Page 372 - Fundamentals of Gas Shale Reservoirs

352 WETTABILITY OF GAS SHALE RESERVOIRS

samples exposed to XG solutions indicates that water uptake interfacial tension, wettability, boundary conditions, and
is partly controlled through preferential adsorption of water sample shape. The objective of this section is to compare the
molecules by the clay particles, and the high viscosity of wettability of intact and crushed samples, using the concept
polymer solution can only partly reduce the imbibition rate. of dimensional analysis. The basic model for scaling labora-
Figure 16.10 also compares the imbibition behavior of tory imbibition data was proposed by Rapoport (1955). For
an anionic surfactant in freshwater (DI + sodium dodecyl- scaling the imbibition results of oil/water/rock systems,
benzenesulfonate (DDBS)), a nonionic surfactant in fresh- Mattax and Kyte (1962) proposed the most frequently used
water (DI + Tergitol (Terg)), an anionic surfactant in 2 wt.% dimensionless time (t ):
D
KCl brine (KCl + DDBS), and a nonionic surfactant in 2
wt.% KCl brine (KCl + Terg). Expectedly, the imbibition k 1
rate of all surfactant solutions is lower than that of DI water, t D t L 2 (16.1)
which is primarily due to their lower surface tension. The gm c
imbibition rate of KCl + DDBS is lower than that of KCl + where μ is the geometric mean of water and oil viscos-
gm
Terg. This difference can be explained by the change of sur- ities (Shouxiang et al., 1997). L is the characteristic length
c
face properties of anionic surfactants in the presence of solu- that depends on samples’ shape and boundary condition
tion ions (Lowe et al., 1999). Takaya et al. (2005) speculated (Zhang et al., 1996). For example, L c L (/ ) for cocur-
2
that the salt particles in water decrease the repulsion forces rent imbibition of a liquid phase into a linear porous
between anionic surfactant molecules, which, in turn, allow medium with the length of L, while L dL/2 d 2 2 L
2
accumulation of more surfactant molecules at the interface. c
The presence of more surfactants at the interface leads to a for countercurrent imbibition into a cylindrical sample
more reduction of surface tension and, in turn, to a more with the thickness of L and diameter of d, fully immersed
reduction of imbibition rate. It is also observed that anionic in the imbibing phase.
DDBS solutions show lower imbibition rates compared with Figure 16.11 compares the normalized mass of water
nonionic Tergitol solutions. This behavior can be related and oil imbibed into the intact and crushed samples versus
to the adsorption properties of clay minerals. Negatively the corresponding dimensionless time. The separation bet-
charged clay particles may repulse negatively charged ween water and oil data on the scaled plots can be inter-
DDBS surfactants, which could decrease the overall adsorp- preted as the difference in the wetting affinity. Therefore,
tion of the surfactant molecules on the clay surface. the higher values of water data compared with oil data,
Surfactants can also influence the imbibition behavior by shown in Figure 16.11a, b, c, and d, confirms that the
changing the rock wettability. For example, Roychaudhuri affinity of crushed samples to oil is higher than that to
et al. (2013) showed that the presence of additives such as water. However, the water data are significantly higher than
cationic surfactants can reduce the fluid loss to the formation oil data in Figure 16.11e and f. This indicates that the
due to change of the wettability to less water‐wet conditions. affinity of intact samples to water is significantly higher
than that to oil. As discussed previously, this discrepancy
can be explained by (i) poor connectivity of hydrophobic
16.5 QUANTITATIVE INTERPRETATION pore network of intact samples compared with crushed
OF IMBIBITION DATA samples and (ii) induction of microcracks in intact samples
by water imbibition.
This section presents the methods to characterize spontaneous
imbibition in gas shales. The results of experiments on intact 16.5.2 Modeling Imbibition Data
samples show that the water imbibition rate is higher than
the oil imbibition rate, while the experiments on crushed One of the earliest models of spontaneous imbibition was
samples show the opposite behavior. In this section, we first presented by Bell and Cameron (1906), who found that the
plot the imbibition data versus dimensionless time to com- movement of water through a porous medium is propor-
pare the water/oil affinity of intact and crushed samples. tional to the square root of time. Lucas (1918) and Washburn
Then, we investigate the performance of the existing imbibi- (1921) combined the Laplace relationship with Poiseuille
tion models for predicting water and oil imbibition in equation, and developed the following relationship between
crushed shale packs. the imbibition length and square root of time:

cos 1
16.5.1 Scaling Imbibition Data Lt() t 2 (16.2)
s
4
The imbibition results are mainly affected by rock/fluid
properties and geometrical parameters. These factors include where L is the distance between the inlet and the imbibition
s
porosity and permeability of porous media, fluid viscosity, front at time t. λ is the effective pore diameter. σ and μ are