Existence and Uniqueness of a Global Solution for Reactive Transport with Mineral Precipitation-Dissolution and Aquatic Reactions in Porous Media
Joachim Ernst Hoffmann, Serge Kräutle, Peter Knabner · SIAM Journal on Mathematical Analysis · 2017
We consider a macroscopic (averaged) model of transport and reaction in the porous subsurface. The model consists of PDEs for the concentrations of the mobile (dissolved) species and of ODEs for the immobile (mineral) species. For the reactions, we assume the kinetic mass action law. The constant activity of the mineral species leads to set-valued rate functions or complementarity conditions coupled to the PDEs and ODEs. In this paper we first prove the equivalence of several formulations in a weak sense. Then we prove the existence and the uniqueness of a global solution for a multispecies multireaction setting with the method of a priori estimates. In addition to mineral precipitation-dissolution reactions, the model also allows for aquatic reactions, i.e., reactions among the mobile species. In both the mineral precipitation-dissolution rates and the aquatic reaction rates we consider polynomial nonlinearities of arbitrarily high order.