Propagation to Reservoir Simulation of Uncertainty Associated with Three-Phase Relative Permeability Models with Hysteresis

Abstract

Abstract We study the way uncertainty associated with estimates of parameters of three-phase relative permeability models, including hysteresis, propagates to responses of reservoir simulations under Water Alternating Gas (WAG) conditions. We model three-phase relative permeabilities by: (i) joint calibration (on three-phase data) of a recent oil relative permeability model (Ranaee et al., 2015) and of the Larsen and Skauge (1998) gas relative permeability hysteretic model; and (ii) the common practice of relying on three-phase oil relative permeability models that are characterized solely on the basis of two-phase information (e.g., Stone, 1970 and Baker, 1988) in conjunction with the formulation of Larsen and Skauge (1998) for three-phase gas relative permeability. While model parameters associated with the former approach are linked to an estimation uncertainty, those of the models relying only on two-phase data are not. A numerical Monte Carlo (MC) framework is employed to estimate propagation to reservoir simulation outputs of uncertainty of parameters estimated through model calibration on three-phase data. Our findings suggest that evaluation of oil relative permeability through a saturation- weighted interpolation Baker model, even in combination with a three-phase gas relative permeability hysteresis model, yields the lowest values of field oil recovery. These are seen to lie outside uncertainty bounds evaluated via the above mentioned MC-based analysis. Relying on the Stone formulations together with the Larsen and Skauge (1998) gas relative permeability model yields (a) values of ultimate field oil recovery comprised within MC uncertainty bound and (b) values of field gas-oil ratio (GOR) which are smaller than those obtained through the Baker model in conjunction with the Larsen and Skauge (1998) formulation, both results falling markedly outside the MC-based confidence interval. Our results document the effect that propagation of uncertainties from calibrating three-phase relative permeability model parameters can have on field-scale simulation outputs, such as ultimate oil recovery and field GOR. They also serve as a baseline against which simulation results based on typical procedures to model three-phase relative permeabilities can be assessed.