A mathematical model for dynamic wettability alteration controlled by water-rock chemistry

Previous experimental studies of spontaneous imbibition on chalk core plugs have shown that seawater may change the wettability in the direction of more water-wet conditions in chalk reservoirs. One possible explanation for this wettability alteration is that various ions in the water phase (sulphate, calcium, magnesium, etc.) enter the formation water due to molecular diffusion. This creates a non-equilibrium state in the pore space that results in chemical reactions in the aqueous phase as well as possible water-rock interaction in terms of dissolution/precipitation of minerals and/or changes in surface charge. In turn, this paves the way for changes in the wetting state of the porous media in question. The purpose of this paper is to put together a novel mathematical model that allows for systematic investigations, relevant for laboratory experiments, of the interplay between (i) two-phase water-oil flow (pressure driven and/or capillary driven); (ii) aqueous chemistry and water-rock interaction; (iii) dynamic wettability alteration due to water-rock interaction.
   In particular, we explore in detail a 1D version of the model relevant for spontaneous imbibition experiments where wettability alteration has been linked to dissolution of calcite. Dynamic wettability alteration is built into the model by defining relative permeability and capillary pressure curves as an interpolation of two sets of end point curves corresponding to mixed-wet and water-wet conditions. This interpolation depends on the dissolution of calcite in such a way that when no dissolution has taken place, mixed-wet conditions prevail. However, gradually there is a shift towards more water-wet conditions at the places in the core where dissolution of calcite takes place. A striking feature reflected by the experimental data found in the literature is that the steady state level of oil recovery, for a fixed temperature, depends directly on the brine composition. We demonstrate that the proposed model naturally can explain this behavior by relating the wettability change to changes in the mineral composition due to dissolution/precipitation. Special attention is paid to the effect of varying, respectively, the concentration of $\text{SO}_4^{2-}$ ions and $\text{Mg}^{2+}$ ions in seawater like brines. The effect of changing the temperature is also demonstrated and evaluated in view of observed experimental behavior.