Page 240 - Enhanced Oil Recovery in Shale and Tight Reservoirs

EOR mechanisms of wettability alteration and its comparison with IFT 223

the above two equations, we have the relative permeability curves with the
trapping number N T and the contact angle q:

e;high e;N T0 cosq cosq 0 e;N T0 e;N To
k ¼ k þ k þ k k
e;N T
rj rj r;b1 r;b2 r;b1
cosðp q 0 Þ cosq 0
(9.19)

e;high 1 þ T j N T0
0
k rj
1 þ T j N T
0
Similarly, the exponents of relative permeabilities are

high cosq cosq 0 high
n N T ¼ n j þ n N T0 þ n N T0 n N To n rj
j
b2
b1
b1
cosðp q 0 Þ cosq 0
1 þ T j0 N T0
1 þ T j0 N T
(9.20)
e
Again, we assume that the end-point value, k , and the exponent n j ,
rj
for the phase j are correlated to the residual saturation of the conjugate
0
phase j through linear interpolation. Actually, the above two equations
double count the effect of wettability, as T j already considers the effect.
After the end-point relative permeabilities and the exponents are defined,
the Brooks-Corey model is used to describe the relative permeability
e n j
k rj ¼ k S j (9.21)
rj
S j S jr
S j ¼ (9.22)
1 S jr S j0r
The effects of IFT and contact angle on capillary pressure are described
with the following equation:
s jj cosq
0
p cjj ¼ p c0jj 0 (9.23)
0
s jj cosq 0
0
where p cjj and p c0jj are the capillary pressures, and s jj and s 0jj are the
0
0
0
0
interfacial tensions at the contact angle q and q 0 , respectively.
9.4.3 A proposed simply model
TheaboveAdibhatlaetal.(2005)modeldoublecountstheeffectofwettability,
and it is complex. Here we propose a new model that sequentially considers
both effects of wettability alteration and IFT reduction (trapping number);