A semi-infinite hydraulic fracture driven by a shear-thinning fluid

Brice Tanguy Alphonse Lecampion, Fatima-Ezzahra Moukhtari
Cambridge University Press, 2018
Article

Résumé

We use the Carreau rheological model which properly accounts for the shear-thinning behaviour between the low and high shear rate Newtonian limits to investigate the problem of a semi-infinite hydraulic fracture propagating at a constant velocity in an impermeable linearly elastic material. We show that the solution depends on four dimensionless parameters: a dimensionless toughness (function of the fracture velocity, confining stress, material and fluid parameters), a dimensionless transition shear stress (related to both fluid and material behaviour), the fluid shear-thinning index and the ratio between the high and low shear rate viscosities. We solve the complete problem numerically combining a Gauss–Chebyshev method for the discretization of the elasticity equation, the quasi-static fracture propagation condition and a finite difference scheme for the width-averaged lubrication flow. The solution exhibits a complex structure with up to four distinct asymptotic regions as one moves away from the fracture tip: a region governed by the classical linear elastic fracture mechanics behaviour near the tip, a high shear rate viscosity asymptotic and power-law asymptotic region in the intermediate field and a low shear rate viscosity asymptotic far away from the fracture tip. The occurrence and order of magnitude of the extent of these different viscous asymptotic regions are estimated analytically. Our results also quantify how shear thinning drastically reduces the size of the fluid lag compared to a Newtonian fluid. We also investigate simpler rheological models (power law, Ellis) and establish the small domain where they can properly reproduce the response obtained with the complete rheology.

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https://infoscience.epfl.ch/record/234541?ln=fr

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Brice Tanguy Alphonse Lecampion, Fatima-Ezzahra Moukhtari
Cambridge University Press, 2018
Article

Résumé

Official source

https://infoscience.epfl.ch/record/234541?ln=fr

À propos de ce résultat

Concepts associés (14)

Concepts associés

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Publications associées (5)

Publications associées

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The tip region of a hydraulic fracture driven by a power law fluid

Brice Tanguy Alphonse Lecampion, Fatima-Ezzahra Moukhtari

We investigate the tip region of a hydraulic fracture driven by a power law fluid propagating at a constant velocity V in an impermeable linear elastic medium. We account for the presence of a fluid lag of a priori unknown length at the tip of the fracture. The fluid pressurized fracture propagates perpendicular to the far-field compressive minimum stress in pure opening mode (see Fig.1a). The solution of this semi-infinite hydraulic fracture problem combines elastic deformation, lubrication flow in the filled region of the fracture and the quasi-static fracture propagation condition. It exhibits a multiscale structure related to the strong fluid solid coupling at play near the fracture tip. For a Newtonian fluid, the solution derived by Garagash & Detournay (2000) transition from the classical linear elastic fracture mechanics asymptote near the tip to the viscous asymptote (Desroches et al., 1994) away from the tip (see Fig.1b). The fluid lag was shown to vanish for large values of a dimensionless fracture toughness encapsulating all the problem parameters.

2016

Chargement

We investigate the tip region of a hydraulic fracture driven by a power law fluid propagating at a constant velocity in an impermeable linear elastic isotropic medium. We account for the presence of a fluid lag of a priori unknown length at the tip of the fracture. The fluid pressurized fracture propagates perpendicular to the far-field compressive minimum stress in pure opening mode. The solution of this semi-infinite hydraulic fracture problem combines elastic deformation, lubrication flow in the filled region of the fracture and the quasi-static equilibrium fracture propagation condition. It exhibits a multiscale structure related to the strong fluid solid coupling at play near the fracture tip. For a Newtonian fluid, the solution derived by Garagash & Detournay (2000) transition from the classical linear elastic fracture mechanics asymptote near the fracture tip to the viscous asymptote (Desroches et al., 1994) away from the tip. The fluid lag was shown to vanish for large values of a dimensionless fracture toughness encapsulating all the problem parameters (viscosity, fracture velocity, plane- strain elastic modulus).

2017

Chargement

Geophysical gravity flows such as avalanches and debris flows belong to a special class of hazardous environmental event, in which a mixture of solids and fluids (e.g. debris and mud, snow and air) flow as a liquid and may run out much further than expected over a slope less steep than the critical angle of repose. Exchange of material between the overriding flow and a loose bed layer underneath is known to affect the characteristics of such a flow however it is not well understood how this plays a part, nor the mechanism of such an exchange, due to the difficulties of seeing inside a flowing mass in the field and experiments. Research has been carried out on an entraining viscous gravity current in an laboratory flume using Particle Image Velocimetry. The aim was to investigate the flow properties in a vertical slice of fluid in the downstream direction, far from the side-walls, when a flowing layer overrides a basal layer of the same material. The parameter varied here is the volume of fluid released from the reservoir, which affects the height and velocity of the encroaching fluid current. An interface was identified between the overriding fluid and the initially stationary bed fluid. PIV was used to show the evolution of the velocity and shear fields throughout the system compared to the location of this interface and how this changes with the volume of fluid released. The overriding fluid displaces the bed fluid, either by plunging or spilling into the erodible layer depending on the initial volume, thus inciting the stationary material downstream and below to move. Initially, a large amount of bed material is suddenly mobilized by the front of overriding fluid and little deposition occurs. Shortly after this we see the clear development of a depositional region (with low velocities, predominantly in the downwards direction) and an eroding region (with high, almost uniformly horizontal velocities) within the front of material that enters the bed, separated by a region of high shear. For larger released volumes, multiple shear bands develop, thus showing distinct regions with different rates of material deposition.

2012

Chargement

2012