Most of porous naturally fractured reservoirs present a two-timescale 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.
Introduction
Representing the correct behaviour of recovery mechanisms in naturally fractured reservoir in flow simulators is a challenging task. For a large class of fractured reservoirs, especially for multiphase production mechanisms, the standard (single-medium) numerical simulators cannot capture the two-scale heterogeneity, and the two-timescale flow behaviour. The dual-medium approach, using a transfer function (TF) to represent the exchange term between fracture (flowing domain) and matrix (stagnant domain) is a possible answer. It has been attempting with some success, since its introduction in the '60s by Barenblatt et al (Barenblatt, 1960), to accurately simulate this dual behaviour, and produce results accurate enough, and close to what fine-grid simulations would give. Nevertheless, it provides a practical solution because data requirement is substantially less and the speed of computation is much greater (Ramirez et al, 2007).
