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We illustrate the way formal model identification criteria can be employed to rank and evaluate a set of alternative models in the context of the interpretation of laboratory scale experiments yielding two-phase relative permeability curves. We consider a set of empirical twophase relative permeability models (i.e., Corey, Chierici and LET) which are typically employed in industrial applications requiring water/oil relative permeability quantifications. Model uncertainty is quantified through the use of a set of model weights which are rendered by model posterior probabilities conditional on observations. These weights are then employed to (a) rank the models according to their relative skill to interpret the observations and (b) obtain model averaged results which allow accommodating within a unified theoretical framework uncertainties arising from differences amongst model structures. As a test bed for our study, we employ high quality two-phase relative permeability estimates resulting from steady-state imbibition experiments on two diverse porous media, a quartz Sand-pack and a Berea sandstone core, together with additional published datasets. The parameters of each model are estimated within a Maximum Likelihood framework. Our results highlight that in most cases the complexity of the problem appears to justify favoring a model with a high number of uncertain parameters over a simpler model structure. Posterior probabilities reveal that in several cases, most notably for the assessment of oil relative permeabilities, the weights associated with the simplest models is not negligible. This suggests that in these cases uncertainty quantification might benefit from a multi-model analysis, including both low-and high-complexity models. In most of the cases analyzed we find that model averaging leads to interpretations of the available data which are characterized by a higher degree of fidelity than that provided by the most skillful model.

2017), Identifiability of parameters of three-phase oil relative permeability models under simultaneous water and gas (SWAG) Petrol. Sci. Eng., 159,[1][2][3][4][5][6][7][8][9][10] 12 Complete reference: Ranaee, E., L. Moghadasi, F. Inzoli, M. Riva, and A. Guadagnini (2017), Identifiability of 13 parameters of three-phase oil relative permeability models under simultaneous water and gas (SWAG) injection, J. Abstract 17We assess the relative performance of a suite of selected models to interpret three-phase oil relative permeability 18 data and provide a quantification of the identifiability of the model parameters. We ground our analysis on 19 observations of Steady-State two-and three-phase relative permeabilities we collect on a water-wet Sand-Pack sample 20 through series of core-flooding experiments. Three-phase experiments are characterized by simultaneous injection of 21 water and gas (SWAG) phases into the core sample initiated at irreducible water saturation, a scenario which is 22 relevant for modern enhanced oil recovery techniques. The selected oil relative permeability models include classical 23 and recent formulations and we consider their performance when (i) solely two-phase data are employed to render 24 predictions of three-phase oil relative permeability (k ro ), and/or (ii) two-and three-phase data are jointly used for 25 model calibration. A maximum likelihood (ML) approach is employed to estimate model parameters in the latter case. 26We assess identifiability of model parameters through the Profile Likelihood (PL) technique. We rely on formal 27 model discrimination criteria for a quantitative evaluation of the interpretive skill of each of the candidate models 28 tested. We also evaluate the relative degree of likelihood associated with the competing models through a posterior 29 probability weight and use ML Bayesian model averaging (BMA) to provide model-averaged estimate of k ro and the 30 associated uncertainty bounds. 31 Results show evaluating identifiability of uncertain parameters to the available dataset can provide us valuable 32 information about the quality of the parameters estimations, thus inferring which model predictions are feasible. Such 33 analysis can reduces computational costs by selecting solely identifiable models among available candidates on the 34 basis of an available dataset. In some cases, PL technique yields more feasible predictions of the estimating 35 parameters confidence intervals compared to the ones resulting from the analysis of covariance matrix of ML 36 estimation errors. 37

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Enhanced oil recovery (EOR) processes may often involve simultaneous flow of two or three immiscible fluids inside the reservoir. A precise evaluation of relative permeabilities is critical to quantify multi-phase flow dynamics, assisting improved management and development of oil- and gas- bearing formations. This study illustrates the results of laboratory-scale investigations of multiphase flow on a sandstone reservoir core sample to evaluate relative permeabilities under two- and three-phase (i.e., water, oil, and gas) conditions. We use the ensuing information to simulate WAG injection at reservoir scale. The experiments are conducted at high temperature, consistent with reservoir conditions, to obtain two- (oil/water and oil/gas) and three-phase (oil/water/gas) relative permeabilities through Steady-State (SS) technique. Our laboratory workflow allows for an improved investigation by combining coreflooding experiments with in-situ X-Ray evaluation of local saturation distribution. The latter technique permits to asses slice-averaged phase saturation along the rock core, enabling to compute saturation profiles and average saturations while flooding, thus yielding significant advantages over traditional methodologies based on mass balance. Three-phase steady state (SS) experiments are performed by following diverse saturation paths, and the complete experimental dataset is provided to (a) assess the occurrence of local three-phase saturation conditions and (b) possibly investigate hysteretic effects of relative permeabilities. We evaluate three-phase relative permeabilities across the entire three-phase saturation region by leveraging a Sigmoid-based model (Ranaee et al., 2015). The resulting set of experimental two- and three-phase coreflooding results constitute a unique dataset which is then employed for reservoir simulation studies mimicking WAG injection and results are discussed in comparison with reservoir production under a waterflooding scenario.