برآورد اثر اندرکنش بین ترک‌های هیدرولیکی

نوع مقاله : مقاله پژوهشی

نویسندگان

1 گروه مهندسی عمران، دانشکده فنی و مهندسی، دانشگاه مازندران، بابلسر، ایران

2 - استادیار گروه مکانیک خاک و پی، دانشکده مهندسی عمران و محیط زیست، دانشگاه تربیت مدرس، تهران، ایران

چکیده

به منظور افزایش بهره‌وری استخراج هیدروکربن‌ها و گسترش ترک‌ها تا محل مخزن آن‌ها، ترک‌ها معمولا عمود بر تنش حداقل و به صورت دسته‌­ای رشد داده می‌شوند. از دهه اخیر، هر ساله در قاره‌ی آمریکا بیش از ده هزار چاه افقی برای ایجاد و رشد ترک عمودی بر تنش کمینه در حال حفاری است و در هر چاه افقی بالغ بر صد ترک هیدرولیکی ایجاد می‌گردد. به منظور کاهش هزینه اجرایی، معمولا 3-8 ترک را به طور هم زمان در یک محدوده 10-30 متری ایجاد می‌کنند و آن‌ها را در مخزن گسترش می‌دهند. رشد هم­زمان ترک‌ها با توجه به شکل، تعداد، موقعیت، فاصله و طول آن‌ها بر چگونگی رشد یکدیگر موثر است. به­عبارت دیگر وقتی ترکی در سطوح خود تحت فشار ناشی از تزریق سیال قرار می­گیرد، باعث رشد آن می­شود اما ممکن است این فشار بر روی رشد ترک‌های مجاور اثر منفی داشته باشد، که به این اثر سایه یا اندرکنش گفته می­شود. مسلما برآورد صحیح از اثر تنش سایه بین ترک‌ها منجر به طراحی بهینه­تری می‌شود در این نوشتار به کمک روش کشش کاذب ارتقا یافته به بررسی اثر اندرکنش بین ترک‌های هیدرولیکی با توجه به فواصل ترک‌ها بر روی یکدیگر پرداخته می‌شود. نتایج نشان می­دهدکه در ترک­های میانی تحت تاثیر تنش سایه بیشتری نسبت به ترک­های کناری قرار دارند و از طرفی افزایش فواصل بین ترک­ها باعث کاهش اثر سایه می­شود. نتایج این پژوهش در تعیین تعداد و فواصل ترک­ها، در طراحی شکست هیدرولیکی بسیار کاربردی است.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Evaluation of Shadow Stress between Hydraulic Fractures

نویسندگان [English]

  • Ali Asgari 1
  • Aliakbar Golshani 2
1 Assistant Professor of Geotechnical Engineering, Faculty of Engineering and Technology, University of Mazandaran, Babolsar, Iran.
2 Department of Civil and Environmental Engineering, Tarbiat Modares University, Tehran, Iran.
چکیده [English]

In order to increase the productivity of extraction of hydrocarbons reservoirs, the well is usually drilled in the direction of the minimum horizontal in situ stress, and hydraulic fractures simultaneously initiate and propagate perpendicular/transverse to the wellbore. In the last decade, more than 10,000 horizontal wells per year have been bored and hydraulically fractured, with up to a hundred hydraulic fractures placed in the horizontal segment of the well. In order to reduce operational cost, it is usual to create several hydraulic fractures at once. The well is there for stimulated in stages, with one stage consisting of a single pumping operation aimed at initiating and propagating simultaneously typically between 3-8 cracks spaced about 10–30 m apart. When the fluid pressure is applied on the surface of the fracture, the crack can propagate in the medium, but the pressure, induced from the fluid injection, may have a negative influence on the extension of adjacent cracks which is stated as shadow or interaction stress.  Certainly, an accurate estimation of interaction/shadow stress between the cracks leads to a more optimal design. In this research, the effect of the interaction between the hydraulic cracks with respect to the spacing and the number of cracks on each other and considering the position of the fractures are evaluated using the pseudo traction method. The results are shown that inner-fractures are further affected by shadow stress compared to outer-fractures. On the other hand as the distance of hydraulic fractures increases, shadow stresses decrease. In the last, the results can be useful in determining the optimum number and spacing of cracks in the design of hydraulic fractures.

کلیدواژه‌ها [English]

  • Multiple hydraulic fractures
  • Shadow stress
  • Simultaneous propagation
  • Pseudo traction technique
  • Analytical method

