Chemical engineering transport & equilibrium foundations of Gas Absorption in Packed Column.
Gas absorption (scrubbing) is a fundamental mass transfer separation operation in chemical plants, environmental emissions control, and synthesis gas purification, responsible for removing acid gases (CO_2, H_2S, SO_2) from gas streams by dissolving them into a liquid solvent. In a counter-current packed tower, gas enters at the bottom and ascends through packing, while liquid solvent is distributed over the top and trickles downward over packing elements (such as Raschig rings or structured gauze). Interfacial mass transfer is described by the two-film theory of Whitman (1923), which posits stagnant gas and liquid films on either side of the phase interface. The volumetric mass transfer rate is N_A · a = K_G a · (P_A - P_A*), where K_G a is the overall volumetric gas-phase mass transfer coefficient, 'a' is the effective gas-liquid interfacial area per unit packed volume, P_A is solute partial pressure in the bulk gas, and P_A* is equilibrium partial pressure over the liquid. For physical absorption of sparingly soluble gases like carbon dioxide in water, liquid film resistance dominates overall transport: 1 / K_G a = 1 / (k_G a) + H / (k_L a), where H is Henry's law constant. According to Onda's classic packed bed mass transfer correlations, liquid-side mass transfer coefficient k_L and wetted specific area 'a' scale with liquid mass velocity as L^0.7. In this laboratory investigation, an instrumented 1.5-meter packed tower absorbing CO_2 into water is operated across liquid irrigation rates from 10.0 to 60.0 L/(min·m^2) to measure K_G a, verify L^0.7 scaling, and determine the Height of a Transfer Unit (HTU).
1. Fundamentals of Gas Absorption in Packed Towers
Gas absorption involves the selective dissolution of one or more soluble gas components into a non-volatile liquid solvent. In chemical manufacturing, absorption columns recover valuable synthesis products (e.g., ammonia, methanol) and capture hazardous environmental contaminants (e.g., $\text{CO}_2, \text{SO}_2, \text{NO}_x$).
2. Two-Film Mass Transfer Theory
According to Walter G. Whitman's two-film model (1923), mass transfer between gas and liquid phases is resisted by laminar fluid films adjacent to the interface. The steady molar transfer flux $N_A$ of solute gas is expressed as:
\[ N_A = k_G (P_{A,b} - P_{A,i}) = k_L (C_{A,i} - C_{A,b}) \]where $k_G$ and $k_L$ are individual film coefficients, $P_{A,b}$ is bulk gas partial pressure, and $C_{A,b}$ is bulk liquid concentration. Thermodynamic phase equilibrium at the interface is governed by Henry's law: $P_{A,i} = H C_{A,i}$. Defining the overall volumetric mass transfer coefficient $K_G a$ based on gas-phase driving force:
\[ N_A a = K_G a (P_{A,b} - P_A^*) \] \[ \frac{1}{K_G a} = \frac{1}{k_G a} + \frac{H}{k_L a} \]For sparingly soluble gases like $\text{CO}_2$ in water, $H$ is large ($H \approx 1400\text{ bar}\cdot\text{L/mol}$), meaning liquid film resistance $H / (k_L a)$ accounts for $> 95\%$ of total resistance, establishing liquid-film control: $K_G a \approx k_L a / H$.
3. Onda Correlation & Liquid Irrigation Scaling
Kakusaburo Onda et al. (1968) correlated mass transfer coefficients and wetted area in packed beds: wetted area $a_w / a_t$ and liquid film coefficient $k_L$ scale with liquid mass flux $L$ as $L^{0.7}$. Combining these gives the volumetric mass transfer model:
\[ K_G a = S \cdot L^{0.7} \]where $S$ is the absorption scaling slope in $\text{kmol/(m}^3\cdot\text{h}\cdot\text{bar)/(L/(min}\cdot\text{m}^2))^{0.7}$.
4. Design Integration: HTU and NTU
Integrating the differential mass balance along column height $Z$:
\[ Z = \left[ \frac{G}{K_G a P} \right] \int_{y_{out}}^{y_{in}} \frac{dy}{y - y^*} = HOG \cdot NOG \]where $HOG = \frac{G}{K_G a P}$ is the Height of an Overall Gas Transfer Unit, and $NOG$ is the Number of Transfer Units.
Viva voce questions & analytical theory
What is the difference between physical absorption and chemical absorption?
Physical absorption (e.g., CO_2 in water) relies purely on physical solubility governed by Henry's law with low solvent capacity; chemical absorption (e.g., CO_2 in aqueous monoethanolamine MEA) involves rapid chemical reaction that converts solute into non-volatile ionic species, dramatically accelerating mass transfer and capacity.
How are the Height of a Transfer Unit (HTU) and Number of Transfer Units (NTU) defined?
Total packed height is Z = HTU × NTU; NTU represents the separation difficulty (dimensionless change in concentration divided by average driving force), while HTU characterizes mass transfer efficiency (smaller HTU means a more efficient packing requiring less height).
Why does liquid irrigation rate L have a strong effect on effective interfacial area 'a'?
At low liquid rates, liquid trickles in narrow rivulets, leaving large portions of packing dry; increasing L wets more of the packing surface, converting dry area into thin liquid films and increasing effective contact area 'a' towards total geometric area a_p.
What is the loading point and flooding point in packed column hydrodynamics?
The loading point is the gas velocity where ascending gas starts to hold up descending liquid, increasing liquid holdup and pressure drop slope; the flooding point occurs when upward drag halts liquid drainage entirely, causing liquid to fill the column and spit out the top.
Why does liquid film resistance control mass transfer in CO_2–water absorption?
Carbon dioxide has low solubility in water (large Henry's constant H ≈ 1400 bar at 20 °C); according to two-film theory 1/K_G a = 1/(k_G a) + H/(k_L a), the second term accounts for > 95% of total resistance, making liquid film transport rate-limiting.
How does Henry's law constant H vary with solvent temperature?
Gas dissolution is an exothermic process (ΔH_sol < 0); increasing solvent temperature decreases gas solubility, increasing Henry's constant H and degrading absorption driving force and capacity.
Experimental precautions and process safety
- Carbon dioxide is an asphyxiant; vent column exhaust gases safely through a dedicated laboratory exhaust duct.
- Ensure liquid distributor holes are clear to prevent localized liquid channeling and dry zones along the wall.
- Monitor column pressure drop continuously; if pressure drop spikes rapidly, decrease gas flow to prevent column flooding.
- Verify water temperature remains at 20.0 ± 0.5 °C, as CO_2 solubility is sensitive to temperature.
Theoretical assumptions & boundary condition limits
- The transport and thermodynamic models apply within the specified calibrated operating window (10.0 to 60.0 L/(min·m^2)).
- Assumes ideal continuum flow and homogeneous phase mixing without unmodeled parasitic wall losses.
- Continuous sensor readings reflect ordinary least-squares regression across successive observations.
- High-temperature or extreme concentration excursions require non-ideal equation-of-state corrections.