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Approach to solving the inverse problem of filtration based on descriptive regularization. (English) Zbl 1439.35554
Summary: This paper presents the results of a study of inverse problem for the nonlinear parabolic equation for the fluid filtration in the fractured media. An approach to solve the inverse problem by using the descriptive regularization method is proposed. A mathematical model for the 3-D flow of a fluid through a pressure sensitive naturally fractured formation, with pseudosteady state matrix-fracture flow is developed. This model includes the effects of wellbore storage and fluid flow in the wellbore. A computational algorithm based on the proposed approach to estimate the dependence of the fractures permeability on pressure from the results of hydrodynamic studies of horizontal well is developed.

35R30 Inverse problems for PDEs
35Q35 PDEs in connection with fluid mechanics
35K59 Quasilinear parabolic equations
76S05 Flows in porous media; filtration; seepage
Full Text: DOI
[1] T. D. van Golf-Racht, Fundamentals of Fractured Reservoir Engineering (Elsevier Scientific, London, 1982).
[2] V. N. Nikolaevsky, K. S. Basniev, A. T. Gorbunov, and G. A. Zotov, Mechanics of Saturated Porous Media (Nedra, Moscow, 1970) [in Russian].
[3] Warren, J. E.; Root, P. J., The behavior of naturally fractured reservoir, Soc. Pet. Eng. J., 03, 245-255 (1963)
[4] Morozov, V. A.; Goldman, N. L.; Samarin, M. K., The method of descriptive regularization and the quality of approximate solutions, Inzh.-Fiz. Zh., 6, 1117-1124 (1977)
[5] Morozov, V. A.; Goldman, N. L.; Malyshev, V. A., The method of descriptive regularization in inverse problems, Inzh.-Fiz. Zh., 6, 695-702 (1993)
[6] Khairullin, M. Kh; Shamsiev, M. N.; Morozov, P. E.; Abdullin, A. I., Interpretation of the hydrodynamic studies of wells in fractured porous reservoir, Geol. Geofiz. Razrab. Neft. Gaz. Mestorozhd., 1, 30-32 (2007)
[7] Khairullin, M. Kh; Shamsiev, M. N.; Morozov, P. E.; Abdullin, A. I., Numerical solution of the coefficient inverse problem for a deformable fractured porous reservoir, Mat. Model., 11, 35-40 (2008) · Zbl 1164.76397
[8] Kappel, F.; Kuntsevich, A. V., An implementation of Shor’s R-algorithm, Comput. Optim. Appl., 2, 193-205 (2000) · Zbl 0947.90112
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