bluuebunny/crossref_metadata_2025 huggingface dataset:
Richardson's Iteration With Dynamic Parameters and the SIP Incomplete Factorization for the Solution of Linear Systems of Equations
Authors: Saylor Paul E.
Published: December 2007

Reservoir simulation yields a system of linear algebraic equations, Ap = q, that may be solved by Richardson's iterative method, p(k+1)= p(k)+ tkr(k), where r(k)= q − Ap(k) is the residual and t0, … tk are acceleration parameters. The incomplete factorization, Kα, of the strongly implicit procedure (SIP) yields an improvement of Richardson's method, p(k+1)=p(k)+tkKα−1r(k). Parameter α originates from SIP. The product of the L and U factors produced by SIP gives Kα = LU. The best values of the tk acceleration parameters may be computed dynamically by an efficient algorithm; the best value of α must be found by trial and error, which is not hard for only one value. The advantages of the method are (1) it always converges, (2) with the exception of the α parameter, parameters are computed dynamically, and (3) convergence is efficient for test problems characterized by heterogeneities and transmissibilities varying over 10 orders of magnitude. The test problems originate from field data and were suggested by industry personnel as particularly difficult. Dynamic computation of parameters is also a feature of the conjugate gradient method, but the iteration described here does not require A to be symmetric. Matrix Kα−1 must be such that the real part of each eigenvalue is nonnegative, or the real part of each is nonpositive, but not both positive and negative. It is in this sense that the method always converges. This condition is satisfied by many simulator-generated matrices. The method also may be applied to matrices arising from the simulation of other processes, such as chemical flooding.
A Numerical Model Coupling Reservoir and Horizontal Well-Flow Dynamics: Transient Behavior of Single-Phase Liquid and Gas Flow
Authors: Vicente Ronaldo , Sarica Cem , Ertekin Turgay
Published: December 2007

A fully implicit, 3D simulator with local refinement around the wellbore is developed to solve reservoir and horizontal well flow equations simultaneously for single-phase liquid and gas cases. The model consists of conservation of mass and Darcy's law in the reservoir, and mass and momentum conservation in the wellbore for isothermal conditions. The coupling requirements are satisfied by preserving the continuity of pressure and mass balance at the sandface. The proposed simulator is tested against and verified with the results obtained from a commercial code ECLIPSE-100, and available public domain simulators and semianalytical models.

The model can be used to simulate the transient pressure and flow rate behavior of both the reservoir and the horizontal wellbore. Traditional decoupling of the wellbore transients from the reservoir transients does not capture the horizontal well pressure and flow rate transients at early times because the interaction between the reservoir and wellbore is inherently neglected. Simulation runs with the proposed model reveal the actual characteristics of horizontal wellbore storage and unloading, as well as flow pattern determination during transient well testing using pressure derivative curves. The effects of permeability, formation thickness, well length, and fluid compressibility are also studied.
Mechanisms Causing Disproportionate Permeability Reduction in Porous Media Treated With Chromium Acetate/HPAM Gels
Authors: Willhite G. Paul , Zhu H. , Natarajan D. , McCool C. S. , Green D. W.
Published: December 2007

It is well established that treatment of porous rocks with gelled polymer systems can cause the permeability of water at residual oil saturation to be reduced by one to three orders of magnitude more than the permeability of oil at the water saturation that is immobile after treatment. This phenomenon is called disproportionate permeability reduction (DPR) and is of interest because application of gel treatments in production wells has potential to reduce water production.

The mechanisms that cause this phenomenon are not well understood. This paper describes how permeability to oil and water is developed in pore space that is filled with a chromium acetate/ partially hydrolyzed polyacrylamide (HPAM) gel and proposes a mechanism for DPR based on the interpretation of the experimental data. Experimental data for the flow of oil and brine were obtained in unconsolidated sandpacks and in Berea sandstone cores with and without residual oil saturation after a chromium acetate/Alcoflood 935 gelant was injected and gelled in situ.

Interpretation of the experimental data suggests that oil permeability develops as oil penetrates into the gel-filled pore space, dehydrating the gel by displacing brine from the gel structure and creating "new flow channels" within or around the gel. The "new pore space" is a fraction of the original porosity, and the permeability to oil is reduced substantially from its value before placement and in-situ gelation of the gelant. Subsequent brine injection displaces oil from these flow channels but traps some of the oil in the new pore space as a residual saturation. The trapping of residual oil in the new pore space causes the disproportionate reduction in brine permeability because the brine flows primarily in the pore channels created by dehydration of the gel even though the gel has some brine permeability. When gelant is placed in a matrix containing residual oil, dehydration of the gel reconnects some of the trapped oil, and the oil permeability increases. Subsequent brine displacement experiments conducted at the same pressure drop showed that initial brine permeability was reduced by factors of 100 to 1,000 more than the oil permeability, verifying the existence of DPR.
Linearly Supported Radial Flow—A Flow Regime in Layered Reservoirs
Authors: Guo Boyun , Stewart George , Toro Mario
Published: December 2007

