| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
|
|
|
|||||||
|
|||||||||
Aquater SpA (ENI Group), Via Miralbello 53, 61047 San Lorenzo in Campo (PU), Italy (now at Aquater Division, Snamprogetti SpA, ENI Group)
* Corresponding author (alfredo.battistelli{at}snamprogetti.eni.it)
Received 5 August 2003.
 |
ABSTRACT |
|---|
 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTSSUMMARY AND CONCLUSIONSAPPENDIXREFERENCES |
|---|
Abbreviations: DCE, dichloroethene • DO, dissolved oxygen • EA, electron acceptor • IFD, integral finite difference • NAPL, nonaqueous phase liquid • NCG, noncondensible gases • N–R, Newton–Raphson • PCE, tetrachloroethene • SVE, soil vapor extraction • TCE, trichloroethene • VC, vinyl chloride • VOC, volatile organic compound
|
INTRODUCTION |
|---|
|
TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSSUMMARY AND CONCLUSIONSAPPENDIXREFERENCES |
|---|
It has been observed in natural systems and verified by laboratory experiments that organic contaminants are actively degraded by naturally occurring microorganisms living in the subsurface that can use VOCs as substrates for their metabolic processes and growth or can transform them by means of cometabolic processes. This observation has led to research and investment in the study of natural attenuation and stimulated research into developing biodegradation processes as a technically feasible and viable clean-up alternative, even from an economic point of view. In this context, modeling tools can be quite useful for the interpretation of coupled processes that govern the migration under multiphase conditions and the biodegradation of organic contaminants in the unsaturated and saturated zones. Until recently, most studies of VOC biodegradation modeling addressed the degradation of VOCs dissolved in groundwater in the saturated zone. Examples of such approaches are given by Borden and Bedient (1986), MacQuarrie et al. (1990), Chilakapati (1995), Essaid and Bekins (1997), Clement (1997) and Waddill and Widdowson (1998), among many others. Fewer examples exist of modeling of VOC biodegradation in saturated–unsaturated conditions, such as those presented by Travis and Rosenberg (1997), Yeh et al. (1998), El-Kadi (2001), and Mayer et al. (2002), as well as in full multiphase conditions, as made by the University of Texas (2000). With the objective of extending the modeling capabilities of the TMVOC numerical reservoir simulator (Pruess and Battistelli, 2002) to handle biodegradation in complex heterogeneous porous media under multiphase conditions such as will be encountered in the vadose zone, TMVOC was enhanced to form TMVOCBio (Aquater, 2002). The new capabilities are important to perform risk assessment studies as well as to evaluate the efficiency of different clean-up alternatives in terms of reduction of contamination level and duration of remediation operations. Modeling studies can also support the interpretation of monitoring data to enhance the understanding of subsurface processes to improve the management of clean-up operations.
|
MATERIALS AND METHODS |
|---|
|
TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSSUMMARY AND CONCLUSIONSAPPENDIXREFERENCES |
|---|
In all simulators of the TOUGH2 family of codes, space discretization is made directly from the integral form of mass and energy balance equations following the integral finite difference (IFD) method (Narasimhan and Witherspoon, 1976). The mass balance equation for the generic component 
for a mixture of NK mass components distributed in NPH phases assumes, for the generic grid element n = 1, N of volume Vn and surface 
n, the following form (Pruess et al., 1999):
 | [1] |
= 1, NK is
 | [2] |
= NK + 1) is
 | [3] |
The advective mass flux of component is given by the sum of fluid phase fluxes through the element surface:
 | [4] |
The advective flux of each fluid phase is computed with the multiphase version of Darcy's equation:
 | [5] |
In addition to the advective flux, TOUGH2 includes the multicomponent molecular diffusion in all phases:
 | [6] |
 | [7] |
The heat flux considers the advective and conductive components:
 | [8] |
For each volume element a set of NK + 1 primary variables is needed to define the thermodynamic state of the fluid mixture and the same number of balance equations must be solved. Time is discretized implicitly following a first-order backward finite difference scheme. The N(NK + 1) partial differential equations describing the whole fluid system are discretized in space using the IFD method obtaining a set of coupled highly nonlinear algebraic equations, with the time-dependent primary variables of all grid blocks as unknowns, which are solved simultaneously using the Newton–Raphson (N–R) iteration. Both direct and iterative solvers are available within the TOUGH2 architecture (Pruess et al., 1999). Time steps can be automatically adjusted during a simulation run, depending on the convergence rate of the N–R iteration process for a more efficient solution of multiphase flow problems. Thus, TOUGH2 uses a fully coupled approach in which the governing equations are numerically solved as a single system.
