Geodesic
The incomplete coupling problem of hydraulic fracturing equations
Matematičeskoe modelirovanie, Tome 29 (2017) no. 6, pp. 115-134

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We consider a problem of evolution of the state of poroelastic media coupled with slow motions of the viscous fluid inside hydraulic fracture in 3D setting. The fluid flow is induced by injection of fluid into the fracture. The fluid flow is described using Reynolds lubrication equations. External poroelasric media is governed by Biot poroelasticity equations. We analyze interplay of the different geomechanical processes in the media and the fracture using asymptotic framework. As a result, it is shown that the complete coupled problem can be reduced to the three one-way coupled problems which can be solved sequentially. The approach allows to analyze certain process related to the hydraulic fracture analysis as well as some other ones. At the same time the approach provides theoretical background for construction of new physically-based iterative and preconditioning techniques suitable for solution of the complete coupled problem.
Keywords: hydraulic fracture problem, poroelastic medium, equilibrium crack, incomplete coupling principle. 
@article{MM_2017_29_6_a7,
     author = {A. V. Karakin and M. M. Ramazanov and V. E. Borisov},
     title = {The incomplete coupling problem of hydraulic fracturing equations},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {115--134},
     publisher = {mathdoc},
     volume = {29},
     number = {6},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2017_29_6_a7/}
}
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A. V. Karakin; M. M. Ramazanov; V. E. Borisov. The incomplete coupling problem of hydraulic fracturing equations. Matematičeskoe modelirovanie, Tome 29 (2017) no. 6, pp. 115-134. http://geodesic.mathdoc.fr/item/MM_2017_29_6_a7/