Mathematical model for calcium carbonate acid mine drainage reaction: a multiple time scale approach

In this paper we present a mathematical model for the flow of an acid solution through a reacting porous medium. The solid matrix is supposed to be formed by families of spheres with different radii and the fluid is supposed to saturate the pores. The system is described by the evolution of the overall ion concentration and the radii of the spheres. The structure of the mathematical problem is multi-scale in time and for each time-scale different simplified problems can be obtained. We give some analytical results and display some numerical simulations to show the behavior of the solutions. The main practical application of this model is the flow of acid solution through neutralizing cartridges in which solid particles of CaCO3 are used to neutralize a given flow of an acid mine drainage.