Uncertainty quantification for subsurface petroleum reservoirs

In this talk, I will describe the main principals of the ensemble Kalman-like data assimilation systems for parameter estimation — the basis of the approach as an approximation of a “minimization-for-simulation” method and a few algorithmic choices that make the method successful on large history matching problems. I illustrate the use of use of the methodology with a modest sized benchmark reservoir history matching case, where the ensemble Kalman-like methods outperformed all other approaches. I will additionally show how the posterior ensemble of realizations was used to optimise the expected behavior of the reservoir. Despite the success, the ensemble methods have several limitations. The most severe might be the use of a single ensemble-average estimate of the sensitivity of observations to model parameters, which results in a uni-modal estimate of the posterior distribution for model parameters. The second major limitation might be the use of a minimization approach to posterior sampling without weighting of the realizations. I will discuss modifications to the algorithm that allow the use of local estimates of sensitivity for composite observation operators, and a second modification that allows computation of particle weights after assimilation of data.