Geodesic
Modeling of unsteady filtration in a formation–hydraulic fracture system
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 77 (2022), pp. 158-168 Cet article a éte moissonné depuis la source Math-Net.Ru

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This paper presents the results of modeling of unsteady fluid filtration in the formation penetrated by a well, which intersects a vertical hydraulic fracture throughout the entire thickness of the formation. The model of a bilinear fluid flow in a formation vertical hydraulic fracture system is considered in the case when the horizontal extent of the formation is considered to be infinite, and the fracture is of a finite length. The bilinearity of the flow means that in the formation–fracture system there are two mutually perpendicular fluid flows: from the formation to the fracture and along the fracture to the well. The analytical solution to a system of equations describing fluid filtration in the formation and fracture is obtained using the Laplace transform method. Analyzing the derived solution, main characteristic features of the filtration in the formation–fracture system are determined.
Mots-clés : formation
Keywords: hydraulic fracture, unsteady filtration, analytical solution, Laplace transform method, pressure distribution, well flow rate. 
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     title = {Modeling of unsteady filtration in a formation{\textendash}hydraulic fracture system},
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I. L. Khabibullin; A. A. Khisamov. Modeling of unsteady filtration in a formation–hydraulic fracture system. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 77 (2022), pp. 158-168. http://geodesic.mathdoc.fr/item/VTGU_2022_77_a11/

[1] Kanevskaya R.D., Matematicheskoe modelirovanie razrabotki mestorozhdenii nefti i gaza s primeneniem gidravlicheskogo razryva plasta, Nedra-Biznestsentr, M., 1999, 212 pp.

[2] Cinco-Ley H., Samaniego-V. F., “Transient Pressure Analysis for Fractured Wells”, j. Pet. Tech., 9 (1981), 1749–1766 | DOI

[3] Cinco-Ley H., Samaniego-V. F., Dominguez A.N., “Transient Pressure Behavior for a Well with a Finite-Conductivity Vertical Fracture”, Soc. Pet. Eng. J., 18:04 (1978), 253–264 | DOI

[4] Nagaeva Z.M., Shagapov V.Sh., “Ob uprugom rezhime filtratsii v treschine, raspolozhen noi v neftyanom ili gazovom plaste”, Prikladnaya matematika i mekhanika, 81:3 (2017), 319–329 | MR

[5] Khabibullin I.L., Khisamov A.A., “Nestatsionarnaya filtratsiya v plaste s treschinoi gidrorazryva”, Izvestiya Rossiiskoi akademii nauk. Mekhanika zhidkosti i gaza, 2019, no. 5, 6–14

[6] Khabibullin I.L., Khisamov A.A., “Modelirovanie nestatsionarnoi filtratsii vokrug skvazhiny s vertikalnoi treschinoi gidrorazryva”, Vestnik Bashkirskogo universiteta, 22:2 (2017), 309–313

[7] Khabibullin I.L., Khisamov A.A., “K teorii bilineinogo rezhima filtratsii v plastakh s treschinami gidrorazryva”, Vestnik Bashkirskogo universiteta, 23:4 (2018), 958–963

[8] Dech G., Rukovodstvo k prakticheskomu primeneniyu preobrazovaniya Laplasa, Nauka, M., 1971, 288 pp.

[9] Beitmen G., Erdeii P., Tablitsy integralnykh preobrazovanii, v. 1, Nauka, M., 1969

[10] Basniev K.S., Dmitriev N.M., Rozenberg G.D., Neftegazovaya gidromekhanika, In-t kompyuternykh issled, M.–Izhevsk, 2005, 544 pp. | MR