Reduced-Degrees-of-Freedom Gaussian-Mixture-Model Fitting for Large-Scale History-Matching Problems
- Guohua Gao (Shell Global Solutions US) | Hao Jiang (Shell Global Solutions US) | Chaohui Chen (Shell Exploration and Production Company) | Jeroen C. Vink (Shell Global Solution International) | Yaakoub El Khamra (Shell Global Solutions US) | Joel Ita (Shell Global Solutions US) | Fredrik Saaf (Shell Global Solutions US)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- February 2020
- Document Type
- Journal Paper
- 37 - 55
- 2020.Society of Petroleum Engineers
- Bayesian inference, distributed Gauss-Newton optimization, Gaussian mixture model, uncertainty quantification, history matching
- 11 in the last 30 days
- 99 since 2007
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It has been demonstrated that the Gaussian-mixture-model (GMM) fitting method can construct a GMM that more accurately approximates the posterior probability density function (PDF) by conditioning reservoir models to production data. However, the number of degrees of freedom (DOFs) for all unknown GMM parameters might become huge for large-scale history-matching problems. A new formulation of GMM fitting with a reduced number of DOFs is proposed in this paper to save memory use and reduce computational cost. The performance of the new method is benchmarked against other methods using test problems with different numbers of uncertain parameters. The new method performs more efficiently than the full-rank GMM fitting formulation, reducing the memory use and computational cost by a factor of 5 to 10. Although it is less efficient than the simple GMM approximation dependent on local linearization (L-GMM), it achieves much higher accuracy, reducing the error by a factor of 20 to 600. Finally, the new method together with the parallelized acceptance/rejection (A/R) algorithm is applied to a synthetic history-matching problem for demonstration.
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