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


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Abstract

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.

About the authors

A. V. Karakin

Keldysh Institute of Applied Mathematics; Oil and Gas Research Institute

Author for correspondence.
Email: avkarakin@gmail.com
Russian Federation, Moscow; Moscow

M. M. Ramazanov

Keldysh Institute of Applied Mathematics; Institute for Geothermal Problems, Dagestan Scientific Center

Email: avkarakin@gmail.com
Russian Federation, Moscow; Makhachkala

V. E. Borisov

Keldysh Institute of Applied Mathematics

Email: avkarakin@gmail.com
Russian Federation, Moscow

I. S. Men’shov

Keldysh Institute of Applied Mathematics

Email: avkarakin@gmail.com
Russian Federation, Moscow

E. B. Savenkov

Keldysh Institute of Applied Mathematics

Email: avkarakin@gmail.com
Russian Federation, Moscow

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