مقایسه‌ی انتشار ترک‌های هیدرولیکی دوبعدی کرنش صفحه‌ای و شعاعی در مقیاس گرانروی با رویکرد تحلیلی

اصغری سراسکانرود، ص.، فرامرزی عوری، ب.، نوری، ت.، عابدینی، م.، 1402. شناسایی مناطق امیدبخش برای انرژی ژئوترمال با استفاده از داده‌های ماهواره‌ای در منطقه سبلان. هیدروژئولوژی.

عسگری، ع.، گلشنی، ع. ا.، 1394. تحلیل انتشار صفحه‌یی ترک هیدرولیکی در سنگ شکننده‌ی نفوذناپذیر با درنظرگرفتن اثر اینرسی سیال. مجله‌ی مهندسی عمران شریف، 31.2 (3.2): 23-29.

عسگری، ع.، گلشنی، ع. ا.، 1398. تحلیل مدل ریاضی انتشار ترک هیدرولیکی در محیط کشسان: رژیم سختی - گرانروی. مجله‌ی مهندسی عمران شریف، 35.2 (2.2): 17-28.

عسگری، ع.، گلشنی، ع. ا.، 1399. تحلیل رشد ترک هیدرولیکی در مقیاس سختی با درنظرگرفتن اثر اندرکنش فراسنج‌های ماند و گرانروی: ترم‌های مرتبۀ بالاتر. نشریه مهندسی عمران امیرکبیر، 52 (2): 469-494.

عسگری، ع.، گلشنی، ع. ا.، 1400. برآورد اثر اندرکنش بین ترک‌های هیدرولیکی. نشریه مهندسی عمران امیرکبیر، 53 (2): 707-722.

عسگری، ع.، گلشنی، ع. ا.، لکی روحانی، ع.، 1395. مدل ریاضی انتشار ترک هیدرولیکی در سنگ شکننده با در نظر گرفتن اثر اندرکنش (مضروبی) پارامترهای اینرسی و گرانروی. مجله‌ی مهندسی عمران شریف، 32.2 (2.1): 59-66.

علوی، س. غ.، ناصری، ح.، جمادی، م.، پرخیال، س.، 1398. هیدروژئوشیمی سیالات گرمابی مخازن ژئوترمال غرب سبلان- شمال‌غرب ایران. هیدروژئولوژی، 4 (1): 80-96.

Abe, H., Keer, L., Mura, T., 1976. Growth rate of a penny-shaped crack in hydraulic fracturing of rocks, 2. Journal of Geophysical Research, 81(35): 6292-6298.

Abou-Sayed, A., Andrews, D., Buhidma, I., 1989. Evaluation of oily waste injection below the permafrost in Prudhoe Bay field. SPE California Regional Meeting, Bakersfield, California.       

Abramowitz, M., Stegun, I.A., 1972. Handbook of mathematical functions: with formulas, graphs, and mathematical tables. New York NY: Dover Publications Inc.  

Adachi, J. and Detournay, E., 2002. Self similar solution of a plane strain fracture driven by a power law fluid. International Journal for Numerical and Analytical Methods in Geomechanics, 26(6): 579-604.

Adachi, J.I., 2001. Fluid-driven fracture in permeable rock. Ph.D. thesis, University of Minnesota.        

Adachi, J.I., Detournay, E., Peirce, A. P., 2010. Analysis of the classical pseudo-3D model for hydraulic fracture with equilibrium height growth across stress barriers. International Journal of Rock Mechanics and Mining Sciences, 47(4): 625-639.

Adachi, J.I. and Peirce, A. P., 2008. Asymptotic analysis of an elasticity equation for a finger-like hydraulic fracture. Journal of Elasticity, 90(1): 43-69.

Advani, S.H., Lee, T., Lee, J., 1990. Three-dimensional modeling of hydraulic fractures in layered media: part I-finite element formulations. Journal of energy resources technology, 112(1): 1-9.

Andrews, G.E., Askey, R., Roy, R., 1999. Special functions, Vol. 71, Cambridge UK: Cambridge university press.

Asgari, A., 2022. Extended power series solution for Perkins-Kern-Nordgren model of hydraulic fracture. AUT Journal of Civil Engineering, 6(4): 461-468.

