Page 219 - Reservoir Formation Damage

200 Reservoir Formation Damage

and particles and constant injection rate, the total volumetric particle
balance equation is given by:

= 0 (10-84)

subject to

(10-85)

and

(10-86)

Cernansky and Siroky (1985) expressed the net rate of particle deposi-
tion in porous media as the difference between the deposition by pore
throat plugging and entrainment by hydrodynamic mobilization. Consider-
ing the critical shear stress necessary to mobilize the deposited particles
in porous media, Civan et al. (1989) modified their rate equation as:

(10-87)

in which the shear-stress is expressed as

(10-88)

where D is the hydraulic tube diameter, and the pressure gradient is
represented by Darcy's law:
(10-89)

The instantaneous porosity is given by:

(10-90)

where <|> 0 is the initial porosity. Thus, substituting Eqs. 10-88 through
10-90 into Eq. 10-87 yields:

(10-91)

in which k' e=k eD/4 and l' cr=4i cr/D are the redefined entrainment
coefficient and critical shear-stress. ^ = 0 when u\L/K <i' cr. At equili-
brium,