×

zbMATH — the first resource for mathematics

A fully coupled porous flow and geomechanics model for fluid driven cracks: a peridynamics approach. (English) Zbl 1311.74043
Summary: A state-based non-local peridynamic formulation is presented for simulating fluid driven fractures in an arbitrary heterogeneous poroelastic medium. A recently developed peridynamic formulation of porous flow has been coupled with the existing peridynamic formulation of solid and fracture mechanics resulting in a peridynamic model that for the first time simulates poroelasticity and fluid-driven fracture propagation. This coupling is achieved by modeling the role of pore pressure on the deformation of porous media and vice versa through porosity variation with medium deformation, pore pressure and total mean stress. The poroelastic model is verified by simulating the one-dimensional consolidation of fluid saturated rock. An additional porous flow equation with material permeability dependent on fracture width is solved to simulate fluid flow in the fractured region. Finally, single fluid-driven fracture propagation with a two-dimensional plane strain assumption is simulated and verified against the corresponding classical analytical solution.

MSC:
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
76S05 Flows in porous media; filtration; seepage
74R10 Brittle fracture
74L10 Soil and rock mechanics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Dahi Taleghani, A; Olson, JE, How natural fractures could affect hydraulic-fracture geometry, SPE J, 19, 161-171, (2014)
[2] Warpinski, NR; Branagan, PT, Altered-stress fracturing, J Pet Technol, 41, 990-997, (1989)
[3] Fisher MK, Wright CA, Davidson BM, Goodwin AK, Fielder EO, Buckler WS, Steinsberger NP (2002) Integrating fracture mapping technologies to optimize stimulations in the Barnett Shale SPE annual technical conference and exhibition society of petroleum engineers. San Antonio, Texas. doi:10.2118/77441-MS · Zbl 1253.80002
[4] Warpinski, NR; Lorenz, JC; Branagan, PT; Myal, FR; Gall, BL, Examination of a cored hydraulic fracture in a deep gas well (includes associated papers 26302 and 26946), SPE Prod Facil, 8, 150-158, (1993)
[5] Fast, RE; Murer, AS; Timmer, RS, Description and analysis of cored hydraulic fractures, lost hills field, kern county, California, SPE Prod Facil, 9, 107-114, (1994)
[6] Gale, JFW; Reed, RM; Holder, J, Natural fractures in the barnett shale and their importance for hydraulic fracture treatments, AAPG Bull, 91, 603-622, (2007)
[7] Hossain, MM; Rahman, MK, Numerical simulation of complex fracture growth during tight reservoir stimulation by hydraulic fracturing, J Pet Sci Eng, 60, 86-104, (2008)
[8] Warpinski, NR; Moschovidis, ZA; Parker, CD; Abou-Sayed, IS, Comparison study of hydraulic fracturing models-test case: GRI staged field experiment no. 3 (includes associated paper 28158), SPE Prod Facil, 9, 7-16, (1994)
[9] Yew CH (1997) Mechanics of hydraulic fracturing. Gulf Pub. Co, Houston
[10] Simonson, ER; Abou-Sayed, AS; Clifton, RJ, Containment of massive hydraulic fractures, Soc Pet Eng, 18, 17-32, (1978)
[11] Settari A, Cleary MP (1986) Development and testing of a pseudo-three-dimensional model of hydraulic fracture geometry. SPE Prod Eng. doi:10.2118/10505-PA · Zbl 1159.74316
[12] Warpinski NR, Smith MB (1989) Rock mechanics and fracture geometry. In: Gidley JL (ed) Recent advances in hydraulic fracturing, Monograph Vol 12
[13] Dong, CY; Pater, CJ, Numerical implementation of displacement discontinuity method and its application in hydraulic fracturing, Comput Methods Appl Mech Eng, 191, 745-760, (2001) · Zbl 1064.74688
[14] Rungamornrat J, Wheeler MF, Mear ME (2005) Coupling of fracture/non-newtonian flow for simulating nonplanar evolution of hydraulic fractures SPE annual technical conference and exhibition society of petroleum engineers. Dallas, Texas. doi:10.2118/96968-MS · Zbl 0970.74030
[15] Dahi-Taleghani, A; Olson, JE, Numerical modeling of multistranded-hydraulic-fracture propagation: accounting for the interaction between induced and natural fractures, SPE J, 16, 575-581, (2011)
[16] Olson JE, Wu K (2012) Sequential vs. simultaneous multizone fracturing in horizontal wells: insights from a non-planar, multifrac numerical model SPE hydraulic fracturing technology conference society of petroleum engineers, The Woodlands, Texas, USA. doi:10.2118/152602-MS
[17] Wu, K; Olson, JE, Investigation of the impact of fracture spacing and fluid properties for interfering simultaneously or sequentially generated hydraulic fractures, SPE-140253-MS, 28, 427-436, (2013)
[18] Shin DH, Sharma MM (2014) Factors controlling the simultaneous propagation of multiple competing fractures in a horizontal well SPE hydraulic fracturing technology conference society of petroleum engineers. The Woodlands, Texas, USA. doi:10.2118/168599-MS
[19] Hwang J, Sharma MM (2013) A 3-dimensional fracture propagation model for long-term water injection 47th US rock mechanics/geomechanics symposium American Rock Mechanics Association. California, San Francisco
[20] Kresse, O; Weng, X; Gu, H; Wu, R, Numerical modeling of hydraulic fractures interaction in complex naturally fractured formations, Rock Mech Rock Eng, 46, 555-568, (2013)
[21] Weng, X; Kresse, O; Cohen, CE; Wu, R; Gu, H, Modeling of hydraulic fracture network propagation in a naturally fractured formation, SPE-140253-MS, 26, 368-380, (2011)
[22] Rahman, MM; Rahman, MK, A review of hydraulic fracture models and development of an improved pseudo-3D model for stimulating tight oil/gas sand, Energy Sources, Part A, 32, 1416-1436, (2010)
[23] Garcia JG, Teufel LW (2005) Numerical simulation of fully coupled fluid-flow / geomechanical deformation in hydraulically fractured reservoirs SPE production operations symposium society of petroleum engineers. Oklahoma City, Oklahoma. doi:10.2118/94062-MS
[24] Secchi, S; Schrefler, BA, A method for 3-D hydraulic fracturing simulation, Int J Fract, 178, 245-258, (2012)
[25] Carter BJ, Desroches J, Ingraffea AR, Wawrzynek PA (2000) Simulating fully 3D hydraulic fracturing. In: Zaman M, Booker J, Gioda G (eds) Modeling in geomechanics. Wiley Publishers, New York · Zbl 1120.74003
[26] Medlin, WL; Fitch, JL, Abnormal treating pressures in massive hydraulic fracturing treatments, J Pet Technol; (United States), 40, 633-642, (1988)
[27] Palmer, ID; Veatch, RW, Abnormally high fracturing pressures in step-rate tests, SPE Prod Eng, 5, 315-323, (1990)
[28] Bažant Z (1984) Size effect in blunt fracture: concrete, rock metal. J Eng Mech 110:518-535. doi:10.1061/(ASCE)0733-9399(1984)110:4(518)
[29] Bažant, ZkP; Chen, E-P, Scaling of structural failure, Appl Mech Rev, 50, 593-627, (1997)
[30] Shimizu, H; Murata, S; Ishida, T, The distinct element analysis for hydraulic fracturing in hard rock considering fluid viscosity and particle size distribution, Int J Rock Mech Min Sci, 48, 712-727, (2011)
[31] Shimizu H, Murata S, Ishida T (2009) The distinct element analysis for hydraulic fracturing considering the fluid viscosity American Rock Mechanics Association
[32] Potyondy, DO; Cundall, PA, A bonded-particle model for rock, Int J Rock Mech Min Sci, 41, 1329-1364, (2004)
[33] Silling, SA, Reformulation of elasticity theory for discontinuities and long-range forces, J Mech Phys Solids, 48, 175-209, (2000) · Zbl 0970.74030
