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Journal of Porous Media
Facteur d'impact: 1.49 Facteur d'impact sur 5 ans: 1.159 SJR: 0.43 SNIP: 0.671 CiteScore™: 1.58

ISSN Imprimer: 1091-028X
ISSN En ligne: 1934-0508

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Journal of Porous Media

DOI: 10.1615/JPorMedia.2019025665
pages 939-956


Alex Hardcastle
Department of Civil Engineering, University of Nottingham, Nottingham, United Kingdom
Mohaddeseh Mousavi Nezhad
Civil Research Group, School of Engineering, University of Warwick, Coventry, UK
Mohammad Rezania
School of Engineering, University of Warwick, Coventry, United Kingdom
Walid Tizani
Department of Civil Engineering, University of Nottingham, Nottingham, United Kingdom
P. G. Ranjith
Department of Civil Engineering, Monash University, Melbourne, Australia


A computational framework for modeling hydraulic fracture on the basis of combining continuum porous media and damage theories is presented. By considering the continuum as two separate domains of damaged and intact porous domains, model components are isolated and considered separately. This simplifies the whole modeling approach. The mathematical model used consists of a set of coupled partial differential equations in continuum space that govern compressible flow in damaged and intact porous media, mechanical deformation of the domains, and damage evolution. We particularly focus on the flow of fluid within the intact and damaged porous zones. The porous domain typically has a lower permeability than the fractured zone, therefore a more complicated flow of fluid is expected within the damage zone. To model the exchange of fluid in the interface of damage zone and intact porous domain, a double permeability concept has been utilized. The evolution of cracks is modeled using Francfort and Marigo's variational theory which approximates the fracture by a diffusive damage zone using a phase field variable. The governing model equations are discretized and solved using a finite element method. The framework capabilities are verified using experimental data from a one-dimensional consolidation test and a plane stress pressured penny crack benchmark example. The framework performance highlights its capabilities in analyzing hydraulic driven fracture process and the associated permeability variations.


  1. Addis, M.A. and Yassir, N., An Overview of Geomechanical Engineering Aspects of Tight Gas Sand Developments, in SPE/DGS Saudi Arabia Section Technical Symposium and Exhibition, Society of Petroleum Engineers, 2010.

  2. An, S., Yao, J., Yang, Y., Zhang, L., Zhao, J., and Gao, Y., Influence of Pore Structure Parameters on Flow Characteristics based on a Digital Rock and the Pore Network Model, J. Nat. Gas Sci. Eng., vol. 31, pp. 156-163, 2016.

  3. Bunger, A.P. and Detournay, E., Experimental Validation of the Tip Asymptotics for a Fluid-Driven Crack, J. Mech. Phys. Solids, vol. 56, no. 11, pp. 3101-3115,2008.

  4. Bunger, A.P., Gordeliy, E., and Detournay, E., Comparison between Laboratory Experiments and Coupled Simulations of Saucer-Shaped Hydraulic Fractures in Homogeneous Brittle-Elastic Solids, J. Mech. Phys. Solids, vol. 61, no. 7, pp. 1636-1654,2013.

  5. Bonet, J. and Wood, R.D., Nonlinear Continuum Mechanics for Finite Element Analysis, Cambridge, UK: Cambridge University Press, 1997.

  6. Bourdin, B., Francfort, G.A., and Marigo, J.J., Numerical Experiments in Revisited Brittle Fracture, J. Mech. Phys. Solids, vol. 48, no. 4, pp. 797-826, 2000.

  7. Boutin, C. and Venegas, R., Assessment of the Effective Parameters of Dual Porosity Deformable Media, Mech. Mater., vol. 102, pp. 26-46,2016.

  8. Christenson, D.P., Goldfarb, J.L., and Kriner, D.L., Costs, Benefits, and the Malleability of Public Support for "Fracking," Energy Policy, vol. 105, pp. 407-417,2017.

  9. Chen, Y.F., Cai, D.M., Fan, Z.F., Li, K.C., and Jun, N.I., 3D Geological Modeling of Dual Porosity Carbonate Reservoirs: A Case from the Kenkiyak Pre-Salt Oilfield, Kazakhstan, Petrol. Explor. Dev., vol. 35, no. 4, pp. 492-497, 2008.

  10. Del Piero, G., Lancioni, G., and March, R., A Variational Model for Fracture Mechanics: Numerical Experiments, J. Mech. Phys. Solids, vol. 55, no. 12, pp. 2513-2537, 2007.

  11. Feng, G.Q., Liu, Q.G., Zhang, L.H., andZeng, Y., Pressure Transient Behavior Analysis in a Dual-Porosity Reservoir with Partially Communicating Faults, J. Nat. Gas Sci. Eng., vol. 32, pp. 373-379, 2016.

  12. Flekkey, E.G., Malthe-Serenssen, A., and Jamtveit, B., Modeling Hydrofracture, J. Geophys. Res.-Sol. Ea., vol. 107, no. B8, pp. ECV1-1-ECV 1-11,2002.

