SubFace Matrix-Fracture Transfer Function: Improved Model of Gravity Drainage/Imbibition

Abstract

Abstract Gravity is a major recovery mechanism of naturally fractured reservoirs, where fracture gas drains matrix oil until equilibrium is reached with the capillary forces (wrt fluid densities, matrix gas capillary pressure and block height). The challenge of modelling gravity drainage in dual-medium simulation is to match the final maximum recovery, using integrated pseudo-capillary pressure curve, and the correct recovery kinetics. The paper suggests an approach to improve the simulation of the recovery kinetics in gravity drainage by dividing the matrix block for the fluid transfer function in two specific parts: saturation front part (SFP) and initial state part (ISP). As the invading gas enters the matrix the SFP and ISP areas increase and decrease respectively, until the final recovery is reached at equilibrium point. The contributions from each part are summed up to equal a mass conservation equation at each time step for each matrix cell. Properties of SFP depend on the invading fluid saturation and ISP hold the initial state properties, hence its name. This SubFace formulation can be implemented in flow simulator for reservoirs exhibiting a dual-medium behaviour. Our SubFace Transfer Function approach (SF), performs well versus not only conventional transfer functions (Kazemi, Gilman), but also versus two improved ones: Quandalle-Sabathier, and Lu-Blunt (non-Warren-Root General Transfer Function) in matching the results of fine-grid single-medium models under various parameters (capillary pressure, matrix shape and mobility). We also tested SF in mixed-wet water-oil system to assess its capability of modelling gravity and capillary imbibition. This new formulation improves dual-medium simulations of fractured reservoirs with an accurate representation of matrix-fracture exchanges, and better reserves assessment and reservoir management. Introduction For a large class of fractured reservoirs produced through multiphase production mechanisms, the standard flow simulators cannot capture the two-timescale flow behaviour. The dual-medium approach is a compromise between a fully upscaled representation, where matrix and fracture properties are lumped together, and an explicit modelling of both domains which would lead to huge simulation models. Between the two domains overlapping each other, between fracture (flowing domain) and matrix (stagnant domain) the flow exchanges are usually represented by a transfer function (Barenblatt et al. 1960, Warren and Root 1963, Kazemi et al. 1976). During the last three decades, various formulations have been proposed, and we reviewed some of them in Abushaikha et al. (2008a). One condition to ensure reliable analysis and prediction of naturally fractured reservoir performance is to define such transfer functions (TF) that simulate the behaviour of the main recovery mechanisms occurring between the two media correctly, in particular for capillary and gravity drainage/ imbibition mechanisms. In Abushaikha et al. (2008a) we assessed and compared the usual Kazemi (1976) approach, the improved Gilman et al (1983) formulation for gravity, the Quandalle et al (1989) splitting method, which improved the simulation of mixed wet systems in particular and the Lu et al (2006, 2007, 2008) generalised transfer function (GTF), which adopts an idea from Zimmerman et al. (1993) and Mathias et al (2003). Since then Lu (2008) proposed a gravity corrected variation of the GTF, which has been used in this study to benchmark our approach. In order to face the challenge of a more accurate representation of both early and late time, which is the weak point of any Warren-Root-based TF, we suggested a way to eliminate the semi-steady state approach in matrix capillary imbibition (Abushaikha, 2008b). The so-called SubFace TF depends on time, space and two recovery periods (early and late time).