Fluids and Rocks - Introduction to Carbon Capture and Sequestration - page 423

only able to displace brine from the large pores. To further decrease the
brine saturations, we need to increase our pressure on the CO 2 to dis-
place the water in the smaller pores. We can continue to increase the
pressure until the non-wetting phase dominates the pore space. At this
point we have a disconnected, immobile, brine phase. As the CO 2 can
bypass these pockets of brine, a further increase of the CO 2 pressure
does not displace any brine. The relation between the capillary pressure
and the brine saturation is illustrated in Figure 9.7.2. The capillary pres-
sure increases when the volume fraction of the non-wetting phase in the
pores increases. The maximum capillary pressure is reached when the
wetting phase is at its lowest point of saturation, the point of residual
saturation or irreducible saturation .
Models have been developed to describe the relative permeability
and capillary pressure as a function of the saturation. The functions
k r,g ( S g ), k r,w ( S g ), and p c ( S g ) are referred to as the characteristic curves of
the porous medium. Several semi-empirical relations have been pro-
posed for modeling these curves, for example:

m

( )

0.5 1/ m

∗ ∗

k = S 11 − − S (I)

r,w

1 − m

− 1/ m

∗

(II)

c ppS

= − 1

0

2

( )

2

(III)

k =− 1 S ′ 1 − S ′

r,g

where p 0 (MPa) and m are fi tting parameters and S ∗ and S ' are rescaled
brine saturations:

SS − SS −

w , r w , r

∗

S = and S ′ =

1 − S S − S − S

w, r w w, r g, r

The rescaled brine saturations take into account the residual brine satu-
ration of the porous medium S w, r and the residual CO 2 saturation S g, r .
The proposed equations (I-III) suitably describe expected trends: p c
is greater than zero and increases with S g , as pressure must be applied