Subsurface spills of gasoline

and other petroleum products are a

common environmental problem

throughout the industrialized world.

The U.S. Environmental Protection

Agency has estimated that 40 percent

of the more than 200,000 retail service

stations in the United States have had

accidental releases of petroleum

hydrocarbons to the subsurface (U.S.

Environmental Protection Agency,

1991). Restoration of a contaminated

aquifer to regulatory standards is a

technically difficult problem even

when best engineering strategies are

applied.

Natural attenuation, a

remediation strategy that relies on

intrinsic physical, chemical, and

biological processes to decrease

contaminant concentrations, is gaining

widespread acceptance in aquifer

restoration efforts (Tremblay and

others, 1995). The potential for

successful remediation by natural

attenuation depends on the fate of the

organic constituents of the spilled

product, which may include additives

such as methyl tert-butyl ether

(MTBE). These compounds can

dissolve in ground water, adsorb to

subsurface sediments, volatilize and

diffuse through the unsaturated zone,

or undergo chemical and biological

reactions (fig. 1). Volatilization and

biodegradation near the water table are

two processes that can contribute

significantly to the natural attenuation

of volatile organic compounds (VOCs)

in shallow ground water (McAllister

and Chiang, 1994). To date, quantitative information on the rates at which

these processes occur has been

limited.

R-UNSAT, a computer model

designed for quantifying rates of

volatilization and biodegradation of

organic compounds near the water

table, was developed and documented

by the U.S. Geological Survey

(USGS) and is now available to the

public. R-UNSAT also can be applied,

however, to other unsaturated-zone

transport problems that involve gas

diffusion, such as radon migration,

and the deposition of compounds from

the atmosphere to shallow ground

water. This fact sheet describes the

transport model and demonstrates its

capabilities through applications to

point- and nonpoint-source contamination.

MODEL DESCRIPTION

CAPABILITIES AND LIMITATIONS

R-UNSAT is designed to

simulate reactive, multispecies

transport in a layered unsaturated zone

with variable moisture content (fig. 2).

Two-dimensional (axisymmetric)

model equations are solved by using a

finite-difference algorithm. Analytical

solutions for simulating one-dimensional, vertical transport of a

nonreactive species in a homogeneous

unsaturated zone also are provided.

Gas transport is based on Fick’s Law

of diffusion; therefore, application of

R-UNSAT is inappropriate if gasphase advection is significant (for

example, in soil-vapor extraction

applications). R-UNSAT can be

applied, however, to simulate advective transport of compounds in the

aqueous phase associated with

ground-water recharge. R-UNSAT

accounts for equilibrium partitioning

of mass among immiscible (the

petroleum-product source), solid,

aqueous, and gaseous phases. The

immiscible phase is assumed to be

stationary and is modeled as a

U.S. Department of the Interior

U.S. Geological Survey

Fact Sheet FS-019-98

January 1998

Figure 1. Conceptualization of the fate of petroleum hydrocarbons in a groundwater system.

SIMULATING TRANSPORT OF VOLATILE ORGANIC COMPOUNDS IN THE

UNSATURATED ZONE USING THE COMPUTER MODEL R-UNSAT

Volatilization

Diffusion

Recharge

Gasoline

Well

Unsaturated

zone

Precipitation

Land

surface

Water table Saturated

zone

Biodegradation
boundary condition.

Biogeochemical reactions can be

sources or sinks for each modeled

species. The user can select either a zeroor first-order kinetics model for these

purposes. A single species can be ratelimiting or the reaction kinetics can be

coupled; for example, the production rate

of one species can be defined by the

consumption rate of another. If the

available kinetics models are not appropriate, the user can substitute his or her

own model directly into the computer

program. The modular format of the

Fortran 77 code easily accommodates this

type of modification.

