCARB

NH - Position number corresponding to the hydrogen element in the element array ELEMNT.

NNA - Position number corresponding to the sodium element in the element array ELEMNT.

NCA - Position number corresponding to the calcium element in the element array ELEMNT.

NMG - Position number corresponding to the magnesium element in the element array ELEMNT.

NCARB - Position number corresponding to the carbonate pseudo-element in the element array

ELEMNT.

Note: A value of zero is required if the element is not considered.
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3.5.7 NALU, NSILI, NOXY

NALU - Position number corresponding to the aluminum element in the element array ELEMNT.

NSILI - Position number corresponding to the silicon element in the element array ELEMNT.

NOXY - Position number corresponding to the oxygen element in the element array ELEMNT.

Note: A value of zero is required if the element is not considered.

3.5.8 NACD (This line is read only if IREACT=3)

NACD - Position number corresponding to the petroleum acid pseudo-element in the element array

ELEMNT.

3.5.9 NCR, NHFD, NCRFD (This line is read only if IREACT=4)

NCR - Position number corresponding to the chromium element in the element array ELEMNT.

NHFD - Position number corresponding to the hydrogen ion element in the fluid species array

FLDSPS.

NCRFD - Position number corresponding to the CR(III) ion in the fluid species array FLDSPS.

3.5.10 ELEMNT(I), ELCRG(I) for I=1, NELET

ELEMNT(I) - Name of the Ith element.

ELCRG(I) - Charge for Ith element

Note: The name of each element may not exceed 32 characters and each name and charge must be

on a separate line of the input file. The order in which these elements must be listed

corresponds to the order in which the injection concentrations need to be specified on input

line 3.7.7.a with the exceptions of calcium and chloride (if they exist) since Components 5

and 6 are reserved for these elements.

3.5.11 FLDSPS(I), for I=1, NFLD

FLDSPS(I) - Name of the Ith fluid species.

Note: The name of each fluid species may not exceed 32 characters and each name must

be on a separate line of the input file. If IREACT=3, the last fluid species must be

HAw (petroleum acid in water).

3.5.12 SLDSPS(I), for I=1, NSLD (This line is read only if NSLD>0)

SLDSPS(I) - Name of the Ith solid species.

Note: The name of each solid may not exceed 32 characters and each name must be on a

separate line of the input file.

3.5.13 SORBSP(I), for I=1, NSORB (This line is read only if NSORB>0)

SORBSP(I) - Name of the Ith adsorbed cation.

Note: The name of each adsorbed cation may not exceed 32 characters and each name

must be on a separate line of the input file.

3.5.14 ACATSP(I), for I=1, NACAT (This line is read only if NACAT>0)

ACATSP(I) - Name of the Ith surfactant adsorbed cation.

Note: The name of each surfactant adsorbed cation may not exceed 32 characters and each

name must be on a separate line of the input file.
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3.5.15 NSORBX(I), for I=1, NEX (This line is read only if NSORB>0)

NSORBX(I) - Number of cations for Ith exchanger.

3.5.16 AR(I,J), for J=1, NFLD, for I=1, NELET << or >>

AR(I,J), for J=1, NFLD, for I=1, NELET-1

AR(I,J) - Stoichiometric coefficient of Ith element in Jth fluid species.

Note: If ICHRGE=0, then NFLD × NELET values are required by the program. If ICHRGE=1,

then NFLD × (NELET-1) values are required by the program.

3.5.17 BR(I,J), for J=1, NSLD, for I=1, NELET << or >>

BR(I,J), for J=1, NSLD, for I=1, NELET-1 (This line is read only if NSLD>0)

BR(I,J) - Stoichiometric coefficient of Ith element in Jth solid species.

Note: If ICHRGE=0, then NSLD × NELET values are required by the program. If ICHRGE=1,

then NSLD × (NELET-1) values are required by the program.

3.5.18 DR(I,J), for J=1, NSORB, for I=1, NELET << or >>

DR(I,J), for J=1, NSORB, for I=1, NELET-1 (This line is read only if NSORB>0)

DR(I,J) - Stoichiometric coefficient of Ith element in Jth sorbed species.

Note: If ICHRGE=0, then NSORB × NELET values are required by the program. If ICHRGE=1,

then NSORB × (NELET-1) values are required by the program.

3.5.19 ER(I,J), for J=1, NACAT, for I=1, NELET << or >>

ER(I,J), for J=1, NACAT, for I=1, NELET-1 (This line is read only if NACAT>0)

ER(I,J) - Stoichiometric coefficient of Ith element in Jth surfactant associated cation.

Note: If ICHRGE=0, then NACAT × NELET values are required by the program. If ICHRGE=1,

then NACAT × (NELET-1) values are required by the program.

3.5.20 BB(I,J), for J=1, NIAQ+NSORB+NACAT, for I=1, NFLD+NSORB+NACAT

BB(I,J) - Exponent of the Jth independent fluid species concentration when the Ith fluid species is

expressed in terms of independent species concentrations.

3.5.21 EXSLD(I,J), for J=1, NIAQ, for I=1, NSLD (This line is read only if NSLD>0)

EXSLD(I,J) - Exponent of the Jth independent fluid species concentration in the solubility product

definition of the Ith solid.

3.5.22 CHARGE(I), for I=1, NFLD

CHARGE(I) - Charge of the Ith fluid species.

3.5.23 SCHARG(I,J), for J=1, NSORBX(I), for I=1, NEX (This line is read only if NSORB>0)

SCHARG(I,J) - Charge of the Jth sorbed species on the Ith exchanger.

3.5.24 EQK(I), for I=1, NFLD

EQK(I) - Equilibrium constant for Ith fluid species when expressed in independent species

concentrations only.
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3.5.25 EXK(I,J), for J=1, NSORBX(I)-1, for I=1, NEX (This line is read only if NEX>0)

EXK(I,J) - Exchange equilibrium constant for Jth exchange equilibrium of the Ith insoluble

exchanger.

3.5.26 EXEX(I,J,K), for K=1, NIAQ+NSORB+NACAT, for J=1, NSORBX(I)-1, for I=1, NEX (This

line is read only if NEX>0)

EXEX(I,J,K) - Exponent of Kth independent species in Jth equilibrium relation of the Ith exchanger

3.5.27 REDUC(I,J), for J=1, NSORBX(I)-1, for I=1, NEX (This line is read only if NEX>0)

REDUC(I,J) - Valence difference of the two cations involved in the exchange reaction J on

exchanger I.

Note: This value is positive if the higher valence cation bulk concentration has a positive exponent

in EXEX(I,J) definition and is negative otherwise.

3.5.28 EXCAI(I), for I=1, NEX (This line is read only if NEX>0)

EXCAI(I) - Exchange capacity of Ith insoluble exchanger.

Units: meq/ml pore volume

3.5.29 SPK(I), for I=1, NSLD (This line is read only if NSLD•1)

SPK(I) - Solubility product of Ith solid defined in terms of independent fluid species concentrations

only.

3.5.30 CHACAT(I), for I=1, NACAT (This line is read only if NACAT•1)

CHACAT(I) - Charge of Ith surfactant associated cation.

3.5.31 ACATK(I), for I=1, NACAT-1 (This line is read only if NACAT•1)

ACATK(I) - Equilibrium constant for Ith exchange equilibrium for cation exchanges on surfactant.

3.5.32 EXACAT(I,J) for J=1, NIAQ+NSORB+NACAT, for I=1, NACAT-1 (This line is read only if

NACAT•1)

EXACAT(I,J) - Exponent of Jth independent species in Ith equilibrium for cation exchange on

surfactant.

3.5.33 CI(J), for J=1, NACAT (This line is read only if NACAT•1)

CI(J) - Initial concentration of Jth surfactant associated cation.

Units: moles/liter pore volume

3.5.34 C5I, C6I

C5I - Initial concentration of non-reacting anions.

Units: equivalents/liter

C6I - Initial concentration of calcium in aqueous phase.

Units: equivalents/liter

3.5.35 CELAQI(J), for J=1, NGC

CELAQI(J) - Initial concentrations of Jth geochemistry component.

Units: equivalents/liter
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3.5.36 CAC2I (This line is read only if IREACT=3)

CAC2I - Initial concentration of acid in oil.

Units: moles/liter oil

3.5.37 CAQI(J), for J=1, NIAQ

CAQI(J) - Initial guesses for Jth independent species concentration.

Units: moles/liter water

3.5.38 CSLDI(I), for I=1, NSLD (This line is read only NSLD>0)

CSLDI(I) - Initial concentration of Ith solid.

Units: moles/liter pore volume

3.5.39 CSORBI(I), for I=1, NSORB (This line is read only if NSORB>0)

CSORBI(I) - Initial concentration of Ith adsorbed cation.

Units: moles/liter pore volume

3.5.40 C1I, C2I (This line is read only if IREACT=3)

C1I - Initial concentration of water in aqueous phase.

Units: volume fraction

C2I - Initial concentration of oil in oleic phase.

Units: volume fraction

3.5.41 ACIDIS, EQWPS (This line is read only if IREACT=3)

ACIDIS - Dissociation constant of the petroleum acid.

EQWPS - Equivalent weight of petroleum acid.

3.6 Data for Biodegradation Option

The sixth input section consists of physical property data that is required only if IBIO=1.

This section includes the biodegradation and mass transfer parameters required to model the

biodegradation of chemical species. This section is read only if IBIO=1. The data is read by a

separate subroutine called BIOREAD, and is input in the standard UTCHEM format. Section 9 of

this report gives more details on this option.

3.6.1 DIAMP, DENBLK, CMIN, EPSBIO

DIAMP - Average particle size diameter (used to calculate mass transfer coefficient). A value of

DIAMP must be input whether or not mass transfer is considered. The value is ignored if

mass transfer is not considered.

Units: cm

DENBLK - Bulk density of the porous medium (mass of porous medium per unit total volume).

Units: g/cm3

CMIN - Minimum concentration of substrate and electron acceptor that is of interest. This

parameter is used for two purposes. First, if concentrations of all substrates and electron

acceptors in a gridblock are below CMIN, then biodegradation reactions are assumed

negligible at the gridblock and are not modeled. Second, when the concentration of all

substrates and electron acceptors fall below CMIN during solution of the biodegradation
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211

reaction expressions, further biodegradation reactions are assumed to be negligible and

program execution returns to the main program.

Units: mg/L

EPSBIO - Convergence tolerance for solution of the biodegradation equations.

Note: Values of 10-4 to 10-6 are recommended, although larger values can also result in

accurate simulations. Small values ensure accurate solutions of the biodegradation

equations but increase run times, while larger values decrease run times at the

expense of some accuracy.

3.6.2 NBC, NMET, IBKIN

NBC - Total number of chemical and biological species that are considered in biodegradation

reactions, including oil components, surfactants, products generated by abiotic and

biodegradation reactions, nutrients required for biological growth, electron acceptors, and

biological species.

NMET - Number of substrate-electron acceptor-biological species metabolic combinations. Include

combinations of biodegrading products-electron acceptor-biological species for each product

that also biodegrades.

IBKIN - Flag specifying the type of biodegradation kinetics.

Possible Values:

0 - No reaction (useful for restart runs)

1 - Monod kinetics and external mass transfer resistances

2 - Monod kinetics with no mass transfer

3 - Instantaneous kinetics (stoichiometric reactions)

Note: First order kinetics can be also be modeled by adjusting the values of the Monod parameters.

See input line 3.6.6 below.

3.6.3 KC(I), ITYPE(I), CINIT(I), RABIO(I), NPABIO(I), for I=1, NBC

Note: One line is required for each chemical and biological species that participates in

biodegradation reactions.

KC(I) - Index of the Ith chemical or biological species.

ITYPE(I) - Flag indicating whether the I'th component is a chemical or biological species.

Possible values:

1 - The Ith component is a chemical species

2 - The Ith component is a biological species

CINIT(I) - Initial concentration of chemical or free-floating (unattached) biological species I in the

aqueous phase.

Units: mg/l

Note: Although a value of CINIT must be entered for organic species that participate in

biodegradation reactions, these values are ignored by the program. Initial

concentrations of these components are input on input lines 3.3.32 through 3.3.35.

RABIO(I) - First-order abiotic reaction rate constant.

Units: 1/days

Note: Although a value of RABIO can be specified for biological as well as chemical

species, biomass decay should not be controlled with RABIO. Instead, use the

parameters ENDOG and ENDOGB to control endogenous decay of unattached and

attached biomass, respectively. RABIO should normally be set to 0.0 for biological

species.
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NPABIO(I) - Number of products generated by a first-order abiotic reaction of chemical species I.

Note: A value must be entered for biological species as well, although the value is ignored

by the program because generation of products from decay of biomass is not allowed.

3.6.4 KC(I), DENBIO(I), RCOL(I), TCOL(I), COLNUM(I), ENDOG(I), ENDOGB(I), CBI(I),

CBIOMN(I) for I=1, NBS

Note: One line is required for each biological species.

KC(I) - Index of the biological species.

DENBIO(I) - density of attached biological species I (biofilm density).

Units: g cells / cm3 biomass

RCOL(I) - radius of an attached microcolony of biological species I.

Units: cm

Note: The parameter RCOL is used to calculate the surface area of a single attached

microcolony. Although microcolonies are assumed to be disk-shaped by the model,

the user may specify any desired surface area per microcolony using RCOL. TCOL

can then be adjusted to obtain the desired volume of the microcolony since the

thickness of the microcolony does not affect external mass transfer into the attached

biomass.

TCOL(I) - Thickness of a single attached microcolony of biological species I.

Units: cm

COLNUM(I) - Number of bacterial cells per microcolony of biological species I.

Units: cells/colony

ENDOG(I) - endogenous decay coefficient of unattached cells of biological species I.

Units: 1/days

ENDOGB(I) - endogenous decay coefficient of attached cells of biological species I.

Units: 1/days

CBI(I) - Number of attached bacterial cells of biological species I per gram of dry soil.

Units: cells/gram of solid.

CBIOMN(I) - Lower limit of number of attached bacterial cells of biological species I.

Units: cells/gram of solid.

Note: A population of attached microorganisms, sustained by naturally occurring organic

matter, is assumed to exist in the porous media regardless of the concentration of

other chemical species. This concentration is CBIOMN, and the concentration of

biomass is not allowed to fall below this value.

3.6.5 ISUB(I), IEA(I), IBS(I), BRMAX(I), BRMAXB(I), YXS(I), AKS(I), AKA(I), FEA(I), for I=1,

NMET

Note: One line is read for each metabolic combination.

ISUB(I) - Substrate index for metabolic combination I.

IEA(I) - Electron acceptor index for metabolic combination I.

IBS(I) - Biological species index for metabolic combination I.

BRMAX(I) - maximum specific growth rate of unattached microorganisms for metabolic

combination I.

Units: 1/days

BRMAXB(I) - Maximum specific growth rate of attached microorganisms for metabolic

combination I.

Units: 1/days
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YXS(I) - Yield coefficient for metabolic combination I.

Units: mg/l

AKS(I) - Substrate half-saturation coefficient for metabolic combination I.

Units: mg/l

AKA(I) - Electron acceptor half-saturation coefficient for metabolic combination I.

Units: mg/l

FEA(I) - Electron acceptor utilization coefficient (mass of electron acceptor consumed per mass of

substrate biodegraded).

3.6.6 ISUB(I), IEA(I), IBS(I), NCOMPS(I), NIHB(I), NPROD(I), NNUT(I), ICOMET(I), for I=1,

NMET

Note: One line is read for each metabolic combination.

ISUB(I) - Substrate index for metabolic combination I.

IEA(I) - Electron acceptor index for metabolic combination I.

IBS(I) - Biological species index for metabolic combination I.

NCOMPS(I) - Number of other substrates competing with substrate ISUB in metabolic combination

I.

NIHB(I) - Number of other chemical species that inhibit metabolic combination I.

NPROD(I) - Number of products generated from metabolic combination I.

NNUT(I) - Number of nutrients that limit the biodegradation rate through Monod terms for

metabolic combination I.

ICOMET(I) - Flag indicating whether or not the substrate in metabolic combination I is biodegraded

through aerobic cometabolism.

Possible Values:

0 - Substrate ISUB(I) serves as a primary substrate

1 - Substrate ISUB(I) is biodegraded through aerobic cometabolism

Note: Users may specify multiple competing substrates, nutrients, and inhibiting constituents for

each metabolic combination. Substrate competition, inhibition and cometabolism cannot be

modeled if instantaneous kinetics are selected. However, values for the biodegradation rate

parameters must be specified even if instantaneous kinetics are specified.

First-order biodegradation kinetics can be modeled by using a very large value of KS, and

adjusting the ratio of mmax/KS to be equal to the desired first-order biodegradation rate

coefficient.

3.6.7 ISUB(I), IEA(I), IBS(I), (ICSUB(I,J), for J=1, Number of competing substrates), for I=1, NMET

(This line is read only if there are competing substrates)

Note: One line is read for each metabolic combination for which there is substrate competition

between two or more substrates.

ISUB(I) - Substrate index for metabolic combination I.

IEA(I) - Electron acceptor index for metabolic combination I.

IBS(I) - Biological species index for metabolic combination I.

ICSUB(J) - Indices of other substrates that compete with substrate ISUB(I) in metabolic

combination I.

Note: The number of input lines required must equal the number of species that are competing,

since complementary lines are required to fully describe the competition. For example, if

substrate 12 in metabolic combination 12-15-16 must compete with substrates 13 and 14 that
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214

are also biodegraded by biological species 16 using electron acceptor 15, then the required

input lines are:

12 15 16 13 14

13 15 16 12 14

14 15 16 12 13

3.6.8 ISUB(I), IEA(I), IBS(I), IHB(I), BSIHB(I), for I=1, Number of metabolic combination and

inhibiting compound associations (This line is only read if there are metabolic combination and

inhibiting compound associations)

Note: One input line is read for each association of metabolic combination and inhibiting

compound.

ISUB(I) - Substrate index for metabolic combination I.

IEA(I) - Electron acceptor index for metabolic combination I.

IBS(I) - Biological species index for metabolic combination I.

IHB(I) - Index of chemical species that inhibits metabolic combination I.

BSIHB(I) - Inhibition constant for metabolic combination I.

Units: mg/l

Note: The total number of lines are

I = NIHB(J)

J=1

NMET

∑ .

For example, suppose there are two substrate-electron acceptor-biological species metabolic

combinations: 9-10-12 and 9-11-12. Metabolic combination 9-10-12 is inhibited by the

substrate itself (9) and electron acceptor 11, while metabolic combination 9-11-12 is

inhibited by only the substrate. Then the input lines for this scenario would be:

9 10 12 9 0.001

9 10 12 11 0.001

9 11 12 9 0.001

3.6.9 ISUB(I), IEA(I), IBS(I), IPR(I), FPR(I), for I=1, Number of biodegradation product formation and

metabolic combination associations (This line is read only if there are biodegradation product

formation described with Monod kinetics and metabolic combination associations)

Note: One line is read for each association of product formation and metabolic combination.

ISUB(I) - Substrate index for metabolic combination I.

IEA(I) - Electron acceptor index for metabolic combination I.

IBS(I) - Biological species index for metabolic combination I.

IPR(I) - Index of product generated by metabolic combination I.

FPR(I) - Product generation coefficient (stoichiometric ratio - mass of product generated per mass

of substrate biodegraded).

Note: Number of lines are

I = NPRODT(J)

J=1

NMET

∑ .

For example, if metabolic combination 9-14-15 generates products 10 and 11, and metabolic

combination 12-14-15 generates product 13, then the input lines would be:

9 14 15 10 2.0

9 14 15 11 1.0

12 14 15 13 1.5
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Parameters for generation of products through first-order reactions are described on input

line 3.6.10.

3.6.10 ISUB(I), IPR(I), FPR(I), for I=1, Number of products generated by first-order reactions of the

biodegradation species. (This line is read only if there are products of first-order reactions of

biological species)

ISUB(I) - Index of chemical species that reacts abiotically to generate a product.

IPR(I) - Index of product generated by abiotic reaction of ISUB(I).

FPR(I) - Product generation coefficient (stoichiometric ratio - mass of product generated per mass

of reactant reacted).

Note: Number of lines are

I = NPABIO(J)

J=1

NBC

∑ .

For example, if the abiotic products 11, 12 and 13 were generated from the first-order

reaction of biodegradation species 9 and 10, then the input lines would be:

9 11 1.0

9 12 1.0

10 13 2.0

3.6.11 ISUB(I), IEA(I), IBS(I), INUT(I), AKN(I), FN(I), for I=1, Number of metabolic combination and

limiting nutrient associations (This line is read only if there are metabolic combination and

limiting nutrient associations)

Note: One line is read for each association of metabolic combination and limiting nutrient.

ISUB(I) - Substrate index for metabolic combination I.

IEA(I) - Electron acceptor index for metabolic combination I.

IBS(I) - Biological species index for metabolic combination I.

INUT(I) - Index of nutrient limiting the rate of biodegradation through a Monod term in metabolic

combination I.

AKN(I) - Nutrient half-saturation coefficient for metabolic combination I.

Units: mg/l

FN(I) - Nutrient utilization coefficient (mass of nutrient consumed per mass of substrates

biodegraded) for metabolic combination I.

Note: Number of lines are I = NNUTT(J)

J=1

NMET

∑ .

3.6.12 ISUB(I), IEA(I), IBS(I), TC(I), IRLIM(I), for I=1, Number of cometabolic combinations for which

aerobic cometabolism exists (This line is read only if there are cometabolic combinations for

which aerobic cometabolism exists for at least one metabolic combination specified in line 3.6.6)

Note: One input line is required for each cometabolic combination for which aerobic

cometabolism exists.

ISUB(I) - Substrate index for metabolic combination I.

IEA(I) - Electron acceptor index for metabolic combination I.

IBS(I) - Biological species index for metabolic combination I.

TC(I) - Transformation capacity for cometabolism of substrate ISUB(I) (mass of substrate utilized

per mass of biomass destroyed).
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IRLIM(I) - Flag indicating whether reducing power limitations are considered for cometabolic

combination I.

Possible Values:

0 - No reducing power limitations are considered

1 - Cometabolic reaction consumes reducing power

Note: Reducing power limits the biodegradation rate through Monod terms in the manner

of Chang and Alvarez-Cohen [1995]. The loss of a biological species' reducing

power reduces its activity toward all substrates, not just the cometabolite.

Note: The total number of lines are I = COMET(J)

J=1

NMET

∑ .

3.6.13 ISUB(I), IEA(I), IBS(I), IGROW(I), REDI(I), AKR(I), FRP(I), FRC(I), for I=1, Number of

cometabolic biodegradation reactions in which reducing power limitations are considered (This

line is read only if there are cometabolic biodegradation reactions in which reducing power

limitations are considered and IRLIM(I)>0 for at least one metabolic combination specified in line

3.6.11)

Note: One line is required for each cometabolic biodegradation reaction in which reducing power

limitations are considered.

ISUB(I) - Substrate index for metabolic combination I.

IEA(I) - Electron acceptor index for metabolic combination I.

IBS(I) - Biological species index for metabolic combination I.

IGROW(I) - Index of growth substrate for cometabolism of substrate ISUB(I).

REDI(I) - Initial intracellular reducing power (NADH) concentration.

Units: mmol/mg of biomass

AKR(I) - Reducing power half-saturation coefficient.

Units: mmol/mg of biomass

FRP(I) - Reducing power generation coefficient for metabolic combination (IGROW(I), IEA(I),

IBS(I) (mmol reducing power generated per mg of growth substrate consumed).

FRC(I) - Reducing power consumption coefficient for cometabolic combination (ISUB(I), IEA(I),

IBS(I)) (mmol reducing power consumed per mg of substrate consumed by cometabolism).

Note: The total number of lines are

I = IRLIM(J)

J=1

K

∑

where

K = COMET(J)

J=1

NMET

∑ .

3.7 Recurrent Injection/Production Data Set

The sixth input section consists of the recurrent injection/production well data. Please

remember that there are seven comment lines at the beginning of this section and that each line is

preceded by three comment lines.
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217

3.7.1 IBOUND

IBOUND - The flag to specify if constant potential boundaries at the left and right sides of the

simulation model are specified.

Possible Values:

0 - No boundary is specified

1 - Boundary is specified

Note: This option of IBOUND=1 is not currently available for the vadose zone or when gas

is present (IGAS•1)

3.7.2 IBL, IBR (This line is read only if IBOUND=1)

IBL - The flag to specify if the left hand side constant potential boundary is specified.

Possible Values:

0 - No boundary is specified

1 - Boundary is specified

IBR - The flag to specify if the right hand side constant potential boundary is specified.

Possible Values:

0 - No boundary is specified

1 - Boundary is specified

3.7.3 PBL, C1BL, C5BL, C6BL (This line is read only if IBOUND=1 and IBL=1)

PBL- Pressure at the center of the top layer at the left boundary.

Units: psia (IUNIT=0) or kPa (IUNIT=1)

C1BL- Concentration of water in aqueous phase at the left boundary.

Units: volume fraction

C5BL - Concentration of chloride in aqueous phase at the left boundary.

Units: meq/ml

C6BL - Concentration of calcium in aqueous phase at the left boundary.

Units: meq/ml

3.7.4 PBR, C1BR, C5BR, C6BR (This line is read only if IBOUND=1 and IBR=1)

PBR - Pressure at the center of the top layer at the right boundary.

Units: psia (IUNIT=0) or kPa (IUNIT=1)

C1BR - Concentration of water in aqueous phase at the right boundary.

Units: volume fraction

C5BR - Concentration of chloride in aqueous phase at the right boundary.

Units: meq/ml

C6BR - Concentration of calcium in aqueous phase at the right boundary.

Units: meq/ml

Note: For the biodegradation option (IBIO=1), the concentrations of all species considered at the

boundary are set to the initial concentrations.

3.7.5 NWELL, IRO, ITIME, NWREL

NWELL - Number of wells used for the simulation including the pseudowells to mimic an open

boundary.

Note: If ICOORD=2, NWELL must be equal to 1 and the MXW parameter in the source

code must be set equal to 2.

IRO - Flag indicating the equivalent well radius model to be used.
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Possible Values:

1 - Babu and Odeh model is used

2 - Peaceman model is used

Note: The Babu and Odeh model (IRO=1) does not work for ICOORD=4.

ITIME - Flag indicating the units to be used when specifying the minimum and maximum time step.

Possible Values:

0 - Minimum and maximum time steps are input in days

1 - Minimum and maximum time steps are input as Courant numbers

Note: This option is only used if IMES>1 and is not a shut-in period. If IMES=1, this flag

is ignored. For a shut-in period you need to use ITIME=0

NWREL - Number of actual wells used for the simulation excluding the pseudowells.

Note: The history data are written only for NWREL wells.

Note: See Section A.8 of this appendix for more details on the Courant number and time step

selection options.

The following values for minimum and maximum Courant numbers are recommended for

different simulations as follows:

Process Min. Courant # Max. Courant #

Waterflood/tracer 0.04 0.4

Polymerflood 0.02 0.2

Surfactant/polymerflood 0.01 0.1

Geochemical process 0.01 0.1

See Section 10 of this report for well model information.

3.7.6 The data on input lines 3.7.6.a through 3.7.6.d are repeated for M=1 to NWELL times.

Important note: Input the actual wells first (NWREL) and then the pseudowells.

3.7.6.a IDW(M), IW(M), JW(M), IFLAG(M), RW(M), SWELL(M), IDIR(M), IFIRST(M), ILAST(M),

IPRF(M)

IDW(M) - Well I.D. number for the Mth well.

Possible Values: Must be between 1 and MXW (the source code parameter indicating the

maximum number of wells)

Note: This number is used by UTCHEM to keep track of which well is being described in

the recurrent injection/production well section. The history profile data for the well

indicated by IDW(M) will be written to FORTRAN UNIT number 18 + IDW(M).

IW(M) - First index of the reservoir gridblock containing the Mth well.

Possible Values: Between 1 and the number of gridblocks in the pertinent direction,

inclusive

Note: If the Mth well is completed parallel to the X-axis, IW(M) is the Y direction

index—if the well is completed parallel to the Y- or Z-axis, IW(M) is the X

direction index. See example below.

If ICOORD=2, IW(1)=JW(1)=1.

JW(M) - Second index of the reservoir gridblock containing the Mth well.

Possible Values: Between 1 and the number of gridblocks in the pertinent direction,

inclusive
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Note: If the Mth well is completed parallel to the X- or Y-axis, JW(M) is the Z direction

index—if the well is completed parallel to the Z-axis, JW(M) is the Y direction

index. See example below.

If ICOORD=2, IW(1)=JW(1)=1.

IFLAG(M) - Flag indicating type of well constraint specification for Mth well.

Possible Values:

1 - Rate constrained injection well

2 - Pressure constrained production well (This option is available only if

ICOORD=1 or 3)

3 - Pressure constrained injection well (This option is available only if ICOORD=1

or 3)

4 - Rate constrained production well

RW(M) - Radius of Mth well.

Units: feet (IUNIT=0) or m (IUNIT=1)

SWELL(M) - Skin factor for Mth well.

Units: dimensionless

IDIR(M) - Flag indicating the direction in which the Mth well is completed.

Possible Values:

1 - Well completed parallel to the X-axis

2 - Well completed parallel to the Y-axis

3 - Well completed parallel to the Z-axis

Note: If ICOORD=2, IDIR(1) must be equal to 3.

IFIRST(M) - Index of the first block in which the Mth well is completed.

Possible Values: Between 1 and the number of gridblocks in the pertinent direction,

inclusive

ILAST(M) - Index of the last block in which the Mth well is completed.

Possible Values: Between IFIRST(M) and the number of gridblocks in the pertinent

direction, inclusive

IPRF(M) - Flag indicating if partial completion of the well is considered.

Possible Values:

0 - The well is fully completed

1 - The well is partially completed

Example: For a vertical well (completed through all the layers) as illustrated in the 4 × 4 × 3

example below, note the values of IDIR(M), IW(M), JW(M), IFIRST(M), and ILAST(M):
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For a horizontal well (completed from the first to last gridblock in the X direction and

parallel to the X-axis) as illustrated in the 4 × 4 × 3 example below, note the values of

IDIR(M), IW(M), JW(M), IFIRST(M), and ILAST(M):

Note: Horizontal wells can be used for 2-D X-Y or 3-D simulations.

3.7.6.b KPRF(M,IWB), for IWB=1, NWBC (This line is read only if IPRF=1)

KPRF(M,IWB) - Flag indicating if the IWBth well block of the Mth well is perforated or not.

Possible Values:

0 - The well block is not perforated

1 - The well block is perforated

3.7.6.c WELNAM(M)

WELNAM(M) - Name of the Mth well.

Note: The name can consist of any combination of up to 18 alphanumeric characters.

This information will be printed—along with the well I.D. number, IDW(M)—at

the beginning of the history output files.

3.7.6.d ICHEK(M), PWFMIN(M), PWFMAX(M), QTMIN(M), QTMAX(M)

ICHEK(M) - The flag to specify whether to check the rate or pressure caps for the Mth well.

Possible Values:

0 - There will be no check on the rate or pressure limits and no automatic shut in

for the pressure constraint injector

1 - There will be no automatic shut in for the pressure constraint injector but the

pressure or rate limits are checked

2 - There will be both the automatic shut in and the check on the pressure or rate

limits

PWFMIN(M) - Minimum flowing bottom hole pressure (specified at the top layer) for the Mth

well.

Units: psi (IUNIT=0) or kPa (IUNIT=1)

PWFMAX(M) - Maximum flowing bottom hole pressure (specified at the top layer) for the Mth

well.

Units: psi (IUNIT=0) or kPa (IUNIT=1)

QTMIN(M) - Minimum total flow rate (specified at the top layer) for the Mth well.

Units: ft3/day (IUNIT=0) or m3/day (IUNIT=1)
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QTMAX(M) - Maximum total flow rate (specified at the top layer) for the Mth well.

Units: ft3/day (IUNIT=0) or m3/day (IUNIT=1)

Note: – PWFMIN(M) and PWFMAX(M) are the pressure caps for a rate constraint injector or

producer well. QTMIN(M) and QTMAX(M) are the total rate caps for a pressure

constraint injector or producer well. If the Mth pressure constraint injector or producer

produces at total rate less than QTMIN(M), the Mth well will be switched to a rate

constraint well with total rate of QTMIN(M) for the rest of the injector or production

period. On the other hand, if the total rate is greater than the QTMAX(M), the Mth well

then will be switched to a rate constraint well with the total rate of QTMAX(M). The

similar concept is applied to a rate constraint injector or producer.

– The user can skip the well control calculation by specifying very small values for

QTMIN(M) and PWFMIN(M) and very large values for QTMAX(M) and PWFMAX(M).

– The code still has the automatic option for shut in of a pressure constraint injector

injecting at a rate of less than QTMIN(M).

3.7.7 The data on input lines 3.7.7.a, 3.7.7.b, 3.7.7.c, and 3.7.7.d are repeated for M=1 to NWELL

times.

Notes: – For injection wells that are on rate constraint only injection rates and concentrations for

each phase are listed. For injection wells that are on pressure constraint the injection

pressure is also specified. In this case the injection rates are treated as phase cuts in the

injected fluid. For producer pressure constraint only the bottom hole pressure is specified.

For producer rate constraint only the total production rate is specified.

– The user can shut in a pressure constraint well by specifying a negative bottom hole

pressure or a rate constraint well by specifying a value of zero for rate (QI).

3.7.7.a ID(M), (QI(M,L), (C(M,KC,L), for KC=1, N), for L=1, MXP) (This set of data is read only if

IFLAG(M)=1 or 3)

ID(M) - Well I.D. number for the Mth well.

Possible Values: Must be between 1 and MXW (the source code parameter indicating the

maximum number of wells)

Note: See note for IDW(M) on input line 3.7.6.a.

QI(M,L) - Injection rate of Lth phase in Mth well (see note below).

Units: ft3/day (IUNIT=0) or m3/day (IUNIT=1)

C(M,KC,L) - Concentration of KCth component in Lth phase in Mth well.

Units: vary according to component (see note below)

Notes: – See Section A.7 of this appendix for component and phase numbering scheme and the

concentration units for each species.

