{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,14]],"date-time":"2025-11-14T21:31:58Z","timestamp":1763155918313,"version":"build-2065373602"},"reference-count":49,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2017,7,3]],"date-time":"2017-07-03T00:00:00Z","timestamp":1499040000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the Fundamental Research Funds for the Central Universities","award":["2017BSCXB44"],"award-info":[{"award-number":["2017BSCXB44"]}]},{"name":"Postgraduate Research &amp; Practice Innovation Program of Jiangsu Province","award":["KYCX17_1555"],"award-info":[{"award-number":["KYCX17_1555"]}]},{"name":"Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions","award":["PAPD"],"award-info":[{"award-number":["PAPD"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Energies"],"abstract":"<jats:p>Hydraulic fracturing is an important method to enhance permeability in oil and gas exploitation projects and weaken hard roofs of coal seams to reduce dynamic disasters, for example, rock burst. It is necessary to fully understand the mechanism of the initiation, propagation, and coalescence of hydraulic fracture network (HFN) caused by fluid flow in rock formations. In this study, a coupled hydro-mechanical model was built based on synthetic rock mass (SRM) method to investigate the effects of natural fracture (NF) density on HFN propagation. Firstly, the geometrical structures of NF obtained from borehole images at the field scale were applied to the model. Secondly, the micro-parameters of the proposed model were validated against the interaction between NF and hydraulic fracture (HF) in physical experiments. Finally, a series of numerical simulations were performed to study the mechanism of HFN propagation. In addition, confining pressure ratio (CPR) and injection rate were also taken into consideration. The results suggested that the increase of NF density drives the growth of stimulated reservoir volume (SRV), concentration area of injection pressure (CAIP), and the number of cracks caused by NF. The number of tensile cracks caused by rock matrix decrease gradually with the increase of NF density, and the number of shear cracks caused by rock matrix are almost immune to the change of NF density. The propagation orientation of HFN and the breakdown pressure in rock formations are mainly controlled by CPR. Different injection rates would result in a relatively big difference in the gradient of injection pressure, but this difference would be gradually narrowed with the increase of NF density. Natural fracture density is the key factor that influences the percentages of different crack types in HFN, regardless of the value of CPR and injection rate. The proposed model may help predict HFN propagation and optimize fracturing treatment designs in fractured rock formations.<\/jats:p>","DOI":"10.3390\/en10070914","type":"journal-article","created":{"date-parts":[[2017,7,3]],"date-time":"2017-07-03T10:27:31Z","timestamp":1499077651000},"page":"914","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":26,"title":["Numerical Investigation into the Effect of Natural Fracture Density on Hydraulic Fracture Network Propagation"],"prefix":"10.3390","volume":"10","author":[{"given":"Zhaohui","family":"Chong","sequence":"first","affiliation":[{"name":"Key Laboratory of Deep Coal Resource, Ministry of Education of China, School of Mines, China University of Mining and Technology, Xuzhou 221116, China"},{"name":"Faculty of Engineering and Information Sciences, University of Wollongong, Wollongong 2522, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9420-8635","authenticated-orcid":false,"given":"Xuehua","family":"Li","sequence":"additional","affiliation":[{"name":"Key Laboratory of Deep Coal Resource, Ministry of Education of China, School of Mines, China University of Mining and Technology, Xuzhou 221116, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiangyu","family":"Chen","sequence":"additional","affiliation":[{"name":"Key Laboratory of Deep Coal Resource, Ministry of Education of China, School of Mines, China University of Mining and Technology, Xuzhou 221116, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ji","family":"Zhang","sequence":"additional","affiliation":[{"name":"Beijing Computational Science Research Center, Beijing 100193, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jingzheng","family":"Lu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Deep Coal Resource, Ministry of Education of China, School of Mines, China University of Mining and Technology, Xuzhou 221116, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,7,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"478","DOI":"10.1016\/j.scitotenv.2015.09.030","article-title":"A review on risk assessment techniques for hydraulic fracturing water and produced water management implemented in onshore unconventional oil and gas production","volume":"539","author":"Torres","year":"2016","journal-title":"Sci. Total Environ."