×

A node-splitting discrete element model for fluid-structure interaction. (English) Zbl 1395.76094

Summary: A new discrete element model (DEM) has been developed for the purpose of simulating dynamic fracturing driven by the internal generation of fluids in low permeability elastic solid bodies. The elastic material is represented by a network of nodes connected by springs, and fracture nucleation and propagation is implemented by splitting nodes and reconnecting the spring network. This produces realistic fracture shapes, and reduces lattice artefacts compared with DEM models in which fracturing is implemented by breaking/removal of springs. Fracture volumes and surfaces are explicitly represented in terms of the voids in the reconnected spring network, simplifying the coupling between mechanical deformation and fluid pressure in the fractures, and facilitating the modelling of fluid transport. The model is illustrated by applying it to fracturing driven by internal fluid generation in an impermeable quasi two-dimensional system. This is relevant for many geological processes, including primary migration of oil and gas in low-permeability source rock. The model may also be adapted to hydraulic fracturing processes, which are of industrial interest in connection with unconventional oil and gas production.

MSC:

76S05 Flows in porous media; filtration; seepage
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
76M10 Finite element methods applied to problems in fluid mechanics
74S05 Finite element methods applied to problems in solid mechanics
34A33 Ordinary lattice differential equations
39A60 Applications of difference equations
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Hydraulic fracturing, (2012), Association of American State Geologists, URL: http://www.stategeologists.org/fact_sheet.php
[2] The future of natural gas, (2011), Massachusetts Institute of Technology Energy Initiative, URL: http://mitei.mit.edu/publications/reports-studies/future-natural-gas
[3] Tissot, B. P.; Welte, D. H., Petroleum formation and occurrence: A new approach to oil and gas exploration, (1978), Springer-Verlag New York, NY
[4] Berg, R. R.; Gangi, A. F., Primary migration by oil-generation microfracturing in low-permeability source rocks: application to the Austin chalk, Texas, AAPG Bulletin, 83, 727-756, (1999)
[5] Bons, P. D.; van Milligen, B. P., New experiment to model self-organized critical transport and accumulation of melt and hydrocarbons from their source rocks, Geology, 29, 919-922, (2001)
[6] Quattrocchi, F., In search of evidence of deep fluid discharges and pore pressure evolution in the crust to explain the seismicity style of the umbria-marche 1997-1998 seismic sequence (central Italy), Ann. Geofis., 42, 609-636, (1999)
[7] Miller, S. A.; Collettini, C.; Chiaraluce, L.; Cocco, M.; Barchi, M.; Kaus, B. J., Aftershocks driven by a high-pressure CO_{2} source at depth, Nature, 427, 724-727, (2004)
[8] McIver, R. D., Role of naturally occurring gas hydrates in sediment transport, AAPG Bull., 66, 789-792, (1982)
[9] Davies, J. H., The role of hydraulic fractures and intermediate-depth earthquakes in generating subduction-zone magmatism, Nature, 398, 142-145, (1999)
[10] Kutty, T.; Chandrasekharan, K.; Panakkal, J.; Ghosh, J., Fracture toughness and fracture surface energy of sintered uranium dioxide fuel pellets, J. Mater. Sci. Lett., 6, 260-262, (1987)
[11] Fan, Z.; Jin, Z.-H.; Johnson, S., Subcritical propagation of an oil-filled penny-shaped crack during kerogen-oil conversion, Geophys. J. Int., 182, 1141-1147, (2010)
[12] Gundersen, E.; Flekkøy, E.; Bjørlykke, K.; Feder, J.; Jamtveit, B., Fracture spacing during hydro-fracturing of cap-rocks, Geofluids, 11, 280-293, (2011)
[13] Fan, Z.; Jin, Z.-H.; Johnson, S., Gas-driven subcritical crack propagation during the conversion of oil to gas, Pet. Geosci., 18, 191-199, (2012)
[14] Fan, Z.; Jin, Z.-H.; Johnson, S., Modelling petroleum migration through microcrack propagation in transversely isotropic source rocks, Geophys. J. Int., 190, 179-187, (2012)
[15] Z.-Q. Fan, Z.-H. Jin, S.E. Johnson, Subcritical crack propagation and coalescence induced by the oil-gas transformation, in: 13th International Conference on Fracture, 2013.
[16] Oliyer, J., Continuum modelling of strong discontinuities in solid mechanics using damage models, Comput. Mech., 17, 49-61, (1995) · Zbl 0840.73051
[17] Dolbow, J.; Belytschko, T., A finite element method for crack growth without remeshing, Internat. J. Numer. Methods Engrg., 46, 131-150, (1999) · Zbl 0955.74066
