Page 262 - Reservoir Formation Damage

242 Reservoir Formation Damage

Eq. 11-1 over all species j in phase J and considering that the dispersion
terms of various species j cancel each other out in a given phase, the
volumetric equation of continuity for phase J is obtained as:

- + -^- + q J=Q ; J = W,N,wS,nS,tS (11-3)
dt dx

in which the volumetric loss of all types of particles from phase J is
given by:

<*» (11-4)

Finally, by summing Eq. 11-3 for all phases /, the total equation of
continuity for the multi-phase fluid system is obtained as:

(11-5)
dt dx

where the total volumetric flux and all types of particles lost by the multi-
phase fluid system are given, respectively, by:

« = 5X (11-6)

9 = SX (11-7)

Considering the possibility of the generation of inertial effects by rapid
flow due to the narrowing of pores during formation damage, the volumetric
flux of phase J is represented by the non-Darcy flow equation given by:

_ Kk rJN ndJ(d Pj
u, =- = W,N (11-8)
dx

where 0 is the angle of inclination of the flow path and PJ and |i y are
the pressure and viscosity of phase J. k rj is the relative permeability of
phase / and K is the permeability of porous media. N ndJ is the phase J
non-Darcy number given according to the Forchheimer equation as:

(11-9)