A Theoretical Approach Representing Hysteresis in Capillary Pressure-Saturation Relationship Based on Connectivity in Void Space

This study presents a new theoretical model for description of hysteretic constitutive relationships between capillary pressure and saturation under capillary-dominated multiphase flow conditions in porous media. Hysteretic relationships are required for the accurate prediction of the spatial and temporal distribution of multiphase fluids in response to successively occurring drainage and imbibition events in porous media. In addition to contact angle effects, the connectivity of the void space in the porous medium plays a central role for the macroscopic manifestation of hysteresis behavior and capillary entrapment of wetting and non-wetting fluids. The hysteretic constitutive model developed in this work uses void-size distribution and a measure of connectivity of void space to compute the hysteretic curves and to predict entrapped fluid phase saturations. Two functions, the probability of drainage and the probability of wetting, are introduced to characterize connectivity of fluids in void space during drainage and wetting processes. These functions can be estimated through pore-scale simulations in computer-generated porous media or from traditional experimental measurements of primary drainage and main wetting curves. The hysteresis model results are verified by comparing the model predicted scanning curves with 3D pore-scale simulations as well as with actual data sets obtained from column experiments found in the literature.