An Approach for Implementing Dual Porosity Models in Existing Simulators

Abstract

Abstract In dual porosity modeling of naturally fractured reservoirs, the reservoir is idealized as a set of disconnected matrix blocks within a highly conductive fracture network. It has been well recognized that the conventional dual porosity model does not accurately model matrix/fracture transfer flow. In the recent literature, matrix blocks have been further discretized to account for transient flow. Unfortunately, this approach greatly increases computational cost and requires much code modification if one tries to add a dual porosity option to an existing single porosity simulator. In this paper, a new dual porosity modeling approach is presented for oil/water flow in fractured reservoirs. In the formulation, matrix blocks are also discretized. The resulting finite-difference equations for the matrix blocks, however, are mathematically decoupled from the fracture equations. The equations for the fracture system are the same as for single porosity models except for a source and/or sink term for each grid. This scheme does not affect the formulation of the original simulator, since the matrix computations are decoupled. This also greatly reduces computational and coding effort. Also, implicitness of the primary variables is maintained. The model is verified by solution of Warren and Root's classical dual porosity model and an analytical solution which incorporates transient flow in matrix blocks. Results of the new model are also compared with fine-grid simulation of a fractured reservoir, in which both the fracture network and matrix blocks are discretized. Excellent agreement is achieved for a variety of reservoir properties. The simulator is also used to model published laboratory experiments and to conduct field-scale simulation studies. These results show that the new simulator provides computationally efficient and accurate means of modeling fractured reservoirs. The formulation developed can easily be extended to other recovery processes by modifying existing single porosity simulators. Introduction The most efficient approach to modeling fractured reservoirs appears to be the dual porosity model, proposed by Barenblatt et al. (1960) and introduced to the petroleum industry by Warren and Root (1963). The dual porosity model assumes that two equivalent continuous porous media are superimposed: one for the fracture system and another for the rock matrix. Continuity equations for each system are connected by so-called transfer functions that characterize flow between matrix blocks and fractures. Since Kazemi et al. (1976) introduced the first multiphase dual porosity model, almost all subsequent dual porosity models have been based on modifications of the transfer functions. These transfer functions are what distinguish various dual porosity models in the literature. Various transfer functions in the literature can be classified into three categories:the basic transfer function and its modifications,subgrid methods, anddiffusion methods. P. 461^