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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

Volumes:
Volume 22, 2019 Volume 21, 2018 Volume 20, 2017 Volume 19, 2016 Volume 18, 2015 Volume 17, 2014 Volume 16, 2013 Volume 15, 2012 Volume 14, 2011 Volume 13, 2010 Volume 12, 2009 Volume 11, 2008 Volume 10, 2007 Volume 9, 2006 Volume 8, 2005 Volume 7, 2004 Volume 6, 2003 Volume 5, 2002 Volume 4, 2001 Volume 3, 2000 Volume 2, 1999 Volume 1, 1998

Journal of Porous Media

DOI: 10.1615/JPorMedia.2018025971
pages 923-938

A NUMERICAL INVESTIGATION OF PULSE HYDRAULIC FRACTURING TREATMENTS USING THE X-FEM TECHNIQUE

Mohammad Vahab
School of Civil and Environmental Engineering, the University of New South Wales, Sydney 2052, Australia
Zakieh Harif
Faculty of Civil Engineering, K.N. Toosi University of Technology, Tehran, Iran
Nasser Khalili
School of Civil and Environmental Engineering, the University of New South Wales, Sydney 2052, Australia

RÉSUMÉ

Traditional hydraulic fracturing (THF) treatments suffer difficulties such as high injection pressure, poor controllability, and local stress concentration. In many cases, THF leads to the activation of a relatively small number of perforations with limited contribution to the enhancement of the overall permeability of the reservoir. Alternatively, pulse water pressure may be exerted inside the borehole as a remedy to produce multiple macroscopic main cracks along the borehole axial and radial directions. To reach a better understanding of this technique so as to improve its efficiency in practice, the role of the contributing elements, namely, the fracturing fluid mean pressure, its amplitude, and its frequency, needs to be investigated in conjunction with the properties of the bulk. In this paper, an extended finite element framework is developed to study pulse hydraulic fracturing (PHF) within a tight-low permeability reservoir. To this end, the momentum balance equation of the medium is solved in conjunction with the flow continuity equations of the fracturing fluid using the staggered Newton algorithm. In the context of X-FEM, the displacement field is enhanced using the Heaviside enrichment function to account for the discontinuities due to cracks in the body. The hydrofracture inflow is modeled for both the laminar and turbulent flow regimes. The nonlinearities within the hydrofracture tip are taken into account using the potential-based cohesive zone model, where the crack growth direction and increment are determined by taking advantage of the energy-based cohesive stress functions. Using the developed computational framework, the performance of PHF treatments is investigated through various numerical simulations.

RÉFÉRENCES

  1. Anderson, T.L., Fracture Mechanics: Fundamentals and Applications, Boca Raton, FL: CRC Press, 2017.

  2. Barenblatt, G.I., The Mathematical Theory of Equilibrium Cracks in Brittle Fracture, Adv. Appl. Mech, vol. 7, pp. 55-129, 1962.

  3. Boone, T.J. and Ingraffea, A.R., A Numerical Procedure for Simulation of Hydraulically Driven Fracture Propagation in Poroelas- tic Media, Int. J. Numer. Anal. Meth. Geomech., vol. 14, pp. 27-47, 1990.

  4. Camacho, G.T. and Ortiz, M., Computational Modelling of Impact Damage in Brittle Materials, Int. J. Solids Struct., vol. 33, pp. 2899-2938, 1996.

  5. Cao, J. and Chung, D., Defect Dynamics and Damage of Concrete under Repeated Compression, Studied by Electrical Resistance Measurement, Cem. Concr. Res, vol. 31, pp. 1639-1642, 2001a.

  6. Cao, J. and Chung, D., Minor Damage of Cement Mortar during Cyclic Compression, Monitored by Electrical Resistivity Measurement, Cem. Concr. Res, vol. 31, pp. 1519-1521, 2001b.

  7. Changyou, L., Jingxuan, Y., and Bin, Y., Rock-Breaking Mechanism and Experimental Analysis of Confined Blasting of Borehole Surrounding Rock, Int. J. Min. Sci. Technol., vol. 27, pp. 795-801,2017.

  8. Denoual, C. and Hild, F., Dynamic Fragmentation of Brittle Solids: A Multi-Scale Model, Eur. J. Mech. A. Solids, vol. 21, pp. 105-120, 2002.

  9. Detournay, E., Propagation Regimes of Fluid-Driven Fractures in Impermeable Rocks, Int. J. Geomech., vol. 4, pp. 35-45, 2004.

  10. Dugdale, D., Yielding of Steel Sheets Containing Slits, J. Mech. Phys. Solids, vol. 8, pp. 100-104,1960.

  11. Emerman, S.H., Turcotte, D., and Spence, D., Transport of Magma and Hydrothermal Solutions by Laminar and Turbulent Fluid Fracture, Phys. Earth Planet. Inter, vol. 41, pp. 249-259, 1986.

