Page 168 - Enhanced Oil Recovery in Shale and Tight Reservoirs

152 Enhanced Oil Recovery in Shale and Tight Reservoirs

recovery factor was 0.515, indicating not much oil produced after the
breakthrough.
One may think that water preferentially invades into smaller pores, as the
capillary pressure as a driving force is higher. However, the resistance in
smaller pores is also higher. As a result, water imbibition velocity is higher
in large pores (Sheng, 2017c). This can be explained as follows.
Based on Poiseuille’s law, Washburn (1921) derived an equation to
describe the imbibition velocity in a single capillary tube. The velocity equa-
tion can be restated as follows without including the coefficient of slip or a
noncapillary drive force:

dl s cos q
¼ r (7.1)
dt 4m l
w
In the Eq 7.1, l is the imbibition distance, t is the imbibition time, s is the
interfacial tension, m w is the wetting phase viscosity, q is the contact angle,
and r is the capillary radius. We can see that the imbibition velocity into a
larger pore is lower than that into a smaller pore. A small radius corresponds
p ffiffiffiffiffiffiffiffi
to a low permeability reservoir because r is proportional to k=4. Now we
can understand that in the low-permeability rock, although the capillary
force is higher, the viscous force is high as well; by considering these two
forces, the imbibition velocity in the low-permeability rock is actually lower
than that in the high-permeability rock. Note that the above ignores the slip
flow. For the slip flow to take place, the capillary diameter needs to be
smaller than approximately 3 nm (Sharp et al., 2001). This was confirmed
by an experimental and theoretical study by Koo and Kleinstreuer (2003).
Thus, the continuum theory is still applicable to fluid flow through nano-
pores in shale matrix in a practical sense.
The above theory is consistent with what was observed by Lin et al.
(2016) as shown in Fig. 7.1. This figure also shows that when there was a
fracture, the water could much more quickly imbibe into the neighbor ma-
trix. Another important mechanism is the imbibed water increase reservoir
pressure and local pressure so that the drive energy is boosted. From the
imbibition point of view, water-wet formation is preferred. This conclusion
is supported by experimental data by Huang and Xiang (2004). By the way,
Sun et al. (2015) attributed their slower imbibition rate after the cores
were dried in an oven to the fractures generated during the earlier water
imbibition. They argued that the existence of fractures with openings in mi-
crometers reduced capillary pressure; thus the imbibition rate was decreased.
As discussed here, the resistance in fractures is lower and the resulting