Microscopic modelling of the hydraulic fracturing process
Tóm tắt
A microscopic perspective is introduced in this study which offers a detailed insight at the inter-particle level to the geo-mechanical responses caused by fluid injection and the resulting pressure build-up. This was achieved by employing the Discrete Element Method (DEM) to model the pressure development and the subsequent fracturing and/or cavity propagation. This technique represents the formation material as an assembly of discrete particles linked to each other through contacts. Numerical experiments were carried out on two sample materials. For the first instance, tests were carried out on a bulk material, representative of a generic intact rock, with the breakage of inter-particle bonds indicating the formation of cracks. The second series of tests was carried out on granular type materials such as sand, where particle separation signified cavity initiation and separation. It was observed from the DEM modelling results that the intact rock material showed a predominance of mode II fracturing at high fluid velocities. However, when the fluid velocity is reduced considerably the fracturing behaviour tended towards more of mode I. Also, records of the pressure development were taken from the numerical results and were used to monitor the fracturing events. The outcome of this study highlights important aspects of the hydraulic fracturing process especially at the particle–particle scale, and thus provides a strong basis for more exhaustive studies involving larger scale reservoir modelling and more complex fracturing scenarios.
Tài liệu tham khảo
Al-Busaidi A, Hazzard JF, Young RP (2005) Distinct element modelling of hydraulically fractured Lac du Bonnet granite. J Geophys Res 110:B06302
Alqahtani NB, Miskimins JL (2010) 3D finite element modeling of laboratory hydraulic fracture experiments. In: SPE EUROPE/EAGE annual conference and exhibition in Barcelona, Spain, 14–17 June
Athavale AS, Miskimins JL (2008) Laboratory hydraulic fracturing on small homogeneous and laminated blocks. In: 42nd US rock mechanics symposium, San Francisco June 29–July 2
Bachu S, Bonijoly D, Bradshaw J, Burruss R, Holloway S, Christensen NP, Mathiassen OM (2007) CO2 storage capacity estimation: methodology and gaps. Int J Greenhouse Gas Control 1(4):430–443
Bear J (1979) Hydraulics of groundwater. McGraw-Hill, New York
Birkholzer JT, Zhou QL, Tsang CF (2009) Large-scale impact of CO2 storage in deep saline aquifers: a sensitivity study on pressure response in stratified systems. Int J Greenhouse Gas Control 3(2):181–194
Boone TJ, Ingraffea AR (1990) A numerical procedure for simulation of hydraulically driven fracture propagation in poroelastic media. Int J Numer Anal Meth Geomech 14(1):27–47
Bouillard JX, Lyczkowski RW, et al (1989) Porosity distributions in a fluidized bed with an immersed obstacle. AIChE J 35(6):908–922
Boutt DF, Cook BK, McPherson BJOL, Williams JR (2007) Direct simulation of fluid-solid mechanics in porous media using the discrete element and lattice-Boltzmann methods. J Geophys Res 112
Boutt DF, Cook BK, Williams JR (2011) A coupled fluid-solid model for problems in geomechanics: application to sand production. Int J Numer Anal Meth Geomech 35:997–1018
Bradshaw J, Bachu S, Bonijoly D, Burruss R, Holloway S, Christensen NP, Mathiassen OM (2007) CO2 storage capacity estimation: issues and development of standards. Int J Greenhouse Gas Control 1(1):62–68
Cappa F, Rutqvist J (2011) Modeling of coupled deformation and permeability evolution during fault reactivation induced by deep underground injection of CO2. Int J Greenhouse Gas Control 5:336–346
Casas L, Miskimins JL, Black A, Green S (2006) Laboratory hydraulic fracturing test on a rock with artificial discontinuities. In: SPE annual technical conference and exhibition, San Antonio, Texas, 24–27 September, SPE 103617
Chang H (2004) Hydraulic fracturing in particulate materials, Ph.D. thesis. Georgia Institute of Technology, GA
Cheng KW, Fries T-P (2010) Higher-order XFEM for curved strong and weak discontinuities. Int J Numer Meth Eng 82(5):564–590
Cho N, Martin CN, Sego DC (2007) A clumped particle model for rock. Int J Rock Mech Min Sci 44:997–1010
