Skip to main content
SpringerLink
Log in

3D DEM analysis of analogue proppant–fractured rock system interaction

  • Original Paper
  • Published:
Bulletin of Engineering Geology and the Environment Aims and scope Submit manuscript

Abstract

We investigated the interaction of proppant simulant (impactor) colliding on the surface of a fractured rock by performing 3-dimensional discrete-based numerical simulations. The fractured rock represented a medium-strength clastic material, and the linear parallel bond contact model was implemented to simulate the bonding properties. The ratio of the impactor to rock particle size was equal to 30, which represents, based on the relative dimensions of the problem, typical proppants of 40/70 mesh colliding on fine-grained siltstone. A parametric study was conducted, taking into account the influence of existing fractures within the rock mass as well as their aperture and distance from the impact zone. Significant differences were observed based on the collision velocity (with a distinction in low- and high-velocity impacts), even for intact rock simulations, while, because of the second-order roughness of the rock due to its clastic nature, the impacts were oblique, resulting in the partition of the total kinetic energy. Energy losses, penetration depth, stress transmission through the rock mass, and the influence of the structural characteristics of the analogue rock were systematically investigated to provide some insights into the fundamental contributing mechanisms of impactor-fracture rock interactions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  • Ahamed MAA, Perera MSA, Dong-yin Li, Ranjith PG, Matthai SK (2019) Proppant damage mechanisms in coal seam reservoirs during the hydraulic fracturing process: a review. Fuel 253:615–629

    Google Scholar 

  • Aryaei A, Hashemnia K, Jafarpur K (2010) Experimental and numerical study of ball size effect on restitution coefficient in low velocity impacts. Int J Impact Eng 37:1037–1044

    Google Scholar 

  • Awasthi A, Wang Z, Broadhurst N, Geubelle P (2015) Impact response of granular layers. Granular Matter 17:21–31

    Google Scholar 

  • Aziznejad S, Esmaieli K, Hadjigeorgiou J, Labrie D (2018) Responses of jointed rock masses subjected to impact loading. J Rock Mech Geotech Eng 10(4):624–634

    Google Scholar 

  • Bandara KMAS, Ranjith PG, Rathnaweera TD, Perera MSA, Kumari WGP (2018) Thermally-induced mechanical behaviour of a single proppant under compression: insights into the long-term integrity of hydraulic fracturing in geothermal reservoirs. Measurement 120:76–91

    Google Scholar 

  • Bandara KMAS, Ranjith PG, Rathnaweera TD (2020a) Laboratory-scale study on proppant behaviour in unconventional oil and gas reservoir formations. J Nat Gas Sci Eng 78, 103329.

  • Bandara KMAS, Ranjith PG, Rathnaweera TD, Wanniarachchi WAM, Yang SQ (2020b) Crushing and embedment of proppant packs under cyclic loading: an insight to enhanced unconventional oil/gas recovery. Geosci Front [Published online]. https://doi.org/10.1016/j.gsf.2020.02.017.

  • Banks M, Bridges NT, Benzit M (2005) Measurements of the coefficient of restitution of quartz sand on basalt: implications for abrasion rates on earth and mars. 36th Annual Lunar and Planetary Science Conference 2116.

  • Bourrier F, Nicot F, Darve F (2008) Physical processes within a 2D granular layer during impact. Granular Matter 10:415–437

    Google Scholar 

  • Calvetti F, di Prisco CG, Vairaktaris E (2017) DEM assessment of impact forces of dry granular masses on rigid barriers. Acta Geotech 12:129–144

    Google Scholar 

  • Chau KT, Wu SZ, Zhu WC, Tang CA, Yu TX (2003) Dynamic fracture and fragmentation of spheres. 16th ASCE Engineering Mechanics Conference, Seattle.