This paper discusses pressure responses from a formation with two communicating layers in which a fully penetrated high-permeability layer is adjacent to a low-permeability layer. An analytical reservoir model is presented for well-test analysis of the layered systems, with the bottom of the low-permeability layer being a constant-pressure boundary. The strength of the support from the low-permeability layer is characterized with two parameters: layer bond constant and storage capacity.
Interpretation of Horizontal-Well Production Logs: Influence of Logging Tool
Authors: Ozkan E. , Sarica C. , Haci M.
Published: December 2007

This paper investigates the disturbance of horizontal-wellbore flow conditions by a production-logging tool and its influence on well-bore flow-rate and pressure measurements. An analytical model is used in the investigation, and single-phase liquid flow is assumed. It is shown that the influence of the production-logging tool manifests itself in low-conductivity and high-rate wells; this effect may be ignored if the dimensionless well conductivity exceeds 500 and the Reynolds number is lower than 100,000. Results indicate that production logs in low-conductivity horizontal wells may not display low-permeability zones along the well.
Validation of Near-Wellbore Fracture-Network Models With MDT
Authors: Verga F.M. , Giglio G. , Masserano F. , Ruvo L.
Published: December 2007

A new approach was attempted to validate the reconstructed internal geometry of a fractured reservoir by reproducing the reservoir dynamic behavior monitored during modular dynamic tests (MDTs). The description of the reservoir fracture network was achieved by integrating relevant data that could be collected from wireline logs, conventional cores, small drilling-mud-loss analysis, and field-scale observations from outcrop analog inspection. Fracture types, properties, and distributions were thus defined, and a static model of the fractured reservoir was generated stochastically. The dynamic behavior of the fractured system was reproduced by a finite-element flow model. Consistency was required between the observed and simulated pressure data to ensure that the reservoir geometry was modeled adequately. Analysis of the model response as a function of the assigned fracture parameters and comparison between the observed and simulated dynamic behavior allowed achievement of a satisfactory description of the reservoir effective fracture network.
Fast and Robust Algorithm for Compositional Modeling: Part I—Stability Analysis Testing
Authors: Firoozabadi Abbas , Pan Huanquan
Published: December 2007

Given pressure, temperature, and composition of a fluid, one desires to determine whether the single phase state is stable. This problem is, in principle, much simpler than phase-behavior calculations. For certain applications, such as compositional-reservoir modeling, stability testing can be the most important item for efficient phase-behavior calculations.

In this paper, we use the tangent-plane-distance (TPD) in the reduced space to perform stability analysis testing. The results reveal that there are major advantages in the reduced space. One interesting feature of the transformation is that the TPD surface becomes smooth and has one minimum. The combination of a single minimum and the surface smoothness contributes to a remarkable robustness in calculations.
Hydraulic Characterization of Fractured Reservoirs: Simulation on Discrete Fracture Models
Authors: Sarda S. , Jeannin L. , Basquet R. , Bourbiaux B.
Published: December 2007

Advanced characterization methodology and software are now able to provide realistic pictures of fracture networks. However, these pictures must be validated against dynamic data like flow-meter, well-test, interference-test, or production data and calibrated in terms of hydraulic properties. This calibration and validation step is based on the simulation of those dynamic tests. What has to be overcome is the challenge of both accurately representing large and complex fracture networks and simulating matrix/fracture exchanges with a minimum number of gridblocks. This paper presents an efficient, patented solution to tackle this problem. First, a method derived from the well-known dual-porosity concept is presented. The approach consists of developing an optimized, explicit representation of the fractured medium and specific treatments of matrix/fracture exchanges and matrix/matrix flows. In this approach, matrix blocks of different volumes and shapes are associated with each fracture cell depending on the local geometry of the surrounding fractures. The matrix-block geometry is determined with a rapid image-processing algorithm. The great advantage of this approach is that it can simulate local matrix/fracture exchanges on large fractured media in a much faster and more appropriate way. Indeed, the simulation can be carried out with a much smaller number of cells compared to a fully explicit discretization of both matrix and fracture media. The proposed approach presents other advantages owing to its great flexibility. Indeed, it accurately handles the cases in which flows are not controlled by fractures alone; either the fracture network may be not hydraulically connected from one well to another, or the matrix may have a high permeability in some places. Finally, well-test cases demonstrate the reliability of the method and its range of application.
Deconvolution of Well-Test Data as a Nonlinear Total Least-Squares Problem
Authors: Schroeter T. von , Hollaender F. , Gringarten A. C.
Published: December 2007

We present a new time-domain method for the deconvolution of well test data which is characterized by three novel features: (1) Instead of the rate-normalized pressure derivative itself, we estimate its logarithm, which makes explicit sign constraints unnecessary; (2) the formulation accounts for errors in both rate and pressure data, and thus amounts to a Total Least Squares (TLS) problem; and (3) regularization is based on a measure of the overall curvature of its graph. The resulting separable nonlinear TLS problem is solved using the Variable Projection algorithm. A comprehensive error analysis is given. The paper also includes tests with a simulated example and an application to a large field example.
The Application of Pulsed Neutron Decay Time Logs To Monitor Waterfloods With Changing Salinity
Authors: Youngblood W.E.
Published: December 2007

A combination of a pulsed neutron decay time log (TDT) TM) and an induction log has been successful in monitoring the early stages of a low- salinity waterflood. This technique has proved successful in determining the salinity of the mixture of flood-water and formation water so that water saturation can be determined behind the floodfront.

