Modeling Two-Phase Flow in Tight Core Plugs with an Application for Relative Permeability Measurement

The two-phase flow of immiscible fluids in porous media has been studied for a long time in different disciplines of engineering. Relative permeability (kr) is one of the constitutional relationships in the general equation governing immiscible displacement that needs to be determined. Due to the complexity and nonlinear nature of governing equations of the problem, there is no unique model for relative permeability. The modified Brooks and Corey (MBC) model is the most common model for kr prediction. Here, a practical technique is presented to measure kr for low-permeability tight rocks. We use this experimental data to tune the empirical constants of the MBC model. The proposed method is based on a simple mathematical technique that uses assumptions of frontal advance theory to model the pressure drop along the core plug during two-phase immiscible displacement at constant injection flow rate. We make simplifying assumptions about the highest point on the observed pressure profile and use those assumptions to determine relative permeability of a tight rock sample. In the end, the amount of work for an immiscible displacement is calculated as the area under the pressure-profile curve. The effect of initial water saturation (Swi) and interfacial tension (IFT) is studied on the work required for an immiscible displacement. Using this concept, it is concluded that adding chemical additives such as surfactants to fracturing fluids can help the reservoir oil to remove the water blockage out of the rock matrix more easily while maintaining the flow rate at an economic level.