  • Clelland R, Hrenya CM (2002) Simulations of a binary-sized mixture of inelastic grains in rapid shear flow. Phys Rev E 65(3):031301. https://doi.org/10.1103/PhysRevE.65.031301

    Article  Google Scholar 

  • Clout JMF, Manuel JR (2015) Minerology, chemical, and physical characteristics of iron ore Iron Ore, Woodhead Publishing 45–84. https://doi.org/10.1016/B978-1-78242-156-6.00002-2

  • Crüger B, Heinrich S, Antonyuk S, Deen NG, Kuipers JAM (2016) Experimental study of oblique impact of particles on wet surfaces. Chem Eng Res Des 110:209–219

    Google Scholar 

  • Cui Y (2019) Effect of joint type on the shear behavior of synthetic rock. Bull Eng Geol Environ 78:3395–3412

    Google Scholar 

  • Cui Y, Choi CE, Lui LHD, Ng CWW (2018) Effects of particle size of mono-disperse granular flows impacting a rigid barrier. Nat Hazards 91:1179–1201

    Google Scholar 

  • De Silva VRS, Ranjith PG (2019a) Intermittent and multi-stage fracture stimulation to optimise fracture propagation around a single injection well for enhanced in-situ leaching applications. Eng Fract Mech 220, 106662.

  • De Silva VRS, Ranjith PG (2019b) Evaluation of injection well patterns for optimum fracture network generation host-rock formations: an application in in-situ leaching. Miner Eng 137:319–333

    Google Scholar 

  • Dong KJC, He WH, Wang M (2019) Effect of surface wettability of ceramic proppant on oil flow performance in hydraulic fractures. Energy Science and Engineering 7(2):504–514

    Google Scholar 

  • Duan K, Kwok CY (2015) Discrete element modeling of inherently anisotropic rock under Brazilian test conditions. Int J Rock Mech Min Sci 78:46–56

    Google Scholar 

  • Duan K, Kwok CY, Wu W (2018a) DEM modeling of hydraulic fracturing in permeable rock: influence of viscosity, injection rate and in-situ states. Acta Geotech 13(5):1187–1202

    Google Scholar 

  • Duan K, Wu W, Kwok CY (2018b) Discrete element modelling of stress-induced instability of directional drilling boreholes in anisotropic rock. Tunn Undergr Space Technol 81:55–67

    Google Scholar 

  • Duan K, Kwok CY (2020) On the initiation, propagation and reorientation of simultaneously-induced multiple hydraulic fractures. Computers and Geotechnics 117, 103226.

  • Duan K, Li Y, Yang W (2021) Discrete element method simulation of the growth and efficiency of multiple hydraulic fractures simultaneously-induced from two horizontal wells. Geomech. Geophys. Geo-energ. Geo-resour. 7(3). https://doi.org/10.1007/s40948-020-00196-4.

  • Giacomini A, Buzzi O, Renard B, Giani GP (2009) Experimental studies on fragmentation of rock falls on impact with rock surfaces. Int J Rock Mech Min Sci 46:708–715

    Google Scholar 

  • Hadei MR, Veiskarami A (2020) An experimental investigation of hydraulic fracturing of stratified rocks. Bull Eng Geol Env 80:491–506

    Google Scholar 

  • He H, Luo L, Senetakis K (2020) Effect of normal load and shearing velocity on the interface friction of organic shale – proppant simulant. Tribol Int 144:106119. https://doi.org/10.1016/j.triboint.2019.106119.144,106119

    Article  Google Scholar 

  • He H, Senetakis K (2020) A micromechanical study of shale rock-proppant composite interface. J Petrol Sci Eng 184:106542. https://doi.org/10.1016/j.petrol.2019.106542

    Article  Google Scholar 

  • Higham JE, Shepley P, Shahnam M (2019) Measuring the coefficient of restitution for all six degrees of freedom. Granular Matter 21(15). https://doi.org/10.1007/s10035-019-0871-0.

  • Hu J, Li L, Shi S, Zhou Z, Liu H, He P (2018) Field, experimental, and numerical investigation of a rockfall above a tunnel portal in southwestern China. Bull Eng Geol Env 77:1365–1382

    Google Scholar 

  • Hu Y, Li X, Zhang Z, He J, Li G (2020) Numerical investigation on the hydraulic stimulation of naturally fractured Longmaxi shale reservoirs using an extended discontinuous deformation analysis (DDA) method. Geomech. Geophys. Geo-energ. Geo-resour. 6(73). https://doi.org/10.1007/s40948-020-00195-5.