Introduction

During the early development of the giant Ghawar and Abqaiq fields of Saudi Arabia, Arabian American Oil Co. (Aramco) decided that the most efficient means of maintaining reservoir pressure would be through a peripheral water injection system. Accordingly, injection wells were located downdip from the original oil/water contact and as far away as 5 km from the nearest producing well.Initially, the sources of injection water were massive sandstone aquifers of the Wasia and Biyadh formations, which overlie the entire Ghawar and Abqaiq structure. Water salinities from these aquifers vary from 5,000 to 18,000 ppm. Water from the oil-producing zone of the Arab-D reservoir has salinities of about 200,000 ppm. In addition to the Wasia and Biyadh source, seawater with salinities of about 57,000 ppm now is being used in some areas.The producing interval, the Arab-D reservoir, typically is a calcarenitic-to-aphanitic limestone with some dolomitic stringers. Porosity is 20% on the average but can be as high as 30 to 32% in the upper part of the reservoir. Permeabilities range from a few part of the reservoir. Permeabilities range from a few millidarcies to over 1 darcy. Normally the producing wells are completed openhole with 7-in. casing set to the top of the reservoir. Usually the reservoir section is drilled out below the 7-in. casing approximately 200 to 250 ft below the casing shoe, several hundred feet above the present oil/water contact. Two-in. tubing, which will act as a kill string, normally is run just above the casing shoe, and the well is produced up the casing annulus.Most injection wells are completed openhole, the same way as producers. Injection rates tend to vary from area to area, ranging from 5,000 to more than 50,000 B/D.As early as 1960, a feasibility study made by Aramco successfully determined the rate of oil/water contact advance and calculated the oil displacement efficiency of waterflooding in the Arab-D reservoir. For this study, observation wells were drilled into the oil/water contact to observe fluid changes with time. The wells were completed openhole with a highly resistive fluid such as fuel oil in the wellbore. Initially the induction and sonic logs were run through the reservoir section. Subsequent induction logging was done at regularly scheduled periods to observe changes in oil saturation with time.The study assumed, at the time, that the advancing water at the oil/water contact would be entirely Arab-D formation water. Therefore, the values of water saturation could be calculated from induction and sonic logs using the classic Archie equation:

(1)

JPT

P. 957
Production Data Integration in Sand/Shale Reservoirs Using Sequential Self-Calibration and GeoMorphing: A Comparison
Authors: Wen X. -H. , Tran T. T. , Behrens R. A. , Gomez-Hernandez J. J.
Published: December 2007

The stochastic inversion of spatial distribution of lithofacies from multiphase production data is a difficult problem. This is true even for the simplest case, addressed here, of a sand/shale distribution and under the assumption that reservoir properties are constant within each lithofacies. Two geostatistically based inverse techniques, sequential self-calibration (SSC) and GeoMorphing (GM), are extended for such purposes and then compared with synthetic reference fields. The extension of both techniques is based on the one-to-one relationship existing between lithofacies and Gaussian deviates in truncated Gaussian simulation. Both techniques attempt to modify the field of Gaussian deviates while maintaining the truncation threshold field through an optimization procedure. Maintaining a fixed threshold field, which has been computed previously on the basis of prior lithofacies proportion data, well data, and other static soft data, guarantees preservation of the initial geostatistical structure. Comparisons of the two techniques using 2D and 3D synthetic data show that the SSC is very efficient in producing sand/shale realizations matching production data and reproducing the large-scale patterns displayed in the reference fields, although it has difficulty in reproducing small-scale features. GM is a simpler algorithm than SSC, but it is computationally more intensive and has difficulty in matching complex production data. Better results could be obtained with a combination of the two techniques in which SSC is used to generate realizations identifying large-scale features; then, these realizations could be used as input to GM for a final update to match small-scale details.
Dynamic Optimization of Waterflooding With Smart Wells Using Optimal Control Theory
Authors: Brouwer D. R. , Jansen J.-D.
Published: December 2007

We used optimal control theory as an optimization algorithm for the valve settings in smart wells. We focused on their use in injectors and producers for the waterflooding of heterogeneous reservoirs. As a followup to an earlier intuitive optimization approach, a systematic dynamic optimization approach based on optimal control theory was developed. The objective was to maximize recovery or net present value of the waterflooding process over a given time period. We investigated the scope for optimization under purely pressure- and purely rate-constrained operating conditions, and concluded that: (1) for wells operating on bottomhole-pressure constraints, the benefit of using smart wells is mainly reduced water production rather than increased oil production, and (2) for wells operating on rate constraints, there is generally a large scope for accelerating production and increasing recovery, in combination with a drastic reduction in water production.
Combining Global and Local Optimization Techniques for Automatic History Matching Production and Seismic Data
Authors: Mantica S. , Cominelli A. , Mantica G.
Published: December 2007