– The KC index changes the fastest, the L index changes the next fastest, and the M index

changes the slowest. A separate data line should be in the input file for each phase—that

is, M × L lines will be read by the program. MXP is equal to 3 (IGAS=0) or 4 (IGAS•1).

3.7.7.b ID(M), PWF(M) (This line is read only if IFLAG(M)=2 or 3)

ID(M) - Well I.D. number for the Mth well.

Possible Values: Must be between 1 and MXW (the source code parameter indicating the

maximum number of wells)
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Note: See note for IDW(M) on input line 3.7.6.a. For IFLAG(M)=3, the rates (QI(M,L))

are used an injected volume fraction for each phase.

PWF(M) - Flowing bottom hole pressure for the Mth well.

Units: psia (IUNIT=0) or kPa (IUNIT=1)

3.7.7.c ID(M), TEMINJ(M) (This line is read only if IENG=1 and IFLAG(M)=1 or 3)

ID(M) - Well I.D. number for the Mth well.

Possible Values: Must be between 1 and MXW (the source code parameter indicating the

maximum number of wells)

Note: See note for IDW(M) on input line 3.7.6.a.

TEMINJ(M) - Injection temperature for Mth well.

Units: •F (IUNIT=0) or •C (IUNIT=1)

3.7.7.d ID(M), QI(M,1) (This line is read only if IFLAG(M)=4)

ID(M) - Well I.D. number for the Mth well.

Possible Values: Must be between 1 and MXW (the source code parameter indicating the

maximum number of wells)

Note: See note for IDW(M) on input line 3.7.6.a.

QI(L) - Total production rate for Mth well.

Units: ft3/day (IUNIT=0) or m3/day (IUNIT=1)

Note: This value needs to be input as a negative number.

3.7.8 TINJ, CUMPR1, CUMHI1, WRHPV, WRPRF, RSTC

TINJ - Cumulative injection time.

Units: days or pore volumes (dependent on value of ISTOP flag on input line 3.2.1)

CUMPR1 - Indicates interval at which profiles should be written to UNIT 4.

Units: pore volumes or days (dependent on value of ICUMTM flag on input line 3.2.1)

CUMHI1 - Indicates interval at which production data should be written to UNIT 4.

Units: pore volumes or days (dependent on value of ICUMTM flag on input line 3.2.1)

WRHPV - Indicates interval at which production histories should be written to output file(s) for

history plotting.

Units: pore volumes or days (dependent on value of ICUMTM flag on input line 3.2.1)

Note: If WRHPV > total pore volume injected or maximum simulation time, the data will

not be printed. The unit number of the file to be written to starts at 19 and continues

upward. For example, for a run with three producers, UNITS 19, 20 and 21 would

be used. The history of reservoir properties and overall rates from all the producing

wells is written to UNIT 9.

WRPRF - Indicates interval at which concentration, pressure, saturation, tracer phase concentration,

capacitance property, gel property, alkaline property, and temperature profiles should be

written to UNITS 8, 11, 12, 13, 14, 10, 15, and 18 respectively.

Units: pore volumes or days (dependent on value of ICUMTM flag on input line 3.2.1)

Note: If WRPRF > total pore volume injected or maximum simulation time, the data will

not be written.

RSTC - Indicates the interval at which restart data should be written to UNIT 7.

Units: pore volumes or days (dependent on value of ICUMTM flag on input line 3.2.1)

Note: A 7th variable (CUMH12) which used to control production data printing to UNIT 3 is no

longer available with the latest version of UTCHEM.
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Time Step Selection Data (Lines 3.7.9-3.7.13)

See Section A.8 of this appendix for more details on the time step selection options.

3.7.9 DT (This line is read only if IMES=1 and ITIME=0)

DT - Time step size for constant time step option.

Units: days

3.7.10 DT, DCLIM, DTMAX, DTMIN (This line is read only if IMES=2 and ITIME=0)

DT - Initial time step size.

Units: days

DCLIM - Tolerance for concentration change for the first three components.

Units: volume fraction

DTMAX - Maximum time step size.

Units: days

DTMIN - Minimum time step size.

Units: days

3.7.11 DT, DCLIM, CNMAX, CNMIN (This line is read only if IMES=2, ITIME=1, and at least one

well is not shut-in.)

DT - Initial time step size.

Units: days

DCLIM - Tolerance for concentration changes for the first three components.

Units: volume fraction

CNMAX - Maximum Courant number.

Units: dimensionless

CNMIN - Minimum Courant number.

Units: dimensionless

3.7.12 DT, (DELC(KC), for KC=1, N), DTMAX, DTMIN (This line is read only if IMES=3 or 4 and

ITIME=0)

DT - Initial time-step size.

Units: days

DELC(KC) - Tolerance for concentration change of KCth component (IMES=3) or relative

tolerance for concentration change of KCth component (IMES=4).

Units: IMES=3: volume fraction, weight percent, meq/ml, or ppm (depending on which

component the tolerance is for—see note for input line 3.7.7.a)

IMES=4: dimensionless

Note: DELC(KC) is the dimensionless relative change in concentration. For example:

DELC(3)=0.1 indicates a 10% change in concentration of component 3.

DTMAX - Maximum time step size.

Units: days

DTMIN - Minimum time step size.

Units: days
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3.7.13 DT, (DELC(KC), for KC=1, N), CNMAX, CNMIN (This line is read only if IMES=3 or 4,

ITIME=1, and all the wells are not shut-in)

DT - Initial time step size.

Units: days

DELC(KC) - Tolerance for concentration change of KCth component (IMES=3) or relative

tolerance for concentration change of KCth component (IMES=4).

Units: IMES=3: volume fraction, weight percent, meq/ml, or ppm (depending on which

component the tolerance is for—see note for input line 3.7.7.a)

IMES=4: dimensionless

CNMAX - Maximum Courant number.

Units: dimensionless

CNMIN - Minimum Courant number.

Units: dimensionless

IMPORTANT NOTE: The data on lines 3.7.14 through 3.7.23 describe the changes in boundary

conditions and are repeated until the injected time (TINJ on input line 3.7.8) is greater than or equal to the

maximum simulation time (TMAX on input line 3.3.1).

3.7.14 IRO, ITIME, (IFLAG(M), for M=1, NWELL)

IRO - Flag indicating the equivalent well radius model to be used.

Possible Values:

1 - Babu and Odeh model is used

2 - Peaceman model is used

ITIME - Flag indicating the units to be used when specifying the minimum and maximum time

step.

Possible Values:

0 - Minimum and maximum time steps are input in days

1 - Minimum and maximum time steps are input as Courant numbers

Note: This option is only used if IMES>1 and it is not a shut-in period. If IMES=1, this

flag is ignored.

IFLAG(M) - Flag indicating type of well constraint specification for Mth well.

Possible Values:

1 - Rate constrained injection well

2 - Pressure constrained production well (This option is available only if

ICOORD=1 or 3)

3 - Pressure constrained injection well (This option is available only if ICOORD=1

or 3)

4 - Rate constrained production well

3.7.15 NWEL1

NWEL1 - Number of wells with changes in location (IW(M), JW(M)), skin, direction, perforation,

name, or minimum and maximum bottomhole pressure or minimum or maximum rate.

3.7.16 The data on input lines 3.7.16.a through 3.7.16.d are repeated for M=1 to NWEL1 times.

3.7.16.a ID, IW(ID), JW(ID), RW(ID), SWELL(ID), IDIR(ID), IFIRST(ID), ILAST(ID), IPRF(ID)

ID - Well ID number with changes from the previous slug injection period.
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IW(ID) - First index of the reservoir gridblock containing the IDth well.

Possible Values: Between 1 and the number of gridblocks in the pertinent direction,

inclusive

Note: See note for input line 3.7.6.a.

JW(ID) - Second index of the reservoir gridblock containing the IDth well.

Possible Values: Between 1 and the number of gridblocks in the pertinent direction,

inclusive

Note: See note for input line 3.7.6.a.

RW(ID) - Radius of IDth well.

Units: feet (IUNIT=0) or m (IUNIT=1)

SWELL(ID) - Skin factor for IDth well.

Units: dimensionless

IDIR(ID) - Flag indicating the direction in which the IDth well is completed.

Possible Values:

1 - Well completed parallel to the X-axis

2 - Well completed parallel to the Y-axis

3 - Well completed parallel to the Z-axis

Note: If ICOORD=2, IDIR(1) must be equal to 3.

IFIRST(ID) - Index of the first block in which the IDth well is completed.

Possible Values: Between 1 and the number of gridblocks in the pertinent direction,

inclusive

ILAST(ID) - Index of the last block in which the IDth well is completed.

Possible Values: Between IFIRST(ID) and the number of gridblocks in the pertinent

direction, inclusive

Note: At this time, UTCHEM assumes the well is completed continuously between

IFIRST(ID) and ILAST(ID).

IPRF(ID) - Flag indicating if partial completion of the well is considered.

Possible Values:

0 - The well is fully completed

1 - The well is partially completed

3.7.16.b KPRF(ID,IWB), for IWB=1, NWBC (This line is read only if IPRF=1)

KPRF(ID,IWB) - Flag indicating if the IWBth well block of the IDth well is perforated or not.

Possible Values:

0 - The well block is not perforated

1 - The well block is perforated

3.7.16.c WELNAM(ID)

WELNAM(ID) - Name of the IDth well.

Note: The name can consist of any combination of up to 18 alphanumeric characters.

This information will be printed—along with the well I.D. number, IDW(ID)—at

the beginning of the history output files.

3.7.16.d ICHEK(ID), PWFMIN(ID), PWFMAX(ID), QTMIN(ID), QTMAX(ID)

ICHEK(ID) - The flag to specify whether to check the rate or pressure caps for the IDth well.

Possible Values:
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0 - There will be no check on the rate or pressure limits and no automatic shut in

for the pressure constraint injector

1 - There will be no automatic shut in for the pressure constraint injector but the

user specified pressure or rate limits are checked

2 - There will be both the automatic shut in and the check on the user specified

pressure or rate limits

PWFMIN(ID) - Minimum flowing bottom hole pressure (specified at the top layer) for the IDth

well.

Units: psi (IUNIT=0) or kPa (IUNIT=1)

PWFMAX(ID) - Maximum flowing bottom hole pressure (specified at the top layer) for the IDth

well.

Units: psi (IUNIT=0) or kPa (IUNIT=1)

QTMIN(ID) - Minimum total flow rate (specified at the top layer) for the IDth well.

Units: ft3/day (IUNIT=0) or m3/day (IUNIT=1)

QTMAX(ID) - Maximum total flow rate (specified at the top layer) for the IDth well.

Units: ft3/day (IUNIT=0) or m3/day (IUNIT=1)

Note: See the note for input line 3.7.6.d.

3.7.17 NWEL2, (IDWW(J), for J=1, NWEL2)

NWEL2 - Number of wells with changes in rate, concentration or bottomhole pressure.

IDWW(J) - ID number for Jth well with changes.

3.7.18 The data on input lines 3.7.18.a through 3.7.18.d are repeated for M=1 to NWEL2 times.

3.7.18.a ID, QI(ID,L), (C(ID,KC,L), for KC=1,N), for L=1, MXP (This set of data is read only if

IFLAG(ID)=1 or 3)

ID - Well ID number with changes from the previous slug injection period.

QI(ID,L) - Injection rate of Lth phase in IDth well (see note for input line 3.7.7.a).

Units: ft3/day (IUNIT=0) or m3/day (IUNIT=1)

C(ID,KC,L) - Concentration of KCth component in Lth phase for IDth well.

Units: vary according to component (see note for line 3.7.7.a)

Note: If IGAS=0, then MXP=3. If IGAS•1, then MXP=4.

3.7.18.b ID, PWF(ID) (This line is read only if IFLAG(ID)=2 or 3)

ID - Well ID number with changes from the previous slug injection period.

PWF(ID) - Flowing bottom hole pressure for the IDth well.

Units: psia (IUNIT=0) or kPa (IUNIT=1)

3.7.18.c ID, TEMINJ(ID) (This line is read only if IENG=1 and IFLAG(ID)=1 or 3)

ID - Well ID number with changes from the previous slug injection period.

TEMINJ(ID) - Injection temperature for the IDth well.

Units: •F (IUNIT=0) or •C (IUNIT=1)

3.7.18.d ID, QI(ID,1) (This line is read only if IFLAG(ID)=4)

ID - Well ID number with changes from the previous slug injection period.

QI(ID,1) - Total production rate for IDth well.
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Units: ft3/day (IUNIT=0) or m3/day (IUNIT=1)

Note: This value needs to be input as a negative number.

3.7.19 TINJ, CUMPR1, CUMHI1, WRHPV, WRPRF, RSTC

TINJ - Cumulative injection time.

Units: days or pore volumes (dependent on value of ISTOP flag on input line 3.2.1)

CUMPR1 - Indicates interval at which profiles should be written to UNIT 4.

Units: pore volumes or days (dependent on value of ICUMTM flag on input line 3.2.1)

CUMHI1 - Indicates interval at which production data should be written to UNIT 4.

Units: pore volumes or days (dependent on value of ICUMTM flag on input line 3.2.1)

WRHPV - Indicates interval at which production histories should be written to output file(s) for

history plotting.

Units: pore volumes or days (dependent on value of ICUMTM flag on input line 3.2.1)

Note: If WRHPV > total pore volume injected or maximum simulation time, the data will

not be printed. The unit number of the file to be written to starts at 19 and continues

upward. For example, for a run with three producers, UNITS 19, 20, and 21 would

be used. The history of reservoir properties and the total rate from all the producing

wells is written to UNIT 9.

WRPRF - Indicates interval at which concentration, pressure, saturation, tracer phase

concentration, capacitance property, pressure difference, gel property, alkaline property,

and temperature profiles should be written to UNITS 8, 11, 12, 13, 14, 10, 15 and 18

respectively.

Units: pore volumes or days (dependent on value of ICUMTM flag on input line 3.2.1)

Note: If WRPRF > total pore volume injected or maximum simulation time, the data will

not be written.

RSTC - Indicates the interval at which restart data should be written to UNIT 7.

Units: pore volumes or days (dependent on value of ICUMTM flag on input line 3.2.1)

Note: A 7th variable (CUMH12) which used to control production data printing to UNIT 3 is no

longer available with the latest version of UTCHEM.

3.7.20 DT (This line is read only if IMES=1 and ITIME=0)

DT - Time step size for constant time step option.

Units: days

3.7.21 DT, DCLIM, DTMAX, DTMIN (This line is read only if IMES=2 and ITIME=0)

DT - Initial time step size.

Units: days

DCLIM - Tolerance for concentration change for the first three components.

Units: volume fraction

DTMAX - Maximum time step size.

Units: days

DTMIN - Minimum time step size.

Units: days

3.7.22 DT, DCLIM, CNMAX, CNMIN (This line is read only if IMES=2, ITIME=1, and at least one

well is not shut-in)

DT - Initial time step size.
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Units: days

DCLIM - Tolerance for concentration changes for the first three components.

Units: volume fraction

CNMAX - Maximum Courant number.

Units: dimensionless

CNMIN - Minimum Courant number.

Units: dimensionless

3.7.23 DT, (DELC(KC), for KC=1, N), DTMAX, DTMIN (This line is read only if IMES=3 or 4 and

ITIME=0)

DT - Initial time-step size.

Units: days

DELC(KC) - Tolerance for concentration change, •Clim,κ, of KCth component (IMES=3) or

relative tolerance for concentration change of KCth component (IMES=4).

Units: IMES=3: volume fraction, weight percent, meq/ml, or ppm (depending on which

component the tolerance is for—see note for input line 3.7.7.a)

IMES=4: dimensionless

DTMAX - Maximum time step size.

Units: days

DTMIN - Minimum time step size.

Units: days

3.7.24 DT, (DELC(KC), for KC=1, N), CNMAX, CNMIN (This line is read only if IMES=3 or 4,

ITIME=1, and reservoir is not shut-in)

DT - Initial time step size.

Units: days

DELC(KC) - Tolerance for concentration change of KCth component (IMES=3) or relative

tolerance for concentration change of KCth component (IMES=4).

Units: IMES=3: volume fraction, weight percent, meq/ml, or ppm (depending on which

component the tolerance is for—see note for input line 3.7.7.a)

IMES=4: dimensionless

CNMAX - Maximum Courant number.

Units: dimensionless

CNMIN - Minimum Courant number.

Units: dimensionless
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A.4 OUTPUT FILES

The following sections describe: (4.1) data that is automatically written to the profile data

file, (4.2) restart run procedure, (4.3) data written to stored restart data file, (4.4) data written to

history files for each well, (4.5) data written to history of reservoir properties and overall injection

and production rates from all the wells, and (4.6) data written to aqueous phase tracer concentration

data files.

4.1 Default Data Written to Profile Data File

The information in the following lists is always written to the profile data file (PROFIL) and

is not controlled by the various print control flags in the input files.

Printed at each CUMHI1 interval:

Time, number of time steps

Time step size

Courant number

Cumulative pore volume injected

Original in place for each component

Cumulative injection for each component

Cumulative production for each component

Amount retained for each component

Relative error for each component

Fraction of oil recovered

If IREACT • 2:

Average number of iterations, computation time

For each well:

Position of the well, first and last well block completed

Cumulative injection/production

Bottomhole pressure for each well block

All well related information (such as pressure for each phase, phase concentration,

phase cut, etc.)

Producer wellbore temperature and phase cut and concentration

Printed at each CUMPR1 interval:

Reservoir temperature if IENG=1

Phase saturation profile for each phase

Aqueous phase pressure profile

Concentration of each component in the fluid

If IBIO=1 and IBPR=1:

Concentration of aqueous phase biodegradation species

If IBKIN=1:

Concentration of biodegradation species within attached biomass

If tracers are present and ICAP•0:

Flowing concentration

Dendiritic concentration

Flowing saturation

Dendiritic saturation
Appendix A - UTCHEM 6.1 User's Guide

230

4.2 Restart Run Procedure

The restart procedure is available with UTCHEM. This enables a user to continue a run past

the initial time period or to break a large run up into smaller segments. Each time you run

UTCHEM, a file called RESTAR is created. This file (described in Section 6.3) contains all the

information necessary to continue the run at a later time. In order to do so, the user needs to:

1.- Rename the output file RESTAR from the previous run to INPUT2

2.- Set the variable IMODE equal to 2 on line 3.1.3 of input file INPUT

3.- Change the value of TMAX on input line 3.3.1 of file INPUT to the new injection period

being simulated in the restart run

4.- Change the value of TINJ on input line 3.7.8 of file INPUT if appropriate

5.- Add additional information for input lines 3.7.14 through 3.7.24 of file INPUT if the well

conditions are different for the new injection period

Note: Make sure the source code you run the restart problem (IMODE=2) has the same values for

the array sizes in the parameter statement as the one used in original run (IMODE=1).

4.3 Data Written to Stored Restart Run Data File

The information in the following list is always written to the stored restart data file

(RESTAR). If the user is running a RESTART run, this data file needs to be renamed to correspond

to the INPUT2 input file. The values in parentheses are the FORTRAN variable names as they

appear in the code.

Printed at the end of each run:

Time (T), injection time (TINJ), time step size (DT), number of time steps (ICNT)

New slug injection or restart flag (IINJ), number of time step reduction (INEC), cumulative

pore volume injection (CUMPV), number of blocks in X-direction minus 1 (NXM1)

Cumulative injection (CUMI), cumulative production (CUMP), original in place (OIP) for

each component

Cumulative injection/production (CUMQI and CUMQP) for each well

Phase concentration (C), phase saturation (S), effective salinity (CSE), overall concentration

(CTOT), number of phases (NPHASE)

If ICOORD=2:

Boundary concentration (CE), boundary pressure (PE)

Viscosity (VIS), relative permeability (RPERM), injection rate (QI), total rate for each well

(QT), phase rate (Q), bottomhole pressure (PWF)

Pressure (P)

If IADSO=1:

Organic adsorption (C2ADSS)

If LMO=1:

Multiple organic adsorption (CS1DSK)

Surfactant adsorption (C3ADSS), surfactant adsorption parameter (A3DS), polymer

adsorption (C4ADSS)
Appendix A - UTCHEM 6.1 User's Guide

231

Permeability reduction factor (RKF), calcium concentration (C6JO), calcium adsorbed by

clay (C6ADSS), calcium adsorbed by surfactant (C6HATS)

Alcohol 7 partitioning coefficient (X7OLD), alcohol 8 partitioning coefficient (X8OLD)

Oil breakthrough (BTO), tracer breakthrough (TBT), tracer injection concentration (CINJT),

tracer retardation factor (TRD)

Lower effective salinity (CSEL), upper effective salinity (CSEU)

Density (DEN), capillary pressure (PRC)

Total surfactant (TSURF)

If IPERM=2 and IHYST=1:

Minimum water saturation (SWMIN)

If ICAP=1:

Dendiritic concentration (CD), dendiritic saturation (SD), flowing saturation (SF),

total flowing concentration (CTF)

If NG•0:

Chromium adsorption (C14ADS), gel adsorption (C15ADS), cation exchange

capacity of clay (QW)

If IENG=1:

Cum. heat inj. (CUMHI), cum. heat prod. (CUMHP), temperature (TEM), total

volumetric heat capacity (TVHC)

If IENG=1 and IHLOS=1:

Cum. heat loss (TQLOS), integral for overburden and underburden heatloss

calculations (RINO, RINU), time of change of overburden temp. from the reservoir

block (TTCHG), overburden temperature (TEMPOB), underburden temperature

(TEMPUB)

If IENG =1 and ICOORD =2:

Boundary enthalpy (ENTHE)

If IREACT >1:

Solid concentration (CSLDT), adsorbed concentration (CSORBT), species

concentration (CAQSP), surf. associated cation concentration (CACATT), cation

concentration (CACAT)

Cumulative no. of iteration for geochem option (ITCUM)

If IBIO =1:

Concentrations of attached biomass and intra-biomass concentrations of chemical

species (CB)

Concentrations of reducing power in aqueous phase biomass (RED) and attached

biomass (REDB)

4.4 Data Written to Well History Plotting Data File(s)

The information in the following list is always written to the well history plotting data files

(HIST01-HISTl) for each production well.

Printed at each WRHPV interval:

Cumulative pore volume, time [days], cumulative production [ft3, m3, or STB], water oil

ratio, cumulative oil recovery, total production rate [ft3/day, m3/day, or STB/day]

If IGAS =1: Water cut, oil cut, microemulsion cut, gas cut

Wellbore pressure for each well block [psi or kPa]

If IENG =1: Wellbore temperature [•F or •C]
Appendix A - UTCHEM 6.1 User's Guide

232

For I=1, N:

If ICF(I) =1: phase concentration for component N (C(I,L), L=1,MXP), total

concentration of component N (CTOT(I))

If IREACT>1 or ICF(3)=1: Lower effective salinity, upper effective salinity, effective

salinity

If IBIO =1 and IBPR =1:

Concentrations of attached biomass and intra-biomass concentrations of chemical

species (CMGL) [mg/l]

If IBIO=1, IBPR=1, and there are cometabolic biodegradation reactions in which reducing

power limitations are considered:

Concentrations of reducing power (NADH) in aqueous phase and attached biomass

If IREACT >1:

Independent species concentration (CAQSP(KK), KK=1, NIAQ) [mole/liter of

water]

If IRSPS >0: Dependent species concentration (CAQSP(KK), KK=NIAQ+1,NFLD)

[mole/liter of water]

If IREACT =3 or 5: Phase concentration of injected + generated surfactant

(PSURF(I,L), L=1,3), total concentration of injected + generated surfactant

(TSURF)

If NSLD >0: Concentration of solid components (CSLDT(KK), KK=1, NSLD)

[mole/liter of pore volume]

If ICNM >0: Log10 of interfacial tension between water/microemulsion and

oil/microemulsion (XIFT1, XIFT2) [dyne/cm]

The information in the following list is always written to the well history plotting data files for each

injection well.

Printed at each WRHPV interval:

Cumulative pore volume, time in days, cumulative injection [ft3, m3, or STB],

injection rate [ft3/day, m3/day, or STB/day]

Wellbore pressure for each well block [psi or kPa]

Pressure drop between the wells (for the specific case of one injector and one

producer only) or pressure drop between the pressure tabs (when NG>0,

NY=1, NZ=1, see line 3.4.167) [psi or kPa]

4.5 Data Written to Overall History Plotting Data File

The information in the following list is always written to the overall history plotting data file

(OVERAL).

Printed at each WRHPV interval:

Cumulative pore volume, time in days, volumetric averaged reservoir pressure (psi or kPa),

cumulative oil produced (%OOIP), cumulative oil produced (bbls or m3), volumetric

averaged reservoir temperature (•F or •C) (only if IENG=1)

Total injection rate (B/D or m3/day), total production rate (B/D or m3/day), total fluid

injected (1000 bbls or m3), total fluid produced (1000 bbls or m3) [Note: The fluid

injected and produced values are calculated for the last time step before the print

interval.]
Appendix A - UTCHEM 6.1 User's Guide

233

Overall production rate for each phase (QBAR(L) for L=1, MXP where MXP=3 if IGAS=0

and MXP=4 if IGAS =1) (B/D or m3/day)

Average cut for each phase (FBAR(L) for L=1, MXP where MXP=3 if IGAS=0 and MXP=4

if IGAS =1)

Average saturation for each phase (SBAR(L) for L=1, MXP where MXP=3 if IGAS=0 and

MXP=4 if IGAS =1)

If ICF(3)=1: Cumulative surfactant injected (bbls or m3), Cumulative surfactant produced

(bbls or m3), adsorbed surfactant (bbls or m3), retained surfactant (bbls or m3),

adsorbed surfactant (ml/ml PV)

If ICF(4)=1: Cumulative polymer injected (wt%), Cumulative polymer produced (wt%),

adsorbed polymer (wt%), retained polymer (wt%), adsorbed polymer (wt. % / PV)

4.6 Data Written to Tracer Concentration Observation Point Data File(s)

The information in the following list is written to the tracer observation history plotting data

files (TRAC01-TRACn) for each tracer (if IPOBS=0).

Printed at each WRHPV interval:

Time in days, cumulative pore volume

If IGAS=0:

Aqueous phase tracer concentration at NOBS observation locations

If IGAS•1:

Gas phase tracer concentration at NOBS observation locations

A.5 GEOCHEMISTRY OPTION (IREACT>1)

This section gives an example list of elements and reactive species for the geochemistry

options of IREACT=2 or IREACT=4.

Elements or pseudo-element: Hydrogen (reactive), Sodium, Calcium, Magnesium,

Carbonate, Aluminum, Silicon, Oxygen, Chlorine, S

(Injected surfactant)

Independent aqueous or oleic

species: H+, Na+,Ca2+, Mg2+, Al3+, CO2-

3

, Cl-, S-, H4SiO4, H2O

Dependent aqueous or oleic species: Ca(OH)+, Mg(OH)+, Al(OH)2-,Al(OH)2

-

, Ca(HCO3)

+,

Mg(HCO3)

+, OH-

, HCO3, H3SiO4

-

, H2SiO4

2-

, HSi2O6

3-

,

Si2O5

2-, Al(OH)4

-

, H2CO3, CaCOo

3

 , MgCOo

3

 

Solid species: CaCO3 (Calcite), Al2Si2O5(OH)4 (Kaolinite), MgCO3

(Magnesite), NaAlSi2O6.H2O (Analcite), SiO2 (Silica),

Mg(OH)2 (Magnesium Hydroxide)

Adsorbed cations on rock surface:

__

H + , 

__

Na + , 

__

Ca 2+, 

__

Mg 2+

Adsorbed cations on micelles: =

Na +, 

=

Ca 2+, 

=Mg 2+

Aqueous reactions Equilibrium constant
Appendix A - UTCHEM 6.1 User's Guide

234

H2O 

K

eq

1 ∅♦

 H

+

 + OH- K

eq

1

 = [ H ]

+ [ OH ]-

 

H

+

 + CO2-

3

K

eq

2 ∅♦

 HCO3 K

eq

2

 = 







 HCO3

[ H ]

+







CO 

2-

3

Ca2+

 + H2O 

K

eq

3 ∅♦

 Ca(OH)+ + H+

K

eq

3

 = 

[ Ca(OH) ]

+

[ H ]

+

[ Ca ]

2+

Mg2+

 + H2O 

K

eq

4 ∅♦

 Mg(OH)+ + H+

K

eq

4

 = 

[ Mg(OH) ]

+

[ H ]

+

[ Mg ]

2+

Al3+ + H2O 

K

eq

5 ∅♦

 Al(OH)2+ + H+ K

eq

5

 = 

[Al(OH) ]

2+ [H ]+

[Al ]

3+

Al3+ + 2H2O 

K

eq

6 ∅♦

Al(OH)2

+ + 2H+ K

eq

6

 = 

[ Al(OH)2 ]

+ [H ]+ 2

[Al ]

3+

Aqueous reactions (cont.) Equilibrium constant (cont.)

Al3+ + 4H2O 

K

eq

7 ∅♦

Al(OH)4

-

 + 4H+ K

eq

7

 = 

[ Al(OH)4 ]

-

[H ]

+ 4

[Al ]

3+

H4SiO4

K

eq

8 ∅♦

 H

+

 + H3SiO4

-

K

eq

8

 = 

[ H ]

+

[ H3SiO4 ]

-

[ H4 ]

SiO4

H4SiO4

K

eq

9 ∅♦

 2H+ + H2SiO4

2-

K

eq

9

 = 

[ H ]

+ 2

[ H2SiO4 ]

2-

[ H4 ]

SiO4

Ca2+ + H++ CO2-

3

K

eq

10 ∅♦

 Ca(HCO3)

+

K

eq

10 = 







 Ca(HCO3

)

+

[ Ca ]

2+ 





CO 

2-

3

[ H ]

+

Mg2+

 + H++ CO2-

3

K

eq

11 ∅♦

 Mg(HCO3)

+

K

eq

11 = 





 Mg(HCO 3

)

+

[ Mg ]

2+







 CO2-

3

[ H ]

+

2H++ CO2-

3

K

eq

12 ∅♦

 H2CO3 K

eq

12 = 

[ H2

CO3]







CO 

2-

3

[ H ]

+ 2

2H4SiO4

K

eq

13 ∅♦

 2H2O + 3H+ + HSi2O6

3-

K

eq

13 = 

[ H ]

+ 3

[ HSi2O6 ]

3-

[ H4 ]

SiO4

2

2H4SiO4

K

eq

14 ∅♦

 2H+ + 3H2O + Si2O5

2-

K

eq

14 = 

[ H ]

+ 2

[ Si2O5 ]

2-

[ H4 ]

SiO4

2
Appendix A - UTCHEM 6.1 User's Guide

235

Solid species Solubility product

CaCO3 K

sp

1

 = [ Ca ]

2+ 





CO 

2-

3

MgCO3 K

sp

2

 = [ Mg ]

2+ 





CO 

2-

3

SiO2 K

sp

3

 = [H4SiO4]

Al2Si2O5(OH)4 K

sp

4

 = [ H ]

+ -6[ Al ]3+ 2

[H4SiO4]

2

NaAlSi2O6.H2O K

sp

5

 = [ H ]

+ -4[ Na ]+

[ Al ]

3+ [H4SiO4]

2

Mg(OH)2 K

sp

6

 = [ Mg ]

2+ [ H ]+ -2
Appendix A - UTCHEM 6.1 User's Guide

236

Exchange reactions (on matrix) Exchange equilibrium constant

2

__

Na

+

 + Ca2+ 

K

ex

1 ∅♦

 2Na+ + 

__

Ca 2+

K

ex

1

 = 







__ 

Ca2+ [ Na ]

+ 2

[ Ca ]

2+ 





__ 

Na

+ 2

2

__

Na

+

 + Mg2+ 

K

ex

2 ∅♦

 2Na+ + 

__

Mg 2+

K

ex

2

 = 







__ 

Mg2+ [ Na ]

+ 2

[ Mg ]

2+ 





__ 

Na

+ 2

_

H

+

 + Na+ + OH- K

ex

3 ∅♦

 

__

Na

+

 + H2O

K

ex

3

 = 

[ Na ]

+











_ 

H

+







__ 

Na

+

[ H ]

+

Exchange reactions (on micelle) Exchange equilibrium constant

2

=

Na + + Ca2+ 

K

exm

1 ∅♦

 2Na+ + 

=

Ca 2+

K

exm

1

 = 







= 

Ca2+ [ Na ]

+ 2







= 

Na+ 2

[ Ca ]

2+

where Kexm

1

= β

exm

1

[S-]

2

=

Na + + Mg2+ 

K

exm

2 ∅♦

 2Na+ + 

=Mg 2+

K

exm

2

 = 







=  Mg2+ [ Na ]

+ 2







= 

Na+ 2

[ Mg ]

2+

where Kexm

2

= β

exm

2

[S-]
Appendix A - UTCHEM 6.1 User's Guide

237

A.6 MAIN PROGRAM FLOW OUTLINE

The following outline represents the basic flow through the main program of UTCHEM (that

is, the order in which major subroutines are called).

