A model for interpretation of brine-dependent spontaneous imbibition experiments

Previous experimental results for spontaneous imbibition experiments in the context of chalk cores have revealed a rather puzzling behavior: the oil recovery curves, both the shape as well as the steady state level which is reached, depend strongly on the brine composition. In particular, it has been demonstrated that Mg2+,SO42-, and Ca2+ play a central role in this physico-chemical system. A good theoretical understanding of these experimental results, in terms of mathematical models that can suggest possible explanations of the lab experiments as well as predict behavior not yet tested in the lab, seems to still be lacking. The purpose of this paper is to try to shed light on some important modeling aspects. The model we propose is an extended version of the classical Buckley–Leverett (BL) equation for two-phase spontaneous imbibition where the water saturation equation has been coupled to a system of reaction–diffusion (RD) equations describing water–rock chemistry relevant for chalk core plugs. As far as water–rock chemistry is concerned we focus in this work on the combined effect of transport and dissolution/precipitation of calcite, magnesite, and anhydrite. The line we pursue is to couple changes of the wetting state, expressed in terms of the relative permeability and capillary pressure functions, to the water–rock chemistry behavior. More precisely, we build into the model the mechanism that the rock surface will become more water-wet at the places where dissolution of calcite takes place. In particular, we illustrate and analyze how different compositions of the imbibing brine then lead to different water–rock interaction scenarios which in turn gives qualitative and quantitative differences in the solution of the saturation equation describing spontaneous imbibition. Comparison with relevant experimental behavior is included as well as illustration of some possible interesting and non-trivial characteristic features of the model reflecting the nonlinear coupling mechanisms between the RD model for the water–rock chemistry and the BL equation for the water–oil transport.

► We explore a model for brine-dependent oil recovery in chalk.
► The model couples water–rock chemistry and change of wetting state.
► Comparison is made between model behavior and relevant experimental results.
► The role played by sulfate and magnesium as a modifier of the wetting state is highlighted.