Gradient-based optimization techniques are increasingly adopted by oil industries for computer-aided history matching because of the great timesaving they can offer over conventional trial-anderror approaches. However, these methods lead to the identification of a single set of parameters, thus neglecting the inherent nonuniqueness of the solution of the underlying inverse problem. In this paper we propose a new approach that couples a chaotic sampling of parameter space with a local minimization technique. Through the evolution of a nonlinear dynamical system, we identify several points to be successively used as initial guesses for a local gradient-based optimizer. This provides a series of alternative matched models with different production forecasts that improve the understanding of the possible reservoir behaviors. The validity of this approach has been proven on a synthetic reservoir derived from a real west Africa field.
Mobility of Foam in Heterogeneous Media: Flow Parallel and Perpendicular to Stratification
Authors: Tanzil Dicksen , Hirasaki George J. , Miller Clarence A.
Published: December 2007

Experiments in homogeneous and heterogeneous sand-packed columns showed that the foam mobility in the two cases could differ by two orders of magnitude. The difference is because of the generation of foam lamellae by snap-off for flow across an abrupt increase in permeability. This mechanism is shown to be dependent on the degree of permeability contrast and the gas fractional flow. It has important implications for the degree of gravity segregation of gas and liquid in field-scale recovery processes.
Electrofacies Characterization and Permeability Predictions in Complex Reservoirs
Authors: Lee Sang Heon , Kharghoria Arun , Datta-Gupta Akhil
Published: December 2007

We propose a two-step approach to permeability prediction from well logs that uses nonparametric regression in conjunction with multivariate statistical analysis. First, we classify the well-log data into electrofacies types. This classification does not require any artificial subdivision of the data population; it follows naturally based on the unique characteristics of well-log measurements reflecting minerals and lithofacies within the logged interval. A combination of principal components analysis (PCA), model-based cluster analysis (MCA), and discriminant analysis is used to characterize and identify electrofacies types. Second, we apply nonparametric regression techniques to predict permeability using well logs within each electrofacies. Three nonparametric approaches are examined—alternating conditional expectations (ACE), generalized additive model (GAM), and neural networks (NNET)—and the relative advantages and disadvantages are explored.

We have applied the proposed technique to the Salt Creek Field Unit (SCFU), a highly heterogeneous carbonate reservoir in the Permian Basin, west Texas. The results are compared with three other approaches to permeability predictions that use data partitioning based on reservoir layering, lithofacies information, and hydraulic flow units (HFUs). An examination of the error rates associated with discriminant analysis for uncored wells indicates that data classification based on electrofacies characterization is more robust compared to other approaches. For permeability predictions, the ACE model appears to outperform the other nonparametric approaches.
Productivity of Selectively Perforated Vertical Wells
Authors: Yildiz Turhan
Published: December 2007

This study presents analytical models to predict the productivity of selectively perforated vertical wells. The models consider arbitrary phasing angle, nonuniform perforation size and length, and formation damage around perforations. The accuracy of the models was verified against the results from the experimental studies, the semi-analytical correlation, and the numerical models all available in the literature. Unique applications of the models are presented. A comprehensive sensitivity study showing the impact of different perforation schemes on well productivity is documented.
Thermal Stability of Surfactants for Reservoir Application
Authors: Handy L. L. , Amaefule J. O. , Ziegler V. M. , Ershaghi I.
Published: December 2007

The thermal stabilities of several sulfonate surfactants and one nonionic surfactant have been evaluated. The decomposition reactions have been observed to follow first-order kinetics. Consequently, a quantitative measure of a surfactant's stability at a given temperature is its half-life. Furthermore, the activation energy can be estimated from rate data obtained at two or more temperatures. This permits limited extrapolation of the observed decomposition rates to lower temperatures for which the rates are too low for convenient measurement. The surfactants we investigated are being considered for steamflood additives and need to be relatively stable at steam temperatures.

None of the surfactants evaluated to date has the requisite stability for use in steamfloods. The most stable petroleum sulfonate we have investigated has a half-life of 11 days at 180°C (356°F). With this half-life, substantial overdosing would be required to maintain the minimum effective surfactant concentration for the life of the flood. On the other hand, the estimated half-life for this surfactant at 93°C (200°F), calculated by extrapolation, would be 33 years.

