Cluster Analysis Assisted Float-Encoded Genetic Algorithm for a More Automated Characterization of Hydrocarbon Reservoirs

Affiliation(s)

Department of Geophysics, University of Miskolc, Miskolc, Hungary.

kavreka@gmail.com.

Department of Geophysics, University of Miskolc, Miskolc, Hungary.

kavreka@gmail.com.

ABSTRACT

A genetic algorithm-based joint inversion method is presented for evaluating hydrocarbon-bearing geological formations. Conventional inversion procedures routinely used in the oil industry perform the inversion processing of borehole geophysical data locally. As having barely more types of data than unknowns in a depth, a set of marginally over-determined inverse problems has to be solved along a borehole, which is a rather noise sensitive procedure. For the reduction of noise effect, the amount of overdetermination must be increased. To fulfill this requirement, we suggest the use of our interval inversion method, which inverts simultaneously all data from a greater depth interval to estimate petrophysical parameters of reservoirs to the same interval. A series expansion based discretization scheme ensures much more data against unknowns that significantly reduces the estimation error of model parameters. The knowledge of reservoir boundaries is also required for reserve calculation. Well logs contain information about layer-thicknesses, but they cannot be extracted by the local inversion approach. We showed earlier that the depth coordinates of layerboundaries can be determined within the interval inversion procedure. The weakness of method is that the output of inversion is highly influenced by arbitrary assumptions made for layer-thicknesses when creating a starting model (*i.e.* number of layers, search domain of thicknesses). In this study, we apply an automated procedure for the determination of rock interfaces. We perform multidimensional hierarchical cluster analysis on well-logging data before inversion that separates the measuring points of different layers on a lithological basis. As a result, the vertical distribution of clusters furnishes the coordinates of layer-boundaries, which are then used as initial model parameters for the interval inversion procedure. The improved inversion method gives a fast, automatic and objective estimation to layer-boundaries and petrophysical parameters, which is demonstrated by a hydrocarbon field example.

Cite this paper

N. Szabó, M. Dobróka and R. Kavanda, "Cluster Analysis Assisted Float-Encoded Genetic Algorithm for a More Automated Characterization of Hydrocarbon Reservoirs,"*Intelligent Control and Automation*, Vol. 4 No. 4, 2013, pp. 362-370. doi: 10.4236/ica.2013.44043.

N. Szabó, M. Dobróka and R. Kavanda, "Cluster Analysis Assisted Float-Encoded Genetic Algorithm for a More Automated Characterization of Hydrocarbon Reservoirs,"

References

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[2] M. Alberty and K. Hashmy, “Application of ULTRA to log Analysis,” SPWLA Symposium Transactions, 1984, pp. 1-17.

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[5] M. Dobróka and N. P. Szabó, “Interval Inversion of Well-Logging Data for Automatic Determination of Formation Boundaries by Using a Float-Encoded Genetic Algorithm,” Journal of Petroleum Science and Engineering, Vol. 86-87, 2012, pp. 144-152.

http://dx.doi.org/10.1016/j.petrol.2012.03.028

[6] M. Dobróka, N. P. Szabó and E. Turai, “Interval Inversion of Borehole Data for Petrophysical Characterization of Complex Reservoirs,” Acta Geodaetica et Geophysica Hungarica, Vol. 47, No. 2, 2012, pp. 172-184.

http://dx.doi.org/10.1556/AGeod.47.2012.2.6

[7] M. Dobróka, P. N. Szabó, E. Cardarelli and P. Vass, “2D Inversion of Borehole Logging Data for Simultaneous Determination of Rock Interfaces and Petrophysical Parameters,” Acta Geodaetica et Geophysica Hungarica, Vol. 44, No. 4, 2009, pp. 459-479.

http://dx.doi.org/10.1556/AGeod.44.2009.4.7

[8] M. Dobróka and P. N. Szabó, “Combined Global/Linear Inversion of Well-Logging Data in Layer-Wise Homogeneous and Inhomogeneous Media,” Acta Geodaetica et Geophysica Hungarica, Vol. 40, No. 2, 2005, pp. 203214. http://dx.doi.org/10.1556/AGeod.40.2005.2.7

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[10] W. B. Hempkins, “Multivariate Statistical Analysis in Formation Evaluation,” SPE California Regional Meeting, 1978, pp. 1-20. http://dx.doi.org/10.2118/7144-MS

