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Transport in Porous Media

, Volume 11, Issue 3, pp 243–262 | Cite as

On the use of conventional cocurrent and countercurrent effective permeabilities to estimate the four generalized permeability coefficients which arise in coupled, two-phase flow

  • Ramon G. Bentsen
  • Abdalla A. Manai
Article

Abstract

In the case of coupled, two-phase flow of fluids in porous media, the governing equations show that there are four independent generalized permeability coefficients which have to be measured separately. In order to specify these four coefficients at a specific saturation, it is necessary to conduct two types of flow experiments. The two types of flow experiments used in this study are cocurrent and countercurrent, steady-state permeability experiments. It is shown that, by taking this approach, it is possible to define the four generalized permeability coefficients in terms of the conventional cocurrent and countercurrent effective permeabilities for each phase. It is demonstrated that a given generalized phase permeability falls about midway between the conventional, cocurrent effective permeability for that phase, and that for the countercurrent flow of the same phase. Moreover, it is suggested that the conventional effective permeability for a given phase can be interpreted as arising out of the effects of two types of viscous drag: that due to the flow of a given phase over the solid surfaces in the porous medium and that due to momentum transfer across the phase 1-phase 2 interfaces in the porous medium. The magnitude of the viscous coupling is significant, contributing at least 15% to the total conventional cocurrent effective permeability for both phases. Finally, it is shown that the nontraditional generalized permeabilities which arise out of viscous coupling effects cannot equal one another, even when the viscosity ratio is unity and the surface tension is zero.

Key words

Countercurrent flow effective permeability generalized permeability viscous coupling 

Nomenclature

Roman Letters

g

gravity vector, m2/s

gi

function defined by Equation (23)

gij

functions defined by Equations (19) to (22)

k

absolute permeability, m2

ki

effective permeability of phasei; i = 1, 2, m2

kij

coefficient of generalized permeability for phasei; i, j = 1, 2, m2

krij

coefficient of generalized relative permeability for phasei; i, j = 1, 2

kro

relative permeability to oil

krw

relative permeability to water

kvi

coefficient of viscous coupling for phasei; i = 1, 2, m2

L

length of core, m

Pc

capillary pressure, N/m2

pi

pressure in phasei; i = 1, 2, N/m2

ΔPi

pressure drop for phasei; i = 1, 2, N/m2

qi

Darcy flow velocity for phasei; i = 1, 2, m/s

R12

ratio of pressure gradients (phase 1/phase 2)

S

\(\frac{{S_w - S_{wi} }}{{1 - S_{or} - S_{wi} }}\)=normalized saturation

Sor

residual oil saturation

Sw

water saturation

Swi

irreducible water saturation

Greek Letters

α

interfacial tension, N/m

ηi

fraction of pore space occupied by phasei; i = 1,2

Μi

viscosity of phasei; i = 1, 2, Pa/s

ρi

density of phasei; i = 1, 2, kg/m3

Subscripts and Superscripts

1

wetting phase

2

nonwetting phase

*

countercurrent flow

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Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • Ramon G. Bentsen
    • 1
  • Abdalla A. Manai
    • 2
  1. 1.Department of Mining, Metallurgical and Petroleum EngineeringUniversity of AlbertaEdmontonCanada
  2. 2.Apex Energy ConsultantsCalgaryCanada

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