Unified Finite Difference Modeling of Transient Flow in Naturally Fractured Carbonate Karst Reservoirs-A 3D Case Study

摘要

The modeling and numerical simulation of fluid flow in naturally fractured carbonate karst reservoirs are extremely challenging due to non-Darcy flow in vugs and caves connected by fracture networks. The momentum balance of such flow has been shown to be better described by the Brinkman equation both physically and mathematically, and many methods have been proposed in the literature dealing with the steady-state Brinkman model. We carry Brinkman’s idea one step further and propose a transient flow model which consists of the Brinkman equation and a generalized material balance equation. The generalized material balance equation has proven to be exact in the fractured carbonate karst reservoir. Finite differences are implemented for the solution of the proposed transient flow model. This solution method is more straightforward, easier to derive and implement, and more apt to generalization from 2D to 3D cases than alternative techniques. Numerical simulation of the transient Brinkman model requires explicit solution of not only pressure at the center of each grid block, but also velocities at the interfaces between the blocks, which exaggerates the computational cost. In this paper, we propose a simplified finite difference formulation of our transient flow model, which significantly reduces the computational time of the simulation process, and improves the accuracy and stability of the simulation results. We have updated our reservoir simulator with this new formulation and illustrate it with a 3D carbonate karst reservoir model. The results of this study form the foundation for future 3D multi-phase reservoir cases.