Multi-fidelity Proxy Models for Reservoir Engineering

Proxy models are built to approximate outputs that depend on many uncertain parameters using few evaluations. In reservoir engineering, they can strongly reduce the number of flow simulations required for sensitivity analysis, history matching or production optimization. However, a large number of simulations can still be necessary to compute predictive proxy models. We propose to build multi-fidelity proxy models based on co-kriging to speed up the process. This approach introduces coarser resolution levels for the reservoir model that are less informative, but faster to estimate. These coarser levels can be obtained using a fluid flow simulator with simplified physics or an upscaled reservoir model. Then, the fine and coarse level evaluations are combined to build a proxy model of the reference – or fine – level. The objective is to retrieve as much information as possible from the faster levels in order to limit the calls to the fine, but most expensive ones. Sequential design strategies can also help reduce the number of simulations required to get predictive proxy models by iteratively defining the appropriate location of the added point or the appropriate fidelity level to consider when in multi-fidelity context. Sequential design strategies that take advantage of some kriging/co-kriging features (kriging variance and cross-validation predictions) were thus introduced to fully exploit the potential of the proposed approach. Comparisons of time saving between the simple and multi-fidelity proxy modeling methodologies were then performed through a sensitivity analysis for the Brugge field.