BOUNDARY AND INITIAL

CONDITIONS

The availability of alternative

boundary and initial conditions provides

the flexibility to apply R-UNSAT to a

wide variety of transport problems. For

example, one of the following boundary

conditions can be selected to characterize

the source (fig. 3):

Option 1: Specified-flux boundary

(upper- or lower-vertical

boundary)

Option 2: Specified-concentration

boundary (upper- or lowervertical boundary) 1

Option 3: Time-dependent-concentration boundary 1

Option 4: Constant-radial-flux boundary

____________________________ 1

 Available only with numerical solver

Options 1 and 2 are designed for

modeling a source at land surface or at

the water table. The source strength

remains constant over the duration of the

simulated event, and the transport of one

species does not affect transport of

another. These options were applied by

Lahvis and Baehr (1996) to estimate rates

of aerobic hydrocarbon biodegradation in

a shallow ground-water plume. Option 3

is appropriate for multispecies transport

modeling if the product source is at or

above the water table. In this option, the

source composition varies as a function

of time in accordance with constituentmass fluxes across source boundaries.

Baehr (1987) applied this boundary

condition to simulate the long-term

compositional evolution of a gasolinespill source. Option 4 is designed to

simulate a constant-source flux in the

unsaturated zone--for example, a tracer

experiment to estimate effective-diffusive

coefficients of unsaturated-zone

sediments.

The remaining (upper- and/or

lower-vertical and far-lateral) boundaries

are modeled as variable-flux boundaries

that can be mixed for more complex

applications. For example, one part of

the boundary can be modeled as a

semipervious condition and another part

can be modeled as an impervious

condition.

The initial condition of each

species can be specified as a constant

concentration throughout the model

domain or defined spatially with an input

file. The latter option is useful for

evaluating transport after the contaminant

source has been removed or when

incorporating data from a soil-gas survey.

An example of selected model input to RUNSAT is shown in table 1.

MODEL APPLICATIONS

R-UNSAT can be used for calibration or prediction purposes. In a calibration mode, R-UNSAT can be used to

quantify rates of mass transport, reaction

rates, or the transport properties of

unsaturated-zone sediments. Parameter

values are computed by calibration to gas

or aqueous concentrations measured in

the unsaturated zone. R-UNSAT also can

be used to predict the distribution of a

species as a function of time and space

and to estimate mass-loss or loading rates

across model boundaries. Examples of

both types of applications are presented

below.

APPLICATIONS TO ANALYSIS OF

POINT-SOURCE CONTAMINATION

Predicting the Evolution of a GasolineSpill Source

Large volumes of gasoline can

remain trapped in the unsaturated and

capillary zones of an aquifer after

primary remediation efforts have ceased.

Because gasoline is composed of

constituents with diverse phasepartitioning properties, the source

concentration of each constituent varies

over time as constituents are selectively

removed from the residual product.

Baehr (1987) applied a preliminary

version of R-UNSAT in a predictive

mode to demonstrate that release rates for

aromatic constituents such as benzene,

Figure 2. Flow diagram of R-UNSAT transport model.

R-UNSAT TRANSPORT MODEL

one-dimensional MODEL DOMAIN axisymmetric

SOURCE/SINK REACTIONS optional

Constant 

 Radial Flux

SOURCE BOUNDARY CONDITIONS

OPTION 3

Time-Dependent

 Concentration 

OPTION 2 OPTION 4

Specified 

Concentration

OPTION 1

Specified Flux 

no

SEDIMENT

PROPERTIES

STRATIGRAPHY

depth

moisture content, 

diffusivity, porosity

variable

depth

moisture content, 

diffusivity, porosity depth

uniform OR

depth

analytical SOLVER numerical

variable

uniform

two-layered
toluene, ethylbenzene, and xylenes

(BTEX) are greatest at some time after

the spill incident. This lag in the peak

release rate is caused by the increasing

enrichment of the aromatic fraction of the

residual phase as more volatile aliphatic

compounds are selectively removed by

volatilization.

