Henry's Law & Gas Absorption

The Thermodynamics of Absorption

Gas absorption (scrubbing) is the process of removing a specific pollutant gas (like $H_2S$, $CO_2$, or $NH_3$) from a gas stream by dissolving it into a liquid solvent.

Before we can calculate the mass transfer rate, we must know the absolute maximum amount of gas the liquid is capable of holding. This thermodynamic limit is defined by the gas's solubility.

Henry's Law

For dilute solutions (where the gas concentration in the liquid is small, typically < 5 mole percent), solubility is governed by Henry's Law, discovered by William Henry in 1803.

It states that the partial pressure of the gas above the liquid is directly proportional to the concentration of the dissolved gas in the liquid:

$$ P_i = H \cdot x_i $$

Where:

• $P_i$ = Partial pressure of the gas component in the vapor phase (atm)
• $x_i$ = Mole fraction of the dissolved gas in the liquid phase
• $H$ = Henry's Law Constant (atm/mole fraction)

Interpreting the Henry's Constant ($H$)

The value of $H$ is specific to the exact Gas-Solvent pair (e.g., $CO_2$ in water, or $H_2S$ in amine) and is highly dependent on temperature.

• Large $H$: (e.g., Oxygen in water, $H \approx 43,000 \text{ atm}$). The gas is highly insoluble. Even at high pressures, very little gas dissolves into the liquid. It requires a massive amount of liquid solvent to scrub a small amount of this gas.
• Small $H$: (e.g., Ammonia in water, $H \approx 1 \text{ atm}$). The gas is highly soluble. It dissolves eagerly into the liquid. A very small flow of solvent can scrub massive amounts of this gas.

The Temperature Effect (Stripping)

Almost universally, gas solubility decreases as temperature increases. (Heating a liquid boils the dissolved gases out of it). Mathematically, this means $H$ increases exponentially with temperature.

Process engineers exploit this exact thermodynamic reality to build regeneration loops:

1. Absorption: The scrubber operates at cold temperatures (e.g., 30°C). $H$ is small. The gas easily dissolves into the solvent.
2. Stripping (Regeneration): The "rich" solvent is pumped to a Stripper column and heated with steam to 120°C. $H$ becomes massive. The gas is violently forced out of solution, regenerating the "lean" solvent to be reused in the scrubber.