Tests with the nonionic surfactant, nonylphenoxy-polyethanol, have shown this material to have a very short half-life at steam temperatures, but it does appear to be more stable at concentrations greater than the critical micelle concentration (CMC). In limited tests, the sulfonates showed increased stability in the presence of a 2-M salt solution.
Impact of Rock Plasticity on Hydraulic Fracture Propagation and Closure
Authors: van Dam D. B. , Papanastasiou P. , de Pater C. J.
Published: December 2007

We performed scaled laboratory experiments of hydraulic fracture propagation and closure in soft artificial rock and outcrop rock samples. We also performed numerical simulations of the fracture behavior in plastic rocks with independently measured rock properties. The simulations aided in interpreting the measurements and extrapolating the results to field scale.

Compared with elastic rock, plasticity induces a larger width for a given net pressure. However, the pressure to propagate fractures is only marginally increased and, in the case of the laboratory tests, was actually lower than expected from elastic behavior. The most dramatic effect of plasticity is that closure is much lower than the confining stress because of strong stress redistribution along the fracture.
Use of Fluorochemical Surfactants in Nonaqueous Stimulation Fluids
Authors: Clark Henry B.
Published: December 2007

This paper discusses a fluorochemical surfactant that is surface-active in hydrocarbon liquids such as kerosene and xylene and can function as an effective foaming agent for these liquids. A new apparatus for evaluating foaming capability in the laboratory is described, and data for hydrocarbon liquids foamed with this surfactant using this apparatus are presented. Field tests are described.

Introduction

Various types of foamed aqueous stimulation fluids have found considerable use in the oil field, but in many instances water can damage a formation, and foamed hydrocarbon liquids would be preferable. In addition, there are cases where foaming of hydrocarbon solvents would make them more efficient and where condensate removal by foaming would be desirable.A fluorochemical foaming agent has been developed which is capable of foaming nonpolar hydrocarbon liquids such as kerosene, xylene, and condensate for a variety of oilfield applications. This fluorochemical, identified as FC-C in this article, is a mixture of nonionic fluorochemical surfactants belonging to the chemical class of fluorinated alkyl esters. Other fluorinated alkyl esters were less effective in foaming nonpolar hydrocarbon liquids, but some showed greater surface tension reduction in hydrocarbons and some foamed alcohols. Laboratory foaming data on FC-C, and three field tests illustrating various applications of this foamer, are discussed.

Laboratory Experiments

To study the foam-generating capabilities of this fluorochemical surfactant, a foam generator was constructed; the apparatus and experimental procedure for its use are discussed in detail in Ref. 4. This equipment and procedure appear to provide a valuable and reproducible method for determining the foaming characteristics of liquids.Using this apparatus, the procedure to test foam consists of placing a liquid in a suitable vessel so it can be subjected to a constant pressure of 150 psi (1 MPa), passing the liquid through an aspirating inline generator, and collecting the foam in a tared graduated cylinder for measurement of foam quality and half-life. Foam quality is defined as percent by volume of gas phase in the foam, and half-life is defined as the time required for one-half of the liquid in the foam to drain from the foam, regardless of whether the foam actually breaks or simply drains.Using this procedure, hydrocarbon liquids were foamed using FC-C, and foam data are summarized in Table 1. For comparison, this table includes equivalent data for an aqueous foam generated by this same procedure, using a well-known aqueous foamer (Adofoam BF-1(TM) from Nalco Chemical Co.). It is evident that under these conditions, FC-C at 0.1% (solids) foams kerosene and diesel oil about as effectively as the aqueous foamer foams water at 0.5% (solids). It also produces good foam in xylene and fairly good foam in 55 degrees API gravity (0.75-g/cm3) condensate but does not foam hexane.

JPT

P. 1695＾
Gannet E Subsea ESP: The Application of Technology in Practice
Authors: Harrall S. J. , Nevelsteen D.
Published: December 2007

The Gannet E single-well subsea electric submersible pump (ESP) development has been onstream since January 1998. This is the first such installation in the North Sea and only the third development of its kind in the world. At a 14-km step-out from the Gannet Alpha platform, Gannet E represents a world record in terms of electrical transmission distance for such developments. Since startup, flow rates of 18,000 barrels of oil per day (BOPD) have been sustained while valuable operating experience has been acquired in a relatively short time. During the project planning and execution phases, emphasis was placed on anticipating potential operational pitfalls that could jeopardize the overall success of the development. Areas of concern lay in the fields of

ESP control and run life. Control of the platform facilities. Electrical power transmission. Data gathering. ESP flexibility with respect to flow rates and required delivery pressures. Reservoir-related uncertainties. Well completion installation.

This paper describes the technology and techniques applied to maximize the safeguards in the overall system integrity and to deliver a robust development. Actual startup and running experience is discussed in relation to the planning effort. Attention is paid to trip analysis and evaluating operability limits over the whole system. Major learning points that are being carried into further projects of this nature are also presented.
Effect of Viscosity on Downhole Gas Separation in a Rotary Gas Separator
Authors: Lackner G. , Doty D. R. , Shirazi S. A. , Schmidt Z.
Published: December 2007

Electrical submersible pump (ESP) installations are commonly used in the oil industry to aid fluid flow from the reservoir to the surface. As with any pump, the presence of free gas at the pump intake can adversely affect the operation of an ESP. One method of reducing the amount of free gas the pump has to process is to install a rotary gas separator.

