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Propagation, proppant transport and the evolution of transport properties of hydraulic fractures

Published online by Cambridge University Press:  19 September 2018

Jiehao Wang Open the ORCID record for Jiehao Wang [Opens in a new window] ,
Derek Elsworth  and
Martin K. Denison
Jiehao Wang*
Affiliation:
Department of Energy and Mineral Engineering, EMS Energy Institute and G3 Center, Pennsylvania State University, University Park, PA 16802, USA
Derek Elsworth
Affiliation:
Department of Energy and Mineral Engineering, EMS Energy Institute and G3 Center, Pennsylvania State University, University Park, PA 16802, USA
Martin K. Denison
Affiliation:
Reaction Engineering International, 77 West 200 South, Suite 210, Salt Lake City, UT 84101, USA
*
†Email address for correspondence: [email protected]
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Abstract

Hydraulic fracturing is a widely used method for well stimulation to enhance hydrocarbon recovery. Permeability, or fluid conductivity, of the hydraulic fracture is a key parameter to determine the fluid production rate, and is principally conditioned by fracture geometry and the distribution of the encased proppant. A numerical model is developed to describe proppant transport within a propagating blade-shaped fracture towards defining the fracture conductivity and reservoir production after fracture closure. Fracture propagation is formulated based on the PKN-formalism coupled with advective transport of an equivalent slurry representing a proppant-laden fluid. Empirical constitutive relations are incorporated to define rheology of the slurry, proppant transport with bulk slurry flow, proppant gravitational settling, and finally the transition from Poiseuille (fracture) flow to Darcy (proppant pack) flow. At the maximum extent of the fluid-driven fracture, as driving pressure is released, a fracture closure model is employed to follow the evolution of fracture conductivity with the decreasing fluid pressure. This model is capable of accommodating the mechanical response of the proppant pack, fracture closure of potentially contacting rough surfaces, proppant embedment into fracture walls, and most importantly flexural displacement of the unsupported spans of the fracture. Results show that reduced fluid viscosity increases the length of the resulting fracture, while rapid leak-off decreases it, with both characteristics minimizing fracture width over converse conditions. Proppant density and size do not significantly influence fracture propagation. Proppant settling ensues throughout fracture advance, and is accelerated by a lower viscosity fluid or greater proppant density or size, resulting in accumulation of a proppant bed at the fracture base. ‘Screen-out’ of proppant at the fracture tip can occur where the fracture aperture is only several times the diameter of the individual proppant particles. After fracture closure, proppant packs comprising larger particles exhibit higher conductivity. More importantly, high-conductivity flow channels are necessarily formed around proppant banks due to the flexural displacement of the fracture walls, which offer preferential flow pathways and significantly influence the distribution of fluid transport. Higher compacting stresses are observed around the edge of proppant banks, resulting in greater depths of proppant embedment into the fracture walls and/or an increased potential for proppant crushing.

JFM classification

Multiphase and Particle-laden Flows: Multiphase and Particle-laden Flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 855 , 25 November 2018 , pp. 503 - 534
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Copyright
© 2018 Cambridge University Press 

