Page 217 - Reservoir Formation Damage

198 Reservoir Formation Damage

Substituting Eqs. 10-66 and 67, and rearranging Eq. 10-65 becomes:

(10-68)

subject to the initial condition given by:

•
= 4UW = 1, 2, •-, n, t = 0 (10-69)
(<!>Pp/) y
and the boundary condition given by:

(10-70)

The mass balance of particles captured at the pore throats is given by:

dm p /dt = r r (10-71)

subject to

= 0, t = 0 (10-72)
m p
The mass balance of indigeneous particles remaining on pore surfaces is

dm* p/dt = -r e (10-73)

subject to

rn p=m po,t = (10-74)

where m po is the mass of particles initially available on pore surface.
The rate of particle entrainment by the flowing phase is assumed both
colloidally and hydrodynamically induced.

r=oc m l +oc, |T — T Ifl (10-75)
T
e c ' p h V c ) s
T is shear stress. a s is the specific pore surface area. <*£, is the colloidally
induced release coefficient given by (Khilar and Fogler, 1983):

(10-76)