Uncertainty propagation and reduction in reservoir forecasting

In this work we focus on nonparametric regression techniques based on Gaussian process, considering both the frequentist and the Bayesian approach. A new sequential experimental design strategy referred to as hierarchical adaptive experimental design is proposed and tested on synthetic functions and on realistic reservoir models using a commercial oil reservoir multiphase flow simulator. Our numerical results show that the method effectively approximate the simulators output with the required approximation accuracy using an affordable number of simulator runs. Moreover, the number of simulations necessary to reach a given approximation accuracy is sensibly reduced respect to other existing experimental designs such as maximin latin hypercubes, or other classical designs used in commercial softwares.;Once an accurate emulator of the simulator output is obtained, it can be also used to calibrate the simulator model using data observed on the real physical system. This process, referred to as history matching in reservoir forecasting, is fundamental to tune input parameters and to consequently reduce output uncertainty. An approach to model calibration using Bayesian inversion is proposed in the last part of this work. Here again a hierarchical emulator is adopted. An innovative sequential design is proposed with the objective of increasing the emulator accuracy around possible history matching solutions. The excellent performances obtained on a very complicated reservoir test case, suggest the high potential of the method to solve complicated inverse problems. The proposed methodology is about to be commercialized in an industrial environment to assist reservoir engineers in uncertainty analysis and history matching.