A modeling approach to represent hysteresis in capillary pressure‐saturation relationship based on fluid connectivity in void space

[1] This study presents a new 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 accurate prediction of 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, 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 nonwetting fluids. The hysteretic constitutive model developed in this work uses void-size distribution and a measure of connectivity for void space to compute the hysteretic curves and to predict entrapped fluid-phase saturations. Two functions, the drainage connectivity function and the wetting connectivity function, 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 3-D pore-scale simulations as well as with actual data sets obtained from column experiments found in the literature.