مدل‌سازی زمین‌آماری چندنقطه‌ای رخساره‌های ناهمگون مخازن نفتی به‌منظور کنترل تولید ماسه

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشکده مهندسی معدن، نفت و ژئوفیزیک، دانشگاه صنعتی شاهرود، ایران.

2 دانشکده مهندسی معدن، نفت و ژئوفیزیک، دانشگاه صنعتی شاهرود، شاهرود، ایران

3 مرکز آب زمین محیط زیست، موسسه ملی تحقیقات علمی، دانشگاه کبک، کبک، کانادا

4 دانشکده مهندسی معدن، نفت و ژئوفیزیک، دانشگاه صنعتی شاهرود، ایران

چکیده

انتخاب موقعیت مناسب چاه‌های تولید با در نظر گرفتن مشخصات ژئومکانیکی رخساره‌های مخزن می‌تواند نقش بسیار مهمی در کاهش تولید شن و ماسه در فرآیند تولید نفت از مخازن ماسه‌سنگی داشته باشد.گام اصلی در تعیین مشخصات ژئومکانیکی رخساره‌های مخزن، ایجاد منطقه‌بندی ژئومکانیکی است. با توجه به تغییرپذیری فضایی ذاتی و همچنین ناهمگونی شدید رخساره‌های نفتی، ایجاد چنین منطقه‌بندی بدون داشتن یک مدل ساختاری مطمئن از رخساره‌های مخزن، با عدم قطعیت نسبتاً بالایی همراه است. شبیه‌سازی‌های چندنقطه‌ای زمین‌آماری نه تنها به عنوان روشی قدرتمند در تخمین ویژگی‌های ژئومکانیکی مخزن بلکه به عنوان ابزاری برای مدل‌سازی رخساره‌های به شدت ناهمگون از چند دهه اخیر مورد توجه زیادی قرار گرفته‌اند. اهمیت ایجاد یک مدل دقیق از رخساره‌های زیرسطحی موجب شده است تا الگوریتم‌های متنوعی به منظور بهبود دقت و راندمان محاسباتی ارائه شوند. در این مقاله یک الگوریتم جدید برای مدل‌سازی عددی رخساره‌های ناهمگون در مخازن نفتی پیشنهاد شده است. الگوریتم پیشنهادی مبتنی بر تبدیل موجک گسسته (Discrete Wavelet Transform) و تابع همبستگی متقابل (Cross Correlation) است. به همین دلیل الگوریتم پیشنهادی CCWSIM نامیده شد. دقت و راندمان محاسباتی الگوریتم پیشنهادی با یکی دیگر از الگوریتم‌های شناخته شده شبیه‌سازی چندنقطه‌ای بنام CCSIM، در مدل‌های مصنوعی مختلف دوبعدی مخزن مقایسه می‌شوند. نتایج حاصل از مقایسه تحقق‌ها، دقت بالای الگوریتم پیشنهادی (CCWSIM) در بازتولید رخساره‌های ناهمگون مخزن را به خوبی نشان می‌دهد. همچنین الگوریتم پیشنهادی دارای راندمان بسیار بالاتری نسبت به الگوریتم CCSIM است.

کلیدواژه‌ها


عنوان مقاله [English]

Geostatistical multiple-point modeling of heterogeneous facies of petroleum reservoirs in order to control of the sand production

نویسندگان [English]

  • Mojtaba Bavand Savadkoohi 1
  • Behzad Tokhmechi 2
  • Erwan Gloaguen 3
  • Alireza Arab-Amiri 4
1 Faculty of Mining, Petroleum, and Geophysics, Shahrood University of Technology, Iran.
2 Associate Professor; Faculty of Mining Eng., Petroleum and Geophysics, Shahrood University of Technology
3 Centre Eau Terre Environnement, Institut National de la Recherche Scientifique, Québec, Canada
4 Faculty of Mining Eng., Petroleum and Geophysics, Shahrood University of Technology
چکیده [English]

Considering the geomechanical characteristics of the subsurface facies in well location can play an important role in reducing the sand production from reservoirs. The main step in the geomechanical characterization in the reservoirs is to create an accurate geomechanical zoning. Due to the intrinsic spatial variability and also the high heterogeneity of the facies making such geomechanical zoning is accompanied with high uncertainty without having a reliable structural model of the reservoir facies. In recent decades, multiple-point simulations (MPS) have been considered not only as an efficient gadget to estimate the geomechanical properties in the reservoirs but also as a tool for the modeling of the heterogeneous facies. The importance of generating an accurate model of the subsurface facies has led to the development of various algorithms to improve accuracy and computational efficiency. In this paper, a new algorithm is proposed for numerical modeling of heterogeneous facies in oil reservoirs. The proposed algorithm is based on Discrete Wavelet Transform (DWT) and the Cross Correlation (CC) function. For this reason, the proposed algorithm is called CCWSIM. The accuracy and computational efficiency of the proposed algorithm are compared with another well-known MPS algorithm, called MS-CCSIM, in a two-dimensional synthetic model of the reservoir. The results of the comparison show high accuracy of the proposed algorithm (CCWSIM) in the reproduction of heterogeneous reservoir facies. In addition, the proposed algorithm is more efficient than MS-CCSIM algorithm.

