Robust simulation of mineral precipitation-dissolution problems with variable mineral surface area - Kräutle, Serge; Hodai, Jan; Knabner, Peter (Journal of Engineering Mathematics, 2021)
We consider a macroscale model of transport and reaction of chemical species in a porous medium with a special focus on mineral precipitation–dissolution processes. In the literature, it is frequently proposed that the reaction rate should depend on the reactive mineral surface area, and so on the amount of mineral. We point out that a frequently used model is ill posed in the sense that it admits non-unique solutions. We investigate what consequences this non-uniqueness has on the numerical solution of the model. The main novelty in this article is our proposal of a certain substitution which removes the ill-posedness from the system and which leads to better numerical results than some “ad hoc methods.” We think that the proposed substitution is a rather elegant way to get rid of the non-uniqueness and the numerical difficulties and is much less technical than other ideas. As a proof of concept, we present some numerical tests and simulations for the new mode
Keywords: Complementarity problem; Dissolution; Mineral reactions; Newton’s method; Non-Lipschitz; Precipitation; Reactive transport; Uniqueness