Geodesic
Modelling of hydraulic fracture in poroelastic medium
Matematičeskoe modelirovanie, Tome 18 (2006) no. 6, pp. 53-69

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At present the hydraulic fracture is the most effective and frequently used method. The modeling of this process is a serious problem and is very important for prognostication the operation efficiency. Calculation of local stressed state of porous media and liquid flows is necessary for the design hydraulic fracture. In this article the set of processes in the saturated porous media is considered according to the quasi-stationary Biot model, and the Coulomb–More criterion used for modeling the crack evolution. The geological medium is essentially non-homogeneous. The non-orthogonal and multiblock grids adapted to the formation structure are used and the support operator method is developed for the approximation of the Biot equations. 
@article{MM_2006_18_6_a4,
     author = {T. T. Garipov},
     title = {Modelling of hydraulic fracture in poroelastic medium},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {53--69},
     publisher = {mathdoc},
     volume = {18},
     number = {6},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2006_18_6_a4/}
}
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T. T. Garipov. Modelling of hydraulic fracture in poroelastic medium. Matematičeskoe modelirovanie, Tome 18 (2006) no. 6, pp. 53-69. http://geodesic.mathdoc.fr/item/MM_2006_18_6_a4/