Solids dispersion is an important part of hydraulic fracturing, both in helping to understand phenomena such as tip screen-out and spreading of the pad, and in new process variations such as cyclic pumping of proppant. Whereas many frac fluids have low viscosity, e.g. slickwater, others transport proppant through increased viscosity. In this context, one method for influencing both dispersion and solids-carrying capacity is to use a yield stress fluid as the frac fluid. We propose a model framework for this scenario and analyse one of the simplifications. A key effect of including a yield stress is to focus high shear rates near the fracture walls. In typical fracturing flows this results in a large variation in shear rates across the fracture. In using shear-thinning viscous frac fluids, flows may vary significantly on the particle scale, from Stokesian behaviour to inertial behaviour across the width of the fracture. Equally, according to the flow rates, Hele-Shaw style models give way at higher Reynolds number to those in which inertia must be considered. We develop a model framework able to include this range of flows, while still representing a significant simplification over fully three-dimensional computations. In relatively straight fractures and for fluids of moderate rheology, this simplifies into a one-dimensional model that predicts the solids concentration along a streamline within the fracture. We use this model to make estimates of the streamwise dispersion in various relevant scenarios. This model framework also predicts the transverse distributions of the solid volume fraction and velocity profiles as well as their evolutions along the flow part.
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Propagation of extended fractures by local nucleation and rapid transverse expansion of crack-front distortion
Fractures are ubiquitous and can lead to the catastrophic material failure of materials. Although fracturing in a two-dimensional plane is well understood, all fractures are extended in and propagate through three-dimensional space. Moreover, their behaviour is complex. Here we show that the forward propagation of a fracture front occurs through an initial rupture, nucleated at some localized position, followed by a very rapid transverse expansion at velocities as high as the Rayleigh-wave speed. We study fracturing in a circular geometry that achieves an uninterrupted extended fracture front and use a fluid to control the loading conditions that determine the amplitude of the forward jump. We find that this amplitude correlates with the transverse velocity. Dynamic rupture simulations capture the observations for only a high transverse velocity. These results highlight the importance of transverse dynamics in the forward propagation of an extended fracture.
more » « less- NSF-PAR ID:
- 10488238
- Publisher / Repository:
- Nature Publishing Group
- Date Published:
- Journal Name:
- Nature Physics
- Volume:
- 20
- Issue:
- 4
- ISSN:
- 1745-2473
- Format(s):
- Medium: X Size: p. 660-665
- Size(s):
- ["p. 660-665"]
- Sponsoring Org:
- National Science Foundation
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Hydraulic fracturing can be recognized as an emerging method used in the mining of heat in Enhanced Geothermal Systems as well as in the extraction of oil and gas entrapped within shale formations. While there are several experimental studies focusing on the initiation and propagation of hydraulically-induced fractures under uniaxial and biaxial loading conditions, a very limited number of experimental studies investigate the effect of triaxial loading conditions on fracture initiation and propagation. This study describes an experimental setup, which was designed to allow one to independently apply and control three orthogonal stresses in prismatic granite specimens while simultaneously applying a hydraulic pressure inside pre-fabricated flaws. Moreover, the test setup allows one to observe and subsequently interpret the fracturing processes through visual and acoustic emission (AE) monitoring. The observations obtained in the current study using a triaxial state of stress were interpreted and compared with existing experimental studies that used other states of stress. It was observed that whitening of some grains and high-amplitude AE events occurred where visible cracks eventually developed for the triaxial state of stress investigated. Comparison with previous studies, in which only vertical loads (uniaxial) were applied, shows that the aperture of the hydraulically-induced fractures for the triaxial condition is significantly smaller than for the uniaxial loadings and that the coalescence patterns are, in general, stress-state-dependent. In terms of AE data, the total number of AE events in the specimens subject to triaxial stresses were significantly higher than in the tests using uniaxial stresses, even though most of the events (65%) had a relatively low-amplitude (<50dB) in contrast to the uniaxial tests, in which low-amplitude events were typically less than 50%.more » « less
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