Efficient Algorithms for Modeling the Transport and Biodegradation of Chlorinated Ethenes in Groundwater

Abstract

Predicting the fate of chlorinated ethenes in groundwater requires the solution of equations that describe both the transport and the biodegradation of the contaminants. Here, we present a model that accounts for (1) transport of chlorinated ethenes in flowing groundwater, (2) mass transfer of contaminants between mobile groundwater and stationary biofilms, and (3) diffusion and biodegradation within the biofilms. Equations for biodegradation kinetics account for biomass growth within the biofilms, the effect of hydrogen on dechlorination, and competitive inhibition between vinyl chloride and cis-dichloroethene. The overall model consists of coupled, non-linear, partial differential equations; solution of such a model is challenging and requires innovative numerical algorithms. We developed and tested two new numerical algorithms to solve the equations in the model; these are called system splitting with operator splitting (SSOS) and system splitting with Picard iteration (SSPI). We discuss the conditions under which one of these algorithms is superior to the other. The contributions of this paper are as follows: first, we believe that the mathematical model presented here is the first transport model that also accounts for diffusion and nonlinear biodegradation of chlorinated ethenes in biofilms; second, the SSOS and SSPI are new computational algorithms developed specifically for problems of transport, mass transfer, and non-linear reaction; third, we have identified which of the two new algorithms is computationally more efficient for the case of chlorinated ethenes; and finally, we applied the model to compare the biodegradation behavior under diffusion-limited, metabolism-limited, and hydrogen-limited (donor-limited) conditions.

Biological Limitations of Dechlorination of cis-Dichloroethene during Transport in Porous Media

“…Mathematical Model for Transport and Reaction. In a previous paper 18 we presented a mathematical model that accounts for three important processes: transport of dissolved cis-DCE in the mobile fluid by advection and dispersion, mass transfer of chemical species between the mobile fluid and stationary biofilms, and diffusion and nonlinear Monod kinetics (for both bacterial growth and biodegradation) within the biofilms. The Monod-kinetic model, adopted here, was presented by Cupples et al 21 and describes reductive dehalogenation from cis-DCE to ethene under substratelimiting conditions and competitive inhibition between cis-DCE and VC.…”

“…The equations describing these processes are coupled, nonlinear, partial differential equations, for which efficient solution algorithms were also developed. 18,19 A nondimensional version of the system of equations, with definitions of all variables, is presented in the SI.…”

“…Therefore, the objectives of this paper are (1) to apply the mathematical model of Mendoza-Sanchez and Cunningham 18 to the experimental data of Mendoza-Sanchez et al; 17…”

Kinetic modelling of a diesel-polluted clayey soil bioremediation process

“…Furthermore, it is also possible to find models that couple mass transfer phenomena with kinetics to study the bioremediation process of hydrocarbon polluted groundwater in the literature. Thus, some researchers have developed models that couple the transport of hydrocarbons with Monod kinetics for hydrocarbon biodegradation in groundwater (Mendoza-Sanchez and Cunningham, 2012;Song et al, 2014). Song et al (2014) developed a mathematical model to simulate groundwater flow, naphthalene transport and biokinetic parameters that provides a general description of the experimental trends, although there are some discrepancies between the observed and simulated data.…”

Modeling alginate encapsulation system for biological hydrogen production

“…Models have been developed to describe diffusion and reaction in wastewater‐based biofilms (Boltz, Johnson, Daigger, & Sandino, ; Boltz, Johnson, Daigger, Sandino, & Elenter, ; Cunningham & Mendoza‐Sanchez, ; Mendoza‐sanchez & Cunningham, ; Williamson & McCarty, , ) as well as in aerobic systems containing pure cultures of encapsulated microorganisms (de Gooijer, Wijffels, & Tramper, ; Wijffels, de Gooijer, Kortekaas, & Tramper, ). Modification of these basic models should result in a model that is able to describe a more complex anaerobic encapsulated mixed culture, however, which has not been done.…”