In this work, the effect of viscosity on the separator's performance is investigated. New experimental data were gathered that covered a broad range of operational conditions in terms of pressures, liquid flow rates, gas-liquid ratios (GLRs), and rotational speeds. The experiments were conducted on a field-scale experimental facility with a commercially available separator. The working fluids were water, two mineral oils, and air. An existing mechanistic model (based on physical principles) predicting the bottomhole gas-separation efficiency in ESP installations was then evaluated with the data. Based on this investigation, improvements were implemented in the model to better capture the influence of viscosity on the downhole gas-separation process.

The results of the study indicate that there are two regions of separation efficiency with a pronounced transition between them: one region in which the rotary gas separator is very effective (separation efficiencies between 80 and 100%), and the other in which it is not effective at all (separation efficiencies between 30 and 55%). The transition location depends on the fluid physical properties, operational conditions, and geometry of the separator. The mechanistic model can predict this behavior and agrees well with the data that are obtained during this investigation. Fluid viscosity in the range of investigation (1 to 50 cp at 100°F) is found to have only little influence on gas-separation efficiency. This may indicate that the effects of turbulence at high rotational speeds dominate the behavior of flow inside the separator.
A Case History for Massive Hydraulic Fracturing the Cotton Valley Lime Matrix, Fallon and Personville Fields
Authors: Kozik H.G. , Holditch S.A.
Published: December 2007

This report summarizes the results of an active stimulation program on the Cotton Valley Lime as evaluated using reservoir production and pressure transient data. Using standard economic parameters and reservoir permeabilities determined by history matching, a detailed study was made to determine the well spacing and fracture length radius necessary for optimum development of the Fallon and North Personville fields.

Introduction

Considerable emphasis has been placed in recent years on recovering gas from "tight-gas" basins. One step that shows promise for unlocking tight gas is massive hydraulic fracturing (MHF). A case in point is the evolution of the stimulation in the Cotton Valley Lime at Fallon and North Personville fields, about 10 miles southeast of Mexia in Limestone County, TX (Fig. 1).The Jurassic Cotton Valley group on the west flank of the East Texas basin generally consists of a succession of about 1,000 ft of terrestrial and marine sands and shales, 800 ft of dark (Bossier) shale, and 300 to 500 ft of limestone at the bottom known as the Cotton Valley Lime or Haynesville. The group covers more than 250,000 sq miles in the East Texas basin and adjacent parts of Louisiana and southeast Arkansas.The Cotton Valley Lime in the Fallon and North Personville area has been a known gas area since its discovery in 1969. However, its poor permeability pay at a depth of about 11,000 ft had produced at rates too low for commercial development under the price schedules and technology of the past decade. Due to fracture porosity, beginning rates were moderately good (1 to 4 MMcf/D), but the natural fracture system was not sufficient to maintain the high rates of flow; consequently, the rates dropped to 0.200 to 0.500 MMcf/D in less than 2 years.Lately, advances in stimulation technology and improved economic incentives renewed interest in this area. Conventional acid stimulations and small fracturing jobs brought some improvement. Bigger fracturing jobs brought further improvement, but MHF appears worthwhile.These are the objectives of this report:1. Document the evolution of stimulation technology of the Cotton Valley Lime at the Fallon and North Personville fields.2. Using a computer reservoir simulator, history match the production and pressure transient data of the Muse No. 1 well before and after MHF and determine the uniqueness of this solution.3. History match the production of the Muse-Duke No. 1 after a super-MHF treatment.4. Optimize the development of the Cotton Valley Lime reservoir with respect to fracture length and well density using reservoir data and economic guidelines.5. Document the design of a super-MHF job (see Appendix).

Reservoir Characteristics Rock Parameters

The Cotton Valley Lime formation is generally gray, massive, oolitic to pistolitic, and finely crystalline to micritic. The better porosities appear to be related to the oolitic zones, ranging from 2 to 12% with some local thin zones of 14%.

JPT

P. 229^
Analysis of Dynamic and Static Foam Behavior
Authors: Lord D.L.
Published: December 2007

An equation of state describing pressure, volume, and temperature interactions of compressible foam is presented. Also shown is how this equation of state, when used in a unique solution of the mechanical energy balance for compressible-fluid flow, permits prediction of static and dynamic foam properties. A fracturing-treatment case history is presented for illustration.

