Groundwater Management: Quantity and Quality (Proceedings of theBenidorm Symposium, October 1989). IAHSPubl no. 188,1989.

A numerical model for simulating the in-situ volatilization of hydrocarbon contaminants in soils

G.P. SABADELL» D.K. SUNADA & N.S.GRIGG Civil Engineering Department, Colorado State University, Fort. Collins, Colorado, 80523,USA

Abstract A three-dimensional model of the advective transport of organic contaminants in the gaseous phase of the unsaturated zone has been developed and tested against selected analytical solutions. The model accounts for the evaporation of contaminants from a pure liquid surface, partitioning of a contaminant from an aqueous solution and the adsorption/desorption of organics with soil particle surfaces. The results predict the concentrations of volatile organics throughout the soil profile allowing the user to estimate the amounts of hydrocarbons leaving the soil via volatilization. The model can aid the analysis, design and operation of remediation efforts using an In Situ Volatilizaton (ISV) system. The ISV is used to prevent volatile organic compounds from migrating with infiltrating water through the vadose zone to the underlying groundwater table.

Un modèle numérique de simulation de la Volatilisation In Situ (ISV) des contaminants d'hydrocarbones dans les sols

Résumé Cette étude décrit un modèle tri-dimensionnel de transport convectif de contaminants organiques, en phase gazeuse, dans la zone non-saturée, ainsi que les tests faits à partir de quelques solutions analytiques. Le modèle tient compte de l'évaporation des contaminants sur une surface liquide pure, du partage des contaminants d'une solution aqueuse et de l'adsorption/désorption des matières organiques avec les surfaces des particules du sol. Les résultats prédisent les concentrations de matières organiques volatiles dans tout le profil du sol et permettent d'évaluer les quantités d'hydrocarbones qui se volatilisent. Le modèle peut aussi contribuer à l'analyse et à la conception, ainsi qu'à l'élaboration d'une méthode de protection à l'aide d'un système de Volatilisation In Situ (ISV). Le système ISV est utilisé pour empêcher la migration de composés organiques volatiles avec l'eau d'infiltration jusqu'à la nappe phréatique sous-jacente, en passant par la zone d'aération. Grâce au système ISV, les efforts

381

G.P. Sabadell et al 382

de protection peuvent être calculés en termes de durée et de rendement.

INTRODUCTION

In recent years contamination of groundwater by industrial chemicals, especially petroleum products and halogenated solvents, has become a problem of major concern. Many of these compounds are toxic and slightly water soluble, and they pose a potential threat to groundwater. In addition, many of these compounds have significant vapour pressures. Nonaqueous phase liquids (NAPLs) and their associated vapours in the unsaturated zone become sources of contamination by slowly dissolving into infiltrating water or the fluctuating water table.

In Situ Volatilization (ISV) has become an effective method for the elimination or reduction of volatile organic compounds (VOCs) from the vadose zone. Removal is enhanced by the air flow created when the soil is ventilated. The induced flow advects the organic vapour laden air to extraction vents where the contaminated gas may be treated prior to venting to the atmosphere. Figure 1 schematically illustrates an ISV system. ISV lessens the likelihood of groundwater contamination due to spills or leaks and can be an economic solution to site contamination problems. In situ remediation methods also have lower safety, environmental and public health risks than other methods that require excavation, transportation, storage and handling of hazardous wastes.

This paper presents a numerical model which has been developed for characterizing the transport of VOCs resulting from soil vapour extraction through a porous medium. The model simulates the three-dimensional soil gas pressure distribution throughout the study region. The distribution of the contaminant vapour concentration is computed based on the flowfield results, accounting for the mass transfer between the residual liquid phases and the dynamic gas phase. The model may be used to assist in the design and operation of an ISV system used to avoid contaminating a groundwater source and the costly remediation efforts associated with a polluted aquifer.

MASS TRANSFER PROCESS

There are two main approaches for predicting the behaviour of most reactive contaminants in porous media: the chemical mass transfer of a contaminant emanating from a continuous or temporary source; and the transformation/degradation of compounds due to chemical and/or biological reactions. This paper concentrates on the mass transfer problem where the transport of the contaminants in the gas phase occurs more rapidly than the transformation/degradation reactions.

383 Simulating in-situ volatilization of hydrocarbons

Fig .1 Schematic of an ISV system and several system options. Source: Anastos, 1985.

The mass transfer processes which are significant for the migration of VOCs in the soil gas phase are evaporation from organic liquid surfaces, partitioning of the contaminant from aqueous solution into the gas phase and desorption of the contaminant from soil particle surfaces. The reverse of the above processes retards the transport of vapours and is equally important.

