Multi-fidelity meta-modeling for reservoir engineering - application to history matching

International audienceDefining representative reservoir models usuallycalls for a huge number of fluid flow simulations, whichmay be very time-consuming. Meta-models are built tolessen this issue. They approximate a scalar function fromthe values simulated for a set of uncertain parameters. Fortime-dependent outputs, a reduced-basis approach can beconsidered. If the resulting meta-models are accurate, theycan be called instead of the flow simulator. We proposehere to investigate a specific approach named multi-fidelitymeta-modeling to reduce further the simulation time. Weassume that the outputs of interest are known at various levelsof resolution: a fine reference level, and coarser levelsfor which computations are faster but less accurate. Multifidelitymeta-models refer to co-kriging to approximate theoutputs at the fine level using the values simulated at alllevels. Such an approach can save simulation time by limitingthe number of fine level simulations. The objective ofthis paper is to investigate the potential of multi-fidelity forreservoir engineering. The reduced-basis approach for timedependentoutputs is extended to the multi-fidelity context.Then, comparisons with the more usual kriging approachare proposed on a synthetic case, both in terms of computationtime and predictivity. Meta-models are computed toevaluate the production responses at wells and the mismatchbetween the data and the simulated responses (historymatching error), considering two levels of resolution. Theresults show that the multi-fidelity approach can outperformkriging if the target simulation time is small. Last, itspotential is evidenced when used for history matching