Fluid-fluid reactions and gas-liquid reactors
Gas-liquid reactions with the two-film model: Henry's law, physical absorption, Hatta number regimes, enhancement factor, the overall rate expression and contactor selection, with worked absorption-rate examples.
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Why it matters
Hydrogenations, oxidations with air, chlorinations, CO₂ and H₂S scrubbing with amines, and many fermentations all bring a gas into contact with a liquid in which it reacts. The overall rate can be limited by gas-film transfer, liquid-film transfer or chemical reaction, and the controlling regime decides whether you need a contactor with lots of interfacial area (packed or spray tower) or lots of liquid volume (bubble column, stirred tank).
Key ideas
Two-film picture. Gas A diffuses through a gas film to the interface, dissolves (equilibrium at the interface, Henry's law pAi = HA·CAi), diffuses through a liquid film, and reacts with dissolved B either in the film, in the bulk liquid, or both. B is non-volatile and stays in the liquid.
Physical absorption (no reaction). Rate per unit interfacial area: N_A = kAg·(pA − pAi) = kAl·(CAi − CA). Combining with Henry's law gives the overall rate with resistances in series: 1/KAg = 1/kAg + HA/kAl. For sparingly soluble gases (large HA, e.g. O₂ in water), the liquid film controls.
Enhancement factor. Reaction in the liquid film steepens the concentration gradient and speeds absorption: E = (rate with reaction)/(rate of physical absorption with the same driving force). E ≥ 1.
Hatta number. Compares maximum reaction in the film with maximum transport through it. For A + bB → products with −rA = k·CA·CB and B roughly uniform (pseudo-first-order k1 = k·CB): Ha = √(DA·k·CB)/kAl.
- Ha < 0.3: slow reaction — negligible reaction in the film; A dissolves and reacts in the bulk. Rate depends on liquid holdup and on kAl·a. Very slow reactions are kinetically controlled (bulk liquid nearly saturated).
- 0.3 < Ha < 3: intermediate — reaction in both film and bulk.
- Ha > 3: fast reaction — A reacts entirely within the film; E ≈ Ha (pseudo-first order, when B is not depleted), and the rate per area becomes CAi·√(DA·k·CB), independent of kAl. Interfacial area is what matters.
- Instantaneous reaction: A and B meet at a reaction plane inside the film; E = Ei = 1 + DB·CB/(b·DA·CAi). If CB is high enough the plane reaches the interface and gas-film resistance alone controls.
General rate expression (per unit contactor volume). For pseudo-first-order kinetics with A in the gas phase: −rA''' = pA / [1/(kAg·a) + HA/(kAl·a·E) + HA/(k·CB·fl)], where a is interfacial area per contactor volume and fl the liquid volume fraction. The three terms are gas-film, liquid-film (with enhancement) and bulk-liquid reaction resistances.
Choosing a contactor.
- Fast reactions (Ha > 3), gas-film or instantaneous: maximise interfacial area — packed towers, spray towers, plate columns.
- Slow reactions (Ha < 0.3): maximise liquid volume — bubble columns, sparged stirred tanks.
- Flow patterns (countercurrent plug flow vs mixed) are chosen as for single-phase reactors; countercurrent towers give the largest driving force.
- Selectivity, heat removal and handling of solids (slurry catalysts) can override these rules.
Temperature effects. Raising temperature speeds the reaction and diffusion but lowers gas solubility (HA rises), so the net effect on absorption rate can be small or even negative for physically controlled systems.
Formulas
pAi = HA·CAi (Henry's law)
- HA: Henry constant (Pa·m³/mol); pAi: interfacial partial pressure (Pa); CAi: interfacial liquid concentration (mol/m³).
N_A = kAl·(CAi − CA); rate per volume = kAl·a·(CAi − CA) (physical absorption)
- kAl: liquid-film coefficient (m/s); a: interfacial area per volume (m²/m³).
1/KAg = 1/kAg + HA/kAl (overall coefficient, no reaction)
- kAg: gas-film coefficient (mol/m²·Pa·s).