Mass transfer rates across interphase boundaries are highly dependent on the contact areas. Due to the heterogeneity of porous media and the effect of capillary forces between fluids and pore size, it is virtually impossible to determine the interphase surface areas. However, a simplified approach such as that used for describing the mass transfer rates during packed tower aeration may be used. Packed tower aeration is a separation technique by which a contaminant is transferred from liquid solution to gas solution by contacting the phases in a column packed with materials to enhance interphase contacting (McKinnon & Dyksen, 1984). The transfer rates for this type of separation equipment are represented by a linear expression in which the mass transfer driving force is proportional to the difference

G.P. Sabadell et al 384

between equilibrium and actual solution concentrations (Gross & TerMaath, 1985). The mass transfer coefficient used to describe packed tower aeration accounts for the influence of packing type and gas-liquid distribution within the column. Sleep & Sykes (1989) used a similar approach for describing the fate of VOCs in variably saturated porous media.

For the volatilization of pure liquid organic, Raoult's law may be employed to quantify the ideal reference state for equilibrium between liquid and vapour phase, and may be written as

% =jt-r (i)

where cge is the equilibrium concentration in the gas phase, M is the molecular weight, R is the universal gas constant, T is the absolute temperature and P* is the vapour pressure at the specified temperature. The rate of change in concentration due to volatilization of organic compounds into the air phase is given by

-0gii = w = 08Xv(c8-c^ (2)

where Co represents the bulk concentration of organics in the porous media, <pg is the effective gas porosity, Xv is the characteristic mass transfer coefficient for volatilization into the air phase and eg is the concentration in the gas phase.

The partitioning of an organic solute from an aqueous solution may be determined from Henry's law. In essence, Henry's law states that the concentration of a constituent in the gas above an aqueous solution is proportional to the concentration of that constituent in the aqueous phase (CA)- For a system at equilibrium Munz & Roberts (1987) express Henry's law as

*-£-;or « where CAS is the concentration in the pure solvent and He is Henry's

law constant. Under induced gas flow conditions it is best to express the partitioning

concentration of organic vapours in terms of rate of change in concentration, similar to how the volatilizaton rate of pure liquid was determined. The rates of change of organic concentration in both the gas and aqueous phase may be expressed as

385 Simulatingin-situ volatilization of hydrocarbons

-eA^ = 0g^- = 0gXh (HeCA - cg) (4)

where Ah is the gas-liquid partitioning mass transfer coefficient and 6A is the volumetric water content.

Vapour phase sorption reactions have been shown to be dependent on soil properties which do not appear as significant in controlling sorption in saturated systems. Chiou & Shoup (1985) experimentally demonstrated that under unsaturated conditions soil minerals may control organic vapour partitioning. Peterson et al. (1988) found that the vapour phase sorption of trichloroethylene (TCE) on a simulated aquifer material was strongly dependent on the gas phase moisture content and indicated that for dry soils the vapour-solid partitoning due to adsorption may be as much as 10 times larger than the gas-liquid partitioning from an aqueous solution. Based on these results it is evident that sorption strongly affects the concentration of organic vapours in the soil gas.

The adsorption model of Brunauer-Emmet-Teller (BET) is generally used to characterize the adsorption of gases into solids (Hiemenz, 1977). At low vapour pressures of the gas, the BET model reduces to a linear isotherm and may be expressed as

Cs=XIM = Kdcg (5)

where JQ is the soil-vapour partition coefficient, X is the mass of adsorbed vapour, M is the mass of solid sorbent and Cs is the sorbed concentration (mass sorbed/mass solid). This process occurs rapidly and is considered to be at equilibrium relative to the above mass transfer mechanisms. The change in concentration of the soil gas due to sorption may then be written as

dCg _ Kd pb dCg dt 0g dt

where pb is the bulk density of the soil.

(6)

SOIL GAS FLOW

Equations describing fluid flow through porous media are obtained by combining Darcy's law with the mass continuity equation. For compressible gas flow through a porous medium the resulting equation may be written as

| (V/>2) p dt V>

G.P. Sabadell et al 386

where k is the intrinsic permeability of the soil,fi is the viscosity of the fluid and P is the soil gas pressure.

In the development of the above equation for compressible gas flow through soils the ideal gas equation of state was used for expressing the relationship between density and pressure of the fluid. Inherent in the formulation of Equation 7 are the assumptions that the system is isothermal, the effects of gravity on fluid flow are negligible and the effects of porous medium compressibility are small compared to the soil porosity and may be neglected. Due to the nature of ISV operations and the coarser soils to which this technology is applied, the effects of gas slippage, or the Klinkenberg effect, have been neglected (McWhorter, 1988).

