An analysis of crystal dissolution fronts in flows through porous media part 2: incompatible boundary conditions

Abstract

A model for transport of solutes in a porous medium participating in a dissolutionprecipitation reaction, in general not in equilibrium, is studied. Ignoring diffusiondispersion 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.

Crystal dissolution and precipitation in porous media: Pore scale analysis

“…Therefore we call t * the waiting time of the dissolution front. This agrees with [4], where the same waiting time was established for the macroscopic model.…”

“…A second equation for c 12 results from a description of the precipitation and dissolution processes. Following the detailed discussion in Knabner et al [12] (see also [3] and [4]), we have…”

“…Such models received much attention during the past years: e.g. see [4], [1], [2], [6], [8], or [13].…”

“…For a better understanding of the upscaled model we consider thin strips in Section 4. For vanishing width/length ratio, we end up with the model discussed in [12], [3] and [4] and thus provide existence of a suitable weak solution. For completeness we also show uniqueness.…”

Homogenization Approach to the Dispersion Theory for Reactive Transport through Porous Media

“…This case is well-understood even for reactive flows (see e.g. the papers [16], [18], [20], [21], [22], [17]). If the flow rate is increased so that the Péclet's number Pe is much larger than one, then there is a time scale at which transversal molecular diffusion smears the contact discontinuity into a plug.…”