Mathematical modeling of two-phase fluid transport through fractured media: irregular parallel plate system

Abstract

A mathematical model was developed to predict the behavior of biphasic flow through a fractured medium analyzed as a system of irregular parallel plates with the fractal dimension perpendicular and longitudinal to the flow. The results predict a symmetric annular flow pattern when a fluid with higher affinity is injected into the wall. The same behavior is achieved for liquids with equal affinity to the wall if the less viscous fluid is injected into the wall. The model can describe the injection of water into fractured reservoirs to increase oil production. Compared with other models, it allows estimation of the pressure gradient, velocity profiles, and mass flow of two-phase systems.