A 3-D NAPL Flow and Biodegradation Model


Phillip C. de Blanc, Daene C. McKinney and Gerald E. Speitel Jr.

Department of Civil Engineering, University of Texas at Austin

ABSTRACT


A three-dimensional, multi-phase, multi-component porous media flow model has been developed and is described. The flow model simulates the transport and biodegradation of lighter-than-water non-aqueous phase liquids (LNAPLs) and denser-than-water non-aqueous phase liquids (DNAPLs). Multiple pumping and injection wells can be specified to test remediation schemes. The biodegradation model describes biological transformation of the organic contaminants originating from NAPL sources, and can accommodate multiple substrates, electron acceptors, and biological species. The biodegradation model includes inhibition, sequential use of electron acceptors, and cometabolism. Example simulations illustrate the model capabilities.

INTRODUCTION


The University of Texas is completing improvements to a multi-phase flow simulator called UTCHEM. Advanced biodegradation capabilities have recently been incorporated into UTCHEM that allow both the flow of non-aqueous phase liquids (NAPLs) and the fate of organic NAPL constituents to be described within the same model. This paper describes the multi-phase flow and biodegradation model components, discusses the biodegradation model equations and features, and provides two example UTCHEM simulations that demonstrate some of the biodegradation model capabilities.

MODEL DESCRIPTION AND FEATURES


UTCHEM is a multi-phase, multi-component, three-dimensional, numerical model that simulates the fate and transport of both dissolved and non-aqueous phase organic contaminants in porous media. The model can be used to simulate spills of either lighter-than-water NAPLs (LNAPLs) or denser-than-water NAPLs (DNAPLs). The NAPL phase can contain up to five organic constituents. The transfer of organic contaminants from the NAPL to the aqueous phase is described through either equilibrium partitioning or a linear driving force non-equilibrium mass transfer model. Adsorption of organic constituents is modeled through equilibrium partitioning. An arbitrary number of injection and pumping wells can be specified so that bioremediation schemes can be modeled and bioremediation designs can be optimized. The previous version of the UTCHEM model is described in detail by Delshad et al. (1996).

UTCHEM also simulates the biodegradation of chemical compounds that can serve as substrates (carbon and/or energy sources) for microorganisms. The model simulates the destruction of substrates, the consumption of electron acceptors (e.g. oxygen, nitrate, etc.), and the growth of biomass. Substrates can be biodegraded by free-floating microorganisms in the aqueous phase or by attached biomass present as microcolonies in the manner of Molz et al. (1986). Multiple substrates, electron acceptors and biological species are accommodated by the model. Important assumptions for the biodegradation model are:
  1. Biodegradation reactions occur only in the aqueous phase.

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

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

  4. Biomass is prevented from decaying below a lower limit by metabolism of naturally occurring organic matter unless cometabolic reactions act to reduce the active biomass concentrations below natural levels.

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

The biodegradation model includes the following features:

BIODEGRADATION EQUATIONS AND SOLUTION PROCEDURE


The biodegradation model equations describe the transport of substrate and electron acceptor from the aqueous phase into attached biomass, the loss of substrate and electron acceptor through biodegradation reactions, and the resulting growth of the free-floating or attached biomass. The flow and biodegradation system is solved through operator splitting, in which the solution to the flow equations is used as the initial conditions for the biodegradation reactions. This approach is convenient because modifications can be made to the system of biodegradation equations without having to reformulate the partial differential equations that describe advection and dispersion.

The biodegradation equations comprise a system of ordinary differential equations that must be solved at each grid block and each time step after the advection and dispersion terms are calculated. Because the mass transfer terms can make the system of equations stiff, the system is solved using a Gear's method routine published by Kahaner et al. (1989). The characteristics and numerical solution of this system of equations is discussed by de Blanc et al. (1996).

For a simple system of a single substrate, electron acceptor and biological species, the system of biodegradation equations is:

1)

2)

3)

4)

5)

6)

where:
S = concentration of substrate in the aqueous phase (ML-3)

= concentration of substrate in attached biomass (ML-3)

A = concentration of electron acceptor in the aqueous phase (ML-3)

= concentration of electron acceptor in attached biomass (ML-3)

X = concentration of free-floating biomass (ML-3)

= concentration of attached biomass (mass of attached biomass per volume of porous medium, ML-3)

E = mass of electron acceptor consumed per mass of substrate biodegraded

= surface area of a single microcolony (L2)

= mass transfer coefficient (LT-1)

max = maximum specific growth rate (T-1)

mk = mass of a single microcolony (M)

x = biomass density (ML-3)

Vk = volume of a single microcolony (L3)

Y = yield coefficient; mass of biomass produced per mass of substrate biodegraded

Ks = substrate half-saturation coefficient (ML-3)

Ka = electron acceptor half-saturation coefficient (ML-3)

b = endogenous decay coefficient (T-1)

kabio = first-order abiotic rate constant (T-1)

These equations are similar to the system of equations solved by Molz et al. (1984) and Chen et al. (1992). Equation 1 includes three mechanisms for loss of substrate from the aqueous phase: diffusion of substrate across a stagnant liquid layer into attached biomass; biodegradation of substrate by unattached microorganisms in the aqueous phase; and abiotic loss of the substrate through first-order reactions. The biodegradation reactions are limited by both the substrate and electron acceptor concentrations through the Monod terms.

