Identifiability of parameters of three-phase oil relative permeability models under simultaneous water and gas (SWAG) injection

We assess the relative performance of a suite of selected models to interpret three-phase oil relative permeability data and provide a procedure to determine identifiability of the model parameters. We ground our analysis on observations of Steady-State two- and three-phase relative permeabilities we collect on a water-wet Sand-Pack sample through series of core-flooding experiments. Three-phase experiments are characterized by simultaneous injection of water and gas into the core sample initiated at irreducible water saturation, a scenario which is relevant for modern enhanced oil recovery techniques. The selected oil relative permeability models include classical and recent formulations and we consider their performance when (i) solely two-phase data are employed and/or (ii) two- and three-phase data are jointly used to render predictions of three-phase oil relative permeability, kro. We assess identifiability of model parameters through the Profile Likelihood (PL) technique. We rely on formal model discrimination criteria for a quantitative evaluation of the interpretive skill of each of the candidate models tested. We also evaluate the relative degree of likelihood associated with the competing models through a posterior probability weight and use Maximum Likelihood Bayesian model averaging to provide model-averaged estimate of kro and the associated uncertainty bounds. Results show that assessing identifiability of uncertain model parameters on the basis of the available dataset can provide valuable information about the quality of the parameter estimates and can reduce computational costs by selecting solely identifiable models among available candidates.