A model for transport of solutes in a porous medium participating in a dissolution–precipitation reaction, in general not in equilibrium, is studied. Ignoring diffusion–dispersion the initial value problem for piecewise constant initial states is studied, which e.g. for ionic species include a change of the ionic composition of the solution. The mathematical solution, nearly explicitly found by the method of characteristics up to the (numerical) solution of an integral equation for the position of the dissolution front, exhibits a generalized expanding plateau-structure determined by the dissolution front and the water flow (or salinity) front.
Duijn, van, C. J., Knabner, P., & Schotting, R. J. (1998). An analysis of crystal dissolution fronts in flows through porous media. Part 2: Incompatible boundary conditions. Advances in Water Resources, 22(1), 1-16. https://doi.org/10.1016/S0309-1708(97)00038-9