مراجع

[1] A. Bunger, Analysis of the power input needed to propagate multiple hydraulic fractures, International Journal of Solids and Structures, 50(10) (2013) 1538-1549.
[2] A. Bunger, R.G. Jeffrey, X. Zhang, Constraints on simultaneous growth of hydraulic fractures from multiple perforation clusters in horizontal wells, SPE Journal, 19(04) (2014, a) 608-620.
[3] A.P. Bunger, A.P. Peirce, Numerical Simulation of Simultaneous Growth of Multiple Interacting Hydraulic Fractures from Horizontal Wells, in:  Shale Energy Engineering -Technical Challenges, Environmental Issues, and Public Policy, ASCE, 2014, b, pp. 201-210.
[4] L.N. Germanovich, L.M. Ring, D.K. Astakhov, J. Shlyapobersky, M.J. Mayerhofer, Hydraulic fracture with multiple segments II. Modeling, International Journal of Rock Mechanics and Mining Sciences, 34(3) (1997) 98. e91-98. e15.
[5] B. Lecampion, J. Desroches, Simultaneous initiation and growth of multiple radial hydraulic fractures from a horizontal wellbore, Journal of the Mechanics and Physics of Solids,  (2015).
[6] V.M. Narendran, Analysis of growth and interaction of multiple hydraulic fractures, in:  SPE Reservoir Simulation Symposium, Society of Petroleum Engineers, 1983.
[7] A. Peirce, A. Bunger, Interference Fracturing: Nonuniform Distributions of Perforation Clusters That Promote Simultaneous Growth of Multiple Hydraulic Fractures, SPE Journal, 20(02) (2015) 384-395.
[8] K. Yamamoto, T. Shimamoto, S. Sukemura, Multiple fracture propagation model for a three-dimensional hydraulic fracturing simulator, International Journal of Geomechanics, 4(1) (2004) 46-57.
[9] A. Zerzar, Y. Bettam, Interpretation of multiple hydraulically fractured horizontal wells in closed systems, in:  Canadian International Petroleum Conference, Petroleum Society of Canada, 2004.
[10] G.A. Waters, B.K. Dean, R.C. Downie, K.J. Kerrihard, L. Austbo, B. McPherson, Simultaneous hydraulic fracturing of adjacent horizontal wells in the Woodford Shale, in:  SPE hydraulic fracturing technology conference, Society of Petroleum Engineers, 2009.
[11] C. Cheng, A.P. Bunger, Reduced order model for simultaneous growth of multiple closely-spaced radial hydraulic fractures, Journal of Computational Physics, 376 (2019) 228-248.
[12] C. Cheng, A.P. Bunger, Optimizing fluid viscosity for systems of multiple hydraulic fractures, AIChE Journal, 65(5) (2019).
[13] G. Lu, E. Gordeliy, R. Prioul, G. Aidagulov, A. Bunger, Modeling simultaneous initiation and propagation of multiple hydraulic fractures under subcritical conditions, Computers and Geotechnics, 104 (2018) 196-206.
[14] I. Sneddon, The distribution of stress in the neighbourhood of a crack in an elastic solid, in:  Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, The Royal Society, 1946, pp. 229-260.
[15] A.P. Bunger, T. Menand, A. Cruden, X. Zhang, H. Halls, Analytical predictions for a natural spacing within dyke swarms, Earth and Planetary Science Letters, 375 (2013) 270-279.
[16] M. Fisher, J. Heinze, C. Harris, B. Davidson, C. Wright, K. Dunn, Optimizing horizontal completion techniques in the Barnett shale using microseismic fracture mapping, in:  SPE Annual Technical Conference and Exhibition, Society of Petroleum Engineers, 2004.
[17] B.R. Meyer, L.W. Bazan, A discrete fracture network model for hydraulically induced fractures-theory, parametric and case studies, in:  SPE Hydraulic Fracturing Technology Conference, Society of Petroleum Engineers, 2011.
[18] H.H. Abass, M.Y. Soliman, A.M. Al-Tahini, J.B. Surjaatmadja, D.L. Meadows, L. Sierra, Oriented fracturing: A new technique to hydraulically fracture an openhole horizontal well, in:  SPE Annual Technical Conference and Exhibition, Society of Petroleum Engineers, 2009.
[19] H. Horii, S. Nemat-Nasser, Elastic fields of interacting inhomogeneities, International journal of solids and structures, 21(7) (1985) 731-745.
[20] H. Horii, S. Nemat-Nasser, Compression-induced microcrack growth in brittle solids: axial splitting and shear failure, Journal of Geophysical Research, 90(B4) (1985) 3105-3125.
[21] S. Nemat-Nasser, M. Hori, Toughening by partial or full bridging of cracks in ceramics and fiber reinforced composites, Mechanics of materials, 6(3) (1987) 245-269.
[22] N.I. Muskhelishvili, J. Radok, Some basic problems of the mathematical theory of elasticity, Cambridge Univ Press, 1953.
[23] A.T. Zehnder, Fracture Mechanics, Lecture Notes in Applied and Computational Mechanics, Springer Netherlands: 62, Pages XIV, 226, 2012.
[24] A. Asgari, Hydraulic Fracture Propagation in Brittle Rock: Based on Hydro-Mechanical Model, Tarbait Modares University, Tehran, 2016.
[25] H. Tada, P. Paris, G. Irwin, The analysis of cracks handbook, New York: ASME Press, 2000.
[26] R. Hoagland, J. Embury, A treatment of inelastic deformation around a crack tip due to microcracking, Journal of the American Ceramic Society, 63(7) (1980) 404-410.
[27] A. Chudnovsky, M. Kachanov, Interaction of a crack with a field of microcracks, International Journal of Engineering Science, 21(8) (1983) 1009-1018.
[28] L. Rose, Microcrack interaction with a main crack, International journal of fracture, 31(3) (1986) 233-242.
[29] A. Golshani, Y. Okui, M. Oda, T. Takemura, A micromechanical model for brittle failure of rock and its relation to crack growth observed in triaxial compression tests of granite, Mechanics of materials, 38(4) (2006) 287-303.
[30] A. Golshani, T. Tran-Cong, Energy analysis of hydraulic fracturing, KSCE Journal of Civil Engineering, 13(4) (2009) 219-224.
[31] J.E. Olson, Predicting fracture swarms—The influence of subcritical crack growth and the crack-tip process zone on joint spacing in rock, Geological Society, London, Special Publications, 231(1) (2004) 73-88.
[32] K. Wu, J.E. Olson, Simultaneous multifracture treatments: fully coupled fluid flow and fracture mechanics for horizontal wells, SPE journal, 20(02) (2015) 337-346.
[33] J. Benthem, W. Koiter, Asymptotic approximations to crack problems, in:  Methods of analysis and solutions of crack problems, Springer, 1973, pp. 131-178.
نشریه مهندسی عمران امیرکبیر
دوره 53، شماره 2
اردیبهشت 1400
صفحه 707-722

فایل ها

هم رسانی

ارجاع به این مقاله

آمار