The Elder Problem with Reactive Infiltration Effects

The occurrence of buoyancy-driven flow and reactive solute transport in a fluid-saturated porous medium can be induced by either natural processes or human activities. Typical examples include the groundwater salinization in carbonate-rock aquifers and the acid treatment of oil wells in petroleum drilling industry. In this paper, the classical Elder problem of buoyancy-driven convection in two-dimensional porous media is extended to include the local chemical interactions between the solute in the pore liquid (e.g. salt such as NaCl or acids such as HCl and HCl/HF mixtures) and the solid space of the porous medium (e.g. minerals such as calcite and dolomite). Effects of the geochemical processes on the flow and mass transport are investigated. For the reactive, strongly solute-driven case in the regime dominated by the diffusive mass transport, a decrease in the net solute concentration is found as compared to the non-reactive case. This decrease is pronounced at higher values of the Damköhler number when the solute reaction rate becomes larger than the solute diffusion rate. Furthermore, the flow structure is affected by products generated by the chemical reaction when the Rayleigh number for the products is sufficiently high. In that case, numerical simulations show the formation of diluted fluid tongues exhibiting damped periodic oscillations about a nonzero mean. The results are obtained using the pseudospectral numerical method, verified against the analytical solution for the non-reactive, purely diffusive case.