Page 310 - Enhanced Oil Recovery in Shale and Tight Reservoirs

Spontaneous imbibition 283

according to the Handy derivation; k w is the effective water permeability at
S w ; 4 is the porosity; A is the flow cross-section area; and m w is the water
viscosity. It is assumed that water displaces air in a pistonlike manner. No
gravity is assumed to play the role in the process. Only the capillary force
overcomes the viscous force within the imbibition zone. As more water is
imbibed, water saturation S w is increased and k w is increased, but p c is
declined exponentially with S w . Handy’s experimental data through cores
confirmed the above linear relationship. Makhanov’s (2013) experimental
data also demonstrated the above relationship, but some imbibition data
showed that the imbibition rate slowed at later time.

10.2.3 Mattax and Kyte (1962) method
The imbibition oil recovery in laboratory needs to be converted to the field
scale. Based on the Rapoport (1955) scaling work, Mattax and Kyte (1962)
verified that the spontaneous imbibition behavior (resultant oil recovery) is
determined by the dimensionless time t D :
s ffiffiffi
k s
t D ¼ t (10.3)
4 m L 2
w c
Their equation does not consider gravity, matrix shape, wettability, rela-
tive permeability functions, boundary conditions, fluid viscosity ratios, or
initial fluid distributions. L c is the characteristic linear dimension of the
block.
Based on the Mattax and Kyte (1962) equation, Ma et al. (1997) consid-
p
ered viscosity ratio by replacing m w with m m :
ffiffiffiffiffiffiffiffiffiffiffiffiffi
w nw
s ffiffiffi
k s
t D ¼ t (10.4)
0:5 2
4 ðm m Þ L
w nw c
Gupta and Civan (1994) introduced the wettability effect in the Ma et al.
equation by multiplying s by cosq:
s ffiffiffi
k scosq
t D ¼ t (10.5)
0:5 2
4 ðm m Þ L
w nw c
q is the contact angle. Zhang et al. (2018) observed that, from the exper-
imental data of their research group, the imbibition recovery was not
strongly dependent on the interfacial tension s but inversely proportional
to porosity. They further modified the above dimensionless time as follows: