Quantifying Value of Information using Ensemble Variance Analysis

Abstract

Abstract Data acquisition programs such as surveillance and pilots play an important role in minimizing subsurface risks and improving decision quality for reservoir management. In order for design optimization and investment justification of these programs, it is crucial to be able to quantify the expected uncertainty reduction and the value of information (VOI) attainable from a given design. This problem is challenging as the data from the acquisition program is uncertain at the time of the analysis. In this paper a method called ensemble variance analysis (EVA) is proposed. Based on a multi-Gaussian assumption between the observation data and the objective function, the EVA method quantifies the expected uncertainty reduction from covariance information that is estimated from an ensemble of simulations. The result of EVA can then be used with a decision tree to quantify the VOI of a given data acquisition program. The proposed method has several novel features compared to existing methods. Firstly, the EVA method considers data-objective function relationship directly. Therefore it can handle nonlinear forward models and an arbitrary number of parameters. Secondly, for cases when the multi-Gaussian assumption between the data and objective function does not hold, the EVA method still provides a lower bound on expected uncertainty reduction, which can be useful in providing a conservative estimate of the surveillance/pilot performance. Finally, EVA also provides an estimate of the shift in the mean of the objective function distribution, which is crucial for VOI calculation. In this paper, the EVA workflow for expected uncertainty reduction quantification is described. The result from EVA is benchmarked with recently proposed rigorous sampling methods, and the capacity of the method for VOI quantification is demonstrated for a pilot analysis problem using a field-scale reservoir model.