Ι. INOUT

A. FILE1

B. PRINTS

C. PRINTI

D. INNAME (called only if NO>1 and IOD is not equal to 1)

E. MOPPST (called only if NO>1)

1. SLV2EQ

F. PRINTO (called only if NO>1)

G. WMEACN (called only if NO>1 and IOD is not equal to 1)

H. GEOREAD (called only if IREACT>1)

I. BIOREAD (called only if IBIO=1)

J. METRIC (called only if IUNIT=1)

K. WELLIX

1. RADIUS

L. FILE3

M. FILE2

N. GRDFAC

ΙΙ. RSTART (called only if IMODE=2)

A. NSLUG

B. WELLIX

1. RADIUS

III. TIME0

A. OMOFR (called only if NO>1)

B. DENSTY

IV. TRAN1

V. ASIGN1

VI. TRANS (Transmissibilities)

VII. SOLMAT (Pressure Eq.)

A. WELL

B. BUNDRY (called only if IBOUND=1)

C. JCG

VIII. QRATE

IX. CONEQ (Conservation Eq.)

A. GEL

X. ADSORB

XI. REACTR (called only if IREACT>1)

A. RENAM1

B. TOTALS

C. MANIPL

D. JACUP

1. GAUSS

2. SOLVE

E. RENAM2
Appendix A - UTCHEM 6.1 User's Guide

238

XII. CSECAL

A. ALCPTN (called only if IALC=1)

1. TWOALC

2. CUBIC

B. CSEOD (called only if NO>1 and IOD is not equal to 1)

C. IONCNG

D. PHASC (called only if surfactant is not present and IREACT<1)

1. NONEQ

2. ODISWO (called only if NO>1)

a. NONEQK

E. PHCOMP (called only if surfactant is present or IREACT>1)

1. NONEQ

2. ODISWO

3. TIELIN

a. TRY

4. REVISE

5. VGAMMA

6. SINGLE

7. ODISTM (called only if IHAND=0)

8. ODISTM1 (called only if IHAND=1)

XIII. BIOSOLVE (called only if IBIO=1)

A. INST (called only if IBKIN =3)

B. SDRIV2 (called only if IBKIN = 1 or 2 and running Cray version of code)

1. F

2. G

C. DDRIV2 (called only if IBKIN = 1 or 2 and running double precision version of

code)

1. F

2. G

XIV. OMOFR (called only if NO>1)

XV. TCAP (called only if ICAP=1)

XVI. TDIFFU (called only if ICAP=2)

XVII. DENSTY

XVIII. ASIGN2

XIX. ENGBAL (called only if IENG=1)

XX. LAUWER (called only if IENG=1 and IANAL=1)

XXI. CAPNUM (called only if ITRAP=1)

XXII. TRAPNO (called only if ITRAP=2 and IGAS=0)

XXIII. TRAP (called only if IGAS=0)

XXIV. TRAPG (called only if IGAS•1)

XXV. HYST1 (called only if IPERM=2)

XXVI. UTFOAM (called only if IGAS=2)

XXVII. VISCOS

XXVIII. WELLCK

XXIX. OUTDT1

XXX. OUTDT2

A. PRINTI
Appendix A - UTCHEM 6.1 User's Guide

239

B. PRINTS

XXXI. NSLUG

A. WELLIX

1. RADIUS

XXXII. RSTART

XXXIII. Go to step V (ASIGN1) if not done

XXXIV. SUMTAB
Appendix A - UTCHEM 6.1 User's Guide

240

A.7 PHASES AND SPECIES IN UTCHEM

This section gives the component numbering scheme in UTCHEM and the unit for each

component.

The following values for L correspond to the indicated phase:

L Phase

1 Aqueous phase

2 Oleic phase

3 Microemulsion phase

4 Gas phase

The following indices correspond to the indicated components [corresponding concentration units

are listed in square brackets]:

For all values of IREACT:

Index Component [conc. units]

1 Water [volume fraction]

2 Oil [volume fraction]

3 Surfactant [volume fraction]

4 Polymer or silicate (KGOPT=3) [weight percent]

5 Total nonsorbing anions concentration, assumed to all be

chloride anions [meq/ml]

6 Divalent cations, assumed to all be calcium for

IREACT<2 [meq/ml]

7 Alcohol 1 [volume fraction]

8 Alcohol 2 or Gas [volume fraction]

Organic species (IBIO=0 and NO>1):

Index Component [conc. units]

9 First organic species [volume fraction]

8+NO Last organic species [volume fraction]

Tracers (NT>0):

Index Component [conc. units]

9+NO First tracer [dependent on user input]

8+NO+NTW+NTA Last tracer [dependent on user input]

Geochemistry option species (IREACT=2 or IRECAT=3):

Index Component [conc. units]

9+NO+NTW+NTA First geochemistry component

[meq/ml]

8+NO+NTW+NTA+NGC Last geochemistry component

[meq/ml]
Appendix A - UTCHEM 6.1 User's Guide

241

Gel model species (IREACT=1 and NG>0):

Index

KGOPT=1

Component

[conc. units]

KGOPT=2

Component

[conc. units]

KGOPT=3

Component

[conc. units]

NG1* Na2Cr2O7 [ppm] — —

NG2 CSN2H4 [ppm] Malonate ion [ppm] —

NG3 Cr3+ [ppm] Cr3+ [ppm] OH-

 [ppm]

NG4 Gel [ppm] Gel [ppm] Gel [ppm]

NG5 Hydrogen [meq/ml] Hydrogen [meq/ml] —

*where NG1 = 9+NO+NTW+NTA

Geochemistry/Gel option species (IREACT=4 and NG>0):

Index Component [conc. units]

9+NO+NTW+NTA First geochemistry component

[meq/ml]

8+NO+NTW+NTA+NGC Last geochemistry component

[meq/ml]

Index

KGOPT=1

Component [conc. units]

KGOPT=2

Component [conc. units]

NG1* Na2Cr2O7 [ppm] —

NG2 CSN2H4 [ppm] Malonate ion [ppm]

NG3 Cr3+ [ppm] Cr3+ [ppm]

NG4 Gel [ppm] Gel [ppm]

*where NG1 = 9+NO+NTW+NTA+NGC

Biological model species (IBIO=1):

Index Component

[conc. units]

9+NO+NTW+NTA+NGC+NG First biological species

[mg/l]

8+NO+NTW+NTA+NGC+NG+NOTH Last biological species

[mg/l]
Appendix A - UTCHEM 6.1 User's Guide

242

A.8 TIME-STEP SELECTION

This section discusses the automatic time-step selection options available in UTCHEM:

(E.1) selector based on method of relative changes for the first three components, (E.2) selector

based on method of relative changes for all the components, and (E.3) selector based on changes in

dimensionless concentration for all the components.

The Courant number, C, is defined as:

C = 

Q Δt

Δx Δy Δz φ

where Q is maximum injection/production per wellblock.

8.1 Method of Relative Changes for First Three Components (IMES=2)

Minimum and maximum time step in days (option ITIME=0):

The time step selection is based on the method of relative changes for the first three

components (water, oil, and surfactant) as:

Δt

n+1

= Δt

n min ΔClim

i=1

NBL

max ΔCi,κ

 

 

 

  

 

 

 

  

 κ = 1, 2, 3 (E.1)

where •tn+1 is limited to: •tmin••tn+1••tmax. •tmin and •tmax are the input time step values and ΔClim

is the input value for concentration tolerance (DCLIM) on input line 3.7.10.

Minimum and maximum time step in days (option ITIME=1):

The minimum and maximum time steps in days are computed based on the minimum and

maximum Courant number as:

Δtmin = 

CNMIN

min

M=1

nwell

max

i=1

nwbc Qi

Δxi Δyi Δzi φi

 

  

 

  

and

Δtmax = 

CNMAX

min

M=1

nwell

max

i=1

nwbc Qi

Δxi Δyi Δzi φi

 

  

 

  

where Courant number (C) is limited to: CNMIN•C•CNMAX. CNMIN and CNMAX are the input

Courant number values in line 3.7.11. The time step is then calculated from Eq. E.1.

8.2 Method of Relative Changes for All Components (IMES=3)

For IMES=3, the method of relative changes is applied to all the components in the

simulation run:
Appendix A - UTCHEM 6.1 User's Guide

243

Δt

n+1

= Δt

n min

ΔClim,κ

i=1

NBL

max ΔCi,κ

 

 

 

  

 

 

 

  

 κ = 1, ..., nc

where •tn+1 is limited to: •tmin••tn+1••tmax. •Clim,κ is a fraction of the initial or injected

concentration (whichever is larger) of the KCth component, DELC(KC) in input lines 3.7.12 or

3.7.13. For example: •Clim,3 = 0.1 × C3 where C3 is the total concentration of component 3. If

•Clim,κ of the KCth component is entered as zero, that component is not considered in the time-step

size selection.

8.3 Method of Relative Changes Using Dimensionless Concentration for All Components

(IMES=4)

For IMES=4, the method of relative changes is applied to all the components in the

simulation run:

Δt

n+1

= Δt

n min

Rlim,κ

i=1

NBL

max

ΔCi,κ

Ci,κ

 

 

 

 

 

  

 

 

 

 

 

  

 κ = 1, ..., nc

where •tn+1 is limited to: •tmin••tn+1••tmax. Rlim,κ is the input dimensionless relative change in

concentration of component κ (DELC(KC)) on input lines 3.7.12 or 3.7.13. For example Rlim,3=0.1

indicates a 10% change in concentration of Component 3.
Appendix A - UTCHEM 6.1 User's Guide

244

A.9 DESCRIPTION OF work.job FILE

This section contains a detailed description of the contents of the example work.job file

found in Section 2.3 of this appendix.

Command line Description

rm -r EX01.dir Removes the EX01.dir directory if it

already exists. Make sure you've

copied files from previous runs (if you

want to save them) to another location

before executing the work.job file

because all files in the EX01.dir

directory will be deleted when the

directory is deleted.

mkdir EX01.dir Create a subdirectory in which to place

the new simulation results.

cd EX01.dir Make EX01.dir the current working

directory.

ln -s ../ex01.data INPUT Create a symbolic link to the

ex01.data input data file (which is

located up one level in the directory

structure). When the program looks for

the file INPUT, it will automatically be

pointed to the ex01.data file.

time ../utchem.exe Run the program (which is located up

one level in the directory structure).

mv TTABLE ex01.ttable

mv ECHO ex01.echo

mv MESH ex01.mesh

mv PROFIL ex01.prof

mv CONCP ex01.con

mv PRESP ex01.presp

#mv ALKP ex01.alkp

mv SATP ex01.satp

mv GFILEP ex01.gel

mv TEMPP ex01.temp

mv HIST01 ex01.hist01

mv HIST02 ex01.hist02

mv HIST03 ex01.hist03

mv HIST04 ex01.hist04

#mv HIST05 ex01.hist05

#mv HIST06 ex01.hist06

#mv HIST07 ex01.hist07

mv OVERAL ex01.overal

mv RESTAR ex01.rest

mv WARN ex01.warn

Change the default UTCHEM output

file names to something more

meaningful. The main reason for doing

this optional step is to simplify

identification of files at a later date.

Files that do not appear as part of the

current run are commented out using

the pound sign (#) in the first column

of the work.job file.

gzip * Add this line to the work.job file to

compress all files in order to save space

(if necessary).
239

Appendix B

UTCHEM Local Grid Refinement User's Guide

B.1 INTRODUCTION

UTCHEM is a three-dimensional chemical flooding simulator. The solution scheme is

analogous to IMPES, where pressure is solved for implicitly, but concentrations rather than

saturations are then solved for explicitly. Phase saturations and concentrations are then solved in a

flash routine. An energy balance equation is solved explicitly for reservoir temperature. The

energy balance equation includes heat flow between the reservoir and the over- and underburden

rocks. The major physical phenomena modeled in the simulator are:

dispersion

dilution effects

adsorption

interfacial tension

relative permeability

capillary trapping

cation exchange

phase density

compositional phase viscosity

phase behavior (pseudoquaternary)

aqueous reactions

partitioning of chemical species between oil and water

dissolution/precipitation

cation exchange reactions involving more than two cations

in-situ generation of surfactant from acidic crude oil

pH dependent adsorption

polymer properties: shear thinning viscosity, inaccessible pore volume, permeability

reduction, adsorption

gel properties: viscosity, permeability reduction, adsorption

tracer properties: partitioning, adsorption, radioactive decay, reaction (ester hydrolization)

temperature dependent properties: viscosity, tracer reaction, gel reactions

The following options are available with UTCHEM: isothermal or non-isothermal

conditions, a constant or variable time-step, constant pressure or constant rate well conditions,

horizontal and vertical wells, and a radial or cartesian geometry. Please refer to the dissertation

“Field Scale Simulation of Chemical Flooding” by Naji Saad [1989] for a more detailed discussion

of the UTCHEM simulator and its formulation.
Appendix B - UTCHEM Local Grid Refinement User's Guide

240

B.2 LOCAL GRID REFINEMENT SPECIFICATIONS

This section describes the special requirements unique to the Local Grid Refinement (LGR)

version of UTCHEM.

Input Notes:

This code is applicable to water flooding, Surfactant flooding and Tracer flooding.

Can use components: (1, 2, 3, 5, 6, 7, 8, 9, 10, 11)

Methods

Single Point upstream, 2 point upstream, higher order

Models

Water flooding

Salinity

Adsorption

Tracer

Surfactant / alcohol

phase behavior

Capillary number

Interfacial Tension

Full tensor physical diffusion

Capillary pressure

Solubilization (oil in water)

hysteresis

Wells - Peaceman Model

Global flow gradient

Gravity

Variable Permeability

The reservoir is initially defined by a coarse grid (called a base grid) with NXCxNYCxNZC

standard cells (gridblocks).

Subject to memory limitations any combination of the base grid cells can be refined by one local

level NXFxNYFxNZF which is of fixed resolution for all refined cells.

The locally refined cells are called ZONES.

Memory and ARRAYS.

Arrays must be set in PARAMS.INC and UTCHEMLGR.FOR

Edit PARAMS.INC to see 3 sections:

1) UTwork space, 2) Coarse, 3) Fine
Appendix B - UTCHEM Local Grid Refinement User's Guide

241

Coarse and Fine correspond to the base grid and Zone requirements respectively. Note NREFI

defines maximum number of zones and total memory is proportional to

NXXCxNYYCxNZZC + NREFI * NXXFxNYYFxNZZF

+

max(NXXCxNYYCxNZZC , NXXFxNYYFxNZZF)

UTwork space arrays = max(Coarse, Fine)

e.g. NNX = max (NNXC, NNXF)

UTBASE.F only contains work space arrays; e.g., NNX only (not NNXC or NNXF)

LOCAL REFINEMENT = ADD ZONES

New Input Parameters

The input data set consists of the usual UTCHEM data set for the base grid, and a UTCHEM data

set for each ZONE (i.e., each refined base cell) again with appropriate minor modifications

described below. The input format is identical to the standard UTCHEM manual in each case.

Coordinate Definition

LGR is used with ICOORD = 1

For BASE grid data set

READ (5,*) NXC,NYC,NZC,IDXYZ,IUNIT

READ (5,*) DXC,DYC,DZC

For ZONE data set

READ (5,*) NXF,NYF,NZF,IDXYZ,IUNIT

READ (5,*) DXF,DYF,DZF

(Must have NXF > 1, NYF > 1, NZF > 1 in 3-D)

Note: for uniform grids

DXF = DXC / NXF

DYF = DYC / NYF

DZF = DZC / NZF

otherwise for non-uniform grids

DXC = DXF j ∑j

, DYC = DYF j ∑j, DZC = DZFj ∑j

Note: neighboring non-uniform grids must have the same spacing in the direction tangential to the

common interface.

Gravity

D111 is the depth of the center of the first BASE cell in the top layer.
Appendix B - UTCHEM Local Grid Refinement User's Guide

242

If a coarse cell is refined the corresponding depths of the local ZONE cells are appropriately defined

by the code.

Set D111 = 0 in all ZONE domain data sets following the BASE data set.

Permeability

A pre-processing program LGRPERM is supplied which will extract portions of a fine grid global

permeability map that correspond to zones chosen by the user.

The approach is as follows;

Define a base grid.

Refine the base grid to a specified level.

Create a fine grid permeability map for the entire fine domain then use LGRPERM to

define the permeability maps for the local zones. An LGR simulation can then be

performed with the specified zones that correspond locally to the fine domain. In

effect some base cells are unrefined and appropriate upscaling should be employed

for rock properties of these cells. At present LGRPERM assigns an average value to

these cells.

Alternatively the user is free to define the local variation over each zone.

Caution: The larger the grid interface ratio (number of fine cells adjacent to a coarse cell) the larger

the potential for error in the solution. A large variation in permeability over the interface may give

rise to spurious pressure distributions, and in extreme cases may even cause convergence problems

for the pressure equation solver.

WELL DATA

Inflow - Outflow

A fine zone can be adjacent to an inflow or out flow boundary. In this case the local zone data set is

of identical format to the standard spec and

IBOUND =1.

If the zone is adjacent to an inflow boundary

IBL = 1, IBR = 0.

If the zone is adjacent to an outflow boundary

 IBL = 0, IBR = 1.

WELLS

Wells can either be completed through adjoining base cells which are NOT refined, OR through

adjoining ZONES. Wells are NOT allowed to be completed across any coarse-fine interface

between a ZONE and a non-refined base cell.
Appendix B - UTCHEM Local Grid Refinement User's Guide

243

Spatial (i,j,k) Indexing

Base grid: as per standard.

Zones: as per standard with respect to the local domain. The well spatial (i,j,k) indexing works with

respect to the local domain.

Each well has a globally unique ID number; i.e., upon entering a new domain the "counting" of the

wells begins from current ID number + 1 . If a well is completed through neighboring zones then it

has the same ID in both zones, otherwise the same ID cannot be assigned to different wells in

separate domains.

Caution: By definition, the method will give relatively poor results if wells are placed in fine cells

at coarse/fine interfaces of the grid.

SLUGS

Slug data for the base grid and all zones is tagged on the very end of the entire input file. First input

the base grid well data modifications followed by each of the ZONE well data modifications as per

standard spec. If the base grid or a ZONE is not modified or has no wells then this is flagged by

 8 standard lines

CC

CC

then input

IRO,ITIME, (IFLAG(IDW(M)), M= 1 , NWELL)

enter all zeros if no wells,

or

repeat previous data if wells unchanged.

CC

CC

 -1

Similarly repeat for each unchanged well in a domain.

NOTE: TINJ should have the same time value for each domain section until the very last

specification of TINJ, which should have TINJ > TMAX.

Restart Data

Currently a single line is added to the top of the restart data set to handle well data for the zones.

Enter

1
Appendix B - UTCHEM Local Grid Refinement User's Guide

244

for each existing zone (of the first simulation) not containing a well and for each new zone that has

been added.

Enter

-1

for each existing zone (of the first simulation) containing a well so that the restart well data is read,

this data can only be modified via a slug.

The order of entry is strictly according to the occurrence of each zone with respect to the global

index IIG(L) = I + (J - 1) * NXC + (K - 1) * NXC*NYC.

e.g., if in the first simulation there are 3 zones with a well in the first zone and 5 restart zones are

flagged, then (assuming the new zone global indices are greater than the first zone global index)

upon restarting the calculation enter

-1 1 1 1 1

OUTPUT

The output is written per domain in standard UTCHEM format. The base cell and refinement

number are printed at the top of each domain data set, "layers" now refers to layers in the local

domain.

The velocity field is written for each cell face of each zone. Therefore neighboring interior zones

will have the same face velocity field at the common interface locations.

B.3 OPERATION OF THE SIMULATOR

The UTCHEM simulator is run on a CRAY Y/MP at the University of Texas High

Performance Computing Facility (UNICOS operating system), a number of DEC Alpha systems

(DEC 4000/610, 3000/500 & 3000/300X) at the Department of Petroleum and Geosystems

Engineering (OSF/1 operating system), and a DEC Alpha system (DEC 3000/500) at the

Department of Petroleum and Geosystems Engineering (OpenVMS operating system). The same

code is executed on all three systems, except for the use of double precision (64-bit words) on the

DEC machines—we differentiate between "Cray" and "DEC" versions of the code by adding a "V"

prior to the version number for the "Cray" version and a "D" prior to the version number for the

"DEC" (or double-precision) version. Several intrinsic Cray functions need to be implemented

when not running on the Cray; these routines are "commented" out in the "Cray" version. Please

check the source code for additional information about necessary changes when running on different

computers.

B.3.1 Input and Output Files

UTCHEM requires one input file for non-restart runs. For restart runs, a restart file is

required in addition to the original input data file used for the previous run. A detailed input data

description is given in section B.3 of this appendix and the data in the restart data file is documented

in section B.6. The number of output files generated by UTCHEM varies depending upon several

control flags set by the user in the input file. The number of history plot files depends on the value
Appendix B - UTCHEM Local Grid Refinement User's Guide

245

of the MXW parameter in the source code. The FORTRAN unit number for the history plot file is

incremented by one for each well. For example, if MXW is equal to three, then three history plot

files would be generated corresponding to FORTRAN unit numbers 19, 20, and 21 even if the run

only has two wells. The input and output files are summarized in the following table.

Unit Number File Name Contents

1 TEMPL Analytical temp. profile, created if IENG=1 and IANAL=1

2 ECHO Echo print of the input file information

3 SUMARY Summary data

4 PROFIL Formatted profile data; described in section 6.1 of this appendix

5 INPUT Input data; described in detail in section B.3 of this appendix

6 TTABLE Table of time steps and Courant numbers

7 RESTAR Stored restart run data; described in section 6.3 of this appendix

8 CONCP Component concentration profile plotting data, created if IPCTOT>0

9 OVERAL History of overall properties; described in section 6.5 of this

appendix

10 GFILEP Gel property profile plotting data, created if IREACT=1

11 PRESP Phase pressure profile plotting data, created if IPPRES>0

12 SATP Phase saturation profile plotting data, created if IPSAT>0

13 TRACP Phase tracer concentration profile plotting data, created if

IPTRAC>0

14 CAPP Capacitance property profile plotting data, created if IPCAP>1

15 ALKP Alkaline option related profile plotting data, created if IREACT>1

16 INPUT2 Restart run data (input file created by an earlier run)

17 WARN Warning messages

18 TEMPP Temperature profile, created if IENG =1 and IPTEMP=1

19 HIST01 Well history plotting data for well #1; described in section 6.4 of this

appendix

20 HIST02 Well history plotting data for well #2

...

l HISTl Well history plotting data for last well

l+1 TRAC01 Aqueous phase tracer concentration at 1st observation point , created

if IPOBS>0; described in section 6.6 of this appendix

l+2 TRAC02 Aqueous phase tracer concentration at 2nd observation point

...

n TRACn Aqueous phase tracer concentration at last observation point

B.3.2 Source Code Array Dimensions

The parameters in the following table are used by the simulator to define array sizes. All the

parameter values must be equal to or greater than the size of the grid dimensions specified in the

input file, unless otherwise noted. Additionally, all instances of each parameter must be the same

throughout the code, so if you want to change the value of one of the parameters, please make sure

you make a global substitution. Please see the note in Section 2 on memory and arrays for LGR

code.

Parameter Definition
Appendix B - UTCHEM Local Grid Refinement User's Guide

246

NNX Number of gridblocks in X-direction (must be set equal or larger to NX in the input

file)

NNY Number of gridblocks in Y-direction (must be set equal or larger to NY in the input

file)

NNZ Number of gridblocks in Z-direction (must be set equal or larger to NZ in the input

file)

MXC Maximum number of components (cannot be less than 8)

MXP Number of phases (must be set equal to 3 when there is no gas phase and must be set

equal to 4 if gas is present)

MXW Maximum number of wells

MXWB Maximum number of well blocks

MXNT Maximum number of tracers

MXELE Maximum number of elements

MXFLD Maximum number of reactive fluid species

MXSLD Maximum number of solids

MXSORB Maximum number of adsorbed species

MXACAT Maximum number of cations associated with surfactant

MXEX Maximum number of insoluble exchangers

B.4 INPUT DATA DESCRIPTION

The UTCHEM input file consists of comment lines and data lines. All comment lines are

ignored by the UTCHEM simulator. It is important to note, however, that the number of comment

lines between data lines is fixed. The first twenty-two lines of the input file are reserved for

comment lines used to briefly describe the input file. Each data line is preceded by three comment

lines (except for the input described in section 4.5 of this appendix). The input file is basically

divided into six sections and each of those input sections (except section 4.5 of this appendix) is

preceded by an additional seven comment lines. The user should update the comment lines as the

input file is modified in order to make using the simulator easier.

All data is free-formatted. This means that for each read statement, it is only necessary to

leave a blank space between data elements. Note that the first data element for a given read

statement must be on a new line in the input file. Subsequent data elements for that read statement

can span as many lines as necessary. Implicit type matching is used; that is, all REAL variables

begin with the letters A-H or O-Z and all integer variables begin with the letters I-N.

The following is a list of variables as they are read by UTCHEM. The variable names

appear in all-caps on a single line in the order they are read by the program. Every list of variables

is followed by a description of each variable and corresponding units or possible values if

applicable. All of the variables listed in the input description will be read by the program unless

otherwise noted; therefore, a dummy value will be read by the program for variables not pertinent to

the problem being run.

B.4.1 Title and Reservoir Description Data

The first input section consists of the title and reservoir description data. Please remember

that there are 22 comment lines at the beginning of this section and that each data line is preceded

by three comment lines.

4.1.1 RUNNO

RUNNO - Run number.
Appendix B - UTCHEM Local Grid Refinement User's Guide

247

Note: The run number can consist of any combination of alphanumeric characters on a

single line (not to exceed 80 characters). This information will be printed as the first

line of every output file.

4.1.2 TITLE

TITLE - Title and run description.

Note: The title can consist of any combination of alphanumeric characters spanning three

lines in the input file (not to exceed 80 characters per line). Please note that the title

must span three lines and that any of those lines can be blank.

4.1.3 NRINIT, IRESTZONE

NRINIT - Number of refined zones.

IRESTZONE - Number of refined zones for restart run.

4.1.4 IXG(J), IYG(J), IZG(J), for J=1, NRINIT

IXG(J), IYG(J), IZG(J) - Base grid integer coordinates of the refined cells.

4.1.5 IXRG(J), IYRG(J), IZRG(J), for J=1, NRINIT (This line is read only if IRESTZONE > 0)

IXRG(J), IYRG(J), IZRG(J) - Base grid integer coordinates of the cells to be refined at restart.

Repeat for IRESTZONE refined base cells.

4.1.6 IMODE, IMES, IDISPC, ICWM, ICAP, IREACT, ICOORD, ITREAC, ITC, IGAS, IENG

IMODE - Flag indicating if the problem to be run is a first run or a restart problem.

Possible Values:

1 - First run problem

2 - Restart problem

IMES - Flag indicating if a constant or automatic time-step is to be used.

Possible Values:

1 - Constant time-step size is used

2 - Automatic time-step size selector based on method of relative changes for the first

three components is used

3 - Automatic time-step size selector based on method of relative changes for all the

components is used

4 - Automatic time-step size selector based on changes in dimensionless

concentration for all the components is used

Note: The automatic time-step selector is recommended. See input lines 4.5.9 through

4.5.12 for more details on the above options. In addition, IMES=1 is the only option fully

tested with the LGR code.

IDISPC - Flag indicating which type of numerical dispersion control is used.

Possible Values:

0 - Single point upstream method is used

1 - Chaudhari's method is used (this method is not available if ICOORD = 2)

2 - Two point upstream method is used

3 - Improved total variation diminishing third order method is used

Note: These methods are applied to both concentration and relative permeability.

ICWM - Flag indicating if the concentration well model is used or not.

Possible Values:
Appendix B - UTCHEM Local Grid Refinement User's Guide

248

0 - Concentration well model is not used

1 - Concentration well model is used

Note: The concentration well model (ICWM = 1) can only be used with vertical wells

(IDIR(M) = 3).

ICAP - Flag indicating if the capacitance model is used or not.

Possible Values:

0 - Capacitance model is not used

1 - Capacitance model is used

IREACT - Flag indicating if gel reactions or alkaline options are used or not.

Possible Values:

0 - Gel reactions are not used

1 - Gel reactions are used

2 - Alkaline option 1 (no silicon, aluminum, or acid)

3 - Alkaline option 2 (no silicon or aluminum; with acidic crude)

4 - Alkaline option 3 (with silicon and aluminum; no acid)

5 - Alkaline option 4 (with silicon, aluminum, and acidic crude)

6 - Alkaline option 3 and gel reactions are used

Note: IREACT=0 is the only option available with the LGR code.

ICOORD - Flag indicating which coordinate system is used.

Possible Values:

1 - Cartesian coordinate system is used

2 - Radial coordinate system is used

3 - Cartesian coordinate system with variable-width gridblock is used (2-D cross

section only)

4 - Curvilinear grid definition of the X-Z cross section is used (2-D or 3-D)

Note: For ICOORD=4, the 3-D grid consists of the 2-D cross sectional grid repeated at

specified intervals (uniform or non-uniform) in the Y direction, according to the

definition of DY1. The curvilinear grid option is not available for the temperature

equation option (IENG must be set to 0 on this input line). In addition, ICOORD=1

is the only option available with the LGR code.

ITREAC - Flag indicating if a tracer reaction is used or not.

Possible Values:

0 - Tracer reaction is not used

1 - Tracer reaction is used

ITC - Flag indicating if second-order time approximation is used or not.

Possible Values:

0 - Second-order time approximation is not used

1 - Second-order time approximation is used

Note: We recommend that second-order time approximation (ITC = 1) only be used with

higher-order dispersion methods (IDISPC > 1).

IGAS - Flag indicating if gas phase is considered or not.

Possible Values:

0 - Gas is not present

1 - Gas is present

IENG - Flag indicating if temperature variation is considered or not.

Possible Values:

0 - Isothermal simulation
Appendix B - UTCHEM Local Grid Refinement User's Guide

249

1 - Temperature equation is solved

Note: IENG must be set equal to 0 if the curvilinear grid option (ICOORD=4 on this input

line) option is used. In addition, IENG=0 is the only option available with the LGR

code.

4.1.7 NX, NY, NZ, IDXYZ, IUNIT

NX - Number of gridblocks along X-axis (ICOORD = 1 or 3) or number of gridblocks in radial

direction (ICOORD = 2).

Note: This value should be equal to or smaller than the NNX parameter in UTCHEM.

NY - Number of gridblocks along Y-axis.

Note: This value should be equal to or smaller than the NNY parameter in UTCHEM. It

should be set equal to 1 if the user is running a 1-D problem or a 2-D cross sectional

problem. If ICOORD = 2, this value is automatically set equal to 1.

NZ - Number of gridblocks along Z-axis.

Note: This value should be equal to or smaller than the NNZ parameter in UTCHEM. It

should be set equal to 1 if the user is running a 1-D problem or a 2-D areal problem.

IDXYZ - Flag indicating constant or variable grid size.

Possible Values:

0 - Constant grid size

1 - Variable grid size on a regional basis

2 - Variable grid size

Note: IDXYZ must be set equal to 2 if ICOORD = 3.

IUNIT - Flag indicating English or Metric units.

Possible values:

0 - English unit

1 - Metric unit

Note: UTCHEM must be compiled and run with the NX, NY, and NZ input values being equal to

or smaller than the NNX, NNY, and NNZ parameters in the code. All 38 occurrences of the

NNX, NNY, and NNZ parameters in the code must be set to the same values which must be

equal to or larger than the NX, NY, and NZ input values. Additionally, since parameter

statements are used for dimensioning arrays in UTCHEM, any time any parameter statement

is changed in the FORTRAN source code, all occurrences of that parameter statement must

be changed (and set to the same value throughout the code) or the code will not function

properly.

4.1.8 XCORD (I), ZCORD(I), for I = 1, (NX+1) × (NZ+1) (This line is read only if ICOORD = 4)

XCORD - Gridblock coordinate of Ith corner point in X-direction.

Units: feet (IUNIT=0) or m (IUNIT=1)

ZCOORD - Gridblock coordinate of Ith corner point in Z-direction.

Units: feet (IUNIT=0) or m (IUNIT=1)

Note: The coordinates of the corners (or vertices) of the 2-D X-Z cross section gridblocks are input

in pairs as follows:

XCORD(1), ZCORD(1)

 . .

 . .

 . .

XCORD(nodes), ZCORD(nodes)
Appendix B - UTCHEM Local Grid Refinement User's Guide

250

where nodes = (NX+1) × (NZ+1) and is the total number of corner points defining the X-Z

cross section and Z is positive downward. The following figure illustrates the input order for

an example X-Z cross section grid:

The number of gridblocks is equal to NX × NZ and the number of coordinate pairs (or

nodes) is equal to (NX+1) × (NZ+1).

Cautionary warning: The X-Z cross section grid should be constructed by the user such that

the curvilinear coordinate system is at least quasi-orthogonal. Departure from

orthogonality will lead to numerical errors in the solution.

4.1.9 DX1, DY1, DZ1 (This line is read only if IDXYZ = 0 and ICOORD = 1)

DX1 - Gridblock size in X direction.

Units: feet (IUNIT=0) or m (IUNIT=1)

DY1 - Gridblock size in Y direction.

Units: feet (IUNIT=0) or m (IUNIT=1)

DZ1 - Gridblock size in Z direction.

Units: feet (IUNIT=0) or m (IUNIT=1)

4.1.10 R(1), DX1, DZ1 (This line is read only if IDXYZ = 0 and ICOORD = 2)

R(1) - Wellbore radius.

Units: feet (IUNIT=0) or m (IUNIT=1)

DX1 - Distance between nodes in radial direction.

Units: feet (IUNIT=0) or m (IUNIT=1)

DZ1 - Gridblock size in Z direction.

Units: feet (IUNIT=0) or m (IUNIT=1)

4.1.11 DY1 (This line is read only if IDXYZ = 0 and ICOORD = 4)

DY1 - Gridblock size in Y direction.

Units: feet (IUNIT=0) or m (IUNIT=1)

4.1.12 II1, II2, DX1 (This line is read only if IDXYZ = 1 and ICOORD = 1 or 3)

II1 - First index for gridblocks with same size in X direction.

II2 - Last index for gridblocks with same size in X direction.
Appendix B - UTCHEM Local Grid Refinement User's Guide

251

DX1 - Gridblock size in X direction

Units: feet (IUNIT=0) or m (IUNIT=1)

Note: This line is repeated until sizes for each of the NX gridblocks in the X direction have been

specified. The first line in the set must have II1 = 1 and the last line must have II2 = NX.

Example: If NX = 11 and the first three gridblocks in the X direction are 3 feet in size, the fourth

through ninth gridblocks in the X direction are 2 feet in size, and the last two gridblocks in

the X direction are 2.5 feet in size, this line would need to be repeated three times to fully

describe the X direction gridblocks as follows:

1 3 3.0

4 9 2.0

10 11 2.5

4.1.13 JJ1, JJ2, DY1 (This line is read only if IDXYZ = 1 and ICOORD = 1 or 3)

JJ1 - First index for gridblocks with same size in Y direction.

