Ensemble-based optimization for history matching, surveillance optimization and uncertainty quantification

In this work, we develop ensemble-based methods to improve two related processes in the closed-loop reservoir management framework, history matching and surveillance optimization. On the history matching side, Emerick and Reynolds recently introduced the ensemble smoother with multiple data assimilations (ES-MDA) method. Via computational examples, they demonstrated that ES-MDA provides both a better data match and a better quantification of uncertainty than is obtained with the ensemble Kalman filter (EnKF). However, like EnKF, ES-MDA can experience near ensemble collapse and can generate too many extreme values of rock property fields for complex problems. These negative effects can be avoided by a judicious choice of the ES-MDA inflation factors but, prior to this work, the optimal inflation factors could only be determined by trial and error. Here, we provide two automatic procedures for choosing the inflation factor for the next data assimilation step adaptively as the history match proceeds. We demonstrate that the adaptive ES-MDA algorithms can be superior to the original ES-MDA algorithm in an extreme, difficult synthetic problem. In more reasonable problems, the adaptive algorithm may still perform better but performance gap is much smaller. We propose a procedure based on ES-MDA to history match data from non-Gaussian reservoir models, with a focus on those generated using multi-point statistics (MPS). ES-MDA is applied to update the permeability field in the normal way but during ES-MDA process, we periodically apply the Expectation-Maximization algorithm to classify the updated permeability fields into channel and non-channel regions. Then we take the average of the new facies distributions over the whole ensemble to obtain a facies probability map which is used in the MPS algorithm as the soft data to generate new facies realizations. Obtaining a reasonable approximation of the correct facies distribution is only half of the problem; we also wish to obtain a plausible distribution of the permeability within each facies. This is done by performing a second data assimilation stage where we nearly fix the facies distribution and only adjust the permeability within each facies. For the examples considered in this research, the procedure is able to provide good data matches as well as posterior facies and permeability fields that reflect the main geological features of the true model. On the surveillance optimization side, we aim to find an efficient method that can determine, among a suite of potential surveillance operations, the most beneficial operation and whether its benefit justifies the cost of collecting the data. The usefulness or the value of information of the data is defined here as the uncertainty reduction in the reservoir variable of interest J (e.g. cumulative oil production or net present value) once the reservoir model is updated by assimilating the data. An exhaustive history matching procedure exists to provide the answer to this problem but the required computational costs make it unfeasible for anything other than simple synthetic reservoir models. We propose an alternate procedure based on information theory where the mutual information between J and the random observed data vector Dobs is estimated using an ensemble of prior reservoir models. This mutual information reflects the strength of the relationship between J and the potential observed data and provides a way to qualitatively rank potential surveillance operations in terms of their usefulness. The expected uncertainty reduction in J is estimated by calculating the conditional entropy of J and translating the obtained value to the expected P90 - P10 of J. The proposed method is applied to four different problems and the results are verified using the exhaustive history matching method.