Estimating Rates of Aerobic

Biodegradation of Hydrocarbons

Associated with Bioventing

Aerobic biodegradation of hydrocarbons in the subsurface by indigenous

microorganisms results in the depletion

of oxygen (O2

) and the production of

carbon dioxide (CO2). Aerobic biodegradation can be inhibited or even halted if

the availability of O2 is limited. In these

cases, bioventing can be used as a

remediation technique to maintain or

enhance the O2

 supply by delivery of

atmospheric O2 to the contaminated

region through vapor extraction. Consequently, near-atmospheric concentrations

of O2

 can be achieved throughout the

unsaturated zone, even immediately

above the water table. If vapor extraction

is terminated temporarily, the redistribution or rebound of O2

 and CO2 concentrations to the antecedent condition occurs

at a rate proportional to the aerobic

biodegradation rate. By calibrating the

R-UNSAT model to the rebound gasconcentration data (fig. 4), Lahvis and

Baehr (1996) calculated aerobic-biodegradation rates of approximately 0.0015

gal/ft2/yr associated with bioventing at a

gasoline-spill site in Galloway Township,

New Jersey.

Estimating Rates of MTBE and

Hydrocarbon Mass Transfer to the

Unsaturated Zone

MTBE is added to gasoline in some

parts of the country to reduce carbon

monoxide and ozone emissions to the

atmosphere. Gasoline oxygenated with

MTBE can contain as much as 14.8

percent MTBE by volume. MTBE is

more soluble and less degradable than

BTEX compounds and, therefore, has

been observed to migrate ahead of BTEX

compounds in ground water at gasolinespill sites (Landmeyer and others, 1996).

Spills of MTBE-oxygenated gasoline are

a challenge to remediation by natural

attenuation because the concept was

developed in the context of BTEX

compounds.

 R-UNSAT is currently (1998)

being applied to quantify the rates of

mass transfer of MTBE and BTEX from

ground water to the unsaturated zone due

to volatilization and diffusive transport at

a gasoline-spill site in South Carolina.

Calibration of R-UNSAT to unsaturatedzone gas-concentration data indicates that

the volatilization rate of MTBE from the

water table source to the unsaturated zone

is similar to the volatilization rate of

BTEX. This finding is critical to the

evaluation of natural-attenuation

remediation, because rates of natural

attenuation in the interior of a groundwater-solute plume are smaller for MTBE

than for BTEX.

Figure 3. Model geometry and boundary conditions available in R-UNSAT.

Table 1. Selected model input to

R-UNSAT transport model

Unsaturated

zone

Injection

well

Monitoring

well

OPTION 3 OPTION 4

Unsaturated

zone

OPTIONS 1 and 2

Source

Unsaturated

zone

Unsaturated

zone

Variable flux

Saturated zone

Specified flux or specified

concentration 

r axis

z axis (axis of symmetry)

Model domain

Source

z axis (axis of symmetry)

r axis

Saturated zone

Model domain

Variable flux

r axis

z axis (axis of symmetry)

Model domain

Time-dependent

concentration

Saturated zone

Variable flux

Source

Specified flux or specified

concentration

r axis

z axis (axis of symmetry)

Saturated zone

Constant-radial

flux

Model

domain

Variable flux

SELECTED MODEL INPUT

Number of modeled constituents 

Molecular weight 

Atomic diffusion volume 

Gaseous-phase diffusivity 

Aqueous-phase diffusivity 

Specific volume 

Henry’s Law constant 

Aqueous-phase solubility 

Adsorption isotherm

Constituent Properties

Gas flux across source boundary (Option 1) 

Gaseous-phase concentration at source 

 boundary (Option 2) 

Initial mole fraction in immiscible plume 

 (Option 3) 

Immiscible plume volumetric content 

 (Option 3) 

Radius of source

Gaseous-phase concentration at other

 model boundaries 

Boundary and Initial Conditions

Total porosity 

Aqueous-phase porosity 

Gaseous-phase tortuosity 

Bulk density 

Unsaturated-zone temperature 

Unsaturated-zone pressure 

Number of sediment layers

Vertical recharge rate 

Longitudinal and transverse dispersivities

Physical Properties of the Unsaturated Zone
APPLICATION TO ANALYSIS OF

NONPOINT-SOURCE

CONTAMINATION--ATMOSPHERIC

DEPOSITION

Advances in analytical chemistry

and sampling techniques have resulted in

the ability to quantify concentrations of

VOC in ground water of 0.1 micrograms

per liter or less. VOC’s have been

detected frequently at these low concentrations in samples of shallow ground

water collected across the country as part

of the USGS National Water Quality

Assessment (NAWQA) program

(Squillace and others, 1995). An understanding of the source of VOC’s detected

in ground water is critical in areas where

surficial aquifers are used for water

supply. If atmospheric deposition is the

source of a VOC in ground water, then

changes in VOC concentration over time

would be constrained and proportional to

changes in atmospheric concentration. If,

however, the VOC presence is due to

coalescing point sources, then concentrations could increase significantly, posing

a more serious threat to the water supply.

