Page 52 - Reservoir Formation Damage

36 Reservoir Formation Damage

shown in Figure 2-22 were obtained using A = k(c { - c^lh = 0.085,
h-\TJ5 = 0.67, and a t= 100(V, - V 0}IV 0 = 3.7 vol.% for the Figure 2 data
of Seed et al. (1962), A = 2.2, h^D = 1.1, and a, = (V t - V 0}IV 0 = 95/V 0
volume fraction for the Figure 9 data of Blomquist and Portigo (1962),
and A = 0.4, /zVZ) = 1.37, and a, = 0.55% for the Figure 4 (Curve F) data
of Chenevert (1970). Note that the initial sample volume V 0 is not given
in the original data. However, this value is not required for the plots of
(1 - oc/oc,) because the V 0 value cancels out in the ratio of oc/a,. Note that
the data points shown in Figure 2-21 are the tick-mark readings of the
plots of the original reported data.
Wild et al. (1996) tested lime-stabilized compacted kaolinite cylinders
containing gypsum and ground granulated blast furnace slag. After moist-
curing for certain periods, they soaked these samples in water and mea-
sured the linear expansion of the samples. Figure 2-23 shows the
representation of the three typical data sets selected from their Figures
5, 6, and 8 by Eq. 2-22 using Eq. 2-6. The first set of data was obtained
using a 7-day moist-cured kaolinite containing 6% lime and 4% gypsum.
The second set of data is for a 28-day moist-cured kaolinite containing
6% lime and 4% gypsum. The third set of data is for a 28-day moist-
cured kaolinite containing 2% lime, 4% gypsum and 8% ground granu-
lated blast furnace slug. The best fits of Eq. 2-22 using Eq. 2-6 to the
first, second, and third data sets were obtained with A = k(c l - c 0}lh =1.1,
W# = 1.0 and a, = 10.8 vol.%, A = 20, h^D = 0.2 and cc, = 1.48 vol.%,
and A = 2.4, H-jD = 0.7 and oc, = 0.655 vol.%, respectively.
Ladd (1960) measured the volume change and water content of the
compacted Vicksburg Buckshot clay samples during swelling. For a lin-
ear plot of Ladd's data first, the S term is eliminated between Eqs. 2-18
and 22 to yield:

W
1-.^L = \^L- (2-23)
w, -w.
Then, inferred by Eq. 2-23, Ladd's data can be correlated on a log-
log scale by a straightline as shown in Figure 2-24. The best linear
fit of Eq. 2-23 was obtained using w 0 = 0.8g, w t = 32g, a, = 13.2/V 0 and
= 1.907. Note that the value of is not given and not required be-
k/k w V 0
cause Eq. 2-23 employs the ratio of a/a r

Porosity Reduction by Swelling
Based on the definition of the swelling coefficient, Civan and Knapp
(1987) expressed the rate of porosity change by swelling of porous
matrix as: