Stochastic models in flow through porous media: An application to bioremediation

A porous medium is any environment consisting of interconnected pores that allows fluids to move through it. Since soil is a porous medium, modeling many underground processes requires understanding of how fluid flows through the channels. Some problems that require the description of the subsurface flow conditions are oil recovery, agricultural solute transport, civil and hydrological engineering, and bioremediation. This paper focuses on modeling flow through porous media in bioremediation setting, a pollution-containing technique using bacteria.; We start the paper with an overview of how bioremediation has been conducted and what its difficulties and future goals are. Treating soil and groundwater in their subsurface positions by possibly introducing a culture of bacteria is termed in situ bioremediation. In situ bioremediation has many obstacles, including the difficulties of having to model the interactions among numerous processes, though there is much interest in pursuing it since it leaves the environment relatively undisturbed, and is relatively inexpensive.; In our models we consider the velocity field being random to better describe the heterogeneous media. We give a description of the physical setting, and a discussion of why a random model is appropriate for the problem. The method used to calculate the random fields is introduced and analyzed both numerically and theoretically on its performance. Model equations are introduced, and numerical techniques in solving them are discussed. In addition we present some numerical examples of the differences in the solutions of the deterministic and related random problems. We end the paper summarizing the chapters and addressing some future directions.