Introduction

Low-permeability gas reservoirs are noted for their retention of water-base stimulation fluids within the matrix following treatment. In addition to retaining treatment fluids, many low-permeability formations are underpressured and water sensitive, creating other possibilities for matrix damage from exposure to water-base treatments. Such conditions indicate the need for a stimulation fluid, other than a hydrocarbon, which has a low water content. Foam has fulfilled that need because, on a volume basis, it is composed of a larger percentage of gas than liquid. Typically, foams used for fracturing and fracture acidizing contain 65 to 80 vol% gaseous nitrogen. Several foam fracturing treatments have placed proppant using a liquid phase composed of a 50/50 mixture of water and methanol. Such treatments further limit matrix exposure to a possibly damaging water phase. Compressible fluids, as a class, normally are considered gases; gases are considered Newtonian fluids. If corrections are made for acceleration losses and provisions made for variable density, it is found that gases follow Newtonian-fluid laminar and turbulent flow relationships. Gas viscosity changes are small compared with density changes that occur with changes in pressure. Foam is composed of gas bubbles, which are dispersed uniformly throughout a continuous liquid phase, and can be treated as a homogeneous fluid with both variable density and viscosity. When considered such a homogeneous fluid, foam is probably the only known compressible non-Newtonian fluid.

Theory

This section presents a state-of-the-art report on equations of state and flow equations for foam. Very few references to an equation of state for foam appear in the literature. However, a number of available references provide methods of estimating dynamic foam behavior.

Equation of State

Ross proposed an equation of state for foam in the following form.

(p ............(1)

Eq. 1 offers little from an engineering viewpoint because it is difficult to determine values for such parameters as Pgf, and . However, this equation does provide considerable understanding of foam physical properties. For example, if Eq. 1 is rearranged to the form

...(2)

we find that interfacial area per unit volume is determined uniquely by (1) the average excess pressure of gas within the foam above that of the surroundings and (2) liquid surface tension. In addition to this equation of state, Ross provides a guide to other foam behavior and to foam morphology.

JPT

P. 39^
The Effect of Fluid Leakoff on Gel Placement and Gel Stability in Fractures
Authors: Ganguly S. , Willhite G. P. , Green D. W. , McCool C. S.
Published: December 2007

Chromium acetate-hydrolyzed polyacrylamide gel systems are applied in fractured reservoirs for conformance control. A portion of the gelant leaks off into the adjoining matrix during placement of the gelant in the fracture. This paper describes an experimental study on the effect of fluid leakoff on the performance of a gel treatment. The stability of a gel that is placed in a fracture and is subjected to a pressure gradient was also investigated.

Physical models of a fracture were developed to conduct displacement experiments. The models were fractured Berea sandstones designed to permit leakoff of the gelant into the matrix on the sides of the fracture. A polyacrylamide-chromium acetate gelant was injected into the fracture under conditions in which there was leakoff and no leakoff into the matrix. A gel did not form, and the gelant was easily displaced from the fracture by subsequent brine injection when the gelant was placed without leakoff. When the gelant was placed with leakoff, a gel formed in the fracture after placement and provided significant flow resistance. It is hypothesized that the lack of gelation in the absence of leakoff was caused by diffusion of chromium from the fracture to the matrix. Diffusion reduced the chromium concentration in the gelant to levels at which gelation would not occur when the gelant was placed without leakoff.

It was discovered that gels that were formed in a fracture ruptured when a brine pressure was applied at the inlet. The pressure where rupture occurred was determined for gels placed in tubing of various lengths and diameters. The rupture pressure was proportional to a length/diameter ratio.
Some Results From Continuum Mechanics Analyses of the Hydraulic Fracturing Process
Authors: Hanson M. E. , Shaffer R. J.
Published: December 2007

We are developing and applying theoretical, numerical models to analyze the hydraulic fracturing process. Applications include fracturing near interfaces, effects of existing fractures near interfaces, pore-pressure effects, and stress-field changes due to embedded lenses. For a well-bonded interface, the calculations indicate that the stress-intensity factor of the leading crack tip decreases as the crack approaches a higher modulus material. As the tip crosses the interface into the higher modulus material, the stress-intensity factor abruptly increases to a higher value than it had in the lower modulus material. When the situation is reversed, the intensity factor increases as the tip approaches the interface and then abruptly decreases when the tip crosses the interface. Further calculations show that when existing cracks are present near the interface, the effects of the change in material properties across the bonded interface are reduced. In addition, our analysis shows that increases in pore pressure due to leakage of fluids from the fracture into the surrounding media causes the stress-intensity factor to drop; a decrease in the stress-intensity factor means a reduction in the tendency to break. In other calculations we analyzed the stress-field disturbance caused by lenses of one material that are embedded in another material. These calculations show that in regions that are not tectonically relaxed, the stress field is modified by the lenses. We conclude that the fracture geometry is modified by the presence of embedded lenses under these conditions.
Interpretation of Radioactive Marker Measurements To Evaluate Compaction in the Northern Adriatic Gas Fields
Authors: Ferronato M. , Gambolati G. , Teatini P. , Baù D.
Published: December 2007

