Impact of Relative Permeability Hysteresis on the Numerical Simulation of WAG Injection

Abstract

Abstract Pore-scale physics, laboratory investigations, and field experience, dictate that three-phase relative permeabilities exhibit strong dependence on the saturation path and the saturation history. Such dependence is especially relevant in water-alternating-gas (WAG) processes, which are characterized by a sequence of three-phase drainage and imbibition cycles. In this paper, we study the influence of relative permeability hysteresis on the field-scale predictions of WAG injection. Because their measurement is difficult and timeconsuming, three-phase relative permeabilities are usually interpolated from two-phase data. The errors associated with this procedure have been investigated by Oak (SPE 20183), who reported that interpolated values may differ significantly from experimental ones. The effect of using different interpolation models in field-scale simulations has been illustrated by a number of authors, who found that recovery predictions could be significantly different depending on the three-phase relative permeability model. Here, we study the impact of using history-dependent saturation functions in reservoir simulations. First, we investigate the degree of accuracy with which different hysteretic models reproduce Oak's three-phase relative permeability data. In doing so, we assess the validity of existing models, and we identify the model parameters subject to most uncertainty. Second, we illustrate how the use of a hysteretic relative permeability model affects reservoir simulations. We use a synthetic model of a quarter five-spot pattern in a homogenous reservoir, and a more realistic heterogeneous reservoir modified from the PUNQ-S3 model. We find that there is striking disparity in the simulation results depending on whether a hysteretic or a nonhysteretic model is employed, and conclude that it is essential to incorporate hysteresis in the relative permeabilities in order to obtain accurate predictions of realistic WAG processes. Introduction Quantitative predictions of multiphase flow in porous media are necessary for the evaluation and management of oil and gas reservoirs. In particular, the simultaneous flow of three separate phases (water, oil and gas) is essential in the characterization and modeling of a number of oil recovery processes, such as waterflooding in the presence of free gas, steam injection, and CO2 flooding.1 Three-phase flow conditions become especially relevant for recovery processes based on water alternating gas (WAG) injection.2 Three-phase flows occur also in environmental applications such as geological CO2 sequestration3 and groundwater contamination by nonaqueous-phase liquids.4 These predictions are now performed routinely using numerical simulations tools. Even though reservoir models continue to increase in size and geometrical complexity, they still rely on a straightforward multiphase flow extension of Darcy's law.5 The cornerstone of multiphase flow models is the relative permeability, which accounts for the reduction in flow due to the mutual interaction of the different flowing phases. Although traditionally understood as unique functions of saturation, there is conclusive theoretical and experimental evidence that relative permeabilities depend on many other rock and fluid descriptors, including rock wettability, fluid viscosity, interfacial tension, flow rate and, of special interest to us, saturation history.6 However, because direct measurement of three-phase relative permeabilities is costly and very time consuming, it is standard practice to rely on two-phase relative permeability experimental data, and use and interpolation model to evaluate the relative permeabilities under three-phase flow conditions.