Modeling biodegradation processes in porous media by the finite cell method

Abstract

In this paper, the finite cell method (FCM) presented by Sun [1999] is extended to the two‐dimensional case and used to simulate complicated biodegradation processes in porous media. FCM is based on the direct simulation of various physical, chemical, and biological phenomena rather than solving advection‐dispersion‐reaction equations. The developed two‐dimensional FCM is able to deal with heterogeneous structures and variable flow fields. Two test problems show that FCM can produce more accurate solutions than other numerical methods. It can keep both local and global mass conservation and avoid numerical dispersion even when the Peclet number becomes infinite. The biodegradation model formulated in this paper consists of five partial differential equations with five unknown concentrations when kinetic mass exchange and rate‐limited attachment of microorganisms are considered. Using FCM to solve this problem, we define two sets of cells, the mobile fluid cells and the immobile solid cells. A mobile fluid cell may contain dissolved substrate, suspended microorganisms, and electron acceptor components, while an immobile solid cell may contain adsorbed substrate and attached biomass. When a mobile cell meets an immobile cell on its way, mass exchanges may occur between them and reactions may occur within them. By directly simulating these processes, all the five unknown concentrations can be obtained explicitly and simultaneously. A numerical example is given that shows the FCM solution of a biodegradation process in a randomly heterogeneous porous media. We expect that the FCM can serve as not only a powerful simulation tool but also a useful tool for mechanism study.