Although released as a free standing code, TMVOC (Pruess and Battistelli, 2002, 2003) is basically an equation of state module compatible with the TOUGH2 numerical simulation architecture developed to model the three-phase nonisothermal flow of water, NCGs, and VOCs fluid mixtures in three-dimensional heterogeneous porous media. It is designed for application to contamination problems that involve the migration in saturated and unsaturated zones of hydrocarbon fuel or organic solvent spills. It can model contaminants behavior under "natural" environmental conditions, as well as for engineered systems, such as SVE, groundwater pumping, or steam-assisted source remediation. In TMVOC the fluid mixture is composed by a set of NK (
20) components, including water; user-defined NCGs that can be chosen among O2, N2, CO2, CH4, ethane, ethylene, acetylene, and pseudo-component air; and NHC user-defined VOCs (hydrocarbons or organic solvents). Assuming local thermodynamic equilibrium conditions, these components are distributed in any of the three possible flowing phases: gas, aqueous, and the NAPL, including the optional adsorption on rock grain surfaces. Any combination of the three phases and related possible phase transitions are modeled by TMVOC as shown in Fig. 1
, using a compositional approach basically derived from that developed for multicomponent organic mixtures by Adenekan (1992). A detailed description of the thermodynamic and numerical formulations of TMVOC is outside the scope of this paper, but interested readers can refer to Pruess and Battistelli (2002). Below, we give an overview of the theory and equations to extend TMVOC to include biodegradation reactions.
|
The occurrence of these reactions in the subsurface depends on the availability of different EAs and on redox conditions, which can vary substantially as a result of contaminant biodegradation or other natural conditions. In the presence of organic substrates and dissolved oxygen (DO), microorganisms capable of aerobic metabolism will predominate over anaerobic forms. As DO is rapidly consumed in the interior of contaminant plumes, anaerobic bacteria begin to utilize other EAs to metabolize dissolved organic contaminants. The principal factors influencing the utilization of the various EAs include (i) the relative biochemical energy provided by the reaction, (ii) the availability of individual or specific EAs, and (iii) the kinetics of the microbial reactions associated with the different EAs. The modeling of biodegradation reactions requires the description of the role of living organisms whose behavior in subsurface systems is rather complex. The discussion of phenomena like the delayed metabolic response of bacteria to changes in local substrate conditions (Wood et al., 1995), the transport of bacteria and their partitioning between aqueous and solid phase, and the role of maintenance and endogenous respiration (Van Loosdrecht and Henze, 1999) are outside the scope of this introductory section. Reference is made to technical literature, such as the review recently presented by Ginn et al. (2002) and related references.
