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.