Absorption - Introduction to Carbon Capture and Sequestration - page 199

If we assume that we have a steady state, with boundary conditions
c CO 2 (0)

c CO 2 , where L is the thickness of the bound-
ary layer between the gas and bulk liquid, the solution is:

c CO 2 and c CO 2 (L) = =

( )

z

()

0 0 *

c z = c − c − c

CO CO

CO CO

L

2 2

2 2

For practical applications we are interested in the fl ux of CO 2 across our
unit interface, which follows directly from Fick's law:

D

( ) ( )

CO

0 * eff 0 *

j =

2

c − c = k c − c

CO CO CO

CO CO

L

2 2 2

2 2

In this equation, we have defi ned an effective mass transport coeffi cient
k eff . The total amount of CO 2 we have to remove is given by the total
amount of fl ue gas. For a given solvent, we have a corresponding value
for k eff . Therefore in order to ensure that we can capture all the CO 2 , we
either need to increase the total area in the absorber, or we need to
increase the driving force (c 0 CO 2 - c ∗ CO 2 ). If our effective mass transfer
coeffi cient is suffi ciently large, we can allow for a very small driving force.
Another interpretation of this driving force is that the actual concentration
in the solvent c CO 2 differs from the equilibrium concentration c CO 2 :

j

CO

∗ 0

c = c −

2

k

CO 2

CO 2

eff

This is the origin of the shift in the equilibrium line shown in Figure 5.4.1 .

Chemical reaction

In our design, we assumed that absorption can be simply described with
Henry's constant or solubility. But with amine solutions, we have to take
into account how the chemical reaction is infl uencing the absorption
process.
Let us assume we introduce a chemical “B” into the water. “B” reacts
with CO 2 via a fi rst order reaction:

B + CO 2 BCO 2