Absorption - Introduction to Carbon Capture and Sequestration - page 174

Box 5.2.2 Henry's Law

Henry's law can be derived in several different ways. Here we start with a simple kinetic
argument. We are interested in the relation between the partial pressure of CO 2 in the
gas phase and the solubility in the liquid phase. If we are at equilibrium, the number of
CO 2 molecules per unit of time escaping from the liquid phase into the gas phase should
be equal to the number of CO 2 molecules that go from the gas phase to the liquid:

Φ CO 2 (gas → liquid) = Φ CO 2 (liquid → gas)

If we assume that CO 2 behaves like an ideal gas, the fl ux from the gas to the
liquid phase is simply proportional to the number of gas molecules that collide with the
surface. This number is proportional to the partial pressure of CO 2 :

Φ CO 2 (gas → liquid) ∝ N CO 2 = p CO 2 = y CO 2 p

Also for the liquid we can assume that if the liquid behaves as an ideal solution, in
which CO 2 molecules are not infl uenced by the presence of other molecules, the fl ux
of CO 2 molecules escaping the liquid phase is proportional to the mole fraction:

Φ CO 2 (liquid → gas) ∝ x CO 2

Equating the two fl uxes gives us:

y
x

CO
CO

=κ

2

2

For a real fl uid, our assumptions only hold in the limit of very low pressure, which is
often called the Henry regime. In this regime, we have an ideal gas and our equation
can be rewritten in terms of the density of CO 2 molecules that are absorbed in a liquid
and the partial pressure of CO 2 :

ρ CO 2 = K CO 2 p CO 2 ,

where ρ CO 2 is the density of CO 2 in the liquid (number of moles per unit volume) and

K CO 2 is the Henry coeffi cient of the solvent. The units of the Henry coeffi cient can vary.
Here we have number of moles per unit volume per unit pressure, but if we express
the concentration of the solvent in kg CO 2 per kg liquid, the dimension of the Henry
coeffi cient is per unit pressure.

relation between the mole fraction of CO 2 in the solvent and in the
flue gas:

y CO 2 = κ x CO 2