کلیدواژه‌ها [English]

  • Sand production
  • Reservoir Geomechanics
  • Subsurface heterogeneity
  • Geostatistical modeling
  • Multiple-point simulation
Allard, D. (1994). Simulating a geological lithofacies with respect to connectivity information using the truncated Gaussian model, Geostatistical simulations, Springer, pp 197-211.
Arpat, G. B. & Caers, J. (2007). Conditional simulation with patterns, Mathematical Geology, Vol. 39(2), pp 177-203.
Bavand Savadkoohi, M., Tokhmechi, B., Gloaguen, E. & Arab-Amiri, A. R. (2018). A comprehensive benchmark between two filter-based multiple point simulation algorithms, Journal of Mining and Environment, (In Prres).
Boutt, D., Cook, B. & Williams, J. (2011). A coupled fluid–solid model for problems in geomechanics: application to sand production, International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 35(9), pp 997-1018.
Caers, J .(2001) .Geostatistical reservoir modelling using statistical pattern recognition, Journal of Petroleum Science and Engineering, Vol. 29(3-4), pp 177-188.
Caers, J. & Zhang, T. (2004). Multiple-point geostatistics: a quantitative vehicle for integrating geologic analogs into multiple reservoir models, pp 383-394.
Cordua, K. S., Hansen, T. M. & Mosegaard, K. (2015). Improving the pattern reproducibility of multiple - point-based prior models using frequency matching, Mathematical Geosciences, Vol. 47(3), pp 317-343.
Crouse, M. S., Nowak, R. D. & Baraniuk, R. G. (1998). Wavelet-based statistical signal processing using hidden Markov models, IEEE Transactions on signal processing, Vol. 46(4), pp 886-902.
da Cruz, P. S., Horne, R. N. & Deutsch, C. V. (1999). The quality map: a tool for reservoir uncertainty quantification and decision making, SPE Annual Technical Conference and Exhibition, Society of Petroleum Engineers.
Deutsch, C. V. (2006). What in the reservoir is geostatistics good for?, Journal of Canadian Petro leum Technology, Vol. 45(04).
Deutsch, C. V. & Wang, L. (1996). Hierarchical object-based stochastic modeling of fluvial reservoirs, Mathematical Geology, Vol. 28(7), pp 857-880.
Efros, A. A. & Freeman, W. T. (2001). Image quilting for texture synthesis and transfer, Proceedings of the 28th annual conference on Computer graphics and interactive techniques, AC, pp. 341-346.
Fan, G. & Xia, X.-G. (2003). Wavelet-based texture analysis and synthesis using hidden Markov models, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, Vol. 50(1), pp 106-120.
Feyen, L. & Caers, J. (2006). Quantifying geological uncertainty for flow and transport modeling in multimodal heterogeneous formations, Advances in Water Resources, Vol. 29(6), pp 912-929.
Gardet, C., Le Ravalec, M. & Gloaguen, E. (2016). Pattern-based conditional simulation with a raster path: a few techniques to make it more efficient, Stochastic environmental research and risk assessment, Vol. 30(2), pp 429-446.
Goovaerts, P. (1998 .)Geostatistical tools for characterizing the spatial variability of microbiological and physico-chemical soil properties, Biology and Fertility of soils, Vol. 27(4), pp 315-334.
Guardiano, F. B. & Srivastava, R. M. (1993). Multivariate geostatistics: beyond bivariate moments. Geostatistics Troia’92, Springer, pp 133-144.
Honarkhah, M. & Caers, J. (2010). Stochastic simulation of patterns using distance-based pattern modeling, Mathematical Geosciences, Vol. 42(5), pp 487-517.
Isaaks, E. H. & Srivastava, R .M. (1989). An introduction to applied geostatistics, Oxford university press, pp 471-479.
Larter, S., Adams, J., Gates, I., Bennett, B. & Huang, H. (2006). The origin, prediction and impact of oil viscosity heterogeneity on the production characteristics of tar sand and heavy oil reservoirs, Canadian International Petroleum Conference, Petroleum Society of Canada.
Liu, Y. (2006). Using the Snesim program for multiple-point statistical simulation, Computers & Geosciences, Vol. 32(10), pp 1544-1563.
Mallat, S. G .(1989) .A theory for multiresolution signal decomposition: the wavelet representation, IEEE transactions on pattern analysis and machine intelligence, Vol. 11(7), pp 674-693.
Mariethoz, G. (2018). When should we use multiple-point geostatistics? Handbook of Mathematical Geosciences: Fifty Years of IAMG, Springer, 645-653.
Mariethoz, G. & Caers, J. (2014). Multiple-point geostatistics: stochastic modeling with training images, John Wiley & Sons.
