The Impact of the Near-Tip Logic on the Accuracy and Convergence Rate of Hydraulic Fracture Simulators Compared to Reference Solutions

Lecampion, Brice; Peirce, Anthony; Detournay, Emmanuel; Zhang, Xi; Chen, Zuorong; Bunger, Andrew P.; Detournay, Christine; Napier, J.A.L.; Abbas, Safdar; Garagash, Dmitry I.; Cundall, P.A.

doi:10.5772/56212

Cited by 35 publications

(48 citation statements)

References 20 publications

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“…This allows one to conclude that the accuracy of the computations by the universal algorithm is related to the type of problem being analyzed. We believe that this feature is not unique to the proposed scheme, as similar trends were reported in [32,38,68]. Fig.…”

Section: Pkn Modelsupporting

confidence: 81%

“…As a consequence of (56), the qualitative asymptotic behaviour of the pertinent spatial functions remains the same as their time-dependent counterparts (i.e.ŵ(x) complies with (38),v with (39) andφ with (50)). The elasticity equation (23) is converted to:…”

Section: Representation Of the Solutionmentioning

confidence: 85%

“…While computing the respective integrals in (75) - (77), it is crucial to preserve the appropriate asymptotic behaviour of the integrands, resulting from (38) and (50). Hence,ŵ (j) computed at this stage satisfies the respective elasticity relation and boundary condition (69) 1 through the regularized boundary condition:…”

Section: Numerical Realization Of the Algorithm For The Self-similar mentioning

confidence: 99%

“…It is well known that the small toughness case constitutes an extremely challenging computational problem due to the immense reduction of the process zone [38]. It necessitates special measures to stabilize the computations and preserve the solution accuracy, which results in an appreciable increase in the computational cost (in comparison with a moderate toughness case, the solution time was 100 times higher).…”

Section: Kgd Model: Small Toughness Casementioning

confidence: 99%

“…All these factors clearly indicate that a proper understanding of the solution structure and the correct application of the tip asymptotics in the computational schemes are crucial for the accuracy, credibility and robustness of computations. In the recent paper by Lecampion et al [38] it was shown that the algorithms which utilize the appropriate multiscale hydraulic fracture tip asymptote perform much better than those that do not apply it. The advantages of employing enhanced asymptotic representation in the numerical algorithm have been demonstrated in [17,27,30] (special tip element), [2,8,21,22,23,37,67] (BEM and XFEM formulations).…”

Section: Introductionmentioning

confidence: 99%

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Universal hydrofracturing algorithm for shear-thinning fluids: Particle velocity based simulation

Perkowska

Wróbel

Mishuris

2016

Computers and Geotechnics

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A universal particle velocity based algorithm for simulating hydraulic fractures, previously proposed for Newtonian fluids, is extended to the class of shear-thinning fluids. The scheme is not limited to any particular elasticity operator or crack propagation regime. The computations are based on two dependent variables: the crack opening and the reduced particle velocity. The application of the latter facilitates utilization of the local condition of Stefan type (speed equation) to trace the fracture front. The condition is given in a general explicit form which relates the crack propagation speed (and the crack length) to the solution tip asymptotics. The utilization of a modular structure, and the adaptive character of its basic blocks, result in a flexible numerical scheme. The computational accuracy of the proposed algorithm is validated against a number of analytical benchmark solutions.

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Section: Pkn Modelsupporting

confidence: 81%

Section: Representation Of the Solutionmentioning

confidence: 85%

Section: Numerical Realization Of the Algorithm For The Self-similar mentioning

confidence: 99%

Section: Kgd Model: Small Toughness Casementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Universal hydrofracturing algorithm for shear-thinning fluids: Particle velocity based simulation

Perkowska

Wróbel

Mishuris

2016

Computers and Geotechnics

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The Tipping Point

Peirce¹

2022

Mechanics of Hydraulic Fracturing

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The influence of pumping parameters in fluid‐driven fractures in weak porous formations

Sarris

Papanastasiou

2014

Num Anal Meth Geomechanics

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SUMMARYIn this work, we investigate the main pumping parameters that influence a fluid-driven fracture in cohesive poroelastic and poroelastoplastic weak formations. These parameters include the fluid viscosity and the injection rate. The first parameter dominates in the mapping of the propagation regimes from toughness to viscosity, whereas the second parameter controls the storage to leak-off dominated regime through diffusion.The fracture is driven in weak permeable porous formation by injecting an incompressible viscous fluid at the fracture inlet assuming that the fracture propagates under plane strain conditions. Fluid flow in the fracture is modeled by lubrication theory. Pore fluid movement in the porous formation is based on the Darcy law. The coupling follows the Biot theory, whereas the irreversible rock deformation is modeled with the Mohr-Coulomb yield criterion with associative flow rule. Fracture propagation criterion is based on the cohesive zone approach. Leak-off is also considered. The investigation is performed numerically with the FEM to obtain the fracture opening, length, and propagation pressure versus time.We demonstrate that pumping parameters influence the fracture geometry and fluid pressures in weak formations through the viscous fluid flow and the diffusion process that create back stresses and large plastic zones as the fracture propagates. It is also shown that the product of the propagation velocity and fluid viscosity, μv that appears in the scaling controls the magnitude of the plastic zones and influences the net pressure and fracture geometry. These findings may explain partially the discrepancies in net pressures between field measurements and conventional model predictions for the case of weak porous formation.

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The Impact of the Near-Tip Logic on the Accuracy and Convergence Rate of Hydraulic Fracture Simulators Compared to Reference Solutions

Cited by 35 publications

References 20 publications

Universal hydrofracturing algorithm for shear-thinning fluids: Particle velocity based simulation

Universal hydrofracturing algorithm for shear-thinning fluids: Particle velocity based simulation

The Tipping Point

The influence of pumping parameters in fluid‐driven fractures in weak porous formations

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