Barenblatt, G.I., 1959. The formation of equilibrium cracks during brittle fracture. General ideas and hypotheses. Axially-symmetric cracks. Journal of Applied Mathematics and Mechanics, 23(3): 622-636.

Barenblatt, G.I., 1996. Scaling, self-similarity, and intermediate asymptotics: dimensional analysis and intermediate asymptotics, Vol. 14, Cambridge University Press.

Batchelor, G., 1967. An Introduction to Fluid Dynamics Cambridge Univ. Press, Bentley House, London.

Bilby, B. and Eshelby, J., 1968. Fracture (Ed. H. Liebowitz), Vol. 1, In: Academic Press, New York.

Broyden, C.G., 1970. The convergence of a class of double-rank minimization algorithms 1. general considerations. IMA Journal of Applied Mathematics, 6(1): 76-90.

Bunger, A.P. and Detournay, E., 2005, a. Asymptotic solution for a penny-shaped near-surface hydraulic fracture. Engineering fracture mechanics, 72(16): 2468-2486.

Bunger, A.P., Detournay, E., Jeffrey, R.G., 2005. Crack tip behavior in near-surface fluid-driven fracture experiments. Comptes Rendus Mecanique, 333(4): 299-304.

Bunger, A.P., Menand, T., Cruden, A., Zhang, X., Halls, H., 2013. Analytical predictions for a natural spacing within dyke swarms. Earth and Planetary Science Letters, 375: 270-279.

Carbonell, R.S., 1996a. Self-similar solution of a fluid-driven fracture. Ph.D. thesis, University of Minnesota.    

Carbonell, R.S., 1996b. Self-similar solution of a fluid-driven fracture in a zerotoughness elastic solid. Proc .Roy. Soc. London.

Clifton, R.J. and Abou-Sayed, A.S., 1981. A variational approach to the prediction of the three-dimensional geometry of hydraulic fractures. SPE/DOE Low Permeability Gas Reservoirs Symposium, Denver, Colorado.    

De Laguna, W., Tamura, T., Weeren, H., Struxness, E., McClain, W., Sexton, R., 1968. Engineering development of hydraulic fracturing as a method for permanent disposal of radioactive wastes. No. ORNL-4259., Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States).

Desroches, J., Detournay, E., Lenoach, B., Papanastasiou, P., Pearson, J., Thiercelin, M., and Cheng, A., 1994. The crack tip region in hydraulic fracturing. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 447(1929): 39-48.

Detournay, E., 2004. Propagation regimes of fluid-driven fractures in impermeable rocks. International Journal of Geomechanics, 4(1): 35-45.

Detournay, E., Cheng, A.D., Roegiers, J.C., McLennan, J., 1989. Poroelasticity considerations in in situ stress determination by hydraulic fracturing. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 26(6): 507-513.

Dontsov, E., 2016. An approximate solution for a penny-shaped hydraulic fracture that accounts for fracture toughness, fluid viscosity and leak-off. Royal Society open science, 3(12): 160737.

Economides, M.J., Nolte, K. G., and Ahmed, U., 2000. Reservoir stimulation, Vol. 18, Wiley Chichester.

Erdelyi, A., 1953. Higher trascendental functions. Vol. 2, New York NY: McGraw-Hill.

Esfandiari, M., and Pak, A., 2023. XFEM modeling of the effect of in-situ stresses on hydraulic fracture characteristics and comparison with KGD and PKN models. Journal of Petroleum Exploration and Production Technology, 13(1): 185-201.

Frank, U. and Barkley, N., 1995. Remediation of low permeability subsurface formations by fracturing enhancement of soil vapor extraction. Journal of hazardous materials, 40(2): 191-201.

Garagash, D., 2000. Hydraulic fracture propagation in elastic rock with large toughness. 4th North American Rock Mechanics Symposium, Seattle, Washington.

Garagash, D., 2006. Plane-strain propagation of a fluid-driven fracture during injection and shut-in: Asymptotics of large toughness. Engineering fracture mechanics, 73(4): 456-481.

