Page 239 - Enhanced Oil Recovery in Shale and Tight Reservoirs

222 Enhanced Oil Recovery in Shale and Tight Reservoirs

The superscript “low” and “high” refer to low and high trapping numbers,
high
respectively. Using the above equation, we still need S rj that is generally
assumed zero. Following the above procedures, both effects of wettability
alteration and IFT reduction (through trapping number) on the residual satu-
ration are considered.
From the discussion of the preceding section, it can be seen that the
e
end-point k of a phase increases when the residual saturation of its conjugate
rj
e
phase is decreased. Therefore, the end-point k of a phase may be linearly
rj
interpolated according to the residual saturation of its conjugate phase:
high
k e;NT k e;high S j r S 0 j r
0
rj
rj
¼ (9.15)
e;high e;low low high
k rj k rj S 0 j r S 0 j r
In the above equation, the subscript j denotes the conjugate phase of
0
phase j.
Combining the above two equations results in
k e;N T k e;high
rj rj 1
¼ (9.16)
e;high e;low
k k 1 þ T j N Tj 0
0
rj rj
If the end-point relative permeability at trapping number N T0 is known,
the end-point relative permeability at any trapping number can be estimated
from the following equation, according to the preceding equation:
e;high
k e;N T k
rj rj 1 þ T j0 N T0j0
¼ (9.17)
k e;N T0 k e;high 1 þ T j0 N Tj0
rj rj
e;high
where k e;N T , k e;N T0 ,k rj correspond to the end-point relative permeabil-
rj
rj
ities at N T , N T0 and a very high trapping number. Note T j is the trapping
0
parameter of the conjugate phase of phase j.
To include the effect of wettability on the end-point relative perme-
ability at N T0 , following Eq. 9.12, we may have

cosq cosq 0
k e;N T0 k e;N T0 ¼ k e;N T0 k e;N To (9.18)
rj r;b1 r;b2 r;b1
cosðp q 0 Þ cosq 0
Here it is assumed that we have the relative permeability curves
measured at a certain trapping number N T0 for a pair of base phases with
the contact angle q 0 for the phase b1 and p q 0 for the phase b2. Combining