Numerical solution of the advection-reaction-diffusion equation at different scales

Solving the transport equation for bimolecular reactive processes in porous media involves several difficulties. The mathematical characteristics of the equation depend on the governing process, for example, when time scales for advection t"A, reaction t"R and diffusion t"D have different orders of magnitude. On the other hand, this equation is based on a continuum model, disregarding inhomogeneities that happen at poral level just where reactions take place. To deal with these problems a different way of modeling the advection-reaction-diffusion process is proposed. Based on the Damkohler number an algorithm has been developed to solve the problem for both slow and fast reactions. Spatial segregation of reactants can be incorporated improving the results.