Page 214 - Reservoir Formation Damage

Single-Phase Formation Damage by Fines Migration and Clay Swelling 195

(K/K*f 2 = 1 + C 7[l - exp(-^r)] (10-57)

If only gradual surface deposition is taking place in the outlet region,
then k r » k e . Therefore, dropping the particle retention term and sub-
stituting Eq. 10-46, Eqs. 10-35 and 36 for m pg = 0 are solved to obtain
the amount of particles retained as:

m p=[k rALm po/q][l-exp(-k et)] (10-58)

Then, substituting Eqs. 10-58, 29, and 10 into Eq. 10-28 yields the
following diagnostic equation:

(K/K 0) }/2 = l-C 9[l-exp(-V)] - (10-59)

in which

2
2
C 9 = k rA Lm pC 3KV qp (10-60)
Single Pore Blocking

If the permeability damage is solely due to single pore blocking, then
substituting Eqs. 10-46, 12, 13 and 14 into Eq. 10-28 yields the following
diagnostic equation:

= l-C 7[l-exp(-M)] (10-61)
K/K 0
in which
3
C 7 = 6f dALm pJ(nd p pC 4) (10-62)

Cake Formation
If the permeability damage is by cake formation, then substituting
Eqs. 10-46 and 22 into Eq. 10-17 yields the following diagnostic equation

KJK = l + C 10[l - exp(-* ef)] (10-63)

in which

(10-64)
C lo=k cm pJR m