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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
Article

Abstract

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 

Notation

Cf

Compressibility coefficient

f

Vector function, defined in Equation (80)

g

Gravity acceleration vector

h

Vector function, defined in Equation (24)

n

Normal unit vector

k

Relative permeability

keff

Effective relative permeability

K

Absolute permeability tensor

Keff

Effective permeability tensor

p

Pressure

pc

Capillary pressure

P

Modified pressure

Pc

Modified capillary pressure

r

Position vector

S

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

t

Time

T

Temperature Characteristic time

v

Superficial velocity vector

x

Position vector of the macroscopic scale

y

Position vector of the microscopic scale

z

Position vector equivalent to r, constrained to the unit cell

Greek Letters

δ

Parameter defined by Equation (91)

ε

Perturbation parameter

κ

Absolute permeability ratio

μ

Viscosity

ξ

Volumetric fraction of porous medium 1

ϱ

Density

τ

Tortuosity tensor

φ

Porosity

ψ

Gravitational potential

Ψ

Scalar function, defined in Equation (23)

Indices

0

Denotes reference value

1

Referring to porous medium 1

2

Referring to porous medium 2

(i)

Denotes ith-order term in an asymptotic expansion

α

Relative to the α-phase

β

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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