Page 149 - Reservoir Formation Damage

Multi-Phase and Multi-Species Transport in Porous Media 131

a, =
(7-13)

In the following formulations, the various phases (solid and fluid) in
porous media are denoted by j, s denotes the solid phase, n is the total
number of phases, &• is the volume fraction of the j' h phase in porous
media, fy is the porosity of porous media, and Sj is the saturation or
volume fraction of j th phase in the pore space.
The following equations can be written:

e 5 =l-(J> (7-14)

e i=$S i:j = w,o,g (7-15)

SX=1.0, IX =1.0, IX =1.0, 20, =1.0, 2** =1-0 (7-16)

c
2* ij-Pj (7-17)
i
The density and velocity of a mixture is given by the volume fraction
weighted averages, respectively, as:

(7-18)

and

Pv = 2,<W,. (7-19)
(

Therefore, the density and velocity of a mixture are variable when the
composition varies even if the constituents are incompressible.
For incompressible systems, it is more convenient to use volumetric
balance equations. Therefore, Eqs. 7-18 and 7-19 are replaced by:

(7-20)