Adsorption - Introduction to Carbon Capture and Sequestration - page 244

Typically, the additional variables we look at are the gas velocity that
comes into the bed, the amount of space the particles themselves take
up, or bed voidage . In principle, it is possible to call “Adsorbers-R-Us”
and ask for X pounds of our favorite solid adsorbent. But fi rst, we would
need to know how much is X? To answer this question, let us start with
a fi xed-bed reactor. To simplify our design we assume we have two col-
umns; one for the adsorption and one for the regeneration. We know the
fl ow rate of the fl ue gas from which we need to remove CO 2 . In order to
know how much material to buy, we need to know the equilibrium prop-
erties of the material, including the amount of CO 2 adsorbed per unit
time, the capacity of the porous media, and the selectivity of the porous
media. Furthermore, we need to understand the dynamics of the system
down to the level of diffusion inside the pores. This is not an easy task.
Let us fi rst envision how the CO 2 propagates through these devices.
If we have an ideal adsorbent, equilibrium between the fl ue gas and the
gas adsorbed in the material is established instantaneously. This equili-
brium concentration is given by the adsorption isotherm, which gives the
amount of CO 2 adsorbed inside the material as a function of the partial
pressure. Let us assume we inject the gas in the left of the column. CO 2
adsorbs inside the material until the equilibrium concentration is
reached. At this point the material cannot adsorb CO 2 anymore, so a
CO 2 front will form and slowly move through the column until it has
reached the right of the column. Finally, the CO 2 breaks through the
adsorber and the adsorber needs to be regenerated. This behavior is
illustrated in Figure 6.3.2 .
Figure 6.3.3 shows some breakthrough curves of more realistic sys-
tems (where the CO 2 concentration in the outlet increases more gradu-
ally). Inspection of these qualitative curves informs us that steeper
breakthrough curves result in more effi cient use of the adsorption bed.
We will now show how these breakthrough curves are calculated.
Quantitative analysis of breakthrough curves
We would like to determine the density of CO 2 as a function of the posi-
tion and time in the adsorption bed. If we assume that the adsorber is a
cylinder parallel to the z -direction with a uniform radial profi le of adsorp-
tion, the problem has only one distance dimension, the distance down
the bed. The fi rst step is a mass balance for CO 2 over a control volume