[11] G. N. Lance and W. T. Williams, “A General Theory of Classificatory Sorting Strategies 1. Hierarchical Systems,” The Computer Journal, Vol. 9, No. 4, 1967, pp. 373-380.

http://dx.doi.org/10.1093/comjnl/9.4.373

[12] J. Kovács, P. Tanos, J. Korponai, I. K. Székely, K. Gondár, K. Gondár-Soregi and I. G. Hatvani, “Analysis of Water Quality Data for Scientists,” In: K. Voudouris and D. Voutsa, Eds., Water Quality Monitoring and Assessment, InTech Open Access Publisher, Rijeka, 2012, pp. 65-94.

[13] M. Kazmierczuk and J. Jarzyna, “Improvement of Lithology and Saturation Determined from Well Logging Using Statistical Methods,” Acta Geophysica, Vol. 54, No. 4, 2006, pp. 378-398.

http://dx.doi.org/10.2478/s11600-006-0030-y

[14] V. Tavakoli and A. Amini, ”Application of Multivariate Cluster Analysis in Logfacies Determination and Reservoir Zonation, Case Study of Marun Field, South of Iran,” Journal of Science University of Teheran, Vol. 32, No. 2, 2006, pp. 69-75.

[15] H. H. Perez, A. Datta-Gupta and S. Mishra, “The Role of Electrofacies, Lithofacies, and Hydraulic Flow Units in Permeability Predictions from Well Logs: A Comparative Analysis Using Classification Trees,” SPE Annual Technical Conference and Exhibition, Denver, 2003, pp. 1-11.

http://dx.doi.org/10.2118/84301-MS

[16] G. Asquith and D. Krygowski, “Basic Well Log Analysis,” 2nd Edition, AAPG, Tulsa, 2004.

[17] M. H. Rider,” The Geological Interpretation of Well Logs,” 2nd Edition, Rider-French Consulting Ltd., Sutherland, 2002.

[18] á. Gyulai, M. K. Baracza and é. E. Tolnai, “The Application of Joint Inversion in Geophysical Exploration,” International Journal of Geosciences, Vol. 4, No. 2, 2013, pp. 283-289.

http://dx.doi.org/10.4236/ijg.2013.42026

[19] W. Menke, “Geophysical Data Analysis: Discrete Inverse Theory,” Academic Press Inc., New York, 1984.

[20] J. H. Holland, “Adaptation in Natural and Artificial Systems,” University of Michigan Press, Ann Arbor, 1975.

[21] Z. Michalewicz, “Genetic Algorithms Plus Data Structures Equals Evolution Programs,” Springer-Verlag Inc., New York, 1992.

[22] J. H. Ward, “Hierarchical Grouping to Optimize an Objective Function,” Journal of the American Statistical Association, Vol. 58, No. 301, 1963, pp. 236-244.

http://dx.doi.org/10.1080/01621459.1963.10500845

[1] D. V. Ellis and J. M. Singer, “Well Logging for Earth Scientists,” 2nd Edition, Springer, Dordrecht, 2007.

[2] M. Alberty and K. Hashmy, “Application of ULTRA to log Analysis,” SPWLA Symposium Transactions, 1984, pp. 1-17.

[3] S. M. Ball, D. M. Chace and W. H. Fertl, “The Well Data System (WDS): An Advanced Formation Evaluation Concept in a Microcomputer Environment,” Proceedings of SPE Eastern Regional Meeting, Pittsburgh, 1987, pp. 61-85. http://dx.doi.org/10.2118/17034-MS

[4] C. Mayer, “GLOBAL, a New Approach to ComputerProcessed Log Interpretation,” Proceedings of 55th SPE Annual Technical Conference and Exhibition, 1980, pp. 1-14. http://dx.doi.org/10.2118/9341-MS

[5] M. Dobróka and N. P. Szabó, “Interval Inversion of Well-Logging Data for Automatic Determination of Formation Boundaries by Using a Float-Encoded Genetic Algorithm,” Journal of Petroleum Science and Engineering, Vol. 86-87, 2012, pp. 144-152.

http://dx.doi.org/10.1016/j.petrol.2012.03.028

[6] M. Dobróka, N. P. Szabó and E. Turai, “Interval Inversion of Borehole Data for Petrophysical Characterization of Complex Reservoirs,” Acta Geodaetica et Geophysica Hungarica, Vol. 47, No. 2, 2012, pp. 172-184.