TMVOCBio Methods
The uptake of organic contaminants due to degradation reactions mediated by microorganisms living in the subsurface depends on many coupled processes, including multiphase flow and transport of solutes, reactions involving primary and cometabolic substrates, EAs and nutrients availability, as well as chemical equilibria in the aqueous phase. The complexity of these phenomena has led to the development of many different mathematical models for the simulation of biodegradation reactions in porous media. These models differ in many respects, starting with the way the microorganisms present in the subsurface are conceptualized and treated, either as biofilms, as microcolonies, or according to the so-called macroscopic or unstructured approach (Baveye and Valocchi, 1989; Ginn et al., 2002). Modified forms of the Michaelis–Menten rate equation for enzyme kinetics used to express the uptake rate of substrate accounting for the limitation by either the substrate, the EA, and nutrients have been proposed to model the kinetics of biodegradation reactions in subsurface porous media. One of two main approaches is usually followed in presently available numerical models. In the first approach, it is assumed that all the limiting factors are acting simultaneously to control the substrate uptake rate (the "multiplicative Monod" model of Borden and Bedient, 1986). Second, it is assumed that the substrate uptake rate is controlled by the most limiting factor among those acting for the specific substrate (the "minimum Monod" model, Kindred and Celia, 1989). Whereas in all models both the primary substrate and the EAs are considered in the substrate degradation rate equation, the nutrient availability is either considered to directly limit the substrate degradation rate (Waddill and Widdowson, 1998) or to limit biomass growth rate, without explicitly affecting the substrate degradation rate (Essaid and Bekins, 1997).
Assumptions
For the implementation of biodegradation reactions in TMVOCBio, a number of simplifying assumptions have been considered, in analogy to those used by several authors in the field of numerical modeling of biodegradation reactions in the subsurface:
Mathematical Formulation of Biodegradation Reactions
The degradation rate of the organic substrate for the generic biodegradation process is presented here using the multiplicative Monod kinetic rate model (Borden and Bedient, 1986; Waddill and Widdowson, 1998), even though the minimum Monod model can be chosen. For the sake of simplicity, the following equations are referred to as a single process acting on a primary substrate, and only the limitation due to substrate and EA availability is considered, even though limitations due to any other solute dissolved in the aqueous phase can be modeled by invoking the appropriate Monod term. The degradation rate is
 | [9] |
 | [10] |
 | [11] |
Numerical Solution of Biodegradation Reactions
Biodegradation reactions, treated in analogy to internal sink–source terms in the mass balance equations of TOUGH2/TMVOC, are assembled and separately solved within a dedicated subroutine for each N–R iteration implemented by TMVOCBio in the convergence process of balance equations performed at any time step. Following the numerical approach implemented by Oldenburg (2001) into the T2LBM equation of state module developed to model the biodegradation of solid wastes in municipal landfills, the biomass growth equation can be further expressed in terms of substrate degradation rate by substituting the left-side term of Eq. [9] into Eq. [11]:
 | [12] |
At the end of a generic time step of length 
t the biomass concentration can be evaluated:
 | [13] |
The substrate uptake rate is computed as S = S*. S* is evaluated by interpolation between the substrate concentration at the beginning (S1) and that evaluated at the end of the current time step (S2) according to
 | [14] |
 | [15] |
 | [16] |
Equation [16] is then solved for the new substrate concentration, S2, by the Newton–Raphson iteration. The concentration changes of other mass components Xk,(k = 1,NK), derived by the substrate degradation S, are calculated according to the uptake coefficients 
k for the specific degradation process (Essaid and Bekins, 1997):
 | [17] |
Upon convergence of the time step, assuming there are no changes of the amount of aqueous phase stored in the grid element, the microbial mass fraction in the aqueous phase would be updated according to
 | [18] |
In multiphase conditions, the microbial mass fraction in the aqueous phase is updated considering both the microbial mass growth and death, as well as the change in the aqueous phase mass stored in the porous medium, due to variations of aqueous phase saturation and density. Neglecting the bacteria transport, the mass balances of microbial populations are performed without including the biomass concentration among TMVOCBio primary variables. The ordinary differential equations describing the biodegradation reactions are then solved in TMVOCBio for each time step and at any grid block separately from mass balance equations, as made in split-operator approaches. As biodegradation reactions are treated as internal sink/sources computed for each N–R iteration of TMVOCBio, the algorithm used is similar to that of the iterative split-operator method (Kanney et al., 2003). The numerical solution of nonlinear reactive transport problems performed using split-operator approaches introduces an additional source of numerical error, known as splitting error, generated by the decoupling of governing equations (Valocchi and Malmstead, 1992). The splitting error depends on the time step length and is also related to the magnitude of reaction rates (Kanney et al., 2003; University of Texas, 2000).