Garagash, D., 2006. Transient solution for a plane-strain fracture driven by a shear-thinning, power-law fluid. International Journal for Numerical and Analytical Methods in Geomechanics, 30(14): 1439-1475.

Garagash, D. and Detournay, E., 2002. Viscosity-dominated regime of a fluid-driven fracture in an elastic medium. IUTAM Symposium on Analytical and Computational Fracture Mechanics of Non-Homogeneous Materials, Solid Mechanics and Its Applications, 97: 25–29.

Geertsma, J., 1989. Two-dimensional fracture propagation models. In Recent Advances in Hydraulic Fracturing. SPE Richardson, TX, 12: 81-94.

Geertsma, J. and De Klerk, F., 1969. A rapid method of predicting width and extent of hydraulically induced fractures. Journal of Petroleum Technology, 21(12): 1571-1581.

Geertsma, J. and Haafkens, R., 1979. A comparison of the theories for predicting width and extent of vertical hydraulically induced fractures. Journal of energy resources technology, 101(1): 8-19.

He, P., Lu, Z., Lu, Y., Huang, Y., Pan, L., Ouyang, L., and Zhou, J., 2023. Experimental study on fracture propagation and induced earthquake reduction by pulse hydraulic fracturing in shale reservoirs. Gas Science and Engineering, 110: 204908.

Hu, Z. and Wang, H., 2024. Feasibility study of energy storage using hydraulic fracturing in shale formations. Applied Energy, 354: part B, 122251.

Hui, G., Chen, Z.X., Lei, Z.D., Song, Z.J., Zhang, L.Y., Yu, X.R., Gu, F., 2023. A synthetical geoengineering approach to evaluate the largest hydraulic fracturing-induced earthquake in the East Shale Basin, Alberta. Petroleum Science, 20(1): 460-473.

Ingraffea, A. and Boone, T., 1988. Simulation of hydraulic fracture in poroelastic rock. Numerical Methods in Geomechanics (Innsbruck 1988), Balkema, Rotterdam: 95-105.

Ismail, A., and Azadbakht, S., 2024. A comprehensive review of numerical simulation methods for hydraulic fracturing. International Journal for Numerical and Analytical Methods in Geomechanics, 48(05): 1433-1459.

Khristianovic, S. and Zheltov, Y., 1955. Formation of vertical fractures by means of highly viscous fluids. Proc. 4th world petroleum congress, Rome, Italy.

Kovalyshen, Y. and Detournay, E., 2010. A reexamination of the classical PKN model of hydraulic fracture. Transport in porous media, 81(2): 317-339.

Lecampion, B. and Desroches, J., 2015. Simultaneous initiation and growth of multiple radial hydraulic fractures from a horizontal wellbore. Journal of the Mechanics and Physics of Solids, 82: 235-258.

Ma, Z.Q., Yin, X.Y., Zong, Z.Y., Tan, Y.Y., and Yang, Y.M., 2024. Analytical solution for the effective elastic properties of rocks with the tilted penny-shaped cracks in the transversely isotropic background. Petroleum Science, 21(1): 221-243.

Mack, M.G. and Warpinski, N.R., 2000. Mechanics of hydraulic fracturing. In: Economides, Nolte, editors. Reservoir stimulation, 3rd edition, Chichester, Wiley: Chapter 6.

Naceur, K.B. and Economides, M., 1989. Production from naturally fissured reservoirs intercepted by a vertical hydraulic fracture. SPE formation evaluation, 4(04): 550-558.

Nilson, R., 1981. Gas-driven fracture propagation. Journal of Applied Mechanics; (United States), 48(4): 757-762.

Nordgren, R., 1972. Propagation of a vertical hydraulic fracture. Society of Petroleum Engineers Journal, 12(04): 306-314.

Nygren, A. and Ghassemi, A., 2006. Poroelastic and thermoelastic effects of injection into a geothermal reservoir. Golden Rocks 2006, The 41st US Symposium on Rock Mechanics (USRMS), Colorado, ARMA-06-1053.

Ockendon, H., Ockendon, J.R., 1995. Viscous flow, Vol. 13, 1st edition, Cambridge University Press, pp 122.

Perkins, T. and Kern, L., 1961. Widths of hydraulic fractures. Journal of Petroleum Technology, 13(09): 937-949.

