Self-similar solution of a hydraulic fracture problem for a poroelastic medium

A solution of a coupled problem on the propagation of a hydraulic fracture (HF) with respect to the processes of deformation and flow in a poroelastic medium is considered. The fracture is formed and developed under the impact of a Newtonian fluid pumped into it through a well. The sets of self-simi...

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Bibliographic Details
Published in:Mathematical models and computer simulations 2017-11, Vol.9 (6), p.657-668
Main Authors: Karakin, A. V., Ramazanov, M. M., Borisov, V. E., Men’shov, I. S., Savenkov, E. B.
Format: Article
Language:English
Subjects:
Crack propagation
Deformation
Hydraulic fracturing
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Newtonian fluids
Self-similarity
Simulation and Modeling
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Summary:A solution of a coupled problem on the propagation of a hydraulic fracture (HF) with respect to the processes of deformation and flow in a poroelastic medium is considered. The fracture is formed and developed under the impact of a Newtonian fluid pumped into it through a well. The sets of self-similar solutions are constructed. These solutions are used to describe the evolution of a penny-shaped shallow fracture in a poroelastic medium with a uniform pressure inside the fracture. This work is a part of the HF publication series, which are based on splitting the original equations into components in accordance with the incomplete coupling principle.
ISSN:2070-0482
2070-0490
DOI:10.1134/S2070048217060060