UCRL-AR-135949 Vol. 4 Ch. 4

Volume 4: Potential Ground and Surface

Water Impacts

Chapter 4: Screening Model Evaluation of the Effects

of Ethanol on Benzene Plume Lengths

Authors

Walt McNab*

Stephen E. Heermann1

Brendan Dooher*

Editor

G. Cannon*

Contributor

R. Depue*

December 1999

1Clarkson University, Potsdam, NY 13699

*Lawrence Livermore National Laboratory, Livermore, CA 94550

University of California

Lawrence Livermore National Laboratory
Work performed under the auspices of the U. S. Department of Energy by Lawrence Livermore National

Laboratory under Contract W-7405-Eng-48.
UCRL-AR-135949 Vol. 4 Ch. 4 Potential Ground and Surface Water Impacts December 1999

11-99/Ethanol Ch. 4:rtd 4-iii

Table of Contents

4. Screening Model Evaluation of the Effects of Ethanol on Benzene Plume Lengths ............. 4-1

4.1. Introduction........................................................................................................................ 4-1

4.2. Methodology...................................................................................................................... 4-2

4.2.1. Overview ............................................................................................................... 4-2

4.2.2. Model Construction .............................................................................................. 4-4

4.3. Results and Discussion ..................................................................................................... 4-5

4.3.1. Uncorrelated Biotransformation Rates................................................................ 4-5

4.3.2. Correlated Biotransformation Rates .................................................................... 4-5

4.4. References.......................................................................................................................... 4-6

List of Figures

Figure 4-1. Idealized model of LNAPL gasohol release to the subsurface ............................... 4-11

Figure 4-2. Forecast probability distributions of benzene concentrations 50 ft

downgradient from the center of the LNAPL footprint. A comparison

between gasolines with and without ethanol when benzene

biotransformation rates are uncorrelated with biochemical oxygen demand......... 4-12

Figure 4-3. Forecast probability distributions of benzene concentrations 50 ft

downgradient from the center of the LNAPL footprint. A comparison

between gasolines with and without ethanol when benzene

biotransformation rates are correlated with biochemical oxygen demand............. 4-13

Figure 4-4. Forecast influences of LNAPL flux source term on benzene

concentrations; (a) uncorrelated and (b) correlated benzene

biotransformation rates .............................................................................................. 4-14

Figure 4-5. Forecast relationship between benzene concentrations 50 ft downgradient

from the center of the LNAPL footprint and groundwater velocity, with

and without ethanol, when benzene biotransformation rates are correlated

with biochemical oxygen demand............................................................................. 4-15

Figure 4-6. Influence of input variables on forecast benzene concentrations as a

function of distance, as indicated by rank correlation (for correlated

benzene biotransformation rates ............................................................................... 4-16
UCRL-AR-135949 Vol. 4 Ch. 4 Potential Ground and Surface Water Impacts December 1999

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List of Tables

Table 4-1a. Probability input parameters for modeled Monte Carlo forecasts .......................... 4-19

Table 4-1b. Model constants for input parameters....................................................................... 4-20

Table 4-2. Summary of simulation results indicative blended gasoline plume length

effects.......................................................................................................................... 4-21

Appendices

Appendix A. Semi-analytic Gasohol Solute Transport Model in Three Dimensions with a

Finite, Time-dependent LNAPL Source ................................................................. A-1
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4. Screening Model Evaluation of the Effects of

Ethanol on Benzene Plume Lengths

4.1. Introduction

The possibility of subsurface releases of gasoline from leaking underground fuel tanks

(LUFTs) and piping, along with potential surface spills during tank filling and other activities,

creates scenarios for hydrocarbon plume formation in groundwater downgradient from the

source (See Rice et al., 1999, Vol 4, Chapter 1 of this report). Fuel hydrocarbon plumes that are

not characterized by the presence of ethanol have been studied extensively (for example,

Rice et al., 1995; Mace et al., 1997). However, the potential role of ethanol in influencing the

behavior of benzene, toluene, ethyl benzene, and xylene (BTEX) component plumes needs to be

addressed because:

• A binary water-ethanol mixture can produce a cosolvency effect that serves to enhance the

solubility of nonpolar organic compounds, such as BTEX constituents (see Powers and

Heermann, 1999, Vol 4, Chapter 2 of this report), and

• The rapid biotransformation of ethanol can reduce the biotransformation rates of BTEX

constituents, most notably benzene, by reducing the availability of electron-acceptor species

(for example, dissolved oxygen and nitrate) that participate in biogeochemical oxidation

reactions (see Alvarez and Hunt, 1999, Vol 4, Chapter 3 of this report).

The result of both effects, in theory, may be longer BTEX plume lengths, principally those of

benzene, the constituent of greatest environmental concern.

The most direct means of measuring the effects of ethanol on benzene plume lengths is to

measure benzene concentrations at LUFT sites where ethanol has been used as a gasoline

additive and compare those, using appropriate statistical methods, to benzene concentrations

from LUFT sites where ethanol was not in use. Unfortunately, aside from anecdotal accounts

from experimental studies (for example, Hubbard et al., 1994), a sufficient database of plumes

from gasohol release sites does not yet exist for such an analysis.

