Analysis of biodegradation in a 3-D heterogeneous porous medium using nonlinear stochastic finite element method

Abstract

Probabilistic analysis by Monte Carlo Simulation method (MCSM) is a computationally prohibitive task for a reactive solute transport involving coupled PDEs with nonlinear source/sink terms in 3-D heterogeneous porous media. The perturbation based stochastic finite element method (SFEM) is an attractive alternative method to MCSM as it is computationally efficient and accurate. In the present study SFEM is developed for solving nonlinear reactive solute transport problem in a 3-D heterogeneous medium. Here the solution of the biodegradation problem involving a single solute by a single class of microorganisms coupled with dynamic microbial growth is attempted using this method. The SFEM here produces a second-order accurate solution for the mean and a first-order accurate solution for the standard deviation of concentrations. In this study both the physical parameters (hydraulic conductivity, porosity, dispersivity and diffusion coefficient) and the biological parameters (maximum substrate utilization rate and the coefficient of cell decay) are considered as spatially varying random fields. A comparison between the MCSM and SFEM for the mean and standard deviation of concentration is made for 1-D and 3-D problem. The effects of heterogeneity on the degradation of substrate and growth of biomass concentrations for a range of variances of input parameters are discussed for both 1-D and 3-D problems.