Fluids and Rocks - Introduction to Carbon Capture and Sequestration - page 420

Section 7
Two-phase flow

In the previous section, we looked at the permeation of a single phase
through a geological formation. After injection, most of the CO 2 will
remain in its supercritical form as a free phase fl uid that is mostly immis-
cible with native formation brine for decades to hundreds of years. Hence,
the transport of CO 2 through an aquifer is a two-phase fl ow process.

Relative permeability

In the previous section ( Box 9.6.1 ), we defi ned the single phase perme-
ability using Darcy's law :

k

j =− ∇ p ,

µ

where ∇ p is the pressure gradient, the viscosity of the fl uid, and k is the

single phase permeability of the rock. To extend Darcy's law to two-
phase fl ow, we can defi ne an effective permeability of phase i :

µ

k kk

ij

ri ,

j =− ∇ p =− ∇ p ,

i i i

µ µ

i i

where k ij is the effective permeability of phase i in the presence of phase
j . In the second equation, we have introduced the relative permeability
k r,i of phase i in the presence of phase j , which is defi ned as the effective
permeability divided by the single phase permeability ( Box 9.7.1 ).
To describe the permeation of a two-phase fl uid through our rock, we
need to know how the relative permeability depends on the volume frac-
tion of the pores that is occupied by each of the phases. The fraction of
the pure volume that is occupied by phase i is called the phase satura-
tion (e.g., brine saturation or CO 2 saturation):

VV

i i

S == φ ,

i

VV

p T