For this analysis it is considered that the soil is at or near residual saturation and the liquid phases, NAPL and water, may be considered as immobilized and are, therefore, solely considering the transport of contaminants in the dynamic gas phase. The relation between the three phases is the component mass balance within the system, which may be expressed by the volumetric relation

0 = 0 y + 6A + Oo (8)

where (f) is the soil porosity and 60 is the volumetric organic content. The degree of soil liquid saturation only changes due to volatilization or partitioning as defined in Equations 2 and 4.

TRANSPORT EQUATION

For the induced flow conditions encountered during ISV operations the variation of concentration of contaminants in the soil gas is essentially controlled by advection. Advection refers to the transport of contaminants at the same speed as the average linear velocity of the transporting fluid. The equation for advective transport of VOCs through porous media may be written as

-V(cgvg) = 0 g ^ (9)

Adsorption of contaminant vapours onto soil particle surfaces represents a source of reduction of organic concentration in the soil gas and volatilization from the liquid phase becomes a source of organic concentration into the gas phase. Volatilization of pure organic, gas-liquid partitioning from the soil aqueous solution and the sorption reactions may be added to the transport equation in order to characterize the system better. The transport equation then becomes

387 Simulating in-situ volatilization of hydrocarbons

-V(cgvg) + 0gXv (cge -cg) + 0gXh (HcCA -cg) = [0g + ^ ] ^ (10)

Adding the effects of either injection or extraction vents the final form of the gas transport equation becomes

-V(pgVg) + 0gXv(Cg* -Cg) + 0g*h(HcCA -Cg) + qv(cgv -Cg) =

The gas flow and transport are related to the soil contaminant and water content according to the mass balance equation given in (8). According to the specified initial conditions and distribution of the three phases, a mass balance is maintained for the organic matter and water throughout the soil system.

NUMERICAL MODEL

Analytical solutions to the partial differential equations developed above are possible for rare or simplified conditions which have little applicability for practical situations. A numerical model capable of simulating the flow and transport of organic vapours through soils was developed in order to address the more complex real world problems. The developed model may be used to simulate ISV operations in a heterogeneous and anisotropic porous medium under either transient or steady state flow, and may solve one-, two-or three-dimensional problems.

The flow proportion of the model is solved using a block-centred Finite Difference Method (FDM). The Strongly Implicit Procedure as developed by McDonald & Harbaugh (1984) is used for iteratively solving the system of elliptic equations. The model computes the pressure distribution throughout the soil in the study region due to the artificial influence of the ISV extraction vents. Based on the soil pressure distribution, the gas flow and velocities are computed for use in the transport solution.

The advective transport problem is solved by the Mixing Cell FDM, where the time derivative is approximated by an explicit formulation and the space derivative is expanded in backward difference form. The time steps used for the flow portion of the model are divided into n stable time steps for use in the transport simulation. The Mixing Cell algorithm is a direct solution technique by which the contaminant concentration distribution in the soil is computed. The mass balance of the three phases is performed prior to initiating the solution for the next time step..

G.P.SabadelletaL 388

VALIDATION AND APPLICATION OF THE MODEL

The model was developed in sections in order to ensure that each component accurately characterized the respective physical system. Initially the flowfield portion of the model was created for determining the extent of influence and gas withdrawals due to ISV operations. The flowfield model was validated with one- and two-dimensional steady and unsteady flow analytical solutions (Sabadell et al., 1988). The model was then applied to operating ISV systems in order to validate its applicability to field conditions (Eisenbeis et al, 1989). The ISV systems used for this analysis are located at the Twin Cities Army Ammunition Plant (TCAAP) in New Brighton, Minnesota. There are two systems which are being used to remove TCE and other volatiles from soils. Due to the nature of the activity at these sites, the

Modeled — Observed

Vacuum * 12.5 cm I

+-Modeled Observed

0 Vacuum • 63.5 an water

(a): site D (b): Site G

Fig. 2 application of flowfield model to ISV systems at Sites D and G of the TCAAP facility in Minnesota.

soils are extremely heterogeneous, but the model was able to predict the operation of the two systems. Figure 2 demonstrates the agreement between the model predictions and the observed soil gas pressures. Based on these encouraging results further portions of the model were developed.

Sjostrom (1989) developed and analyzed the advective transport portion of the model. During this study the model was validated with several analytical solutions. For the case of one-dimensional transport under steady flow conditions the model and analytical results are very close. Figure 3a shows the effects of grid dimensions on the numerical solution and Fig. 3b

389 Simulating in-situ volatilization of hydrocarbons

illustrates the sensitivity of the solution to different time steps. Figure 4 demonstrates the capability of the model to predict contaminant transport during unsteady gas flow through a porous medium.