  13. Francfort, G.A. and Marigo, J.J., Revisiting Brittle Fracture as an Energy Minimization Problem, J. Mech. Phys. Solids, vol. 46, no. 8, pp. 1319-1342, 1998.

  14. Gerke, H.H. and Van Genuchten, M., A Dual-Porosity Model for Simulating the Preferential Movement of Water and Solutes in Structured Porous Media, Water Resour. Res., vol. 29, no. 2, pp. 305-319,1993.

  15. Gironacci, E., Mousavi Nezhad, M., Rezania, M., and Lancioni, G., A Non-Local Probabilistic Method for Modeling of Crack Propagation, Int. J. Mech. Sci, vol. 144, pp. 897-908, 2018.

  16. Guo, J.C., Nie, R.S., and Jia, Y.L., Dual Permeability Flow Behavior for Modeling Horizontal Well Production in Fractured-Vuggy Carbonate Reservoirs, J. Hydrol, vol. 464, pp. 281-293, 2012.

  17. Heider, Y. and Markert, B., A Phase-Field Modeling Approach of Hydraulic Fracture in Saturated Porous Media, Mech. Res. Commun., vol. 80, pp. 38-46, 2017.

  18. Huang, Y.H., Yang, S.Q., Ranjith, P.G., and Zhao, J., Strength Failure Behavior and Crack Evolution Mechanism of Granite Containing Pre-Existing Non-Coplanar Holes: Experimental Study and Particle Flow Modeling, Comput. Geotech., vol. 88, pp. 182-198,2017.

  19. Hwang, K.C., Jiang, H., Huang, Y., Gao, H., andHu, N., A Finite Deformation Theory of Strain Gradient Plasticity, J. Mech. Phys. Solids, vol. 50, no. 1, pp. 81-99, 2002.

  20. Jerbi, C., Fourno, A., Noetinger, B., and Delay, F., A New Estimation of Equivalent Matrix Block Sizes in Fractured Media with Two-Phase Flow Applications in Dual Porosity Models, J. Hydrol, vol. 548, pp. 508-523, 2017.

  21. Jiang, T., Shao, J.F., Xu, W.Y., and Zhou, C.B., Experimental Investigation and Micromechanical Analysis of Damage and Permeability Variation in Brittle Rocks, Int. J. Rock Mech. Min., vol. 47, no. 5, pp. 703-713, 2010.

  22. Jing, L., Ma, Y., and Fang, Z., Modeling of Fluid Flow and Solid Deformation for Fractured Rocks with Discontinuous Deformation Analysis (DDA) Method, Int. J. Rock Mech. Min., vol. 38, no. 3, pp. 343-355,2001.

  23. Khoei, A.R., Extended Finite Element Method: Theory and Applications, Hoboken, NJ: John Wiley & Sons, 2014.

  24. Ma, J., Zhao, G., and Khalili, N., An Elastoplastic Damage Model for Fractured Porous Media, Mech. Mater, vol. 100, pp. 41-54, 2016.

  25. Mayer, A., Risk and Benefits in a Fracking Boom: Evidence from Colorado, Extract. Indust. Soc., vol. 3, no. 3, pp. 744-753,2016.

  26. Martinez-Pafieda, E. and Betegon, C., Modeling Damage and Fracture within Strain-Gradient Plasticity, Int. J. Solids Struct., vol. 59, pp. 208-215,2015.

  27. Meschke, G. and Leonhart, D., A Generalized Finite Element Method for Hydro-Mechanically Coupled Analysis of Hydraulic Fracturing Problems Using Space-Time Variant Enrichment Functions, Comput. Methods Appl. M, vol. 290, pp. 438-465, 2015.

  28. Mohammadnejad, T. and Khoei, A.R., An Extended Finite Element Method for Hydraulic Fracture Propagation in Deformable Porous Media with the Cohesive Crack Model, Finite Elem. Anal. Des., vol. 73, pp. 77-95, 2013.

  29. Montgomery, C.T. and Smith, M.B., Hydraulic Fracturing: History of an Enduring Technology, J. Petrol. Technol, vol. 62, no. 12, pp. 26-40,2010.

  30. Mousavi Nezhad, M., Fisher, Q.J., Gironacci, E., and Rezania, M., Experimental Study and Numerical Modeling of Fracture Propagation in Shale Rocks during Brazilian Disk Test, Rock Mech. Rock Eng., vol. 51, no. 6, pp. 1755-1775, 2018.

  31. Mousavi Nezhad, M., Javadi, A.A., and Rezania, M., Modeling of Contaminant Transport in Soils Considering the Effects of Micro- and Macro-Heterogeneity, J. Hydrol., vol. 404, nos. 3-4, pp. 332-338, 2011.

  32. Mousavi Nezhad, M. and Javadi, A.A., Stochastic Finite-Element Approach to Quantify and Reduce Uncertainty in Pollutant Transport Modeling, J. Hazard. Toxic Radioact., vol. 15, no. 3, pp. 208-215,2011.