Extension to Multiple Simultaneous Processes
Following the BIOMOC approach, the above numerical formulation has been extended to model the occurrence of multiple degradation processes simultaneously acting on the same organic substrate but mediated by different microbial populations or based on different redox reactions, thus involving different EAs. A description of the formulation is given in Aquater (2002) and by Battistelli (2003).
|
RESULTS |
|---|
|
TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSSUMMARY AND CONCLUSIONSAPPENDIXREFERENCES |
|---|
|
|
|
trichloroethene [TCE] dichloroethene [DCE] vinyl chloride [VC]), as well as the aerobic degradation of DCE and VC together with benzene and methane dissolved in the groundwater. The complete problem specifications are given by Essaid and Bekins (1997), and reference to their work is made for detailed information. Essaid and Bekins simulated one-dimensional flow and reactive transport along a 457-m-long streamline located on the plume axis, by specifying the groundwater flow velocity and the recharge of surface water rich in DO taking place in the first 198 m of the streamline. Initial conditions were zero concentrations for all the solutes, whereas constant solute concentrations at the inlet boundary were specified during the 8-yr simulation. Steady-state conditions were reached at the end of the simulated period.
Seven different degradation processes were simulated: three anaerobic processes representing the dechlorination chain PCE TCE DCE VC and four aerobic processes involving DCE, VC, benzene, and methane. Including DO, seven reactive solutes were modeled. Two nongrowing microbial populations were simulated, one anaerobic and one aerobic. Figure 5 and 6
show the TMVOCBio simulated results compared with the field data reported by Essaid and Bekins. The TMVOCBio simulated results reproduced the field data with an accuracy that is comparable to that obtained by BIOMOC. There is, however, a visible difference in the concentration of DO, DCE, VC, and benzene in the first 100 m. Because of the initial low content of DO in inflowing groundwater, anaerobic degradation of PCE, TCE, and DCE occurs. The O2 added through surface water recharge is consumed for the aerobic degradation of CH4, primarily, and to a lesser extent, of DCE, benzene, and VC. After the first 70 m, the CH4 concentration is reduced to levels that slow down the DO consumption, so its concentration in groundwater starts to increase to about 150 m from the inlet. Dissolved oxygen concentration becomes almost constant up to about 200 m, where water recharge stops, and then decreases in the final section because of aerobic degradation reactions. Anaerobic reactions are simulated with a first-order decay rate using the Monod model. They are inhibited by the presence of DO using a noncompetitive inhibition approach to slow down the reductive dehalogenation of solvents in aerobic conditions. The aerobic reactions are limited by the DO availability as well, using a multiple Monod approach with a fairly low half saturation concentration of DO, 0.1 µg L–1. This low concentration allows the aerobic reactions to occur at a relatively high rate even at low O2 concentrations. The Dover Air Force Base simulation results obtained with BIOMOC are shown in Fig. 7
. They were produced by running BIOMOC using the original input file. BIOMOC simulates a constant DO concentration of 52.6 µg L–1 in the first 70 m, whereas TMVOCBio gives a much lower concentration. The lower DO concentration modeled by TMVOCBio still allows the degradation of CH4, which is present at high concentrations, but results in a lower degradation of VC and benzene compared with that simulated by BIOMOC.