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"557","DOI":"10.1016\/j.ijmst.2016.05.004","article-title":"DEM simulation of confining pressure effects on crack opening displacement in hydraulic fracturing","volume":"26","author":"Abdollahipour","year":"2016","journal-title":"Int. J. Min. Sci. Technol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"430","DOI":"10.1016\/j.jngse.2016.02.047","article-title":"Numerical simulation of fracture network generation in naturally fractured reservoirs","volume":"30","author":"Zeng","year":"2016","journal-title":"J. Nat. Gas Sci. Eng."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1016\/j.jngse.2015.11.042","article-title":"Modeling and simulation of complex fracture network propagation with SRV fracturing in unconventional shale reservoirs","volume":"28","author":"Ren","year":"2016","journal-title":"J. Nat. Gas Sci. Eng."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"976","DOI":"10.1016\/j.ijrmms.2011.06.004","article-title":"Hydraulic fracturing after water pressure control blasting for increased fracturing","volume":"48","author":"Huang","year":"2011","journal-title":"Int. J. Rock Mech. Min."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/j.ijmst.2015.11.017","article-title":"In-situ stress measurements and stress change monitoring to monitor overburden caving behaviour and hydraulic fracture pre-conditioning","volume":"26","author":"Puller","year":"2016","journal-title":"Int. J. Min. Sci. Technol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"468","DOI":"10.1016\/j.petrol.2014.09.021","article-title":"Applying complex fracture model and integrated workflow in unconventional reservoirs","volume":"124","author":"Weng","year":"2014","journal-title":"J. Petrol. Sci. Eng."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"977","DOI":"10.1016\/j.jngse.2014.10.020","article-title":"A comprehensive model for simulating fracturing fluid leakoff in natural fractures","volume":"21","author":"Guo","year":"2014","journal-title":"J. Nat. Gas Sci. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1357","DOI":"10.1016\/j.jngse.2015.11.018","article-title":"Reactivation mechanism of natural fractures by hydraulic fracturing in naturally fractured shale reservoirs","volume":"27","author":"Cheng","year":"2015","journal-title":"J. Nat. Gas Sci. Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"234","DOI":"10.1016\/0148-9062(94)00037-4","article-title":"An experimentally verified criterion for propagation across unbounded frictional interfaces in brittle, linear elastic materials","volume":"32","author":"Renshaw","year":"1995","journal-title":"Int. J. Rock Mech. Min."},{"key":"ref_11","unstructured":"Gu, H., and Weng, X. (2010, January 27\u201330). Criterion for fractures crossing frictional interfaces at non-orthogonal angles. Proceedings of the 44th US Rock Mechanics Symposium and 5th US-Canada Rock Mechanics Symposium, Salt Lake City, UT, USA."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"21","DOI":"10.2118\/8347-PA","article-title":"Effects of friction on hydraulic fracture growth near unbonded interfaces in rocks","volume":"21","author":"Anderson","year":"1981","journal-title":"Soc. Pet. Eng. J."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1016\/j.juogr.2014.07.001","article-title":"Modeling of complex hydraulic fractures in naturally fractured formation","volume":"9","author":"Weng","year":"2015","journal-title":"J. Unconv. Oil Gas Resour."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jsg.2016.01.004","article-title":"Numerical investigation of hydraulic fracture network propagation in naturally fractured shale formations","volume":"84","author":"Zou","year":"2016","journal-title":"J. Struct. Geol."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Wu, Y., and Li, X. (2016). Numerical simulation of the propagation of hydraulic and natural fracture using Dijkstra\u2019s algorithm. Energies, 9.","DOI":"10.3390\/en9070519"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"8451","DOI":"10.1007\/s12665-014-4005-z","article-title":"Simulation of the hydraulic fracturing process of fractured rocks by the discrete element method","volume":"73","author":"Marina","year":"2015","journal-title":"Environ. Earth Sci."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2278","DOI":"10.1002\/nag.2135","article-title":"An explicitly coupled hydro-geomechanical model for simulating hydraulic fracturing in arbitrary discrete fracture networks","volume":"37","author":"Fu","year":"2013","journal-title":"Int. J. Numer. Anal. Methods Geomech."