A semi-infinite hydraulic fracture propagating in a poroelastic medium
Abstract
We solve the near-tip coupled hydromechanical problem of a hydraulic fracture propagating in a permeable poroelastic medium, represented locally as a semi-infinite crack moving at constant velocity. In the moving tip frame, all fracture fields are steady. The porous solid obeys linear poroelasticity, fracture propagation follows LEFM, fluid flow within the tensile fracture is governed by lubrication theory, and the fracturing and pore fluids are treated as identical Newtonian liquids. The primary unknowns are the fracture opening and the fluid displacement function along the fracture, determined from the resulting non-linear system of equations. In a viscosity--toughness scaling, the problem depends on four dimensionless parameters: a dimensionless permeability ϱ (associated with the intensity of fluid leak-in), a dimensionless effective confining stress Σ0' (measuring the relative importance of fluid leak-off and leak-in), the drained--undrained Poisson's ratio contrast β, and the poroelastic stress coefficient η. The solution evolves from a drained, toughness-dominated near-tip asymptote with uniform net pressure to an undrained, storage-viscosity-dominated far-field asymptote. Numerical solutions are obtained over parameter ranges representative of various rock types. The fully coupled model is compared with simplified models, namely uncoupled and one-way coupled formulations, over distances from the fracture front spanning laboratory-to-field scales. The resulting relative difference maps in the (ϱ,Σ0') parameter space identify four characteristic regimes: negligible poroelastic effects, dominance of the direct mechanical poroelastic response, importance of the poroelastic backstress, and a fully coupled regime. The latter occurs mainly at large ϱ and small Σ0', corresponding to strong leak-in relative to leak-off.
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BibTeX
@misc{kanin2026semiinfinite,
title = {{A semi-infinite hydraulic fracture propagating in a poroelastic medium}},
author = {Evgenii Kanin and Andreas Möri and Dmitry Garagash and Brice Lecampion},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.14049},
eprint = {2610.14049},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.14049},
}
RIS
TY - UNPB
TI - A semi-infinite hydraulic fracture propagating in a poroelastic medium
AU - Evgenii Kanin
AU - Andreas Möri
AU - Dmitry Garagash
AU - Brice Lecampion
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.14049
UR - https://arxiv.org/abs/2610.14049
AB - We solve the near-tip coupled hydromechanical problem of a hydraulic fracture propagating in a permeable poroelastic medium, represented locally as a semi-infinite crack moving at constant velocity. In the moving tip frame, all fracture fields are steady. The porous solid obeys linear poroelasticity, fracture propagation follows LEFM, fluid flow within the tensile fracture is governed by lubrication theory, and the fracturing and pore fluids are treated as identical Newtonian liquids. The primary unknowns are the fracture opening and the fluid displacement function along the fracture, determined from the resulting non-linear system of equations. In a viscosity--toughness scaling, the problem depends on four dimensionless parameters: a dimensionless permeability ϱ (associated with the intensity of fluid leak-in), a dimensionless effective confining stress Σ_0' (measuring the relative importance of fluid leak-off and leak-in), the drained--undrained Poisson's ratio contrast β, and the poroelastic stress coefficient η. The solution evolves from a drained, toughness-dominated near-tip asymptote with uniform net pressure to an undrained, storage-viscosity-dominated far-field asymptote. Numerical solutions are obtained over parameter ranges representative of various rock types. The fully coupled model is compared with simplified models, namely uncoupled and one-way coupled formulations, over distances from the fracture front spanning laboratory-to-field scales. The resulting relative difference maps in the (ϱ,Σ_0') parameter space identify four characteristic regimes: negligible poroelastic effects, dominance of the direct mechanical poroelastic response, importance of the poroelastic backstress, and a fully coupled regime. The latter occurs mainly at large ϱ and small Σ_0', corresponding to strong leak-in relative to leak-off.
ER -