A Novel Assisted History Matching Workflow and its Application in a Full Field Reservoir Simulation Model

Document Type: Research Paper


1 PICO International Petroleum, Cairo, Egypt.

2 Petroleum Engineering, Cairo University, Giza, Egypt.



The significant increase in using reservoir simulation models poses significant challenges in the design and calibration of models. Moreover, conventional model calibration, history matching, is usually performed using a trial and error process of adjusting model parameters until a satisfactory match is obtained. In addition, history matching is an inverse problem, and hence it may have non-unique solutions. In typical reservoir simulation problems with a large number of unknown parameters, the problem could be ill-posed. In recent years, assisted history matching approach has been offered to solve this problem hopefully. In this paper, proposes an efficient assisted history matching workflow is recommended, and its application in a full field reservoir simulation model of a mature gas-cap reservoir is presented. In addition, Sobol sequence experimental design technique, Kriging proxy modeling, and three novel metaheuristic optimization algorithms are used to assist the history match of 28 years of historical production and pressure data. Finally, the results are compared with those obtained using a manual history matching procedure and with those obtained using the most widely used assisted history matching workflow. Also, in the proposed workflow, a significant improvement in terms of match quality and solution time is shown.



Kantorovich L., “The Mathematical Method of Production Planning and Organization,” Management Science, 1939, 6(4), 363-422.

Shams M., El-Banbi A. H., and Sayyouh H., “A Comparative Study of Experimental Design Techniques in Assisted History Matching,” in SPE Middle East Oil and Gas Show and Conference, 2017.

Shams M., El-Banbi A. H., and Sayyouh H., “A Comparative Study of Proxy Modeling Techniques in Assisted History Matching,” in the SPE Kingdom of Saudi Arabia Annual Technical Symposium and Exhibition, 2017.

Fisher R. A., “Statistical Methods for Research Workers,” (5th ed.), Edinburgh: Oliver and Boyd, Genesis Publishing, 1925, 1-235.

Damsleth E., Hage A., and Volden R, “Maximum Information at Minimum Cost: Development Study with an Experimental Design”, SPE Journal of Petroleum Technology, SPE-23139-PA, 1992, 1350-1356.

Montgomery D., “Reservoir Monitoring and Continuous Model Updating Using Ensemble Kalman Filter,” In SPE the Annual Technical Conference and Exhibition, 2000.

Mackay M., Beckman R., and Conover W., “A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code,” Technometrics, 1979, 21(2), 239-245.

Sobol I. M., “On the Distribution of Points in a Cube and the Approximate Evaluation of Integrals,” USSR Computational Mathematics and Mathematical Physics, 1967, 7(4), 86-112.

Van der Corput J. G., “Verteilungs Funktionen,” Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen, 1935, 38, 813-821.

Bianchetti M., Sergei K., and Stefano S., “Better Pricing and Risk Management with High Dimensional Quasi Monte Carlo,” in the Fixed Income Conference, 2014.

Saltelli A., Ratto M., Andres M. F., Campolongo J. Cariboni, and et al., “Global Sensitivity Analysis,” John Wiley and Sons, Ltd, 2008, 1-16.

Box G. E. P. and Wilson K. B., “Experimental Attainment of Optimum Conditions,” Journal of the Royal Statistical Society, 1951, 13, 1-45.

Nocedal J., “Theory of Algorithms for Unconstrained Optimization,” Actanumerica, 1992, 1, 199-242.

Wright S. J. and Nocedal J., “Numerical Optimization,” New York: Springer, 1999.

Byrd R. H., Lu P., Nocedal J., and Zhu C., “A Limited Memory Algorithm for Bound Constrained Optimization,” SIAM Journal on Scientific Computing, 1995, 16(5), 1190–1208.

Zhu C., Byrd R. H., Lu P., and Nocedal J., “Algorithm 778: L-BFGS-B: FORTRAN Subroutines for Large-scale Bound-constrained Optimization,” ACM Transactions on Mathematical Software (TOMS), 1997, 23(4), 550-560.

Eide A., Holden L., Reiso E., and Aanonsen S., “Automatic History Matching by Use of Response Surfaces and Experimental Design,” in the 4th European Conference on the Mathematics of Oil Recovery, 1994.

Gauss C., “General Investigations of Curved Surfaces,” Raven Press, New York, translated by A. M. Hiltebeital and J.C. Morehead, 1928.

Bates D. and Watts. D., “Nonlinear Regression, Analysis and Applications,” Wiley, 1988.

Krige D. G., “A Statistical Approach to Some Basic Mine Valuation Problems on the Witwatersrand,” Journal of the Chemical, Metallurgical, and Mining, 1951, 52(6), 119–139.