Class H, Ebigbo A, Helmig R, Dahle HK, Nordbotten JM, Celia MA, Audigane P, Darcis M, Ennis-King J, Fan Y, Flemisch B, Gasda SE, Jin M, Krug S, Labregere D, Beni AN, Pawar RJ, Sbai A, Thomas SG, Trenty L, Wei L (2009) A benchmark study on problems related to CO2 storage in geologic formations. Comput Geosci 13:409–434
Daneshy AA (1978) Hydraulic fracture propagation in layered formations. SPE J 18(1):33–41
Dean RH, Schmidt JH (2009) Hydraulic-fracture predictions with a fully coupled geomechanical reservoir simulator. SPE J 14(4):707–714
Dennis I, Pretorius J, Steyl G (2010) Effect of fracture zone on DNAPL transport and dispersion: a numerical approach. Environ Earth Sci 61(7):1531–1540
Du C, Zhang X, Zhan L, Gu H, Hay B, Tushingham K, Ma YZ (2010) Modeling hydraulic fracturing induced fracture networks in shale gas reservoirs as a dual porosity system. International Oil and Gas Conference and Exhibition in China. Society of Petroleum Engineers, Beijing
Economides M, Boney C (2000) Reservoir stimulation in petroleum production. Reservoir stimulation. Wiley, England
Eigestad GT, Dahle HK, Hellevang B, Riis F, Johansen WT, Oian E (2009) Geological modeling and simulation of CO2 injection in the Johansen formation. Comput Geosci 13(4):435–450
El Shamy U, Zeghal M (2005) Coupled continuum-discrete model for saturated granular soils. J Eng Mech 131(4):413–426
Fjaer E, Holt RM, Horsrud P, Raaen AM, Risnes R (2008) Petroleum related rock mechanics, 2nd edn. Developments in petroleum science.vol 53. Elsevier, UK
Fries T-P, Baydoun M (2012) Crack propagation with the extended finite element method and a hybrid explicit–implicit crack description. Int J Numer Methods Eng 89(12):1527–1558
Fries T-P, Belytschko T (2010) The extended/generalized finite element method: an overview of the method and its applications. Int J Numer Methods Eng 84(3):253–304
Griffith C, Dzombak D, Lowry GV (2011) Physical and chemical characteristics of potential seal strata in regions considered for demonstrating geological saline CO2 sequestration. Environ Earth Sci 64(4):925–948
Grof Z, Cook J, et al (2009) The interaction between small clusters of cohesive particles and laminar flow: coupled DEM/CFD approach. J Petrol Sci Eng 66(1–2):24–32
Hoffman BT, Chang WM (2009) Modeling hydraulic fractures in finite difference simulators: application to tight gas sands in Montana. J Petrol Sci Eng 69(1–2):107–116
Hubbert MK, Willis D (1957) Mechanics of hydraulic fracturing. Society of Petroluem Engineers of AIME 210:153–168
Hubbert MK, Willis DG (1972) Mechanics of hydraulic fracturing. Mem Am Assoc Petroleum Geol 18:239–257
Hurt RS, Wu R, Germanovich LN, Chang H, van Dyke P (2005) On mechanisms of hydraulic fracturing in cohesionless materials. American Geophysical Union, Fall Meeting (abstract H41B–0416)
IPCC (2005) IPCC special report of carbon dioxide capture and storage, Chap 5. Underground geological storage. IPCC report
Ishida T (2001) Acoustic emission monitoring of hydraulic fracturing in laboratory and field. Constr Build Mater 15:283–295
Ishida T, Sasaki S, Matsunaga I, Chen Q, Mizuta Y (2000) Effect of grain size in granite rocks on hydraulic fracturing mechanism. Trends in rock mechanics. Geotech Spec Publ 102:128–139
Ishida T, Chen Q, Mizuta Y, Roegiers J-C (2004) Influence of fluid viscosity on the hydraulic fracturing mechanism. J Energy Res Technol 126:190–200
Itasca Consulting Group Inc (2008) PFC2D user manual, Minneapolis
Jaeger JC, Cook NGW, et al (2007) Fundamentals of rock mechanics. Blackwell Publishing, Oxford
Koike K, Liu C, Sanga T (2012) Incorporation of fracture directions into 3D geostatistical methods for a rock fracture system. Environ Earth Sci 1–12 (online first)
Kopp A, Class H, Helmig R (2009) Investigations on CO2 storage capacity in saline aquifers. Part 2: estimation of storage capacity coefficients. Int J Greenhouse Gas Control 3(3):277–287
Kristinof R, Ranjith P, Choi SK (2010) Finite element simulation of fluid flow in fractured rock media. Environ Earth Sci 60(4):765–773
Laborde P, Pommier J, Renard Y, Salaun M (2005) High-order extended finite element method for cracked domains. Int J Numer Methods Eng 64(3):354–381
Lam KY, Cleary MP (1986) A complete three-dimensional simulator for analysis and design of hydraulic fracturing. In: SPE unconventional gas technology symposium, Louisville, May 18–21
Lee C–C, Lee C-H, Yeh H-F, Lin H-I (2011) Modeling spatial fracture intensity as a control on flow in fractured rock. Environ Earth Sci 63(6):1199–1211
Liao XW, Shangguan YN (2009) Research of the estimation method of CO2 saline aquifer storage capacity. In: 2009 Asia-Pacific power and energy engineering conference (Appeec), vol 1–7, pp 3143–3149
Lindeberg E, Bergmo P (2003) The long-term fate of CO2 injected into an aquifer. In: Proceedings of greenhouse gas control technologies, vols I and II, pp 489–494
Lujun L, Settari A, Sullivan RB (2007) A novel hydraulic fracturing model fully coupled with geomechanics and reservoir simulator. In: SPE annual technical conference and exhibition, Anaheim, November 11–14, p 200
Luque A, Ruiz-Agudo E, Cultrone G, Sebastian E, Siegesmund S (2011) Direct observation of microcrack development in marble caused by thermal weathering. Environ Earth Sci 62(7):1375–1386
Martin T, Valko P (2007) Hydraulic fracturing design for production enhancement. Modern fracturing: enhancing natural gas production. Energy Tribune, Houston
Mathias SA, Hardisty PE, Trudell MR, Zimmerman RW (2009) Screening and selection of sites for CO2 sequestration based on pressure buildup. Int J Greenhouse Gas Control 3(5):577–585
Matsunaga I, Kobayashi H, Ishida T (1993) Studying hydraulic fracturing mechanism by laboratory experiments with acoustic emission monitoring. Int J Rock Mech Min Sci Geomech 30(7):909–912
McLennan JD, Hasegawa HS, Roegiers JC, Jessop AM (1986) Hydraulic fracturing experiments at the University of Regina Campus. Can Geotech J 23:548–555
Medlin WL, Masse L (1984) Laboratory experiments in fracture propagation. Soc Petrol Eng J 24:256–268
Moon T, Nakagawa M, et al (2007) Measurement of fracture toughness using the distinct element method. Int J Rock Mech Min Sci 44:449–456
Müller C, Siegesmund S, Blum P (2010) Evaluation of the representative elementary volume (REV) of a fractured geothermal sandstone reservoir. Environ Earth Sci 61(8):1713–1724
Murdoch LC (1993a) Hydraulic fracturing of soil during experiments, part I. Methods and observations. Geotechnique 43:255–265
Murdoch LC (1993b) Hydraulic fracturing of soil during experiments, part II. Propogation. Geotechnique 43:267–276
Murdoch LC (1993c) Hydraulic fracturing of soil during experiments, part III: Theoretical analysis . Geotechnique 43:277–287
Natarajan S, Mahapatra DR, Bordas SPA (2010) Integrating strong and weak discontinuities without integration subcells and example applications in an XFEM/GFEM framework. Int J Numer Meth Eng 83(3):269–294
Nicot JP (2008) Evaluation of large-scale CO2 storage on fresh-water sections of aquifers: an example from the Texas Gulf Coast Basin. Int J Greenhouse Gas Control 2(4):582–593
Nicot J-P, Hovorka SD, Choi J-W (2009) Investigation of water displacement following large CO2 sequestration operations. Energy Procedia 1(1):4411–4418
Nordbotten JM, Celia MA, et al (2004) Analytical solutions for leakage rates through abandoned wells. Water Resour Res 40(4)
Nordbotten JM, Celia MA, Bachu S (2005a) Injection and storage of CO2 in deep saline aquifers: analytical solution for CO2 plume evolution during injection. Transp Porous Media 58(3):339–360
Nordbotten JM, Celia MA, Bachu S, Dahle HK (2005b) Semianalytical solution for CO2 leakage through an abandoned well. Environ Sci Technol 39:602–611
Nordbotten JM, Kavetski D, Celia MA, Bachu S (2009) Model for CO2 leakage including multiple geological layers and multiple leaky wells. Environ Sci Technol 43(3):743–749
Nunez-Lopez V, Holtz MH, Wood DJ, Ambrose WA, Hovorka SD (2008) Quick-look assessments to identify optimal CO2 EOR storage sites. Environ Geol 54(8):1695–1706
Okwen RT, Stewart MT, Cunningham JA (2010) Analytical solution for estimating storage efficiency of geologic sequestration of CO2. Int J Greenhouse Gas Control 4(1):102–107
Papanastasiou PC (1997) A coupled elastoplastic hydraulic fracturing model. Int J Rock Mech Min Sci 34(3–4):240
Potyondy DO, Cundall PA (2004) A bonded-particle model for rock. Int J Rock Mech Min Sci 41:1329–1364
Pruess K (2005) Numerical studies of fluid leakage from a geologic disposal reservoir for CO2 show self-limiting feedback between fluid flow and heat transfer. Geophys Res Lett 32(14)
Pruess K (2008a) Leakage of CO2 from geologic storage: role of secondary accumulation at shallow depth. Int J Greenhouse Gas Control 2:37–46
Pruess K (2008b) On CO2 fluid flow and heat transfer behavior in the subsurface, following leakage from a geologic storage reservoir. Environ Geol 54:1677–1686
Pruess K, Garcia J, et al (2004) Code intercomparison builds confidence in numerical simulation models for geologic disposal Of CO2. Energy 29(9–10):1431–1444
Ranjith P (2010) An experimental study of single and two-phase fluid flow through fractured granite specimens. Environ Earth Sci 59(7):1389–1395
Rungamornrat JM, Wheeler F, et al (2005) Coupling of fracture/non-newtonian flow for simulating nonplanar evolution of hydraulic fractures In: SPE annual technical conference and exhibition, Dallas, Texas
Rutqvist J, Birkholzer J, Cappa F, Tsang CF (2007) Estimating maximum sustainable injection pressure during geological sequestration of CO2 using coupled fluid flow and geomechanical fault-slip analysis. Energy Convers Manage 48(6):1798–1807
Rutqvist J, Birkholzer J, Tsang CF (2008) Coupled reservoir-geomechanical analysis of the potential for tensile and shear failure associated with CO2 injection in multilayered reservoir-caprock systems. Int J Rock Mech Min Sci 45:132–143
Shimizu Y (2006) Three-dimensional simulation using fixed coarse-grid thermal-fluid scheme and conduction heat transfer scheme in distinct element method. Powder Technol 165(3):140–152
Shimizu H, Murata S, Ishida T (2009) The distinct element analysis for hydraulic fracturing considering the fluid viscosity. In: 43rd US rock mechanics symposium and 4th US-Canada rock mechanics symposium. American Rock Mechanics Association, Asheville
Shimizu H, Murata S, Ishida T (2011) The distinct element analysis for hydraulic fracturing in hard rock considering fluid viscosity and particle size distribution. Int J Rock Mech Min Sci Geomech 48(5):712–727
Streit JE (2002) Estimating fluid pressures that can induce reservoir failure during hydrocarbon depletion. In: SPE/SRM rock mechanics conference, Irving, 20–23 October
Streit EE, Hillis RR (2004) Estimating fault stability and sustainable fluid pressures for underground storage of CO2 in porous rock. Energy 29(9–10):1445–1456
Tarancon JE, Vercher A, Giner E, Fuenmayor FJ (2009) Enhanced blending elements for XFEM applied to linear elastic fracture mechanics. Int J Numer Meth Eng 77(1):126–148
Warpinski NR, Clark JA, Schmidt RA, Huddle CW (1982) Laboratory investigation on the effect of in situ stresses on hydraulic fracture containment. SPE J. SPE paper No. 9834:333–340
Watanabe N, Wang W, Taron J, Gorke UJ, Kolditz O (2012) Lower-dimensional interface elements with local enrichment: application to coupled hydro-mechanical problems in discretely fractured porous media. Int J Numer Meth Eng 90(8):1010–1034
Wei LL, Saaf F (2009) Estimate CO2 storage capacity of the Johansen formation: numerical investigations beyond the benchmarking exercise. Comput Geosci 13(4):451–467
Xu TF, Sonnenthal E, Spycher N, Pruess K (2006) TOUGHREACT—a simulation program for non-isothermal multiphase reactive geochemical transport in variably saturated geologic media: applications to geothermal injectivity and CO2 geological sequestration. Comput Geosci 32(2):145–165
Yang B, Jiao Y, et al (2006) A study on the effects of microparameters on macroproperties for specimens created by bonded particles. Int J Comput-Aid Eng Soft 23(6):607–631
Yamamoto K, Shimamoto T, Maezumi S (1999) Development of a true 3D hydraulic fracturing simulator. In: SPE Asia Pacific oil and gas conference and exhibition, Jakarta, April 20–22
Yew CH, Liu GF (1993) Fracture tip and critical stress intensity factor of a hydraulically induced fracture. SPE Prod Facil 8(3):171–177
Zhou QL, Birkholzer JT, Tsang CF, Rutqvist J (2008) A method for quick assessment of CO2 storage capacity in closed and semi-closed saline formations. Int J Greenhouse Gas Control 2(4):626–639