Quantification of uncertainty in relative permeability for coarse-scale reservoir simulation

Reservoir simulation to predict production performance requires two steps: one is history-matching, and the other is uncertainty quantification in forecasting. In the process of history-matching, rock relative permeability curves are often altered to reproduce production data. However, guidelines for changing the shape of the curves have not been clearly established. The aim of this paper is to clarify the possible influence of relative permeabilities on reservoir simulation using the uncertainty envelope. We propose a method for adjusting the shape of relative permeability curves during history-matching at the coarse scale, using the Neighbourhood Approximation algorithm and B-spline parameterisation. After generating multiple history-matched models, we quantify the uncertainty envelope in a Bayesian framework. Our approach aims at encapsulating sub-grid heterogeneity in multi-phase functions directly in the coarse-scale model, and predicting uncertainty. In this sense, the framework differs from conventional procedures which perturb fine-scale features, upscale the models and evaluate each performance. In addition, B-spline parameterisation is flexible allowing the capture of local features in the relative permeability curves. The results of synthetic cases showed that the lack of knowledge of the subgrid permeability and the insufficient production data provoked a substantial amount of uncertainty in reservoir performance forecasting.