Adaptive Experimental Design for Non-Linear Modeling – Application to Quantification of Risk for Real Field Production

One of the most important aspect in reservoir engineering is to quantify uncertainty in reservoir behavior. Because of the large number of parameters and the physical complexity of the reservoir, fluid flow models are complex and time consuming. In order to control the cost of an uncertainty study, traditional uncertainty management is routinely performed using proxy models of the production, advocated by experimental design methodology. This problem is complex since the impact of variables in reservoir performances is often non-regular. By selecting optimally the simulation to perform, experimental design technique allows to fit polynomial models of the response but often ignores non-regularity. In this paper, we propose an original methodology to construct irregular proxy models of the fluid flow simulator. Contrary to classical experimental designs which assume a polynomial behavior of the response, we propose to built evolutive experimental design to fit gradually the potentially irregular shape of uncertainty. This methodology benefits from the advantage of experimental design, which allows to control the number of fluid flow simulations, combined with the flexibility to study non-regular behavior. We propose here an original way to increase the prior predictivity of the approximation in the non-explored areas of the experimental domain. Based on the pilot points methodology, the research of the more predictive estimator is realized by constraining the approximation to fictitious data. These data, which are not simulated, are calibrated to ensure a better robustness and quality of the approximation. The proxy model obtained with the evolutive methodology can be considered as a good representation of the fluid flow simulator, whose evaluation is not expensive and therefore allows better risk analysis using Monte Carlo sampling. This innovative approach has been applied to model production behavior for an offshore Brazilian field, and thus to quantify the risk associated with the main reservoir uncertainties.