Scaling of capillary pressure-saturation curve in porous media under various wetting conditions

The capillary pressure curve provides fundamental insights into the dynamics of fluid-fluid displacement and phase distributions. Capillary scaling is crucial for extrapolating capillary pressure-saturation data from laboratory tests to field applications. However, the classic scaling method fails to capture the effect of wettability as the pore surface approaches neutral wetting. Here, inspired by the role of pore-filling events in controlling fluid-fluid displacement, we perform a theoretical analysis of the burst events occurring during drainage processes. We find that the median threshold capillary pressure, which corresponds to the occurrence of burst events for the median pore throat, is closely correlated with the capillary pressure curve across various contact angles. Using this concept, we propose a new scaling method for capillary pressure curves under various wetting conditions. We conduct microfluidic experiments and pore-network modeling across different contact angles, porosities, and disorders to evaluate the new scaling methods, indicating that the new scaling method performs better than the Leverett J-function as the contact angle approaches 90°. We further perform geometry analysis on the critical radius of curvature for burst events in an ideal tetrahedral arrangement and extend the new scaling method to 3D (three-dimensional) porous media. Model evaluation shows that the 3D version of the scaling method also performs well but requires fewer parameters compared to the Leverett J-function. Our work enhances the prediction and interpretation of experimental data for capillary pressure curves under various wet conditions, and more importantly, establishes a methodology that relates Darcy-scale flow behavior to pore-scale fluid displacements.