Global sensitivity analysis of stochastic computer models with joint metamodels

The global sensitivity analysis method used to quantify the influence of uncertain input variables on the variability in numerical model responses has already been applied to deterministic computer codes; deterministic means here that the same set of input variables gives always the same output value. This paper proposes a global sensitivity analysis methodology for stochastic computer codes, for which the result of each code run is itself random. The framework of the joint modeling of the mean and dispersion of heteroscedastic data is used. To deal with the complexity of computer experiment outputs, nonparametric joint models are discussed and a new Gaussian process-based joint model is proposed. The relevance of these models is analyzed based upon two case studies. Results show that the joint modeling approach yields accurate sensitivity index estimatiors even when heteroscedasticity is strong

Toward a Reliable Quantification of Uncertainty on Production Forecasts: Adaptive Experimental Designs

Quantification of uncertainty in reservoir performance is an essential phase of proper field evaluation. The reliability of reservoir forecasts is strongly linked to the uncertainty in the information we have about the variables that control reservoir performance (e.g. permeability, oil-water contact, etc.). The problem is complex, since the effect of the variables on the reservoir performance is often non-linear, which cannot be inferred a priori. Experimental design methods are well-known and widely used to quantify uncertainty and obtain probabilistic representation of production through, for instance, the P90, P50 and P10 production scenarios. By optimally selecting the flow simulations that should be performed, experimental design builds a proxy model that mimics the impact of the uncertain parameters on the reservoir performance. Using experimental design, one can perform risk assessment while performing a limited number of potentially expensive fluid flow simulation runs. However, experimental designs are based on simple polynomial response surface approximations, which show clearly their limits when the production response varies irregularly with respect to reservoir parameters. We present a new approach to properly assess risk even if the impact of the uncertain parameters is highly irregular. Contrary to classical experimental designs which assume a regular, 1st or 2nd degree polynomial-type behavior of the response, we propose to build evolutive designs, to fit gradually the potentially irregular shape of the uncertainty. Starting from an initial trend of the uncertainty behavior, the method determines iteratively new simulations that might bring crucial new information to update the current estimation of the uncertainty. Inspired by statistical methods and experimental designs, this original methodology has demonstrated its efficiency in modeling accurately complex, irregular responses, and thus in providing reliable uncertainty estimation on production forecasts

Toward a Reliable Quantification of Uncertainty on Production Forecasts: Adaptive Experimental Designs

Quantification of uncertainty in reservoir performance is an essential phase of proper field evaluation. The reliability of reservoir forecasts is strongly linked to the uncertainty in the information we have about the variables that control reservoir performance (e.g. permeability, oil-water contact, etc.). The problem is complex, since the effect of the variables on the reservoir performance is often non-linear, which cannot be inferred a priori. Experimental design methods are well-known and widely used to quantify uncertainty and obtain probabilistic representation of production through, for instance, the P90, P50 and P10 production scenarios. By optimally selecting the flow simulations that should be performed, experimental design builds a proxy model that mimics the impact of the uncertain parameters on the reservoir performance. Using experimental design, one can perform risk assessment while performing a limited number of potentially expensive fluid flow simulation runs. However, experimental designs are based on simple polynomial response surface approximations, which show clearly their limits when the production response varies irregularly with respect to reservoir parameters. We present a new approach to properly assess risk even if the impact of the uncertain parameters is highly irregular. Contrary to classical experimental designs which assume a regular, 1st or 2nd degree polynomial-type behavior of the response, we propose to build evolutive designs, to fit gradually the potentially irregular shape of the uncertainty. Starting from an initial trend of the uncertainty behavior, the method determines iteratively new simulations that might bring crucial new information to update the current estimation of the uncertainty. Inspired by statistical methods and experimental designs, this original methodology has demonstrated its efficiency in modeling accurately complex, irregular responses, and thus in providing reliable uncertainty estimation on production forecasts