Page 312 - Enhanced Oil Recovery in Shale and Tight Reservoirs

Spontaneous imbibition 285

Here the subscripts w and nw represent wetting and nonwetting phases,
respectively. The mobility M is defined as k/m, and k is the permeability, and
m is the viscosity. c is the ratio of the gravity force to the capillary force:

b 0
c ¼ (10.13)
a 0

AM e S wf S wi
a 0 ¼ p c (10.14)
L
b 0 ¼ AM e Drg (10.15)
where Dr ¼ r w r nw , p c ¼ p nw p w .
Several conditions for the above equations need to be emphasized. For
the cocurrent flow, it is assumed that wetting phase velocity is equal to
the nonwetting phase velocity:

v w ¼ v nw (10.16)
For the countercurrent flow, those two velocities have the following
relationship:

v w ¼ v nw (10.17)
And the fluids are incompressible and immiscible. Another condition is

vp c p c
¼ (10.18)
vx x
The above equation assumes a pistonlike spontaneous imbibition
(Handy, 1960). Different factors that affect spontaneous imbibition are dis-
cussed next.

10.3 Effect of permeability and porosity

The effect of permeability and porosity is discussed using simulation
data, experimental data, and theories.

10.3.1 Simulation results
When comparing the mechanisms of IFT reduction and wettability alter-
ation in Section 9.5, a base sand model is introduced. The model matrix
2
core has the porosity of 0.24 and the permeability of 0.122 mm .The
model initially is oil-wet, and water cannot imbibe into it. A surfactant so-
lution is added to imbibe the water into the core. To study the effect of