A mathematical model of bioremediation in a porous medium

A simplified model for bacterial remediation of wastes in a porous medium is proposed. The mathematical model consists of a coupled set of nonlinear partial differential equations and an ordinary differential equation. Basic existence, uniqueness and regularity of the system can be proved in three space dimensions, globally in time. The existence of travelling waves can also be established. In a physically relevant limit, a free boundary problem can be formally derived. In this sharp interface limit the shape stability of the moving reaction fronts can be studied using elementary bifurcation analysis. In agreement with industrial observations, these reaction fronts are stable in the early phases of remediation, becoming unstable as the concentration of bacteria becomes high. This could lead to undesirable fingering which would result in some of the waste being inaccessible to the bacteria, greatly reducing the effectiveness of this type of remediation process. (Joint work with Changsheng Chen, Manulife Insurance, Toronto, Cananda)