Page 237 - Enhanced Oil Recovery in Shale and Tight Reservoirs

220 Enhanced Oil Recovery in Shale and Tight Reservoirs

9.4 Mathematical treatments of wettability alteration
and IFT effect

The mechanisms of IFT reduction are more discussed and formulated
in the literature, but not for the mechanisms of wettability alteration. There-
fore, a special section is dedicated to present the mathematical treatments.
Four models are presented in this section: UTCHEM model, Adibhatla
et al. (2005) model, a proposed simple model and a CMG model.

9.4.1 UTCHEM model
A common practice to consider wettability alteration is to modify the rela-
tive permeability term and capillary pressure term of mixed wettability based
on strongly wetting and strongly nonwetting relative permeability and capil-
lary pressure curves (Delshad et al., 2009):
ww ow
k r ¼ uk r þð1 uÞk r (9.8)
p c ¼ up ww þð1 uÞp ow (9.9)
c
c
where the superscript ww and ow mean water-wet and oil-wet, respectively,
k r is the relative permeability, and p c is the capillary pressure. u is the
interpolation scaling factor to describe the effect of wettability and depends
on surfactant adsorption:

b
C surf
u ¼ (9.10)
b
C surf þ C surf
where C surf and C surf are the adsorbed and equilibrium concentrations of
b
surfactant, respectively. Those equations assume that surfactant adsorption
on rock surfaces increases water-wetness. If surfactant adsorption increases
oil-wetness, those equations can be modified accordingly. This model is
implemented in UTCHEM version 9.95 (UT Austin, 2009).
The capillary pressure p Cwo is scaled with the interfacial tension and rock
properties:
r ffiffiffi ww ww
f s cosq S w S wr E pc
ww
wo
p Cwo ¼ C pc ow 1 (9.11)
ow
k s cosq 1 S wr S or
wo
p ffiffiffiffiffiffiffiffi
where C pc f=k takes also into account the effect of permeability and
porosity using the Leverett-J function (Leverett, 1941), f is the porosity and
k is the permeability, s wo is the water-oil interfacial tension, S is the