Matrix-fracture transfer function in dual-medium flow simulation: review, comparison, and validation

Most of porous naturally fractured reservoirs present a two-limescale flow-system, due to a two-scale heterogeneity which cannot be modelled explicitly, nor homogenised in reservoir simulation models. When the only flowing domain is the fracture network, and when the accumulation lies in porous and low permeable matrix blocks, the rate of exchanges between the two domains drives the recovery of such reservoirs. So called dual-porosity simulation models must incorporate an adequate transfer function between fracture and matrix in order to predict the recovery mechanisms for an optimal reservoir management. This is still true for dual-porosity / dual-permeability models, where the matrix domain is also flowing but at lower velocity. During the past 40 years until recently several formulations have been proposed. In order to review, compare and validate some of them, this work first analyse the main recovery drivers in two-phase systems, like drainage and imbibition under capillary and gravity forces, on the basis of explicit (single-porosity) simulations of flows between fracture and a single matrix block on a fine mesh, characterised by the final value and the kinetics of the recovery. Varying the main dynamic parameters these simulations give a set of reference cases to benchmark the dual-medium models, like the classic Kazemi transfer function, the Quandalle-Sabathier one, and a new formulation recently proposed by Blunt et al. These dual porosity single-block transfer functions are easily discretised in time and coded. The main findings are the disqualification of Kazemi formula, even with a gravity term, to represent any mechanism where the gravity is not negligible, especially in mixed-wet water-oil systems. Quandalle-Sabathier and Blunt transfer functions perform better, but the gravity forces remain difficult to be captured. The two first transfer functions are available in some commercial flow simulators, and their results on the same set of cases are consistent.