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 seawatermay change the wettability in the direction of more water-wet conditions in chalk reservoirs.One possible explanation for this wettability alteration is that variousions in the water phase (sulphate, calcium, magnesium, etc.) enter theformation water due to molecular diffusion.This creates a non-equilibrium state in the porespace that results in chemical reactions in the aqueous phase as well aspossible 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 wettingstate of the porous media in question.The purpose of this paper is to put together a novel mathematical modelthat allows for systematic investigations, relevant forlaboratory experiments, of theinterplay 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 relevantfor spontaneous imbibition experimentswhere wettability alteration has been linked to dissolution of calcite.Dynamic wettability alteration is built into the model by definingrelative permeability and capillary pressure curvesas an interpolation of two sets ofend point curves corresponding to mixed-wet and water-wet conditions. Thisinterpolation depends on the dissolution of calcite in such a waythat when no dissolution has taken place, mixed-wetconditions prevail. However, gradually there is a shift towards more water-wetconditions at the places in the core where dissolution of calcite takes place.A striking feature reflected by the experimental data found in the literatureis 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 thisbehavior by relating the wettability change to changes in the mineralcomposition due to dissolution/precipitation.Special attention is paid to the effect of varying, respectively,the concentration of SO₄²⁻ ions and Mg²⁺ions in seawater like brines. The effect of changing the temperature is also demonstratedand evaluated in view of observed experimental behavior.