Benchmarking of Advanced Methods for Assisted History Matching and Uncertainty Quantification
Authors: Araujo Mariela , Chen Chaohui , Gao Guohua , Jennings Jim , Ramirez Benjamin , Xu Zhihua , Yeh Tzu-hao , Alpak Faruk Omer , Gelderblom Paul 
Published: March 2019

Abstract
Increased access to computational resources has allowed reservoir engineers to include assisted history matching (AHM) and uncertainty quantification (UQ) techniques as standard steps of reservoir management workflows. Several advanced methods have become available and are being used in routine activities without a proper understanding of their performance and quality. This paper provides recommendations on the efficiency and quality of different methods for applications to production forecasting, supporting the reservoir-management decision-making process.
Results from five advanced methods and two traditional methods were benchmarked in the study. The advanced methods include a nested sampling method MultiNest, the integrated global search Distributed Gauss-Newton (DGN) optimizer with Randomized Maximum Likelihood (RML), the integrated local search DGN optimizer with a Gaussian Mixture Model (GMM), and two advanced Bayesian inference-based methods from commercial simulation packages. Two traditional methods were also included for some test problems: the Markov-Chain Monte Carlo method (MCMC) is known to produce accurate results although it is too expensive for most practical problems, and a DoE-proxy based method widely used and available in some form in most commercial simulation packages.
The methods were tested on three different cases of increasing complexity: a 1D simple model based on an analytical function with one uncertain parameter, a simple injector-producer well pair in the SPE01 model with eight uncertain parameters, and an unconventional reservoir model with one well and 24 uncertain parameters. A collection of benchmark metrics was considered to compare the results, but the most useful included the total number of simulation runs, sample size, objective function distributions, cumulative oil production forecast distributions, and marginal posterior parameter distributions.
MultiNest and MCMC were found to produce the most accurate results, but MCMC is too costly for practical problems. MultiNest is also costly, but it is much more efficient than MCMC and it may be affordable for some practical applications. The proxy-based method is the lowest-cost solution. However, its accuracy is unacceptably poor.
DGN-RML and DGN-GMM seem to have the best compromise between accuracy and efficiency, and the best of these two is DGN-GMM. These two methods may produce some poor-quality samples that should be rejected for the final uncertainty quantification.
The results from the benchmark study are somewhat surprising and provide awareness to the reservoir engineering community on the quality and efficiency of the advanced and most traditional methods used for AHM and UQ. Our recommendation is to use DGN-GMM instead of the traditional proxy-based methods for most practical problems, and to consider using the more expensive MultiNest when the cost of running the reservoir models is moderate and high-quality solutions are desired.