Similarity solution of a penny-shaped fluid-driven fracture in a zero-toughness linear elastic solid

Savitski, Alexei A.; Detournay, Emmanuel

doi:10.1016/s1620-7742(01)01323-x

Cited by 7 publications

(10 citation statements)

References 5 publications

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“…where p ps denotes the plane strain limit of p(x) calculated using (31). Since, for the case of plane strain, the pressure is known and is given by (2), one may find h ∆σ by equating this plane strain pressure and (32) to obtain…”

Section: Approximate Non-local Elasticitymentioning

confidence: 99%

“…The implementation of the approximation for the non-local elastic interactions requires us to replace the procedure for calculating the pressure using (27) with the approximation given by (31). More details about numerical schemes for the P3D model with non-local elasticity and with this non-local elasticity approximation are given in the appendix.…”

Section: Approximate Non-local Elasticitymentioning

confidence: 99%

“…With regard to the numerical implementation, the pressure calculation using equation (31) requires the numerical evaluation of the two one-dimensional integrals. This is much more efficient than the numerical evaluation of the two-dimensional integral (27).…”

Section: Approximate Non-local Elasticitymentioning

confidence: 99%

“…The only difference between the P3D algorithm with an approximate non-local elasticity operator from the one described above, which includes full elasticity, lies in calculation of elasticity matrix C j in in (51). By approximating both h andw as piece-wise constant functions, equation (31) can be reduced to…”

Section: Computation Of W Conditionmentioning

confidence: 99%

“…First, since h < H in the tip region and only one ellipse is used to approximate the fracture width, w 1 (l(t j )ξ k , t j ) = 4H/(πh(l(t j )ξ k , t j ))w j k and w 2 = 0. Unfortunately, since ∂h/∂x in (31) is singular at the tip element (if a curved fracture tip is used), the piece-wise constant approximation for h precludes an accurate evaluation of the elasticity integral. To deal with this problem, we seek a correction that makes the elasticity integral accurate.…”

Section: Computation Of W Conditionmentioning

confidence: 99%

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An enhanced pseudo-3D model for hydraulic fracturing accounting for viscous height growth, non-local elasticity, and lateral toughness

Dontsov

Peirce

2015

Engineering Fracture Mechanics

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Please cite this article as: Dontsov, E.V., Peirce, A.P., An enhanced pseudo-3D model for hydraulic fracturing accounting for viscous height growth, non-local elasticity, and lateral toughness, Engineering Fracture Mechanics (2015), doi: http://dx. AbstractThe goal of this paper is to develop a more accurate pseudo-3D model for hydraulic fracturing. The primary weaknesses of the classical pseudo-3D model are: 1) its inability to capture viscous height growth, and 2) its failure to include lateral fracture toughness. These flaws are addressed respectively by: 1) introducing an apparent fracture toughness in the vertical direction, and 2) using an approximate non-local elasticity operator. To evaluate the accuracy and the level of improvement of the model we have developed, the results are compared to the predictions calculated using a recently developed fully planar hydraulic fracturing simulator.

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Section: Approximate Non-local Elasticitymentioning

confidence: 99%

Section: Approximate Non-local Elasticitymentioning

confidence: 99%

Section: Approximate Non-local Elasticitymentioning

confidence: 99%

Section: Computation Of W Conditionmentioning

confidence: 99%

Section: Computation Of W Conditionmentioning

confidence: 99%

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An enhanced pseudo-3D model for hydraulic fracturing accounting for viscous height growth, non-local elasticity, and lateral toughness

Dontsov

Peirce

2015

Engineering Fracture Mechanics

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Scaling laws for hydraulic fractures driven by a power‐law fluid in homogeneous anisotropic rocks

Dontsov¹

2018

Num Anal Meth Geomechanics

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Summary This study investigates parametric space of solutions for a planar hydraulic fracture propagating in a homogeneous anisotropic rock. It is assumed that the fracture has an elliptical shape and is driven by a power‐law fluid. The purpose of this study is to investigate the influence of anisotropy and power‐law fluid rheology on the parametric space of solutions. Rock anisotropy is represented by having two values of fracture toughness, one in the vertical direction and another one in the horizontal direction. Similarly, the effect of elastic anisotropy is approximated by using two different effective elastic moduli in the vertical and horizontal directions. In contrast to the isotropic case, for which there are four limiting solutions, the problem for anisotropic rocks features six different limiting cases. These cases represent competition between toughness and viscosity in the vertical and horizontal directions and competition between fluid storage inside the fracture and fluid leak‐off into formation. Approximate expressions for the limiting solutions are obtained using global volume balance and tip asymptotic solutions. Despite the developed solutions rely on a series of approximations, they precisely capture all the scaling laws associated with the problem. Zones of applicability of these limiting solutions are calculated, and their dependence on the problem parameters is investigated.

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Zhang

Detournay

Jeffrey

2002

International Journal of Fracture

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Similarity solution of a penny-shaped fluid-driven fracture in a zero-toughness linear elastic solid

Cited by 7 publications

References 5 publications

An enhanced pseudo-3D model for hydraulic fracturing accounting for viscous height growth, non-local elasticity, and lateral toughness

An enhanced pseudo-3D model for hydraulic fracturing accounting for viscous height growth, non-local elasticity, and lateral toughness

Scaling laws for hydraulic fractures driven by a power‐law fluid in homogeneous anisotropic rocks

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