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2681","DOI":"10.1007\/s13369-015-1829-0","article-title":"Investigation of hydraulic fracture networks in shale gas reservoirs with random fractures","volume":"41","author":"Hou","year":"2016","journal-title":"Arab. J. Sci. Eng."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1623","DOI":"10.1007\/s10040-016-1441-8","article-title":"Review: Mathematical expressions for estimating equivalent permeability of rock fracture networks","volume":"24","author":"Liu","year":"2016","journal-title":"Hydrogeol. J."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1271","DOI":"10.1016\/j.jngse.2016.06.072","article-title":"A numerical method for simulating fluid flow through 3-D fracture networks","volume":"33","author":"Huang","year":"2016","journal-title":"J. Nat. Gas Sci. Eng."},{"key":"ref_21","unstructured":"Meyer, B.R., and Bazan, L.W. (November, January 30). A discrete fracture network model for hydraulically induced fractures: Theory, parametric and case studies. Proceedings of the SPE Hydraulic Fracturing Technology Conference: Society of Petroleum Engineers, Denver, CO, USA."},{"key":"ref_22","first-page":"368","article-title":"Modeling of hydraulic-fracture-network propagation in a naturally fractured formation","volume":"26","author":"Weng","year":"2011","journal-title":"SPE Prod. Oper."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1007\/s10596-013-9396-5","article-title":"Modeling fluid injection in fractures with a reservoir simulator coupled to a boundary element method","volume":"18","author":"Ganis","year":"2014","journal-title":"Comput. Geosci."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1007\/s11242-015-0554-1","article-title":"Pressure transient behavior of horizontal wells intersecting multiple hydraulic fractures in naturally fractured reservoirs","volume":"110","author":"Biryukov","year":"2015","journal-title":"Transp. Porous Media"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"548","DOI":"10.1016\/j.jngse.2015.12.009","article-title":"Multi-phase fracturing fluid leakoff model for fractured reservoir using extended finite element method","volume":"28","author":"Liu","year":"2016","journal-title":"J. Nat. Gas Sci. Eng."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/j.jngse.2016.05.001","article-title":"Numerical simulation of hydraulic fracturing in orthotropic formation based on the extended finite element method","volume":"33","author":"Wang","year":"2016","journal-title":"J. Nat. Gas Sci. Eng."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1016\/j.jngse.2015.01.008","article-title":"A novel ECBM extraction technology based on the integration of hydraulic slotting and hydraulic fracturing","volume":"22","author":"Yan","year":"2015","journal-title":"J. Nat. Gas Sci. Eng."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"995","DOI":"10.1007\/s10040-011-0731-4","article-title":"The role of pore pressure during hydraulic fracturing and implications for groundwater outbursts in mining and tunnelling","volume":"19","author":"Yang","year":"2011","journal-title":"Hydrogeol. J."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1169","DOI":"10.1007\/s12665-012-1818-5","article-title":"Microscopic modelling of the hydraulic fracturing process","volume":"68","author":"Eshiet","year":"2013","journal-title":"Environ. Earth Sci."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1016\/j.ijrmms.2014.04.011","article-title":"Simulation of shale\u2013proppant interaction in hydraulic fracturing by the discrete element method","volume":"70","author":"Deng","year":"2014","journal-title":"Int. J. Rock Mech. Min."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1016\/j.ijrmms.2010.11.014","article-title":"The synthetic rock mass approach for jointed rock mass modelling","volume":"48","author":"Pierce","year":"2011","journal-title":"Int. J. Rock Mech. Min."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1329","DOI":"10.1016\/j.ijrmms.2004.09.011","article-title":"A bonded-particle model for rock","volume":"41","author":"Potyondy","year":"2004","journal-title":"Int. J. Rock Mech. Min."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Eberhardt, E., Stead, D., and Morrison, T. (2007). A synthetic rock mass model for jointed rock. Rock Mechanics: Meeting Society\u2019s Challenges and Demands, Taylor and Francis Group.","DOI":"10.1201\/NOE0415444019"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Al-Busaidi, A., Hazzard, J., and Young, R.P. (2005). Distinct element modeling of hydraulically fractured Lac du Bonnet granite. J. Geophys. Res., 110.","DOI":"10.1029\/2004JB003297"},{"key":"ref_35","unstructured":"Hazzard, J.F., Young, R.P., and Oates, S.J. (2002, January 7\u201310). Numerical modeling of seismicity induced by fluid injection in a fractured reservoir. Proceedings of the 5th North American Rock Mechanics Symposium, Toronto, ON, Canada."