Part 2: Oil displacement by foam injection in Hele-Shaw cell with a pattern of impermeable regions

Foam flooding is an enhanced oil recovery (EOR) technique that is used to control gas mobility, particularly in heterogeneous and fractured reservoirs. This paper aims to numerically investigate the effect of foam flooding on oil displacement efficiency at the fracture scale. Also, an empirical model for relative permeability, which remains difficult and troublesome to measure, is proposed and implemented in the numerical model. The experimental data used in this study include five injection methods that are water, gas, tertiary gas, foam, and tertiary foam. Fluid injection was performed through 2D-printed models of an actual rock cross-section, which was obtained from high-resolution micro-computed tomography. In the numerical model used, pressure and saturation equations of injected fluids were solved using the COMSOL software. Based on the findings, both experimental data and numerical simulation results of the five injection methods were in good agreement, which shows the robustness of the proposed relative permeability model with a single fitting parameter. The oil recovery factor predicted using the proposed model outperformed that of the Buckley-Leverett and Brooks-Corey models. Also, the relative permeability model was further tested against coreflooding experimental data from the literature. This study provides more insight into numerical modeling of foam flooding at the fracture scale. Moreover, we believe that the proposed relative permeability model is robust and capable of capturing the evolution of relative permeability with saturation along the injection process, which encourages further investigation and improvement by the subsurface community. Further field-scale studies, including sensitivity and optimization, can be performed based on this work.