JJ2 - Last index for gridblocks with same size in Y direction.

DY1 - Gridblock size in Y direction.

Units: feet (IUNIT=0) or m (IUNIT=1)

Note: This line is repeated until sizes for each of the NY gridblocks in the Y direction have been

specified. The first line in the set must have JJ1 = 1 and the last line must have JJ2 = NY.

See the example for input line 4.1.9.

4.1.14 KK1, KK2, DZ1 (This line is read only if IDXYZ = 1 and ICOORD = 1 or 3)

KK1 - First index for gridblocks with same size in Z direction.

KK2 - Last index for gridblocks with same size in Z direction.

DZ1 - Gridblock size in Z direction.

Units: feet (IUNIT=0) or m (IUNIT=1)

Note: This line is repeated until sizes for each of the NZ gridblocks in the Z direction have been

specified. The first line in the set must have KK1 = 1 and the last line must have KK2 =

NZ. See the example for input line 4.1.9.

4.1.15 R(1) (This line is read only if IDXYZ = 1 and ICOORD = 2)

R(1) - Wellbore radius.

Units: feet (IUNIT=0) or m (IUNIT=1)

4.1.16 II1, II2, DX1 (This line is read only if IDXYZ = 1 and ICOORD = 2)

II1 - First index for radial node distances of the same size.

II2 - Last index for radial node distances of the same size.

DX1 - Distance between nodes in radial direction.

Units: feet (IUNIT=0) or m (IUNIT=1)

Note: This line is repeated until the NX-1 distances between the NX nodes in the radial direction

have been specified. The first line in the set must have II1 = 1 and the last line must have

II2 = NX-1.

4.1.17 KK1, KK2, DZ1 (This line is read only if IDXYZ = 1 and ICOORD = 2)

KK1 - First index for gridblocks with same size in Z direction.

KK2 - Last index for gridblocks with same size in Z direction.

DZ1 - Gridblock size in Z direction.
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252

Units: feet (IUNIT=0) or m (IUNIT=1)

Note: This line is repeated until sizes for each of the NZ gridblocks in the Z direction have been

specified. The first line in the set must have KK1 = 1 and the last line must have KK2 =

NZ. See the example for input line 4.1.9.

4.1.18 JJ1, JJ2, DY1 (This line is read only if IDXYZ=1 and ICOORD=4)

JJ1 - First index for gridblocks with same size in Y direction.

JJ2 - Last index for gridblocks with same size in Y direction.

DY1 - Gridblock size in Y direction.

Units: feet (IUNIT=0) or m (IUNIT=1)

Note: This line is repeated until sizes for each of the NY gridblocks in the Y direction have been

specified. The first line in the set must have JJ1 = 1 and the last line must have JJ2 = NY.

See the example for input line 4.1.9.

4.1.19 DX(I), for I = 1, NX (This line is read only if IDXYZ = 2 and ICOORD = 1 or 3)

DX(I) - Grid size of Ith block in X direction.

Units: feet (IUNIT=0) or m (IUNIT=1)

4.1.20 DY(J), for J = 1, NY (This line is read only if IDXYZ = 2 and ICOORD = 1 or 4)

DY(J) - Grid size of Jth block in Y direction.

Units: feet (IUNIT=0) or m (IUNIT=1)

4.1.21 DY(I), for I = 1, NX (This line is read only if IDXYZ = 2 and ICOORD = 3)

DY(I) - Thickness of Ith block.

Units: feet (IUNIT=0) or m (IUNIT=1)

4.1.22 DZ(K), for K = 1, NZ (This line is read only if IDXYZ = 2 and ICOORD = 1 or 3)

DZ(K) - Grid size of Kth block in Z direction.

Units: feet (IUNIT=0) or m (IUNIT=1)

4.1.23 R(1) (This line is read only if IDXYZ = 2 and ICOORD = 2)

R(1) - Wellbore radius.

Units: feet (IUNIT=0) or m (IUNIT=1)

4.1.24 DX(I), for I = 1, NX-1 (This line is read only if IDXYZ = 2 and ICOORD = 2)

DX(I) - Distance between the Ith node and the I+1th node in the radial direction.

Units: feet (IUNIT=0) or m (IUNIT=1)

4.1.25 DZ(K), for K = 1, NZ (This line is read only if IDXYZ = 2 and ICOORD = 2)

DZ(K) - Grid size of Kth block in Z direction.

Units: feet (IUNIT=0) or m (IUNIT=1)

4.1.26 N, NTW, NTA, NG

N - Total number of components in the run (including tracers and reactive components).

Possible Values: 1 – 21

NTW - Number of water/oil tracers.

Possible Values: see note
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NTA - Number of oil/gas tracers.

Possible Values: see note

NG - Number of gel components.

Possible Values: 4 or 5 when IREACT = 1

 4 when IREACT = 6

Note: The combined total number of water/oil and oil/gas tracers (NTW+NTA) must be:

1) less than or equal to MXNT (see section 3.2) and

2) between 0 and 3 (inclusive) if IREACT>1 or between 0 and 13 (inclusive) if

IREACT=1.

The components will be listed in the following order for the corresponding values of

IREACT:

Inde

x

Component

(IREACT =

0)

Component

(IREACT =

1)

Component

(IREACT =

2)

Component

(IREACT =

3)

Component

(IREACT =

4)

Component

(IREACT =

5)

Component

(IREACT =

6)

1 Water Water Water Water Water Water Water

2 Oil Oil Oil Oil Oil Oil Oil

3 Surfactant Surfactant Surfactant Surfactant Surfactant Surfactant Surfactant

4 Polymer Polymer Polymer Polymer Polymer Polymer Polymer

5 Chloride Chloride Chloride Chloride Chloride Chloride Chloride

6 Calcium Calcium Calcium Calcium Calcium Calcium Calcium

7 Alcohol 1 Alcohol 1 Alcohol 1 Alcohol 1 Alcohol 1 Alcohol 1 Alcohol 1

8 Alcohol 2

or Gas

Alcohol 2

or Gas

Alcohol 2

or Gas

Alcohol 2

or Gas

Alcohol 2

or Gas

Alcohol 2

or Gas

Alcohol 2

or Gas

9 Tracer 1 Tracer 1 Tracer 1 Tracer 1 Tracer 1 Tracer 1 Tracer 1

10 Tracer 2 Tracer 2 Tracer 2 Tracer 2 Tracer 2 Tracer 2 Tracer 2

11 Tracer 3 Tracer 3 Tracer 3 Tracer 3 Tracer 3 Tracer 3 Tracer 3

12 Tracer 4 Na2Cr2O7 Sodium Sodium Sodium Sodium Sodium

13 Tracer 5 CSN2H4 Hydrogen Hydrogen Hydrogen Hydrogen Hydrogen

14 Tracer 6 Cr3+ Magnesium Magnesium Magnesium Magnesium Magnesium

15 Tracer 7 Gel Carbonate Carbonate Carbonate Carbonate Carbonate

16 Tracer 8 Hydrogen — Acid Comp.

of Crude

Oil

Aluminum Aluminum Aluminum

17 Tracer 9 — — — Silica Silica Silica

18 Tracer 10 — — — — Acid Comp.

of Crude

Oil

Na2Cr2O7

19 Tracer 11 — — — — — CSN2H4

20 Tracer 12 — — — — — Cr3+

21 Tracer 13 — — — — — Gel

If IREACT > 0, N must be set to the maximum number of components shown for each case

in the above table, whether all the components are present or not. For example, if IREACT

= 3, N must be set to 16. The shaded cells indicate options not available to the LGR code.

4.1.27 TRNAME(IT), for IT = 1, NTW+NTA (This line is read only if NTW+NTA > 0)

TRNAME(IT) - Name of ITth tracer.
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Note: The name of each tracer may not exceed 16 characters and each name must be on a

separate line of the input file.

4.1.28 ITRU(I), for I = 1, NTW (This line is read only if NTW > 0 and ITREAC = 1)

ITRU(I) - Flag indicating the units of the Ith tracer.

Possible Values:

1 - Ith tracer units are in volume %

2 - Ith tracer units are in weight %

4.1.29 ICF(KC), for KC = 1, N

ICF(KC) - Flag indicating if KCth component is included in the concentration calculations or not.

Possible Values:

0 - The KCth component is not included in the calculations

1 - The KCth component is included in the calculations

Example: If 11 components are considered but Alcohol 2 is not present, this line would appear as

follows:

1 1 1 1 1 1 1 0 1 1 1

B.4.2 Output Option Data

The second input section consists of output options. Please remember that there are seven

comment lines at the beginning of this section and that each data line is preceded by three comment

lines.

4.2.1 ICOPSM, ICUMTM, ISTOP

ICOPSM - Flag indicating if data will be written to UNIT 3.

Possible Values:

0 - Data will be written to UNIT 3 as directed by CUMHI2 flag

1 - Data will not be written to UNIT 3

ICUMTM - Flag indicating if the output intervals indicated by the CUMPR1, CUMHI1, CUMHI2,

WRHPV, WRPRF and RSTC variables on input line 4.5.8 are specified in pore volumes or

days.

Possible Values:

0 - Data will be written in pore volume intervals

1 - Data will be written in day intervals

Note: The day interval output option (ICUMTM = 1) is particularly useful if there is a shut

in period.

ISTOP - Flag indicating if the maximum and injection times (variables TMAX on input line 4.3.1

and TINJ on input line 4.6.8) are specified in pore volumes or days.

Possible Values:

0 - TMAX and TINJ are specified in days

1 - TMAX and TINJ are specified in pore volumes

4.2.2 IPRFLG(KC), for KC = 1, N

IPRFLG(KC) - Flag indicating if profile of KCth component should be written to UNIT 8.

Possible Values:

0 - Profile of KCth component will not be written
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1 - Profile of KCth component will be written

Note: If IPCTOT=0, none of the component profiles will be written.

Example: If 11 components are present and only profiles for the oil, surfactant, and polymer

components are desired, this line would appear as follows:

0 1 1 1 0 0 0 0 0 0 0

4.2.3 IPPRES, IPSAT, IPCTOT, IPTRAC, IPCAP, IPGEL, IPALK, IPTEMP

IPPRES - Flag indicating if profile of phase pressures should be written to UNIT 11.

Possible Values:

0 - Profile of phase pressures will not be written

1 - Profile of phase pressures will be written

IPSAT - Flag indicating if profile of phase saturations should be written to UNIT 12.

Possible Values:

0 - Profile of phase saturations will not be written

1 - Profile of phase saturations will be written

IPCTOT - Flag indicating if profile of component concentrations should be written to UNIT 8.

Possible Values:

0 - Profile of component concentrations will not be written

1 - Profile of component concentrations will be written

IPTRAC - Flag indicating if profile of tracer phase concentrations should be written to UNIT 13.

Possible Values:

0 - Profile of tracer phase concentrations will not be written

1 - Profile of tracer phase concentrations will be written

IPCAP - Flag indicating if profile of capacitance properties should be written to UNIT 14.

Possible Values:

0 - Profile of capacitance properties will not be written

1 - Profile of capacitance properties will be written

IPGEL - Flag indicating if profile of gel properties should be written to UNIT 10.

Possible Values:

0 - Profile of gel properties will not be written

1 - Profile of gel properties will be written

IPALK - Flag indicating if profile of properties related to the alkaline option should be written to

UNIT 15.

Possible Values:

0 - Profile of properties related to the alkaline option will not be written

1 - Profile of properties related to the alkaline option will be written

IPTEMP - Flag indicating if profile of reservoir temperature should be written to UNIT 18.

Possible Values:

0 - Profile of temperature will not be written

1 - Profile of temperature will be written

4.2.4 IPHP, IADS, ICKL, IVEL, IVIS, IPER, ICNM, IRKF, IPHSE, ICSE

IPHP - Flag indicating if oleic and microemulsion phase pressure data should be printed.

Possible Values:

0 - Oleic and microemulsion phase pressure data will not be printed

1 - Oleic and microemulsion phase pressure data will be printed
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256

IADS - Flag indicating if surfactant, polymer, calcium, gel, chromium, hydrogen, and sodium

adsorption data should be printed.

Possible Values:

0 - Adsorption data will not be printed

1 - Adsorption data will be printed

ICKL - Flag indicating if component concentration data in each phase should be printed.

Possible Values:

0 - Component concentration data in each phase will not be printed

1 - Component concentration data in each phase will be printed

IVEL - Flag indicating if X, Y, and Z direction phase fluxes should be printed.

Possible Values:

0 - X, Y, and Z direction phase fluxes will not be printed

1 - X, Y, and Z direction phase fluxes will be printed

IVIS - Flag indicating if phase viscosities should be printed.

Possible Values:

0 - Phase viscosities will not be printed

1 - Phase viscosities will be printed

IPER - Flag indicating if relative permeabilities should be printed.

Possible Values:

0 - Relative permeabilities will not be printed

1 - Relative permeabilities will be printed

ICNM - Flag indicating if phase capillary numbers and interfacial tensions should be printed.

Possible Values:

0 - Capillary numbers and interfacial tensions will not be printed

1 - Capillary numbers and interfacial tensions will be printed

IRKF - Flag indicating if permeability reduction factors should be printed.

Possible Values:

0 - Permeability reduction factors, polymer viscosities, and equivalent shear rate will

not be printed

1 - Permeability reduction factors, polymer viscosities, and equivalent shear rate will

be printed

IPHSE - Flag indicating if phase environment indexing should be printed.

Possible Values:

0 - Phase environment indexing will not be printed

1 - Phase environment indexing will be printed

Note: The indices for the phase environment are as follows:

1 - single phase

2 - two phase oil/water or oil/microemulsion or water/microemulsion

3 - three phase oil/microemulsion/water

4 - lobe II(+) of type III

5 - lobe II(-) of type III

ICSE - Flag indicating if effective salinity should be printed.

Possible Values:

0 - Effective salinity information will not be printed

1 - Effective salinity will be printed to PROFIL and history data files
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257

Note: These flags give the option of printing a very detailed description (all flags = 1) every

CUMPR1 pore volume interval or a very limited description (all flags = 0) to UNIT 4. See

section B.6 for a list of the values that are written to UNIT 4 automatically.

4.3 Reservoir Properties

The third input section consists of the reservoir properties. Please remember that there are

seven comment lines at the beginning of this section and that each data line is preceded by three

comment lines.

4.3.1 TMAX

TMAX - Total injection period (maximum simulated time).

Units: days or pore volumes (dependent on value of ISTOP flag in line 4.2.1)

4.3.2 COMPR, PSTAND

COMPR - Rock compressibility.

Units: 1/psi (IUNIT=0) or 1/kPa (IUNIT=1)

PSTAND - Reference pressure at which pore volume and fluid compressibilities are specified.

Units: psi (IUNIT=0) or kPa (IUNIT=1)

4.3.3 IPOR1, IPERMX, IPERMY, IPERMZ

IPOR1 - Flag indicating constant or variable porosity for reservoir.

Possible Values:

0 - Constant porosity for whole reservoir

1 - Constant porosity for each layer

2 - Variable porosity over reservoir

IPERMX - Flag indicating constant or variable X direction permeability (ICOORD = 1 or 3) or

radial direction permeability (ICOORD = 2) for reservoir.

Possible Values:

0 - Constant permeability for whole reservoir

1 - Constant permeability for each layer in the X direction (ICOORD = 1 or 3) or

radial direction (ICOORD = 2)

2 - Variable permeability over reservoir

IPERMY - Flag indicating constant or variable Y direction permeability for reservoir.

Possible Values:

0 - Constant permeability for whole reservoir

1 - Constant permeability for each layer in the Y direction

2 - Variable permeability over reservoir

3 - Y direction permeability is dependent on X direction permeability

IPERMZ - Flag indicating constant or variable Z direction permeability for reservoir.

Possible Values:

0 - Constant permeability for whole reservoir

1 - Constant permeability for each layer in the Z direction

2 - Variable permeability over reservoir

3 - Z direction permeability is dependent on X direction permeability

4.3.4 PORC1 (This line is read only if IPOR1 = 0)

PORC1 - Reservoir porosity.
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258

Units: fraction

Note: All elements of the POR array will be set equal to PORC1.

4.3.5 POR(K), for K = 1, NZ (This line is read only if IPOR1 = 1)

POR(K) - Porosity of Kth layer.

Units: fraction

Note: NZ values are actually read into a workspace array (WKSP1) and then the first set of

NX × NY elements (corresponding to layer 1) of the POR array are set equal to

WKSP1(1), the second set of NX × NY elements (corresponding to layer 2) of the

POR array are set equal to WKSP1(2), etc.

4.3.6 POR(I), for I = 1, NX × NY × NZ (This line is read only if IPOR1 = 2)

POR(I) - Porosity of Ith gridblock

Units: fraction

Note: The three-dimensional grid system is being read into a one-dimensional array. The

first index (column) of the three-dimensional system

 fastest, the second index (row) varies next fastest, and the third index (layer) varies slowest.

Example: If you had a 4 × 3 × 2 system (4 columns—NX=4, 3

rows—NY=3, and 2 layers—NZ=2), the values would be read in the following order:

1,1,1 2,1,1 3,1,1 4,1,1

1,2,1 2,2,1 3,2,1 4,2,1

1,3,1 2,3,1 3,3,1 4,3,1

1,1,2 2,1,2 3,1,2 4,1,2

1,2,2 2,2,2 3,2,2 4,2,2

1,3,2 2,3,2 3,3,2 4,3,2

4.3.7 PERMXC (This line is read only if IPERMX = 0)

PERMXC - Permeability of the reservoir in the X direction (ICOORD = 1 or 3) or in the radial

direction (ICOORD = 2).

Units: millidarcies = 10-3 μm2

Note: All elements of the PERMX array will be set equal to PERMXC.

4.3.8 PERMX(K), for K = 1, NZ (This line is read only if IPERMX = 1)

PERMX(K) - Permeability of the Kth layer in the X direction (ICOORD = 1 or 3) or in the radial

direction (ICOORD = 2).

Units: millidarcies = 10-3 μm2

Note: See the note for input line 4.3.5.

4.3.9 PERMX(I), for I = 1, NX × NY × NZ (This line is read only if IPERMX = 2)

PERMX(I) - Permeability of the Ith gridblock in the X direction (ICOORD = 1 or 3) or in the radial

direction (ICOORD = 2).

Units: millidarcies = 10-3 μm2

Note: See the note and example for input line 4.3.6 for the order of the permeability values.

4.3.10 PERMYC (This line is read only if IPERMY = 0 and ICOORD = 1 or 3)

PERMYC - Permeability of the reservoir in the Y direction.
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259

Units: millidarcies = 10-3 μm2

Note: All elements of the PERMY array will be set equal to PERMYC.

4.3.11 PERMY(K), for K = 1, NZ (This line is read only if IPERMY = 1 and ICOORD = 1 or 3)

PERMY(K) - Permeability of the Kth layer in the Y direction.

Units: millidarcies = 10-3 μm2

Note: See note for input line 4.3.5.

4.3.12 PERMY(I), for I = 1, NX × NY × NZ (This line is read only if IPERMY = 2 and ICOORD = 1 or

3)

PERMY(I) - Permeability of the Ith gridblock.

Units: millidarcies = 10-3 μm2

Note: See the note and example for input line 4.3.6 for the order of the permeability

values.

4.3.13 FACTY (This line is read only if IPERMY = 3 and ICOORD = 1 or 3)

FACTY - Constant permeability multiplier for Y direction permeability.

Units: dimensionless

Note: The X direction permeabilities are multiplied by FACTY to obtain the Y direction

permeabilities.

4.3.14 PERMZC (This line is read only if IPERMZ = 0)

PERMZC - Permeability of the reservoir in the Z direction.

Units: millidarcies = 10-3 μm2

Note: All elements of the PERMZ array will be set equal to PERMZC.

4.3.15 PERMZ(K), for K = 1, NZ (This line is read only if IPERMZ = 1)

PERMZ(K) - Permeability of the Kth layer in the Z direction.

Units: millidarcies = 10-3 μm2

Note: See note for input line 4.3.5.

4.3.16 PERMZ(I), for I = 1, NX × NY × NZ (This line is read only if IPERMZ = 2)

PERMZ(I) - Permeability of the Ith gridblock.

Units: millidarcies (10-3 μm2)

Note: See the note and example for input line 4.3.6 for the order of the permeability

values.

4.3.17 FACTZ (This line is read only if IPERMZ = 3 and ICOORD = 1 or 3)

FACTZ - Constant permeability multiplier for Z direction permeability.

Units: dimensionless

Note: The X direction permeabilities are multiplied by FACTZ to obtain the Z direction

permeabilities.

4.3.18 IDEPTH, IPRESS, ISWI

IDEPTH - Flag indicating type of depth measurement of the top layer.

Possible Values:
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0 - Single value for depth of the top layer is specified

1 - Depth of top gridblock (1,1,1) and the reservoir dip angles are specified

2 - Depth of each gridblock in the top layer is specified

Note: If ICOORD = 2, this value is automatically set equal to 0.

The depth is specified at the middle of a gridblock.

IPRESS - Flag indicating type of reservoir initial pressure measurement.

Possible Values:

0 - Single value for reservoir initial pressure is used for all gridblocks

1 - Initial pressure for a point at a specified depth is specified by user

2 - Initial pressure for each gridblock is specified by user

ISWI - Flag indicating type of initial water saturation measurement.

Possible Values:

0 - Single value for initial water saturation is used for all gridblocks

1 - Constant value for water saturation for each layer is specified by user

2 - Initial water saturation for each gridblock is specified by user

4.3.19 D111 (This line is read only if IDEPTH = 0)

D111 - Depth of the top layer of the reservoir measured from the surface (reference plane), positive

downward.

Units: feet (IUNIT=0) or m (IUNIT=1)

Note: If IDEPTH=0 and ICOORD=4, D111 is the reference depth of the first gridblock.

4.3.20 D111, THETAX, THETAY (This line is read only if IDEPTH = 1)

D111 - Depth of the first gridblock (1,1,1).

Units: feet (IUNIT=0) or m (IUNIT=1)

THETAX - Reservoir dip angle in X direction, positive downward.

Units: radians

THETAY - Reservoir dip angle in Y direction, positive downward.

Units: radians

Note: If ICOORD=4, set THETAY equal to 0 (dip angle in X-Z plane).

4.3.21 EL(I), for I = 1, NX × NY (This line is read only if IDEPTH = 2)

EL(I) - Depth of Ith gridblock in the top layer (K=1).

Units: feet (IUNIT=0) or m (IUNIT=1)

Note: See the note and example for input line 4.3.6 for the order of the gridblock depths.

4.3.22 PRESS1 (This line is read only if IPRESS = 0)

PRESS1 - Initial reservoir pressure.

Units: psi (IUNIT=0) or kPa (IUNIT=1)

4.3.23 PINIT, HINIT (This line is read only if IPRESS = 1)

PINIT - Initial reservoir pressure at HINIT depth.

Units: psia (IUNIT=0) or kPa (IUNIT=1)

HINIT - Depth of the point where PINIT initial pressure is specified.

Units: feet (IUNIT=0) or m (IUNIT=1)

Note: Initial pressure is assumed to be the aqueous phase pressure.
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4.3.24 P(I), for I = 1, NX × NY × NZ (This line is read only if IPRESS = 2)

P(I) - Initial pressure of each gridblock in the reservoir.

Units: psia (IUNIT=0) or kPa (IUNIT=1)

Note: See the note and example for input line 4.3.6 for the order of the initial pressure

values. This is assumed to be the aqueous phase pressure.

4.3.25 SWI (This line is read only if ISWI = 0)

SWI - Initial water saturation for all gridblocks of the reservoir.

Units: fraction of pore volume

4.3.26 S(K,1), for K = 1, NZ (This line is read only if ISWI = 1)

S(K,1) - Initial water saturation for Kth layer.

Units: fraction of pore volume

Note: See the note for input line 4.3.5.

4.3.27 S(I,1), I = 1, NX × NY × NZ (This line is read only if ISWI = 2)

S(I,1) - Initial water saturation for Ith block.

Units: fraction of pore volume

Note: See the note and example for input line 4.3.6 for the order of the initial water

saturation values.

4.3.28 ISGI (This line is read only if IGAS = 1)

ISGI - Flag indicating type of initial gas saturation.

Possible Values:

0 - Constant initial gas saturation for whole reservoir

1 - Constant initial gas saturation for each layer

2 - Initial gas saturation for each gridblock is specified by user

4.3.29 SGI (This line is read only if IGAS = 1 and ISGI = 0)

SGI - Initial gas saturation for all gridblocks of the reservoir.

Units: fraction of pore volume

4.3.30 S(K,4), for K = 1, NZ (This line is read only if IGAS = 1 and ISGI = 1)

S(K,4) - Initial gas saturation for Kth layer.

Units: fraction of pore volume

Note: See the note for input line 4.3.5.

4.3.31 S(I,4), I = 1, NX × NY × NZ (This line is read only if IGAS = 1 and ISGI = 2)

S(I,4) - Initial gas saturation for Ith block.

Units: fraction of pore volume

Note: See the note and example for input line 4.3.6 for the order of the initial gas

saturation values.

4.3.32 C50, C60

C50 - Initial brine salinity.

Units: meq/ml of brine

Note: This is assumed to be all the anions (in equivalents).
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C60 - Initial divalent cation concentration of brine.

Units: meq/ml of brine

Note : C50 and C60 are replaced by the input values of C5I and C6I in line 4.5.33 when

IREACT>1.

B.4.4 Physical Property Data

The fourth input section consists of the physical property data. Please remember that there

are seven comment lines at the beginning of this section and that each data line is preceded by three

comment lines.

4.4.1 C2PLC, C2PRC, EPSME

C2PLC - Oil concentration at plait point in type II(+) region.

Units: volume fraction

C2PRC - Oil concentration at plait point in type II(-) region.

Units: volume fraction

EPSME - Critical micelle concentration (CMC)—minimum surfactant concentration for the

formation of micelles.

Units: volume fraction

4.4.2 HBNS70, HBNC70, HBNS71, HBNC71, HBNS72, HBNC72

HBNS70 - Slope for maximum height of binodal curve vs. fraction of Alcohol 1—Component 7—

associated with surfactant at zero salinity.

Units: volume fraction

HBNC70 - Intercept of maximum height of binodal curve at zero fraction of Alcohol 1—

Component 7—associated with surfactant at zero salinity.

Units: volume fraction

HBNS71 - Slope for maximum height of binodal curve vs. fraction of Alcohol 1—Component 7—

associated with surfactant at optimal salinity.

Units: volume fraction

HBNC71 - Intercept of maximum height of binodal curve at zero fraction of Alcohol 1—

Component 7—associated with surfactant at optimal salinity.

Units: volume fraction

HBNS72 - Slope for maximum height of binodal curve vs. fraction of Alcohol 1—Component 7—

associated with surfactant at twice optimal salinity.

Units: volume fraction

HBNC72 - Intercept of maximum height of binodal curve at zero fraction of Alcohol 1—

Component 7—associated with surfactant at twice optimal salinity.

Units: volume fraction

Note: These parameters are obtained by matching the volume fraction diagrams corresponding to

at least three different total chemical (alcohol + surfactant) compositions. For the first

iteration, the slope parameters are set to zero and the intercept parameters are adjusted in

order to obtain a reasonable match of the volume fraction diagrams. Then the slope

parameters are obtained as follows:
Appendix B - UTCHEM Local Grid Refinement User's Guide

263

Having obtained the slope parameters, the matching procedure is repeated for further

improvements. See Satoh's thesis for example.

4.4.3 HBNS80, HBNC80, HBNS81, HBNC81, HBNS82, HBNC82

HBNS80 - Slope for maximum height of binodal curve vs. fraction of Alcohol 2—Component 8—

associated with surfactant at zero salinity.

Units: volume fraction

HBNC80 - Intercept of maximum height of binodal curve at zero fraction of Alcohol 2—

Component 8—associated with surfactant at zero salinity.

Units: volume fraction

HBNS81 - Slope of maximum height of binodal curve vs. fraction of Alcohol 2—Component 8—

associated with surfactant at optimal salinity.

Units: volume fraction

HBNC81 - Intercept of maximum height of binodal curve at zero fraction of Alcohol 2—

Component 8—associated with surfactant at optimal salinity.

Units: volume fraction

HBNS82 - Slope for maximum height of binodal curve vs. fraction of Alcohol 2—Component 8—

associated with surfactant at twice optimal salinity.

Units: volume fraction

HBNC82 - Intercept of maximum height of binodal curve at zero fraction of Alcohol 2—

Component 8—associated with surfactant at twice optimal salinity.

Units: volume fraction

Note: See the note for input line 4.4.2 to see how values should be determined.
Appendix B - UTCHEM Local Grid Refinement User's Guide

264

4.4.4 CSEL7, CSEU7, CSEL8, CSEU8

CSEL7 - Lower effective salinity limit for type III phase region determined when Alcohol 1—

Component 7—and calcium approach zero.

Units: meq/ml

CSEU7 - Upper effective salinity limit for type III phase region determined when Alcohol 1—

Component 7—and calcium approach zero.

Units: meq/ml

CSEL8 - Lower effective salinity limit for type III phase region determined when Alcohol 2—

Component 8—and calcium approach zero.

Units: meq/ml

CSEU8 - Upper effective salinity limit for type III phase region determined when Alcohol 2—

Component 8—and calcium approach zero.

Units: meq/ml

Note: The values are calculated as follows:

CSEU7 = lim

f

7

s →0

f

6

s →0

(CSEU )

CSEL7 = lim

f

7

s →0

f

6

s →0

CSEL ( )

CSEU8 = lim

f

8

s →0

f

6

s →0

(CSEU )

CSEL8 = lim

f

8

s →0

f

6

s →0

CSEL ( )

and

CSE = 

C51

1 − β6f 6

s

( )1 + β7f 7

s

+ β8f8

s

( )

4.4.5 BETA6, BETA7, BETA8

BETA6 - The CSE slope parameter, β6, for calcium.

Units: dimensionless

BETA7 - The CSE slope parameter, β7, for Alcohol 1—Component 7.

Units: dimensionless

BETA8 - The CSE slope parameter, β8, for Alcohol 2—Component 8.

Units: dimensionless

Note: See notes for input line 4.4.4.

BETA6 is limited to less than 1

f 6

s

4.4.6 IALC, OPSK7O, OPSK7S, OPSK8O, OPSK8S

IALC - Flag indicating choice of alcohol partition model to use.

Possible Values:

0 - Hirasaki's model will be used
Appendix B - UTCHEM Local Grid Refinement User's Guide

265

1 - Prouvost's model will be used

OPSK7O - Alcohol partition coefficient (oil/water) for Alcohol 1—Component 7.

Units: dimensionless

OPSK7S - Alcohol partition coefficient (surfactant/water) for Alcohol 1—Component 7.

Units: dimensionless

OPSK8O - Alcohol partition coefficient (oil/water) for Alcohol 2—Component 8.

Units: dimensionless

OPSK8S - Alcohol partition coefficient (surfactant/water) for Alcohol 2—Component 8.

Units: dimensionless

Note: If IALC = 0 then OPSK7O, OPSK7S, OPSK8O, and OPSK8S remain fixed. If OPSK7O,

OPSK7S, OPSK8O, and OPSK8S are equal to zero and IALC = 0, then alcohol is lumped

with surfactant as a single component (total chemical). OPSK7O, OPSK7S, OPSK8O, and

OPSK8S are only used when Hirasaki's model is chosen.

4.4.7 NALMAX, EPSALC

NALMAX - Maximum number of iterations for alcohol partitioning for two alcohol system.

Note: The suggested value is 20 and a value of zero would result in no iterations.

EPSALC - Tolerance for convergence of iterations for two alcohol system.

Note: Suggested values are 10-3 and 10-4.

4.4.8 AKWC7, AKWS7, AKM7, AK7, PT7

AKWC7, AKWS7 - Parameters used to determine partition coefficient of monomeric Alcohol 1—

Component 7—between aqueous and oleic pseudophases.

Units: dimensionless

AKM7 - Partition coefficient of monomeric Alcohol 1—Component 7—between surfactant and

oleic pseudophases.

Units: dimensionless

AK7 - Self-association constant of Alcohol 1—Component 7—in oleic pseudophase.

Units: dimensionless

PT7 - Ratio of molar volume of Alcohol 1—Component 7—to equivalent molar volume of

surfactant.

Units: dimensionless

Note: These values can be calculated using PROPACK and are only required when using

Prouvost's model (IALC = 1).

4.4.9 AKWC8, AKWS8, AKM8, AK8, PT8

AKWC8, AKWS8 - Parameters used to determine partition coefficient of monomeric Alcohol 2—

Component 8—between aqueous and oleic pseudophases.

Units: dimensionless

AKM8 - Partition coefficient of monomeric Alcohol 2—Component 8—between surfactant and

oleic pseudophases.

Units: dimensionless

AK8 - Self-association constant of Alcohol 2—Component 8—in oleic pseudophase.

Units: dimensionless

PT8 - Ratio of molar volume of Alcohol 2—Component 8—to equivalent molar volume of

surfactant.

Units: dimensionless
Appendix B - UTCHEM Local Grid Refinement User's Guide

266

Note: These values can be calculated using PROPACK and are only required when using

Prouvost's model (IALC = 1).

4.4.10 G11, G12, G13, G21, G22, G23 (This line is read only if IFT = 0)

G11, G12, G13 - Interfacial tension parameters for water-microemulsion interface.

G21, G22, G23 - Interfacial tension parameters for oil-microemulsion interface.

Units : Dimensionless

Note: The equations used to calculate the interfacial tension parameters are discussed in Camilleri,

et. al. [1987b].

4.4.11 XIFTW

XIFTW - log10 σwo where σwo is the interfacial tension of the water-oil interface.

Units: dynes/cm = mN/m

4.4.12 IMASS

IMASS - Flag indicating the choice of oil solubility in water.

Possible Values

0 - No solubility of oil in water in the absence of surfactant (component number 3)

1 - Allow for solubility of oil in water in the absence of surfactant or allow for

nonequilibrium transfer of oil in water

4.4.13 WSOL, CNEM2 (This line is read only if IMASS=1 and IGAS=0 in the presence of surfactant

(component no.3))

WSOL - Equilibrium concentration of oil in water in the absence of surfactant.

