Unconventional tight-oil and shale-gas reservoirs are usually naturally fractured, and developing this kind of reservoirs requires stimulation via hydraulic fracturing to create conductive fluid flow paths via open fracture networks for practical exploitation. The presence of the multi-scale fracture network, including hydraulic fractures, stimulated and non-stimulated natural fractures, and micro-fractures, increases the complexity of the reservoir simulation. The matrix block sizes are not uniform, and they can vary in a very wide range, from several tens of centimeters to several tens of meters. In such a reservoir, the matrix provides most of the pore volume for storage, but makes few contributions to the global flow, while the fracture supplies the flow, however, with negligible contributions to reservoir porosity. The hydrocarbon is mainly produced from matrix-fracture interaction. So, it is essential to model accurately the matrix-fracture transfers with a reservoir simulator.

For the fluid flow simulation in tight-oil and shale-gas reservoirs, dual-porosity models are widely used. In a dual-porosity model, fractures are homogenized, and a shape factor, based on the homogenized matrix block size, is applied to model the matrix-fracture transfer. However, in real cases, the discrete fracture networks are very complex and non-uniformly distributed. One cannot determine an equivalent matrix block to compute the shape factor. So, a dual-porosity model is not accurate for the simulation of tight-oil and shale-gas reservoirs due to the presence of complex multi-scale fracture networks.

In this paper, we will study the MINC (Multiple Interacting Continua) method for the flow modeling in fractured reservoirs. MINC is usually considered as an improvement of the dual-porosity model. However, a standard MINC approach, using transmissibilities derived from the MINC proximity function, cannot always handle correctly the matrix-fracture transfers when the matrix block sizes are not uniformly distributed. To overcome this insufficiency, we present some new approaches for the MINC subdivision and the transmissibility computations. Several examples are presented to show that using the new approaches improves significantly the dual-porosity model and the standard MINC method for non-uniform block size distributions.

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