Geodesic
2D step-by-step model of hydrofracturing
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 11 (2011) no. 3, pp. 36-60

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The 2D model of hydraulic fracture propagation is proposed. The model describes simultaneously stress-strained state of the rock near bore hole and fracture, fluid flow and leakage in the fracture and direction of fracture propagation. Effective numerical algorithm for step-by-step simulation of the hydraulic fracture propagation is built. The algorithm joins together these three different subproblems. Analysis of the influence of model parameters on the solution is carried out. The dependences of fracture trajectory, pressure and fracture opening on configuration of perforations, pump rate and fluids rheology are obtained. It is established that the strong fracture trajectory deformation, caused by the deviation of perforation from the direction across the smallest in-situ principal stress, leads to fracture pinching. Theis effect considerably increases pressure in the bore hole.
Keywords: hydrofracturing, non-Newtonian fluid, nonlinear problem.
Mots-clés : fracture propagation 
@article{VNGU_2011_11_3_a2,
     author = {O. P. Alekseenko and D. V. Esipov and D. S. Kuranakov and V. N. Lapin and S. G. Cherny},
     title = {2D step-by-step model of hydrofracturing},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {36--60},
     publisher = {mathdoc},
     volume = {11},
     number = {3},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2011_11_3_a2/}
}
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O. P. Alekseenko; D. V. Esipov; D. S. Kuranakov; V. N. Lapin; S. G. Cherny. 2D step-by-step model of hydrofracturing. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 11 (2011) no. 3, pp. 36-60. http://geodesic.mathdoc.fr/item/VNGU_2011_11_3_a2/