Geodesic
The analytical investigation of hydraulic fracture dynamics according to the incomplete coupling principle
Matematičeskoe modelirovanie, Tome 29 (2017) no. 11, pp. 3-18

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In the paper we present a self-similar solution of the coupling problem about slow movement in the hydraulic fracture and corresponding deformation and fluid percolation in the external medium. These movements are generated with fluid uploading into well. The flow in a crack is described with the hydrodynamics Stokes equations in the approach of the lubricating layer. The outer problem is described with the poroelasticity equations. We consider an option of the heterogeneous pressure into a crack in three- and two-dimensions. In the second case one can have the self-similar solution in the analytical form.
Keywords: hydraulic fracture problem, self-similar solution, incomplete coupling principle, equilibrium crack. 
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     author = {M. M. Ramazanov and A. V. Karakin and V. E. Borisov},
     title = {The analytical investigation of hydraulic fracture dynamics according to the incomplete coupling principle},
     journal = {Matemati\v{c}eskoe modelirovanie},
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M. M. Ramazanov; A. V. Karakin; V. E. Borisov. The analytical investigation of hydraulic fracture dynamics according to the incomplete coupling principle. Matematičeskoe modelirovanie, Tome 29 (2017) no. 11, pp. 3-18. http://geodesic.mathdoc.fr/item/MM_2017_29_11_a0/