Nonlinear model of a porous body with fluid-driven fracture under cohesion contact conditions and fluid volume control Full article
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Mathematical Models and Methods in Applied Sciences
ISSN: 0218-2025 |
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| Output data | Year: 2025, Volume: 35, Number: 11, Pages: 2311-2328 Pages count : 18 DOI: 10.1142/s021820252550040x | ||||||||
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Abstract:
The quasi-static problem describes a nonlinear porous body with a non-penetrating Barenblatt’s crack driven by the fracturing fluid, and its propagation is under investigation. By this, a bulk modulus of the porous body depends linearly on the density, the fracture faces allow contact with cohesion, and leak-off of the fluid into reservoir is accounted by the model. The mathematical problem consists in finding time-continuous
functions of a displacement and a mean fluid pressure in the fracture, which satisfy the coupled system of the variational inequality and the fluid mass balance, which is controlled by the volume of fracking fluid pumped into the fracture. Well-posedness of the governing relations is proved rigorously by applying the method of Lagrange multipliers and using optimality conditions for the constrained minimization problem.
Cite:
Itou H.
, Kovtunenko V.A.
, Rajagopal K.R.
Nonlinear model of a porous body with fluid-driven fracture under cohesion contact conditions and fluid volume control
Mathematical Models and Methods in Applied Sciences. 2025. V.35. N11. P.2311-2328. DOI: 10.1142/s021820252550040x WOS Scopus РИНЦ OpenAlex
Nonlinear model of a porous body with fluid-driven fracture under cohesion contact conditions and fluid volume control
Mathematical Models and Methods in Applied Sciences. 2025. V.35. N11. P.2311-2328. DOI: 10.1142/s021820252550040x WOS Scopus РИНЦ OpenAlex
Identifiers:
| Web of science: | WOS:001530078500001 |
| Scopus: | 2-s2.0-105010906873 |
| Elibrary: | 82832015 |
| OpenAlex: | W4411286199 |