Equation 2 describes the loss of substrate within attached biomass and is written for a single microcolony (Molz et al., 1986) This equation describes the diffusion of substrate into attached biomass and the biodegradation of the substrate within the biomass.

Equations 3 and 4 describe the loss of the electron acceptor. These equations are similar to Equations 1 and 2 in that they describe diffusion across a liquid film and loss in biodegradation reactions. The biodegradation rate expressions are multiplied by the factor E, the mass of electron acceptor consumed per mass of substrate biodegraded. Equations 4 and 5 describe the growth and decay of unattached and attached biomass, respectively.

When biodegradation reactions with more than one substrate are being modeled, equations similar to Equations 1 and 2 are solved for each additional substrate. Similarly, equations similar to Equations 3 and 4 are solved for each additional electron acceptor. Substrates can be biodegraded by microorganisms using more than one electron acceptor, and each electron acceptor can be used for biodegradation of multiple substrates.

When substrate competition is considered, the half-saturation coefficient of each Monod term is modified in the following manner (Bailey and Ollis, 1986):

7)

where:

S1, S2 = concentration of substrates 1 and 2, respectively (ML-3)

Ks1,Ks2 = concentration of half-saturation coefficients for substrates 1 and 2, respectively (ML-3)

If sequential electron acceptor utilization occurs (e.g., oxygen consumption followed by consumption of nitrate), then the equations for substrate loss, electron acceptor consumption and biomass growth are modified by multiplying the biodegradation rate expressions by an inhibition factor of the form (Widdowson et al., 1988):

8)

where I is an experimentally determined inhibition constant. The inhibition factor approaches 0 as the concentration of the inhibiting substance increases. For nitrate respiration, for example, this term keeps denitrification rates very small until oxygen is nearly exhausted.

When cometabolic reactions are considered, the equation describing attached biomass growth is (Chang and Alvarez-Cohen, 1995):

9)

where Tc is the transformation capacity, defined as the mass of substrate biodegraded per mass of biomass deactivated by the reaction. The second expression in Equations 9 describes the deactivation of biomass through cometabolism reactions, which can produce toxic by-products that damage cells (Chang and Alvarez-Cohen, 1995).

MODEL TESTING AND VALIDATION


The biodegradation component of UTCHEM was tested to ensure that correct solutions to the biodegradation equations are produced. The testing consisted of batch biodegradation simulations, in which the solutions to the equations provided by the model for simple systems were compared to solutions calculated in spreadsheets. Complete biodegradation solutions were also compared to literature solutions (Molz et al., 1986) to ensure that the simultaneous transport and biodegradation of substrates and electron acceptors produced reasonable results. The biodegradation model has not yet been validated by comparison to experimental or field data.

EXAMPLE SIMULATIONS


The multi-phase flow and biodegradation capabilities of the model are demonstrated through the simulation of hypothetical LNAPL and DNAPL spills. In these simulations, the modeling domain consists of a confined aquifer that is 125 m long by 54 m wide by 6 m thick. The domain is simulated with 25 grid blocks in the x direction, 11 grid blocks in the y direction, and 5 grid blocks in the z direction. Groundwater is flowing from left to right with an average velocity of 0.1 m/day. The spills are modeled by injecting the NAPL into the center of grid block (5, 6, 1), which is approximately 22 meters from the left boundary in the center of the modeling grid. There is no air phase in these simulations; the top boundary is a no-flow boundary.

LNAPL Simulation Example


Sequential use of electron acceptors and partitioning of multiple components into the aqueous phase are illustrated with an example LNAPL simulation. The LNAPL example simulates a leak of 1,000 gallons of crude oil containing approximately 1% by volume of benzene and 6% by volume of toluene into a shallow, confined aquifer. The leak is assumed to occur over a four-day period.

Figure 1 shows the evolution of the oil lens in a vertical slice down the center of the aquifer in the x-z plane. As seen in Figure 1, the oil moves little once the oil lens is established. The oil lens gradually decreases in size as the organic constituents dissolve into the flowing groundwater.

As the benzene and toluene partition out of the crude oil into the aqueous phase, they become available to microorganisms as substrates. For simplicity, a single population of microorganisms capable of biodegrading the benzene and toluene is assumed to exist in the aquifer. This biological species biodegrades both benzene and toluene aerobically and biodegrades toluene anaerobically with nitrate as the electron acceptor. Biodegradation kinetic parameters used for the simulation were obtained from Chen et al. (1992).

Figure 2 compares the concentration of benzene in the aqueous phase at 500 days to the concentration of benzene that would exist if no biodegradation reactions were occurring. The figure shows that significant biodegradation of dissolved benzene has occurred. The toluene plume is also shown in Figure 2. Although toluene has a lower solubility than benzene, the maximum toluene concentration in the dissolved phase is higher than the maximum concentration of the benzene plume because its concentration in the crude oil is greater than the benzene crude oil concentration. Toluene concentrations are nearly as low as benzene concentrations at the fringes of the plume because toluene is biodegraded both aerobically and anaerobically, where oxygen is exhausted, but the benzene is not.

