A model for calcium carbonate neutralization in the presence of armoring

In this paper we present a mathematical model for the reaction between calcium carbonate (CaCO3) and a solution containing sulfuric acid (H2SO4). We assume that Ca2+ ions (liberated on the reaction surface) react with SO42- ions to form solid gypsum crystals (CaSO4) which, in turn, may accumulate on the reaction surface, hindering the neutralizing process (armoring). We suppose that neutralization is governed by a first order reaction, with the reaction rate depending on the superficial density of solid CaSO4. We prove that the problem is multiscale in time and study the problem in fast time scale (order of hours), showing numerical and analytical results. In particular we determine the conditions that guarantee complete neutralization.