Ha = √(DA·k·CB)/kAl
- DA: diffusivity of A in liquid (m²/s); k: second-order rate constant (m³/mol·s); CB: bulk concentration of B (mol/m³).
E = Ha/tanh(Ha) (pseudo-first-order, film theory; E ≈ Ha for Ha > 3)
Ei = 1 + DB·CB/(b·DA·CAi) (instantaneous reaction)
−rA''' = pA / [1/(kAg·a) + HA/(kAl·a·E) + HA/(k·CB·fl)] (overall rate per contactor volume, pseudo-first order)
- fl: liquid volume fraction (dimensionless).
Worked examples
Example 1 (standard, physical absorption). A gas with pA = 20 kPa is absorbed in a stirred tank where kAl·a = 0.05 s⁻¹; HA = 4000 Pa·m³/mol and the gas film is negligible. The bulk liquid concentration is kept near zero. Find the absorption rate.
- CAi = pA/HA = 20 000/4000 = 5 mol/m³.
- Rate = kAl·a·(CAi − 0) = 0.05 × 5 = 0.25 mol/m³·s.
Rate = 0.25 mol/m³·s.
Example 2 (GATE level, Hatta number and enhancement). A dissolves (CAi = 5 mol/m³) into a liquid with excess B; pseudo-first-order constant k·CB = 400 s⁻¹, DA = 1.5 × 10⁻⁹ m²/s, kAl = 2 × 10⁻⁴ m/s, a = 100 m²/m³. Find Ha, the regime, E and the absorption rate per unit volume; compare with physical absorption.
- Ha = √(1.5 × 10⁻⁹ × 400)/2 × 10⁻⁴ = √(6 × 10⁻⁷)/2 × 10⁻⁴ = 7.746 × 10⁻⁴/2 × 10⁻⁴ = 3.87.
- Ha > 3, so the reaction is fast and occurs in the film; E = Ha/tanh(Ha) = 3.87/0.999 = 3.88.
- Rate = kAl·a·E·CAi = 2 × 10⁻⁴ × 100 × 3.88 × 5 = 0.388 mol/m³·s.
- Physical absorption alone: 2 × 10⁻⁴ × 100 × 5 = 0.100 mol/m³·s.
Ha ≈ 3.9 (fast regime); E ≈ 3.9; rate ≈ 0.39 mol/m³·s, about four times physical absorption. With k·CB = 100 s⁻¹, Ha would be 1.94 — the intermediate regime, where bulk-liquid volume also matters.
Common mistakes
- Using a Henry constant in one convention (mol/L·atm) with a formula written for the other (Pa·m³/mol).
- Forgetting that for fast reactions extra liquid volume does nothing — only area helps.
- Assuming E ≈ Ha even when B is depleted near the interface (then E is capped by Ei).
- Ignoring the gas-film resistance for very soluble gases or instantaneous reactions.
- Assuming higher temperature always increases absorption, overlooking falling solubility.
For GATE CH
Expect NAT questions on interfacial concentration from Henry's law, physical absorption rate from kLa, Hatta number and the resulting regime, enhancement factor for fast pseudo-first-order or instantaneous reactions, and contactor selection MCQs. Practise the series-resistance expression and unit conversions of Henry constants.
Quick check
- Ha = 0.1: where does the reaction occur?
- For a fast reaction, should you choose a bubble column or a packed tower?
- What is E for Ha = 5 (pseudo-first order)?
- With pA = 50 kPa and HA = 10 000 Pa·m³/mol, what is CAi?
Answers: 1. in the bulk liquid (slow reaction); 2. a packed tower (large interfacial area); 3. about 5; 4. 5 mol/m³.
Interview questions
All Chemical Reaction Engineering interview questionsTry answering each one aloud before you open it.
1.What is a fluid-fluid reaction in the context of chemical reaction engineering?Concept
A fluid-fluid reaction involves two or more reactants that are in different fluid phases, such as gas-liquid or liquid-liquid. These reactions are characterized by the transfer of mass and energy across the interface of the phases, and they often require careful control of mixing and contact time to achieve desired reaction rates and selectivity.
