Optimal Choice of a Surveillance Operation Using Information Theory

We consider the problem of choosing among a suite of potential reservoir surveillance operations. We frame the problem in terms of two questions: (1.) Which surveillance operation is the most useful? (2.) What is the expected value of the reduction in uncertainty in the reservoir variable J (e.g. cumulative oil production) that would be achieved if we were to conduct each surveillance operation to collect and history-match the data obtained? Note that the objective is to answer these questions with an uncertain reservoir description and without any actual measurements. We propose a procedure based on information theory to answer these questions. Question 1 is answered by calculating the mutual information between J and the vector of observed data. Question 2 is answered by estimating the expected value of the standard deviation (or P90-P10) of J in the posterior model from the conditional entropy of J. We apply the proposed method to two simple problems, a nonlinear toy problem and a simple water flooding problem. The results are verified by an exhaustive history matching procedure, which is reasonably rigorous but very computationally demanding. We find that the mutual information approach is a fast and reliable alternative to the history matching approach.