  • Huang H, Babadagli T, Li H, Develi K, Zhou D (2020) A visual experimental study on proppants transport in rough vertical fractures. Int J Rock Mech 134, 104446.

  • ISRM, International Society for Rock Mechanics (1978) Suggested methods for quantitative description of discontinuities in rock masses. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts 15(6):319–368

    Google Scholar 

  • Iverson RM (1997) The physics of debris flows. Rev Geophys 35(3):245–296. https://doi.org/10.1029/97RG00426

    Article  Google Scholar 

  • Jiang M, Liu J, Crosta GB, Li T (2017) DEM analysis of the effect of joint geometry on the shear behavior of rocks. Comptes Rendus Mécanique 345(11):779–796

    Google Scholar 

  • Jiang S, Shen L, Guillard F, Einav I (2018) Energy dissipation from two-glass-bead chains under impact. Int J Impact Eng 114:160–168

    Google Scholar 

  • Jiang Z, Du J, Rieck C, Bück A, Tsotsas E (2019) PTV experiments and DEM simulations of the coefficient of restitution for irregular particles impacting on horizontal substrates. Powder Technol 360:352–365

    Google Scholar 

  • Kasyap SS, Senetakis K (2020) An experimental investigation on the tribological behaviour of quartz grains with dry to saturated gouge material. Pure Appl Geophys 177:3283–3300

    Google Scholar 

  • Kasyap SS, Senetakis K, Coop MR, Zhao JD (2021) Micromechanical behaviour in shearing of reproduced flat LBS grains with strong and weak artificial bonds. Acta Geotech 16:1355–1376

    Google Scholar 

  • Le H-K, Huang W-C, Chien C-C (2021) Exploring micromechanical behaviors of soft rock joints through physical and DEM modeling. Bull Eng Geol Env 80:2433–2446

    Google Scholar 

  • Li X, Zhao J (2018) A unified CFD-DEM approach for modeling of debris flow impacts on flexible barriers. Int J Numer Anal Meth Geomech 42:1643–1670. https://doi.org/10.1002/nag.2806

    Article  Google Scholar 

  • Li X, Dong M, Li S, Shang Y (2019) Experimental and theoretical studies of the relationship between dry and humid normal restitution coefficients. J Aerosol Sci 129:16–27

    Google Scholar 

  • Li Z, Li X, Yu J, Cao W, Liu Z, Wang M, Liu Z, Wang X (2020) Influence of existing natural fractures and beddings on the formation of fracture network during hydraulic fracturing based on the extended finite element method. Geomech. Geophys. Geo-energ. Geo-resour. 6(58). https://doi.org/10.1007/s40948-020-00180-y.

  • Li N, Zhou Y, Li H (2021) Experimental study for the effect of joint surface characteristics on stress wave propagation. Geomech. Geophys. Geo-energ. Geo-resour. 7(50). https://doi.org/10.1007/s40948-021-00235-8.

  • Ma T, Chen P, Zhao J (2016) Overview on vertical and directional drilling technologies for the exploration and exploitation of deep petroleum resources. Geomech Geophys Geo-Energ Geo-Resour 2(4):365–395

    Google Scholar 

  • Marinack Jr MC, Musgrave RE, Higgs III CF (2013) Experimental investigations on the coefficient of restitution of single particles. Tribol Trans 56:572–580

    Google Scholar 

  • Marzulli V, Torres Cisneros LA, di Lernia A, Cafaro F, Pöschel T (2020) Impact on granular bed: validation of discrete element modeling results by means of two-dimensional finite element analysis. Granular Matter 22(1):27

    Google Scholar 

  • Melosh HJ, Collins GS (2005) Meteor crater formed by low-velocity impact, Nature 434(157). https://doi.org/10.1038/434157a.

