Analysis and numerical computation of geochemical systems with kinetic precipitation and dissolution reactions involving several minerals

In this paper, we study underground media where chemical interactions involve aqueous and mineral species. In most kinetic models, a mineral species is involved in a single precipitation or dissolution reaction. In this work, we consider more general precipitation and dissolution kinetic reactions, which can include several minerals, which can each participate in several reactions. We propose a differential inclusion model, with reaction rates defined by set-valued functions, in order to ensure positive quantities of species. We also develop a regularized model, with reaction rates defined by regularized Heaviside functions and blendings if several minerals dissolve in the same reaction. We prove that the unique solution of this system of ODEs converges towards a solution of the differential inclusion model. We run numerical experiments by using a classical ODEs solver for computing the regularized solution. We get good numerical approximations of the quantities of species and the discontinuous reaction rates.