2.Explain the role of gas-liquid reactors in chemical processes.Concept
Gas-liquid reactors are used to facilitate reactions between gaseous and liquid reactants. They are essential in processes where a gas needs to be absorbed into a liquid phase to react, such as in hydrogenation, oxidation, or chlorination reactions. These reactors are designed to maximize the contact area between the gas and liquid phases, often using spargers, agitators, or packed columns to enhance mass transfer.
3.Why is mass transfer important in gas-liquid reactions?Application
Mass transfer is crucial in gas-liquid reactions because it determines the rate at which the gaseous reactant is absorbed into the liquid phase. Efficient mass transfer ensures that the reactants are available at the reaction site, which can significantly affect the overall reaction rate and yield. Poor mass transfer can lead to incomplete reactions and lower product quality.
4.What happens if the gas flow rate is too high in a gas-liquid reactor?Application
If the gas flow rate is too high, it can lead to excessive turbulence and foaming, which may cause operational issues such as flooding or entrainment. High gas flow rates can also reduce the residence time of the gas in the reactor, potentially decreasing the extent of the reaction if the gas does not have sufficient time to dissolve and react in the liquid phase.
5.Describe the effect of temperature on gas-liquid reaction rates.Application
Raising temperature increases the reaction rate constant strongly and the liquid diffusivity moderately, which helps both kinetically controlled and fast film reactions. But gas solubility usually falls with temperature (the Henry constant rises), lowering the interfacial concentration CAi that drives absorption. For mass-transfer-controlled or physically limited systems the net effect can be small or even negative, whereas for slow, kinetically controlled reactions the rate generally increases. Side reactions, solvent losses and degradation set the upper temperature limit.
6.How does the presence of a catalyst affect gas-liquid reactions?Application
A catalyst can significantly enhance the rate of gas-liquid reactions by providing an alternative reaction pathway with a lower activation energy. In gas-liquid systems, catalysts can be present in the liquid phase, as a solid in a slurry, or as a solid in a packed bed. The choice of catalyst and its form can influence the efficiency of mass transfer and the overall reaction rate.
7.What is the significance of the Hatta number in gas-liquid reactions?Concept
The Hatta number is a dimensionless parameter used to characterize the regime of gas-liquid reactions. It indicates whether the reaction is controlled by mass transfer or by chemical kinetics. A Hatta number much greater than one suggests that the reaction is fast compared to mass transfer, while a number much less than one indicates that the reaction is slow and mass transfer is not limiting.
8.Calculate the volumetric mass transfer coefficient (kLa) if the rate of oxygen absorption in a reactor is 0.02 mol/s, the concentration difference is 0.1 mol/m³, and the reactor volume is 2 m³.Numerical
To find the volumetric mass transfer coefficient (kLa), use the formula: Rate of absorption = kLa × Concentration difference × Volume. Rearranging gives kLa = Rate of absorption / (Concentration difference × Volume). Substituting the given values: kLa = 0.02 mol/s / (0.1 mol/m³ × 2 m³) = 0.1 s⁻¹.
9.A gas-liquid reactor operates at a pressure of 5 atm and a temperature of 300 K. If the Henry's law constant for the gas is 0.05 mol/(L·atm), calculate the solubility of the gas in the liquid.Numerical
According to Henry's law, the solubility of a gas in a liquid is given by S = kH × P, where S is the solubility, kH is the Henry's law constant, and P is the pressure. Substituting the given values: S = 0.05 mol/(L·atm) × 5 atm = 0.25 mol/L.
10.Explain how the design of a packed column enhances gas-liquid mass transfer.Application
A packed column enhances gas-liquid mass transfer by providing a large surface area for contact between the gas and liquid phases. The packing material, which can be made of various shapes and materials, increases the turbulence and promotes better mixing, leading to improved mass transfer rates. The design of the packing and the column height are optimized to ensure efficient contact and minimize pressure drop.
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