In the absence of field data, we can employ screening-level mathematical modeling to

explore plausible plume behavior scenarios. In this present evaluation, we have chosen to

generate synthetic populations of benzene plumes, both with and without ethanol as a cosolute,

using a physically-based, semi-analytical model with distributions of model input parameters that

represent the ranges of conditions encountered in shallow aquifer settings. Model output

consisted of concentrations of benzene, ethanol, and the implied biochemical oxygen demand

(BOD) induced by biotransformation of ethanol for random combinations of input variables.
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4.2. Methodology

4.2.1. Overview

The plume model is based upon the solution presented by Baetsle (1969) for an

instantaneous, solute point-source in an infinite, homogeneous, three-dimensional (3-D) domain

with uniform groundwater flow, dispersivity tensor, and biotransformation rate (modeled by

first-order kinetics). Numerical integration of the source term in both space and time allows for

the simulation of a finite-sized source (for example, a lens of light nonaqueous phase liquid

(LNAPL) floating on the water table) and a finite release with respect to time (that is, a

continuous source as opposed to an instantaneous one). Although such a semi-analytical solution

is highly idealized (neglecting, for example, heterogeneities in the flow domain), it does provide

a useful average model of plume behavior that can be used, in conjunction with a Monte Carlo

simulation strategy, to produce probability distributions of concentrations as well as a means for

assessing model sensitivity to input parameters.

One reason for utilizing probabilistic approaches in evaluating the mathematical transport

model stems from the lack of sufficient field data on site-specific features of plume behavior.

Probabilistic modeling of contaminant transport involves employing user-specified probability

distributions of physical and chemical model variables, based on available data, to produce

forecasts through multiple Monte Carlo realizations. Monte Carlo analyses are routinely used in

engineering probability forecasting applications (for example, Ang and Tang [1984]).

Woodbury et al. (1995) applied Monte Carlo analyses to practical groundwater engineering

problems. In this report, the Monte Carlo approach permits uncertainties in hydrogeological

data (the groundwater velocity, for example), the nature of the source, and chemical data

(biotransformation rates, for example) to be translated into uncertainties regarding contaminant

concentrations as a function of time and space. Parameter sensitivities can be evaluated by

performing regression analyses of model output values against those of input variables.

The conceptual model for the gasohol release is a source, such as a LUFT, continually

discharging a small flux of LNAPL (less than 3 gal/day), which spreads along the water table,

maintaining a square footprint and a fixed thickness-to-length ratio (Figure 4-1). This

corresponds to a “slow drip” scenario representative of a chronic, undetected LUFT condition

and is the most likely release scenario to be encountered. The “slow drip” release scenario is in

contrast to a catastrophic release scenario, which would include different source dynamics but

which would, presumably, be subject to an immediate detection and remediation response.

Ethanol is assumed to be present at either a 10% volume fraction in the gasohol (for half of

the realizations) or else is absent. Because of its high affinity for water, the ethanol, when

present, is assumed to leach completely and instantaneously across a specified portion of the

LNAPL/groundwater interface into the water (that is, all of the ethanol contained within the

source flux is assumed to be injected into the aquifer along a specified portion of the interface).

The ethanol migrates through the aquifer, carried along by advection as well as longitudinal,

transverse, and vertical dispersion. Benzene enters the aquifer by diffusion and vertical

dispersion across the LNAPL/groundwater interface, with its limited solubility, in principle, a

function of the ethanol concentration at the interface.
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In theory, biotransformation of the ethanol produces an anaerobic zone that, in turn, will

presumably affect the biotransformation rate of benzene on a local scale (Alvarez and Hunt,

1999, Vol. 4, Chapter 3 of this report). However, there is a paucity of biotransformation rates for

benzene under the most anaerobic conditions (that is, sulfate-reducing and methanogenic).

Moreover, although the presence of ethanol may pose significant issues, such as competitive

substrate utilization and shifts in the nature of the local microbial population, there is an absence

of biotransformation rate data that can be readily adapted for modeling purposes. Given the

current state of knowledge, it is problematic to justify or construct a mathematical model

(analytical or numerical) that specifically addresses spatial dependencies of the benzene

biotransformation rate on the extent of the anaerobic shadow. At the screening level addressed

by our model, therefore, we have chosen to use a global average biotransformation rate for

benzene—a rate that is inversely correlated with the BOD signature in the vicinity of the source

area. In other words, we assumed that, in the lognormal distribution of biotransformation rates,

the slowest globally averaged rates are associated with a high BOD near the source area; whereas

the highest rates occur in realizations where the ethanol-induced BOD values are comparatively

low. This is a very conservative assumption because it neglects the replenishment of electron

acceptors from other sources, such as diffusion of atmospheric oxygen from the vadose zone

across the water table and from dissolution of ferrous and manganese-bearing oxyhydroxide

minerals in the sediments. The assumption is also additionally conservative in that ethanol

biotransformation effects are the only presumed influence on benzene biotransformation rates,

thus leading to a very high inverse correlation between benzene plume lengths and BOD in the

source area.

The present study uses a conservative assumption and neglects retardation as a result of

adsorption. This is because (1) the Baetsle (1969) model does not directly address retardation,

and (2) the superposition calculations used to quantify BOD are not valid when retardation of the

substrate (ethanol) is significant. Because the organic carbon partitioning coefficients of

benzene and ethanol are low, retardation resulting from adsorption would not be expected to play

a large role in influencing the fate of the plumes in comparison to the influence of

biotransformations. Furthermore, because the purpose of our screening model exercise is to

compare benzene plume lengths between ethanol and no-ethanol scenarios, and because ethanol

is not likely to exert significant effects on benzene adsorption away from the source area, the

omission of retardation is not likely to exert a significant effect on the findings.

