We aim at developing a viable workflow for the characterization of reservoir responses under Water Alternating Gas (WAG) conditions for enhanced oil recovery. We do so through a numerical Monte Carlo (MC) framework and by relying on (i) a classical approach, which is grounded on employing results from laboratory-scale core-flooding experiments or (ii) an approach based on relative permeability curves inferred from pore-scale numerical simulations. In these settings we investigate (i) the way uncertainties associated with the parameters of a reservoir model estimated through these approaches propagate to target modeling goals and (ii) assess (through Global Sensitivity Analyses) the relative importance of the uncertain quantities controlling the reservoir behavior via given model outcomes.
We consider uncertainty in (a) porosity and absolute permeability as well as (b) parameters of relative permeability models. Three scenarios are assessed, accounting for spatial distribution of porosity and absolute permeability with differing degrees of complexity and corresponding to (i) homogeneous; (ii) randomly heterogeneous; and (iii) well-connected randomly heterogeneous fields. Spatial realizations of the heterogeneous fields are generated considering Gaussian random fields with a Gaussian kernel variance driving the degree of spatial correlation. The two modeling approaches considered take advantage of two-phase relative permeability curves, which are interpreted via commonly used models with uncertain parameters. Three-phase relative permeabilities are then characterized through a previously developed and tested sigmoid-based oil relative permeability model by taking into account hysteretic behavior of gas relative permeability. All field-scale simulations are performed on a simple reservoir model and are set within the MRST suite.
In the case of a homogeneous reservoir, we note that reservoir simulation responses are strongly sensitive to the degree of convexity of the two-phase relative permeability curves. In the case of heterogeneous reservoir settings, results are almost similarly sensitive to porosity, characteristics of the relative permeability model, and the degree of heterogeneity of the reservoir. In the case of well-connected (randomly) heterogeneous fields, the importance of the porosity is stronger than in the heterogeneous setting lacking well connected regions.
Characterization of reservoir model attributes relying on pore-scale simulation approaches in the presence of uncertainty can provide a robust term of comparison which can be integrated within a classical reservoir simulation approach relying on relative permeability data stemming from core-flooding experiments. Our results document that uncertainties in the evaluation of (i) reservoir model petrophysical attributes (porosity/permeability) and (ii) relative permeability model parameters can differently influence field-scale simulation outputs, depending on the degree of spatial heterogeneity of the reservoir.