Page 281 - Enhanced Oil Recovery in Shale and Tight Reservoirs

258 Enhanced Oil Recovery in Shale and Tight Reservoirs

The relationship among the transverse relaxation time T 2 in porous me-
dia, the transverse relaxation time of the bulk liquid T 2,bulk , the surface area
A of the pore, the surface relativity r, and the volume of the pore is (Looyes-
tijn and Hofman, 2006)
1 1 A
¼ þ r (9.44)
T 2 T 2;bulk V
The effect of fluid diffusion (DGT E g/12) can be added in the above
2
equation, D is the fluid diffusion coefficient (cm /s), G is the magnetic
gradient, T E is the echo spacing of measurement sequence (ms), and g is
the gyromagnetic ratio. In the experiment conditions where the magnetic-
field of the NMR apparatus is relatively uniform, and the magnetic gradient
G is too small, the diffusion relaxation can be ignored. The bulk relaxation
T 2,bulk may not be considered because it takes much longer time than the
surface relaxation in a tight porous medium. Thus, the T 2 relaxation time
measured is mainly determined by the surface relaxation. If the pores are
smaller, the area-volume ratio is larger, T 2 will be shorter. A fluid in large
pores has higher T 2 value because more nuclei are available to exhibit the
NMR effect, and the fluid in small pores has lower T 2 value. T 2 relaxation
time is in inverse proportion to specific surface of samples (Appel, 2004). In
other words, the pore radius r is proportional to T 2 (Zhao et al., 2015):

T 2 ¼ Cr (9.45)
where C is the conversion constant.
The above equation can be applied to the system of oil and water that
covers different areas of the solid A o and A w , respectively:

1 1 A w
¼ þ r w (9.46)
T 2;w T 2;bulk;w VS w
1 1 A o
¼ þ r o (9.47)
T 2;o T 2;bulk;o VS o
where the subscript w and o refer to water and oil, respectively, and S de-
notes the saturation. It can be understood that if the solid is more water-wet,
water will cover more of the solid surface. Therefore, the wetting index I w
may be defined as
surface wetted by water surface wetted by oil
I w ¼ (9.48)
total surface