  • Mindlin RD, Deresiewicz H (1953) Elastic spheres in contact under varying oblique force, Trans. ASME. J Appl Mech 20:327–344

    Google Scholar 

  • Moriguchi S, Borja RI, Yashima A, Sawada K (2009) Estimating the impact force generated by granular flow on a rigid obstruction. Acta Geotech 4:57–71

    Google Scholar 

  • Naghi Dehghan A, Goshtasbi K, Ahangari K, Jin Y (2014) Experimental investigation of hydraulic fracture propagation in fractured blocks. Bull Eng Geol Env 74:887–895

    Google Scholar 

  • Oh J, Li Y, Mitra R, Canbulat I (2017) A numerical study on dilation of a saw-toothed rock joint under direct shear. Rock Mech Rock Eng 50(4):913–925

    Google Scholar 

  • Patil D, Higgs III CF (2017) Experimental investigations on the coefficient of restitution for sphere-thin plate elastoplastic impact. J Tribol 140(1), 011406.

  • Peng J, Wong LNY, Teh CI (2017) Effects of grain size-to-particle size ratio on micro-cracking behavior using a bonded-particle grain-based model. Int J Rock Mech Min Sci 100:207–217

    Google Scholar 

  • Peng J, Wong LNY, Teh CI (2018) A re-examination of slenderness ratio effect on rock strength: insights from DEM grain-based modelling. Eng Geol 246:245–254

    Google Scholar 

  • Peng J, Wong LNY, Teh CI (2021) Influence of grain size on strength of polymineralic crystalline rock: new insights from DEM grain-based modeling. J Rock Mech Geotech Eng [Ahead of Print]. https://doi.org/10.1016/j.jrmge.2021.01.011.

  • Potyondy DO (2011) Parallel-bond refinements to match macro properties of hard rock. In Continuum and distinct element numerical modeling in geomechanics, Proceedings of Second International FLAC/DEM Symposium, Melbourne, Australia, 459–465.

  • Potyondy DO (2015) The bonded-particle model as a tool for rock mechanics research and application: current trends and future directions. Geosystem Engineering 18(1):1–28

    Google Scholar 

  • Potyondy DO, Cundall PA (2004) A bonded-particle model for rock. Int J Rock Mech Min Sci 41(8):1329–1364

    Google Scholar 

  • Sandeep CS, Luo L, Senetakis K (2020) Effect of grain size and surface roughness on the normal coefficient of restitution of single grains. Materials 814:1–13

    Google Scholar 

  • Sandeep CS, Senetakis K, Cheung DKH, Choi CE, Wang Y, Coop MR, Ng CWW (2021) Experimental study on the coefficient of restitution of grain against block interfaces for natural and engineered materials. Can Geotech J 58(1):35–48

    Google Scholar 

  • Sandeep CS, Senetakis K (2018) Effect of Young’s modulus and surface roughness on the inter-particle friction of granular materials. Materials 11, 217.https://doi.org/10.3390/ma11020217.

  • Sandeep CS, Senetakis K (2019) An experimental investigation of the microslip displacement of geological materials. Comput Geotech 107:55–67

    Google Scholar 

  • Shen WG, Zhao T, Crosta GB, Dai F (2017) Analysis of impact-induced rock fragmentation using a discrete element approach. Int J Rock Mech Min Sci 98:33–38

    Google Scholar 

  • Shen WG, Zhao T, Zhao JD, Dai F, Zhou GD (2018) Quantifying the impact of dry debris flow against a rigid barrier by DEM analyses. Eng Geol 241:86–96

    Google Scholar 

  • Shen WG, Zhao T, Dai F, Jiang M, Zhou GGD (2019) DEM analyses of rock block shape effects on the response of rockfall impact against a soil buffering layer. Eng Geol 249:60–70

    Google Scholar 

  • Sivakugan N, Shukla SK, Das BM (2013) Rock mechanics: an introduction. CRC Press, Taylor & Francis Group, New York, USA.

