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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: jiehao.wang@psu.edu
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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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