Exact analytical solutions for a diffusion problem coupled with a precipitation-dissolution reaction and feedback of porosity change

摘要

We present exact analytical solutions for a one-dimensional diffusion problem coupled with the precipitation-dissolution reaction A_(aq) + B_(aq) ←→ and feedback of porosity change. The solutions are obtained in the form of traveling waves and describe spatial and temporal evolutions of solute concentration, porosity, and mineral distribution for a set of initial and boundary conditions. The form of the solutions limits the choice of admissible boundary conditions, which might be difficult to adapt in natural systems, and thus, the solutions are of limited use for such a system. The main application of the derived solutions is therefore the benchmarking of numerical reactive transport codes for systems with strong porosity change. To test the performance of numerical codes, numerical solutions obtained by using a global implicit finite volume technique are compared to the analytical solutions. Good agreement is obtained between the analytical solutions and the numerical solutions when a sufficient spatial discretization resolves the spatial concentration gradients at any time. In the limit of fast kinetics (local equilibrium), steep concentration fronts cannot be resolved in a numerical discretization schema.