Page 307 - Reservoir Formation Damage

Cake Filtration: Mechanism, Parameters and Modeling 287

derivatives of the filtrate volume data beyond the range of the experi-
mental data is q M =0.017mL/min and close to the values obtained by the
regression method. This is an indication of the validity of the filtration model.
Using q x =0.014mL/min in Eq. 12-29 yields the limiting filter cake
thickness as 5^ =0.24cm. The predicted cake thickness data presented
in Figure 10 of Jiao and Sharma (1994) indicates a value of approxi-
mately 0.17cm. Therefore, their prediction of the limiting filter cake
thickness appears to be an underestimate compared to the 0.24cm value
obtained by Civan (1998a).
The above obtained values can now be used to determine the values
of the model parameters as following. The filter cake permeability can
be calculated by Eq. 12-74. Equations 12-70, 12-71, 12-75, 12-77, and
12-78 form a set of alternative equations to determine the deposition
and erosion rate constants, k d and k e. Here, Eqs. 12-70 and 12-75
were selected for this purpose. However, Jiao and Sharma (1994) do not
offer any data on the cake porosity ty c and the critical shear stress i cr
necessary for detachment of the particles from the progressing cake
surface. Therefore, the § c and T cr parameters had to be estimated and
used with Eqs. 12-70 and 12-75 to match the filtration data over the
period of the filtration process. Then, the <j) c and i cr values obtained this
way were used in Eqs. 12-70 and 12-75 to calculate the k d and k e values.
Using the slurry tangential velocity of v = 8.61cm/s, the typical parti-
cle diameter of d = 2.5 x 10" 4 cm, and the particle separation distance of
/ = 2. x 10~ 7 cm in Eq. 12-5, the critical shear stress for particle detachment
2
3
is estimated to be t cr =1.25 xlO dyne/cm . Whereas, the prevailing
2
shear stress calculated by Eq. 12-5 is only T = 16 dyne/cm . Under these
conditions, theoretically the cake erosion should not occur because
T«:i cr. Therefore, the value of the coefficient B should be zero.
In contrast, as indicated by Eq. 12-86, the present analysis of the
4
data has led to a small but nonzero value of B = 3.x 10" cm/min. Recall
that we used this value in Eq. 12-72 to calculate the limiting flow rate
of q x =0.013mL/min. This value was shown to be very close to the
q x =0.014mL/min value calculated by Eq. 12-79 and the approximate
value of q x =0.017mL/min obtained by extrapolating the filtrate flow
rate data beyond the range of the experimental data. Thus, it is reasonable
4
to assume that B = 3. x 10" cm/min is a meaningful value and not just a
numerical result of the least-squares regression of Eq. 12-11 to data,
2
because the coefficient of regression R = 0.9873 is very close to one.
Hence, it can be inferred that 1 > i cr and the cake erosion occurred in
the actual experimental conditions of Jiao and Sharma (1994). In view
of this discussion, it becomes apparent that the theoretical value obtained
by Eq. 12-6 is not realistic.