CONCLUSIONS

The purpose of this model is to enable the simulation of the operation of an ISV system. An effective ISV system can be extremely beneficial because it is an economical remediation technique and may also eliminate the possibility of groundwater contamination due to spills or leaks of VOCs into the subsurface. The model may aid in the design of an ISV system by determining the effects of vent spacing or use of an impermeable cover to enhance the radial influence and may also be used to size and cost equipment. The

LEGEND

-K- AX = 22.9 a

-•- AX * 30. 5 a

-A- AX » 38.1 a

ANALYTICAL

PARAMETERS

T = 3 Days

v = 45.3 a/day

At » 12 br

100 0 100 200 300" 400 500

Distance (a)

(a): Effects of grid dimension LEGEND

- * - At = 4 nr

- • - At » 6 hr

-M- At - 8 hr

-*r- At » 12 hr

ANALYTICAL

PARAMETERS

T " 3 Days

v « 60.7 a/day

Ax = 30.5 a

-100 0 100 200 300 400

Distance (a)

(b): Effects of time step

Fig. 3 Advective transport in one-dimensional steady flow.

management and operation of an ISV system may be facilitated with this model by determining how the system reacts to different withdrawal rates and

i . e.

S 0 .8

0 .2 -

j . . t.

o 0.8

0.4

0 .2 -

""« I

CRSabadeUetaL 390

LEGEND

ANALYTICAL

NUMERICAL

PARAMETERS

P/Pi =1.5

At = 2 hz

Ax = .3a

0 0.5 1 1.5 2 2.5 3 3.5 4

Distance (m) Fig. 4 Advective transport in one-dimensional unsteady flow.

operating the vents in order to ensure that air flow is enhanced in the contaminated regions.

Continuing the modelling efforts of soil decontamination due to soil venting is justified by the results obtained. Future work should evaluate the importance of diffusion and degradation/transformation reactions to the fate of contaminants in the soil gas. It is also important to characterize the air stripping relationships effectively for a soil environment and to apply these results to actual field conditions. These are problems which the staff at Colorado State University are continuing to investigate in the hopes of better developing our understanding of this new and innovative technology.

Acknowledgements The authors would like to thank the Energy and Environmental Science Division of Argonne National Laboratory, the U.S. Army Toxic and Hazardous Materials Agency and the Colorado State University Experiment Station Project 1-51101 for funding provided for completion of this work.

o o

o

c CD U a o u tu

> •H 4->

CO

0,6 -

0.4 -

0.2

391 Simulating in-situ volatilization of hydrocarbons

REFERENCES

Anastos, G.H.(1985) In situ air stripping of soils. Pilot study. U.S. Army Toxic and Hazardous Materials Agency, Report AMXTH-TE-TR 85026. Aberdeen, Maryland, USA

Chiou, C.T. & Sboup, T.D. (1985) Soil sorption of organic vapours and effects of humidity on sorptive mechanism and capacity. Environ. ScL Technol 19(12), 1196-1200.

Eisenbeis, J.J.; Sabadell, G.P.; Van Zyl, D. & Warner, J.W. (1989) In-situ volatilization flowfield model: field calibration and validation. Report, Argonne National Laboratory, Ar-gonne, Illinios, USA

Gross, R.L. & TerMaath, S.G. (1985) Packed tower aeration strips trichloroethylene from groundwater. Environ. Prog. 4(2), 119-123.

Hiemenz, P.C. (1977) Principles of Colloid and Surface Chemistry. 306-347. Marcel Dekker, Inc., New York.

McDonald, M.G. & Harbaugh, AW. (1984) A modular three-dimensional finite-difference groundwater flow model. Report, U.S. Geological Survey, Reston, Virginia, USA

McKinnon, RJ. & Dyksen, J.E. ( 1984) Removing organics from groundwater through aeration plus GAC. J. American Water Works Ass., MAI.

McWhorter, D.B. (1988) Unsteady radial flow of gas in the vadose zone. Submitted to /. Contaminant Hydrol

Munz, C. & Roberts, P.V. (1987) Ar-water phase equilibria of volatile organic solutes. /. American Water Works Ass., 62-69.

Peterson, M.S.; Lion, L.W. & Shoemaker, C.A (1988) Influence of vapour-base sorption and diffusion on the fate of trichloroethylene in an unsaturated aquifer system. Environ. Sci. Technol 22(5), 571-578.

Sabadell, G.P.; Eisenbeis, J J.; Van Zyl, D. & Sunada, D.K. (1988) CSUGAS; Flowfield model for in-situ volatilizaton of organic compounds in soils. Report, Argonne National Laboratory, Argonne, Illinois, USA

Sjostrom, J.W. (1989) Numerical simulation of volatile organic compound transport by advection in. soils. MS Thesis Colorado State Univ., Ft. Collins, CO, USA

Sleep, B.E. & Sykes, J.F. (1989) Modelling the transport of volatile organics in variably saturated media. Wat. Resour. Res. 25(1), 81-92.