Page 304 - Reservoir Formation Damage

284 Reservoir Formation Damage

Applications

The numerical solutions of the present models require the information
on the characteristics of the slurries, particulates, carrier fluids, filters and
filter cakes, the actual conditions of the tests conducted, and the measure-
ments of all the system parameters and variables. The reported studies
of the slurry filtration have measured only a few parameters and the
filtrate volumes or rates and do not offer a complete set of suitable data
that is needed for full scale experimental verification of the present
models. Civan (1998a) used the Willis et al. (1983) and Jiao and Sharma
(1994) data for linear filtration, and the Fisk et al. (1991) data for radial
filtration, because these data provide more information than the other
reported studies. The data is presented in Table 12-1 in consistent Darcy
units, which are more convenient for flow through porous media.

Linear Filtration Applications

Jiao and Sharma (1994) carried out linear filtration experiments using
concentrated bentonite suspensions. They only measured the filtrate
volume and predicted the filter cake thickness using a simple algebraic
model. These data are given in their Figures 3 and 10, respectively. In
Figures 12-5 to 12-7, their data are plotted according to the linear
plotting schemes presented in the previous section for determination of
parameters. As can be seen from these figures, the coefficients of Eqs.
12-76, 12-29, and 12-11 obtained by the least-squares regression method
and the corresponding coefficients of regression are given, respectively, by:

6 3 2
A/C = 8.297min/cm , B/C = 0.1136 cm- , R = 0.8713 (12-84)
4
C = 0.0034cm /min, D = 0.0076cm, R 2 = 0.949 (12-85)
2 2
A = 0.0229 cnT , B = 0.0003 cm/min, R = 0.9873 (12-86)

The coefficients of regressions very close to 1.0 indicate that the pre-
sent equations closely represent the data. The coefficient of regression
2
R =0.8713 indicated by Figure 12-5 and Eq. 12-84 is lower than those
indicated by Figures 12-6 and 12-7 and Eqs. 12-85 and 12-86, inferring
the possibility of larger measurement errors involved in the filtrate volume
data. Another source of errors may be due to the three-point finite
difference numerical differentiation of the filtrate volume data to obtain
the filtrate flow rate data used to construct Figure 12-5. The data necessary
for Figure 12-5 were obtained by a series of numerical procedures, first