Units: volume fraction

CNEM2 - Coefficient of nonequilibrium mass transfer of oil in aqueous phase with or without

surfactant, M

Units: vol. of water/(bulk vol.-day)

Note: The input value of zero for CNEM2 represents an equilibrium mass transfer. The nonequilibrium mass transfer (CNEM2>0) calculation is valid for type II(-) and lobe II(-) of

type III with the plait point in the corner (C2PLC = 0) and in the absence of gas phase

(IGAS=0).

 

∂ S( lC2lφ)

∂t

= M C2l

eq ( − C2l ) , for l =1 or 3

 

C2 l

eq is the computed composition from the hand equations when the surfactant is present

and is the input value of WSOL in the absence of surfactant or when

the surfactant concentration is below CMC.

4.4.14 ITRAP, T11, T22, T33

ITRAP - Flag indicating whether residual saturations and relative permeabilities are dependent on

capillary number or not.

Possible Values:

0 - Residual saturations are not dependent on capillary number; endpoint and

exponent of relative permeability curves are constant

1 - Residual saturations and relative permeabilities are dependent on capillary

number
Appendix B - UTCHEM Local Grid Refinement User's Guide

267

T11 - Capillary desaturation curve parameter, T1

, for aqueous phase.

T22 - Capillary desaturation curve parameter, T2

, for oleic phase.

T33 - Capillary desaturation curve parameter, T3

, for microemulsion phase.

Note: The expressions for capillary desaturation are:

 

Slr

− Slrc=

Slrw − Slrc

1+ Tl

Ncl

 , l=1,2,3

where

 

Ncl = (2. 23x10−5)

kx

∂Φ

∂x

 

 

 

 

2

+ ky

∂Φ

∂y

 

 

  

 

2

+ kz

∂Φ

∂z

 

 

 

 

2

σ

ll'

,l=1,2,3

For l = 1, σll'

 = σwm. For l = 2, σll' = σmo. For l = 3, σll' = σwm if the aqueous

phase is mobile, σmo otherwise.

T11, T22, and T33 are determined by matching experimental capillary desaturation curves.

4.4.15 IPERM

IPERM - Flag indicating the saturation history direction for relative permeability and capillary

pressure calculations

Possible Values:

0 - Imbibition Corey

1 - First drainage Corey (only for IOW=0 and two phase water/oil flow)

4.4.16 ISRW, IPRW, IEW

ISRW - Flag indicating type of residual saturation.

Possible Values:

0 - Constant residual saturation for entire reservoir

1 - Constant residual saturation for each layer

2 - Residual saturation for each gridblock

IPRW - Flag indicating type of endpoint relative permeability.

Possible Values:

0 - Constant endpoint relative permeability for entire reservoir

1 - Constant endpoint relative permeability for each layer

2 - Constant endpoint relative permeability for each gridblock

IEW - Flag indicating type of relative permeability exponent.

Possible Values:

0 - Constant relative permeability exponent for entire reservoir

1 - Constant relative permeability exponent for each layer

2 - Constant relative permeability exponent for each gridblock

4.4.17 S1RWC, S2RWC, S3RWC (This line is read only if ISRW = 0)

S1RWC - Residual saturation of aqueous phase displaced by oil at low capillary number for entire

reservoir.

Units: fraction

S2RWC - Residual saturation of oleic phase displaced by water at low capillary number for entire

reservoir.

Units: fraction
Appendix B - UTCHEM Local Grid Refinement User's Guide

268

S3RWC - Residual saturation of microemulsion phase displaced by water at low capillary number

for entire reservoir.

Units: fraction

4.4.18 S1RWC(K), for K = 1, NZ (This line is read only if ISRW = 1)

S1RWC(K) - Residual saturation of aqueous phase displaced by oil or gas at low capillary number

for Kth layer.

Units: fraction

4.4.19 S2RWC(K), for K = 1, NZ (This line is read only if ISRW = 1)

S2RWC(K) - Residual saturation of oleic phase displaced by water at low capillary number for Kth

layer.

Units: fraction

4.4.20 S3RWC(K), for K = 1, NZ (This line is read only if ISRW = 1)

S3RWC(K) - Residual saturation of microemulsion phase displaced by water or oil at low capillary

number for Kth layer.

Units: fraction

Note: See the note for input line 4.4.42. Additionally, S3RWC(K) must begin a separate line in

the input file for each layer.

4.4.21 S1RW(I), for I = 1, NX × NY × NZ (This line is read only if ISRW = 2)

S1RW(I) - Residual saturation of aqueous phase displaced by oil or gas at low capillary number for

I

th gridblock.

Units: fraction

4.4.22 S2RW(I), for I = 1, NX × NY × NZ (This line is read only if ISRW = 2)

S2RWC(K) - Residual saturation of oleic phase displaced by water at low capillary number for Ith

gridblock.

Units: fraction

4.4.23 S3RW(I), for I = 1, NX × NY × NZ (This line is read only if ISRW = 2)

S3RW(I) - Residual saturation of microemulsion phase displaced by water or oil at low capillary

number for Ith gridblock.

Units: fraction

4.4.24 P1RWC, P2RWC, P3RWC (This line is read only if IPRW = 0)

P1RWC - End point relative permeability of water at low capillary number for entire reservoir.

Units: dimensionless

P2RWC - End point relative permeability of oil at low capillary number for entire reservoir.

Units: dimensionless

P3RWC - End point relative permeability of microemulsion at low capillary number for entire

reservoir.

Units: dimensionless
Appendix B - UTCHEM Local Grid Refinement User's Guide

269

4.4.25 P1RWC(K), for K = 1, NZ (This line is read only if IPRW = 1)

P1RWC(K) - Constant endpoint relative permeability of water at low capillary number for Kth

layer.

Units: dimensionless

4.4.26 P2RWC(K), for K = 1, NZ (This line is read only if IPRW = 1)

P2RWC(K) - Constant endpoint relative permeability of oil at low capillary number for Kth layer.

Units: dimensionless

4.4.27 P3RWC(K), for K = 1, NZ (This line is read only if IPRW = 1)

P3RWC(K) - Constant endpoint relative permeability of microemulsion at low capillary number for

Kth layer.

Units: dimensionless

Note: See the note for input line 4.4.42. Additionally, P1RWC(K) must begin a separate line in

the input file for each layer.

4.4.28 P1RW(I), for I = 1, NX × NY × NZ (This line is read only if IPRW = 2)

P1RW(I) - Endpoint relative permeability of water at low capillary number for Ith gridblock.

Units: dimensionless

4.4.29 P2RW(I), for I = 1, NX × NY × NZ (This line is read only if IPRW = 2)

P2RWC(K) - Endpoint relative permeability of oil at low capillary number for Ith gridblock.

Units: dimensionless

4.4.30 P3RW(I), for I = 1, NX × NY × NZ (This line is read only if IPRW = 2)

P3RW(I) - Endpoint relative permeability of microemulsion at low capillary number for Ith

gridblock.

Units: dimensionless

4.4.31 E1WC, E2WC, E3WC (This line is read only if IEW = 0)

E1WC - Phase relative permeability exponent for aqueous phase at low capillary number for entire

reservoir.

Units: dimensionless

E2WC - Phase relative permeability exponent for oleic phase at low capillary number for entire

reservoir.

Units: dimensionless

E3WC - Phase relative permeability exponent for microemulsion phase at low capillary number

system for entire reservoir.

Units: dimensionless

4.4.32 E1WC(K), for K = 1, NZ (This line is read only if IEW = 1)

E1WC(K) - Relative permeability exponent of aqueous phase at low capillary number for Kth layer.

Units: dimensionless

4.4.33 E2WC(K), for K = 1, NZ (This line is read only if IEW = 1)

E2WC(K) - Relative permeability exponent of oleic phase at low capillary number for Kth layer.
Appendix B - UTCHEM Local Grid Refinement User's Guide

270

Units: dimensionless

4.4.34 E3WC(K), for K = 1, NZ (This line is read only if IEW = 1)

E3WC(K) - Relative permeability exponent of microemulsion phase at low capillary number for

Kth layer.

Units: dimensionless

Note: See the note for input line 4.4.42. Additionally, E1WC(K) must begin a separate line in the

input file for each layer.

4.4.35 E1W(I), for I = 1, NX × NY × NZ (This line is read only if IEW = 2)

E1W(I) - Relative permeability exponent of aqueous phase at low capillary number for Ith

gridblock.

Units: dimensionless

4.4.36 E2W(I), for I = 1, NX × NY × NZ (This line is read only if IEW = 2)

E2WC(K) - Relative permeability exponent of oleic phase at low capillary number for Ith

gridblock.

Units: dimensionless

4.4.37 E3W(I), for I = 1, NX × NY × NZ (This line is read only if IEW = 2)

E3W(I) - Relative permeability exponent of microemulsion phase at low capillary number for Ith

gridblock.

Units: dimensionless

4.4.38 S1RC, S2RC, S3RC

S1RC - Residual saturation of aqueous phase at high capillary number.

Units: fraction

S2RC - Residual saturation of oleic phase at high capillary number.

Units: fraction

S3RC - Residual saturation of microemulsion phase at high capillary number.

Units: fraction

4.4.39 P1RC, P2RC, P3RC

P1RC - End point relative permeability of aqueous phase at high capillary number condition.

Units: dimensionless

P2RC - End point relative permeability of oleic phase at high capillary number condition.

Units: dimensionless

P3RC - End point relative permeability of microemulsion phase at high capillary number condition.

Units: dimensionless

4.4.40 E13C, E23C, E31C

E13C, E23C, E31C - Parameters used for calculating exponents for relative permeability

calculations at high capillary number.

Units: dimensionless

Note: For IGAS = 0, imbibition Corey relative permeabilities are calculated from:

 

krl = krl

o

Snl

( )

el

, l = 1, 2, 3
Appendix B - UTCHEM Local Grid Refinement User's Guide

271

where

 

Snl =

Sl − Slr

1− S1r − S2r − S3r

 

krl

o

= krlw

o

for ITRAP=0

 

krl

o

= krlw

o

+

Sl

'

rw

− Sl

'

r

Sl

'

rw − Sl

'

rc

krlc

o

− kr lw

o

( ) for ITRAP =1

and

 

el = elw

for ITRAP=0

 

el = elw

+

Sl

'

rw

− Sl

'

r

Sl

'

rw

− Sl

'

rc

elc

− elw

( ) for ITRAP=1

The phase indices are assigned values according to the type of flow:

for water/oil: l = 1, l' = 2, elc = E13C, elw = E1W

for water/microemulsion: l = 1, l' = 3, elc = E23C, elw = E2W

for oil/microemulsion: l = 2, l' = 3, elc = E31C, elw = E3W

For two phase oil/water drainage (IPERM =1), S2r is set to 0.0.

4.4.41 VIS1, VIS2, TSTAND

VIS1 - Water viscosity at reference temperature, μ1,ref.

Units: cp = mPa.s

VIS2 - Oil viscosity at reference temperature, μ2,ref .

Units: cp = mPa.s

TSTAND - Reference temperature, Tref.

Units: •F (IUNIT=0) or •C (IUNIT=1)

Note: For IENG=0, If TSAND = 0.0, the water component viscosity will be constant and

equal to the input value VIS1. If TSATND > 0.0, water component viscosity will be

calculated as a function of reservoir temperature, pressure, and local salinity for each

gridblock.

4.4.42 VIS4, VSLOPG (This line is read only if IGAS = 1)

VIS4 - Gas viscosity at reference temperature and reference pressure, μ4,ref.

Units: cp = mPa.s

VSLOPG - Slope of gas viscosity, μ4,s.

Units: (psi)-1 (IUNIT=0) or (kPa)-1 (IUNIT=1)

Note: Gas viscosity is computed from:

μ4 = μ4,ref 1 + μ4,s P ( ( 1 − PSTAND))

4.4.43 BVI(1), BVI(2) (This line is read only if IENG = 1)

BVI(1) - Parameter for calculating water viscosity as a function of reservoir temperature, b1.

Units: (•K)-1

BVI(2) - Parameter for calculating oil viscosity as a function of reservoir temperature, b2.

Units: (•K)-1

Note: The phase viscosities as a function of temperature are calculated from:
Appendix B - UTCHEM Local Grid Refinement User's Guide

272

 

μl= μl,ref exp bl

1

T

−

1

Tref

 

 

  

   

 

  

  for l = 1,2

where T and Tref are in absolute •K.

4.4.44 BVI(4) (This line is read only if IGAS =1 and IENG = 1)

BVI(4) - Parameter for calculating gas viscosity as a function of reservoir temperature, b4.

Units: (•K)-1

Note: Gas viscosity as a function of temperature is computed from:

μ4 = μ4,ref (1 + μ4,s(P − PSTAND)) exp 1+ b4

1

T

−

1

Tref

 

 

  

   

 

  

  

where T and Tref are in absolute •K.

4.4.45 S2RWC4, S4RWC (This line is read only if IGAS = 1 and ISRW = 0)

S2RWC4 - Constant residual oil saturation to displacing gas phase for entire reservoir.

Units: fraction

S4RWC - Constant residual gas saturation for entire reservoir.

Units: fraction

4.4.46 S2RWC4(K), for K = 1, NZ (This line is read only if IGAS = 1 and ISRW = 1)

S2RWC4(K) - Constant residual oil saturation to displacing gas phase for Kth layer.

Units: fraction

4.4.47 S4RWC(K), for K = 1, NZ (This line is read only if IGAS = 1 and ISRW = 1)

S4RWC(K) - Constant residual gas saturation for Kth layer.

Units: fraction

4.4.48 S2RW4(I), for I = 1, NX × NY × NZ (This line is read only if IGAS = 1 and ISRW = 2)

S2RW4(I) - Constant residual oil saturation to displacing gas phase for Ith gridblock.

Units: fraction

4.4.49 S4RW(I), for I = 1, NX × NY × NZ (This line is read only if IGAS = 1 and ISRW = 2)

S4RW(I) - Residual gas saturation for Ith gridblock.

Units: fraction

4.4.50 P4RWC (This line is read only if IGAS = 1 and IPRW = 0)

P4RWC - Constant gas endpoint relative permeability for entire reservoir.

Units: dimensionless

4.4.51 P4RWC(K), for K = 1, NZ (This line is read only if IGAS = 1 and IPRW = 1)

P4RWC(K) - Constant gas endpoint relative permeability for Kth layer.

Units: dimensionless

4.4.52 P4RW(I), for I = 1, NX × NY × NZ (This line is read only if IGAS = 1 and IPRW = 2)

P4RW(I) - Constant gas endpoint relative permeability for Ith gridblock.
Appendix B - UTCHEM Local Grid Refinement User's Guide

273

Units: dimensionless

4.4.53 E4WC (This line is read only if IGAS = 1 and IEW = 0)

E4WC - Constant gas relative permeability exponent for entire reservoir.

Units: dimensionless

4.4.54 E4WC(K), for K = 1, NZ (This line is read only if IGAS = 1 and IEW = 1)

E4WC(K) - Constant gas relative permeability exponent for Kth layer.

Units: dimensionless

4.4.55 E4WC(I), for I = 1, NX × NY × NZ (This line is read only if IGAS = 1 and IEW = 2)

E4WC(I) - Constant gas relative permeability exponent for Ith gridblock.

Units: dimensionless

4.4.56 S4RC, P4RC, E4C, T44, XIFTG (This line is read only if IGAS = 1)

S4RC - Residual gas saturations at high capillary number.

Units: fraction

P4RC - Gas endpoint relative permeability at high capillary number.

Units: dimensionless

E4C - Gas relative permeability exponent at high capillary number.

Units: dimensionless

T44 - Gas phase trapping parameter.

Units: dimensionless

XIFTG - Log of interfacial tension between gas and either water or oil.

Units: dyne/cm = mN/m

4.4.57 ALPHA1, ALPHA2, ALPHA3, ALPHA4, ALPHA5

ALPHA1 - Compositional phase viscosity parameter α1.

ALPHA2 - Compositional phase viscosity parameter α2.

ALPHA3 - Compositional phase viscosity parameter α3.

ALPHA4 - Compositional phase viscosity parameter α4.

ALPHA5 - Compositional phase viscosity parameter α5.

Note: Compositional phase viscosity is calculated as:

μl = C1l μp exp[α1 (C2l + C3l)] +

C2l μo exp[α2 (C1l + C3l)] +

C3l α3 exp[α4 C1l + α5 C2l]

Polymer viscosity •p is replaced by water viscosity when no polymer is present.

4.4.58 AP1, AP2, AP3

AP1, AP2, AP3 - Parameters used for calculating polymer viscosity at zero shear rate as a function

of polymer and electrolyte concentrations.

Units: (wt. %)-1, (wt. %)-2, (wt. %)-3

Note: Polymer viscosity at zero shear rate, •o, is given by:

• EMBED "Equation" "Word Object11" \* mergeformat •••

Ap1, Ap2, and Ap3 are empirical constants for a given polymer and are measured

experimentally.
Appendix B - UTCHEM Local Grid Refinement User's Guide

274

4.4.59 BETAP, CSE1, SSLOPE

BETAP - Parameter, •P, for calculating the effective divalent salinity, CSEP, used to calculate polymer viscosity

(see the note for input line 4.4.60).

Units: dimensionless

Note: CSEP is given by:

CSEP =

C9 + βpC6

C1

CSE1 - Value below which the polymer viscosity is considered to be independent of salinity

(minimum value of CSEP—see the note for input line 4.4.60).

Units: meq/ml

SSLOPE - Slope, Sp, of μo vs. CSEP on a log-log plot—assumed to be constant (see the note for

input line 4.4.60).

Units: dimensionless

Note: This value is usually large and negative for hydrolyzed polyacrylamides and small

and positive for polysaccharides.

4.4.60 GAMMAC, GAMHF, POWN

GAMMAC - Coefficient,γ Ý 

c

, in shear rate equation below.

Units: day(darcy)

1 2

ft − sec

 (IUNIT=0) or 

day μm

2

( )

1 2

m − sec

 (IUNIT=1)

GAMHF - Shear rate, γ Ý 1 2

, at which polymer viscosity is one half polymer viscosity at zero shear

rate.

Units: sec-1

POWN - Exponent, Pα, for calculating shear rate dependence of polymer viscosity.

Units: dimensionless

Note: The shear rate dependence of polymer viscosity is modeled by Meter's equation:

μp = μ∞ +

μo− μ∞

1 +

γ Ý 

eq

γ Ý 1 2

 

  

 

  

pα−1

where the equivalent shear rate γ Ý eq is calculated as:

γ Ý 

eq =

3n +1

4n

 

   

n

n−1 4uc

8kkrwφsw

= γ Ý 

c

u

kkrwφsw

where u is in ft/day, k is in Darcies, and γ Ý eq is in 1/sec. Using n = 0.8 and with the unit

conversion we have γ Ý 

c

 = 3.94 C. The value of shear rate coefficient C can be calculated as:

C = 4.8

0.167

Nv

 

 

  

 

1

1−Pα

where Nv is in cm/sec. Nv is a dimensional group called viscosity number computed as:

Nv =

k krw φsw

Θo u

n−1

Please refer to Wreath [1989] and Wreath, et al. [1990] for more detail.
Appendix B - UTCHEM Local Grid Refinement User's Guide

275

4.4.61 IPOLYM, EPHI3, EPHI4, BRK, CRK

IPOLYM - Flag indicating type of polymer partitioning.

Possible values:

0 - All polymer exists in aqueous phase if aqueous phase exists; otherwise, it exists

completely in microemulsion phase

1 - Partitioning of polymer to water component is constant

EPHI3 - Effective porosity for surfactant—ratio of apparent porosity for surfactant to actual

porosity.

Units: dimensionless

EPHI4 - Effective porosity for polymer—ratio of apparent porosity for polymer to actual porosity.

Units: dimensionless

BRK - Parameter for calculating permeability reduction factor Rk.

Units: volume of polymer − rich phase

weight% polymer

CRK - Parameter for calculating permeability reduction factor Rk.

Units: (darcy)1/2 (100 g/g)-1/3 = (μm2)

1/2 (100 g/g)-1/3)

Note: EPHI3 and EPHI4 are used to account for inaccessible pore volume in the case of surfactant

and polymer.

φsurfactant = φ × EPHI3

φpolymer = φ × EHPI4

The effect of permeability reduction or residual resistance is to reduce the mobility of the

polymer rich phase. This is accounted for by multiplying the viscosity of the phase by Rk.

4.4.62 DEN1, DEN2, DEN3, DEN7, DEN8, IDEN

DEN1 - Specific weight, γ1, or density of water—Component 1.

Units: psi/ft (IUNIT=0) or g/cm3 (IUNIT=1)

DEN2 - Specific weight, γ2, or density of oil—Component 2.

Units: psi/ft (IUNIT=0) or g/cm3 (IUNIT=1)

DEN3 - Specific weight, γ3, or density of surfactant—Component 3.

Units: psi/ft (IUNIT=0) or g/cm3 (IUNIT=1)

DEN7 - Specific weight, γ7, or density of Alcohol 1—Component 7.

Units: psi/ft (IUNIT=0) or g/cm3 (IUNIT=1)

DEN8 - Specific weight, γ8, or density of Alcohol 2 (when IGAS = 0) or gas (when IGAS = 1) —

Component 8.

Units: psi/ft (IUNIT=0) or g/cm3 (IUNIT=1)

IDEN - Flag indicating if gravity effect should be considered.

Possible values:

1 - Do not consider gravity effect

2 - Consider gravity effect

Note: Specific weight for pure water is 0.433 psi/ft (density of 1 g/cm3)

4.4.63 ISTB

ISTB - Flag indicating the units to be used when printing injection and production rates.

Possible Values:
Appendix B - UTCHEM Local Grid Refinement User's Guide

276

0 - Rates printed at bottomhole condition in ft3 or m3

1 - Rates printed at surface condition in BBLS

4.4.64 FVF(L), for L = 1, MXP (This line is read only if ISTB = 1 and IUNIT=0)

FVF(L) - Formation volume factor for Lth phase.

Units: SCF/ft3

Note: MXP = 3 when IGAS = 0 and MXP = 4 when IGAS = 1.

4.4.65 COMPC(1), COMPC(2), COMPC(3), COMPC(7), COMPC(8)

COMPC(1) - Compressibility of brine—Component 1.

Units: 1/psi (IUNIT=0) or 1/kPa (IUNIT=1)

COMPC(2) - Compressibility of oil—Component 2.

Units: 1/psi (IUNIT=0) or 1/kPa (IUNIT=1)

COMPC(3) - Compressibility of surfactant—Component 3.

Units: 1/psi (IUNIT=0) or 1/kPa (IUNIT=1)

COMPC(7) - Compressibility of Alcohol 1—Component 7.

Units: 1/psi (IUNIT=0) or 1/kPa (IUNIT=1)

COMPC(8) - Compressibility of Alcohol 2 (when IGAS = 0) or gas (when IGAS = 1) —

Component 8.

Units: 1/psi (IUNIT=0) or 1/kPa (IUNIT=1)

Note: For incompressible fluids, values of zero should be used for the COMPC values listed

above.

4.4.66 ICPC, IEPC, IOW

ICPC - Flag indicating type of capillary pressure endpoint, cpc.

Possible Values:

0 - Constant capillary pressure endpoint for entire reservoir

1 - Constant capillary pressure endpoint for each layer

2 - Capillary pressure endpoint for each gridblock

IEPC - Flag indicating type of capillary pressure exponent, npc.

Possible Values:

0 - Constant capillary pressure exponent for entire reservoir

1 - Constant capillary pressure exponent for each layer

2 - Capillary pressure exponent for each gridblock

IOW - Flag indicating the wettability for capillary pressure calculations.

Possible Values:

0 - The capillary pressure curve is for water-wet rock

1 - The capillary pressure curve is for oil-wet rock (zero at residual water

saturations)

4.4.67 CPC0 (This line is read only if ICPC = 0)

CPC0 - Capillary pressure endpoint for entire reservoir, cpc.

Units: psi darcies (IUNIT=0) or kPa μm

2

 (IUNIT=1)

4.4.68 CPC(K), for K = 1, NZ (This line is read only if ICPC = 1)

CPC(K) - Capillary pressure endpoint for Kth layer, cpc.
Appendix B - UTCHEM Local Grid Refinement User's Guide

277

Units: psi darcies (IUNIT=0) or kPa μm

2

 (IUNIT=1)

4.4.69 CPC(I), for I = 1, NX × NY × NZ (This line is read only if ICPC = 2)

CPC(I) - Capillary pressure endpoint for Ith gridblock, cpc.

Units: psi darcies (IUNIT=0) or kPa μm

2

 (IUNIT=1)

4.4.70 EPC0 (This line is read only if IEPC = 0)

EPC0 - Capillary pressure exponent for entire reservoir, npc.

Units: dimensionless

4.4.71 EPC(K), for K = 1, NZ (This line is read only if IEPC = 1)

EPC(K) - Capillary pressure exponent for Kth layer, npc.

Units: dimensionless

4.4.72 EPC(I), for I = 1, NX × NY × NZ (This line is read only if IEPC = 2)

EPC(I) - Capillary pressure exponent for Ith gridblock, npc.

Units: dimensionless

Note: The CPC and EPC values are determined by curve fitting a plot of water-oil capillary

pressure vs. normalized water saturation (see the note for input line 4.4.42). For imbibition

two phases:

 

P

Cll' = cpc

φ

ka

σ

ll'

σwo

1 − Snl

( )

npc

For three phases:

PC13 = PCwm = cpc

φ

ka

σwm

σwo

1 − Sn1

( )

npc

and

PC32 = PCmo = cpc

φ

ka

σmo

σwo

Sn2

Sn3 + Sn 2

 

 

  

  

npc

For two phase oil/water drainage (IPERM =1):

PCow = cpc

φ

ka

Sw − Swr

1 − Swr

 

 

  

  

npc

The value for npc must be non-zero.

4.4.73 D(KC,1), for KC = 1, N

D(KC,1) - Molecular diffusion coefficient of KCth component in aqueous phase.

Units: ft2/day (IUNIT=0) or m2/day (IUNIT=1)

4.4.74 D(KC,2), for KC = 1, N

D(KC,2) - Molecular diffusion coefficient of KCth component in oleic phase.

Units: ft2/day (IUNIT=0) or m2/day (IUNIT=1)
Appendix B - UTCHEM Local Grid Refinement User's Guide

278

4.4.75 D(KC,3), for KC = 1, N

D(KC,3) - Molecular diffusion coefficient of KCth component in microemulsion phase.

Units: ft2/day (IUNIT=0) or m2/day (IUNIT=1)

4.4.76 D(KC,4), for KC = 1, N (This line is read only if IGAS = 1)

D(KC,4) - Molecular diffusion coefficient of KCth component in gas phase.

Units: ft2/day (IUNIT=0) or m2/day (IUNIT=1)

4.4.77 ALPHAL(1), ALPHAT(1)

ALPHAL(1) - Longitudinal dispersivity of aqueous phase.

Units: feet (IUNIT=0) or m (IUNIT=1)

ALPHAT(1) - Transverse dispersivity of aqueous phase.

Units: feet (IUNIT=0) or m (IUNIT=1)

4.4.78 ALPHAL(2), ALPHAT(2)

ALPHAL(2) - Longitudinal dispersivity of oleic phase.

Units: feet (IUNIT=0) or m (IUNIT=1)

ALPHAT(2) - Transverse dispersivity of oleic phase.

Units: feet (IUNIT=0) or m (IUNIT=1)

4.4.79 ALPHAL(3), ALPHAT(3)

ALPHAL(3) - Longitudinal dispersivity of microemulsion phase.

Units: feet (IUNIT=0) or m (IUNIT=1)

ALPHAT(3) - Transverse dispersivity of microemulsion phase.

Units: feet (IUNIT=0) or m (IUNIT=1)

4.4.80 ALPHAL(4), ALPHAT(4) (This line is read only if IGAS = 1)

ALPHAL(4) - Longitudinal dispersivity of gas phase.

Units: feet (IUNIT=0) or m (IUNIT=1)

ALPHAT(4) - Transverse dispersivity of gas phase.

Units: feet (IUNIT=0) or m (IUNIT=1)

4.4.81 AD31, AD32, B3D, AD41, AD42, B4D

AD31 - Surfactant adsorption parameter, a31.

Units: 

 

volume ofphasel

pore volume

AD32 - Surfactant adsorption parameter, a32.

Units: ml/meq

B3D - Surfactant adsorption parameter, b3.

Units: 

 

1

volume of surfactant in phase l

AD41 - Polymer adsorption parameter, a41.

Units: dimensionless

AD42 - Polymer adsorption parameter, a42.

Units: ml/meq

B4D - Polymer adsorption parameter, b4.
Appendix B - UTCHEM Local Grid Refinement User's Guide

279

Units: volume of water

weight% polymer

Note: Langmuir-type isotherms are used to model surfactant and polymer adsorption. Surfactant

adsorption is irreversible with respect to surfactant concentration:

 

C 3 =

a3C3l

1 + b3C3l

Units: volume of adsorbed surfactant

pore volume

a3 = a31 + a32 CSE

When a32 = 0, there will be no salinity dependence.

A Langmuir-type isotherm is used to describe the adsorption level of polymer, component

4, as a function of the concentration of polymer in the water as:

C 4 =

a4C4

*

1 + b4C4

*

Units: weight% adsorbed polymer

volume of water

where C4

*

=

C  ̃ 4 − C 4

C1

 and a4 = a41 + a42 CSEP

4.4.82 QV, XKC, XKS, EQW

QV - Cation exchange capacity of clays.

Units: meq/ml of pore volume

XKC - Cation exchange constant, βC, for clays.

Units: (meq/ml)-1

XKS - Cation exchange constant, βS, for surfactant.

Units: (meq/ml)-1

EQW - Equivalent weight of surfactant.

Note: The cation exchange model is:

C ( 9 )

2

C 6

= β

CQv

C9

o

( )

2

C6

o

 for clay

C9

s

( )

2

C6

s

= β

CC3

C9

o

( )

2

C6

o

 for micelles

EQW must be non-zero.

4.4.83 TK(I), for I = 1, NTW+NTA (This line is read only if NTW+NTA > 0)

TK(I) - Tracer partitioning coefficient, Kκ,ref, for Ith water/oil tracer at initial chloride (C50)

concentration and reference temperature (TSTAND). A value of 0.0 indicates a water or

gas tracer and a value of -1.0 indicates an oil tracer.

Units: fraction

Note: Kκ,ref =

Cκo

Cκw

for oil/water tracer
Appendix B - UTCHEM Local Grid Refinement User's Guide

280

Kκ,ref =

Cκo

Cκg

for oil/gas tracer

4.4.84 TKS(I), for I = 1, NTW (This line is read only if NTW > 0)

TKS(I) - Parameter for calculating water/oil tracer partitioning coefficient, Kκ, for Ith tracer as a

function of salinity, TKSk.

Units: (meq/ml)-1

Note: Kκ = Kκ,ref 1 + TKSκ

(C51 − C50 ( ))

4.4.85 TKT(I), for I = 1, NTW+NTA (This line is read only if NTW+NTA > 0 and IENG = 1)

TKT(I) - Parameter for calculating tracer partitioning coefficient, Kκ, for Ith tracer as a function of

reservoir temperature, TKTk.

Units: (•F)-1 (IUNIT=0) or (•C)-1 (IUNIT=1)

Note: Kκ = Kκ,ref 1 + TKTκ

(T − Tref ( ))

4.4.86 RDC(I), for I = 1, NTW+NTA (This line is read only if NTW+NTA > 0)

RDC(I) - Radioactive decay coefficient, λκ, for Ith tracer. A value of 0.0 indicates a non–

radioactive tracer.

Units: 1/days

Note: C = C0

e

−λκ(t−t0 )

where

λk= −

ln (0. 5)

t

1 2, k

t

1 2, k

= half life of radioactive tracer, day

4.4.87 RET(I), for I = 1, NTW+NTA (This line is read only if NTW+NTA > 0)

RET(I) - Tracer retardation factor DS—adsorbed concentration/flowing concentration. A value of

0.0 indicates no retardation.

Units: dimensionless

Note: The retardation factor is defined as:

 

DS

=

C 

C

=

(1 − φ)ρr

aT

φρlCTl

where l = 1 for oil/water tracer and l = 4 for gas/water tracer.

This factor causes a reduction in tracer velocity:

Vt =

u φ

1 + DS

4.4.88 FFL(1), FFH(1), CM(I,1), for I = 1, NTW (This line is read only if NTW > 0 and ICAP = 1)

FFL(1) - Value of flowing fraction for phase 1 when fractional flow = 0.0.

Units: dimensionless

FFH(1) - Value of flowing fraction for phase 1 when fractional flow = 1.0.

Units: dimensionless

CM(I,1) - Mass transfer coefficients for Ith tracer in phase 1.
Appendix B - UTCHEM Local Grid Refinement User's Guide

281

Units: 1/sec

4.4.89 FFL(2), FFH(2), CM(I,2), for I = 1, NTW (This line is read only if NTW > 0 and ICAP = 1)

FFL(2) - Value of flowing fraction for phase 2 when fractional flow = 0.0.

Units: dimensionless

FFH(2) - Value of flowing fraction for phase 2 when fractional flow = 1.0.

Units: dimensionless

CM(I,2) - Mass transfer coefficients for Ith tracer in phase 2.

Units: 1/sec

4.4.90 FFL(3), FFH(3), CM(I,3), for I = 1, NTW (This line is read only if NTW > 0 and ICAP = 1)

FFL(3) - Value of flowing fraction for phase 3 when fractional flow = 0.0.

Units: dimensionless

FFH(3) - Value of flowing fraction for phase 3 when fractional flow = 1.0.

Units: dimensionless

CM(I,3) - Mass transfer coefficients for Ith tracer in phase 3.

Units: 1/sec

4.4.91 TAK1 (This line is read only if NTW > 0 and ITREAC = 1)

TAK1 - Rate constant for a first-order aqueous phase reaction at reference temperature (Tref) in

which Tracer 2 (component 10) hydrolyzes to form Tracer 3 (component 11) according to

C11,1 = TAK1 C10,1.

