Page 151 - Reservoir Formation Damage

Multi-Phase and Multi-Species Transport in Porous Media 133

or by

e =e
P, y *y %• (7-28)

The mass concentration of species / in phase j is given by:

c ( ,=p,-o ( , (7-29)

The molar concentration of species / in phase j is given by:

C^Cy/M; (7-30)

The volume flux of species / in phase j is given by:

«</=<Vry (7-31)

where u r- is the volume flux of phase j.
The mass flux of species i in phase j is given by:

C U C U
~ ij rj ~ ikj rkj (7-32)

Multi-Species and Multi-Phase
Macroscopic Transport Equations

The macroscopic description of transport in porous media is obtained
by elemental volume averaging (Slattery, 1972). The formulations of the
macroscopic equations of conservations in porous media have been carried
out by many researchers. A detailed review of these efforts is presented
by Whitaker (1999). The mass balances of various phases are given by
(Civan, 1996, 1998):

, p,) + -( 9 j uj) = V• (e, Dj • Vp y )+ (7-33)
V
where u rj is the fluid flux relative to the solid phase, t is the time and
V • is the divergence operator. p ; is the phase density, m • is the net mass
rate of the phase j added per unit volume of phase j. Dj is the hydraulic
dispersion coefficient which has been omitted in the petroleum engineer-
ing literature.