Investigation of the sampling performance of ensemble-based methods with a simple reservoir model

• Published in: Computational geosciences Vol. 17; no. 2; pp. 325 - 350
• Main Authors: Emerick, Alexandre A., Reynolds, Albert C.
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.04.2013; Springer Nature B.V
• Subjects: Algorithms; Computational efficiency; Computer simulation; Crude oil; Earth and Environmental Science; Earth Sciences; Geotechnical Engineering & Applied Earth Sciences; Hydrogeology; Kalman filters; Markov chains; Mathematical Modeling and Industrial Mathematics; Monte Carlo methods; Monte Carlo simulation; Nonlinearity; Original Paper; Petroleum; Reservoirs; Sampling; Soil Science & Conservation; Uncertainty; Uncertainty quantification; Ensemble smoother; Randomized maximum likelihood; History matching; Ensemble Kalman filter; Markov chain Monte Carlo
• ISSN: 1420-0597; 1573-1499
• DOI: 10.1007/s10596-012-9333-z

The application of the ensemble Kalman filter (EnKF) for history matching petroleum reservoir models has been the subject of intense investigation during the past 10 years. Unfortunately, EnKF often fails to provide reasonable data matches for highly nonlinear problems. This fact motivated the development of several iterative ensemble-based methods in the last few years. However, there exists no study comparing the performance of these methods in the literature, especially in terms of their ability to quantify uncertainty correctly. In this paper, we compare the performance of nine ensemble-based methods in terms of the quality of the data matches, quantification of uncertainty, and computational cost. For this purpose, we use a small but highly nonlinear reservoir model so that we can generate the reference posterior distribution of reservoir properties using a very long chain generated by a Markov chain Monte Carlo sampling algorithm. We also consider one adjoint-based implementation of the randomized maximum likelihood method in the comparisons.