TY - JOUR

T1 - On the layer crossing problem for a semi-infinite hydraulic fracture

AU - Valov, A.V.

AU - Dontsov, E.V.

N1 - The authors would like to thank Dr. S.V. Golovin and A.N. Baykin for useful discussions at the inception of this project.

PY - 2023/12/1

Y1 - 2023/12/1

N2 - This paper analyses the problem of a semi-infinite fluid-driven fracture propagating through multiple stress layers in a permeable elastic medium. Such a problem represents the tip region of a planar hydraulic fracture. When the hydraulic fracture crosses a stress layer, the use of a standard tip asymptotic solution may lead to a considerable reduction of accuracy, even for the simplest case of a height-contained fracture. In this study, we propose three approaches to incorporate the effect of stress layers into the tip asymptote: non-singular integral formulation, toughness-corrected asymptote, and an ordinary differential equation approximation of the non-singular integral formulation mentioned above. As illustrated in the paper, these approaches for stress-corrected asymptotes differ in computational complexity, the complexity of implementation, and the accuracy of the approximation. In addition, the size of the validity region of the stress-corrected asymptote is evaluated, and it is shown to be greatly reduced relative to the case without layers. In order to address the issue, the stress relaxation factor is introduced. This, in turn, allows for enhancing the accuracy of the layer-crossing computation on a relatively coarse mesh to utilize the stress-corrected asymptote in hydraulic fracturing simulators for the purpose of front tracking.

AB - This paper analyses the problem of a semi-infinite fluid-driven fracture propagating through multiple stress layers in a permeable elastic medium. Such a problem represents the tip region of a planar hydraulic fracture. When the hydraulic fracture crosses a stress layer, the use of a standard tip asymptotic solution may lead to a considerable reduction of accuracy, even for the simplest case of a height-contained fracture. In this study, we propose three approaches to incorporate the effect of stress layers into the tip asymptote: non-singular integral formulation, toughness-corrected asymptote, and an ordinary differential equation approximation of the non-singular integral formulation mentioned above. As illustrated in the paper, these approaches for stress-corrected asymptotes differ in computational complexity, the complexity of implementation, and the accuracy of the approximation. In addition, the size of the validity region of the stress-corrected asymptote is evaluated, and it is shown to be greatly reduced relative to the case without layers. In order to address the issue, the stress relaxation factor is introduced. This, in turn, allows for enhancing the accuracy of the layer-crossing computation on a relatively coarse mesh to utilize the stress-corrected asymptote in hydraulic fracturing simulators for the purpose of front tracking.

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85176961910&origin=inward&txGid=edcfa5da4b8d1a24ba5c46b19e58d3c4

UR - https://www.mendeley.com/catalogue/920cc0d3-6da6-3da2-80bb-3bedd5d9d218/

U2 - 10.1016/j.engfracmech.2023.109730

DO - 10.1016/j.engfracmech.2023.109730

M3 - Article

VL - 293

JO - Engineering Fracture Mechanics

JF - Engineering Fracture Mechanics

SN - 0013-7944

M1 - 109730

ER -