Units: days-1

4.4.92 TMW(I), for I = 1, NTW (This line is read only if NTW > 0 and ITREAC = 1)

TMW(I) - Molecular weight of the Ith tracer.

Units: The user can specify the molecular weight in any unit as long as the units are the

same for all the tracers. It is assumed that the reaction of 1 mole of primary tracer

produces 1 mole of secondary tracer. If not, use "equivalent" molecular weights.

4.4.93 TDEN(I), for I = 1, NTW (This line is read only if NTW > 0 and ITREAC = 1)

TDEN(I) - Density of the Ith tracer.

Units: g/cm3

4.4.94 TAKT (This line is read only if NTW > 0 and ITREAC = 1 and IENG = 1)

TAKT - Parameter for calculating rate constant for a first-order aqueous phase reaction as a

function of reservoir temperature.

Units: (•K)-1

Note: TAK = TAK1 exp TAKT

1

T

−

1

Tref

 

 

  

   

 

  

  

4.4.95 AK1, AK2, SCR, X4, X14, X16, WM4 (This line is read only if NG>0)

AK1 - Kinetic rate coefficient for Cr3+ at reference temperature (Tref), AK1ref.

Units: ppm-1 days-1

AK2 - Kinetic rate coefficient for gel at reference temperature (Tref), AK2ref.
Appendix B - UTCHEM Local Grid Refinement User's Guide

282

Units: (mole/liter)1-X4-X14+X16 days-1

Note: In order to achieve the same results achieved in versions previous to UTCHEM-V5.0, please use the following conversion:

AK2new =

SCR× M

Cr3+ ×Mpolymer

2 ×109

(1+ SCR)

AK2old

SCR - Stoichiometric ratio in mass between Cr3+ and polymer.

Units: dimensionless

Note: SCR =

n × M

Cr3+

Mpolymer

X4 - Exponent to be used for polymer component of gelation reaction.

Units: dimensionless

X14 - Exponent to be used for chromium component of gelation reaction.

Units: dimensionless

X16 - Exponent to be used for hydrogen ion component of gelation reaction.

Units: dimensionless

WM4 - Molecular weight of polymer.

Units: g/mole

4.4.96 AK1T, AK2T (This line is read only if NG>0 and IENG = 1)

AK1T - Parameter for calculating Kinetic rate coefficient for Cr3+ as a function of reservoir

temperature.

Units: (•K)-1

AK2T - Parameter for calculating Kinetic rate coefficient for gel as a function of reservoir

temperature.

Units: (•K)-1

Note: The kinetic rate coefficients as a function of temperature are computed from:

AK1 = AK1ref exp AK1T

1

T

1

Tref

 

 

  

   

 

  

  

AK2 = AK2ref exp AK2T

1

T

−

1

Tref

 

 

  

 

  

 

  

 

 

4.4.97 AG1, AG2, CRG, AGK, BGK (This line is read only if NG>0)

AG1 - Flory-Huggins parameter for gel viscosity, Ag1.

Units: cp ppm-1 = mPa.s ppm-1

AG2 - Flory-Huggins parameter for gel viscosity, Ag2.

Units: cp ppm-2 = mPa.s ppm-2

CRG - Constant, Cδ, in the dimensionless pore radius reduction group. This constant depends on

the gel type.

Units: darcy (wt%)

1 3

 = μm

2

(wt%)

1 3

AGK, BGK - Permeability reduction parameters, A15 and B15, for Langmuir correlation with gel

concentration.

Units: dimensionless

Note: Dimensionless pore radius reduction group:
Appendix B - UTCHEM Local Grid Refinement User's Guide

283

Nδ = Cδ

[μ]

1 3

kxk [ y φ]

1 2

Cδ = 3. 9 × 10−3 Ng Mpolymer

1 3

 

[μ] = lim

Ý γ →0

C4l→0

μp − μw

μwC4l

 

 

  

  

From this the permeability reduction factor for idealized case is expressed as:

RRFmax =

kw , before gel treatment

kw , after gel treatment

= (1 − Nδ )

−4

The "Langmuir-type" isotherm for permeability reduction as a function of gel concentration

is:

RRF = 1 +

(RRFmax − 1)A15 C15,1

1 + B15 C15,1

Note: Gel viscosity is calculated from

μgel = μw 1 + Ag1C15,1 + Ag2C15, 1

2

[ ]

if there is flowing polymer concentration, add μgel to the μp calculation. See note for input

line 4.4.62.

4.4.98 A15D, B15D, ICREX, A14D, B14D, CRNAK, HNAK, C160 (This line is read only if NG>0)

A15D, B15D - Gel adsorption parameters.

Units: vol. of water / ppm gel

ICREX - Flag indicating if Cr3+ will be allowed to exchange with clays.

Possible Values:

0 - Cr3+ exchange with clays is not allowed

1 - Cr3+ exchange with clays is allowed

A14D, B14D - Chromium adsorption parameters.

Units: vol. of water / ppm chromium

CRNAK - Chromium-sodium exchange reaction equilibrium constant.

HNAK - Hydrogen-sodium exchange reaction equilibrium constant.

C160 - Initial hydrogen ion concentration.

Units: meq/ml

Note: The "Langmuir-type" isotherm for chromium and gel adsorption is expressed as:

C κ =

aκ Cκ,1

1 + bκ Cκ,1

, κ =

14 for chromium

15 for gel

   

The input values of CRNAK, HNAK, and C160 are ignored for IREACT=6

4.4.99 IP1, IP2 (This line is read only if NG>0, NY = 1 and NZ = 1)

IP1, IP2 - Gridblock locations where calculated pressure values should be printed to UNIT 19.

Note: These values are intended to be used for comparison with pressure tab data of 1-D

experiments.
Appendix B - UTCHEM Local Grid Refinement User's Guide

284

4.4.100 TEMPI (This line is read only if IENG = 1)

TEMPI- Constant initial reservoir temperature.

Units : •F (IUNIT=0) or •C (IUNIT=1)

4.4.101 DENS, CRTC, CVSPR, CVSPL(L), L=1,MXP (This line is read only if IENG = 1)

DENS - Reservoir rock density.

Units: lb/ft3 (IUNIT=0) or g/cm3 (IUNIT=1)

CRTC - Reservoir thermal conductivity.

Units: Btu (day-ft-•F)-1 (IUNIT=0) or kJ (day-m-•K)-1 (IUNIT=1)

CVSPR - Reservoir rock heat capacity.

Units: Btu (lb-•F)-1 (IUNIT=0) or kJ (kg-•K)-1 (IUNIT=1)

CVSPL(L) - Phase L heat capacity (MXP is equal to 3 (IGAS=0) or 4 (IGAS=1)).

Units: Btu (lb-•F)-1 (IUNIT=0) or kJ (kg-•K)-1 (IUNIT=1)

4.4.102 IHLOS, IANAL (This line is read only if IENG = 1)

IHLOS - Flag indicating if the heatloss calculation to overburden and underburden rock is

considered or not. Heat flux into the reservoir from the overburden/underburden is

calculated from the model of Vinsome and Westerveld [1980].

Possible Values:

0 - Heatloss is not considered

1 - Heatloss is considered

IANAL - Flag indicating if the temperature profile is calculated from analytical solution (only 1-

D).

Possible Values:

0 - Analytical solution is not considered

1 - Analytical solution is considered

4.4.103 TCONO, DENO, CVSPO, TCONU, DENU, CVSPU (This line is read only if IENG = 1 and

IHLOS = 1)

TCONO - Thermal conductivity of overburden rock.

Units: Btu (day-ft-•F)-1 (IUNIT=0) or kJ (day-m-•K)-1 (IUNIT=1)

DENO - Density of overburden rock.

Units: lb/ft3 (IUNIT=0) or g/cm3 (IUNIT=1)

CVSPO - Heat capacity of overburden rock.

Units: Btu (lb-•F)-1 (IUNIT=0) or kJ (kg-•K)-1 (IUNIT=1)

TCONU - Thermal conductivity of underburden rock.

Units: Btu (day-ft-•F)-1 (IUNIT=0) or kJ (day-m-•K)-1 (IUNIT=1)

DENU - Density of underburden rock.

Units: lb/ft3 (IUNIT=0) or g/cm3 (IUNIT=1)

CVSPU - Heat capacity of underburden rock.

Units: Btu (lb-•F)-1 (IUNIT=0) or kJ (kg-•K)-1 (IUNIT=1)

B.4.5 Physical Property Data for Geochemical Options

The fifth input section consists of physical property data that is read only if IREACT > 1.

The data for this section is generated by a preprocessor program (EQBATCH) and does not have the

same format as the rest of the input data for UTCHEM. This input section is not preceded by the
Appendix B - UTCHEM Local Grid Refinement User's Guide

285

usual seven comment lines and individual data lines are not preceded by three comment lines.

Sections 6.6 through 6.9 of this appendix give a list of elements, fluid species, solid species, and

adsorbed species for geochemical options.

4.5.1 IRSPS, IPHAD (This line is read only if IREACT > 1)

IRSPS - Flag indicating if the reactive species concentrations should be printed.

Possible Values:

0 - Reactive species concentrations will not be printed

1 - Independent aqueous reactive species, solid species, and sorbed species

concentrations will be printed

2 - All aqueous species, solid species, and sorbed species concentrations will be

printed

IPHAD - Flag indicating whether surfactant adsorption is pH dependent or not.

Possible Values:

0 - Surfactant adsorption is not pH dependent

1 - Surfactant adsorption is pH dependent

4.5.2 PHC, PHT, PHT1, HPHAD (This line is read only if IREACT > 1 and IPHAD > 0)

PHC - Critical pH above which surfactant adsorption is pH dependent.

PHT - Extrapolated pH value at zero surfactant adsorption.

PHT1 - pH value above which surfactant adsorption is constant.

HPHAD - Fraction of the low-pH adsorption plateau retained at a pH above PHT1.

4.5.3 CSELP, CSEUP (This line is read only if IREACT = 3 or 5)

CSELP - Lower optimum salinity limit for generated surfactant.

Units: meq/ml

CSEUP - Upper optimum salinity limit for generated surfactant.

Units: meq/ml

4.5.4 NELET, NFLD, NSLD, NSORB, NACAT, ICHRGE (This line is read only if IREACT > 1)

NELET - Total number of elements less non reacting element.

Maximum Value: 9

NFLD - Total number of fluid species.

NSLD - Total number of solid species.

NSORB - Total number of sorbed species.

NACAT - Total number of surfactant associated cations.

ICHRGE - Flag indicating whether an oxygen balance or a charge balance will be used.

Possible Values:

0 - Oxygen balance used

1 - Charge balance in solution used

Note: If solid SiO2 is considered, the oxygen balance must be used.

4.5.5 NIAQ, NEX, NSLEL, NSURF1 (This line is read only if IREACT > 1)

NIAQ - Total number of independent fluid species.

NEX - Total number of insoluble exchangers.

NSLEL - Total number of elements comprising the solid species.
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NSURF1 - Position number corresponding to the in situ generated surfactant anion in the fluid

species array FLDSPS.

Note: NSURF1 is automatically set to 0 by the program if IREACT = 2 or 4.

4.5.6 NH, NNA, NCA, NMG, NCARB (This line is read only if IREACT > 1)

NH - Position number corresponding to the hydrogen element in the element array ELEMNT.

NNA - Position number corresponding to the sodium element in the element array ELEMNT.

NCA - Position number corresponding to the calcium element in the element array ELEMNT.

NMG - Position number corresponding to the magnesium element in the element array ELEMNT.

Note: If magnesium is not considered, NMG must be set equal to 0.

NCARB - Position number corresponding to the carbonate pseudo-element in the element array

ELEMNT.

4.5.7 NALU, NSILI, NOXY (This line is read only if IREACT > 3)

NALU - Position number corresponding to the aluminum element in the element array ELEMNT.

NSILI - Position number corresponding to the silicon element in the element array ELEMNT.

NOXY - Position number corresponding to the oxygen element in the element array ELEMNT.

4.5.8 NACD (This line is read only if IREACT = 3 or 5)

NACD - Position number corresponding to the petroleum acid pseudo-element in the element array

ELEMNT.

4.5.9 ELEMNT(I), for I = 1, NELET (This line is read only if IREACT > 1)

ELEMNT(I) - Name of the Ith element.

Note: The name of each element may not exceed 32 characters and each name must be on a

separate line of the input file.

4.5.10 FLDSPS(I), for I = 1, NFLD (This line is read only if IREACT > 1)

FLDSPS(I) - Name of the Ith fluid species.

Note: The name of each fluid species may not exceed 32 characters and each name must

be on a separate line of the input file. If IREACT = 3 or 5, the last fluid species

must be HAw (petroleum acid in water).

4.5.11 SLDSPS(I), for I = 1, NSLD (This line is read only if IREACT > 1 and NSLD > 0)

SLDSPS(I) - Name of the Ith solid species.

Note: The name of each solid may not exceed 32 characters and each name must be on a

separate line of the input file.

4.5.12 SORBSP(I), for I = 1, NSORB (This line is read only if IREACT > 1 and NSORB > 0)

SORBSP(I) - Name of the Ith adsorbed cation.

Note: The name of each adsorbed cation may not exceed 32 characters and each name

must be on a separate line of the input file.

4.5.13 ACATSP(I), for I = 1, NACAT (This line is read only if IREACT > 1 and NACAT > 0)

ACATSP(I) - Name of the Ith surfactant adsorbed cation.

Note: The name of each surfactant adsorbed cation may not exceed 32 characters and each

name must be on a separate line of the input file.
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4.5.14 NSORBX(I), for I = 1, NEX (This line is read only if IREACT > 1 and NSORB > 0)

NSORBX(I) - Number of cations for Ith exchanger.

4.5.15 AR(I,J), for J = 1, NFLD, for I = 1, NELET << or >>

AR(I,J), for J = 1, NFLD, for I = 1, NELET-1 (This line is read only if IREACT > 1)

AR(I,J) - Stoichiometric coefficient of Ith element in Jth fluid species.

Note: If ICHRGE = 0, then NFLD × NELET values are required by the program. If

ICHRGE = 1, then NFLD × (NELET-1) values are required by the program.

4.5.16 BR(I,J), for J = 1, NSLD, for I = 1, NELET << or >>

BR(I,J), for J = 1, NSLD, for I = 1, NELET-1 (This line is read only if IREACT > 1 and NSLD >

0)

BR(I,J) - Stoichiometric coefficient of Ith element in Jth solid species.

Note: If ICHRGE = 0, then NSLD × NELET values are required by the program. If

ICHRGE = 1, then NSLD × (NELET-1) values are required by the program.

4.5.17 DR(I,J), for J = 1, NSORB, for I = 1, NELET << or >>

DR(I,J), for J = 1, NSORB, for I = 1, NELET-1 (This line is read only if IREACT > 1 and

NSORB > 1)

DR(I,J) - Stoichiometric coefficient of Ith element in Jth sorbed species.

Note: If ICHRGE = 0, then NSORB × NELET values are required by the program. If

ICHRGE = 1, then NSORB × (NELET-1) values are required by the program.

4.5.18 ER(I,J), for J = 1, NACAT, for I = 1, NELET << or >>

ER(I,J), for J = 1, NACAT, for I = 1, NELET-1 (This line is read only if IREACT > 1 and

NACAT > 1)

ER(I,J) - Stoichiometric coefficient of Ith element in Jth surfactant associated cation.

Note: If ICHRGE = 0, then NACAT × NELET values are required by the program. If

ICHRGE = 1, then NACAT × (NELET-1) values are required by the program.

4.5.19 BB(I,J), for J = 1, NIAQ+NSORB+NACAT, for I = 1, NFLD+NSORB+NACAT (This line is read

only if IREACT > 1)

BB(I,J) - Exponent of the Jth independent fluid species concentration when the Ith fluid species is

expressed in terms of independent species concentrations.

4.5.20 EXSLD(I,J), for J = 1, NIAQ, for I = 1, NSLD (This line is read only if IREACT > 1 and NSLD •

1)

EXSLD(I,J) - Exponent of the Jth independent fluid species concentration in the solubility product

definition of the Ith solid.

4.5.21 CHARGE(I), for I = 1, NFLD (This line is read only if IREACT > 1)

CHARGE(I) - Charge of the Ith fluid species.
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4.5.22 SCHARG(I,J), for J = 1, NSORBX(I), for I = 1, NEX (This line is read only if IREACT > 1 and

NSORB • 1)

SCHARG(I,J) - Charge of the Jth sorbed species on the Ith exchanger.

4.5.23 EQK(I), for I = 1, NFLD (This line is read only if IREACT > 1)

EQK(I) - Equilibrium constant for Ith fluid species when expressed in independent species

concentrations only.

4.5.24 EXK(I,J), for J = 1, NSORBX(I)-1, for I = 1, NEX (This line is read only if IREACT > 1 and

NEX > 0)

EXK(I,J) - Exchange equilibrium constant for Jth exchange equilibrium of the Ith insoluble

exchanger.

4.5.25 EXEX(I,J,K), for K = 1, NIAQ+NSORB+NACAT, for J = 1, NSORBX(I)-1, for I = 1, NEX (This

line is read only if IREACT > 1 and NEX > 0)

EXEX(I,J,K) - Exponent of Kth independent species in Jth equilibrium relation of the Ith

exchanger.

4.5.26 REDUC(I,J), for J = 1, NSORBX(I)-1, for I = 1, NEX (This line is read only if IREACT > 1 and

NEX > 0)

REDUC(I,J) - Valence difference of the two cations involved in the exchange reaction J on

exchanger I.

Note: This value is positive if the higher valence cation bulk concentration has a positive

exponent in EXEX(I,J) definition and is negative otherwise.

4.5.27 EXCAI(I), for I = 1, NEX (This line is read only if IREACT > 1 and NEX >0)

EXCAI(I) - Exchange capacity of Ith insoluble exchanger.

Units: meq/ml pore volume

4.5.28 SPK(I), for I = 1, NSLD (This line is read only if IREACT > 1 and NSLD • 1)

SPK(I) - Solubility product of Ith solid defined in terms of independent fluid species concentrations

only.

4.5.29 CHACAT(I), for I = 1, NACAT (This line is read only if IREACT > 1 and NACAT • 1)

CHACAT(I) - Charge of Ith surfactant associated cation.

4.5.30 ACATK(I), for I = 1, NACAT-1 (This line is read only if IREACT > 1 and NACAT • 1)

ACATK(I) - Equilibrium constant for Ith exchange equilibrium for cation exchanges on surfactant.

4.5.31 EXACAT(I,J) for J = 1, NIAQ+NSORB+NACAT, for I = 1, NACAT-1 (This line is read only if

IREACT > 1 and NACAT • 1)

EXACAT(I,J) - Exponent of Jth independent species in Ith equilibrium for cation exchange on

surfactant.

4.5.32 CI(J), for J = 1, NACAT (This line is read only if IREACT > 1 and NACAT • 1)

CI(J) - Initial concentration of Jth surfactant associated cation.

Units: moles/liter pore volume
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4.5.33 C5I, C6I (This line is read only if IREACT > 1)

C5I - Initial concentration of non reacting anions.

Units: equivalents/liter

C6I - Initial concentration of calcium in aqueous phase.

Units: equivalents/liter

4.5.34 CELAQI(J), for J = 1, N-NO6 (This line is read only if IREACT > 1)

CELAQI(J) - Initial concentrations of (J+11)th component.

Units: equivalents/liter

Note : NO6 = 11 for 1< IREACT<6

NO6 = 15 for IREACT = 6

4.5.35 CAC2I (This line is read only if IREACT = 3 or 5)

CAC2I - Initial concentration of acid in oil.

Units: moles/liter oil

4.5.36 CAQI(J), for J = 1, NIAQ (This line is read only if IREACT > 1)

CAQI(J) - Initial guesses for Jth independent species concentration.

Units: moles/liter water

4.5.37 CSLDI(I), for I = 1, NSLD (This line is read only if IREACT > 1 and NSLD • 1)

CSLDI(I) - Initial concentration of Ith solid.

Units: moles/liter pore volume

4.5.38 CSORBI(I), for I = 1, NSORB (This line is read only if IREACT > 1 and NSORB • 1)

CSORBI(I) - Initial concentration of Ith adsorbed cation.

Units: moles/liter pore volume

4.5.39 C1I, C2I (This line is read only if IREACT = 3 or 5)

C1I - Initial concentration of water in aqueous phase.

Units: volume fraction

C2I - Initial concentration of oil in oleic phase.

Units: volume fraction

4.5.40 ACIDIS, EQWPS (This line is read only if IREACT = 3 or 5)

ACIDIS - Dissociation constant of the petroleum acid, Ka.

EQWPS - Equivalent weight of petroleum acid.

B.4.6 Recurrent Injection/Production Data Set

The sixth input section consists of the recurrent injection/production well data. Please

remember that there are seven comment lines at the beginning of this section and that each line is

preceded by three comment lines.

4.6.1 IBOUND

IBOUND - The flag to specify if constant potential boundaries at the left and right sides of the

simulation model are specified.
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Possible Values:

0 : No boundary is specified

1 : Boundary is specified

4.6.2 IBL, IBR (This line is read only if IBOUND = 1)

IBL - The flag to specify if the left-hand side constant potential boundary is specified.

Possible Values:

0 : No boundary is specified

1 : Boundary is specified

IBR - The flag to specify if the right-hand side constant potential boundary is specified.

Possible Values:

0 : No boundary is specified

1 : Boundary is specified

4.6.3 PBL, C1BL, C5BL, C6BL (This line is read only if IBOUND = 1 and IBL = 1)

PBL- Pressure at the center of the top layer at the left boundary.

Units : psia (IUNIT=0) or kPa (IUNIT=1)

C1BL- Concentration of water in aqueous phase at the left boundary.

Units : volume fraction

C5BL - Concentration of chloride in aqueous phase at the left boundary.

Units : meq/ml

C6BL - Concentration of calcium in aqueous phase at the left boundary.

Units : meq/ml

4.6.4 PBR, C1BR, C5BR, C6BR (This line is read only if IBOUND = 1 and IBR = 1)

PBR - Pressure at the center of the top layer at the right boundary.

Units : psia (IUNIT=0) or kPa (IUNIT=1)

C1BR - Concentration of water in aqueous phase at the right boundary.

Units : volume fraction

C5BR - Concentration of chloride in aqueous phase at the right boundary.

Units : meq/ml

C6BR - Concentration of calcium in aqueous phase at the right boundary.

Units : meq/ml

4.6.5 NWELL, IRO, ITIME

NWELL - Maximum number of wells used for the simulation.

Note: If ICOORD = 2, NWELL must be equal to 1 and the MXW parameter in the source

code must be set equal to 2.

IRO - Flag indicating the equivalent well radius model to be used.

Possible Values:

1 - Babu and Odeh model is used

Note: This model (IRO=1) does not work for ICOORD = 4.

2 - Peaceman model is used (this was the default in versions previous to UTCHEMV-5.0)

Note: For information see Babu and Odeh [1989].

ITIME - Flag indicating the units to be used when specifying the minimum and maximum time step.

Possible Values:
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0 - Minimum and maximum time steps are input in days

1 - Minimum and maximum time steps are input as Courant numbers

Note: This option is only used if IMES > 1 and is not a shut-in period. If IMES = 1,

this flag is ignored. For a shut-in period you need to use ITIME = 0

Note: The Courant number is defined as:

• EMBED "Equation" "Word Object1" \* mergeformat •••

The following values for minimum and maximum Courant numbers are recommended for

different simulations as follows:

Process Min. Courant # Max. Courant #

Waterflood/tracer 0.04 0.4

Polymerflood 0.02 0.2

Surfactant/polymerflood 0.01 0.1

Geochemical process 0.01 0.1

4.6.6 The data on input lines 4.6.6.a through 4.6.6.d are repeated for M = 1 to NWELL times.

4.6.6.a IDW(M), IW(M), JW(M), IFLAG(M), RW(M), SWELL(M), IDIR(M), IFIRST(M), ILAST(M),

IPRF(M)

IDW(M) - Well I.D. number for the Mth well.

Possible Values: Must be between 1 and MXW (the source code parameter indicating the

maximum number of wells)

Note: This number is used by UTCHEM to keep track of which well is being described in

the recurrent injection/production well section. The history profile data for the well

indicated by IDW(M) will be written to FORTRAN UNIT number 18 + IDW(M).

IW(M) - First index of the reservoir gridblock containing the Mth well.

Possible Values: Between 1 and the number of gridblocks in the pertinent direction,

inclusive

Note: If the Mth well is completed parallel to the X-axis, IW(M) is the Y direction

index—if the well is completed parallel to the Y- or Z-axis, IW(M) is the X

direction index. See example below.

If ICOORD = 2, IW(1) = JW(1) = 1.

JW(M) - Second index of the reservoir gridblock containing the Mth well.

Possible Values: Between 1 and the number of gridblocks in the pertinent direction,

inclusive

Note: If the Mth well is completed parallel to the X- or Y-axis, JW(M) is the Z direction

index—if the well is completed parallel to the Z-axis, JW(M) is the Y direction

index. See example below.

If ICOORD = 2, IW(1) = JW(1) = 1.

IFLAG(M) - Flag indicating type of well constraint specification for Mth well.

Possible Values:

1 - Rate constrained injection well

2 - Pressure constrained production well (this option is available only if ICOORD =

1 or 3)
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3 - Pressure constrained injection well (this option is available only if ICOORD = 1

or 3)

4 - Rate constrained production well

RW(M) - Radius of Mth well.

Units: feet (IUNIT=0) or m (IUNIT=1)

SWELL(M) - Skin factor for Mth well.

Units: dimensionless

IDIR(M) - Flag indicating the direction in which the Mth well is completed.

Possible Values:

1 : Well completed parallel to the X-axis

2 : Well completed parallel to the Y-axis

3 : Well completed parallel to the Z-axis

Note: If ICOORD = 2, IDIR(1) must be equal to 3.

IFIRST(M) - Index of the first block in which the Mth well is completed.

Possible Values: Between 1 and the number of gridblocks in the pertinent direction,

inclusive

ILAST(M) - Index of the last block in which the Mth well is completed.

Possible Values: Between IFIRST(M) and the number of gridblocks in the pertinent

direction, inclusive

IPRF(M) - Flag indicating if partial completion of the well is considered.

Possible Values:

0 - The well is fully completed

1 - The well is partially completed

Example: For a vertical well (completed through all the layers) as illustrated in the 4 × 4 × 3

example below, note the values of IDIR(M), IW(M), JW(M), IFIRST(M), and ILAST(M):

For a horizontal well (completed from the first to last gridblock in the X direction and

parallel to the X-axis) as illustrated in the 4 × 4 × 3 example below, note the values of

IDIR(M), IW(M), JW(M), IFIRST(M), and ILAST(M):
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Note: Horizontal wells can be used for 2-D X-Y or 3-D simulations.

4.6.6.b KPRF(M,IWB), for IWB = 1, NWBC (This line is read only if IPRF = 1)

KPRF(M,IWB) - Flag indicating if the IWBth well block of the Mth well is perforated or not.

Possible Values:

0 - The well block is not perforated

1 - The well block is perforated

4.6.6.c WELNAM(M)

WELNAM(M) - Name of the Mth well.

Note: The name can consist of any combination of up to 18 alphanumeric characters.

This information will be printed—along with the well I.D. number, IDW(M)—at

the beginning of the history output files.

4.6.6.d ICHEK(M), PWFMIN(M), PWFMAX(M), QTMIN(M), QTMAX(M)

ICHEK(M) - The flag to specify whether to check the rate or pressure caps for the Mth well.

Possible Values:

0 - There will be no check on the rate or pressure limits and no automatic shut in

for the pressure constraint injector

1 - There will be no automatic shut in for the pressure constraint injector but the

pressure or rate limits are checked

2 - There will be both the automatic shut in and the check on the pressure or rate

limits

PWFMIN(M) - Minimum flowing bottom hole pressure (specified at the top layer) for the Mth

well.

Units: psi (IUNIT=0) or kPa (IUNIT=1)

PWFMAX(M) - Maximum flowing bottom hole pressure (specified at the top layer) for the Mth

well.

Units: psi (IUNIT=0) or kPa (IUNIT=1)

QTMIN(M) - Minimum total flow rate (specified at the top layer) for the Mth well.

Units: ft3/day (IUNIT=0) or m3/day (IUNIT=1)

QTMAX(M) - Maximum total flow rate (specified at the top layer) for the Mth well.

Units: ft3/day (IUNIT=0) or m3/day (IUNIT=1)

Note: – PWFMIN(M) and PWFMAX(M) are the pressure caps for a rate constraint injector or

producer well. QTMIN(M) and QTMAX(M) are the total rate caps for a pressure
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294

constraint injector or producer well. If the Mth pressure constraint injector or producer

produces at total rate less than QTMIN(M), the Mth well will be switched to a rate

constraint well with total rate of QTMIN(M) for the rest of the injector or production

period. On the other hand, if the total rate is greater than the QTMAX(M), the Mth well

then will be switched to a rate constraint well with the total rate of QTMAX(M). The

similar concept is applied to a rate constraint injector or producer.

– The user can skip the well control calculation by specifying very small values for

QTMIN(M) and PWFMIN(M) and very large values for QTMAX(M) and PWFMAX(M).

– The code still has the automatic option for shut in of a pressure constraint injector

injecting at a rate of less than QTMIN(M).

4.6.7 The data on input lines 4.6.7.a, 4.6.7.b, 4.6.7.c, and 4.6.7.d are repeated for M = 1 to NWELL

times.

Note 1: For injection wells that are on rate constraint only injection rates and concentrations for

each phase are listed. For injection wells that are on pressure constraint the injection

pressure is also specified. In this case the injection rates are treated as phase cuts in the

injected fluid. For producer pressure constraint only the bottom hole pressure is specified.

For producer rate constraint only the total production rate is specified.

Note 2: The user can shut in a pressure constraint well by specifying a negative bottom hole

pressure or a rate constraint well by specifying a value of zero for rate (QI).

4.6.7.a ID(M), QI(M,L), (C(M,KC,L), for KC = 1, N), for L = 1, MXP (This set of data is read only if

IFLAG(M) = 1 or 3)

ID(M) - Well I.D. number for the Mth well.

Possible Values: Must be between 1 and MXW (the source code parameter indicating the

maximum number of wells)

Note: See note for IDW(M) on input line 4.6.6.a.

QI(M,L) - Injection rate of Lth phase in Mth well (see note).

Units: ft3/day (IUNIT=0) or m3/day (IUNIT=1)

C(M,KC,L) - Concentration of KCth component in Lth phase in Mth well.

Units: vary according to component (see note)

Note: The KC index changes the fastest, the L index changes the next fastest, and the M index

changes the slowest. A separate data line should be in the input file for each phase - - that

is, M × L lines will be read in. MXP is equal to 3 (IGAS = 0) or 4 (IGAS = 1).

– The following values for L correspond to the indicated phase:

1 - Aqueous phase

2 - Oleic phase

3 - Microemulsion phase

4 - Gas phase

– The following values for KC correspond to the indicated component (corresponding

concentration units are in parentheses):

For all values of IREACT:

1 - Water (volume fraction)

2 - Oil (volume fraction)

3 - Surfactant (volume fraction)

4 - Polymer (weight percent)
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5 - Total nonsorbing anions concentration, assumed to all be chloride anions

(meq/ml)

6 - Divalent cations, assumed to all be calcium for IREACT<2 (meq/ml)

7 - Alcohol 1 (volume fraction)

8 - Alcohol 2 (volume fraction) or Gas (volume fraction)

9 - Tracer 1

10 - Tracer 2

11 - Tracer 3

For IREACT = 0:

12 - Tracer 4

13 - Tracer 5

...

20 - Tracer 12

21 - Tracer 13

For IREACT = 1:

12 - Na2Cr2O7 (ppm)

13 - CSN2H4 (ppm)

14 - Cr3+ (ppm)

15 - Gel (ppm)

16 - Hydrogen (meq/ml)

For IREACT = 2, 3, 4, 5, or 6:

12 - Sodium (meq/ml)

13 - Hydrogen (meq/ml)

14 - Magnesium (meq/ml)

15 - Carbonate (meq/ml)

For IREACT = 3:

16 - Acid component of crude oil (meq/ml)

For IREACT = 4 , 5, or 6:

16 - Aluminum (meq/ml)

17 - Silica (meq/ml)

For IREACT = 5:

18 - Acid component of crude oil (meq/ml)

For IREACT = 6

18 - Na2Cr2O7 (ppm)

19 - CSN2H4 (ppm)

20 - Cr3+ (ppm)

21 - Gel (ppm)

4.6.7.b ID(M), PWF(M) (This line is read only if IFLAG(M) = 2 or 3)

ID(M) - Well I.D. number for the Mth well.

Possible Values: Must be between 1 and MXW (the source code parameter indicating the

maximum number of wells)

Note: See note for IDW(M) on input line 4.6.6.a.

PWF(M) - Flowing bottom hole pressure for the Mth well.

Units: psia (IUNIT=0) or kPa (IUNIT=1)
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4.6.7.c ID(M), TEMINJ(M) (This line is read only if IENG=1 and IFLAG(M) = 1 or 3)

ID(M) - Well I.D. number for the Mth well.

Possible Values: Must be between 1 and MXW (the source code parameter indicating the

maximum number of wells)

Note: See note for IDW(M) on input line 4.6.6.a.

TEMINJ(M) - Injection temperature for Mth well.

Units: •F (IUNIT=0) or •C (IUNIT=1)

4.6.7.d ID(M), QI(M,1) (This line is read only if IFLAG(M) = 4)

ID(M) - Well I.D. number for the Mth well.

Possible Values: Must be between 1 and MXW (the source code parameter indicating the

maximum number of wells)

Note: See note for IDW(M) on input line 4.6.6.a.

QI(L) - Total production rate for Mth well.

Units: ft3/day (IUNIT=0) or m3/day (IUNIT=1)

Note: This value needs to be input as a negative number

4.6.8 TINJ, CUMPR1, CUMHI1, CUMHI2, WRHPV, WRPRF, RSTC

TINJ - Cumulative injection time.

