Upscaling of Dynamic Capillary Pressure of Two‐Phase Flow in Sandstone

Abstract

AbstractDynamic capillary pressure (DCP) is the capillary pressure defined under transient flow condition during displacement, and it is vital for predicting two‐phase behavior in porous media. This article studies the effect of pore scale force and interfacial area by using captivating Lattice Boltzmann method based on a pseudo‐potential model developed for simulating incompressible multiphase flow in porous media. We analyze the relationship between pore scale forces and DCP based on the energy conservation law and define DCP as a function of energy rate of pressure and viscosity of each phase. We present two‐phase displacement simulations on a computed tomography (CT) image‐based porous model and analyze the effects of injection rate and wettability on DCP based on the proposed upscaling method, where the wettability is defined as the contact angle of the nonwetting phase. The primary results show that (1) the DCP curves are higher than that of the quasi‐static capillary pressure, and a higher injection rate leads to a larger DCP and a faster saturation change. (2) Significant effects of wettability on DCP and the DCP coefficients are observed, where the DCP coefficient is defined as the ratio of the difference between DCP and static capillary pressure over the rate of change of saturation. A larger contact angle results in a higher DCP and a lower change rate of saturation, and consequently induces a larger DCP coefficient. The average DCP coefficient is found to vary from 4.56 × 106 to 3.55 × 105Pa · ms when the nonwetting phase contact angle changes from 140° to 105° in the saturation range of 0.3 to 0.8. This study indicates that the proposed upscaling method is valid to investigate the DCP of two‐phase flow in sandstone.