Page 314 - Reservoir Formation Damage

294 Reservoir Formation Damage

(12-87)

e, c p2s (12-88)
dt

(12-89)

(12-90)

Eqs. 12-87 to 90 apply over the cake, located within r c < r < r w , and for
t > 0. e. s and G, denote the volume fractions of the bulk cake system
occupied by the cake forming particles and the carrier fluid, respectively.
3
and p, are the densities of the particles and the carrier fluid (g/cm ).
p p
and are the volumetric fluxes of the compressing filter cake and
u s u t
2
3
the carrier fluid flowing through the cake (cm / cm • s). c p2s and c p2l
denote the small particle masses contained per unit volume of the cake-
3
forming particles and the carrier fluid flowing through the cake (g/cm ).
t and r denote the time and radial distance (cm), respectively.
is the mass rate of particle deposition from the slurry over to the
R ps
3
moving cake surface (g/s/cm ) given by:
(12-91)
where R° ls and R° 2s denote, respectively, the mass rates of large and
3
small particles deposition from the slurry over the cake surface (g/s/cm ).
is usually negligible unless the small particles are retained by
Rp 2s
a process of jamming of small particles across the pores of the
large particles, such as described by Civan (1994, 1996) and Liu and
Civan (1996).