Analytical Pore-Network Approach (APNA): A novel method for rapid prediction of capillary pressure-saturation relationship in porous media

The relationship between capillary pressure and wetting fluid saturation is one of the most important functions required for the modelling of immiscible displacement within porous media. Commonly, time consuming laboratory experiments or computationally expensive pore-scale numerical simulations are performed to estimate capillary pressure− saturation relationships for a given porous media. In this research, we introduce Analytical Pore-Network Approach (APNA): a new method to forecast capillary pressure-saturation relationships in porous media. APNA is a fully coupled analytical model, that is derived using the concept of Representative Elementary Volume (REV), and underpinned by geometrical analysis of the studied pore network using pore-scale images collected by a range of imaging modalities (e.g. thin section photomicrograph, x-ray micro computed tomography, confocal microscopy, etc.). In comparison to conventional laboratory measurements and numerical simulation techniques, APNA is trivial to implement, and is capable of providing rapid estimates of capillary pressure− saturation relationships for a broad range of porous materials. We validated APNA against empirical capillary pressure− saturation data published in the literature, revealing satisfactory agreement between APNA and the experimental studies.