A dual-porosity simulation model is a coarse upscaled representation of a naturally fractured reservoir. Fluid transfer between the matrix and the fracture is described by a matrix-fracture transfer function, which is dependent on a shape factor. However, the basic formulation assumes pseudosteady-state conditions and requires modifications to capture transient effects. This paper describes the use of a dynamic shape factor for matrix-fracture transmissibility with block-to-block effects to improve the simulation of oil recovery in a dual-porosity model.
A simple fine-grid single-porosity model is compared with a coarse-grid dual-porosity equivalent for a gas-oil system under gravity drainage without capillary effects. A time-varying relationship between the shape factor and the matrix oil saturation is derived by numerical analysis. Vertical block-to-block connections are included in the model to match oil reinfiltration from the fractures to the matrix. The saturation-dependent shape factor correlation is generalized for other matrix block sizes. An improved match to fine-grid recovery is achieved in the dual-porosity simulation through use of a dynamic transfer function and block-to-block effects. The methodology is shown to be appropriate for a range of matrix sizes and, with different relative permeability curves, for the matrix blocks. However, attention must be paid to the relationship between simulation grid cell size and geologic matrix block size. Additional study of block-to-block flows is recommended to further improve the predictive capability of the model.
Fast and accurate simulation of flow in naturally fractured reservoirs is often difficult to achieve. The standard matrix-fracture transfer model is unsuitable for many situations. In the example presented here, we show how a coarse simulation model can be used effectively to capture variations in dynamic matrix-fracture transfer behavior over time for a specific case. The approach can be generalized and applied to similar studies.