Combining meta-modeling and categorical indicators for global sensitivity analysis of long-running flow simulators with spatially dependent inputs

Variance-based global sensitivity analysis (GSA) is a powerful procedure for importance ranking of the uncertain input parameters of a given flow model. The application of GSA is made possible for long-running flow simulators (computation (CPU) time more than several hours) by relying on meta-modeling techniques. However, such flow models can involve one or several spatial inputs, for instance, the permeability field of a reservoir and of a caprock formation in the context of CO₂ geological storage. Studying the sensitivity to each of these spatial inputs motivated the present work. In this view, we propose a strategy which combines (1) a categorical indicator (i.e., a pointer variable taking discrete values) assigned to the set of stochastic realizations associated with each spatial input (spatial maps) and (2) meta-modeling techniques, which jointly handle continuous and categorical inputs. In a first application case, a costless-to-evaluate numerical multiphase flow model was used to estimate the sensitivity indices. Comparisons with results obtained using the meta-model showed good agreement using a two-to-three ratio of the number of learning samples to the number of spatial maps. On this basis, the strategy can be recommended for cases where the number of maps remains tractable (i.e., a few hundred), for example, for moderately complex geological settings, or where a set of such maps can be selected in a preliminary stage using ranking procedures. Finally, the strategy was applied to a more complex multiphase flow model (CPU time of a few hours) to analyze the sensitivity of CO₂ saturation and injection-induced pressure build-up to seven homogeneous rock properties and two spatial inputs.