As an additional analysis, prior to calculating the Monte Carlo realizations, a sensitivity

analysis was performed to assess whether the mass transfer of ethanol into groundwater would

best be modeled as a point source or be distributed over all or some finite fraction of the gasoline

lens. Because of its hydrophyllic nature, ethanol may not spread laterally to the same extent as

the gasoline but may instead partition into the groundwater over some smaller area near the

source of the leak. These analyses considered only ethanol and assumed that ethanol would

biotransform based on a conservative first-order constant of 0.01 day-1. It was expected that the

point-source approach would lead to a localized increase in the cosolvency effect because

concentrations will be greater. However, the increased cosolvency effect presumably would

occur over a much smaller area, and the differences between the two modeling approaches may

be insignificant.
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4.2.2. Model Construction

MathCad (Mathsoft, Inc.) was used as the computational engine for the model. Parameter

definitions, the complete set of governing equations, and internal model documentation are

shown in Appendix A. We conducted a total of 50 Monte Carlo realizations1 for each of two

different benzene biotransformation scenarios that are described below. The probability

distributions and modeling constants associated with the variable input parameters are presented

in Tables 4-1a and 4-1b, respectively. For each realization, the model steps may summarized as

follows:

1. The footprint of the LNAPL is calculated as a function of time based on the LNAPL flux,

the porosity, the fixed LNAPL thickness-to-length ratio, and the ethanol content.

2. The ethanol plume is modeled via a prescribed flux boundary condition, where the

injection of ethanol (the product of the LNAPL flux rate and the ethanol volume fraction

in the LNAPL) is divided across the full spatial extent of the LNAPL.

3. BOD is calculated by superposition where, at any location and time, the BOD is indicated

by the difference between the hypothetical ethanol degradation if ethanol was a

conservative species (that is, a biotransformation rate of zero) minus the concentration

predicted with a finite biotransformation rate, adjusted for mineralization reaction

stoichiometry.

4. The source term for the benzene plume is modeled by a prescribed boundary condition,

with the benzene boundary concentration (that is, its effective solubility) determined by

the average ethanol concentration under the LNAPL, according to a relationship

developed by Heermann and Powers (1998). The benzene flux across the prescribed

concentration boundary is modeled using a relationship suggested by Johnson and

Pankow (1992). The Johnson and Pankow (1992) model is for a steady-state plume; we

assumed, therefore, that the benzene plume in the vicinity of the source jumps from

steady-state to new steady-state as time advances. In practice, this simplifying

assumption is reasonable, given that simulated plumes stabilize fairly quickly,

particularly near the source, when a finite transformation rate is employed.

It is important to note that all concentrations are measured with respect to a specific depth

(for example, 5 ft below the water table), owing to the three-dimensional nature of the model. In

reality, groundwater samples always reflect an average across a finite depth interval because of

the finite length of wells screens and sampling techniques that require some form of purging. In

comparison to real water samples collected from wells with large screened intervals, model

results are likely to be conservative because they do not account for sample dilution resulting

from the inevitable mixing with nearby less contaminated water.

An initial set of realizations was simulated assuming no relationship between the benzene

biotransformation rates and any other modeled variables (that is, the “uncorrelated” scenario).

However, because the BOD values were recorded for each realization, we developed a second set

of simulations, which employed the identical input parameter set except that the benzene

 1

 The complexity of the calculations involved in the semi-analytic model, as shown in Appendix A, resulted in

relatively slow computational execution times, so that only a small number of realizations could be run easily.
UCRL-AR-135949 Vol. 4 Ch. 4 Potential Ground and Surface Water Impacts December 1999

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biotransformation rates were now inversely correlated with the BOD values 50 ft from the center

of the LNAPL footprint (that is, the “correlated” scenario).

4.3. Results and Discussion

4.3.1. Uncorrelated Biotransformation Rates

A comparison of probability distributions of benzene concentration at 50 ft downgradient of

the source location (that is, the center of the LNAPL footprint) between the scenarios with and

without ethanol suggests that the cosolvency effect of ethanol is negligible, at least according to

the model used in this study (Figure 4-2). This finding arises because the aqueous ethanol

concentrations remain well below the volume percent-level concentrations needed to produce a

cosolvency effect as a result of dilution by flowing groundwater and dispersion along the

LNAPL/groundwater interface.

Additional sensitivity analyses pertaining to the ethanol source-term distribution showed that

cosolvency effects are negligible whether the ethanol is added at a point source or distributed

over the entire footprint of the gasoline pool. For example, it was found that when ethanol

solubilized into the groundwater at 0.3 gal/day at a point, the maximum ethanol concentrations

would be expected to range between 10,000 mg/L and 50,000 mg/L. In this range of aqueous

ethanol concentrations, benzene solubilities would be expected to increase between 5% and 30%

as a result of cosolvency (Heermann and Powers, 1998). However these increases occur over an

area less than 2 m2 and comprise a small fraction of the gasoline pool. When the 0.3 gal/day of

ethanol was distributed over a finite area of 25 m2 or greater, ethanol concentrations in

groundwater were found to be less than 5000 mg/L. Below this ethanol concentration, increases

in benzene solubilities are less than 3%.

