Estimation of Distribution Algorithms Applied to History Matching
- Asaad Abdollahzadeh (Heriot-Watt University) | Alan Reynolds (Heriot-Watt University) | Michael Christie (Heriot-Watt University) | David W. Corne (Heriot-Watt University) | Glyn J.J. Williams (BP) | Brian J. Davies (BP)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- April 2013
- Document Type
- Journal Paper
- 508 - 517
- 2013. Society of Petroleum Engineers
- 5.5.8 History Matching, 7.2.3 Decision-making Processes, 5.5 Reservoir Simulation
- 2 in the last 30 days
- 466 since 2007
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The topic of automatically history-matched reservoir models has seen much research activity in recent years. History matching is an example of an inverse problem, and there is significant active research on inverse problems in many other scientific and engineering areas. While many techniques from other fields, such as genetic algorithms, evolutionary strategies, differential evolution, particle swarm optimization, and the ensemble Kalman filter have been tried in the oil industry, more recent and effective ideas have yet to be tested. One of these relatively untested ideas is a class of algorithms known as estimation of distribution algorithms (EDAs). EDAs are population-based algorithms that use probability models to estimate the probability distribution of promising solutions, and then to generate new candidate solutions. EDAs have been shown to be very efficient in very complex high-dimensional problems.
An example of a state-of-the-art EDA is the Bayesian optimization algorithm (BOA), which is a multivariate EDA employing Bayesian networks for modeling the relationships between good solutions. The use of a Bayesian network leads to relatively fast convergence as well as high diversity in the matched models.
Given the relatively limited number of reservoir simulations used in history matching, EDA-BOA offers the promise of high-quality history matches with a fast convergence rate.
In this paper, we introduce EDAs and describe BOA in detail. We show results of the EDA-BOA algorithm on two history-matching problems. First, we tune the algorithm, demonstrate convergence speed, and search diversity on the PUNQ-S3 synthetic case. Second, we apply the algorithm to a real North Sea turbidite field with multiple wells. In both examples, we show improvements in performance over traditional population-based algorithms.
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Barker, J.W., Cuypers, M., and Holden, L. 2001. QuantifyingUncertainty in Production Forecasts: Another Look at the PUNQ-S3 Problem.SPE J. 6 (4): 433-441. SPE-74707-PA. http://dx.doi.org/10.2118/74707-PA.
Bos, C.F.M. 1999. Production Forecasting with UncertaintyQuantification: PUNQ-2. Technical Report NITG 99-255-A, Netherlands Instituteof Applied Geoscience (TNO), The Hague, The Netherlands.
Carter, J. 2007. PUNQ-S3 Test Case. Online dataset comparisonstudy, Department of Earth Science and Engineering, Imperial College London,London http://www3.imperial.ac.uk/earthscienceandengineering/research/perm/punq-s3model/(accessed 1 July 2010).
Coats, K.H., Dempsey, J.R., and Henderson, J.H. 1970. A NewTechnique for Determining Reservoir Description from Field Performance Data.SPE J. 10 (1): 66-74. SPE-2344-PA. http://dx.doi.org/10.2118/2344-PA.
Erbas, D. and Christie, M.A. 2007. Effect of SamplingStrategies on Prediction Uncertainty Estimation. Presented at the SPE ReservoirSimulation Symposium, Houston, 26-28 February. SPE-106229-MS. http://dx.doi.org/10.2118/106229-MS.
Evensen, G., Hove, J., Meisingset, H.C. et al. 2007. Using theEnKF for Assisted History Matching of a North Sea Reservoir Model. Presented atthe SPE Reservoir Simulation Symposium, Houston, 26-28 February. SPE 106184. http://dx.doi.org/10.2118/106184-MS.
Floris, F.J.T., Bush, M.D., Cuypers, M. et al. 2001. Methodsfor quantifying the uncertainty of production forecasts: A comparative study.Pet. Geosci. 7 (Supplement, 1 May): 87-96.
Goldberg, D.E. 1989. Genetic Algorithms in Search,Optimization, and Machine Learning. Columbus, Ohio: Addison-Wesley.
Hajizadeh, Y. 2010. Ants Can Do History Matching. Presented atthe SPE Annual Technical Conference and Exhibition, Florence, Italy, 19-22September. SPE-141137-STU. http://dx.doi.org/10.2118/141137-STU.