|
|
|
|
SUMMARY AND CONCLUSIONS |
|---|
|
TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSSUMMARY AND CONCLUSIONSAPPENDIXREFERENCES |
|---|
Preserving the capabilities of the original code, TMVOCBio allows the modeling of aerobic and anaerobic degradation reactions of multiple organic compounds in the subsurface under multiphase flow conditions. TMVOCBio uses a general formulation of degradation reactions that is a modified version of that developed for the BIOMOC simulator by Essaid and Bekins (1997). It allows the user to define a number of simultaneous degradation processes mediated by different microbial populations. Through the specification of uptake coefficients for all the simulated compounds for each degradation process, TMVOCBio can simulate the consumption of primary substrates, EAs, and nutrients, as well as the generation of reaction by-products. Reaction rates are computed using either the multiplicative or minimum Monod model, accounting for the availability of primary substrates, EAs, and nutrients. Inhibitive effects, including competitive, noncompetitive, and Haldane inhibitions, can be simulated, as well as the inhibition of biomass growth. TMVOCBio can be used to simulate both the degradation of primary organic substrates and the degradation of chlorinated solvents under aerobic conditions through cometabolism and through reductive dehalogenation under anaerobic conditions. TMVOCBio can be used to model both naturally occurring and stimulated biodegradation reactions taking place in aquifers as well as in the unsaturated zone. Thus, both the contaminant distribution in the unsaturated zone beneath spill areas and the related evolution of groundwater contaminated plumes can be modeled. Additional code validation against experimental data collected in unsaturated conditions is necessary.
The improvement of TMVOCBio by accounting for the effects of solutes concentration on the aqueous phase properties is underway. The simulation of density dependent flow is important for the modeling of coastal contaminated aquifers, where seawater intrusion can substantially affect the transport of contaminant plumes. Additional efforts must be directed to study time discretization strategies and their effects on the accuracy of numerical solutions. The need for limitation of the time-step size depending on the maximum substrate degradation rate has already been pointed out (Aquater, 2002). TMVOCBio does not simulate the EAs occurring as solid phases (i.e., ferric Fe and oxidized Mn). The inclusion of mass components occurring as solid phases can be pursued in future code developments.
|
APPENDIX |
|---|
|
TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSSUMMARY AND CONCLUSIONSAPPENDIXREFERENCES |
|---|
B0mass fraction of biomass at the beginning of time step
CRrock specific heat (J °C–1 kg–1)
EEA mass fraction
fdiffusive flux of component (kg m–2 s–1)
Fflux of component (kg m–2 s–1)
fTinhibitive function of temperature
fSWinhibitive function of aqueous phase saturation
gacceleration of gravity (m s–1)
hspecific enthalpy (J kg–1)
IBbiomass growth inhibition factor
ICcompetitive inhibition factor
IHHaldane inhibition factor due to toxicity effects
INCnoncompetitive inhibition factor
kintrinsic permeability (m2)
krßrelative permeability to phase ß
KEAEA half saturation constant
KSsubstrate half saturation constant
Maccumulation term of component (kg m–3)
Ppressure (Pa)
qsink or source specific rate of component (kg s–1 m–3)
Ssubstrate mass fraction
Sßsaturation of phase ß
ttime (s)
Ttemperature (°C)
uDarcy velocity (m s–1)
ußinternal energy of phase ß (J kg–1)
Vnvolume of grid element n (m–3)
winterpolation weight factor
Xcomponent mass fraction
Ybiomass yield coefficient
uptake coefficient
ßphase indicator
first-order biomass death rate constant (s–1)
ttime step length (s)
rock porosity
nsurface area of grid element n (m2)
thermal conductivity of porous medium (W m–1 s–1)
µdynamic viscosity (Pa s)
µmax,Bmaximum specific substrate utilization rate by biomass (s–1)
µ0,Bspecific substrate utilization rate (s–1)
density (kg m–3)
tortuosity factor
|
ACKNOWLEDGMENTS |
|---|
|
REFERENCES |
|---|
|
TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSSUMMARY AND CONCLUSIONSAPPENDIXREFERENCES |
|---|
This article has been cited by other articles:
|
|
 |
|
  A. Battistelli Modeling Multiphase Organic Spills in Coastal Sites with TMVOC V.2.0 Vadose Zone J., February 25, 2008; 7(1): 316 - 324. [Abstract] [Full Text] [PDF]
|
|
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
| The SCI Journals | Agronomy Journal | Crop Science | |||
| Journal of Natural Resources and Life Sciences Education |
Soil Science Society of America Journal | ||||
| Journal of Plant Registrations | Journal of Environmental Quality |
The Plant Genome | |||
