Page 57 - Hybrid Enhanced Oil Recovery Using Smart Waterflooding

CHAPTER 3 Modeling of Low-Salinity and Smart Waterflood 49

The first methodology, empirical model, adopts the
kgDr (3.62)
N B ¼
contact angle as an interpolation factor for wettability
s cos q
modification modeling. In addition, it introduces a where N T is the trapping number, N c is the capillary
third-degree polynomial relationship between contact number, v is the velocity, N B is the Bond number, s is
angle and salinity. Using the polynomial relationship the interfacial tension, k is the permeability, Dr is the
between contact angle and salinity, the residual oil difference of densities between displacing and displaced
saturation and oil relative permeability between low
fluids, and g is the gravitational acceleration.
and high threshold conditions are interpolated by the
In terms of the residual oil saturation, the funda-
salinity-dependent contact angle. The linear modifica-
mental model employs the modified version of capillary
tion of residual oil saturation follows Eq. (3.56). The
desaturation curve (CDC) (Pope et al., 2000) to relate
normalized contact angle of Eq. (3.57) rather than the
the residual oil saturation with trapping number as
contact angle is introduced to modify the residual oil
shown in Eq. (3.63). For the endpoint and Corey’s
saturation. The modification of oil relative permeability
exponent modifications of oil relative permeability, it
employs the modifications of endpoint and Corey’s
uses the linear and natural logarithm relations, which
exponent of oil relative permeability. The interpolations
are functions of the trapping parameters and trapping
of oil endpoint and Corey’s exponent are functions
number. Because the trapping number is a function of
of contact angle as shown in Eqs. (3.58) and (3.59).
contact angle, as shown in Eqs. (3.60)e(3.62), the alter-
The validation of the empirical model is performed
ation of contact angle during LSWF modifies the residual
against the coreflooding of experiments. The proposed oil saturation, endpoint, and Corey’sexponent of oil
empirical model successfully matches the oil recoveries relative permeability.
from the experiments.
high
S low S or
LS

S or ¼ q S þð1 q ÞS HS (3.56) S or ¼ S high þ or (3.63)
or or or 1 þ T o ðN T Þ s o
HS high low
q q where S or and S are the residual oil saturations at the
q ¼ (3.57) or
LS HS
q q high and low trapping numbers, T o is the first trapping
k o LS k o HS parameter, and s o is the second trapping parameter,
o ro ro o HS
k ¼ e þ k (3.58)
ro ro which incorporates the effects of heterogeneity and
q
1 þ
a initial oil saturation on residual oil saturation.
In the fundamental model, the LSWF is assumed to
n o;max n LS LS modify contact angle contributing to the trapping
o
n o ¼ e þ n o (3.59)
q number. It employs two approaches modifying contact
1 þ
a angle during LSWF. The first approach adopts the poly-
where q is the contact angle, q* is the normalized nomial relation between contact angle and salinity,
contact angle between high and low salinity threshold used in the first methodology of empirical model. The
HS LS second approach for calculating contact angle considers
conditions, q and q are contact angle at the high
and low threshold conditions, k o ro is the endpoint of the EDL thickness or Debye length as shown in
oil relative permeability, k o HS and k o LS are the end- Eq. (3.64). The Debye length is approximately
ro ro
points of oil relative permeability, respectively, at high determined by Eq. (3.65). The fundamental model
and low threshold conditions, a is the inflection point successfully matches the historical observations of
from curve fitting, and e is the hill slope. coreflooding experiments.
The second approach of fundamental model interpo-
B
lates the residual oil saturation and oil relative perme- q ¼ A þ 1 (3.64)
k
ability by the trapping number. For the horizontal s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
system, the trapping number is defined with capillary 1 ε r ε 0 k B T
¼ 2 (3.65)
k
number, the ratio of viscous to capillary forces, and 2N A e I
Bond number, the ratio of gravity to capillary forces as where A and B are the fitting parameters, N A is the
shown in Eqs. (3.60)e(3.62).
Avogadro constant, and e is the elementary charge.
q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi The third approach of wettability modification
2
N T ¼ N þ N 2 (3.60)
c B
modeling is the mechanistic model using the effective
molar Gibbs free energy of solution. The effective
vm
N c ¼ (3.61)
molar Gibbs free energy of solution is defined as the
s cos q