A semi-analytical model for computation of capillary entry pressures and fluid configurations in uniformly-wet pore spaces from 2D rock images

A novel semi-analytical model for computation of capillary entry pressures and associated fluid configurations in arbitrary, potentially non-convex, 2D pore space geometries at uniform wettability is developed. The model computes all possible centre positions of circular arcs, and physically sound criteria are implemented to determine the set of these arcs that correspond to geometrically allowed interfaces. Interfaces and pore boundary segments are connected to form closed boundaries of identified geometrical regions. These regions are classified as either oil regions, located in the wider parts of the pore space, or as water regions located in pore space constrictions. All possible region combinations are identified and evaluated for each radius value in an iterative procedure to determine the favourable entry radius and corresponding configuration based on minimisation of free energy. The model has been validated by comparison with known analytical solutions in idealised pore geometries. In cases where different analytical solutions are geometrically possible, the model generates several oil and water regions, and the valid solution is determined by the region combination that corresponds to the most favourable entry pressure, consistent with the analytical solution. Entry pressure radii and configurations are computed in strongly non-convex pore spaces extracted from an image of Bentheimer sandstone, which demonstrates that the model captures successfully well-known characteristics of capillary behaviour at different wetting conditions. The computations also demonstrate the importance of selecting the fluid configuration of minimum change in free energy. In some cases, a merged region formed by a combination of oil and water regions corresponds to the favourable entry configuration of oil, whereas in other cases, an individual oil region may correspond to the favourable oil entry configuration. It is also demonstrated that oil entry configurations may constitute merged regions for weakly water-wet conditions and individual oil regions for strongly water-wet conditions in the same pore space. The computations show that the ratio of pore area to perimeter multiplied by the cosine of the contact angle under-predicts the entry pressure radii in Bentheimer sandstone pore spaces. An alternative formula is proposed for prediction of entry radii for nonzero contact angles based on the entry radii obtained for zero contact angles.