A Mathematical Model for Interpretation of Brine-Dependent Spontaneous Imbibition Experiments

In this paper we consider a mathematical model that seeks to explain possible mechanisms for brine-dependent oil recovery in chalk. It is well documented through lab experiments that the brine composition has a strong impact on oil recovery. In particular, the role of the divalent ions (Ca2+, Mg2+ and SO24−) present in seawater have been extensively studied. Also the effect of salinity which is mainly controlled by the monovalent ions Na+ and Cl− has been carefully investigated. It has been observed that chemical reactions occur between rock and brine when seawater or seawater-like brines are injected or diffuse into chalk at high temperature. Different chemical mechanisms are involved like ion exchange, adsorption, and precipitation/dissolution of minerals such as calcite, magnesite and anhydrite. Hence, these experiments suggest that for spontaneous imbibition tests the produced oil is a result of an interplay between capillary forces and the imposed water-rock chemistry. We are interested in formulating a theory for this observed behavior based on a proper combination of geochemical and two-phase model components. The mathematical model we present couples geochemical reactive transport with the capillary forces trapping the oil. When a brine different from the formation brine enters pore space the water-rock chemistry induces changes on the rock surface. It is suggested that this leads to correspond- ing changes of the wetting state as represented by relative permeability and capillary pressure curves. Different hypothesis concerning the possible link between geochemical changes of the rock-surface and changes of wetting state are explored. Specifically, we employ the model to dis- cuss some previously published lab experiments where systematic variations in Ca2+ and SO24− in imbibing and initial brine were explored. The model suggests that at 70◦C neither dissolution nor precipitation are the main contributors for wettability alteration. Rather, a conceptual sulfate adsorption mechanism coupled to the surface activity of calcium readily explain how adding more sulfate and calcium to the system would increase oil recovery. Hence, we demonstrate how the model can be used as a tool for systematic investigations aiming at identifying key mechanisms important for mobilization of oil as a function of brine composition.