oa Quantification of Uncertainties in Reservoir Models from Multi-fidelity Response Surfaces

To predict fluid flows in a reservoir and help decision-making for its development, engineers need to define representative models of this reservoir. Several workflows have been proposed that provide a set of reservoir models constrained to the static and dynamic data collected on the field. One of the main limitations is the computation time required by the fluid-flow simulations performed for each new model investigated during the process. An alternative to reduce this computational time consists in building a meta-model to approximate the response of interest in the parameter space from a limited number of simulated values. This model can be substituted to the fluid-flow simulator at some steps of the workflow. Until now, meta-models were built from simulations performed on the same level of resolution. We propose here to investigate another type of meta-models, called multi-fidelity meta-models, which combine information obtained at several levels of accuracy. These models, rooted in cokriging, approximate the function on the fine level, using the values computed at every level. The tests performed on reservoir models considering grids with various spatial resolutions show that, compared to kriging, meta-models of equivalent or higher predictivity can be obtained within less simulation times.