The semismooth Newton method for multicomponent reactive transport with minerals

In this article a method is proposed for the efficient simulation of reactive systems or reactive transport problems including (equilibrium) mineral precipitation–dissolution. The difficulty lies in the fact that for larger systems it is usually a priorily not known for which mineral the fluid is saturated and for which it is undersaturated. Currently wide-spread algorithms use some trial-and-error strategy requiring repeated computations, or an approximation of equilibrium precipitation–dissolution by a kinetic description. In this article we propose to formulate the problem as a so-called complementarity problem (CP) and to solve it with the semismooth Newton method, a solution strategy well known in the field of optimization theory. The CP formulation of the mineral reactions is then combined with a reformulation for the full multicomponent reactive transport problem which leads to a reduction of the number of unknowns. The reactive transport problem is tackled in the sense of a one step (global implicit) method.