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Truncated conjugate gradient and improved LBFGS and TSVD for history matching

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Abstract

We propose a new algorithm for solving the history matching problem in reservoir simulation, truncated conjugate gradient (TCG), which involves a model reparameterization based on the factorization of the prior covariance matrix, C M = L L T. We also revisit the LBFGS algorithm, framing it into the same reparametrization, introducing M-LBFGS. We present numerical evidence that this reparameterization has an important regularizing impact on the solution process. We show how TCG and M-LBFGS, as well as TSVD, can be implemented without the need of actually computing the factor L. Our numerical experiments, including the PUNQ-S3 and the Brugge cases, indicate that TCG and M-LBFGS are effective schemes for history matching.

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Acknowledgments

The authors are grateful to Petrobras (Brazil) for the support provided in the development of this work. F. Dickstein also acknowledges the support of CNPq (Brazil). Finally, the authors thank ESSS for providing their software Kraken for pre- and post-processing of simulation data.

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Authors and Affiliations

  1. IM/UFRJ, Cx. Postal 68530, 21941-909, Rio de Janeiro, RJ, Brazil

    Flávio Dickstein & Paulo Goldfeld

  2. Institute of Industrial Science, the University of Tokyo, 4 Chome-6-1 Komaba, Meguro, Tokyo, 153-8505, Japan

    Gustavo T. Pfeiffer

  3. LabMAPetro/IM/UFRJ, Rio de Janeiro, RJ, Brazil

    Renan V. Pinto

Authors
  1. Flávio Dickstein
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  2. Paulo Goldfeld
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  3. Gustavo T. Pfeiffer
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  4. Renan V. Pinto
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Correspondence to Flávio Dickstein.

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Dickstein, F., Goldfeld, P., Pfeiffer, G.T. et al. Truncated conjugate gradient and improved LBFGS and TSVD for history matching. Comput Geosci 22, 309–327 (2018). https://doi.org/10.1007/s10596-017-9694-4

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