Page 311 - Enhanced Oil Recovery in Shale and Tight Reservoirs

284 Enhanced Oil Recovery in Shale and Tight Reservoirs

s ffiffiffi
k absðlog sÞcosq 2
t D ¼ t 4 (10.6)
0:5 2
4 ðm m Þ L
w nw c
10.2.4 Li and Horne (2006) method
Our objective to study imbibition is to study the oil recovery by imbibition.
Li and Horne (2006) derived a spontaneous imbibition equation which re-
lates to almost all the parameters: gravity, initial fluid saturation, capillary
pressure, and relative permeability of the wetting and nonwetting phases.
Their equation is
* *
t D ¼ R ln 1 R (10.7)
*
where R is the normalized oil recovery:
*
R ¼ cV w (10.8)
V w is the pore volumes of imbibed wetting phase:

Ax4 S wf S wi
V w ¼ (10.9)
V p
t D is the dimensionless time:

2 M e p c S wf S wi
t D ¼ c t (10.10)
4L 2
c
V p is the pore volume. A is the cross-sectional area of the core perpendic-
ular to the flow direction. x is the distance the front transports. 4 is the
porosity. L c is the characteristic length equal to core length. S wf is the average
wetting phase saturation behind the imbibition front. S wi is the initial water
saturation in the core sample. M e and p c are the effective mobility and capillary
pressure at the front wetting phase saturation S wf . The effective mobility for
cocurrent flow is defined as:

M w M nw
M e ¼ (10.11)
M nw M w
The effective mobility for countercurrent flow is defined as:

M w M nw
M e ¼ (10.12)
M nw þ M w