Units: days or pore volumes (dependent on value of ISTOP flag on input line 4.2.1)

CUMPR1 - Indicates interval at which profiles should be written to UNIT 4.

Units: pore volumes or days (dependent on value of ICUMTM flag on input line 4.2.1)

CUMHI1 - Indicates interval at which production data should be written to UNIT 4.

Units: pore volumes or days (dependent on value of ICUMTM flag on input line 4.2.1)

CUMHI2 - Indicates interval at which production data should be written to UNIT 3.

Units: pore volumes or days (dependent on value of ICUMTM flag on input line 4.2.1)

WRHPV - Indicates interval at which production histories should be written to output file(s) for

history plotting.

Units: pore volumes or days (dependent on value of ICUMTM flag on input line 4.2.1)

Note: If WRHPV > total pore volume injected or maximum simulation time, the data will

not be printed. The unit number of the file to be written to starts at 19 and continues

upward. For example, for a run with three producers, UNITS 19, 20 and 21 would

be used. The history of reservoir properties and overall rates from all the producing

wells is written to UNIT 9.

WRPRF - Indicates interval at which concentration, pressure, saturation, tracer phase concentration,

capacitance property, gel property, alkaline property , and temperature profiles should be

written to UNITS 8, 11, 12, 13, 14, 10, 15, and 18 respectively.

Units: pore volumes or days (dependent on value of ICUMTM flag on input line 4.2.1)

Note: If WRPRF > total pore volume injected or maximum simulation time, the data will

not be written.

RSTC - Indicates the interval at which restart data should be written to UNIT 7.

Units: pore volumes or days (dependent on value of ICUMTM flag on input line 4.2.1)

4.6.9 DT (This line is read only if IMES = 1 and ITIME = 0)

DT - Time step size for constant time step option.

Units: days
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297

4.6.10 DT, DCLIM, DTMAX, DTMIN (This line is read only if IMES = 2 and ITIME = 0)

DT - Initial time step size, •ti

.

Units: days

DCLIM - Tolerance for concentration change for the first three components, •Clim.

Units: volume fraction

DTMAX - Maximum time step size, •tmax.

Units: days

DTMIN - Minimum time step size, •tmin.

Units: days

Note: The time step selection is based on the method of relative changes for the first three

components (water, oil, and surfactant) as:

Δt

n+1

= Δt

n min ΔClim

i =1

NBL

max ΔCi,κ

 

 

  

 

 

  κ = 1, 2, 3

•tn+1 is limited to: •tmin • •tn+1 • •tmax

4.6.11 DT, DCLIM, CNMAX, CNMIN (This line is read only if IMES = 2, ITIME = 1, and at least one

well is not shut-in.)

DT - Initial time step size, •ti

.

Units: days

DCLIM - Tolerance for concentration changes for the first three components.

Units: volume fraction

CNMAX - Maximum Courant number.

Units: dimensionless

CNMIN - Minimum Courant number.

Units: dimensionless

Note: The minimum and maximum time steps in days are computed based on the minimum and

maximum Courant number as:

Δtmin = 

CNMIN

min

M=1

nwell

max

i=1

nwbc Qi

Δxi Δyi Δzi φi

 

 

  

  

and

Δtmax = 

CNMAX

min

M=1

nwell

max

i=1

nwbc Qi

Δxi Δyi Δzi φi

 

 

  

  

4.6.12 DT, (DCLIM(KC), for KC = 1, N), DTMAX, DTMIN (This line is read only if IMES = 3 or 4 and

ITIME = 0)

DT - Initial time-step size, •ti

.

Units: days

DCLIM(KC) - Tolerance for concentration change, •Clim,κ, of KCth component (IMES = 3) or

relative tolerance for concentration change, Rlim,κ, of KCth component (IMES = 4).

Units: IMES = 3: volume fraction, weight percent, meq/ml, or ppm (depending on which

component the tolerance is for—see note for input line 4.6.7.a)
Appendix B - UTCHEM Local Grid Refinement User's Guide

298

IMES = 4: dimensionless

DTMAX - Maximum time step size, •tmax.

Units: days

DTMIN - Minimum time step size, •tmin.

Units: days

Note: For IMES = 3, the method of relative changes is applied to all the components in the

simulation run:

Δt

n+1

= Δt

n min ΔClim

i=1

NBL

max ΔCi,κ

 

 

 

 

 

 

 

 κ = 1, ..., nc

•tn+1 is limited to: •tmin • •tn+1 • •tmax

•Clim,κ is a fraction of the initial or injected concentration (whichever is larger) of

the KCth component. For example: •Clim,3 = 0.1 × C3 where C3 is the total

concentration of component 3. If •Clim,κ of the KCth component is entered as zero,

that component is not considered in the time-step size selection.

For IMES = 4, the new time-step size is calculated according to:

Δt

n+1

= Δt

n min

Rlim,κ

i=1

NBL

max

ΔCi,κ

Ci,κ

 

 

 

 

 

 

 

 

 

 

 κ = 1, ..., nc

•tn+1 is limited to: •tmin • •tn+1 • •tmax

Rlim,κ is the dimensionless relative change in concentration. For example: Rlim,3 =

0.1 indicates a 10% change in concentration of component 3.

4.6.13 DT, (DCLIM(KC), for KC = 1, N), CNMAX, CNMIN (This line is read only if IMES = 3 or 4,

ITIME = 1, and reservoir is not shut-in.)

DT - Initial time step size, •ti

.

Units: days

DCLIM(KC) - Tolerance for concentration change, •Clim,κ, of KCth component (IMES = 3) or

relative tolerance for concentration change, Rlim,κ, of KCth component (IMES = 4).

Units: IMES = 3: volume fraction, weight percent, meq/ml, or ppm (depending on which

component the tolerance is for—see note for input line 4.6.7.a)

IMES = 4: dimensionless

CNMAX - Maximum Courant number.

Units: dimensionless

CNMIN - Minimum Courant number.

Units: dimensionless

Note: See note for input lines 4.6.11 and 4.6.12 for time step calculation information.

IMPORTANT NOTE: The data on lines 4.6.14 through 4.6.23 describe the changes in boundary conditions

and are repeated until the injected time (TINJ on input line 4.6.8) is greater than or equal to the maximum

simulation time (TMAX on input line 4.3.1).
Appendix B - UTCHEM Local Grid Refinement User's Guide

299

4.6.14 IRO, ITIME, IFLAG(M), M = 1, NWELL

IRO - Flag indicating the equivalent well radius model to be used.

Possible Values:

1 - Babu and Odeh model is used

2 - Peaceman model is used (this was the default in versions previous to UTCHEMV-5.0)

Note: For information see Babu and Odeh [1989].

ITIME - Flag indicating the units to be used when specifying the minimum and maximum time

step.

Possible Values:

0 - Minimum and maximum time steps are input in days

1 - Minimum and maximum time steps are input as Courant numbers

Note: This option is only used if IMES > 1 and it is not a shut-in period. If IMES = 1, this

flag is ignored.

IFLAG(M) - Flag indicating type of well constraint specification for Mth well.

Possible Values:

1 - Rate constrained injection well

2 - Pressure constrained production well (this option is available only if ICOORD =

1 or 3)

3 - Pressure constrained injection well (this option is available only if ICOORD = 1

or 3)

4 - Rate constrained production well

4.6.15 NWEL1

NWEL1 - Number of wells with changes in location (IW(M), JW(M)), skin, direction, perforation,

name, or minimum and maximum bottomhole pressure or minimum or maximum rate.

4.6.16 The data on input lines 4.6.16.a through 4.6.16.d are repeated for M = 1 to NWEL1 times.

4.6.16.a ID, IW(ID), JW(ID), RW(ID), SWELL(ID), IDIR(ID), IFIRST(ID), ILAST(ID), IPRF(ID)

ID - Well ID number with changes from the previous slug injection period.

IW(ID) - First index of the reservoir gridblock containing the IDth well.

Possible Values: Between 1 and the number of gridblocks in the pertinent direction,

inclusive

Note: See note for input line 4.6.6.a.

JW(ID) - Second index of the reservoir gridblock containing the IDth well.

Possible Values: Between 1 and the number of gridblocks in the pertinent direction,

inclusive

Note: See note for input line 4.6.6.a.

RW(ID) - Radius of IDth well.

Units: feet (IUNIT=0) or m (IUNIT=1)

SWELL(ID) - Skin factor for IDth well.

Units: dimensionless

IDIR(ID) - Flag indicating the direction in which the IDth well is completed.

Possible Values:

1 : Well completed parallel to the X-axis

2 : Well completed parallel to the Y-axis
Appendix B - UTCHEM Local Grid Refinement User's Guide

300

3 : Well completed parallel to the Z-axis

Note: If ICOORD = 2, IDIR(1) must be equal to 3.

IFIRST(ID) - Index of the first block in which the IDth well is completed.

Possible Values: Between 1 and the number of gridblocks in the pertinent direction,

inclusive

ILAST(ID) - Index of the last block in which the IDth well is completed.

Possible Values: Between IFIRST(ID) and the number of gridblocks in the pertinent

direction, inclusive

Note: At this time, UTCHEM assumes the well is completed continuously between

IFIRST(ID) and ILAST(ID).

IPRF(ID) - Flag indicating if partial completion of the well is considered.

Possible Values:

0 - The well is fully completed

1 - The well is partially completed

4.6.16.b KPRF(ID,IWB), for IWB = 1, NWBC (This line is read only if IPRF = 1)

KPRF(ID,IWB) - Flag indicating if the IWBth well block of the IDth well is perforated or not.

Possible Values:

0 - The well block is not perforated

1 - The well block is perforated

4.6.16.c WELNAM(ID)

WELNAM(ID) - Name of the IDth well.

Note: The name can consist of any combination of up to 18 alphanumeric characters.

This information will be printed—along with the well I.D. number, IDW(ID)—at

the beginning of the history output files.

4.6.16.d ICHEK, PWFMIN(ID), PWFMAX(ID), QTMIN(ID), QTMAX(ID)

ICHEK(M) - The flag to specify whether to check the rate or pressure caps for the Mth well.

Possible Values:

0 - There will be no check on the rate or pressure limits and no automatic shut in

for the pressure constraint injector

1 - There will be no automatic shut in for the pressure constraint injector but the

user specified pressure or rate limits are checked

2 - There will be both the automatic shut in and the check on the user specified

pressure or rate limits

PWFMIN(ID) - Minimum flowing bottom hole pressure (specified at the top layer) for the IDth

well.

Units: psi (IUNIT=0) or kPa (IUNIT=1)

PWFMAX(ID) - Maximum flowing bottom hole pressure (specified at the top layer) for the IDth

well.

Units: psi (IUNIT=0) or kPa (IUNIT=1)

QTMIN(ID) - Minimum total flow rate (specified at the top layer) for the IDth well.

Units: ft3/day (IUNIT=0) or m3/day (IUNIT=1)

QTMAX(ID) - Maximum total flow rate (specified at the top layer) for the IDth well.

Units: ft3/day (IUNIT=0) or m3/day (IUNIT=1)
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301

Note: See the note for input line 4.6.6.d.

4.6.17 NWEL2, (ID(J), for J = 1, NWEL2)

NWEL2 - Number of wells with changes in rate, concentration or bottomhole pressure.

ID(J) - ID number for Jth well with changes.

4.6.18 The data on input lines 4.6.18.a through 4.6.18.d are repeated for M = 1 to NWEL2 times.

4.6.18.a ID, (QI(ID,L), for L = 1, MXP), (C(ID,KC,L), for KC = 1,N), for L =1, MXP (This set of data is

read only if IFLAG(ID) =1 or 3)

ID - Well ID number with changes from the previous slug injection period.

QI(ID,L) - Injection rate of Lth phase in IDth well (see note for input line 4.6.7.a).

Units: ft3/day (IUNIT=0) or m3/day (IUNIT=1)

C(ID,KC,L) - Concentration of KCth component in Lth phase for IDth well.

Units: vary according to component (see note for line 4.6.7.a)

Note: If IGAS = 0, then MXP = 3. If IGAS = 1, then MXP = 4.

4.6.18.b ID(ID), PWF(ID) (This line is read only if IFLAG(ID) = 2 or 3)

ID(ID) - Well ID number with changes from the previous slug injection period.

PWF(ID) - Flowing bottom hole pressure for the IDth well.

Units: psia (IUNIT=0) or kPa (IUNIT=1)

4.6.18.c ID(ID), TEMINJ(ID) (This line is read only if IENG = 1 and IFLAG(ID) = 1or 3)

ID(ID) - Well ID number with changes from the previous slug injection period.

TEMINJ(ID) - Injection temperature for the IDth well.

Units: •F (IUNIT=0) or •C (IUNIT=1)

4.6.18.d ID(ID), QI(ID,1) (This line is read only if IFLAG(ID) = 4)

ID(ID) - Well ID number with changes from the previous slug injection period.

QI(ID,1) - Total production rate for IDth well.

Units: ft3/day (IUNIT=0) or m3/day (IUNIT=1)

Note: This value needs to be input as a negative number.

4.6.19 TINJ, CUMPR1, CUMHI1, CUMHI2, WRHPV, WRPRF, RSTC

TINJ - Cumulative injection time.

Units: days or pore volumes (dependent on value of ISTOP flag on input line 4.2.1)

CUMPR1 - Indicates interval at which profiles should be written to UNIT 4.

Units: pore volumes or days (dependent on value of ICUMTM flag on input line 4.2.1)

CUMHI1 - Indicates interval at which production data should be written to UNIT 4.

Units: pore volumes or days (dependent on value of ICUMTM flag on input line 4.2.1)

CUMHI2 - Indicates interval at which production data should be written to UNIT 3.

Units: pore volumes or days (dependent on value of ICUMTM flag on input line 4.2.1)

WRHPV - Indicates interval at which production histories should be written to output file(s) for

history plotting.

Units: pore volumes or days (dependent on value of ICUMTM flag on input line 4.2.1)

Note: If WRHPV > total pore volume injected or maximum simulation time, the data will

not be printed. The unit number of the file to be written to starts at 19 and continues
Appendix B - UTCHEM Local Grid Refinement User's Guide

302

upward. For example, for a run with three producers, UNITS 19, 20, and 21 would

be used. The history of reservoir properties and the total rate from all the producing

wells is written to UNIT 9.

WRPRF - Indicates interval at which concentration, pressure, saturation, tracer phase

concentration, capacitance property, pressure difference, gel property, alkaline property ,

and temperature profiles should be written to UNITS 8, 11, 12, 13, 14, 10, 15 and 18

respectively.

Units: pore volumes or days (dependent on value of ICUMTM flag on input line 4.2.1)

Note: If WRPRF > total pore volume injected or maximum simulation time, the data will

not be written.

RSTC - Indicates the interval at which restart data should be written to UNIT 7.

Units: pore volumes or days (dependent on value of ICUMTM flag on input line 4.2.1)

4.6.20 DT (This line is read only if IMES = 1 and ITIME = 0)

DT - Time step size for constant time step option.

Units: days

4.6.21 DT, DCLIM, DTMAX, DTMIN (This line is read only if IMES = 2 and ITIME = 0)

DT - Initial time step size, •ti

.

Units: days

DCLIM - Tolerance for concentration change for the first three components, •Clim.

Units: volume fraction

DTMAX - Maximum time step size, •tmax.

Units: days

DTMIN - Minimum time step size, •tmin.

Units: days

Note: See note for input line 4.6.10.

4.6.22 DT, DCLIM, CNMAX, CNMIN (This line is read only if IMES = 2, ITIME = 1, and at least one

well is not shut-in.)

DT - Initial time step size, •ti

.

Units: days

DCLIM - Tolerance for concentration changes for the first three components.

Units: volume fraction

CNMAX - Maximum Courant number.

Units: dimensionless

CNMIN - Minimum Courant number.

Units: dimensionless

Note: See note for input line 4.6.11.

4.6.23 DT, (DCLIM(KC), for KC = 1, N), DTMAX, DTMIN (This line is read only if IMES = 3 or 4 and

ITIME = 0)

DT - Initial time-step size, •ti

.

Units: days

DCLIM(KC) - Tolerance for concentration change, •Clim,κ, of KCth component (IMES = 3) or

relative tolerance for concentration change, Rlim,κ, of KCth component (IMES = 4).
Appendix B - UTCHEM Local Grid Refinement User's Guide

303

Units: IMES = 3: volume fraction, weight percent, meq/ml, or ppm (depending on which

component the tolerance is for—see note for input line 4.6.7.a)

IMES = 4: dimensionless

DTMAX - Maximum time step size, •tmax.

Units: days

DTMIN - Minimum time step size, •tmin.

Units: days

Note: See note for input line 4.6.12.

4.6.24 DT, (DCLIM(KC), for KC = 1, N), CNMAX, CNMIN (This line is read only if IMES = 3 or 4,

ITIME = 1, and reservoir is not shut-in.)

DT - Initial time step size, •ti

.

Units: days

DCLIM(KC) - Tolerance for concentration change, •Clim,κ, of KCth component (IMES = 3) or

relative tolerance for concentration change, Rlim,κ, of KCth component (IMES = 4).

Units: IMES = 3: volume fraction, weight percent, meq/ml, or ppm (depending on which

component the tolerance is for—see note for input line 4.6.7.a)

IMES = 4: dimensionless

CNMAX - Maximum Courant number.

Units: dimensionless

CNMIN - Minimum Courant number.

Units: dimensionless

Note: See note for input lines 4.6.11 and 4.6.12 for time step calculation information.

B.5 NOMENCLATURE

The nomenclature consists of the names of the variables as they appear in equations in this

text (and related reports) and descriptions of those variables. FORTRAN names of the variables as

they appear in the UTCHEM simulator appear in parenthesis where applicable.

aT = Adsorbed tracer amount per unit mass of rock.

a3 = Surfactant adsorption parameter

a31 = Surfactant adsorption parameter (AD31)

a32 = Surfactant adsorption parameter (AD32)

a4 = Polymer adsorption parameter

a41 = Surfactant adsorption parameter (AD41)

a42 = Polymer adsorption parameter (AD42)

aκ = Adsorption parameter for κth component (A14D, A15D)

Ap1 = Polymer viscosity parameter (AP1)

Ap2 = Polymer viscosity parameter (AP2)

Ap3 = Polymer viscosity parameter (AP3)

A15 = Permeability reduction parameter for Langmuir correlation with gel concentration (AGK)

B15 = Permeability reduction parameter for Langmuir correlation with gel concentration (BGK)

b3 = Surfactant adsorption parameter (B3D)

b4 = Polymer adsorption parameter (B4D)

bκ = Adsorption parameter for κth component (B14D, B15D)

cpc = Capillary pressure parameter (CPC)

C = Shear rate coefficient

Ci,κ = Total concentration of component κ in gridblock i
Appendix B - UTCHEM Local Grid Refinement User's Guide

304

ΔCi,κ = Change in total concentration of component κ in gridblock i over the current time-step

ΔClim,κ = Tolerance for concentration change of component κ

Co = Initial condition for tracer used in radioactive decay equation

CSE = Effective salinity for phase behavior and surfactant adsorption

CSEL = Type II(–)/III phase boundary or effective salinity limit (CSEL7 for Alcohol 1—Component

7 and CSEL8 for Alcohol 2—Component 8)

CSEP = Effective salinity (ion strength) for polymer properties

CSEU = Type III/II(+) phase boundary or effective salinity limit (CSEU7 for Alcohol 2—Component

7 and CSEU8 for Alcohol 2—Component 8)

CT1 = Concentration of tracer in phase 1

C6

o

= Concentration of free calcium cations

C9

o

= Concentration of free sodium cations

Cδ = Permeability reduction parameter for gel (CRG)

Cκ = Overall concentration of component κ in the mobile phases

C κ = Adsorbed concentration of component κ

Cκo = Concentration of tracer component κ in oil

Cκw = Concentration of tracer component κ in water

 ̃ C κ = Overall concentration of component κ in the mobile and stationary phases

Cκl = Concentration of component κ in phase l

CNMAX = Maximum Courant number

CNMIN = Minimum Courant number

DS = Retardation factor for tracer (RET)

el = Relative permeability exponent for phase l

elc = Relative permeability exponent for phase l at low interfacial tension (E13C, E23C, and

E31C)

 

elw = Relative permeability exponent for phase l at high interfacial tension (E1W, E2W, and

E3W)

f κ

s

= Amount of component κ associated with surfactant

k = Permeability at 100% brine saturation

ka = Apparent permeability used in capillary pressure calculations

krl = Relative permeability of phase l

 

k

rl

o = End point relative permeability of phase l

 

k

rlc

o = End point relative permeability of phase l at low interfacial tension (P1RC for phase 1,

P2RC for phase 2, and P3RC for phase 3)

 

k

rlw

o = End point relative permeability of phase l at high interfacial tension (P1RW for phase 1,

P2RW for phase 2, and P3RW for phase 3)

kx = Absolute permeability in the x-direction (PERMX)

ky = Absolute permeability in the y-direction (PERMY)

kz = Absolute permeability in the z-direction (PERMZ)

Kκ = Tracer κ partition coefficient (TK)

L = Length of the core, or reservoir length

MCr3+ = Molecular weight of chromium component

Mpolymer = Molecular weight of polymer component

n = Cr3+/polymer mass stoichiometric ratio

npc = Capillary pressure exponent (EPC)

Ncl = Capillary number of phase l

Nv = Viscosity number
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305

Nδ = Dimensionless number representing the reduction of the pore radius due to adsorption of gel

PCll' = Capillary pressure between phases l and l'

Pα = Exponent for calculating shear rate dependence of polymer viscosity (POWN)

Qi = Maximum injection/production flow rate in well block i

Qv = Cation exchange capacity of clay (QV)

Rk = Permeability reduction factor

RRF = Residual resistance factor for gel

RRFmax = Maximum residual resistance factor for gel

Snl = Normalized mobile saturation of phase l used in relative permeability and capillary pressure

calculations

Sp = Exponent for calculating salinity dependence of polymer viscosity (SSLOPE)

Sl = Saturation of phase l

Slr = Residual saturation of phase l

Sl'rc = Residual saturation of phase l' at low interfacial tension (S1RWC, S2RWC, and S3RWC for

phases 1, 2 and 3)

Sl'rw = Residual saturation of phase l' at high interfacial tension (S1RW, S2RW, and S3RW for

phases 1, 2 and 3)

SCR = Stoichiometric ratio between Cr3+ and polymer

t = A time variable in the radioactive decay of tracer equation

Δti = Initial time-step size (DT)

Δtmax = Maximum time-step size (DTMAX)

Δtmin = Minimum time-step size (DTMIN)

Δt

n = Time-step size at nth time level

Δt

n+1 = Time-step size at n+1th time level

to = An initial time at which the tracer concentration Co is known; used in the radioactive decay

equation

T1 = Capillary desaturation parameter for aqueous phase (T11)

T2 = Capillary desaturation parameter for oleic phase (T22)

T3 = Capillary desaturation parameter for microemulsion phase (T33)

T4 = Capillary desaturation parameter for gas phase (T44)

u = Flux

Vt = Tracer velocity

•xi = Size of gridblock i in x direction

x4 = Exponent used in gelation reaction

x14 = Exponent used in gelation reaction

x16 = Exponent used in gelation reaction

•yi = Size of gridblock i in y direction

•zi = Size of gridblock i in z direction

Greek Symbols

α1 = Compositional microemulsion phase viscosity parameter (ALPHA1)

α2 = Compositional microemulsion phase viscosity parameter (ALPHA2)

α3 = Compositional microemulsion phase viscosity parameter (ALPHA3)

α4 = Compositional microemulsion phase viscosity parameter (ALPHA4)

α5 = Compositional microemulsion phase viscosity parameter (ALPHA5)

βC = Cation exchange constant for clay (XKC)

βP = Effective salinity parameter for polymer viscosity (BETAP)
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306

βS = Cation exchange constant for surfactant (XKS)

β6 = Effective salinity parameter for calcium—Component 6 (BETA6)

β7 = Effective salinity parameter for Alcohol 1—Component 7 (BETA7)

β8 = Effective salinity parameter for Alcohol 2—Component 8 (BETA8)

γ Ý 

eq = Equivalent shear rate for porous medium

γ Ý 

c = Coefficient in equivalent shear rate equation (GAMMAC)

γ Ý 1/ 2 = Shear rate at which polymer viscosity is one-half the polymer viscosity at zero shear rate

(GAMHF)

γ1 = Specific weight of brine—Component 1 (DEN1)

γ2 = Specific weight of oil—Component 2 (DEN2)

γ3 = Specific weight of surfactant—Component 3 (DEN3)

γ7 = Specific weight of Alcohol 1—Component 7 (DEN7)

γ8 = Specific weight of Alcohol 2 or gas—Component 8 (DEN8)

λκ = Radioactive decay coefficient for κth tracer (RDC)

[μ] = Intrinsic viscosity of a gel solution

μο = Polymer viscosity at zero shear rate

μp = Polymer viscosity

μw = Water viscosity

μl = Viscosity of phase l (VIS1 for phase 1, VIS2 for phase 2, and VIS4 for phase 4)

μ4,ref = Viscosity of gas phase at reference pressure

μ4,s = Slope of gas viscosity function

μ• = Viscosity at infinite shear rate

ρg = Rock density

ρs = Solution density

ρl = Density of phase l

σwo = Interfacial tension between oil and water

σll' = Interfacial tension between phases l and l'

φ = Porosity (POR)

φi = Porosity of gridblock i

Φ = Potential

Θo = Relaxation time coefficient

Subscripts

κ = Component number

For all values of IREACT:

1 = Water

2 = Oil

3 = Surfactant

4 = Polymer

5 = Chloride

6 = Calcium

7 = Alcohol 1

8 = Alcohol 2 or Gas

9 = Tracer 1

10 = Tracer 2

11 = Tracer 3

For IREACT = 0:

12 = Tracer 4
Appendix B - UTCHEM Local Grid Refinement User's Guide

307

13 = Tracer 5

.

.

.

20 = Tracer 12

21 = Tracer 13

For IREACT = 1:

12 = Sodium dichromate (Na2Cr2O7)

13 = Thiourea (CSN2H4)

14 = Trivalent chromium (Cr3+)

15 = Gel

16 = Hydrogen

For IREACT = 2, 3, 4, 5, or 6:

12 = Sodium

13 = Hydrogen

14 = Magnesium

15 = Carbonate

For IREACT = 3:

16 = Acid component of crude oil

For IREACT = 4, 5, or 6:

16 = Aluminum

17 = Silica

For IREACT = 5:

18 = Acid component of crude oil

For IREACT = 6

18 = Sodium dichromate (Na2Cr2O7)

19 = Thiourea (CSN2H4)

20 = Trivalent chromium (Cr3+)

21 = Gel

l = Phase number

1 = Aqueous

2 = Oleic

3 = Microemulsion

4 = Gas

r = Residual

w = Low capillary number values

c = High capillary number values

B.6 OUTPUT FILES AND REACTIONS

The following sections describe: (1) data that is automatically written to the profile data file,

(2) restart run procedure, (3) data written to stored restart data file, (4) data written to history files

for each well, (5) data written to history of reservoir properties and overall injection and production

rates from all the wells, (6) data written to aqueous phase tracer concentration data files, (7) list of

elements and reactions for IREACT=2, (8) list of elements and reactions for IREACT=3, (9) list of

elements and reactions for IREACT=4 or 6, and (10) list of elements and reactions for IREACT=5.
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308

B.6.1 Default Data Written to Profile Data File

The information in the following lists is always written to the profile data file (PROFIL) and

is not controlled by the various print control flags in the input files.

Printed at each CUMHI1 interval:

Time, number of time steps

Time step size

Courant number

Cumulative pore volume injected

Original in place for each component

Cumulative injection for each component

Cumulative production for each component

Amount retained for each component

Relative error for each component

Fraction of oil recovered

If IREACT • 2:

Average number of iterations, computation time

For each well:

Position of the well, first and last well block completed

Cumulative injection/production

Bottomhole pressure for each well block

All well related information (such as pressure for each phase, phase concentration,

phase cut, etc.)

Producer wellbore temperature and phase cut and concentration

Printed at each CUMPR1 interval:

Reservoir temperature if IENG = 1

Phase saturation profile for each phase

Aqueous phase pressure profile

Concentration of each component in the fluid

If tracers are present and ICAP•0:

Flowing concentration

Dendiritic concentration

Flowing saturation

Dendiritic saturation

B.6.2 Restart Run Procedure

The restart procedure is available with UTCHEM. This enables a user to continue a run past

the initial time period or to break a large run up into smaller segments. Each time you run

UTCHEM, a file called RESTAR is created. This file (described in section 6.3 of this appendix)

contains all the information necessary to continue the run at a later time. In order to do so, the user

needs to:

1.- Rename the output file RESTAR from the previous run to INPUT2

2.- Set the variable IMODE equal to 2 on line 4.1.3 of input file INPUT

3.- Change the value of TMAX on input line 4.3.1 of file INPUT to the new injection period

being simulated in the restart run
Appendix B - UTCHEM Local Grid Refinement User's Guide

309

4.- Change the value of TINJ on input line 4.5.8 of file INPUT if appropriate

5.- Add additional information for input lines 4.5.14 through 4.5.24 of file INPUT if the well

conditions are different for the new injection period

Note: Make sure the source code you run the restart problem (IMODE=2) has the same values for

the array sizes in the parameter statement as the one used in original run (IMODE=1).

B.6.3 Data Written to Stored Restart Run Data File

The information in the following list is always written to the stored restart data file

(RESTAR). If the user is running a RESTART run, this data file needs to be renamed to correspond

to the INPUT2 input file. The values in parentheses are the FORTRAN variable names as they

appear in the code.

Printed at the end of each run:

Time (T), injection time (TINJ), time step size (DT), number of time steps (ICNT)

New slug injection or restart flag (IINJ), number of time step reduction (INEC), cumulative

pore volume injection (CUMPV), number of blocks in X-direction minus 1 (NXM1)

Cumulative injection (CUMI), cumulative production (CUMP), original in place (OIP) for

each component

Cumulative injection/production (CUMQ) for each well

Phase concentration (C), phase saturation (S), effective salinity (CSE), overall concentration

(CTOT), number of phases (NPHASE)

If ICOORD=2:

Boundary concentration (CE), boundary pressure (PE)

Viscosity (VIS), relative permeability (RPERM), injection rate (QI), total rate for each well

(QT), phase rate (Q), bottomhole pressure (PWF)

Pressure (P)

Surfactant adsorption (C3ADSS), surfactant adsorption parameter (A3DS), polymer

adsorption (C4ADSS)

Permeability reduction factor (RKF), calcium concentration (C6JO), calcium adsorbed by

clay (C6ADSS), calcium adsorbed by surfactant (C6HATS)

Alcohol 7 partitioning coefficient (X7OLD), alcohol 8 partitioning coefficient (X8OLD)

Variables for writing profiles to UNIT 4 (CUMPRO), histories to UNIT 4 (CUMHIS),

histories to UNIT 3 (CUMHCP)

Oil breakthrough (BTO), tracer breakthrough (TBT), tracer injection concentration (CINJT),

tracer retardation factor (TRD)

Lower effective salinity (CSEL), upper effective salinity (CSEU)

Density (DEN), capillary pressure (PRC)

Total surfactant (TSURF)

If ICAP>0:

Dendiritic concentration (CD), dendiritic saturation (SD), flowing saturation (SF),

total flowing concentration (CTF)

If NG•0:

Chromium adsorption (C14ADS), gel adsorption (C15ADS), cation exchange

capacity of clay (QW)

If IENG = 1

Cum. heat inj. (CUMHI), cum. heat prod. (CUMHP), temperature (TEM), total

volumetric heat capacity (TVHC)
Appendix B - UTCHEM Local Grid Refinement User's Guide

310

If IENG = 1 and IHLOS = 1

Cum. heat loss (TQLOS), integral for overburden and underburden heatloss

calculations (RINO, RINU), time of change of overburden temp. from the reservoir

block (TTCHG), overburden temperature (TEMPOB), underburden temperature

(TEMPUB)

If IENG =1 and ICOORD =2

Boundary enthalpy (ENTHE)

If IREACT >1 :

Solid concentration (CSLDT), adsorbed concentration (CSORBT), species

concentration (CAQSP), surf. associated cation concentration (CACATT), cation

concentration (CACAT)

Cumulative no. of iteration for geochem option (ITCUM)

B.6.4 Data Written to Well History Plotting Data File(s)

The information in the following list is always written to the well history plotting data files

(HIST01-HISTl) for each production well.

Printed at each WRHPV interval:

Cumulative pore volume, time in days, cumulative production (ft3, m3, or STB), water oil

ratio, cumulative oil recovery, total production rate (ft3/day, m3/day, or STB/day)

Water cut, oil cut, microemulsion cut, gas cut (only if IGAS = 1)

Wellbore pressure for each well block (psi or kPa)

Wellbore temperature (•F or •C) (only if IENG=1)

For I = 1, N:

If ICF(I) = 1: phase concentration for component N (C(I,L), L=1,MXP), total

concentration of component N (CTOT(I))

Lower effective salinity, upper effective salinity, effective salinity (only if ICSE = 1)

For IREACT >1

Independent species concentration, mole/liter of water (CAQSP(KK), KK = 1,

NIAQ)

Dependent species concentration, mole/liter of water (CAQSP(KK), KK =

NIAQ+1,NFLD) (only if IRSPS>0)

Phase Concentration of (inj.+genereated) surfactant (PSURF(I,L), L = 1,3), total

concentration of (inj.+ generated) surfactant (TSURF) (only if IREACT = 3 or 5)

Concentration of solid components, mole/liter of pore volume (CSLDT(KK), KK =

1, NSLD) (only if NSLD>0)

Log10 of interfacial tension between water/microemulsion and oil/microemulsion

(XIFT1, XIFT2) (only if ICNM>0) (dyne/cm)

The information in the following list is always written to the well history plotting data files

for each injection well.