The absence of any significant cosolvency effect is attributed to the slow rate of ethanol mass

transfer from the gasoline into the groundwater system. Cosolvency effects are more likely to be

encountered following a catastrophic release of gasoline where large volumes of ethanol may

move rapidly into the groundwater. However, even under this scenario, cosolvency effects are

expected to be small. For example, model simulations by Heermann and Powers (1998) showed

that the length of a BTEX plume would increase by only about 10% due to presence of ethanol in

the gasoline. Despite the absence of cosolvency, the net volume of ethanol and BTEX

solubilizing in groundwater may be much greater for the slow-leak scenario considered in this

analysis than with a catastrophic scenario. The slow leak may go undetected for long periods of

time whereby a catastrophic release would probably be detected much more rapidly.

4.3.2. Correlated Biotransformation Rates

Unlike the uncorrelated scenario, which neglects the effects of ethanol on benzene

biotransformation rates, the correlated scenario indicates an observable difference in benzene

concentration distributions near the source area between the ethanol and no-ethanol realizations

(Figure 4-3). The significance of the biotransformation effect is also evident in comparing the

influence of the LNAPL flux terms (Figure 4-4). When biotransformation rates are uncorrelated

with the BOD, there is little forecast dependence of benzene concentrations on the flux term

because of the limited solubility of benzene in water. Any relationship at all would be a result of
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the expanded size of the LNAPL/groundwater interface. On the other hand, in the correlated

scenario, benzene concentrations are significantly influenced by the LNAPL flux, primarily

because larger quantities of ethanol in the source term imply larger BOD values and, hence,

lower benzene biotransformation rates.

This biotransformation effect on benzene concentrations appears to diminish with distance

downgradient from the source because of changes in parameter sensitivity. For example, near

the source area (for example, 50 ft downgradient from the LNAPL center), benzene

concentrations exhibit a relatively weak dependence on groundwater velocity, but they are

instead somewhat differentiated, based on whether or not ethanol is present as a cosolute

(Figure 4-5). Nevertheless, the linear regression analyses we performed on the relationships

between concentration and input variable (by rank) as a function of distance suggest that

variability in groundwater velocity becomes the dominant influence on variability in

concentration forecast downgradient from the source (Figure 4-6). This is at the expense of the

biotransformation rate influence, which, in turn, declines significantly away from the source

area.

Interpreted median plume lengths, defined by the distance from the LNAPL center to the 1-

and 10-parts-per-billion (ppb) concentration contours, are provided in Table 4-2 for the results of

this study as well as two other recent studies (Malcolm Pirnie, Inc., 1998; Ulrich, 1999). The

agreement between the models is good, suggesting a modest potential for an extension of

benzene plume lengths, less than a factor of two, in the presence of ethanol over cases where

ethanol is not used. It is important to stress, however, that this finding is very preliminary in the

absence of the data needed for more refined estimates. Moreover, its is particularly important to

stress the conservative nature of the model assumptions, notably the global reduction in benzene

biotransformation rates associated with the ethanol-induced BOD, and the non-depth-averaged

benzene concentration predictions. Thus, the model results should be viewed as representing an

expected upper bound to the effects under consideration.

4.4. References

Alvarez, Pedro J.J., and C.S. Hunt (1999). The effect of ethanol on BTEX biodegradation and

natural attenuation. In: Health and Environmental Assessment of the Use of Ethanol as a

Fuel Oxygenate, Vol. 4. Potential Ground and Surface Water Impacts, David W. Rice

and Gloria Cannon (Eds.), Lawrence Livermore National Laboratory, Livermore, CA,

UCRL-AR-135949 Vol. 4 Ch 3.

Ang, A.H.S, and W.H. Tang (1984). Probability Concepts in Engineering and Planning Design,

Vol. 2 : Decision, Risk, and Reliability. John Wiley and Sons, New York, NY.

Baetsle, L.H. (1969). Migration of radionuclides in porous media. In: Progress in Nuclear

Energy Series XII, Health Physics, A. M. F. Duhamel (Ed.), Pergamon Press, Elmsford, NY,

pp. 707–730.

Corseuil, H., C. Hunt, R. dos Santos Ferreira, and P. Alvarez (1998). The influence of the

gasoline oxygenate ethanol on aerobic and anaerobic BTX biodegradation. Wat. Res. 32(7):

2065–2072.
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Dooher, B.P. (1998). Making Risk-Based Management Decisions at Fuel Hydrocarbon Impacted

Sites Under Sparse Data Conditions. Ph.D. Dissertation, University of California at Los

Angeles, Los Angeles, CA.

Gelhar, L.W., C. Welty, K.R. Rehfeldt (1992). A critical review of data on field-scale dispersion

in aquifers. Water Resour. Res. 28(7): 1955–1974.

Guven, O., F.J. Molz, and J.G. Melville (1984). An Analysis of Dispersion in a Stratified

Aquifer. Water Resour. Res. 20: 1337–1354.

Heermann, S.E., and S.E. Powers (1998). Modeling the partitioning of BTEX in waterreformulated gasoline systems containing ethanol. J. Contam. Hydrol. 34: 315–341.

Howard, P.H., R.S. Boethling, W.F. Jarvis, W.M. Meylan, and E.M. Michalenko (1991).

Handbook of Environmental Degradation Rates, H.T. Printup (Ed.). Lewis Publishing,

Chelsea, MI.

Hubbard, C.E, J.F. Barker, S.F. O’Hannesin, M. Vandergriendt, and R.W. Gillam (1994).