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References

Adachi, J., Siebrits, E., Peirce, A. & Desroches, J. 2007 Computer simulation of hydraulic fractures. Intl J. Rock Mech. Min. Sci. 44, 739–757.Google Scholar
Adachi, J. I., Detournay, E. & Peirce, A. P. 2010 Analysis of the classical pseudo-3D model for hydraulic fracture with equilibrium height growth across stress barriers. Intl J. Rock Mech. Min. Sci. 47, 625–639.Google Scholar
Adachi, J. I. & Peirce, A. P. 2008 Asymptotic analysis of an elasticity equation for a finger-like hydraulic fracture. J. Elast. 90, 43–69.Google Scholar
Bandis, S. C., Lumsden, A. C. & Barton, N. R. 1983 Fundamentals of rock joint deformation. Intl J. Rock Mech. Min. Sci. 20, 249–268.Google Scholar
Barton, N., Bandis, S. & Bakhtar, K. 1985 Strength, deformation and conductivity coupling of rock joints. Intl J. Rock Mech. Min. Sci. 22, 121–140.Google Scholar
Boyer, F., Guazzelli, É. & Pouliquen, O. 2011 Unifying suspension and granular rheology. Phys. Rev. Lett. 107, 1–5.Google Scholar
Carman, P. C. 1937 Fluid flow through granular beds. Trans. Chem. Engng 15, 150–166.Google Scholar
Cipolla, C. L., Lolon, E. P., Mayerhofer, M. J. & Warpinski, N. R. 2009 The effect of proppant distribution and un-propped fracture conductivity on well performance in unconventional gas reservoirs. In SPE Hydraulic Fracturing Technology Conference, pp. 1–10.Google Scholar
Detournay, E. 2016 Mechanics of hydraulic fractures. Annu. Rev. Fluid Mech. 48, 311–339.Google Scholar
Detournay, E., Cheng, A. H.-D. & McLennan, J. D. 1990 A poroelastic PKN hydraulic fracture model based on an explicit moving mesh algorithm. J. Energy Res. Technol. 112, 224–230.Google Scholar
Dontsov, E. V. & Peirce, a. P. 2014 Slurry flow, gravitational settling and a proppant transport model for hydraulic fractures. J. Fluid Mech. 760, 567–590.Google Scholar
Dontsov, E. V. & Peirce, A. P. 2015a A Lagrangian approach to modelling proppant transport with tip screen-out in KGD hydraulic fractures. Rock Mech. Rock Engng 48, 2541–2550.Google Scholar
Dontsov, E. V. & Peirce, A. P. 2015b An enhanced pseudo-3D model for hydraulic fracturing accounting for viscous height growth, non-local elasticity, and lateral toughness. Engng Fract. Mech. 142, 116–139.Google Scholar
Dontsov, E. V. & Peirce, A. P. 2015c Proppant transport in hydraulic fracturing: crack tip screen-out in KGD and P3D models. Intl J. Solids Struct. 63, 206–218.Google Scholar
Dontsov, E. V. & Peirce, A. P. 2016 Comparison of toughness propagation criteria for blade-like and pseudo-3D hydraulic fractures. Engng Fract. Mech. 160, 238–247.Google Scholar
Economides, M. J. & Nolte, K. G. 2000 Reservoir Stimulation. vol. 18. Wiley.Google Scholar
Frank, U. & Barkley, N. 1995 Remediation of low permeability subsurface formations by fracturing enhancement of soil vapor extraction. J. Hazard. Mater. 40, 191–201.Google Scholar
Greetesma, J. & de Klerk, F. 1969 A rapid method of predicting width and extent of hydraulic induced fractures. J. Petrol. Tech. 21, 1571–1581.Google Scholar
Gu, M., Dao, E. & Mohanty, K. K. 2015 Investigation of ultra-light weight proppant application in shale fracturing. Fuel 150, 191–201.Google Scholar
Gu, M. & Mohanty, K. K. 2014 Effect of foam quality on effectiveness of hydraulic fracturing in shales. Intl J. Rock Mech. Min. Sci. 70, 273–285.Google Scholar
Jing, L. 2003 A review of techniques, advances and outstanding issues in numerical modelling for rock mechanics and rock engineering. Intl J. Rock Mech. Min. Sci. 40, 283–353.Google Scholar
Khanna, A., Neto, L. B. & Kotousov, A. 2014 Effect of residual opening on the inflow performance of a hydraulic fracture. Intl J. Engng Sci. 74, 80–90.Google Scholar
Khristianovic, S. A. & Zheltov, Y. P. 1955 Formation of vertical fractures by means of highly viscous liquid. In Proceeding 4th World Pet. Congr. 5, Rome, pp. 579–586.Google Scholar
Kovalyshen, Y. & Detournay, E. 2010 A reexamination of the classical PKN model of hydraulic fracture. Transp. Porous Med. 81, 317–339.Google Scholar
Kozeny, J. 1927 Uber Kapillare Leitung der Wasser in Boden. R. Acad. Sci. Vienna, Proc. Cl. I 136, 271–306.Google Scholar