  12. Erarslan, N. and Williams, D., Mixed-Mode Fracturing of Rocks under Static and Cyclic Loading, Rock. Mech. Rock. Eng., vol. 46, pp. 1035-1052,2013.

  13. Farhat, C. and Lesoinne, M., Two Efficient Staggered Algorithms for the Serial and Parallel Solution of Three-Dimensional Nonlinear Transient Aeroelastic Problems, Comput. Meth. Appl. Mech. Eng., vol. 182, pp. 499-515, 2000.

  14. Geertsma, J. and De Klerk, F., A Rapid Method of Predicting Width and Extent of Hydraulically Induced Fractures, J. Petrol. Sci. Eng., vol. 21, pp. 1571-1581, 1969.

  15. Huang, B., Cheng, Q., and Liu, C., Theory and Technical Framework of Hydraulic Fracturing for Coal-Rock Mass, J. Min. Saf. Eng., vol. 28, pp. 167-173, 2011.

  16. Khoei, A.R., Hirmand, M., Vahab, M., and Bazargan, M., An Enriched FEM Technique for Modeling Hydraulically Driven Cohesive Fracture Propagation in Impermeable Media with Frictional Natural Faults; Numerical and Experimental Investigations, Int. J. Numer. Meth. Eng., vol. 104, pp. 439-468, 2015.

  17. Khoei, A.R., Vahab, M., Haghighat, E., and Moallemi, S., A Mesh-Independent Finite Element Formulation for Modeling Crack Growth in Saturated Porous Media based on an Enriched-FEM Technique, Int. J. Fract., vol. 188, pp. 79-108,2014.

  18. Khoei, A.R., Vahab, M., and Hirmand, M., Modeling the Interaction between Fluid-Driven Fracture and Natural Fault Using an Enriched-FEM Technique, Int. J. Fract., vol. 197, pp. 1-24, 2016.

  19. Khoei, A.R., Vahab, M., and Hirmand, M., An Enriched-FEM Technique for Numerical Simulation of Interacting Discontinuities in Naturally Fractured Porous Media, Comput. Meth. Appl. Mech. Eng., vol. 331, pp. 197-231, 2018.

  20. Li, Q., Lin, B., and Zhai, C., A New Technique for Preventing and Controlling Coal and Gas Outburst Hazard with Pulse Hydraulic Fracturing: A Case Study in Yuwu Coal Mine, China, Nat. Hazards, vol. 75, pp. 2931-2946, 2015.

  21. Li, S. and Ghosh, S., Multiple Cohesive Crack Growth in Brittle Materials by the Extended Voronoi Cell Finite Element Model, Int. J. Fract., vol. 141, pp. 373-393, 2006.

  22. Liang, W., Zhang, C., Gao, H., Yang, X., Xu, S., and Zhao, Y., Experiments on Mechanical Properties of Salt Rocks under Cyclic Loading, J. Rock Mech. Geotech. Eng., vol. 4, pp. 54-61, 2012.

  23. Lin, B.Q., Meng, J., Ning, J., Zhang, M.B., Li, Q.G., and Liu, Y., Research on Dynamic Characteristics of Hydraulic Fracturing in Coal Body Containing Gas, J. Min. Saf. Eng., vol. 29, pp. 106-110, 2012.

  24. Liu, E. and He, S., Effects Of Cyclic Dynamic Loading on the Mechanical Properties of Intact Rock Samples under Confining Pressure Conditions, Eng. Geol., vol. 125, pp. 81-91, 2012.

  25. Lu, P., Li, G., Huang, Z., He, Z., Li, X., and Zhang, H., Modeling and Parameters Analysis on a Pulsating Hydro-Fracturing Stress Disturbance in a Coal Seam, J. Nat. Gas Sci. Eng., vol. 26, pp. 253-263,2015.

  26. Ma, C., Jiang, Y., Xing, H., and Li, T., Numerical Modelling of Fracturing Effect Stimulated by Pulsating Hydraulic Fracturing in Coal Seam Gas Reservoir, J. Nat. Gas Sci. Eng., vol. 46, pp. 651-663, 2017.

  27. Matthies, H.G. and Steindorf, J., Partitioned Strong Coupling Algorithms for Fluid-Structure Interaction, Comput. Struct., vol. 81, pp. 805-812,2003.

  28. Mighani, S., Rock Tensile Failure Related to Improving Hydraulic Fracture, MS, University of Oklahoma, 2014. Moody, L.F., Friction Factors for Pipe Flow, Trans. ASME, vol. 66, pp. 671-684, 1944.

  29. Nick, H. and Matthai, S., Comparison of Three FE-FV Numerical Schemes for Single- and Two-Phase Flow Simulation of Fractured Porous Media, Transp. Porous Media, vol. 90, pp. 421-444, 2011.

  30. Ortiz, M. and Pandolfi, A., Finite-Deformation Irreversible Cohesive Elements for Three-Dimensional Crack-Propagation Analysis, Int. J. Numer. Meth. Eng., vol. 44, pp. 1267-1282,1999.