[18] Sukumar, N.; Moës, N.; Moran, B.; Belytschko, T., Extended finite element method for three-dimensional crack modelling, Internat. J. Numer. Methods Engrg., 48, 1549-1570, (2000) · Zbl 0963.74067
[19] Wells, G.; Sluys, L., A new method for modelling cohesive cracks using finite elements, Internat. J. Numer. Methods Engrg., 50, 2667-2682, (2001) · Zbl 1013.74074
[20] I. Aranson, V. Kalatsky, V. Vinokur, Continuum field description of crack propagation, 2000. ArXiv Preprint, cond-mat/0001298.
[21] Karma, A.; Kessler, D. A.; Levine, H., Phase-field model of mode III dynamic fracture, Phys. Rev. Lett., 87, 045501, (2001)
[22] Eastgate, L. O.; Sethna, J. P.; Rauscher, M.; Cretegny, T.; Chen, C.-S.; Myers, C. R., Fracture in mode I using a conserved phase-field model, Phys. Rev. E, 65, 036117, (2002)
[23] Henry, H.; Levine, H., Dynamic instabilities of fracture under biaxial strain using a phase field model, Phys. Rev. Lett., 93, 105504, (2004)
[24] Meakin, P., A simple model for elastic fracture in thin films, Thin Solid Films, 151, 165-190, (1987)
[25] Walmann, T.; Malthe-Sørenssen, A.; Feder, J.; Jøssang, T.; Meakin, P.; Hardy, H., Scaling relations for the lengths and widths of fractures, Phys. Rev. Lett., 77, 5393-5396, (1996)
[26] Malthe-Sørenssen, A.; Walmann, T.; Feder, J.; Jøssang, T.; Meakin, P.; Hardy, H., Simulation of extensional Clay fractures, Phys. Rev. E, 58, 5548-5564, (1998)
[27] Royne, A.; Jamtveit, B.; Mathiesen, J.; Malthe-Sørenssen, A., Controls on rock weathering rates by reaction-induced hierarchical fracturing, Earth Planet. Sci. Lett., 275, 364-369, (2008)
[28] Kun, F.; Herrmann, H. J., A study of fragmentation processes using a discrete element method, Comput. Methods Appl. Mech. Engrg., 138, 3-18, (1996) · Zbl 0881.73106
[29] Kun, F.; Herrmann, H. J., Transition from damage to fragmentation in collision of solids, Phys. Rev. E, 59, 2623-2632, (1999)
[30] Malthe-Sørenssen, A.; Jamtveit, B.; Meakin, P., Fracture patterns generated by diffusion controlled volume changing reactions, Phys. Rev. Lett., 96, 245501, (2006)
[31] E. Aker, H. Khoa, F. Cuisiat, M. Soldal, Acoustic emission experiments and microcrack modelling on porous rock, in: EAGE Passive Seismic Workshop-Exploration and Monitoring Applications, 2009.
[32] Bolander, J.; Saito, S., Fracture analyses using spring networks with random geometry, Eng. Fract. Mech., 61, 569-591, (1998)
[33] Bolander, J.; Hong, G.; Yoshitake, K., Structural concrete analysis using rigid-body-spring networks, Comput.-Aided Civ. Infrastruct. Eng., 15, 120-133, (2000)
[34] Monette, L.; Anderson, M., Elastic and fracture properties of the two-dimensional triangular and square lattices, Modelling Simul. Mater. Sci. Eng., 2, 53-66, (1994)
[35] Flekkøy, E. G.; Malthe-Sørenssen, A.; Jamtveit, B., Modeling hydrofracture, J. Geophys. Res., 107, 2151, (2002), (ECV 1-1-ECV 1-11)
[36] F. Tzschichholz, M. Wangen, Modellization of hydraulic fracturing of porous materials, 2001. ArXiv Preprint, cond-mat/0101369.
[37] Wangen, M., Finite element modeling of hydraulic fracturing on a reservoir scale in 2D, J. Petrol. Sci. Eng., 77, 274-285, (2011)
[38] Kobchenko, M.; Hafver, A.; Jettestuen, E.; Galland, O.; Renard, F.; Meakin, P.; Jamtveit, B.; Dysthe, D. K., Drainage fracture networks in elastic solids with internal fluid generation, Europhys. Lett., 102, 66002, (2013)
[39] Bohn, S.; Douady, S.; Couder, Y., Four sided domains in hierarchical space dividing patterns, Phys. Rev. Lett., 94, 0545503, (2005)
[40] Bohn, S.; Pauchard, L.; Couder, Y., Hierarchical crack pattern as formed by successive domain divisions. I. temporal and geometrical hierarchy, Phys. Rev. E, 71, 046214, (2005)
[41] Bohn, S.; Platkiewicz, J.; Andreotti, B.; Adda-Bedia, M.; Couder, Y., Hierarchical crack pattern as formed by successive domain divisions. II. from disordered to deterministic behavior, Phys. Rev. E, 71, 046215, (2005)
[42] Cohen, Y.; Mathiesen, J.; Procaccia, I., Drying patterns: sensitivity to residual stresses, Phys. Rev. E, 79, 046109, (2009)
[43] Allen, M. P.; Tildesley, D. J., Computer simulation of liquids, (1989), Oxford University Press · Zbl 0703.68099
[44] Westergaard, H. M., Bearing pressures and cracks, J. Appl. Mech., 6, 49-53, (1939)
[45] Sneddon, I., The distribution of stress in the neighbourhood of a crack in an elastic solid, Proc. R. Soc. A, 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.