Transport and Fate of Dissolved Methanol, Methyl-Tertiary-Butyl-Ether, and Monoaromatic

Hydrocarbons in a Shallow Sand Aquifer. American Petroleum Institute, Washington, DC.

Publication No. 4601, April.

Johnson, R.L., and J.F. Pankow (1992). Dissolution of dense chlorinated solvents into

groundwater, 2. Source functions for pools of solvent. Environ. Sci. Technol. 26: 896–901.

Jury, W.A. (1985). Spatial Variability of Soil Physical Parameters in Solute Migration: A

Critical Literature Review. Electric Power Research Institute, Palo Alto, CA, EPRI

EA-4228.

Mace, R. E., C.I. Mayfield, and J.F. Baker (1997). Extent, Mass, and Duration of Hydrocarbon

Petroleum Storage Tank Sites in Texas. Bureau of Economic Geology, University of Texas at

Austin, Austin, TX, Geological Circular 97-1.

Mackay, D.M., P.V. Roberts, and J.A. Cherry (1985). Transport of organic contaminants in

groundwater. Environ. Sci. and Technol. 19: 384–392.

Malcom Pirnie, Inc. (1998). Evaluation of the Fate and Transport of Ethanol in the Environment.

Report prepared for the American Methanol Institute, Washington DC. Malcom Pirnie, Inc.,

Oakland, CA. November. Report No. 3522-001.

Powers, S.E., and S.E. Heermann (1999). A critical review: the effect of ethanol in gasoline on

the fate and transport of BTEX in the subsurface. In: Health and Environmental Assessment

of the Use of Ethanol as a Fuel Oxygenate, Vol. 4 Potential Ground and Surface Water

Impacts, D.W. Rice and G. Cannon (Eds.). Lawrence Livermore National Laboratory,

Livermore, CA, UCRL-AR-135949 Vol. 4 Ch 2.

Rice, D.W., R.D. Grose, J.C. Michaelson, B.P. Dooher, D.H. MacQueen, S.J. Cullen,

W.E. Kastenberg, L.E. Everett, and M.A. Marino (1995). California Leaking Underground

Fuel Tank (LUFT) Historical Case Analyses. Lawrence Livermore National Laboratory,

Livermore, CA, UCRL-AR-122207.
UCRL-AR-135949 Vol. 4 Ch. 4 Potential Ground and Surface Water Impacts December 1999

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Rice, D.W., S.E. Powers, and Pedro J.J.J. Alvarez (1999). Potential scenarios for ethanolcontaining gasoline released into surface and subsurface water. In: Health and

Environmental Assessment of the Use of Ethanol as a Fuel Oxygenate, Vol. 4 Potential

Ground and Surface Water Impacts, D.W. Rice and G. Cannon (Eds.). Lawrence Livermore

National Laboratory, Livermore, CA, UCRL-AR-135949 Vol. 4 Ch 1.

Rice, D.W., W.W. McNab, P.C. Johnson, L.G. Everett, W.E. Kastenberg, M.C. Kavanaugh,

S. Pelmulder, M.C. Small, and R.C. Ragaini (1998). Department of Defense Petroleum

Hydrocarbon Cleanup Demonstration Program Final Report: Risk-Informed Decision

Making at Petroleum Contaminated Sites. Lawrence Livermore National Laboratory,

Livermore, CA, UCRL-AR-131771.

Ulrich, G. (1999). The Fate and Transport of Ethanol-Blended Gasoline in the Environment:

A Literature Review and Transport Modeling (online; pdf). submitted by Governors’

Ethanol Coalition, Lincoln, Nebraska, October 27. Available: <http://www.ethanol-gec.

org/publicat.htm >.

Woodbury, A., F. Render, and T. Ulrych (1995). Practical probabilistic groundwater modeling.

Ground Water 33(4): 532-538.
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UCRL-AR-135949 Vol. 4 Ch4

Figures
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UCRL-AR-135949 Vol. 4 Ch. 4 Potential Ground and Surface Water Impacts December 1999

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Q (LMAPL flux)

Free product footprint

expands with time

Constant EtOH flux

from expanding LNAPL

Benzene concentration

at boundary a function

of ETOH concentration

Calculate Cethanols

Cbenzenes CBOD

V

Figure 4-1. Idealized model of LNAPL gasohol release to the subsurface.
UCRL-AR-135949 Vol. 4 Ch. 4 Potential Ground and Surface Water Impacts December 1999

11-99/Ethanol Ch. 4 A-12

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

1 10 100 1000 10000

No EtOH 10% EtOH

p = 0.816

Cumulative distribution

Benzene concentration (ppb)

Figure 4-2. Forecast probability distributions of benzene concentrations 50 ft downgradient from

the center of the LNAPL footprint. A comparison between gasolines with and without ethanol

when benzene biotransformation rates are uncorrelated with biochemical oxygen demand.
UCRL-AR-135949 Vol. 4 Ch. 4 Potential Ground and Surface Water Impacts December 1999

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0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

1 10 100 1000 10000

No EtOH 10% EtOH

p = 0.112

Cumulative distribution

50 ft from

Benzene concentration (ppb)

Figure 4-3. Forecast probability distributions of benzene concentrations 50 ft downgradient from

the center of the LNAPL footprint. A comparison between gasolines with and without ethanol

when benzene biotransformation rates are correlated with biochemical oxygen demand.
UCRL-AR-135949 Vol. 4 Ch. 4 Potential Ground and Surface Water Impacts December 1999