http://dx.doi.org/10.1556/AGeod.47.2012.2.6

[7] M. Dobróka, P. N. Szabó, E. Cardarelli and P. Vass, “2D Inversion of Borehole Logging Data for Simultaneous Determination of Rock Interfaces and Petrophysical Parameters,” Acta Geodaetica et Geophysica Hungarica, Vol. 44, No. 4, 2009, pp. 459-479.

http://dx.doi.org/10.1556/AGeod.44.2009.4.7

[8] M. Dobróka and P. N. Szabó, “Combined Global/Linear Inversion of Well-Logging Data in Layer-Wise Homogeneous and Inhomogeneous Media,” Acta Geodaetica et Geophysica Hungarica, Vol. 40, No. 2, 2005, pp. 203214. http://dx.doi.org/10.1556/AGeod.40.2005.2.7

[9] N. P. Szabó and M. Dobróka, “Float-Encoded Genetic Algorithm Used for the Inversion Processing of WellLogging Data,” In: A. Michalski, Ed., Global Optimization: Theory, Developments and Applications, Mathematics Research Developments, Computational Mathematics and Analysis Series, Nova Science Publishers Inc., Hauppauge NY, 2013, pp. 79-104.

[10] W. B. Hempkins, “Multivariate Statistical Analysis in Formation Evaluation,” SPE California Regional Meeting, 1978, pp. 1-20. http://dx.doi.org/10.2118/7144-MS

[11] G. N. Lance and W. T. Williams, “A General Theory of Classificatory Sorting Strategies 1. Hierarchical Systems,” The Computer Journal, Vol. 9, No. 4, 1967, pp. 373-380.

http://dx.doi.org/10.1093/comjnl/9.4.373

[12] J. Kovács, P. Tanos, J. Korponai, I. K. Székely, K. Gondár, K. Gondár-Soregi and I. G. Hatvani, “Analysis of Water Quality Data for Scientists,” In: K. Voudouris and D. Voutsa, Eds., Water Quality Monitoring and Assessment, InTech Open Access Publisher, Rijeka, 2012, pp. 65-94.

[13] M. Kazmierczuk and J. Jarzyna, “Improvement of Lithology and Saturation Determined from Well Logging Using Statistical Methods,” Acta Geophysica, Vol. 54, No. 4, 2006, pp. 378-398.

http://dx.doi.org/10.2478/s11600-006-0030-y

[14] V. Tavakoli and A. Amini, ”Application of Multivariate Cluster Analysis in Logfacies Determination and Reservoir Zonation, Case Study of Marun Field, South of Iran,” Journal of Science University of Teheran, Vol. 32, No. 2, 2006, pp. 69-75.

[15] H. H. Perez, A. Datta-Gupta and S. Mishra, “The Role of Electrofacies, Lithofacies, and Hydraulic Flow Units in Permeability Predictions from Well Logs: A Comparative Analysis Using Classification Trees,” SPE Annual Technical Conference and Exhibition, Denver, 2003, pp. 1-11.

http://dx.doi.org/10.2118/84301-MS

[16] G. Asquith and D. Krygowski, “Basic Well Log Analysis,” 2nd Edition, AAPG, Tulsa, 2004.

[17] M. H. Rider,” The Geological Interpretation of Well Logs,” 2nd Edition, Rider-French Consulting Ltd., Sutherland, 2002.

[18] á. Gyulai, M. K. Baracza and é. E. Tolnai, “The Application of Joint Inversion in Geophysical Exploration,” International Journal of Geosciences, Vol. 4, No. 2, 2013, pp. 283-289.

http://dx.doi.org/10.4236/ijg.2013.42026

[19] W. Menke, “Geophysical Data Analysis: Discrete Inverse Theory,” Academic Press Inc., New York, 1984.

[20] J. H. Holland, “Adaptation in Natural and Artificial Systems,” University of Michigan Press, Ann Arbor, 1975.

[21] Z. Michalewicz, “Genetic Algorithms Plus Data Structures Equals Evolution Programs,” Springer-Verlag Inc., New York, 1992.

[22] J. H. Ward, “Hierarchical Grouping to Optimize an Objective Function,” Journal of the American Statistical Association, Vol. 58, No. 301, 1963, pp. 236-244.

http://dx.doi.org/10.1080/01621459.1963.10500845