Investigation of smoothed particle hydrodynamics (SPH) method for modeling of two-phase flow through porous medium: application for drainage and imbibition processes

The drainage and imbibition processes are critical mechanisms in petroleum engineering. These processes in a porous medium are controlled by surface forces and pressure gradients. The study of these processes in the pore scale by common simulators always has limitations in multiphase flow modeling. Also, obtaining relative permeability curves through laboratory analysis requires expensive equipment. Additionally, these laboratory experiments are quite expensive and may introduce significant uncertainties. For this purpose, this study investigated the creation of relative permeability curves and their effect on oil production. Initially, single-phase fluid and two-phase droplet flow within a fracture with both soft and rough surfaces were utilized to validate the formulation of the Smoothed Particle Hydrodynamics (SPH) method. Then, by using three randomly constructed porous medium models, the imbibition and drainage processes have been studied. Finally, sensitivity study has been carried out on critical parameters related to fluid flow dynamics in the porous environment, including pressure changes, wettability, and heterogeneity in drainage and imbibition processes. The simulation results were consistent with current theories; therefore, it is reasonable to consider SPH to characterize the fluid flow dynamic during the drainage and imbibition processes. According to sensitivity studies, pressure gradient (residual saturation of displaced fluid is about 5.65% and 8.44%) and heterogeneity (the residual saturation of the displaced fluid was 4.04% and 2.98%) have the largest impact on flow modeling in both drainage and imbibition processes and wettability (the residual saturation became 36.62% and 5.12%) has significant effect on the drainage process through porous medium. In general, fluid flow dynamic studies can be performed using the SPH method to model fluid flow in simple and complex porous medium under various flow conditions. The SPH method can also be used as an applicable tool to investigate the hydrocarbon fluids flow within larger geometries in the future.