Network model investigation of interfacial area, capillary pressure and saturation relationships in granular porous media

Abstract

We have developed a new approach for generating pore throat cross sections of various shapes based on distributions of shape factors and radii of inscribed circles. These distributions are obtained from analysis of grains packing. General formulas for calculating geometrical properties and entry capillary pressure for given shape factor and inscribed circle radius are developed. These relationships are employed in a pore network, which has a number of special features. In particular, it is highly flexible in terms of location of pore bodies, variable coordination number, as well as variable cross‐sectional shapes. The pore network model is employed for simulating the equilibrium distribution of two fluids in a granular porous medium, under both drainage and imbibition conditions. The pore network model is verified by comparing simulation results with experimental data of quasi‐static drainage and imbibition experiments in a glass bead medium. The pore‐level topology and geometrical description of pore bodies and pore throats, essential for building the network, are rigorously extracted from experimental data using image analysis (3DMA‐Rock software). Calculated capillary pressure‐saturation (Pc − Sw) and specific interfacial area‐saturation (anw − Sw) curves show very good agreement with measured ones, for both drainage and imbibition. We show that the shape factor can significantly influence the form of macroscopic Pc − Sw and anw − Sw curves, if the length and volumes associated to the pore throats are considerable. Furthermore, using continuous generation of shape factor distribution, the model can be validated against the grain size distribution. After validating the model against experiments, in addition to primary and main curves, we simulate many scanning curves to generate Pc − Sw − anw surfaces for drainage and imbibition, separately. Results show that these two surfaces lie very close to each other, and the average normalized difference is small, in the range of simulations uncertainty. Our results illustrate that Pc − Sw − anw surfaces show very little hysteresis and, therefore, specific interfacial area can be considered as an essential variable for reducing or eliminating the hysteresis observed in Pc − Sw curves.