Dispersion, convection, and reaction in porous media

The problem of transport of a reactive solute in a porous medium by convection and diffusion is studied for the case in which the solute particles undergo a first‐order chemical reaction on the surface of the bed. Assuming that the geometry is periodic, the method of homogenization is applied, showing explicitly that the effective equation is given by a Kramers–Moyal expansion, i.e., a partial differential equation of infinite order in which the nth term is the product of the nth gradient of the mean concentration by an nth‐order constant tensor. The effective values of reactivity, solute velocity, diffusivity, and of all the tensorial coefficients in the expansion are independent of the initial solute distribution and are expressed in terms of Peclet’s and Damkohler’s numbers, Pe=aV/D and Da=ak/D, respectively, where a is the cell size, V is the solvent mean velocity, D is the solute molecular diffusivity, and k is the surface reactivity, showing that they are independent of the initial solute distributi...