[34] Silling, SA; Lehoucq, RB, Convergence of peridynamics to classical elasticity theory, J Elast, 93, 13-37, (2008) · Zbl 1159.74316
[35] Silling, SA; Bobaru, F, Peridynamic modeling of membranes and fibers, Int J Non-Linear Mech, 40, 395-409, (2005) · Zbl 1349.74231
[36] Hu W, Ha YD, Bobaru F (2011) Modeling dynamic dracture and damage in a fiber-reinforced composite lamina with peridynamics. 9:707-726 doi:10.1615/IntJMultCompEng002651
[37] Bobaru, F; Ha, Y; Hu, W, Damage progression from impact in layered Glass modeled with peridynamics, Centeurjeng, 2, 551-561, (2012)
[38] Turner, DZ, A non-local model for fluid-structure interaction with applications in hydraulic fracturing, Int J Comput Methods Eng Sci Mech, 14, 391-400, (2013)
[39] Rajagopal KR, Tao L (1995) Mechanics of mixtures. World Scientific, Singapore, River Edge · Zbl 0941.74500
[40] Truesdell C, Toupin R (1960) The classical field theories. Springer, Berlin
[41] Epstein M (2012) The elements of continuum biomechanics John Wiley & Sons, Chichester. West Sussex, Hoboken
[42] Katiyar, A; Foster, JT; Ouchi, H; Sharma, MM, A peridynamic formulation of pressure driven convective fluid transport in porous media, J Comput Phys, 261, 209-229, (2014) · Zbl 1349.76819
[43] Khristianovic SA, Zheltov YP (1955) Formation of vertical fractures by means of highly viscous liquid 4th world petroleum congress world petroleum congress, Rome, Italy
[44] Geertsma, J; Klerk, F, A rapid method of predicting width and extent of hydraulically induced fractures, J Pet Technol, 21, 1571-1581, (1969)
[45] Silling, SA; Epton, M; Weckner, O; Xu, J; Askari, E, Peridynamic states and constitutive modeling, J Elast, 88, 151-184, (2007) · Zbl 1120.74003
[46] Foster, JT; Silling, SA; Chen, WW, Viscoplasticity using peridynamics, Int J Numer Methods Eng, 81, 1242-1258, (2010) · Zbl 1183.74035
[47] Seleson P and Parks M (2011) On the role of the influence function in the peridynamic theory. 9:689-706 doi:10.1615/IntJMultCompEng.2011002527
[48] Foster JT, Silling SA, Chen W (2011) An energy based failure criterion for use with peridynamic states. 9:675-688 doi:10.1615/IntJMultCompEng.2011002407 · Zbl 1183.74035
[49] Tran D, Settari A, Nghiem L (2002) New iterative coupling between a reservoir simulator and a geomechanics module. doi:10.2118/88989-PA
[50] Zhou, K; Gunzburger, M; Lehoucq, RB; Du, Q, A nonlocal vector calculus, nonlocal volume-constrained problems, and nonlocal balance laws, Math Models Methods Appl Sci, 23, 493-540, (2013) · Zbl 1266.26020
[51] Ha YD, Bobaru F (2009) Traction boundary conditions in peridynamics: a convergence study, technical report Department of Engineering Mechanics. University of Nebraska-Lincoln, Lincoln, NE
[52] Lehoucq, RB; Silling, SA, Force flux and the peridynamic stress tensor, J Mech Phys Solids, 56, 1566-1577, (2008) · Zbl 1171.74319
[53] Jaeger JC, Cook NGW, Zimmerman R (2007) Fundamentals of rock mechanics. Wiley, Blackwell
[54] Bobaru, F; Duangpanya, M, A peridynamic formulation for transient heat conduction in bodies with evolving discontinuities, J Comput Phys, 231, 2764-2785, (2012) · Zbl 1253.80002
[55] Bobaru F, Yang M, Alves LF, Silling SA, Askari E, Xu J (2009) Convergence, adaptive refinement, and scaling in 1D peridynamics. Int J Numer Methods Eng 77:852-877. doi:10.1002/nme.2439 · Zbl 1156.74399
[56] Khristianovic SA, Zheltov YP (1955) Formation of vertical fractures by means of highly viscous liquid proceedings of 4th world petroleum congress world petroleum congress, Rome, Italy, pp 579-586
[57] Sneddon, IN, The distribution of stress in the neighbourhood of a crack in an elastic solid, Proc R Soc Lond Ser Math Phys Sci, 187, 229-260, (1946)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.