Wold S., “Spline Functions in Data Analysis,” Technometrics, 1974, 16(1), 1-11.

Hardy R. L., “Multi-quadric Equations of Topography and other Irregular Surfaces,” Journal of Geophysical Research, 1971, 76, 1905-1915.

Freeman J. A. and Skapura D. M., “Neural Networks, Algorithms Applications and Programming Techniques,” Adison-Wesely, 1990.

Veelenturf L. P. J., “Analysis of Artificial Neural Network,” Prentice-Hall, 1995, 14, 259.

Mohaghegh S., “Quantifying Uncertainties Associated with Reservoir Simulation Studies Using Surrogate Reservoir Models,” in the Annual Technical Conference and Exhibition, 2006.

Christie M., Demyanov V., and Erbas D., “Uncertainty Quantification for Porous Media Flows,” Journal of Computational Physics, 2006, 217, 143-158.

Yeten B., Castellini A., Guyaguler B., and Chen W., “A Comparison Study on Experimental Design and Response Surface Methodologies,” in the SPE Reservoir Simulation Symposium, 2005.

Zubarev D., “Pros and Cons of Applying Proxy Models as a Substitute for Full Reservoir Simulations,” in the SPE Annual Technical Conference and Exhibition, 2009.

Anterion F., Eymard R., and Karcher B., “Use of Parameter Gradients for Reservoir History Matching,” in the Symposium on Reservoir Simulation, 1989.

Ouenes A., Meunier G., and Moegen H., “Application of Simulated Annealing Method (SAM) to Gas Storage Reservoir Characterization,” presented in the Annual AIChE National Spring Meeting, 1992.

Ouenes A., Fasanino G., and Lee R., “Simulated Annealing for Interpreting Gas/Water Laboratory,” in the Annual Technical Conference and Exhibition, 1992.

Ouenes A., Brefort B., Meunier G., and Dupere S., “A New Algorithm for Automatic History Matching: Application of Simulated Annealing Method (SAM) to Reservoir Inverse Modeling,” Paper SPE 26297, Unsolicited Manuscript, 1993, 1-16.

Sen M., Datta-Gupta A., Stoffa P., Lake L., and Pope G., “Stochastic Reservoir Modeling Using Simulated Annealing and Genetic Algorithms,” SPE Formation Evaluation J., 1995, 10(1), 49-55.

Holland J., “Adaptation in Natural and Artificial Systems,” University of Michigan Press, Ann Arbor, 1975, 1, 975.

Romero C., Carter J., Zimmerman R., and Gringarten A., “Improved Reservoir Characterization through Evolutionary Computation,” in the Annual Technical Conference and Exhibition, 2000.

Williams N. and Lond D. K., “Kutubu - A Rethink,” in the Asia Pacific Oil and Gas Conference and Exhibition, 2006.

Castellini A., Yeten B., Singh U., Vahedi A., and et al., “History Matching and Uncertainty Quantification Assisted by Global Optimization Techniques,” In ECMOR X-10th European Conference on the Mathematics of Oil Recovery, 2006.

Ballester P. and Carter J., “A Parallel Real-coded Genetic Algorithm for History Matching and Its Application to a Real Petroleum Reservoir,” Journal of Petroleum Science and Engineering, 2007, 59, 157-168.

Rechenberg I., “Cybernetic Solution Path of an Experimental Problem,” Royal Aircraft Establishment, Library Translation Number 1122, Farnborough, UK, 1965.

Schulze-Riegert R., Krosche M., Pajonk O., and Mustafa H., “Data Assimilation Coupled to Evolutionary Algorithms-A Case Example in History Matching,” in the SPE/EAGE Reservoir Characterization and Simulation Conference, 2009.

Haase O., Schulze-Riegert R., and Junker P. L., “Selecting Optimal Cases for Uncertainty Quantification and History Matching,” Oil and Gas European Magazine, 2006, 32(4), 170.

Selberg S., Schulze-Riegert R., and Stekolschikov K., “Event-Targeting Model Calibration Used for History Matching Large Simulation Cases in Reservoir Simulation Symposium,” In SPE Reservoir Simulation Symposium, Society of Petroleum Engineers, 2008.

Sousa S., Maschio C., and Schiozer D., “Scatter Search Metaheuristic Applied to the History-Matching Problem,” in the Annual Technical Conference and Exhibition, 2006.

Banchs R., Klie H., Rodriguez A., Thomas S., and Wheeler M., “A Learning Computational Engine for History Matching,”, in the 10th European Conference on the Mathematics of Oil Recovery, 2006.

