1887

Abstract

Summary

Because of the quasi-gradient update embedded in CMA-ES algorithm, it can outperform most of the population-based algorithms, from a convergence speed standpoint. However, due to the computationally expensive fitness function associated with history matching, the reduction of function (simulation) calls can be favourable.

In this study, an ensemble of surrogates (proxies) with generation-based model-management is proposed to reduce the number of simulation calls efficaciously. Since the fitness function is highly nonlinear, an ensemble of surrogates (Gaussian process) is utilised. The likelihood term is divided into multiple functions, and each is represented via a separate surrogate. This improved the response surface fitting.

In generation-based management, a stochastically selected measure (surrogate or reservoir-simulation) should be used to evaluate all the individuals of each generation. CMA-ES requires ranking of the individuals to select the parents. Therefore, the generation-based model-management fits well in CMA-ES, as surrogates are normally better in ranking the individuals than approximating the fitness.

History matching for a real problem with 59 variables and PUNQ-S3 with eight variables was conducted via a standard CMA-ES and the proposed surrogate-assisted CMA-ES. The results showed that up to 65% and 50% less simulation calls for case#1 and case#2 were required.

Loading

Article metrics loading...

/content/papers/10.3997/2214-4609.201802139
2018-09-03
2024-04-27
Loading full text...

Full text loading...

References

  1. AWOTUNDE, A. A. & NARANJO, C.
    2014. Well Placement Optimization Constrained to Minimum Well Spacing.SPE Latin America and Caribbean Petroleum Engineering Conference.Maracaibo, Venezuela: Society of Petroleum Engineers.
    [Google Scholar]
  2. BOUZARKOUNA, Z., DING, D. Y. & AUGER, A.
    2012. Well placement optimization with the covariance matrix adaptation evolution strategy and meta-models.Computational Geosciences, 16, 75–92.
    [Google Scholar]
  3. FOROUZANFAR, F., POQUIOMA, W. E. & REYNOLDS, A. C.
    2016. Simultaneous and Sequential Estimation of Optimal Placement and Controls of Wells With a Covariance Matrix Adaptation Algorithm.
    [Google Scholar]
  4. HAJIZADEH, Y., CHRISTIE, M. A. & DEMYANOV, V.
    2010. History matching with differential evolution approach; a look at new search strategies.SPE EUROPEC/EAGE Annual Conference and Exhibition.Barcelona, Spain: Society of Petroleum Engineers.
    [Google Scholar]
  5. HANSEN, N.
    2006. The CMA Evolution Strategy: A Comparing Review. In: LOZANO, J. A., LARRAÑAGA, P., INZA, I. & BENGOETXEA, E. (eds.) Towards a New Evolutionary Computation: Advances in the Estimation of Distribution Algorithms.Berlin, Heidelberg: Springer Berlin Heidelberg.
    [Google Scholar]
  6. HANSEN, N. & OSTERMEIER, A.
    2001. Completely Derandomized Self-Adaptation in Evolution Strategies.Evolutionary Computation, 9, 159–195.
    [Google Scholar]
  7. HE, J., XIE, J., WEN, X.-H. & CHEN, W.
    2015. Improved Proxy For History Matching Using Proxy-for-data Approach And Reduced Order Modeling.SPE Western Regional Meeting.Garden Grove, California, USA: Society of Petroleum Engineers.
    [Google Scholar]
  8. JIN, Y.
    2011. Surrogate-assisted evolutionary computation: Recent advances and future challenges.Swarm and Evolutionary Computation, 1, 61–70.
    [Google Scholar]
  9. MASCHIO, C. & SCHIOZER, D. J.
    2014. Bayesian history matching using artificial neural network and Markov Chain Monte Carlo.Journal of Petroleum Science and Engineering, 123, 62–71.
    [Google Scholar]
  10. MOHAMED, L., CHRISTIE, M. A. & DEMYANOV, V.
    2010. Reservoir Model History Matching with Particle Swarms: Variants Study.SPE Oil and Gas India Conference and Exhibition.Mumbai, India: Society of Petroleum Engineers.
    [Google Scholar]
  11. OLIVER, D. S. & CHEN, Y.
    2011. Recent progress on reservoir history matching: a review.Computational Geosciences, 15, 185–221.
    [Google Scholar]
  12. RAZAVI, S., TOLSON, B. A. & BURN, D. H.
    2012. Review of surrogate modeling in water resources.Water Resources Research, 48.
    [Google Scholar]
  13. ROMERO, C. E. & CARTER, J. N.
    2001. Using genetic algorithms for reservoir characterisation.Journal of Petroleum Science and Engineering, 31, 113–123.
    [Google Scholar]
  14. SAYYAFZADEH, M.
    Uncertainty quantification using a self-supervised surrogate-assisted parallel Metropolis-Hastings algorithm. ECMOR XIV-15th European Conference on the Mathematics of Oil Recovery, 2016.
    [Google Scholar]
  15. 2017. Reducing the computation time of well placement optimisation problems using self-adaptive metamodelling. Journal of Petroleum Science and Engineering, 151, 143–158.
    [Google Scholar]
  16. SAYYAFZADEH, M., HAGHIGHI, M., BOLOURI, K. & ARJOMAND, E.
    2012a. Reservoir characterisation using artificial bee colony optimisation.APPEA Journal, 115–128.
    [Google Scholar]
  17. SAYYAFZADEH, M., HAGHIGHI, M. & CARTER, J. N.
    2012b. Regularization in History Matching Using Multi-Objective Genetic Algorithm and Bayesian Framework.SPE Europec/EAGE Annual Conference.Copenhagen, Denmark: Society of Petroleum Engineers.
    [Google Scholar]
  18. SCHULZE-RIEGERT, R. W., KROSCHE, M., PAJONK, O. & MUSTAFA, H.
    2009. Data Assimilation Coupled to Evolutionary Algorithms—A Case Example in History Matching.SPE/EAGE Reservoir Characterization and Simulation Conference.Abu Dhabi, UAE: Society of Petroleum Engineers.
    [Google Scholar]
  19. ZUBAREV, D. I.
    2009. Pros and Cons of Applying Proxy-models as a Substitute for Full Reservoir Simulations.SPE Annual Technical Conference and Exhibition.New Orleans, Louisiana: Society of Petroleum Engineers.
    [Google Scholar]
http://instance.metastore.ingenta.com/content/papers/10.3997/2214-4609.201802139
Loading
/content/papers/10.3997/2214-4609.201802139
Loading

Data & Media loading...

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error