Release:Releases Archive. Вестник ТюмГУ. Физико-математические науки. Информатика (№7, 2013)
About the author:Alexey V. Tatosov, Dr. Sci. (Phys.-Math.), Professor, Department of Fundamental Mathematics and Mechanics, University of Tyumen; firstname.lastname@example.org
Abstract:There has been a lot of domestic and foreign research done on the thories to develop hydraulic fracturing of oil formation. This technology is used to increase the production rate of wells. But the intensive operation of injection wells can lead to unintended fracturing. This paper describes the process of displacement of fluid from a porous medium by filing in another liquid in the new crack. For the purposes of the present research the oil formation is modeled as a cuboid of unlimited length. The hydraulic fracture is directed along its center seam. Initially the formation is saturated with a viscous fluid, the hydraulic fracturing is achieved with a less viscous liquid. It was believed that the internal pressure at the faces of the parallelepiped remains unchanged and equal to the original value. This may be due to the change of rock layers filter factors and their hydraulic geometry. It is shown that in some cases one can expect the expansion and subsequent contraction of cracks while maintaining the intensity of pumping.
1. Perkins, T.K., Kern, L.R. Widths of hydraulic fracturesю J. Petrol. Technol., Paper SPE 89. 1961. Vol. 13. № 9. Pp. 937-949.
2. Novackij, V. Teorija uprugosti [Elasticity Theory]. M.: Mir, 1975. 429 p. (in Russian).
3. Ivashnev, O.E., Smirnov, N.N. Hydrolytic crack development in porous media. Vestnik Moskovskogo universiteta — Moscow University Herald. Series 1. 2003. № 6. Pp. 28-36.
4. Tatosov A.V. Filling in proppant into the crack of hydrolytic fractures. Vestnik Tjumenskogo gosudarstvennogo universiteta — Tyumen State University Herald. 2004. № 4. Pp. 256-261.
5. Basniev, K.S., Kochina, I.N., Maksimov, V.M. Podzemnaja gidromehanika [Underground hydromechanics]. M.: Nedra, 1993. 414 p. (in Russian).
6. Entov, V.M., Zazovskij, A.F. Gidrodinamika processov povyshenija nefteotdachi [Hydrodynamics of the procedures aimed to increase well productivity]. M.: Nedra, 1989. 232 p. (in Russian).
7. Barenblatt, G.I., Entov, V.M., Ryzhik, V.M. Dvizhenie zhidkosti i gazov v prirodnyh plastah [Liquid and gaz movement in natural soil layers]. M.: Nedra, 1984. 530 p. (in Russian).
8. Landau, L.D., Lifshic, E.M. Gidrodinamika [Hydrodynmics]. M.: Fizmatlit, 2006. 731 p.
9. Lojcjanskij, L.G. Mehanika zhidkosti i gaza [Liquid and Gas Mechanics]. М.: Drofa, 2003. 847 p. (in Russian).
10. Sedov, L.I. Metody podobija i razmernosti v mehanike [Similarity and dimension in mechanics]. M.: Nauka, 1987. 430 p. (in Russian).