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. cavities and fractures (Tuncay et al. 1998) and Darcy flow in the porous media makes the coupled solution of fluid transport in these reservoirs very difficult. Various continuum approaches have been developed for the modeling of fluid flow in naturally fractured carbonate karst reservoirs. Methods based on the multiple-continuum concept model fractures and vugs as porous media with high permeability values (

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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, and the latter 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 and makes the computational process more difficult and less stable. In this paper, we propose a simplified finite difference formulation of the transient Brinkman model, which significantly reduces the computational time of the simulation process, and improves accuracy and stability of the simulation results. We update our reservoir simulator with this new formulation and illustrate it with a complex 3D naturally fractured carbonate karst reservoir model. The results of this study form the foundation for future 3D multi-phase reservoir cases.