  We study the diffusion-reaction-advection model for mobile chemical species
together with the dissolution and precipitation of immobile species in a porous
medium at the micro-scale. This leads to a system of semilinear parabolic
partial differential equations in the pore space coupled with a nonlinear
ordinary differential equation at the grain boundary of the solid matrices. The
fluid flow within the pore space is given by unsteady Stokes equation. The
novelty of this work is to do the iterative limit analysis of the system by
tackling the nonlinear terms, monotone multi-valued dissolution rate term,
space-dependent non-identical diffusion coefficients and nonlinear
precipitation (reaction) term. We also establish the existence of a unique
positive global weak solution for the coupled system. In addition to that, for
upscaling we introduce a modified version of the extension operator. Finally,
we conclude the paper by showing that the upscaled model admits a unique
solution.