Rice, J.R., 1968. Mathematical analysis in the mechanics of fracture. Fracture: an advanced treatise, 2: 191-311.

Rutledge, J., Phillips, W., Mayerhofer, M., 2004. Faulting induced by forced fluid injection and fluid flow forced by faulting: An interpretation of hydraulic-fracture microseismicity, Carthage Cotton Valley gas field, Texas. Bulletin of the Seismological Society of America, 94(5): 1817-1830.

Sarvaramini, E. and Garagash, D., 2015. Breakdown of a Pressurized Fingerlike Crack in a Permeable Solid. Journal of Applied Mechanics, 82(6): 061006.

Savitski, A. and Detournay, E., 2001. Similarity solution of a penny-shaped fluid-driven fracture in a zero-toughness linear elastic solid. Comptes Rendus de l'Académie des Sciences-Series IIB-Mechanics, 329(4): 255-262.

Savitski, A., and Detournay, E., 2002. Propagation of a penny-shaped fluid-driven fracture in an impermeable rock: asymptotic solutions. International Journal of Solids and Structures, 39(26): 6311-6337.

Settari, A. and Cleary, M. P., 1986. Development and testing of a pseudo-three-dimensional model of hydraulic fracture geometry. SPE Production Engineering, 1(06): 449-466.

Shah, K., Carter, B. and Ingraffea, A., 1997. Hydraulic fracturing simulation in parallel computing environments. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts

Shan, K., Zheng, Y., Zhang, Y., Shan, Z., Li, Z., 2023. Effects of different fracture parameters on microseisms induced by hydraulic fracturing. Bulletin of Engineering Geology and the Environment, 82(6): 231.

Shapiro, R.A., 1954. The dynamics and thermodynamics of compressible fluid flow. New York: Ronald Press, 2(1).

Simonson, E., Abou-Sayed, A., Clifton, R., 1978. Containment of massive hydraulic fractures. Society of Petroleum Engineers Journal, 18(01): 27-32.

Sneddon, I. N., Lowengrub, M., Mathematician, P., 1969. Crack problems in the classical theory of elasticity. John Wiley and Sons New York, pp. 221.

Sousa, J., Carter, B., Ingraffea, A., 1993. Numerical simulation of 3D hydraulic fracture using Newtonian and power-law fluids. International journal of rock mechanics and mining sciences & geomechanics abstracts, 30(07): 1265-1271.

Spence, D. Sharp, P., 1985. Self-similar solutions for elastohydrodynamic cavity flow. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 400(1819): 289-313.

Szeg, G., 1939. Orthogonal polynomials, Vol. 23, New York NY: Colloquium Publications, American Mathematical Society, pp 432.

Warpinski, N. and Smith, M. B., 1989. Rock mechanics and fracture geometry. Recent Advances in Hydraulic Fracturing, 12: 57-80.

Xue, Y., Liu, S., Chai, J., Liu, J., Ranjith, P., Cai, C., Gao, F., Bai, X., 2023. Effect of water-cooling shock on fracture initiation and morphology of high-temperature granite: Application of hydraulic fracturing to enhanced geothermal systems. Applied Energy, 337: 120858.

Yu, H., Xu, W., Li, B., Huang, H., Micheal, M., Wang, Q., Huang, M., Meng, S., Liu, H., Wu, H., 2023. Hydraulic fracturing and enhanced recovery in shale reservoirs: theoretical analysis to engineering applications. Energy & Fuels, 37(14): 9956-9997.

YuP, Z. and Khristianovitch, S., 1955. On the mechanism of hydraulic fracture of an oil bearing stratum. Izvestiya Akademiia Nauk SSSR, Otd. Tekhn. Nauk, 5: 3-41.

Zhang, X., Detournay, E., Jeffrey, R., 2002. Propagation of a penny-shaped hydraulic fracture parallel to the free-surface of an elastic half-space. International journal of fracture, 115(2): 125-158.

Zhuang, X., Li, X., Zhou, S., 2023. Transverse penny-shaped hydraulic fracture propagation in naturally-layered rocks under stress boundaries: A 3D phase field modeling. Computers and Geotechnics, 155: 105205.