Adaptive design of experiments for calibration of complex simulators - An application to uncertainty quantification of a mature oil field

Abstract

In this work we provide a practical approach to the inverse problem arising when observational data are used to calibrate parameters of an expensive simulation model. Our main application is the history matching problem in oil reservoir forecasting. In such and similar applications, the resulting inverse problem is generally ill-posed, the number of parameters to invert can be very high and the simulation time is very long (up to a few days). In this work a probabilistic approach is adopted to solve the inverse problem; this results in finding a posterior distribution of the simulator uncertain parameters. This posterior distribution is then used to reduce the uncertainty of future forecasts. To reduce the number of simulations, a cheap surrogate of the expensive simulator (an emulator) is build from a limited number of simulations using a Gaussian process regression (kriging) method. A new hierarchical experimental design method is proposed to refine the emulator in the proximity of possible solutions of the inverse problem. These solutions are explored using a Markov Chain Monte Carlo method. At each design iteration, only some accurately chosen points of the obtained posterior sample are simulated. The objective of this design is to iteratively remove the bias of the posterior calculation due to the emulator uncertainty and inaccuracy. This novel methodology is tested on a synthetic water flooded reservoir model that has been used in several previous works: the Imperial College fault model. © 2008 IOP Publishing Ltd.