  • Stronge WJ (2018) Impact mechanics. Cambridge University Press (second Edition). https://doi.org/10.1017/9781139050227

    Article  Google Scholar 

  • Suzuki A, Hakura S, Hamura T, Hattori M, Hayama R et al (2012) Laboratory experiments on crater scaling-law for sedimentary rocks in the strength regime. J Geophys Res Planets 117(E8). https://doi.org/10.1029/2012JE004064.

  • Tan DY, Feng WQ, Yin JH, Zhu ZH, Qin JQ (2021) Numerical study of retention efficiency of a flexible barrier in mitigating granular flow comparing with large-scale physical modeling test data. Acta Geotech 16:433–448

    Google Scholar 

  • Tang ZC, Wong LNY (2016) Influences of normal loading rate and shear velocity on the shear behavior of artificial rock joints. Rock Mech Rock Eng 49(6):2165–2172

    Google Scholar 

  • Tang H, Song R, Dong Y, Song X (2019) Measurement of restitution and friction coefficients for granular particles and discrete element simulation for the tests of glass beads. Materials 12(19):3170

    Google Scholar 

  • Teufelsbauer H, Wang Y, Pudasaini SP, Borja RI, Wu W (2011) DEM simulation of impact force exerted by granular flow on rigid structures. Acta Geotech 6:119

    Google Scholar 

  • Tomac I, Gutierrez M (2015) Micromechanics of proppants agglomeration during settling in hydraulic fractures. Journal of Petrol. Exploration and Production Technology 5:417–434

    Google Scholar 

  • Uehara JS, Ambroso MA, Ojha RP, Durian DJ (2003) Low-speed impact craters in loose granular media. Phys Rev Lett 90, 149902.

  • Walsh AM, Holloway KE, Habdas P, de Bruyn JR (2003) Morphology and scaling of impact craters in granular media. Phys Rev Lett 91, 104301.

  • Wang Y, Tonon F (2011) Discrete element modeling of rock fragmentation upon impact in rock fall analysis. Rock Mech Rock Eng 44:23–35

    Google Scholar 

  • Wang H, Sharma MM (2018) Modeling of hydraulic fracture closure on proppants with proppant settling. J Pet Sci Eng 171:636–645

    Google Scholar 

  • Wang F, Li B, Chen Q, Zhang S (2019) Simulation of proppant distribution in hydraulically fractured shale network during shut-in periods. J Pet Sci Eng 178:467–474

    Google Scholar 

  • Wang Y, Li X, Zhao B, Zhang Z (2020a) Numerical simulation of particle plugging in hydraulic fracture by element partition method. Int. J. Numer. Anal. Methods in Geom. 44(14):1857–1879.

  • Wang L, Zheng Z, Yu Y, Liu T, Zhang Z (2020b) Determination of the energetic coefficient of restitution of maize grain based on laboratory experiments and DEM simulations. Powder Technol 362:645–658

    Google Scholar 

  • Wang S, Xiong X, Liu Y et al (2021) Stress–strain relationship of sandstone under confining pressure with repetitive impact. Geomech. Geophys. Geo-energ. Geo-resour. 7(39). https://doi.org/10.1007/s40948-021-00250-9.

  • Westwood RF, Toon SM, Styles P, Cassidy NJ (2017) Horizontal respect distance for hydraulic fracturing in the vicinity of existing faults in deep geological reservoirs: a review and modelling study. Geomech Geophys Geo-Energ Geo-Resour 3:379–391. https://doi.org/10.1007/s40948-017-0065-3

    Article  Google Scholar 

  • Xiao H, Liu S, Wang D (2016) Tribological properties of sliding shale rock–alumina contact in hydraulic fracturing. Tribol Lett 62(2):1–9

    Google Scholar 

  • Xu Q, Yu Y, Liu R, Cheng W, Yang H (2021) Study on dynamic damage characteristics of coal under alternating hydraulic pressure. Bull Eng Geol Env 80:2385–2397

    Google Scholar 

  • Yang W-M, Geng Y, Zhou Z-Q, Li L-P, Gao C-L et al (2020) DEM numerical simulation study on fracture propagation of synchronous fracturing in a double fracture rock mass. Geomech. Geophys. Geo-energ. Geo-resour. 6(39). https://doi.org/10.1007/s40948-020-00162-0.

