The dual-porosity model concept has been introduced to simulate flows through naturally-fractured reservoirs because of the specificity of those media: fluids are mainly stored in the matrix and flow to the wells through the fracture system. A simplified formulation of matrix-fracture fluid transfers at the scale of a simulator cell uses a pseudo-steady-state (PSS) transfer equation involving a constant exchange coefficient also called shape factor. The shape factor has long remained controversial because a theoretical framework was missing and evidence was given of its dependence on the mechanism of flow. This paper presents different approaches to determine the matrix-fracture transfer behavior and derive the best approximate expression of the shape factor. These methods make use of the joint element technique for discretizing the actual fractured medium and are based on either (a) direct simulation of flow exchanges at local scale, (b) the application of upscaling theory, or (c) the implementation of a novel random walk method. A resolution example is given for a realistic image of a fractured medium in 2D single-phase flow conditions. The whole process of matrix-fracture transfer, including the intial transient states, has been determined from local-scale simulation. All upscaling methods lead to the same approximate expression of the shape factor to be used in the PSS equation describing matrix-fracture transfer. This shape factor is expressed versus equivalent block dimensions, which are in practice determined with a recently-developed nethodology involving geological image processing. Then, an extension to multiphase flow conditions is presented. The local-scale simulation approach is used to compute the exact transient water-oil capillary transfers at dual-porosity cell scale. These transfers are quite well reproduced with a PSS formulation incorporating the shape factor expression defined for single-phase transfers. A transient shape factor, formulated versus simulator unknowns, has also been tested. It turns out that capillary transfers can be reproduced with a dual-porosity simulator without resorting to any parameter tuning. To conclude, reliable simulation tool and upscaling methods are now available to compute matrix-fracture transfers on actual fractured media and derive the optimal PSS formulation to be used in dual-porosity simulators.
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