Mariethoz, G., Renard, P. & Caers, J. (2010). Bayesian inverse problem and optimization with iterative spatial resampling, Water Resources Research, Vol. 46(11), pp.
McLennan, J. & Deutsch, C. V. (2005). Ranking geostatistical realizations by measures of connectivity, SPE International Thermal Operations and Heavy Oil Symposium, Society of Petroleum Engineers.
Morita, N., Whitfill, D. L., Fedde, O. & Lovik, T. (1989). Supplement to SPE 16990, Parametric Study of Sand-Production Prediction: Analytical Approach.
Palmer, I., Vaziri, H., Willson, S., Moschovidis, Z., Cameron, J. & Ispas, I. (2003). Predicting and managing sand production: A new strategy, SPE Annual Technical Conference and Exhibition, Society of Petroleum Engineers.
Papamichos, E., Cerasi, P., Stenebraten, J., Berntsen, A., Ojala, I., Vardoulakis, I., Brignoli, M., Fuh, G.- F., Han, G. & Nadeem, A. (2010). Sand production rate under multiphase flow and water breakthrough, 44th US Rock Mechanics Symposium and 5th US-Canada Rock Mechanics Symposium, American Rock Mechanics Association.
Papamichos, E. & Stavropoulou, M. (1998). An erosion-mechanical model for sand production rate prediction, International Journal of Rock Mechanics and Mining Sciences, Vol. 4(35), pp 531-532.
Parra, A. & Ortiz, J. M. (2011). Adapting a texture synthesis algorithm for conditional multiple point geostatistical simulation, Stochastic environmental research and risk assessment, Vol. 25(8), pp 1101-1111.
Pinheiro, M., Vallejos, J., Miranda, T. & Emery, X. (2016). Geostatistical simulation to map the spatial heterogeneity of geomechanical parameters: A case study with rock mass rating, Engineering Geology, Vol. 205, pp 93-103.
Pyrcz, M. J. & Deutsch, C. V. (2014). Geostatistical reservoir modeling, Oxford university press.
Pyrcz, M. J. & White, C. D. (2015). Uncertainty in reservoir modeling, Interpretation, Vol. 3(2), pp 7-19.
Rahmati, H., Jafarpour, M., Azadbakht, S., Nouri, A., Vaziri, H., Chan, D. & Xiao, Y. (2013). Review of sand production prediction models, Journal of Petroleum Engineering.
Rezaee, H., Mariethoz, G., Koneshloo, M. & Asghari, O. (2013). Multiple-point geostatistical simulation using the bunch-pasting direct sampling method, Computers & Geosciences, Vol. 54, pp 293-308.
Straubhaar, J., Renard, P., Mariethoz, G., Froidevaux, R & .Besson, O. (2011). An improved parallel multiple-point algorithm using a list approach, Mathematical Geosciences, Vol. 43(3), pp 305-328.
Strebelle, S. (2002). Conditional Simulation of Complex Geological Structures Using Multiple -Point Statistics, Mathematical Geology, Vol. 34(1), pp 1-21.
Strebelle, S. B. & Journel, A. G. (2001). Reservoir modeling using multiple-point statistics, SPE Annual Technical Conference and Exhibition, Society of Petroleum Engineers.
Tahmasebi, P., Hezarkhani, A. & Sahimi, M .(2012) .Multiple-point geostatistical modeling based on the cross-correlation functions, Computational Geosciences, Vol. 16(3), pp 779-797.
Tahmasebi, P., Sahimi, M. & Caers, J. (2014). MS-CCSIM: Accelerating pattern-based geostatistical simulation of categorical variables using a multi-scale search in Fourier space, Computers & Geosciences, Vol. 67, pp 75-88.
Tran, T., Mueller, U. & Bloom, L. (2002). Multi-level Conditional Simulation of Two-Dimensional Random Processes using Haar Wavelets.
Vardoulakis, I., Stavropoulou, M. & Papanastasiou, P. (1996). Hydro-mechanical aspects of the sand production problem, Transport in porous media, Vol. 22(2), pp 225-244.
Veeken, C., Davies, D., Kenter, C. & Kooijman, A. (1991). Sand production prediction review: developing an integrated approach, SPE annual technical conference and exhibition, Society of Petroleum Engineers.
Willson, S., Moschovidis, Z., Cameron, J. & Palmer, I. (2002). New model for predicting the rate of sand production, SPE/ISRM Rock Mechanics Conference, Society of Petroleum Engineers.
Xiao, Y. & Vaziri, H. H. (2011). Import of strength degradation process in sand production prediction and management, 45th US Rock Mechanics/Geomechanics Symposium, American Rock Mechanics Association.
Xu ,W., Tran, T., Srivastava, R. & Journel, A. G. (1992). Integrating seismic data in reservoir modeling: the collocated cokriging alternative, SPE annual technical conference and exhibition, Society of Petroleum Engineers.
Zhang, T., Switzer, P. & Journel ,A. (2006). Filter-based classification of training image patterns for spatial simulation, Mathematical Geology, Vol. 38(1), pp 63-80.