Page 51 - Hybrid Enhanced Oil Recovery Using Smart Waterflooding

CHAPTER 3 Modeling of Low-Salinity and Smart Waterflood 43

The selectivity coefficient following Gapon convention z i Fj 0
is written in Eq. (3.33). ln K a ¼ ln K int RT (3.37)
1 where K a is the apparent dissociation constant and K int
þ
Na þ Ca 0:5 -X4Na-X þ Ca 2þ (3.32)
2 is the intrinsic dissociation constant.
The apparent dissociation constant varies with
2þ 0:5

zðNa-XÞ Ca
K Ca=Na ¼ (3.33) the surface potential of rock and can be measured
0
þ
zðCa 0:5 -XÞ½Na Š
experimentally. The intrinsic dissociation constant is a
constant describing the chemical binding. As an
example for the surface complexation, the surface
Surface complexations
In addition to the ion exchange, there are other types of protolysis reaction is shown in Eq. (3.38). Because
the adsorption of the species to the surface of solid. The the charge valence of proton is unity, the apparent
surface complexation describes the attachments of spe- dissociation constant of the surface protolysis reaction
cies to the existing functional groups of the solid surface is depicted in Eqs. (3.39) and (3.40).
of amorphous aluminosilicates, metal oxides/hydrox-
þ
h SOH þ H 4h SOH 2 þ (3.38)
ides, and organic matters (Al-Shalabi & Sepehrnoori,

2017). Generally, there are three models to describe hSOH 2 þ
the surface complexation: (1) constant capacitance K a ¼ ½hSOHŠ½H Š (3.39)
þ
model, (2) the diffuse layer model, and (3) the triple
layer model. Practically, a double layer model can be K a ¼ K int exp Fj 0 (3.40)
RT
applicable to comprehensive fluid-based systems and is
composed of the constant capacitance model and diffuse where the prefix “h” represents the species at the solid
layer model, generally, via the Gouy-Chapman model. surface.
In the double layer model, the description of the
surface complexation using the Gibbs free energy EMPIRICAL MODELING WITHOUT
change has two terms. The first term is a chemical GEOCHEMISTRY
bond between the ions and surface atoms. The second
Research group of BP has published the numerical
one is an electrostatic effect affected by the surface
studies of LSWF modeling in sandstone reservoirs
charge. Therefore, the Gibbs free energy of surface
(Jerauld, Webb, Lin, & Seccombe, 2006, Jerauld,
complexation can be described in Eq. (3.34).
Webb, Lin, & Seccombe, 2008). They hypothesized
(3.34)
DG total ¼ DG chem þ DG coul the potential mechanism for increased oil recovery of
where DG total is the total DG of surface complexation, LSWF is the wettability alteration. They modeled the
DG chem is the DG of the intrinsic chemical reactions at wettability alteration of LSWF and, approximately,
the surface, and DG coul is the DG of electrostatic or physical dispersion of mixing between connate water
Coulombic interaction. and injected water. Conventionally, the wettability
The electrostatic term counts for the electrostatic modification is modeled through the modification of
interaction between an ion and a charged surface. It is relative permeability and capillary pressure curves. The
the difference between energy state of 1 mole of ion at studies have adapted a simple empirical approach to
the surface and that in the bulk of the solution as model the wettability modification because of unclear
defined in Eq. (3.35). predictive physics to explain the wettability modifica-
tion. Experimental works in the previous chapters
DG coul ¼ DG j¼j 0 DG j¼0 ¼ z i Fðj 0 0Þ¼ z i Fj 0 (3.35) have demonstrated that the incremental oil recovery
depends on the salinity of the brine, but it is not simply
where DG j¼0 is the DG of 1 mole ion in the bulk of the
indicates the DG of proportional to the salinity. Therefore, the empirical
solution and equal to zero, DG j¼j 0
1 mole ion at the surface, F is the Faraday constant, and approach assumes that salinity-dependent residual oil
j 0 is the surface potential. saturation is an interpolation factor to modify relative
Introducing Eq. (3.9), the Gibbs free energy change permeability and capillary pressure. In the approach,
of the surface complexation model is rewritten with the residual oil saturation linearly depends on the
mass action constant as shown in Eqs. (3.36) and salinity between the low and high threshold salinities
(3.37). and is to be constant beyond the threshold conditions
(Fig. 3.1). Therefore, the relative permeability and
RT ln K a ¼ DG total ¼ RT ln K int z i Fj 0 (3.36) capillary pressure curves are linearly modified between