  • Yang E, Bui HH, Nguyen GD, Choi CE, Ng CWW, De Sterck H, Bouazza A (2021) Numerical investigation of the mechanism of granular flow impact on rigid control structures. Acta Geotechnica [Published Online]. https://doi.org/10.1007/s11440-021-01162-4.

  • Yu K, Tafti D (2016) Impact model for micrometer-sized sand particles. Powder Technol 294:11–21

    Google Scholar 

  • Zeng J, Li H, Zhang D (2016) Numerical simulation of proppant transport in hydraulic fracture with the upscaling CFD-DEM method. Journal of Natural Gas Science & Engineering 33:264–277. https://doi.org/10.1016/j.jngse.2016.05.030

    Article  Google Scholar 

  • Zhang ZX, Kou SQ, Jiang LG, Lindqvist PA (2000) Effects of loading rate on rock fracture: fracture characteristics and energy partitioning. Int J Rock Mech Min Sci 37:745–762

    Google Scholar 

  • Zhang X-P, Wong LNY (2014) Displacement field analysis for cracking processes in bonded-particle model. Bull Eng Geol Env 73(1):13–21

    Google Scholar 

  • Zhang F, Zhu H, Zhou H Guo J, Huang B (2017) Discrete-element-method/computational-fluid-dynamics coupling simulaiton of proppant embedment and fracture conductivity after hydraulic fracturing. SPE 22(2). https://doi.org/10.2118/185172-PA.

  • Zhang B, Ji B, Liu W (2018) The study on mechanics of hydraulic fracture propagation direction in shale and numerical simulation. Geomech Geophys Geo-Energ Geo-Resour 4:119–127. https://doi.org/10.1007/s40948-017-0077-z

    Article  Google Scholar 

  • Zhang H, Liu S, Xiao H (2019a) Sliding friction of shale rock on dry quartz sand particles. Friction 7(4):307–315

    Google Scholar 

  • Zhang H, Liu S, Xiao H (2019b) Tribological properties of sliding quartz sand particle and shale rock contact under water and guar gum aqueous solution in hydraulic fracturing. Tribol Int 129:416–426

    Google Scholar 

  • Zhang Y, Lu X, Zhang X, Li P (2019c) Numerical simulation of proppant transportation in hydraulic fracture based on DDPM-KTGF Model. ASME-JSME-KSME 2019 8th Joint Fluids Engineering Conference, San Francisco, USA. https://doi.org/10.1115/AJKFluids2019-5613.

  • Zheng W, Tannant DD (2019) Influence of proppant fragmentation on fracture conductivity - insights from three-dimensional discrete element modeling. J Pet Sci Eng 177:1010–1023

    Google Scholar 

  • Zoback MD, Kohli AH (2019) Unconventional reservoir geomechanics: shale gas, tight oil, and induced seismicity. Cambridge University Press

    Google Scholar 

Download references

Funding

The work described in this article was fully supported by the grants from the Research Grants Council of the Hong Kong Special Administrative Region, China, Project No. “CityU 11210419” and Project No. “CityU 11214218” and an SRG-Fd Grant from City University of Hong Kong, Project No. “7005670”.

Author information

Authors and Affiliations

  1. Department of Architecture and Civil Engineering, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong SAR

    S. S. Kasyap & K. Senetakis

  2. Institute of Geotechnical Engineering, Southeast University, Nanjing, 210096, China

    H. He

Authors
  1. S. S. Kasyap
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. He
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. K. Senetakis
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to K. Senetakis.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kasyap, S.S., He, H. & Senetakis, K. 3D DEM analysis of analogue proppant–fractured rock system interaction. Bull Eng Geol Environ 81, 31 (2022). https://doi.org/10.1007/s10064-021-02500-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10064-021-02500-2

Keywords

Search

Navigation