A new formulation for non-equilibrium capillarity effect using multi-gene genetic programming (MGGP): accounting for fluid and porous media properties

Dynamic coefficient as an important parameter in determination of the dynamic behavior of capillary pressure is considered as a function of various fluid and porous media properties. In this study, a new and general formulation for predicting the dynamic coefficient was proposed and developed through which the key fluid and porous media properties are accounted for. For expressing new formulation, multi-gene genetic programming (MGGP) was employed. Efficiency and robustness of the proposed model were investigated through experimental data and statistical measures of performance. A parametric study was designed to evaluate the impact of different parameters on the dynamic coefficient. Results show that the developed model is valid for a wide range of the conditions of two-phase flow in porous media. The model is a prerequisite for the accurate design, modeling, and application of dynamic capillarity effect in various fields of fluid flow in porous media. Furthermore, a new dimensionless number, the so-called dynamic effect number, was proposed and formulated which quantifies dynamic capillary force to viscous force ratio. Such a number would be useful and practical for the upscaling process and quantification of dominant forces in two-phase flow in porous media where limited experimental data are present.