A Semi-Analytical Model for Simulating Fluid Flow in Naturally Fractured Reservoirs with Non-Homogeneous Vugs and Fractures

Abstract

Carbonate reservoirs are characterized of fractures, vugs and cavities. These vugs have a large attribution to reserves of oil and gas. And the fractures provide effective paths for fluids flow in the reservoir. Triple porosity model is an effective conceptual method to capturing rock matrix, vugs and micro-fractures connecting them. However, these fractures and vugs are always non-homogeneous. Macro fractures and vugs cannot be handled with continuum for their low density and high conductivity. In this approach, the triple porosity conceptual model is implemented to characterize rock matrix, micro vugs and fractures. To capture the heterogeneity of fractures and vugs, macro fractures and vugs are represented explicitly with discontinuum model. The boundaries of macro vugs and macro fractures are discretized into several elements. Boundary element method is employed to handle flow into macro fractures and vugs. Finite difference method is applied to handle flow within macro fractures. The flow within macro vugs are assumed to be in pseudo-steady state. With a simple discretization of the boundaries of macro vugs and macro fractures, the proposed model is shown to efficiently simulate the behavior of fractured carbonate reservoirs with heterogeneity. The computational accuracy is demonstrated using an analytical model. On the basis of the proposed model, the effect of heterogeneity of macro fractures and vugs on pressure transient behavior is analyzed. The results show that macro fractures and vugs cannot be handled with triple-continuum models analytically. There will be several "dips" on the derivative of pressure curve if macro vugs are discretely handled. And discretely handling the fractures and vugs will make the calculated dimensionless pressure and the derivative lower than calculated with tripe continuum models. Increasing the porosity of macro vugs, the pressure and the derivative will go down in the flow regimes dominated by macro vugs. The conductivity of macro fractures has a great impact on almost all the flow regimes except boundary dominated flow regimes. The novelty of the new model is in the ability to model the transient behavior carbonate reservoirs with non-homogeneous fractures and vugs. Furthermore, it provides an efficient method for characterizing the heterogeneity of multi-scaled fractures and vugs.