Gao G., “A Parallelized and Hybrid Data-Integration Algorithm for History Matching of Geologically Complex Reservoirs,” SPE Journal, 2016, 21, 2-155.

Jia X., Cunha L. B., and Deutsch C., “Investigation of Stochastic Optimization Methods for Automatic History Matching of SAGD Processes,” Journal of Canadian Petroleum Technology, 2009, 48, 14-18.

Liu N., and Oliver D., “Critical Evaluation of the Ensemble Kalman Filter on History Matching of Geological Facies,”,in the Reservoir Simulation Symposium, 2005.

Valles B. and Naevdal G., “Comparing Different Ensemble Kalman Filter Approaches,” in the European Conference on the Mathematics of Oil Recovery, 2008.

Sarma P. and Chen W., “Generalization of the Ensemble Kalman Filter Using Kernels for Non-Gaussian Random Fields,” in the Reservoir Simulation Symposium, 2009.

Pajonk O., Krosche M., Schulze-Riegert R., Niekamp R., and et al., “Stochastic Optimization Using EA and EnKF–A Comparison,” in European Conference on the Mathematics of Oil Recovery, 2008.

Petrie R., “Localization in the Ensemble Kalman Filter,” Department of Meteorology, University of Reading, 2008, 1-65.

Jardak M., Navan M., and Zupanski M., “Comparison of Sequential Data Assimilation Methods for the Kuramoto-Sivashinsky Equation,” International Journal for Numerical Methods in Fluids, 2009, 62(4), 374-402.

Valles B. and Naevdal G., “Comparing Different Ensemble Kalman Filter Approaches,” in the European Conference on the Mathematics of Oil Recovery, 2008.

Lorentzen R., Naevdal G., Valles B., Berg M., and Grimstad A., “Analysis of the Ensemble Kalman Filter for Estimation of Permeability and Porosity in Reservoir Models,” in the Annual Technical Conference and Exhibition, 2005.

Franssen H. and Kinzelbach W., “Ensemble Kalman Filtering Versus Sequential Self-Calibration for Inverse Modeling of Dynamic Groundwater Flow Systems,” Journal of Hydrology, 2009, 365, 261-274.

Kennedy J. and Eberhart R., “Particle Swarm Optimization,” Proceedings of IEEE International Conference on Neural Networks, 1995, 1942-1948.

Kathrada M., “Uncertainty Evaluation of Reservoir Simulation Models Using Particle Swarm and Hierarchical Clustering,” Ph.D. dissertation, Institute of Petroleum Engineering, Heriot Watt University, UK, 2009.

Mohamed L., “Popular MCMC methods for History Matching and Uncertainty Quantification,” Computational Geosciences, 2012, 16(2), 423–436.

Fernandez J., Echeverria D., and Mukerji T., “Application of Particle Swarm Optimization to Reservoir Modeling and Inversion,” in the IAMG09 Conference, Stanford University, 2009.

Hajizadeh Y., “Population-Based Algorithms for Improved History Matching and Uncertainty Quantification of Petroleum Reservoirs,” Ph.D. Dissertation, Herriot-Watt University, UK, 2011.

Yang X. S., “Firefly Algorithms for Multimodal Optimization,” SAGA. LNCS, Springer, Heidelberg, 2009, 57, 169-178.

Shams M., “Firefly Optimization, A Novel Algorithm to the Arena of Assisted History Matching,” in the Offshore Mediterranean Conference, 2017.

Pham D. T., Ghanbarzadeh A., Koc E., Otri S., and et al., “The Bee Algorithm, Technical Note,” Manufacturing Engineering Center, Cardiff University: Cardiff, UK, 2005.

Shams M, El-Banbi A, and Sayyouh H, “Honey Bees Can Assist History Matching,” Journal of Petroleum Exploration and Development, in press, Submitted 2018.

Geem Z.W, Lee K. S., and Bae K. W., “The Harmony Search Heuristic Algorithm for Discrete Structural Optimization,” Engineering Optimization, 2005, 37(7), 663-684.

Alia O. and Mandava R., “The Variants of the Harmony Search Algorithm: an Overview,” Artificial Intelligence Review, 2011, 36(1), 49-68.

Shams M, El-Banbi A, and Sayyouh H, “Harmony Search Optimization Applied to Reservoir Engineering Assisted History Matching,” Journal of Petroleum Exploration and Development, in press, Submitted 2018.

Goodwin N. and Jutila H., “Schedule Optimization to Complement Assisted History Matching and Prediction under Uncertainty,” in the SPE Europec/EAGE Annual Conference and Exhibition, 2006.