Page 287 - Enhanced Oil Recovery in Shale and Tight Reservoirs

264 Enhanced Oil Recovery in Shale and Tight Reservoirs

Now we consider a water-wet rock. Refer to Eq. (9.49), s os > s ws for
a water-wet rock because the cosine term should be positive. Then the sec-
ond term of the above numerator is positive. Similarly, for the first term of
the above numerator, s as > s ws because a rock generally prefers water-
wet to air-wet; and generally, s oa < s wa ; Thus, the first term is negative.
Now the numerator has one positive value and one negative value. Then
cosq wsa e cosq osa could be negative or positive. Therefore, the q wsa measured
on a water-wet rock may not necessarily be smaller than q osa . That means,
even q wsa is greater than q osa , the rock may still be possibly water-wet. There-
fore, we have Conclusion 2:
In a gas-water-solid system (a gas-liquid system), the water-wetting angle
cannot be used to determine the wettability; similarly, in a gas-oil-solid sys-
tem (a gas-liquid system), the oil-wetting angle cannot be used to determine
the wettability.
One may think that if the volume of water imbibed into a dry core is
higher than the oil volume, the rock is water-wet. According to Washburn’s
(1921) equation, the imbibition velocity of a fluid into a capillary tube of
radius r is:

2scosq
DF þ r 2
dl r
¼ (9.54)
dt 8ml
where l is the imbibition distance, F is the potential, t is the imbibition time,
s is the interfacial tension, m is the phase viscosity, and q is the contact angle.
For spontaneous imbibition, DF is zero. The imbibition volume can be
obtained by integrating the preceding equation:
2
p scosqr 5
2
V ¼ t (9.55)
2m
Then the ratio of spontaneous imbibition volume of water to that of oil is
s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
V w s wa cosq wa m o
¼ (9.56)
V o s oa cosq oa m w
If V w > V o , s wa m o cosq wa > s oa m w cosq oa . Since s wa > s oa , and m o > m w ,
generally, cosq wa may not be necessarily greater than cosq oa . Thus, the rock is
not necessarily water-wet. If V w < V o , s wa m o cosq wa < s oa m w cosq oa . Since
s wa > s oa , and m o > m w , generally, cosq wa must be smaller than cosq oa .
Thus, the rock is oil-wet.