Use of Proxy Models in Risk Analysis of Petroleum Fields

Abstract

Abstract Risk assessment is a crucial process in the development of an oil field. Many tools and methods have been developed and applied in this area, such as reservoir simulation, surface response methodology and emulators. The tool and methodology choices should link to the level of uncertainity and the type of uncertain parameters (continuous, discrete and stochastic attributes), aiming at reliable results with reduced computational time/cost. The main goal of this work is to apply the Response Surface Methodology (RSM) to build proxy models in order to substitute the reservoir simulation model of medium-fidelity yielding to speed up part of the risk analysis processes that demands a high computational effort. The model passes through statistical and cross-validation in order to be used in production prediction. These validations ensure that the model output resides within a previously established confidence interval. Uncertainty analysis is evaluated based on building risk curves and then the curves are compared with the simulation output, to evaluate the proxy model efficiency based on the Normalized Quadratic Deviation with Signal (NQDS). The proxy study involves the following steps: (1) Statistical design to perform a sensitivity analysis of the objective functions; (2) Statistical design to obtain the response surface; (3) Statistical validation through analysis of variance (ANOVA); (4) Consistency check of proxies with the simulator outputs; (5) Latin Hypercube Sampling (LHS) technique to generate equi-probable scenarios during a crossvalidation procedure; (6) Application, building the risk curves through the generated proxy models to assist the decision analysis and (7) Comparison with the curves generated by the simulation using 500 scenarios generated by the LHS. From the LHS tool, 500 equi-probable scenarios were generated to build the risk curves using the proxy model and then compared with those generated by the reservoir simulator. The NQDS indicator measures the distance among curves. If the value resides between the interval of −1 and +1 it means that the proxy is efficiently reproducing the simulator response within a previous defined tolerance (5% in this case). The proposed methodology is shown to be efficient and easy to use. This application allowed the reduction of the number of uncertain attributes, avoiding unnecessary processing, obtaining the response surface and then generating proxy models capable of generating risk curves.