Matrix-Fracture Transfer Function in Dual-Medium Flow Simulation: Review, Comparison, and Validation

Abstract

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).

A Novel Multirate Dual-Porosity Model for Improved Simulation of Fractured and Multiporosity Reservoirs

“…The exchange of oil, gas, and water between the two domains is modeled by transfer func-tions (describing the physics of fluid exchange between fracture and matrix) and a shape factor (describing the geometry of the rock matrix). Much research has been dedicated to the appropriate use of transfer functions (Abushaikha and Gosselin 2008;Lu et al 2008;Al-Kobaisi et al 2009;Babadagli et al 2009;Balogun et al 2009;Ramirez et al 2009) and shape factors (Lim and Aziz 1995;Hassanzadeh and Pooladi-Darvish 2006;Rangel-German and Kovscek 2006;Gong et al 2008), whereas scaling groups have been developed to quantify the rate of oil recovery from matrix blocks and its dependence on rock and fluid properties (Ma et al 1997;Tavassoli et al 2005;Mason et al 2010;Schmid and Geiger 2012).…”

Interface control volume finite element method for modelling multi-phase fluid flow in highly heterogeneous and fractured reservoirs

“…Their dimensions and aperture size (width) affect the kinetics and the final recovery of hydrocarbon reservoirs [38]. In this test, we saw how the fracture width was numerically extended (artificial smearing) by the NCVFE method prompting a delay of flow in the fracture region.…”

Fundamental controls on fluid flow in carbonates: current workflows to emerging technologies

“…Several transfer functions exist and are routinely applied in reservoir simulators (Kazemi et al 1976;Gilman & Kazemi 1983;Quandalle & Sabathier 1989). A major problem is that these transfer functions do not capture the actual physics seen in experiments or high-resolution simulations of fracture-matrix transfer (Abushaikha & Gosselin 2008;Lu et al 2008;Geiger et al 2013;Ahmed Elfeel et al 2013a, b). Not surprisingly, this fundamental shortcoming poses major difficulties in the history matching of fractured carbonate reservoirs.…”