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Blade-shaped (PKN) Hydraulic Fracture Driven By A Turbulent Fluid In An Impermeable Rock | | Navid Zolfaghari
; Colin R. Meyer
; Andrew P. Bunger
; | | Date: |
5 Sep 2016 | | Abstract: | High flow rate, water-driven hydraulic fractures are more common now than
ever in the oil and gas industry. Although the fractures are small, the high
injection rate and low viscosity of the water, lead to high Reynolds numbers
and potentially turbulence in the fracture. Here we present a semi-analytical
solution for a blade-shaped (PKN) geometry hydraulic fracture driven by a
turbulent fluid in the limit of zero fluid leak-off to the formation. We model
the turbulence in the PKN fracture using the Gaukler-Manning-Strickler
parametrization, which relates the the flow rate of the water to the pressure
gradient along the fracture. The key parameter in this relation is the
Darcy-Weisbach friction factor for the roughness of the crack wall. Coupling
this turbulence parametrization with conservation of mass allows us to write a
nonlinear pde for the crack width as a function of space and time. By way of a
similarity ansatz, we obtain a semi-analytical solution using an orthogonal
polynomial series. Embedding the asymptotic behavior near the fracture tip into
the polynomial series, we find very rapid convergence: a suitably accurate
solution is obtained with two terms of the series. This closed-form solution
facilitates clear comparisons between the results and parameters for laminar
and turbulent hydraulic fractures. In particular, it resolves one of the well
known problems whereby calibration of models to data has difficulty
simultaneously matching the hydraulic fracture length and wellbore pressure. | | Source: | arXiv, 1609.1237 | | Services: | Forum | Review | PDF | Favorites | |
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