Capturing CO2 from ambient air - David Keith

3.3.1 CO2 depletion in air
With longer residence times and denser sprays, the CO2 in air becomes depleted toward the bottom of the
tower, leading to lower absorption efficiency there. This is an effect common to a large class of absorbers,
and is generally represented by first order decay (Fair et al., 2001). This effect was already accounted for
in Table 3.1, and is relatively minor unless the system is tuned to capture much more than half of the CO2
from process air.
3.3.2 Changing drop size due to evaporation
There is also an effect of changing drop size due to evaporation as the drops fall. Theoretically, absorption
will decrease because of the smaller surface area as the drop evaporates, but increase because the OH −
becomes more concentrated. We know from Equation 3.5 and the preceding derivation that absorption is
proportional to surface area, As, and to the square root of [OH − ]:
Q ∝ As[OH − ] 1 2.
Replacing those terms with their relationships to drop volume,Vd, we get:
Q ∝ V 2 3
d
·(V −1
d ) 1 2 = V 1 6
d .
As the drop evaporates, Vd gets smaller so absorption declines, but not very quickly. The change in volume
for a single pass should not be very large to begin with, perhaps 20% for a high evaporation rate. This
gives a maximum change in instantaneous absorption rate of about 4%. Thus, changing drop size due to
evaporation does not appear to have a significant effect on scale-up.
3.3.3 Spray droplet collision, coalescence, and breakup
As drops fall through the tower, they collide with each other. If we assume a roughly uniform flow field,
then this process is driven by differential settling. That is, larger drops fall faster and strike smaller drops
beneath them. If the distribution of drops were monodisperse, i.e. all drops were the same size, then no
collisions would occur. With a very wide distribution, collisions tend to be dominated by the largest drops
falling very fast and striking smaller drops along the way. When two drops collide, essentially one of
two things can happen: they can coalesce into a larger stable drop (“coalescence”), or they can coalesce
temporarily then break apart into many, smaller drops (“collisional breakup”) due to internal turbulence
created by the collision or entrained air causing instability. They can also bounce off one another, retaining
their original sizes, but for purposes of calculation this is not considered a collision.
The probability of coalescence given a collision is denoted Ecoal, and so the probability of breakup
given a collision is (1 − Ecoal). Ecoal is a function of the drop sizes, fluid characteristics (surface tension,
viscosity, ...), collision speed and angle. For water drops falling in air and colliding by differential settling,
the only situation we will consider, Ecoal is only a function of drop size and it is found empirically. Values
range from close to 1 for both drops smaller than 50 µm in diameter, to 0.5 for a 300 µm drop striking a
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