  31. Park, K., Choi, H., and Paulino, G.H., Assessment of Cohesive Traction-Separation Relationships in ABAQUS: A Comparative Study, Mech. Res. Commun., vol. 78, pp. 71-78,2016.

  32. Patel, S., Sondergeld, C., and Rai, C., Laboratory Studies of Hydraulic Fracturing by Cyclic Injection, Int. J. Rock Mech. Min. Sci., vol. 95, pp. 8-15,2017.

  33. Prevost, J.H., Partitioned Solution Procedure for Simultaneous Integration of Coupled-Field Problems, Comm. Numer. Methods. Eng., vol. 13, pp. 239-247, 1997.

  34. Rahman, M., Suarez, Y., Chen, Z., and Rahman, S., Unsuccessful Hydraulic Fracturing Cases in Australia: Investigation into Causes of Failures and Their Remedies, J. Petrol. Sci. Eng., vol. 57, pp. 70-81, 2007.

  35. Schrefler, B., Simoni, L., and Turska, E., Standard Staggered and Staggered Newton Schemes in Thermo-Hydro-Mechanical Problems, Comput. Meth. Appl. Mech. Eng., vol. 144, pp. 93-109, 1997.

  36. Schrefler, B.A., Secchi, S., and Simoni, L., On Adaptive Refinement Techniques in Multi-Field Problems Including Cohesive Fracture, Comput. Meth. Appl. Mech. Eng., vol. 195, pp. 444-461, 2006.

  37. Serghides, T., Estimate Friction Factor Accurately, Chem. Eng., vol. 91, pp. 63-64, 1984.

  38. Simoni, L. and Schrefler, B., A Staggered Finite-Element Solution for Water and Gas Flow in Deforming Porous Media, Int. J. Numer. Method. Biomed. Eng., vol. 7, pp. 213-223, 1991.

  39. Spence, D. and Sharp, P., Self-Similar Solutions for Elastohydrodynamic Cavity Flow, Proc. Royal Soc. London A: Math., Phys. Eng. Sci, vol. 400, pp. 289-313,1985.

  40. Vahab, M. and Khalili, N., Numerical Investigation of the Flow Regimes through Hydraulic Fractures Using the X-FEM Technique, Eng. Fract. Mech, vol. 169, pp. 146-162, 2017.

  41. Vahab, M. and Khalili, N., X-FEM Modeling of Multizone Hydraulic Fracturing Treatments within Saturated Porous Media, Rock Mech. Rock. Eng., pp. 1-21, 2018. DOI: 10.1007/s00603-018-1419-z.

  42. Vijay, M., Remisz, J., and Shen, X., Potential of Pulsed Water Jets for Cutting and Fracturing of Hard Rock Formations, Int. J. Min. Reclam. Env, vol. 7, pp. 121-132, 1993.

  43. Wang, W., Li, X., Lin, B., and Zhai, C., Pulsating Hydraulic Fracturing Technology in Low Permeability Coal Seams, Int. J. Min. Sci. Technol., vol. 25, pp. 681-685, 2015.

  44. Wang, Y., Zhang, J., Diao, M., and Qu, J., Experimental Study on Propagation of Fluctuation Pressure in Fissures, J. Hydraul. Eng. (China), vol. 12, pp. 44-48, 2002.

  45. Witherspoon, P.A., Wang, J., Iwai, K., and Gale, J., Validity of Cubic Law for Fluid Flow in a Deformable Rock Fracture, Water Resour. Res, vol. 16, pp. 1016-1024, 1980.

  46. Xu, J., Zhai, C., and Qin, L., Mechanism and Application of Pulse Hydraulic Fracturing in Improving Drainage of Coalbed Methane, J. Nat. Gas Sci. Eng., vol. 40, pp. 79-90,2017.

  47. Ye, Q., Jia, Z., and Zheng, C., Study on Hydraulic-Controlled Blasting Technology for Pressure Relief and Permeability Improvement in a Deep Hole, J. Petrol. Sci. Eng., vol. 159, pp. 433-442, 2017.

  48. Zhang, J., Study on Fluctuating Pressure Transmission in Joint on the Bottom of Plunge Pool, J. Sichuan. Univ., vol. 32, pp. 5-8, 2000.

  49. Zhao, Z., Study of Technology of Variable-Frequency Pulse Water Infusion into Coal Seam, J. Min. Saf. Eng., vol. 25, pp. 486-489, 2008.

  50. Zhu, H., Zhang, M., Shen, J., and Hu, R., Permeability Enhancing Mechanism and Numerical Analysis on Pulsating Water Injection in Low Permeability Coal Seams, J. China. Coal. Soc, vol. 38, pp. 343-347, 2013.

  51. Zienkiewicz, O., Paul, D., and Chan, A., Unconditionally Stable Staggered Solution Procedure for Soil-Pore Fluid Interaction Problems, Int. J. Numer. Meth. Eng., vol. 26, pp. 1039-1055,1988.


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