},{"key":"ref_36","unstructured":"H\u00f6kmark, H., L\u00f6nnqvist, M., and F\u00e4lth, B. (2010). Thermal, Mechanical, Thermo-Mechanical and Hydro-Mechanical Evolution of the Rock at the Forsmark and Laxemar Sites: SKB TR1023, Svensk K\u00e4rnbr\u00e4nslehantering AB, Swedish Nuclear Fuel and Waste Management Co."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1016\/j.geothermics.2014.01.009","article-title":"Numerical investigation on optimized stimulation of intact and naturally fractured deep geothermal reservoirs using hydro-mechanical coupled discrete particles joints model","volume":"52","author":"Yoon","year":"2014","journal-title":"Geothermics"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"WC167","DOI":"10.1190\/geo2011-0025.1","article-title":"Numerical modeling of seismicity induced by fluid injection in naturally fractured reservoirs","volume":"76","author":"Zhao","year":"2011","journal-title":"Geophysics"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"719","DOI":"10.1016\/j.jngse.2016.11.010","article-title":"Numerical investigation of fluid-driven near-borehole fracture propagation in laminated reservoir rock using PFC 2D","volume":"36","author":"Zhou","year":"2016","journal-title":"J. Nat. Gas Sci. Eng."},{"key":"ref_40","first-page":"24","article-title":"Effect of fractures cross connection on fluid flow characteristics of mining-induced rock. Journal of China University of Mining&Technology","volume":"44","author":"Zhu","year":"2015","journal-title":"J. China Univ. Min. Technol."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2017\/7676417","article-title":"Numerical investigation of acoustic emission events of argillaceous sandstones under confining pressure","volume":"2017","author":"Chong","year":"2017","journal-title":"Math. Probl. Eng."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"209","DOI":"10.2118\/13224-PA","article-title":"Influence of geologic discontinuities on hydraulic fracture propagation","volume":"39","author":"Warpinski","year":"1987","journal-title":"J. Pet. Technol."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Blanton, T.L. (1986, January 18\u201321). Propagation of hydraulically and dynamically induced fractures in naturally fractured reservoirs. Proceedings of the SPE15261 Presented at the SPE Unconventional Gas Technology Symposium, Louisville, KY, USA.","DOI":"10.2523\/15261-MS"},{"key":"ref_44","first-page":"20","article-title":"Hydraulic fracture crossing natural fracture at nonorthogonal angles: A criterion and its validation","volume":"27","author":"Gu","year":"2012","journal-title":"SPE Prod. Oper."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.coal.2013.10.012","article-title":"Simulation of hydraulic fracturing using particle flow method and application in a coal mine","volume":"121","author":"Wang","year":"2014","journal-title":"Int. J. Coal Geol."},{"key":"ref_46","unstructured":"Fjar, E., Holt, R.M., Raaen, A.M., Risnes, R., and Horsrud, P. (2008). Petroleum Related Rock Mechanics, Elsevier."},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Zhang, B., Li, X., Zhang, Z., Wu, Y., Wu, Y., and Wang, Y. (2016). Numerical investigation of influence of in-situ stress ratio, injection rate and fluid viscosity on hydraulic fracture propagation using a distinct element approach. Energies, 9.","DOI":"10.3390\/en9030140"},{"key":"ref_48","first-page":"89","article-title":"What is stimulated reservoir volume?","volume":"25","author":"Mayerhofer","year":"2010","journal-title":"SPE Prod. Oper."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"2139","DOI":"10.1007\/s00603-013-0533-1","article-title":"Effect of model scale and particle size distribution on PFC3D simulation results","volume":"47","author":"Ding","year":"2014","journal-title":"Rock Mech. Rock Eng."}],"container-title":["Energies"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1996-1073\/10\/7\/914\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:41:16Z","timestamp":1760208076000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1996-1073\/10\/7\/914"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,7,3]]},"references-count":49,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2017,7]]}},"alternative-id":["en10070914"],"URL":"https:\/\/doi.org\/10.3390\/en10070914","relation":{},"ISSN":["1996-1073"],"issn-type":[{"type":"electronic","value":"1996-1073"}],"subject":[],"published":{"date-parts":[[2017,7,3]]}}}