The concentrations of benzene, toluene, oxygen and nitrate at 500 days are compared in Figure 3. Oxygen immediately downgradient of the spill is practically exhausted. Nitrate is also nearly exhausted from the area immediately downgradient of the spill because sufficient time has elapsed since oxygen depletion to allow denitrification to occur. However, at the forward edge of the plume, relatively high nitrate concentrations still exist in areas where oxygen has been depleted, but not exhausted.


DNAPL Simulation Example


Different model capabilities are illustrated with a DNAPL simulation in which TCE is biodegraded through cometabolism. In this simulation, 7.5 gallons of TCE is spilled in a single day. The cometabolic process is illustrated by injecting water containing methane through five injection wells located approximately 24 meters downgradient of the spill. The water contains 20 mg/L methane and 8 mg/L oxygen. The water injection rate is 1.4 m3 per day per well.

A population of methanotrophic microorganisms capable of biodegrading TCE aerobically through cometabolism is assumed to exist in the aquifer. The methanotrophs use methane as the primary substrate and oxygen as the electron acceptor. TCE biodegradation is assumed to reduce the active biomass and consume reducing power of the methanotrophs, so that TCE biodegradation both reduces the active biomass concentration and reduces the active biomass's biodegradation effectiveness. Once biomass has become deactivated, it does not become active again. Biodegradation rate parameters were obtained from Chang and Alvarez-Cohen (1995).

The effect of the methane injection wells is illustrated in Figure 4, where concentrations of TCE, a hypothetical TCE tracer, oxygen and methane are shown at 170 days. The TCE tracer is simply TCE that is not allowed to biodegrade in the model so that the effects of biodegradation can be seen. Concentration contours of the different constituents are shown in the top 1.2-m layer of the aquifer. Oxygen is depleted downgradient of the plume, but only a small fraction of the oxygen is consumed upgradient of the methane injection wells. Most of the oxygen upgradient of the wells remains because the high TCE concentrations deactivate the biomass and consume reducing power, preventing the TCE from biodegrading and further depleting the oxygen.

Even with a small TCE spill, TCE concentrations in the aquifer are so high that most biomass immediately downgradient of the spill is deactivated. Significant TCE biodegradation occurs only where appreciable methane is present to regenerate the microorganism's reducing power and where TCE concentrations are low. These effects can be seen in Figure 4. The high concentration contours of the TCE and TCE tracer are nearly the same, but biodegradation of the TCE causes a slight retardation in the progress of the TCE plume at low concentrations.

FUTURE MODEL ENHANCEMENTS


The UTCHEM biodegradation model is still in the development stage. The following features are planned for inclusion in the model prior to its completion:

ACKNOWLEDGMENT


The authors wish to acknowledge the significant contributions of Drs. Mojdeh Delshad, Gary A. Pope, and Kamy Sepehrnoori to our understanding of multiphase flow modeling and in the successful integration of the biodegradation modeling component into UTCHEM. This work was supported by the U.S. Environmental Protection Agency Robert S. Kerr Environmental Research Laboratory under grant CR 821897-01-0. This research has not been subjected to Agency review and therefore does not necessarily reflect the view of the Agency and no official endorsement should be inferred.

REFERENCES


Chang, H. and L. Alvarez-Cohen, Model for the cometabolic biodegradation of chlorinated organics, Environmental Science and Technology, 29(9): 2357-2367, 1995.

Chen, Y., L. M. Abriola, P. J. J. Alvarez, P. J. Anid and T. M. Vogel, Modeling transport and biodegradation of benzene and toluene in sandy aquifer material: comparisons with experimental measurements, Water Resources Research, 28(7): 1833-1847, July 1992.

de Blanc, P. C., K. Sepehrnoori, G. E. Speitel Jr. and D. C. McKinney, Investigation of numerical solution techniques for biodegradation equations in a groundwater flow model, Proceedings of the XI International Conference on Computational Methods in Water Resources, Cancun, Mexico, July 22-26, 1996 (in press).

Delshad, M., G. A. Pope and K. Sepehrnoori, A compositional simulator for modeling surfactant enhanced aquifer remediation, In press, Journal of Contaminant Hydrology, 1996.

Kahaner, David, C. Moler and S. Nash, Numerical Methods and Software, Prentice Hall, Englewood Cliffs, NJ, 1989.

Molz, F. J., M. A. Widdowson and L. D. Benefield, Simulation of microbial growth dynamics coupled to nutrient and oxygen transport in porous media, Water Resources Research, 22(8): 1207-1216, August 1986.

Widdowson, M. A., F. J. Molz and L. D. Benefield, A numerical transport model for oxygen- and nitrate-based respiration linked to substrate and nutrient availability in porous media, Water Resources Research, 24(9): 1553-1565, September 1988.



Figure 3. Concentrations of benzene without biodegradation, benzene with biodegradation, toluene, oxygen, and nitrate in upper 1.2 m of aquifer along aquifer center line at 500 days.