Towards multiobjective history matching: Faster convergence and uncertainty quantification

Today we have 50 years of research in assisted history matching that bring us many fascinating frameworks to obtain multiple history matched models. Recently the evolutionary optimization algorithms for history matching have enjoyed an increasing popularity in our community. However these methods are often criticized for their high computational demands. We are looking to improve the convergence speed of these algorithms while maintaining their ability to obtain multiple history-matched models to have realistic uncertainty quantification. In this paper, we discuss a new approach to history matching and uncertainty quantification using multiobjective stochastic population-based optimization. The current practice in industry is to sum the individual match results from wells and minimize a global misfit value in order to get a history matched model. This work proposes a methodology where we can handle different objectives of history matching separately. We extend original differential evolution (DE) algorithm to optimize multiple objectives. The new algorithm is called differential evolution for multiobjective optimization using Pareto ranking (DEMOPR). We couple this algorithm with Bayesian uncertainty quantification framework to estimate the uncertainty in future recovery. The DEMOPR algorithm is tested for history matching and uncertainty quantification of the PUNQ-S3 reservoir. We have discussed the benefits of new multiobjective approach in fulfilling the targets of PUNQ-S3 problem: obtaining good history matching results and accurate prediction of the ultimate oil recovery. Results are very promising and show better final misfit values and simultaneously, two times increase in the speed of history matching in comparison with the original DE algorithm. We also study the number of models required to reach a stable Bayesian credible interval in quantifying the production uncertainty. We show that multiobjective approach stabilizes faster than original DE which means we need fewer simulations to have a reliable uncertainty estimate in the proposed workflow. Copyright 2011, Society of Petroleum Engineers.