Solving the Buckley-Leverett equation with a random coefficient of porosity


  • A.V. Isaeva Lomonosov Moscow State University
  • M.L. Serdobolskaya Lomonosov Moscow State University


Buckley-Leverett equation, geostatistics, hybrid difference schemes


The Buckley-Leverett equation with a random coefficient of porosity is considered. In order to analyze the equation, a combination of analytical (the method of characteristics) and numerical (upwind and hybrid difference schemes) approaches is used. An explicit expression for the stochastic characteristics of the Buckley-Leverett equation is obtained. The statistical parameters of breakthrough time are considered. A comparison between the analytical estimates and the numerical results is discussed.

Author Biographies

A.V. Isaeva

M.L. Serdobolskaya


  1. Баренблатт Г.И., Ентов В.М., Рыжик В.М. Движение жидкостей и газов в природных пластах. M.: Недра, 1984.
  2. Trangenstein J.A. Numerical solution of hyperbolic partial differential equations. Cambridge: Cambridge Univ. Press, 2007.
  3. Андерсон Д., Таннехилл Дж., Плетчер Р. Вычислительная гидромеханика и теплообмен. 1. М.: Мир, 1990.
  4. Петров И.Б., Лобанов А.И. Лекции по вычислительной математике. М.: БИНОМ, 2006.
  5. LeVeque R.J. Finite-volume methods for hyperbolic problems. Cambridge: Cambridge Univ. Press, 2004.
  6. Zhang D., Tchelepi H. Stochastic analysis of immiscible two-phase flow in heterogeneous media // SPE Journal. 1999. 4, N 4. 380-388.
  7. Li H., Zhang D. Efficient and accurate quantification of uncertainty for multiphase flow with the probabilistic collocation method // SPE Journal. 2009. 14, N 4. 665-679.
  8. Владимиров В.С. Уравнения математической физики. М.: Наука, 1981.
  9. Amyx A., Bass D., Whiting R. Petroleum reservoir engineering. New York: McGraw-Hill, 1960.
  10. Deutsch C.V. Geostatistical reservoir modeling. Oxford: Oxford Univ. Press, 2002.



How to Cite

Исаева А., Сердобольская М. Solving the Buckley-Leverett Equation With a Random Coefficient of Porosity // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2012. 13. 517-524



Section 1. Numerical methods and applications