Hajizadeh, Y., Christie, M.A., and Demyanov, V. 2010.Comparative Study of Novel Population-Based Optimization Algorithms for HistoryMatching and Uncertainty Quantification: PUNQ-S3 Revisited. Presented at theAbu Dhabi International Petroleum Exhibition and Conference, Abu Dhabi, UAE,1-4 November. SPE-136861-MS. http://dx.doi.org/10.2118/136861-MS.
Heckerman, D., Geiger, D., and Chickering, D.M. 1994. LearningBayesian networks: The combination of knowledge and statistical data. TechnicalReport MSR-TR-94-09, Microsoft Research, Redmond, Washington (March 1994/rev.December 1994).
Jahns, O.H. 1966. A Rapid Method for Obtaining aTwo-Dimensional Reservoir Description From Well Pressure Response Data. SPEJ. 6 (4): 315-327. SPE-1473-PA. http://dx.doi.org/10.2118/1473-PA.
Mohamed, L., Christie, M., and Demyanov, V. 2010. Comparison ofStochastic Sampling Algorithms for Uncertainty Quantification. SPE J. 15 (1): 31-38. SPE-119139-PA. http://dx.doi.org/10.2118/119139-PA.
Pelikan, M., Goldberg, D.E., and Cantú-Paz, E. 1999. BOA: TheBayesian Optimization Algorithm. In Proceedings of the Genetic andEvolutionary Computation Conference (GECCO '99), W. Banzhaf, J. Daida, A.E.Eiben, et al., Vol. 1, 525-532. San Francisco, California: Morgan KaufmannPublishers.
Pelikan, M., Goldberg, D.E., and Cantú-Paz, E. 2000. LinkageProblem, Distribution Estimation and Bayesian Networks. EvolutionaryComputation 8 (3): 311-340.
Petrovska, I. and Carter, J.N. 2006. Estimation of distributionalgorithms for history-matching. Presented at the 10th European Conference onthe Mathematics of Oil Recovery (ECMOR X), Amsterdam, 4-7 September.
Romero, C.E., Carter, J.N., Gringarten, A.C. et al. 2000. AModified Genetic Algorithm for Reservoir Characterisation. Presented at theInternational Oil and Gas Conference and Exhibition in China, Beijing, 7-10November. SPE-64765-PA. http://dx.doi.org/10.2118/64765-MS.
Rudlof, S. and Köppen, M. 1996. Stochastic Hill Climbing withLearning by Vectors of Normal Distributions. Proc., 1st Online Workshopon Soft Computing, Nagoya, Japan, 19-30 August, 60-70
Schulze-Riegert, R.W., Krosche, M., Pajonk, O. et al. 2009.Data Assimilation Coupled to Evolutionary Algorithms--A Case Example in HistoryMatching. Presented at the SPE/EAGE Reservoir Characterization and SimulationConference, Abu Dhabi, UAE, 19-21 October. SPE-125512-PA. http://dx.doi.org/10.2118/125512-MS.
Subbey, S., Christie, M.A., and Sambridge, M. 2003. A Strategyfor Rapid Quantification of Uncertainty in Reservoir Performance Prediction.Presented at the SPE Reservoir Simulation Symposium, Houston, 3-5 February.SPE-79678-PA. http://dx.doi.org/10.2118/79678-MS.
Sultan, A.J., Ouenes, A., and Weiss, W.W. 1994. AutomaticHistory Matching for an Integrated Reservoir Description and Improving OilRecovery. Presented at the Permian Basin Oil and Gas Recovery Conference,Midland, Texas, USA, 16-18 March. SPE-27712-MS. http://dx.doi.org/10.2118/27712-MS.
Thomas, L.K., Hellums, L.J., and Reheis, G.M. 1972. A NonlinearAutomatic History-Matching Technique for Reservoir Simulation Models. SPEJ. 12 (6): 508-514. SPE-3475-PA. http://dx.doi.org/10.2118/3475-PA.
Yang, C., Nghiem, L., Card, C. et al. 2007. Reservoir ModelUncertainty Quantification Through Computer-Assisted History Matching.Presented at the SPE Annual Technical Conference and Exhibition, Anaheim,California, USA, 11-14 November. SPE-109825-PA. http://dx.doi.org/10.2118/109825-MS.