The USGS has initiated a research project

in southern New Jersey to investigate the

role of atmospheric deposition in

shallow-ground-water contamination by

applying R-UNSAT to compute rates of

VOC migration in the unsaturated zone.

MODEL COMPATIBILITY

AND AVAILABILITY

 The R-UNSAT computer code is

written in Fortran 77 and runs on a

variety of computer platforms, including

mainframes and personal computers. RUNSAT is written in a modular structure

that facilitates modifications to the source

code. If modifications are made, the

program must be recompiled with a

Fortran 77 compiler to incorporate the

changes into the executable version of the

computer code. The compiling procedure

varies depending on the computing

system and the Fortran 77 software.

Documentation of R-UNSAT is available

as a U.S. Geological Survey Open-File

Report (Lahvis and Baehr, 1997). The

documentation, along with the source

code and executable versions, also can be

accessed on the Internet at the following

website address:

http://wwwnj.er.usgs.gov/

Additional information on the fate

and transport of VOC’s in the subsurface

can be obtained at the U.S. Geological

Survey Toxic Substances Hydrology

Program website at

http://toxics.usgs.gov/toxics.

--- Matthew A. Lahvis and Arthur L.

Baehr

REFERENCES CITED

Baehr, A.L., 1987, Selective transport of

hydrocarbons in the unsaturated

zone due to aqueous and vapor

phase partitioning: Water

Resources Research, v. 23, p. 1926-

1938.

Lahvis, M.A., and Baehr, A.L., 1996,

Estimation of rates of aerobic

hydrocarbon biodegradation by

simulation of gas transport in the

unsaturated zone: Water Resources

Research, v. 32, p. 2231-2249.

____ 1997, Documentation of R-UNSAT,

a computer model for the simulation

of reactive, multispecies transport in

the unsaturated zone: U. S.

Geological Survey Open-File

Report 97-630, 104 p.

Landmeyer, J.E., Chapelle, F.H., and

Bradley, P.M., 1996, Assessment of

intrinsic bioremediation of gasoline

contamination in the shallow

aquifer, Laurel Bay Exchange,

Marine Corps Air Station, Beaufort,

South Carolina: U.S. Geological

Survey Water-Resources

Investigations Report 96-4026,

50 p.

McAllister, P.M., and Chiang, C.Y., 1994,

A practical approach to evaluating

natural attenuation of contaminants

in ground water: Ground Water

Monitoring Review, v. 14, p. 161-

173.

Squillace, P.J., Zogorski, J.S., Wilber,

W.G., and Price, C.V., 1995, A

preliminary assessment of the

occurrence and possible sources of

MTBE in ground water of the

United States, 1993-94: U.S.

Geological Survey Open-File

Report 95-456, 15 p.

Tremblay, D., Tulis, D., Kostecki, P., and

Ewald, K., 1995, Innovation

skyrockets at 50,000 LUST sites:

Soil and Groundwater Cleanup,

December 1995, p. 6-13.

U.S. Environmental Protection Agency,

1991, OUST corrective action 45-

day study team report: U.S.

Environmental Protection Agency,

Office of Underground Storage

Tanks, Washington, D.C.

Figure 4. Graph showing model calibration to rebound of carbon of carbon dioxide

concentrations at (A) 8.2 feet, (B) 7.4 feet, and (C) 6.0 feet below land surface.

TIME (HOURS)

0 200 400 600 800 1,000

0

5

1 0

1 5

2 0

2 5

3 0

3 5

4 0

A.

B.

C.

Measured

Simulated

CARBON DIOXIDE CONCENTRATION

IN GASEOUS PHASE

(MILLIGRAMS PER LITER)