A unified finite difference model for the simulation of transient flow in naturally fractured carbonate karst reservoirs
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Copyright 2015 Society of Petroleum Engineers. The presence of cavities connected by fracture networks at multiple levels make the simulation of fluid flow in naturally fractured carbonate karst reservoirs a challenging problem. The challenge arises in properly treating the Darcy and non-Darcy flow in the different areas of fractured medium. In this paper, we present a single-phase transient flow model which is based on the Stokes-Brinkman equation and a generalized material balance equation. The generalized material balance equation proves to be exact in both cavities and porous media, and the Stokes-Brinkman equation mathematically combines Darcy and Stokes flow, thus allowing a seamless transition between the cavities and porous media with only minor amounts of perturbation introduced into the solutions. Finite differences are implemented for the solution of the proposed transient flow model. This solution method provides a smooth transition from standard multiple-porosity/permeability reservoir simulators and moreover, it is physically more straightforward, mathematically easier to derive and implement, and more apt to generalization from two-dimensional to three-dimensional cases than alternative techniques. Application of the derived transient flow model is shown by examples of three fine-scale 2-D geological models. The first two models, although simple, provide verification of the proposed transient flow model. The third example presents a more complex and realistic geological model derived from multiple-point statistics simulation technique with the second model used as the training image. The results of the third model form the foundation for future study of multi-phase and 3-D reservoir cases.
