Modeling microbial-mediated reduction in batch reactors

The governing equations that depict microbially-mediated reduction of heavy metals in the subsurface include a system of coupled nonlinear partial differential equations (PDE's) that describe physical (transport), chemical (sorption), and microbial (reduction/oxidation) processes. The existence of nonlinear reaction terms makes numerical simulations more challenging; however, with the advent of time-splitting solution algorithms, nonlinear reaction terms can be isolated from the convective-dispersive components of the governing transport equations and then solved as a coupled system of nonlinear ordinary differential equations (ODE's). In this paper, four methods are evaluated for solving coupled systems of nonlinear ODE's that describe microbially-mediated reduction/oxidation processes. The evaluation involves a series of comparisons of transient simulations of electron donor oxidation, electron acceptor reduction, and microbial biomass accumulation. The methods evaluation is initiated with a comparison of simulation results obtained with the four methods to those generated with an analytical model. Next, laboratory observations, of nitrite consumption by Nitrobacter winogradski in batch reactors are used in a comparison of batch system simulations generated using each of the four methods and BIOKEMOD (biogeochemical kinetic/equilibrium reaction model). The evaluation finds one of the four methods, the quasi-steady-state approximation (QSSA), to be among the most accurate and easiest to implement. Final validation of the QSSA is performed simulating experimental results of microbially-mediated chromium reductions in batch cultures.