  33. Mousavi Nezhad, M., Gironacci, E., Rezania, M., and Khalili, N., Stochastic Modeling of Crack Propagation in Materials with Random Properties Using Isometric Mapping for Dimensionality Reduction of Nonlinear Data Sets, Int. J. Numer. Methods Eng., vol. 113, no. 4, pp. 656-680, 2018.

  34. Ogden, R.W., Nonlinear Elastic Deformations, Mineola, NY: Dover Publications Inc., 1997.

  35. Osborn, S.G., Vengosh, A., Warner, N.R., and Jackson, R.B., Methane Contamination of Drinking Water Accompanying Gas-Well Drilling and Hydraulic Fracturing, Proc. Nation. Acad. Sci., vol. 108, no. 20, pp. 8172-8176, 2011.

  36. Presho, M., Wo, S., and Ginting, V., Calibrated Dual Porosity, Dual Permeability Modeling of Fractured Reservoirs, J. Petrol. Sci. Eng., vol. 77, nos. 3-4, pp. 326-337, 2011.

  37. Prud'homme, A., Hydrofracking: What Everyone Needs to Know?Oxford, UK: Oxford University Press, 2013.

  38. Rabbani, A., Assadi, A., Kharrat, R., Dashti, N., and Ayatollahi, S., Estimation of Carbonates Permeability Using Pore Network Parameters Extracted from Thin Section Images and Comparison with Experimental Data, J. Nat. Gas Sci. Eng., vol. 42, pp. 85-98, 2017.

  39. Rohan, E., Nguyen, V.H., and Naili, S., Numerical Modeling of Waves in Double-Porosity Biot Medium, Comput. Struct., 2017. DOI: 10.1016/j.compstruc.2017.09.003.

  40. Samimi, S. andPak, A., Three-Dimensional Simulation of Fully Coupled Hydro-Mechanical Behavior of Saturated Porous Media Using Element Free Galerkin (EFG) Method, Comput. Geotech., vol. 46, pp. 75-83, 2012.

  41. Simo, J.C. and Pister, K.S., Remarks on Rate Constitutive Equations for Finite Deformation Problems: Computational Implications, Comput. Methods Appl. Mech. Eng., vol. 46, no. 2, pp. 201-215, 1984.

  42. Shojaei, A., Taleghani, A.D., and Li, G., A Continuum Damage Failure Model for Hydraulic Fracturing of Porous Rocks, Int. J. Plasticity, vol. 59, pp. 199-212,2014.

  43. Tahir, M.W., Hallstrom, S., and Akermo, M., Effect of Dual Scale Porosity on the Overall Permeability of Fibrous Structures, Compos. Sci. Technol, vol. 103, pp. 56-62, 2014.

  44. Tarokh, A. and Fakhimi, A., Discrete Element Simulation of the Effect of Particle Size on the Size of Fracture Process Zone in Quasi-Brittle Materials, Comput. Geotech., vol. 62, pp. 51-60, 2014.

  45. Thararoop, P., Karpyn, Z.T., and Ertekin, T., Development of a Multi-Mechanistic, Dual-Porosity, Dual-Permeability, Numerical Flow Model for Coalbed Methane Reservoirs, J. Nat. Gas Sci. Eng., vol. 8, pp. 121-131,2012.

  46. Wangen, M., A 2D Volume Conservative Numerical Model of Hydraulic Fracturing, Comput. Struct., vol. 182, pp. 448-458,2017.

  47. Wilson, Z.A. and Landis, C.M., Phase-Field Modeling of Hydraulic Fracture, J. Mech. Phys. Solids, vol. 96, pp. 264-290, 2016.

  48. Wong, T.F., David, C., and Zhu, W., The Transition from Brittle Faulting to Cataclastic Flow in Porous Sandstones: Mechanical Deformation, J. Geophys. Res.-Sol. Ea., vol. 102, no. B2, pp. 3009-3025,1997.

  49. Wu, Y.S., Liu, H.H., and Bodvarsson, G.S., A Triple-Continuum Approach for Modeling Flow and Transport Processes in Fractured Rock, J. Contam. Hydrol., vol. 73, nos. 1-4, pp. 145-179, 2004.

  50. Zhang, P., Hu, L., Meegoda, J.N., and Gao, S., Micro/Nano-Pore Network Analysis of Gas Flow in Shale Matrix, Sci. Rep., vol. 5, p. 13501,2015.

  51. Zhou, D., Zheng, P., He, P., and Peng, J., Hydraulic Fracture Propagation Direction during Volume Fracturing in Unconventional Reservoirs, J. Petrol. Sci. Eng., vol. 141, pp. 82-89, 2016.

  52. Zhu, W. and Wong, T.F., The Transition from Brittle Faulting to Cataclastic Flow: Permeability Evolution, J. Geophys. Res.-Sol. Ea., vol. 102, no. B2, pp. 3027-3041, 1997.

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