Lecampion, B., Bunger, A. & Zhang, X. 2018 Numerical methods for hydraulic fracture propagation: a review of recent trends. J. Nat. Gas Sci. Eng. 49, 66–83.Google Scholar
Legarth, B., Huenges, E. & Zimmermann, G. 2005 Hydraulic fracturing in a sedimentary geothermal reservoir: results and implications. Intl J. Rock Mech. Min. Sci. 42, 1028–1041.Google Scholar
Lemmon, E. W.1998 Thermophysical Properties of Fluid Systems. NIST Chem. Webb. NIST Stand. Ref. Database Number 69 20899.Google Scholar
Liu, Y., Leung, J. Y., Chalaturnyk, R., Virues, C. J. J. & Ulc, N. E. 2017 Fracturing fluid distribution in shale gas reservoirs due to fracture closure, proppant distribution and gravity segregation. In SPE Unconventional Resources Conference.Google Scholar
Neto, L. B., Khanna, A. & Kotousov, A. 2015 Conductivity and performance of hydraulic fractures partially filled with compressible proppant packs. Intl J. Rock Mech. Min. Sci. 74, 1–9.Google Scholar
Neto, L. B. & Kotousov, A. 2013a Residual opening of hydraulic fractures filled with compressible proppant. Intl J. Rock Mech. Min. Sci. 61, 223–230.Google Scholar
Neto, L. B. & Kotousov, A. 2013b On the residual opening of hydraulic fractures. Intl J. Fract. 181, 127–137.Google Scholar
Nordgren, R. P. 1972 Propagation of a vertical hydraulic fracture. Soc. Petrol. Engng J. 12, 306–314.Google Scholar
Ouyang, S., Carey, G. F. & Yew, C. H. 1997 An adaptive finite element scheme for hydraulic fracturing with proppant transport. Intl J. Numer. Meth. Fluids 24, 645–670.Google Scholar
Perkins, T. K. & Kern, L. R. 1961 Widths of hydraulic fractures. J. Petrol. Tech. 13, 937–949.Google Scholar
Rahman, M. M. & Rahman, M. K. 2010 A review of hydraulic fracture models and development of an improved pseudo-3D model for stimulating tight oil/gas sand. Energy Sources, Part A Recover. Util. Environ. Eff. 32, 1416–1436.Google Scholar
Shiozawa, S. & McClure, M. 2016 Simulation of proppant transport with gravitational settling and fracture closure in a three-dimensional hydraulic fracturing simulator. J. Petrol. Sci. Engng 138, 298–314.Google Scholar
Tada, H., Paris, P. C. & Irwin, G. R. 2000 Two-dimensional stress solutions for various configurations with cracks. The Stress Analysis of Cracks Handbook. ASME Press.Google Scholar
Wang, J. & Elsworth, D. 2018 Role of proppant distribution on the evolution of hydraulic fracture conductivity. J. Petrol. Sci. Engng 166, 249–262.Google Scholar
Wang, J., Elsworth, D. & Denison, M. K. 2018a Hydraulic fracturing with leakoff in a pressure-sensitive dual porosity medium. Intl J. Rock Mech. Min. Sci. 107, 55–68.Google Scholar
Wang, J., Elsworth, D., Wu, Y., Liu, J., Zhu, W. & Liu, Y. 2018b The influence of fracturing fluids on fracturing processes: a comparison between water, oil and SC-CO2. Rock Mech. Rock Eng. 51, 299–313.Google Scholar
Warpinski, N. 2010 Stress amplification and arch dimensions in proppant beds deposited by waterfracs. SPE Prod. Oper. 25, 1–17.Google Scholar
Yu, W., Zhang, T., Du, S. & Sepehrnoori, K. 2015 Numerical study of the effect of uneven proppant distribution between multiple fractures on shale gas well performance. Fuel 142, 189–198.Google Scholar
Zhang, F., Dontsov, E. & Mack, M. 2017 Fully coupled simulation of a hydraulic fracture interacting with natural fractures with a hybrid discrete-continuum method. Intl J. Numer. Anal. Meth. Geomech. 41, 1430–1452.Google Scholar
Zhang, G., Li, M. & Gutierrez, M. 2017 Numerical simulation of proppant distribution in hydraulic fractures in horizontal wells. J. Nat. Gas Sci. Engng 48, 157–168.Google Scholar
Zhang, Q., Ma, D., Wu, Y. & Meng, F. 2018 Coupled thermal-gas-mechanical (TGM) model of tight sandstone gas wells. J. Geophys. Engng 15, 1743–1752.Google Scholar
Zoback, M. D., Rummel, F., Jung, R. & Raleigh, C. B. 1977 Laboratory hydraulic fracturing experiments in intact and pre-fractured rock. Intl J. Rock Mech. Min. Sci. 14, 49–58.Google Scholar
Zolfaghari, N., Dontsov, E. & Bunger, A. P. 2018 Solution for a plane strain rough-walled hydraulic fracture driven by turbulent fluid through impermeable rock. Intl J. Numer. Anal. Meth. Geomech. 42, 587–617.Google Scholar