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0.1

1

10

100

1000

10000

0.03 0.10 0.32 1.00 3.16

100 ft 1000 ft

Gasohol source flux (gal/day)

0.1

1

10

100

1000

10000

0.03 0.10 0.32 1.00 3.16

100 ft 1000 ft

Gasohol source flux (gal/day)

Benzene concentration (ppb) Benzene concentration (ppb)

Figure 4-4. Forecast influences of LNAPL flux source term on benzene concentrations; (a)

uncorrelated and (b) correlated benzine biotransformation rates.
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1

10

100

1000

10000

1 10 100 1000

No ETOH 10% EtOH

(ft/yr)

Benzene concentration (ppb)

Groundwater velocity

Figure 4-5. Forecast relationship between benzene concentrations 50 ft downgradient from the

center of the LNAPL footprint and groundwater velocity, with and without ethanol, when benzene

biotransformation rates are correlated with biochemical oxygen demand.
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0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 1000 2000 3000

Groundwater velocity

Degradation rate

r

2

Distance downgradient (ft)

Figure 4-6. Influence of input variables on forecast benzene concentrations as a function of

distance, as indicated by rank correlation (for correlated benzene biotransformation rates).
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UCRL-AR-135949 Vol. 4 Ch. 4

Tables
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Table 4-1a. Probability distribution input parameters for modeled Monte Carlo forecasts.

Parameter Description Remarks Prescribed distribution

XEtOH Ethanol fraction in

gasohol

Represents maximum

expected in California

reformulated gasoline

1% and 10%, by mass or mole fraction

Q Rate of NAPL

replenishment

Based on current

uncertainty of tank

release monitoring

Loguniform distribution 3.16–0.0316

[log(uniform range of 0.5 to–1.5)]

T NAPL lens thicknessto-length ratioBased on estimates from

Dooher, 1998

Loguniform distribution 0.1–0.01

[log(uniform range of -1 to -2)]

λEtOH Ethanol first-order

degradation rate

Estimated from

laboratory experiments

of Corseuil et al., 1998;

Alvarez and Hunt, 1999.

Howard et al. (1991)

reports a range of halflives 1/3 to 2/5 faster.

Lognormal distribution.

5th percentile = 1.28 × 10–1 day–1 (t1/2 =

5.43 days)

mean = 2.46 × 10–1 day–1 (t1/2 = 2.82

days)

95th percentile = 4.51 × 10–2 day–1 (t1/2 =

1.67 days)

λBenzene Benzene first-order

degradation rate

Rice et al., 1998. Median

value may be fairly

typical as a macroscopic

average for many sites

(e.g., Ulrich, 1999;

Dooher, 1998).

Lognormal distribution.

5th percentile = 9.75 × 10–5 day–1 (t1/2 =

7110 days or 19.5 years)

mean = 3.65 × 10–2 day-1 (t1/2 = 19 days)

95th percentile = 1.23 × 10–1 day–1 (t1/2 =

5.6 days)

p Fraction of NAPL

footprint over which

ethanol partitions in

water.

Postulation based

(Powers and Heermann,

1999).

Loguniform distribution 0.1– 0.01

[log(uniform range of -1 to -2)]

K Hydraulic

conductivity

Values typifying

California hydrogeology

(Dooher, 1998).

Values supported by

Mackay et al., 1985, and

Guven et al., 1984.

Lognormal distribution.

5th percentile = 3.82 × 10–6 m/s (0.33

m/day)

mean = 1.25 × 10–4 m/s (10.8 m/day)

95th percentile = 4.75 × 10–4 m/s (41

m/day)

∇h Hydraulic gradient Values typifying

California hydrogeology

(Dooher, 1998).

Values supported by

Mackay et al., 1985, and

Guven et al., 1984.

Lognormal distribution.

5th percentile = 1.42 × 10–3

mean = 1.66 × 10–2

9th percentile = 5.58 × 10–2

φ Porosity Based on 252 samples

taken at the Lawrence

Livermore National

Laboratory Superfund

Site (Dooher, 1998) and

Jury (1985).

Normal distribution.

mean = 0.42

standard deviation = 0.07
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Table 4-1b. Model constants for input parameters.

Parameter Description Remarks Prescribed distribution

XBenzene Benzene fraction in

gasahol

Represents maximum expected in

California reformulated gasoline

1.5%, by mass or

mole fraction

αx Longitudinal

dispersivity.

Based on results presented in

Gelhar et al. (1992).

20 ft

αy Horizontal transverse

dispersivity.

Based on results presented in

Gelhar et al. (1992).

2 ft

αz Vertical transverse

dispersivity.

Based on results presented in

Gelhar et al. (1992).

0.5 ft

Cw Benzene solubility in

pure water

1780 ppm

β Volume fraction of

EtOH at the break point

between the linear and

the log-linear model

Powers and Heermann (1999). 0.27

Cβ Benzene solubility at β. Powers and Heermann (1999). 4420 ppm

De Effective molecular

diffusion coefficient

Taken to be identical for ethanol

and benzene.

5x10-10 m2

/s

Table 4-2. Summary of simulation results indicative blended gasoline plume length effects.