Printed at each WRHPV interval:

Cumulative pore volume, time in days, cumulative injection (ft3, m3, or STB), injection rate

(ft3/day, m3/day, or STB/day)

Wellbore pressure for each well block (psi or kPa)
Appendix B - UTCHEM Local Grid Refinement User's Guide

311

Pressure drop between the wells (for the specific case of one injector and one producer only)

or pressure drop between the pressure tabs (when NG>0, NY=1, NZ=1, see line 4.4.93) (psi

or kPa)

B.6.5 Data Written to Overall History Plotting Data File

The information in the following list is always written to the overall history plotting data file

(OVERAL).

Printed at each WRHPV interval:

Cumulative pore volume, time in days, volumetric averaged reservoir pressure (psi or kPa),

cumulative oil produced (%OOIP), cumulative oil produced (bbls or m3), volumetric

averaged reservoir temperature (•F or •C) (only if IENG=1)

Total injection rate (B/D or m3/day), total production rate (B/D or m3/day), total fluid

injected (1000 bbls or m3), total fluid produced (1000 bbls or m3)

Overall production rate for each phase (QBAR(L) for L = 1, MXP where MXP=3 if IGAS=0

and MXP=4 if IGAS =1) (B/D or m3/day)

Average cut for each phase (FBAR(L) for L = 1, MXP where MXP=3 if IGAS=0 and

MXP=4 if IGAS =1)

Average saturation for each phase (SBAR(L) for L = 1, MXP where MXP=3 if IGAS=0 and

MXP=4 if IGAS =1)

If ICF(3) = 1: Cumulative surfactant injected (bbls or m3), Cumulative surfactant produced

(bbls or m3), adsorbed surfactant (bbls or m3), retained surfactant (bbls or m3)

If ICF(4) = 1: Cumulative polymer injected (wt%), Cumulative polymer produced (wt%),

adsorbed polymer (wt%), retained polymer (wt%)

B.6.6 List of Elements and Reactive Species for IREACT = 2

Elements or pseudo-element: Hydrogen (reactive), Sodium, Calcium,

Magnesium, Carbonate, Chlorine, Oxygen, S

(inj. surfactant)

Independent aqueous or oleic

species:

H+, Na+,Ca2+, Mg2+,CO2-

3

, Cl-, S-, H2O

Dependent aqueous or oleic species: Ca(OH)+, Mg(OH)+, Ca(HCO3)

+,

Mg(HCO3)

+, OH-

, HCO3, H2CO3, CaCOo

3

 

, MgCOo

3

 

Solid species: CaCO3 (Calcite), Ca(OH)2 (Calcium

hydroxide), MgCO3 (Magnesite), Mg(OH)2

(Magnesium hydroxide)

Adsorbed cations:

__

H + , 

__

Na + , 

__

Ca 2+, 

__

Mg 2+

Adsorbed cations on micelles: =

Na + , 

=

Ca 2+, 

=Mg 2+
Appendix B - UTCHEM Local Grid Refinement User's Guide

312

Aqueous reactions Equilibrium constant

H2O K

eq

1∅♦

 H

+

 + OH- K

eq

1

 = [ H ]

+

 [ OH ]

-

H

+

 + CO2-

3

K

eq

2 ∅♦

 HCO3 K

eq

2

 = 







 HCO3

[ H ]

+







CO 

2-

3

Ca2+ + H2O K

eq

3∅♦

 Ca(OH)+ + H+

K

eq

3

 = 

[ Ca(OH) ]

+

[ H ]

+

[ Ca ]

2+

Mg2+ + H2O K

eq

4∅♦

 Mg(OH)+ + H+

K

eq

4

 = 

[ Mg(OH) ]

+

[ H ]

+

[ Mg ]

2+

Ca2+ + H+

+ CO2-

3

K

eq

5∅♦

 Ca(HCO3)

+

K

eq

5

 = 







Ca(HCO 

3

)

+

[ Ca ]

2+ 





CO 

2-

3

[ H ]

+

Mg2+ + H+

+ CO2-

3

K

eq

6∅♦

 Mg(HCO3)

+

K

eq

6

 = 





 Mg(HCO 3

)

+

[ Mg ]

2+ 





CO 

2-

3

[ H ]

+

2H+

+ CO2-

3

K

eq

7∅♦

 H2CO3 K

eq

7

 = 

[ H2

CO3]







CO 

2-

3

[ H ]

+ 2

Ca2+ + CO2-

3

K

eq

8∅♦

 CaCOo

3 K

eq

8

 = 







CaCO 

o

3

[ Ca ]

2+ 





CO 

2-

3

Mg2+ + CO2-

3

K

eq

9∅♦

 MgCOo

3 K

eq

9

 = 





 MgCO 

o

3

[ Mg ]

2+ 





CO 

2-

3

Dissolution reactions Solubility product

CaCO3

K

sp

1 ∅♦

 Ca2+ + CO2-

3

 

K

sp

1

 = [ Ca ]

2+ 





CO 

2-

3
Appendix B - UTCHEM Local Grid Refinement User's Guide

313

MgCO3

K

sp

2 ∅♦

 Mg2+ + CO2-

3

 

K

sp

2

 = [ Mg ]

2+ 





CO 

2-

3

Ca(OH)2

K

sp

3 ∅♦

 Ca2+ + 2OH- K

sp

3

 = [ Ca ]

2+ [ H ]+ -2

Mg(OH)2

K

sp

4 ∅♦

 Mg2+ + 2OH- K

sp

4

 = [ Mg ]

2+ [ H ]+ -2

Exchange reactions (on clay) Exchange equilibrium constant

2

__

Na + + Ca2+ 

K

ex

1 ∅♦

 2Na+ + 

__

Ca 2+

K

ex

1

 = 







__ 

Ca2+ [ Na ]

+ 2

[ Ca ]

2+ 





__ 

Na+

2

2

__

Na +

 + Mg2+ 

K

ex

2 ∅♦

 2Na+ + 

__

Mg 2+

K

ex

2

 = 







__ 

Mg2+ [ Na ]

+ 2

[ Mg ]

2+ 





__ 

Na+

2

_

H + + Na+

 + OH- K

ex

3 ∅♦

 

__

Na + + H2O

K

ex

3

 = 

[ Na ]

+







__ 

H

+







__ 

Na+

[ H ]

+

Exchange reactions (on micelle) Exchange equilibrium constant

2

=

Na + + Ca2+ 

K

exm

1 ∅♦

 2Na+ + 

=

Ca 2+

K

exm

1

 = 







= 

Ca2+ [ Na ]

+ 2







= 

Na+ 2

[ Ca ]

2+

where Kexm

1

= β

exm

1

[S-]

2

=

Na + + Mg2+

 

K

exm

2 ∅♦

 2Na+ + 

=Mg 2+

K

exm

2

 = 







=  Mg2+ [ Na ]

+ 2







= 

Na+ 2

[ Mg ]

2+

where Kexm

2

= β

exm

2

[S-]

B.6.7 List of Elements and Reactive Species for IREACT = 3

Elements or pseudo-element: Hydrogen (reactive), Sodium, Calcium,

Magnesium, Carbonate, A (from acid HA),

Oxygen, Chlorine, S (Injected surfactant )
Appendix B - UTCHEM Local Grid Refinement User's Guide

314

Independent aqueous or oleic

species:

H+, Na+,Ca2+, Mg2+,CO2-

3

, HAo, Cl-, S-,

H2O

Dependent aqueous or oleic species: Ca(OH)+, Mg(OH)+, Ca(HCO3)

+, HAw,

Mg(HCO3)

+, OH-

, HCO3, A-, H2CO3,

CaCOo

3

 , MgCOo

3

 

Solid species: CaCO3 (Calcite), Ca(OH)2 (Calcium

hydroxide), MgCO3 (Magnesite), Mg(OH)2

(Magnesium hydroxide)

Adsorbed cations:

__

H + , 

__

Na + , 

__

Ca 2+, 

__

Mg 2+

Adsorbed cations on micelles: =

Na + , 

=

Ca 2+, 

=Mg 2+

Aqueous reactions Equilibrium constant

H2O K

eq

1∅♦

 H

+

 + OH- K

eq

1

 = [ H ]

+

 [ OH ]

-

 

HAw

 + OH- K

eq

2∅♦

 A

-

 + H2O K

eq

2

 = 

[ A ]

-

[ H ]

+

[ HAw ]

H

+

 + CO2-

3

K

eq

3 ∅♦

 HCO3 K

eq

3

 = 







 HCO3

[ H ]

+







CO 

2-

3

Ca2+ + H2O K

eq

4∅♦

 Ca(OH)+ + H+

K

eq

4

 = 

[ Ca(OH) ]

+

[ H ]

+

[ Ca ]

2+

Mg2+ + H2O K

eq

5∅♦

 Mg(OH)+ + H+

K

eq

5

 = 

[ Mg(OH) ]

+

[ H ]

+

[ Mg ]

2+

Ca2+ + H+

+ CO2-

3

K

eq

6∅♦

 Ca(HCO3)

+

K

eq

6

 = 







Ca(HCO 

3

)

+

[ Ca ]

2+ 





CO 

2-

3

[ H ]

+

Mg2+ + H+

+ CO2-

3

K

eq

7∅♦

 Mg(HCO3)

+

K

eq

7

 = 





 Mg(HCO 3

)

+

[ Mg ]

2+ 





CO 

2-

3

[ H ]

+
Appendix B - UTCHEM Local Grid Refinement User's Guide

315

2H+

+ CO2-

3

K

eq

8∅♦

 H2CO3 K

eq

8

 = 

[ H2

CO3]







CO 

2-

3

[ H ]

+ 2

Ca2+ + CO2-

3

K

eq

9∅♦

 CaCOo

3 K

eq

9

 = 







CaCO 

o

3

[ Ca ]

2+ 





CO 

2-

3

Mg2+ + CO2-

3

K

eq

10 ∅♦

 MgCOo

3 K

eq

10 = 





 MgCO 

o

3

[ Mg ]

2+ 





CO 

2-

3

Partitioning of HA Partition coefficient

HAo

KD∅♦

 HAw KD

 = 

[ HAw ] water

[ HAo ] oil

Dissolution reactions Solubility product

CaCO3

K

sp

1 ∅♦

 Ca2+ + CO2-

3

 

K

sp

1

 = [ Ca ]

2+ 





CO 

2-

3

MgCO3

K

sp

2 ∅♦

 Mg2+ + CO2-

3

 

K

sp

2

 = [ Mg ]

2+ 





CO 

2-

3

Ca(OH)2

K

sp

3 ∅♦

 Ca2+ + 2OH- K

sp

3

 = [ Ca ]

2+ [ H ]+ -2

Mg(OH)2

K

sp

4 ∅♦

 Mg2+ + 2OH- K

sp

4

 = [ Mg ]

2+ [ H ]+ -2

Exchange reactions (on matrix) Exchange equilibrium constant

2

__

Na + + Ca2+ 

K

ex

1 ∅♦

 2Na+ + 

__

Ca 2+

K

ex

1

 = 







__ 

Ca2+ [ Na ]

+ 2

[ Ca ]

2+ 





__ 

Na+

2

2

__

Na +

 + Mg2+ 

K

ex

2 ∅♦

 2Na+ + 

__

Mg 2+

K

ex

2

 = 







__ 

Mg2+ [ Na ]

+ 2

[ Mg ]

2+ 





__ 

Na+

2
Appendix B - UTCHEM Local Grid Refinement User's Guide

316

_

H + + Na+

 + OH- K

ex

3 ∅♦

 

__

Na + + H2O

K

ex

3

 = 

[ Na ]

+







__ 

H

+







__ 

Na+

[ H ]

+

Exchange reactions (on micelle) Exchange equilibrium constant

2

=

Na + + Ca2+ 

K

exm

1 ∅♦

 2Na+ + 

=

Ca 2+

K

exm

1

 = 







= 

Ca2+ [ Na ]

+ 2







= 

Na+ 2

[ Ca ]

2+

where Kexm

1

= β

exm

1

{[A-] +[S-]}

2

=

Na + + Mg2+

 

K

exm

2 ∅♦

 2Na+ + 

=Mg 2+

K

exm

2

 = 







=  Mg2+ [ Na ]

+ 2







= 

Na+ 2

[ Mg ]

2+

where Kexm

2

= β

exm

2

{[A-] +[S-]}

B.6.8 List of Elements and Reactive Species for IREACT = 4 or 6

Elements or pseudo-element: Hydrogen (reactive), Sodium, Calcium,

Magnesium, Carbonate, Aluminum, Silicon,

Oxygen, Chlorine, S (Injected surfactant )

Independent aqueous or oleic

species:

H+, Na+,Ca2+, Mg2+, Al3+, CO2-

3

, Cl-, S-,

H4SiO4, H2O

Dependent aqueous or oleic species: Ca(OH)+, Mg(OH)+, Al(OH)2-,Al(OH)2

-

,

Ca(HCO3)

+, Mg(HCO3)+, OH-

, HCO3,

H3SiO4

-

, H2SiO4

2-

, HSi2O6

3-, Si2O52-

,

Al(OH)4

-

, H2CO3, CaCOo

3

 , MgCOo

3

 

Solid species: CaCO3 (Calcite), Al2Si2O5(OH)4

(Kaolinite), MgCO3 (Magnesite),

NaAlSi2O6.H2O (Analcite), SiO2 (Silica),

Mg(OH)2 (Magnesium Hydroxide)

Adsorbed cations on rock surface:

__

H + , 

__

Na + , 

__

Ca 2+, 

__

Mg 2+

Adsorbed cations on micelles: =

Na +, 

=

Ca 2+, 

=Mg 2+
Appendix B - UTCHEM Local Grid Refinement User's Guide

317

Aqueous reactions Equilibrium constant

H2O 

K

eq

1 ∅♦

 H

+

 + OH- K

eq

1

 = [ H ]

+ [ OH ]-

 

H

+

 + CO2-

3

K

eq

2 ∅♦

 HCO -

3 K

eq

2

 = 







 HCO3

[ H ]

+







CO 

2-

3

Ca2+

 + H2O 

K

eq

3 ∅♦

 Ca(OH)+ + H+

K

eq

3

 = 

[ Ca(OH) ]

+

[ H ]

+

[ Ca ]

2+

Mg2+

 + H2O 

K

eq

4 ∅♦

 Mg(OH)+ + H+

K

eq

4

 = 

[ Mg(OH) ]

+

[ H ]

+

[ Mg ]

2+

Al3+ + H2O 

K

eq

5 ∅♦

 Al(OH)2+ + H+ K

eq

5

 = 

[Al(OH) ]

2+ [H ]+

[Al ]

3+

Al3+ + 2H2O 

K

eq

6 ∅♦

Al(OH)2

+ + 2H+ K

eq

6

 = 

[ Al(OH)2 ]

+ [H ]+ 2

[Al ]

3+

Al3+ + 4H2O 

K

eq

7 ∅♦

Al(OH)4

-

 + 4H+ K

eq

7

 = 

[ Al(OH)4 ]

-

[H ]

+ 4

[Al ]

3+

H4

SiO4

K

eq

8 ∅♦

 H

+

 + H3SiO4

-

K

eq

8

 = 

[ H ]

+

[ H3SiO4 ]

-

[ H4 ]

SiO4

H4

SiO4

K

eq

9 ∅♦

 2H+ + H2SiO4

2-

K

eq

9

 = 

[ H ]

+ 2

[ H2SiO4 ]

2-

[ H4 ]

SiO4

Ca2+ + H+

+ CO2-

3

K

eq

10 ∅♦

 Ca(HCO3)

+

K

eq

10 = 







 Ca(HCO3

)

+

[ Ca ]

2+ 





CO 

2-

3

[ H ]

+

Mg2+

 + H++ CO2-

3

K

eq

11 ∅♦

 Mg(HCO3)

+

K

eq

11 = 





 Mg(HCO 3

)

+

[ Mg ]

2+







 CO2-

3

[ H ]

+
Appendix B - UTCHEM Local Grid Refinement User's Guide

318

2H++ CO2-

3

K

eq

12 ∅♦

 H2CO3 K

eq

12 = 

[ H2

CO3]







CO 

2-

3

[ H ]

+ 2

2H4

SiO4

K

eq

13 ∅♦

 2H2O + 3H+ + HSi2O6

3-

K

eq

13 = 

[ H ]

+ 3

[ HSi2O6 ]

3-

[ H4 ]

SiO4

2

2H4

SiO4

K

eq

14 ∅♦

 2H+ + 3H2O + Si2O5

2-

K

eq

14 = 

[ H ]

+ 2

[ Si2O5 ]

2-

[ H4 ]

SiO4

2

Solid species Solubility product

CaCO3 K

sp

1

 = [ Ca ]

2+ 





CO 

2-

3

MgCO3 K

sp

2

 = [ Mg ]

2+ 





CO 

2-

3

SiO2 K

sp

3

 = [H4SiO4]

Al2Si2O5(OH)4 K

sp

4

 = [ H ]

+ -6[ Al ]3+ 2

[H4SiO4]

2

NaAlSi2O6.H2O K

sp

5

 = [ H ]

+ -4[ Na ]+

[ Al ]

3+ [H4SiO4]

2

Mg(OH)2 K

sp

6

 = [ Mg ]

2+ [ H ]+ -2

Exchange reactions (on matrix) Exchange equilibrium constant

2

__

Na

+

 + Ca2+ 

K

ex

1 ∅♦

 2Na+ + 

__

Ca 2+

K

ex

1

 = 







__ 

Ca2+ [ Na ]

+ 2

[ Ca ]

2+ 





__ 

Na

+ 2

2

__

Na

+

 + Mg2+

 

K

ex

2 ∅♦

 2Na+ + 

__

Mg 2+

K

ex

2

 = 







__ 

Mg2+ [ Na ]

+ 2

[ Mg ]

2+ 





__ 

Na

+ 2
Appendix B - UTCHEM Local Grid Refinement User's Guide

319

_

H

+

 + Na+ + OH- K

ex

3 ∅♦

 

__

Na

+

 + H2O

K

ex

3

 = 

[ Na ]

+











_ 

H

+







__ 

Na

+

[ H ]

+

Exchange reactions (on micelle) Exchange equilibrium constant

2

=

Na + + Ca2+ 

K

exm

1 ∅♦

 2Na+ + 

=

Ca 2+

K

exm

1

 = 







= 

Ca2+ [ Na ]

+ 2







= 

Na+ 2

[ Ca ]

2+

where Kexm

1

= β

exm

1

[S-]

2

=

Na + + Mg2+

 

K

exm

2 ∅♦

 2Na+ + 

=Mg 2+

K

exm

2

 = 







=  Mg2+ [ Na ]

+ 2







= 

Na+ 2

[ Mg ]

2+

where Kexm

2

= β

exm

2

[S-]

B.6.9 List of Elements and Reactive Species for IREACT = 5

Elements or pseudo-element: Hydrogen (reactive), Sodium, Calcium,

Magnesium, Carbonate, Aluminum, Silicon,

A (from acid HA), Oxygen, Chlorine, S

(InjectedSurfactant )

Independent aqueous or oleic

species:

H+, Na+, Ca2+, Mg2+, Al3+, CO2-

3

, H4SiO4,

HAo, H2O

Dependent aqueous species: Ca(OH)+, Mg(OH)+, Al(OH)2-, Al(OH)2

-

,

Ca(HCO3)

+, Mg(HCO3)+, A-

, OH-, HCO3,

H3SiO4

-

, H2SiO4

2-

, HSi2O6

3-, Si2O52-

,

Al(OH)4

-

, H2CO3, HAw

Solid species: CaCO3 (Calcite), Al2Si2O5(OH)4

(Kaolinite), MgCO3 (Magnesite),

NaAlSi2O6

.H2O (Analcite), SiO2 (Silica),

Mg(OH)2, (Magnesium Hydroxide)

Adsorbed cations on rock surface:

__

H + , 

__

Na + , 

__

Ca 2+, 

__

Mg 2+

Adsorbed cations on micelles: =

Na +, 

=

Ca 2+, 

=Mg 2+
Appendix B - UTCHEM Local Grid Refinement User's Guide

320

Aqueous reactions Equilibrium constant

H2O 

K

eq

1 ∅♦

 H

+

 + OH- K

eq

1

 = [ H ]

+ [ OH ]-

HAw

 + OH- K

eq

2 ∅♦

 A

-

 + H2O K

eq

2

 = 

[ A ]

-

[ H ]

+

[ HAw ]

H

+

 + CO2-

3

K

eq

3 ∅♦

 HCO3 K

eq

3

 = 







 HCO3

[ H ]

+







CO 

2-

3

Ca2+

 + H2O 

K

eq

4 ∅♦

 Ca(OH)+ + H+

K

eq

4

 = 

[ Ca(OH) ]

+

[ H ]

+

[ Ca ]

2+

Mg2+

 + H2O 

K

eq

5 ∅♦

 Mg(OH)+ + H+

K

eq

5

 = 

[ Mg(OH) ]

+

[ H ]

+

[ Mg ]

2+

Al3+ + H2O 

K

eq

6 ∅♦

 Al(OH)2+ + H+ K

eq

6

 = 

[Al(OH) ]

2+ [H ]+

[Al ]

3+

Al3+ + 2H2O 

K

eq

7 ∅♦

Al(OH)2

+ + 2H+ K

eq

7

 = 

[ Al(OH)2 ]

+ [H ]+ 2

[Al ]

3+

Al3+ + 4H2O 

K

eq

8 ∅♦

Al(OH)4

-

 + 4H+ K

eq

8

 = 

[ Al(OH)4 ]

-

[H ]

+ 4

[Al ]

3+

H4

SiO4

K

eq

9 ∅♦

 H

+

 + H3SiO4

-

K

eq

9

 = 

[ H ]

+

[ H3SiO4 ]

-

[ H4 ]

SiO4

H4

SiO4

K

eq

10 ∅♦

 2H+ + H2SiO4

2-

K

eq

10 = 

[ H ]

+ 2

[ H2SiO4 ]

2-

[ H4 ]

SiO4

Ca2+ + H+

+ CO2-

3

K

eq

11 ∅♦

 Ca(HCO3)

+

K

eq

11 = 







 Ca(HCO3

)

+

[ Ca ]

2+ 





CO 

2-

3

[ H ]

+
Appendix B - UTCHEM Local Grid Refinement User's Guide

321

Mg2+

 + H++ CO2-

3

K

eq

12 ∅♦

 Mg(HCO3)

+

K

eq

12 = 





 Mg(HCO 3

)

+

[ Mg ]

2+







 CO2-

3

[ H ]

+

2H++ CO2-

3

K

eq

13 ∅♦

 H2CO3 K

eq

13 = 

[ H2

CO3]







CO 

2-

3

[ H ]

+ 2

2H4

SiO4

K

eq

14 ∅♦

 2H2O + 3H+ + HSi2O6

3-

K

eq

14 = 

[ H ]

+ 3

[ HSi2O6 ]

3-

[ H4 ]

SiO4

2

2H4

SiO4

K

eq

15 ∅♦

 2H+ + 3H2O + Si2O5

2-

K

eq

15 = 

[ H ]

+ 2

[ Si2O5 ]

2-

[ H4 ]

SiO4

2

Partitioning of HA Partition coefficient

HAo

KD∅♦

 HAw KD

 = 

[ HAw ] water

[ HAo ] oil

Solid species Solubility product

CaCO3 K

sp

1

 = [ Ca ]

2+ 





CO 

2-

3

MgCO3 K

sp

2

 = [ Mg ]

2+ 





CO 

2-

3

SiO2 K

sp

3

 = [H4SiO4]

Al2Si2O5(OH)4 K

sp

4

 = [ H ]

+ -6[ Al ]3+ 2

[H4SiO4]

2

NaAlSi2O6.H2O K

sp

5

 = [ H ]

+ -4[ Na ]+

[ Al ]

3+ [H4SiO4]

2

Mg(OH)2 K

sp

6

 = [ Mg ]

2+ [ H ]+ -2
Appendix B - UTCHEM Local Grid Refinement User's Guide

322

Exchange reactions (on matrix) Exchange equilibrium constant

2

__

Na

+

 + Ca2+ 

K

ex

1 ∅♦

 2Na+ + 

__

Ca 2+

K

ex

1

 = 







__ 

Ca2+ [ Na ]

+ 2

[ Ca ]

2+ 





__ 

Na

+ 2

2

__

Na

+

 + Mg2+

 

K

ex

2 ∅♦

 2Na+ + 

__

Mg 2+

K

ex

2

 = 







__ 

Mg2+ [ Na ]

+ 2

[ Mg ]

2+ 





__ 

Na

+ 2

_

H

+

 + Na+ + OH- K

ex

3 ∅♦

 

__

Na

+

 + H2O

K

ex

3

 = 

[ Na ]

+











_ 

H

+







__ 

Na

+

[ H ]

+

Exchange reactions (on micelle) Exchange equilibrium constant

2

=

Na + + Ca2+ 

K

exm

1 ∅♦

 2Na+ + 

=

Ca 2+

K

exm

1

 = 







= 

Ca2+ [ Na ]

+ 2







= 

Na+ 2

[ Ca ]

2+

where Kexm

1

= β

exm

1

{[A-] +[S-]}

2

=

Na + + Mg2+

 

K

exm

2 ∅♦

 2Na+ + 

=Mg 2+

K

exm

2

 = 







=  Mg2+ [ Na ]

+ 2







= 

Na+ 2

[ Mg ]

2+

where Kexm

2

= β

exm

2

{[A-] +[S-]}
318

Appendix C

Discretized Flow Equations

The coordinate system can be either cartesian, radial, or curvilinear. The discretized equations presented

here are for the cartesian coordinate system referred to as (x, y, z). The finite-difference grid is blockcentered and numbered from 1 to NxNyNz, where Nx, Ny, and Nz correspond to the number of gridblocks in

the x, y, and z directions, respectively. The volume of the mth block (i, j, k) is ΔVm=ΔxmΔymΔzm where i,

j, and k correspond to the x, y, and z coordinate directions, respectively. The time increment δt is from

timestep n to timestep n+1. The delta operator δ denotes discrete differences:

δt

f

n = fn +1 − fn

δx

fm = fm − fm−1,δxf

i = fi − fi−1

δyfm = fm − fm−Nx ,δyf

j = fj − fj−1

δz

fm = fm − fm−NxNy, δzfk = fk − fk −1

(C.1)

Most variables, including pressure, concentrations, adsorbed concentrations, saturations, capillary pressures,

phase properties such as density, viscosity, interfacial tension, and relative permeabilities are calculated and

stored at gridblock centers. Some variables, such as transmissibilities and phase velocities, are evaluated at

the faces between gridblocks. Applying the finite-difference approximations to the species conservation

equations (Eq. C.1) and the pressure equation (Eq. C.10), we obtain a system of finite-difference equations.

For the purpose of simplicity, the system of equations is illustrated for a two-dimensional problem even

though the code is three-dimensional.

The species conservation equation for species κ at gridpoint m is

Faκ

( )m

n +1

= Faκ

( )m

n

+ δt

t

n

Ftκ + F ( qκ )m

n 

(C.2)

The superscript n indicates that the variables are evaluated using both old timestep (n) variables and new

timestep (n+1) variables.

Faκ is the accumulation term

Faκ

( )m

= φRΔV  ̃ C κ

1 + Cf + Cκ

0 { [ ( )(PR − PR0 )]}m

(C.3)

Ftκ is the transport term as
Appendix C - Discretized Flow Equations

319

 

F( tκ )m

n 

= −δx

1 + Cκ

0

[ (PR − PR0 )]m

n+1

(Cxκl )m

n

T ( xl )m

n

{l=1

np

∑

⋅ δx PR

n+1

+ PclR

n

( )m+1

− γ xl

n

( )m

δx(D)m+1

 

 

 

 

+ K xxκl

n ( )m

δx Cκl

n

( )m+1

+ K xyκl

n ( )m

δy Cκl

n

( )m

+ Cκl

n

( )m+ Nx

 

 

 

 

   

−δx

1 + Cκ

0

[ (PR − PR0 )]m

n+1

(Cyκl )m

T ( yl )m

   

l=1

np

∑

⋅ δy

PR

n+1 + PclRn

( )m+Nx

− γ yl

n

( )m

δy(D)m+Nx

 

 

 

 

+ K yyκl

n ( )

m

δy Cκl

n

( )

m+Nx

+ K yxκl

n ( )

m

δ x Cκl

n

( )

m

+ Cκl

n

( )

m+1

 

 

 

 

   

(C.4)

where Cxκl, Cyκl, 

 

T xl , and 

 

T yl are defined by

 

(Cxκl )m

= (Cκl )m+ φm rxm (Cκl ) { [ m ]}δ x (Cκl )m+12

(Cyκl )m

= (Cκl )m+ φm rym (Cκl ) { [ m ]}δ y (Cκl )m+Nx 2

(C.5)

 

T ( xl )m= k( rl )mφm rxm k( rl ) { [ m ]}δxk( rl )m+1 { 2}(Tx μl )m

T ( yl )m= k( rl )mφm rym k( rl ) { [ m ]}δyk( rl )m+Nx { 2}(Ty μl )m

(C.6)

Tx

( )m and (Ty )m, given by

(Tx )m

= 2(ΔyΔz)mΔxm km + Δxm+1 ( km +1)

(Ty )

m

= 2(ΔxΔz)mΔym km + Δym+Nx ( km+Nx )

(C.7)

are transmissibilities.

φm is the flux limiter function defined as follows (Liu et al., 1994):

φ m =

2 fm+1/ 2 ( − fm)

fm+1 − fm

(C.8)

The magnitude of the limiting depends on the smoothness of the data, measured by the ratio of consecutive

cell gradients r:

rm =

fm − fm−1

fm+1 − fm

(C.9)

and φ(r) = max 0, min φb ,

2 + r

3

 

      

     .
Appendix C - Discretized Flow Equations

320

 

rxm (Cκl ) [ m ]= δx (Cκl )mδx (Cκl )m+1

rym (Cκl ) [ m ]= δy (Cκl )m

δy (Cκl )m+ Nx

rxm k( rl ) [ m ]= δ xk( rl )m

δx

k( rl )m+1

rym k( rl ) [ m ]= δ yk( rl )m

δy

k( rl )m +Nx

(C.10)

 

K xxκl, K yyκl,K xyκl,and K yxκl

 are the dispersion coefficients defined by

 

K ( xxκl )m

= Δym Δzm [(Δxm + Δxm+1) 2] φR

SlKxxκl + δtt

n

uxl

2

( φR )m

K ( xyκl )m

= Δym Δzm [Δym + (Δym−Nx + Δym+Nx ) 2] φR

SlKxyκl + δ tt

n

u ( yl φR)m

K ( yyκl )m

= Δx mΔzm [(Δym + Δym+Nx ) 2] φR

SlKyyκl + δtt

n

uyl

2

( φR )m

K ( yxκl )m= Δy mΔzm Δxm + Δxm−1 + Δxm+1 [ ( ) 2] φ RSlKyxκl

+ δt

t

n

uyluxl ( φR )m

(C.11)

The average specific weight of phase l is calculated from

 

γ ( xl )m= γ( lElΔx)m+ γ( lElΔx) [ m+1] (ElΔx)m+ (ElΔx) [ m+1]

γ ( yl )

m

= γ( lElΔy)m+ γ( lElΔx)m+Nx [ ] (ElΔy)m+(ElΔy)m+Nx [ ]

(C.12)

where El is the existence index of phase l and is defined as

 

El

( )m

=

0 (Sl )m

= 0

1 (Sl )m

> 0

 

  

  (C.13)

Fqκ is the source and sink term:

 

F( qκ )

m

n 

= Ql

n + (PI)

l

n Pwf − PR

n+1 − PclRn

[ ( )]Cκl

n

l=1

np

∑

 

  

  

+φRΔV 1 + Cf + Cκ

0

( )PR

n +1

[ ( − PR0)] Sl

n

rκl

+ rκs

l=1

np

∑

 

 

  

 

 

  

 

  

  

m

(C.14)

which includes wells constrained by either rate or pressure and the production from chemical reactions.

The pressure equation at gridpoint m is

Fa

n+1

− Ft1

n ( )

m

= Fa( )m

n

+ δt

t

n

(Ft2 + Fq )m

n

(C.15)

Fa is the total accumulation
Appendix C - Discretized Flow Equations

321

Fa

( )m= φRΔVCt( PR)m(C.16)

Ft1 is the total transport as a function of reference phase pressure:

 

Ft1

n ( )m

= −δx (T xl )m

n

1 + (PR − PR0 ) Cκ

0Cκl

κ =1

ncv

∑

 

 

  

 

 

  

m

n

δx PR

n+1

( )m+1

l =1

np

∑

 

  

  

 

  

  

−δy (T yl )m

n

1 + (PR − PR0 ) Cκ

0Cκl

κ =1

ncv

∑

 

 

  

 

 

  

m

n

δy PR

n+1

( )m+Nx

l =1

np

∑

 

  

  

 

  

  

(C.17)

Both Ft2, the total transport as a function of capillary pressure and gravity, and Fq, the total source or sink,

are evaluated using values of the old timestep:

 

F( t2 )m

= −δx T ( xl )m

1+ (PR − PR0 ) Cκ

0Cκl

κ =1

ncv

∑

 

 

  

 

 

  l=1

np

∑

m

⋅ δ x

P( clR )m+1

− γ ( xl )mδx (D) [ m +1]

 

  

  

 

  

  

−δy T ( yl )m

1+ (PR − PR0 ) Cκ

0Cκl

κ =1

ncv

∑

 

 

  

 

 

  l=1

np

∑

m

⋅ δ y

P( clR )m+Nx − γ ( yl )m

δy

(D) [ m+Nx ]

 

  

  

 

  

  

(C.18)

 

(Fq )m

= Ql +(PI)

l {[ (Pwf − PR − PclR )]Cκl}m

l=1

np

∑

κ =1

ncv

∑ (C.19)

Coefficients of reference phase pressure PR on the left-hand side of Eq. C.15 are concentration-dependent

and are evaluated using values at the old timestep. The equation written for all gridblocks in the spatial

domain results in a system of equations with reference phase pressure PR as the only unknown and is solved

implicitly. The conservation equations (Eq. C.2) are then solved explicitly for overall concentrations.

Phase concentrations and saturations are obtained by phase equilibria calculations. Other phase pressures

are obtained using capillary pressure relations.
322

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