Release:2020. Vol. 6. № 3 (23)
About the authors:Andrey G. Plavnik, Dr. Sci. (Tech.), Chief Researcher, West Siberian Branch of Institute of Petroleum Geology and Geophysics, Siberian Branch of the Russian Academy of Sciences; Professor, Department of Oil and Gas Geology, Industrial University of Tyumen; eLibrary AuthorID, ORCID, ResearcherID, ScopusID, firstname.lastname@example.org
The need for stochastic modeling of the geological objects properties is due to their significant heterogeneity and the limited amount of data. The existing simulation methods, in their formulation, are largely based on the stochastic representation of the model settings laid down and implemented in kriging. Within the framework of other mapping methods that use other model conditions, developing of novel approaches to the problem formulation and to implementation of stochastic simulations methods is necessary.
In this paper, we consider an approach based on the application of the variational-grid method of geological mapping. The method is based on minimizing the quadratic functional with ability taking into account a variety of heterogeneous data, including those of a stochastic nature. The direct stochastic simulation method is proposed and tested. It consists in application of the functionality, which includes three constituent elements responsible for: 1) the data approximation, 2) taking into account general spatial patterns, and 3) for the contribution of the random component to the model constructions. The main features of the method are as follows: 1) a small number of control parameters, 2) a predictable effect of their changing on the simulation results, 3) it provides an easy way to accurately mapping the mathematical expectation of the stochastic simulations options variety, and 4) it is applicable for modeling both continuous and categorical parameters.
The mathematical implementation of the approach allows reducing the problem to solving a system of linear algebraic equations with a symmetric and positive definite matrix. This determines the multioptional calculations’ computational efficiency due to a single execution of matrix factorization. The calculations are presented for two groups of data with significantly different both quantitative and model parameters, demonstrating the possibilities and features of the proposed approach implementation under different conditions. The calculations testify that the variograms’ parameters of the stochastic solutions and of the actual data could be coordinated.
Akhmetsafina A. R., Minniakhmetov I. R., Pergament A. Kh. 2010. “Stochastic methods in geological modeling program”. Vestnik TsKR Rosnedra, no. 1, pp. 34-45. [In Russian]
Baishev R. V., Kuparev D. A., Krivina T. G. 2009. “Selection of geological model variant in stochastic modeling of Shakhpakhty gas condensate field”. Neftegazovoe delo, no. 12, pp. 28-31. [In Russian]
Volkov A. M. 1988. Geological Mapping of Oil and Gas Territories Using a Computer. Moscow: Nedra. 221 pp. [In Russian]
Volkov A. M. 1979. “Map building — a variational task”. Geologiya i geofizika, no. 1, pp. 60-65. [In Russian]
Demyanov V. V., Savelyeva E. A. 2010. Geostatistics: Theory and Practice. Moscow: Nauka. 327 pp. [In Russian]
Plavnik A. G. 2010. “Generalized spline-approximation setting of the task of mapping the properties of geological objects”. Geologiya i geofizika, no. 7 (51), pp. 1027-1037. [In Russian]
Potekhin D. V., Deryushev A. B. 2012. “Experience of three-dimensional modeling of terrigenous Devon on the example of Nizhnetiman deposits of the Kirillovskoye oil field”. Geologiya, geofizika i razrabotka neftyanykh i gazovykh mestorozhdeniy, no. 4, pp. 25-30. [In Russian]
Sidorov A. N., Plavnik A. G., Sidorov A. A., Shutov M. S. et al. 2005. “GST Program Registration Certificate”. Reestr programm dlya EVM Federalnoy sluzhby po intellektualnoy sobstvennosti, patentam i tovarnym znakam. No. 2005612939. [In Russian]
Fedorov A. E., Amineva A. A., Dilmukhametov I. R., Krasnov V. A. et al. 2019. “Analysis of geological uncertainty in stochastic modeling of geological bodies”. Neftyanoe khozyaystvo, no. 9, pp. 24-28. [In Russian]
Almeida J. A. 2010. “Stochastic simulation methods for characterization of lithoclasses in carbonate reservoirs”. Earth-Science Reviews, nos. 3-4 (101), pp. 250-270.
Bangerth W., Klie H., Wheeler M. F., Stoffa P. L. et al. 2006. “On optimization algorithms for the reservoir oil well placement problem”. Computational Geosciences, no. 3 (10), pp. 303-319.
Boucher A., Kyriakidis P. C. 2006. “Super-resolution land cover mapping with indicator geostatistics”. Remote Sensing of Environment, no. 3 (104), pp. 264-282.
Chilès J. P., Delfiner P. 1999. Geostatistics Modeling Spatial Uncertainty. New York: Wiley. 695 pp.
Delbari M., Afrasiab P., Loiskandl W. 2009. “Using sequential Gaussian simulation to assess the field-scale spatial uncertainty of soil water content”. Catena, no. 2 (79), pp. 163-169.
Delhome J. P. 1979. “Spatial variability and uncertainty in groundwater flow parameters: a geostatistical approach”. Water Resources Research, no. 2 (15), pp. 269-280.
Doligez B., Ravalec M., Bouquet S., Adelinet M. 2015. “A review of three geostatistical techniques for realistic geological reservoir modeling integrating multi-scale data”. Bulletin of Canadian Petroleum Geology, no. 4 (63), pp. 277-286.
GST. GeoSpline Technology. http://www.geo-spline.ru/
Karacan C. Ö., Olea R. A., Goodman G. 2012. “Geostatistical modeling of the gas emission zone and its in-place gas content for Pittsburgh-seam mines using sequential Gaussian simulation”. International Journal of Coal Geology, nos. 90-91, pp. 50-71.
Mariethoz G., Renard P., Cornaton F., Jaquet O. 2009. Truncated plurigaussian simulations to characterize aquifer heterogeneity”. Ground Water, no. 1 (47), pp. 13-24.
Pyrcz M. J., Deutsch C. V. 2014. Geostatistical Reservoir Modelling. New York: Oxford University Press. 449 pp.
Yarus J. M., Chambers R. L. (eds.). 1994. Stochastic Modeling and Geostatistics. Principles, Methods, and Case Studies (AAPG Computer Applications in Geology, No. 3). Tulsa, Oklahoma: AAPG. 379 pp.