Coupled capillary pressure and relative permeability using an equation-of-state approach

Accurate and continuous capillary pressure (P_c) and relative permeability (k_r) models are key relations in modeling of enhanced oil recovery (EOR) processes. Current commercial reservoir simulators tune empirical models for relative permeabilities and capillary pressures to experimental data based solely on a limited set of data under immiscible conditions. These empirical models attempt to represent very complex compositional processes, even though they are only a function of phase saturation and type. Thus, "fully" compositional models that use these empirical relations are not fully composition and discontinuities in compositions and saturations result. These discontinuities lead to failed simulations, significant inaccuracies and increased computational time. This paper develops a coupled equation-of-state (EoS) k_r-P_c model that can reproduce important features of the current empirical models, but also yield physically consistent predictions that cannot generate discontinuities. The model parameters use the same inputs for both relative permeability and capillary pressure and are tuned simultaneously. We focus here on capillary hysteresis and understanding the components of the EoS from measured data using saturation, phase distribution (Euler characteristic or phase contact area), and wettability as inputs. The new EoS P_c model maintains a similar functional form as the common Brooks-Corey correlation, and can predict capillary pressure away from the tuned experimental data. The results using CT scans of imbibition and drainage processes show excellent agreement once contact angle hysteresis is included. A quadratic response surface is used to understand better the functional form of the EoS, i.e. partial derivative expressions. The new coupled k_r-P_c approach could improve compositional simulation by making it faster, more robust, and accurate since these key parameters are more continuous and physical.