SubFace matrix-fracture transfer function: Improved model of gravity drainage/imbibition

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 matrixfracture exchanges, and better reserves assessment and reservoir management.