Application of parallel algorithms for solving the problem of fluid flow to wells with complicated configurations in fractured porous reservoirs


  • D.A. Gubajdullin Institute of Mechanics and Engineering - Subdivision of «Kazan Scientific Center of RAS»
  • R.V. Sadovnikov Institute of Mechanics and Engineering - Subdivision of «Kazan Scientific Center of RAS»


параллельные вычисления, моделирование фильтрации, пористые среды, анизотропия коэффициента проницаемости, неструктурированные сетки, численные методы


The questions related to solving the problems of fluid flow to wells with different trajectories (vertical, inclined, horizontal, etc.) on high performance computers are considered. The finite element method is used on unstructured grids of tetrahedrons. The resulting system of linear algebraic equations is solved with the use of the Aztec parallel iterative library that includes a number of Krylov iterative methods with different preconditioners on the basis of the MPI-technology.

Author Biographies

D.A. Gubajdullin

R.V. Sadovnikov


  1. Воеводин В.В., Воеводин Вл.В. Параллельные вычисления. СПб: БХВ-Петербург, 2002.
  2. Peaceman D.W. Interpretation of wellblock pressures in numerical reservoir simulation // SPEJ. June 1978. 183-194.
  3. Wolfsteiner С., Aziz K., Durlofsky L.J. Modeling conventional and non-conventional wells // The Sixth International Forum on Reservoir Simulation. Hof/Salzburg Austria, September 3-7, 2001.
  4. Баренблатт Г.И., Желтов Ю.П., Кочина И.М. Об основных представлениях теории фильтрации однородных жидкостей в трещиноватых породах // Прикл. матем. и механ. 1960. 123, № 3. 852-864.
  5. Aztec. A Massively Parallel Iterative Solver Library for Solving Sparse Linear Systems // (
  6. Warren J., Root P. The behavior of naturally fractured reservoir simulation // SPEJ. Feb. 1983. 42-54.
  7. Желтов Ю.П. Разработка нефтяных месторождений. М.: Недра, 1986.
  8. Schneiders R. Mesh generation & grid generation on the Web // ( roberts/meshgeneration.html).
  9. Frey P.J., George P.-L. Mesh generation. Application to finite elements. Oxford: Hermes Science Publishing, 2000.
  10. Hendrickson B., Leland R. The Chaco user’s guide - version 1.0. Technical Report Sand93-2339. Sandia National Laboratories. Albuquerque. August, 1993.
  11. Zienkiewicz O.C., Taylor R.L. The finite element method. Volume 1: The Basis. Oxford: Butterworth-Heinemann, 2000.
  12. Специализированные параллельные библиотеки (



How to Cite

Губайдуллин Д., Садовников Р. Application of Parallel Algorithms for Solving the Problem of Fluid Flow to Wells With Complicated Configurations in Fractured Porous Reservoirs // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2007. 8. 244-251



Section 1. Numerical methods and applications

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