Page 316 - Enhanced Oil Recovery in Shale and Tight Reservoirs

Spontaneous imbibition 289

to enter the rock, oil must flow out in the same time through countercurrent
flow. These factors make the water imbibition velocity in an oil-water-rock
system lower than what is predicted by Eq. (10.1).
Second, in an oil-wet system, a surfactant must enter the system to alter
the wettability. Surfactant has adsorption. The surfactant has higher
adsorption in a low-permeability rock than in a high-permeability rock.
The adsorption causes the retardation of surfactant transport (Sheng,
2011). The retardation is higher in the low-permeability rock than in
the high-permeability rock. Therefore, the imbibition velocity of a surfac-
tant solution will be lower than that predicted by Eq. (10.1).
Third, a surfactant enters the oil-wet system through diffusion and disper-
sion. The diffusion coefficient in a tortuous pore system is proportional to the
pore porosity (Sheng, 2011). Then the diffusion in a low-porosity (low-
permeability) rock will be lower than that in a high-permeability rock. The
dispersion coefficient is proportional to the fluid velocity (Sheng, 2011).
Thus the dispersion in a low-permeability rock is lower than that in a
high-permeability rock as well. Therefore, both diffusion and dispersion
will be lower in a low-permeability rock than in a high-permeability rock.
As a result, the surfactant imbibition velocity in the low-permeability will
be lower than that in the high-permeability rock.
p ffiffiffi
Fourth, according to scaling theories, if the imbibition time is scaled by k
p ffiffiffiffiffiffiffiffi
or k=f, the oil recovery from water imbibition should be same from a
high-permeability formation and a low-permeability formation (Schmid
and Geiger, 2013). But the simulation result does not show that. This is
because the water imbibition into the oil-wet formation cannot occur before
the wettability is altered by surfactant. The wettability alteration is controlled
by surfactant diffusion and dispersion which are very slow in a tight formation.
p ffiffiffi p ffiffiffiffiffiffiffiffi
Therefore, this invasion is very slow and is not scaled by k or k=f.
10.3.3 Experimental observation

Now we cite some experimental data of water imbibition in rocks of
different permeabilities. Dutta et al. (2014) visualized the water imbibition
profile in about 5e7 mD and about 100 mD cores. They observed that
the imbibition velocities were lower in the lower-permeability cores than
those in the higher-permeability cores. Yang et al. (2016) made the same
observation; their experimental velocities were lower than that predicted
by the theory; according to the theory, the cumulative imbibed volume
increases with the square root of imbibition time (Handy, 1960); the lower