19. Mathematical Models of Uniphase Filtration

  1. Kaplan S. Basniev1,
  2. Nikolay M. Dmitriev1 and
  3. George V. Chilingar2

Published Online: 26 OCT 2012

DOI: 10.1002/9781118533628.ch19

Mechanics of Fluid Flow

Mechanics of Fluid Flow

How to Cite

Basniev, K. S., Dmitriev, N. M. and Chilingar, G. V. (2012) Mathematical Models of Uniphase Filtration, in Mechanics of Fluid Flow, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9781118533628.ch19

Author Information

  1. 1

    Gubkin State University of Oil and Gas, Russia

  2. 2

    University of Southern California, USA

Publication History

  1. Published Online: 26 OCT 2012
  2. Published Print: 8 OCT 2012

ISBN Information

Print ISBN: 9781118385067

Online ISBN: 9781118533628



  • uniphase filtration;
  • mass conservation laws;
  • differential equation;
  • isothermal filtration;
  • incompressible viscous fluid


This chapter contains sections titled:

  • Introductory Notes. The Concept of the Mathematical Model of a Physical Process

  • Mass Conservation Laws in a Porous Medium

  • Differential Equation of Fluid Flow

  • Closing Equations. Mathematical Models of Isothermal Filtration

  • Filtration Model of Incompressible Viscous Fluid under Darcy's Law in a Non-Deformable Reservoir

  • Gas Filtration Model under Darcy's Law. Leibensohn's Function

  • Uniphase Filtration Models in Non-Deformable Reservoir under Non-Linear Filtration Laws

  • Correlation between Fluid Parameters and Porous Medium Parameters with Pressure