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What is Monte Carlo Integration? Monte Carlo, is in fact, the name of the world-famous casino located in the eponymous district of the principality of Monaco on the world-famous French Riviera. It turns out that the casino inspired the minds of famous scientists to devise an intriguing mathematical technique for solving complex problems in statistics, numerical computing, and system simulation. One of the first and most famous uses of this technique was during the Manhattan Project when the chain-reaction dynamics in highly enriched uranium presented an unimaginably complex theoretical calculation to the scientists. Even the genius minds such as John Von Neumann, Stanislaw Ulam, and Nicholas Metropolis could not tackle it in the traditional way.
A better characterization of reservoir heterogeneity is indispensable to improve the prediction accuracy on production performance of heterogeneous petroleum reservoirs. Measuring physical properties at a single point can provide us with local information on reservoir heterogeneity, which is also beneficial in reducing some degree of uncertainty about global reservoir heterogeneity, and thus leads us to an improved prediction accuracy. It is not necessarily the case, however, that an improvement of the prediction accuracy implies an increase of our ability to make a proper decision. In this paper, we discuss how to quantify such a value of single-point data, obtained by measuring physical properties at a single point, for decision making in development of heterogeneous reservoirs by using the value-of-information (VOI) theory. We present an efficient algorithm to evaluate the value of single-point data with the help of reservoir simulation, Gaussian random field models, Monte Carlo integration, and the expectation-maximization (EM) algorithm. We validate our algorithm through a toy problem, and then demonstrate the practical usefulness of our algorithm through numerical experiments.