Advertisement

Lobachevskii Journal of Mathematics

, Volume 40, Issue 11, pp 1892–1896 | Cite as

Approach to Solving the Inverse Problem of Filtration Based on Descriptive Regularization

  • A. I. AbdullinEmail author
Article
  • 7 Downloads

Abstract

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.

Keywords and phrases

inverse problem nonlinear coefficient descriptive regularization filtration stress sensitive reservoir permeability 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    T. D. van Golf-Racht, Fundamentals of Fractured Reservoir Engineering (Elsevier Scientific, London, 1982).Google Scholar
  2. 2.
    V. N. Nikolaevsky, K. S. Basniev, A. T. Gorbunov, and G. A. Zotov, Mechanics of Saturated Porous Media (Nedra, Moscow, 1970) [in Russian].Google Scholar
  3. 3.
    J. E. Warren and P. J. Root, “The behavior of naturally fractured reservoir,” Soc. Pet. Eng. J. 03, 245–255 (1963).CrossRefGoogle Scholar
  4. 4.
    V. A. Morozov, N. L Goldman, and M. K. Samarin, “The method of descriptive regularization and the quality of approximate solutions,” Inzh.-Fiz. Zh. 6, 1117–1124 (1977).Google Scholar
  5. 5.
    V. A. Morozov, N. L Goldman, and V. A. Malyshev, “The method of descriptive regularization in inverse problems,” Inzh.-Fiz. Zh. 6 (65), 695–702 (1993).Google Scholar
  6. 6.
    M. Kh. Khairullin, M. N. Shamsiev, P. E. Morozov, and A. I. Abdullin, “Interpretation of the hydrodynamic studies of wells in fractured porous reservoir,” Geol. Geofiz. Razrab. Neft. Gaz. Mestorozhd. 1, 30–32 (2007).Google Scholar
  7. 7.
    M. Kh. Khairullin, M. N. Shamsiev, P. E. Morozov, and A. I. Abdullin, “Numerical solution of the coefficient inverse problem for a deformable fractured porous reservoir,” Mat. Model. 11 (20), 35–40 (2008).zbMATHGoogle Scholar
  8. 8.
    F. Kappel and A. V. Kuntsevich, “An implementation of Shor’s R-algorithm,” Comput. Optim. Appl. 2 (15), 193–205 (2000).MathSciNetCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Institute of Mechanics and Engineering, Kazan Scientific CenterRussian Academy of SciencesKazanRussia

Personalised recommendations