Dissolution and precipitation via forced-flux injection in a porous medium with spatially variable permeability: Kinetic control in two dimensions

We model kinetically controlled dissolution and precipitation in a porous medium. Using quartz as the reactive mineral, our specific focus is on the spatial distribution of flow velocities and on changes in solute concentration and porosity introduced by heterogeneities in the initial permeability field and by differing the solute concentration of the infiltrating fluid. Upon a background permeability we impose isolated ''crack-like'' zones of high permeability and low surface area to fluid volume ratios. Our two-dimensional modeling of forced-flux injection of oversaturated and undersaturated fluid reveals features inaccessible to previous homogeneous permeability studies. Although realistic velocities can give rise to narrow boundary layers in the solute concentration, disequilibrium is favored in the high-permeability zones yielding plume-like distributions of solute concentration. Aside from the rapid changes in porosity near the injection level, the other regions of rapid porosity change occur just downstream from the crack-like zones, where fluid furthest from equilibrium with respect to quartz encounters regions of higher surface area to fluid volume ratios. Flow rates are significantly enhanced between isolated high-permeability zones, an effect which is even more dramatic for both closer crack spacing. and higher permeability contrasts. Undersaturated injection leads to permeability homogenization along the flow direction due to dissolution at the trailing edges of the cracks. Oversaturated injection tends to increase permeability heterogeneities along the flow direction, due to precipitation at the crack trailing edges. We also discuss the scaling properties of flow lines and reaction rates.