Study

Plume lengths:

regular gasoline

Plume lengths:

blended gasoline

LLNL screening model 200-250 ft at 10 ppb

200-250 ft at 1 ppb

250-300 ft at 10 ppb (~20% longer)

400-500 ft at 1 ppb (~100% longer)

Malcolm Pirnie, Inc. (1998) 145-330 ft at 1 ppb

Median: 240 ft

195-420 ft at 1 (ppb)

Median: 310 ft (~30% longer)

Governor’s Ethanol Coalition (Ulrich,

1999) model of Borden aquifer site

200 ft 365 ft (~80% longer)

Waterloo blended methanol-gasoline

field studya (Hubbard et al., 1994)

~75 ft ~115 ft (50% longer)

a Gasoline with 15% MeOH, introduced as a slug source in a controlled field experiment.
11-99/Ethanol Ch. 4:rtd A-i

UCRL-AR-135949 Vol. 4 Ch. 4

Appendix A

Semi-analytical Gasohol Solute Transport Model in 3-D with a Finite,

Time-dependent LNAPL Source
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11-99/Ethanol Ch. 4 A-1

Semi-Analytical Gasohol Solute Transport Model in 3-D 

with a Finite, Time-Dependent LNAPL Source

This worksheet contains a full 3-D semi-analytical model for the development of ethanol, benzene, and biochemical oxygen demaplumes emanating from a light non-aqueous phase liquid (LNAPL) source as a function of time and space. The LNAPL source itsgrows over time, depending on the input of fresh gasohol. The transport model is based on spatial and temporal integration of the Baetsle (1969) instantaneous point source solution in 3-D. The ethanol source term consists of a prescribed flux boundary conditacross the LNAPL/groundwater interface which changes as a function of time as the LNAPL pool grows. The benzene source terhandled by a prescribed boundary condition, with the prescribed benzene boundary concentration (that is, its effective solubility) determined by the average ethanol concentration under the LNAPL (again, a function of time). The coupling between the source handled by equations provided by Johnson and Pankow (1992) and Heerman and Powers (1998). The biochemical oxygen demacalculated by superposition with respect to the ethanol plume.

Unit definitions and MathCad parameters ... ppb 10 6 gmL ppm 10 3 gmL TOL 1 10 4 . ORIGIN 1

Aquifer properties (for downgradient plume simulation)

Hydraulic conductivity: K 10 ft

day

Hydraulic gradient: I 0.002Porosity: φ 0.25Pore velocity by Darcy's law: v K I.

φ

v 29.219 ft

yr

=

Dispersion tensor: Longitudinal: α x 20 ft D x α x.v

Transverse: α y 2 ft D y α y.vVertical: α z 0.5 ft D z α z.v
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Gasohol source properties

NAPL replenishment rate: Q 0.5 gal

day

Ethanol mass/mole/volume fraction in gasohol: X EtOH 10 %Benzene mass/mole/volume fraction in gasohol: X B 1.5 %NAPL thickness-to-length ratio: T ratio 0.1

Solute properties

First-order decay coefficient for ethanol: λ EtOH 0.01 day 1First-order decay coefficient for benzene: λ B 0.003day 1Effective molecular diffusion coefficient (assume the same for both ethanol and benzene):

D e 5 10 10 . m

2

sec
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Governing equations for ethanol plume model

Size of square-footprint NAPL/groundwater interface

ε 1 cm (Used to prevent divide-by-zero err

(Length of one side of the LNAPL lens as a function of time, correctefor product loss due to ethanol dissolution. LNAPL lens is assumed to have a square footprinwith a thickness to length ratio of Tratio .)

L p( )t

3 Q t. 1 X EtOH .

T ratio.φ

ε

Ethanol source function, assuming a specified flux across the NAPL/groundwater interface

Density of ethanol: ρ EtOH 0.7 gm

cm

3

Implied constant ethanol mass injection rate:

M EtOH Q X EtOH . ρ EtOH .

Fraction of NAPL footprint over within which ethanol partitions into water:

p 25 %

(The implied ethanol flux, based on assumption of complete, instantanepartitioning into the water phase, is over the some portion, p, of the groNAPL footprint.)

M fEtOH( )t

M EtOH

p L p( )t 2 .
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Plume model for ethanol, based on the solution of Baetsle (1969). The solute transport model used for ethanol is basean instantaneous point source (that is, mass slug) solution into a 3-D domain. To modify the mathematical solution for the conditions of interest, the point source is integrated over finite distances in the x- and y-directions to simulate leaching from LNAPL lens and is integrated in time to emulate a finite source (the changing size of the LNAPL lens over time is accounteThe source functions are multiplied by 2 for superposition of the source to account for the boundary condition imposed by twater table.

C1( ) x y, , z, λ t,

0

t

p Lp( ) t τ .

2

p Lp . ( ) t τ

2

p Lp( ) t τ .

2

p Lp . ( ) t τ

2

x

2 M fEtOH( ) t τ .

8 π τ. ( )

32

. D x D y . D z . .

exp

x xs v τ.

2

4 D x . τ.

y y s

2

4 D y . τ.

z

2

4 D z . τ.

λ τ . . d 

Biochemical oxygen demand (BOD) for mineralized of ethanol to CO2

Reaction stoichiometry: EtOH + 3O2 --> 2CO2 + 3H2OMolecular weights: MW EtOH 46.07 gmmol (Ethanol)

MW O2 32 gmmol (O2)

Biochemical oxygen demand weighting factor: w BOD 3

MW O2

MW EtOH

.

