The context of this work is a dynamic data assimilation workflow where a relatively small number of simulator inputs (usually around 10) has been selected in order to calibrate the reservoir simulation model. The probabilistic approach is used to solve this complex ill-posed inverse problem where the objective is to obtain a posterior distribution of the selected parameters. The remaining uncertainty on these simulator inputs is then propagated on the output of interest such as oil, water and gas productions to obtain confidence intervals for future forecasts. To reduce the number of required simulations the objective function is approximated using a non parametric response surface method based on Gaussian Process regression (kriging). To obtain a predictive response surface a sequential design of experiments is adopted that aims at discovering the minima of the objective function and also to accurately reproduce the basins associated to these minima. At each step of the design an MCMC method is used to explore the minima and to select the new simulations to perform. Also, differently than in previous works the response surface estimated variance is included in the posterior computation. As a result, the response surface accuracy improvement obtained by the sequential design produces also a reduction of uncertainty in the obtained estimates of the input posterior distribution. This uncertainty reduction effect together with the accuracy improvement of the response surface are monitored at run time at each iteration of the sequential design. An application is presented on the PUNQS field case with seven uncertain parameters. Less than two hundreds fluid flow simulations were used to produce a reliable sample of the posterior distribution and to propagate the remaining uncertainty on future forecasts.


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