The radioactive marker technique (RMT) appears to be a promising tool to evaluate the in-situ uniaxial vertical compressibility cM of deep producing gas/oil reservoirs. However, when the field consists of multipay layers with the porous-medium heterogeneity scale smaller than the marker spacing (10.5 m), great care must be exercised in the interpretation of an RMT survey. If the monitored depth interval incorporates thin clayey layers or the measurement is made in an active pumping well, cM can be grossly underestimated. Moreover, rock may expand, with the expansion correctly recorded by RMT. In the present paper, a set of RMT measurements made by Eni-E&P over the past decade in three deep boreholes of the Northern Adriatic basin are simulated with the aid of a 3D poroelastic model solved by finite elements (FEs). Use is made of the much detailed lithostratigraphies of the test holes and the cM constitutive equation derived from a previous statistical analysis of the marker data. The modeling results show that the measurements also can be reproduced satisfactorily from a quantitative viewpoint, and they indicate that an efficient marker installation requires that the monitored depth interval be made mostly from an entirely depleted sandy unit, with the markers placed possibly far from a producing well and approximately 10.5 m apart (i.e., the distance between the gamma ray detectors that monitor the marker position). The cM constitutive law used in the numerical analysis is realistically accurate from 2500 to 3000 m depth, while it appears to be underestimated by a factor of 2 between 800 and 1500 m. The measured expansions allow for the assessment of the reservoir cM under unloading conditions. This turns out to be 2.5 times smaller than cM in virgin loading conditions.
An Experimental and Theoretical Investigation of Upward Two-Phase Flow in Annuli
Authors: Lage Antonio C. V. M. , Time Rune W.
Published: December 2007

A steady-state mechanistic model is formulated to predict the mixture behavior for upward two-phase flow in concentric annuli. It consists of a procedure for flow pattern prediction and a set of independent models for calculating gas fraction and pressure drop in bubble, dispersed bubble, slug, and annular flow. Some aspects of churn flow are also discussed.

Experiments are performed in a 1278 m vertical well and in a small-scale U-tube, which comprises a descending pipe and an ascending annulus. Small-scale data available in the literature were also collected and catalogued.

The model is validated against the database. The performance of the model is compared with the performances of other models from the literature. It shows that the proposed model is more accurate than the alternatives.
A Parallel Multiblock Black-Oil Model in Multimodel Implementation
Authors: Lu Qin , Peszynska Malgorzata , Wheeler Mary F.
Published: December 2007

In this paper we discuss the multiblock algorithm for an implicit black-oil model as implemented in the multiphase simulator framework of IPARS (Integrated Parallel Accurate Reservoir Simulator). The multiblock algorithm decomposes the simulation domain into multiple nonoverlapping subdomains, or blocks, according to the geometric, geological, and physical/chemical properties, and well distribution. Each block can have its own grid system, and the grids of the neighboring blocks can be nonmatching on the interface, which allows for local grid refinement, or discrete fault or fracture modeling. Adjacent blocks are coupled across the interface by a set of conditions imposing a continuity of both primary variables and component mass fluxes that is realized through the use of special interface mortar variables. The resulting system is solved by an interface Newton procedure. Regularization techniques and preconditioners are proposed to improve the performance of the solver. The multiblock technique is effective and scalable, as shown by our numerical experiments. In addition, we present how the multiblock black-oil model has been used in the coupling of different physical models.
Nonlinear Regression: The Information Content of Pressure and Pressure-Derivative Data
Authors: Onur Mustafa , Reynolds Albert C.
Published: December 2007

It is shown that commonly used procedures for estimating parameters by regressing on pressure-derivative data are based on incorrect covariance matrices and thus violate the underlying statistical basis for nonlinear least-squares parameter estimation. Although the resulting estimates of model parameters may be reasonable, calculated confidence intervals are meaningless. Here, we show how to compute the correct derivative data covariance matrix that should be used for estimating parameters by nonlinear least squares. It is also shown that the information content of derivative data cannot be greater than the information content of pressure data, in the sense that regression on derivative data with the proper covariance matrix does not yield smaller confidence intervals than those obtained by regressing on pressure data only. In fact, we prove that matching a data set, including all interior derivative data plus two appropriate pressure points, yields exactly the same estimates and confidence intervals that would be obtained by regressing on pressure data only.
Simulation of Dynamic Foam-Acid Diversion Processes
Authors: Cheng L. , Kam S.I. , Delshad M. , Rossen W.R.
Published: December 2007

A new simulator for foam-acid diversion is described. The simulator explicitly accounts for the first time for the effects of gas trapping on gas mobility in foam and in liquid injected after foam and for the effects of pressure gradient on gas trapping. The foam model fits steady-state foam behavior in both high- and low-quality flow regimes and steady-state liquid mobility after foam. Previous laboratory experiments suggested that a relatively slow transition between steady states during foam and acid injection may control the diversion process in the field. The simulator fits this transition period in laboratory corefloods qualitatively with no additional adjustable parameters.

Simulations and new data agree that the transition is faster at higher pressure (with lower gas compressibility) and that response to a shut-in period depends on how much gas escapes during the shut-in (i.e., on how long the shut-in lasts). Simulations and data suggest that a dead volume present upstream of the core in previous studies strongly affects the transition period seen in those experiments.