Ethanol biotransformation shadow δe xy ( )C , , z, λ t, 1 x y, , z,t 0 day 1 , C1( ) x y, , z, λ t,
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Analysis: Ethanol plume and anaerobic shadow

Elapsed time since release began t 30 yrCumulative ethanol mass introduction over release period

Σ EtOH M EtOH t. Σ EtOH 1.452 103 = kg

Concentrations versus position for example parameter set

x 40 ft y 0 ft z 5 ft

Ethanol C 1 x y, , z, λ t EtOH , = 3.227 ppmBOD δe xy, , z, λ t EtOH , w BOD . = 41.847 ppm

x 100 ft y 0 ft z 15 ft

Ethanol C 1 x y, , z, λ t EtOH , = 0.674 ppbBOD δe xy, , z, λ t EtOH , w BOD . = 13.165 ppm
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Governing equations for benzene plume model

Average ethanol concentration vs. time at LNAPL/water boundary. The specified concentration boundary condition for ben(see below) requires that the ethanol concentration at the LNAPL/groundwater interface be known. Because the ethanol source function is a specified flux at the interface, this value cannot be defined precisely at the interface. As an alternative, a finite-thicboundary layer may be delineated underneath the LNAPL where an ethanol boundary concentration may be defined. For compsimplicity, and to meet as much as possible mathematical constraints required for the Johnson and Pankow (1992) solution to h(see below), an average ethanol concentration across the entire LNAPL/groundwater interface is calculated as a function of timvalue is then used to calculated an average benzene boundary concentration. To simplify computations, the averaged ethanol concentrations are stored in an array to avoid having to recalculate the integrals in the equation for C1 as a function of time. Th

necessitates time-discretizing the continuous benzene source term, rather than assuming a continuous integral.

Assumed boundary layer thickness: b 1 mmEthanol density: ρ EtOH 0.7 gm

cm

3

Time discretization: N t 20 ∆t t N t i 1N t .. t di ( ) i 0.5 ∆t .Discretization of NAPL pool length as a function of time: L di L p t diSpatial discretization of NAPL/groundwater interface over time for estimating average ethanol concentration:

N s 5 ∆xi

L di

N s

j 1N s .. xdi j,

Ldi

2

( ) j 0.5 ∆xi .

∆yi

L di

N s

k 1N s .. y di k,

Ldi

2

( ) k 0.5 ∆yi .
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Temporal discretization of average ethanol concentration:

(Average volume fraction of ethanol under the LNAPL pool in ethanol-water mixture over each discrete time interval.) fi j k

C 1 xdi j, y di k, , b2 , t di , λ EtOH ,

N s2 ρ EtOH .

Average benzene concentration and benzene mass flux/area vs. time at the LNAPL/groundwater boundary. Because olimited solubility of benzene in water, the benzene source term is one of a prescribed concentration boundary, as opposed to tpresribed flux boundary condition used for ethanol. Because the cosolvency effect of ethanol can increase the solubility of bethe boundary condition solubility of benzene is calculated from the mean ethanol concentration under the LNAPL pool as a funof time and the method proposed by Heerman and Powers (1998). The mass flux of benzene per unit area is calculated using solution of Johnson and Pankow (1992). Their solution is one for a steady-state plume that has developed beneath a LNAPL In this model, it is assumed that the system jumps from steady-state to steady-state over each discrete time interval. The masis then updated accordingly.Pure benzene solubility in pure water: C w 1780 ppmVolume fraction of ethanol in the aqueous phase at the break point between the linear and log-linear models:

β 0.27

Solubility of benzene at β: C β 4420 ppmEquilibrium concentration of benzene in the binary mixture (for f < β) after Heerman and 

Powers (1998):

C Bi 1

fi

β

C w . X B .

fi

β

C β . X B .

Benzene mass flux/area over discrete time intervals, after Johnson and Pankow (1992):

M fBi C Bi.φ

4 D z D e . .v

π L di .

.
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Plume model for benzene, based on the solution of Baetsle (1969). The form of this mathematical solution for the beplume is similar to that for ethanol, except that the source term has been discretized over a specified finite number of timintervals. The equation has been split into two terms here simply for clarity.

ψ( ) x y, , z, λ t, 2

8 π t. ( )

32

. D x D y . D z . .

exp

x vt. ( )2

4 D x . t.

y

2

4 D y . t.

z

2

4 D z . t.

λ t . .

C 2( ) x y, , z, λ t,

i

t di

∆t

2

t di

∆t

2

τ

Ldi

2

Ldi

2

y s

L di

2

Ldi

2

x M fB s i ψ x xs y y s , , z, λ t τ , . d d d

Concentrations versus position for example parameter set

x 40 ft y 0 ft z 5 ft

Benzene C 2 x y, , z, λ t B , = 399.296 ppb

x 100 ft y 0 ft z 15 ft

Benzene C 2 x y, , z, λ t B , = 10.457 ppb
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References

Baetsle, L.H. (1969). Migration of radionuclides in porous media. In: Progress in Nuclear

Energy Series XII, Health Physics, A. M. F. Duhamel (Ed.), Pergamon Press, Elmsford, NY,

pp. 707–730.

Heermann, S.E., and S.E. Powers (1998). Modeling the partitioning of BTEX in waterreformulated gasoline systems containing ethanol. J. Contam. Hydrol. 34: 315–341.

Johnson, R.L., and J.F. Pankow (1992). Dissolution of dense chlorinated solvents into

groundwater, 2. Source functions for pools of solvent. Environ. Sci. Technol. 26: 896–901.
UCRL-AR-135949 Vol. 4 Ch. 4 Potential Ground and Surface Water Impacts December 1999

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