Bioremediation in a Porous Medium: Modelling, Theory and Applications

Abstract

<p>A 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 this system have been studied in three space dimensions, globally in time. The existence of travelling wave solutions has also been proved. A free boundary problem has been formally derived in the limit of large solid density and the shape stability of the moving reaction interface has been studied using bifurcation methods along with numerical computations. It has been proved that the planar solution to the free boundary problem is the limit of the travelling wave solutions as the solid density becomes large. In some cases, shaped (not planar) reaction interfaces have been found which are unstable. During the early phase of remediation (when the bacteria are capable of freely moving from waste sites already occupied by other bacteria, effectively reducing the viscosity) planar reaction fronts are stable. On the other hand, during later phase (when the concentration of bacteria is high and crowding, effectively increasing the viscosity) planar reaction fronts are unstabIe. This could lead to fingering in the fronts which would result in some of the wastes being inaccesible to the bacteria, greatly reducing the effectiveness of this as a remediation process.</p>