Transport in Porous Media

, Volume 4, Issue 3, pp 213–238 | Cite as

The effective homogeneous behavior of heterogeneous porous media

  • A. E. Sáez
  • Carlos J. Otero
  • Isak Rusinek


The macroscopic equations that govern the processes of one- and two-phase flow through heterogeneous porous media are derived by using the method of multiple scales. The resulting equations are mathematically similar to the point equations, with the fundamental difference that the local permeabilities are replaced by effective parameters. The method allows the determination of these parameters from a knowledge of the geometrical structure of the medium and its heterogeneities. The technique is applied to determine the effective parameters for one- and two-phase flows through heterogeneous porous media made up of two homogeneous porous media.

Key words

Multiple scales double porosity heterogeneous porous media multiphase flow 



Compressibility coefficient


Vector function, defined in Equation (80)


Gravity acceleration vector


Vector function, defined in Equation (24)


Normal unit vector


Relative permeability


Effective relative permeability


Absolute permeability tensor


Effective permeability tensor




Capillary pressure


Modified pressure


Modified capillary pressure


Position vector


Without subscript, saturation of the α-phase With subscript i, saturation of the i-phase




Temperature Characteristic time


Superficial velocity vector


Position vector of the macroscopic scale


Position vector of the microscopic scale


Position vector equivalent to r, constrained to the unit cell

Greek Letters


Parameter defined by Equation (91)


Perturbation parameter


Absolute permeability ratio




Volumetric fraction of porous medium 1




Tortuosity tensor




Gravitational potential


Scalar function, defined in Equation (23)



Denotes reference value


Referring to porous medium 1


Referring to porous medium 2


Denotes ith-order term in an asymptotic expansion


Relative to the α-phase


Relative to the β-phase


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Copyright information

© Kluwer Academic Publishers 1989

Authors and Affiliations

  • A. E. Sáez
    • 1
  • Carlos J. Otero
    • 2
  • Isak Rusinek
    • 2
  1. 1.Departmento de Termodinámica y Fenómenos de TransferenciaUniversidad Simón BolívarCaracasVenezuela
  2. 2.Tecnología de Yacimientos, INTEVEP, S.A.CaracasVenezuela

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