Environmental Engineering Reference
In-Depth Information
Calculation of the advective fl uxes between neighboring simulation
grid blocks requires solving Darcy's law in each fl uid phase. Darcy's law
was introduced in Box 9.6.1 for fl ow in the horizontal directions. In the
vertical direction one has to account for the effect of gravity, which gives:
()
kk
S
p
r,
i
g
i
(I)
u
=−
−ρ
g
j
i
µ
z
i
where i
w or g for the water- and CO 2 -rich phases, p i is the density of the
phase of interest and g is the gravitational acceleration. Values of p g and p w
differ by the capillary pressure p c , a function of CO 2 saturation: p g
=
p w =
p c ( S g ). The characteristic curves relate these properties to the saturation
(see Section 9.7).
Field-scale model assumptions
Here we discuss several phenomena for which we do not yet have the funda-
mental scientifi c understanding required to optimally include them in our fi eld-
scale sequestration models: mixing, the impact of weathering on permeability,
organic and biological effects, confi nement effects, and reactions in adsorbed
water fi lms. The assumptions incorporated in our models simplify or neglect
these effects. A better understanding of these phenomena would signifi cantly
enhance the reliability of our model predictions.
Mixing
An important assumption in fi eld-scale simulations, inherent in their grid-
based discretization of space, is that the system is well-mixed within
Question 10.2.1 Characteristic time scale of CO 2
dissolution in brine
Field-scale sequestration models assume that CO 2(aq) concentration is uniform
in the brine-fi lled pore space between the CO 2 fi ngers. In reality, on what time
scale does CO 2(aq) diffuse into the space between CO 2 fi ngers? The character-
istic time scale τ of diffusion (with diffusion coeffi cient D ) over a distance d is
given by the relation τ d 2 /2 D . The diffusion coeffi cient of CO 2 in water at 50 ° C
is D 4 x 10 9 m 2 s 1 . Calculate τ if the distance between CO 2 fi ngers is either
2 mm or 2 m.
Search WWH ::




Custom Search