A Novel Fully 3D Modeling of Two-Phase Fluid Flow in Fractured-Vuggy Carbonate Formations Using the Transient Brinkman Equation Coupled with the Second-order Gradient Rock Mechanics Equation Including Porosity Evolution

Abstract

Describing the fluid flow behavior in heterogeneous carbonate formations is a challenging task due to the existence of natural fractures and vugs. The fractures and vugs are not porous regions; hence, the fluid flow in those regions cannot be described by Darcy’s law. The Brinkman’s equation describes the co-existing flow in the porous and free-flow regions without the need of using complex boundary conditions on the interface between the two flow regions. A comprehensive model, which considers rock deformation with second-order stress-strain gradient, the transient form of the Brinkman’s equation and the evolution of porosity, has been developed to capture and study the two-phase fluid flow behavior and vug deformation in fractured-vuggy carbonate formations considering the co-existing flows in the porous matrix and in the free-flow regions. The model is designed using advanced numerical techniques so that both the microscale and macroscale heterogeneities can be captured. The model is also designed to handle two-phase flow. The developed model was used to study how the vugs’ shape and volume change with time due to production and how those changes affect the cumulative production. The effect of elasticity was also examined to capture the changes of the vugs’ shape during production and when the production is halted. The finite element mesh was also interrogated to check the effects of the mesh size on the model’s accuracy, convergence and stability. Capillary pressure tests were conducted for the two-phase model to examine the capillary pressure effect on injectivity. The developed model can be extended to other disciplines that deal with conjugate flow problems, and it can also be improved to account for rock dissolution to study the impact of that on the fluid flow behavior.