A Modified Quirk-Millington Equation for Partially Saturated Reactive Porous Media

Diffusion-induced mineral precipitation in partially saturated porous media is observed in various subsurface applications for future energy needs, such as CO 2 sequestration, deep geothermal reservoirs, and deep geological disposal of nuclear waste. The presence of gas might promote mineralization, which can significantly alter the pore space (e.g., geometry, connectivity, diffusivity), possibly causing porosity clogging, and leading to pressure build up and fracturing. Assessing the safety and stability of such systems requires understanding of the effects of mineral precipitation on porosity and effective diffusivity and quantifying the resulting reductions in these properties. Here, we developed a 3D column-diffusion experiment monitored with time resolved micro computed tomography (micro-CT) to evaluate celestine precipitation patterns within partially saturated porous media. In the scans, we can observe enhanced precipitation at the gas-liquid interface and a decrease in porosity with time. The 3D pore structures are used for tracer injection simulation with lattice Boltzmann to determine effective diffusivity. Results from three different experiments with increasing gas content show a decrease in effective diffusivity with time and are used to determine a modified porosity-diffusivity relationship in an evolving pore space as function of water saturation. A comparison with the established power law function of Quirk-Millington (QM) for sandy porous media shows that it overestimates effective diffusivity by several orders of magnitude for some cases. We propose a revised relationship of QM for describing mineralization in partially saturated porous media.