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Gas- Liquid and Gas –Liquid –Solid Reactions. Basic Concepts. Proper Approach to Gas-Liquid Reactions. References Mass Transfer theories Gas-liquid reaction regimes Multiphase reactors and selection criterion Film model: Governing equations, problem complexities

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Proper Approach to Gas-Liquid Reactions

    • References
  • Mass Transfer theories
  • Gas-liquid reaction regimes
  • Multiphase reactors and selection criterion
  • Film model: Governing equations, problem complexities
  • Examples and Illustrative Results
  • Solution Algorithm (computational concepts)
theories for analysis of transport effects in gas liquid reactions
Theories for Analysis of Transport Effects in Gas-Liquid Reactions

Two-film theory

1.W.G. Whitman, Chem. & Met. Eng., 29 147 (1923).

2. W. K. Lewis & W. G. Whitman, Ind. Eng. Chem., 16, 215 (1924).

Penetration theory

P. V. Danckwerts, Trans. Faraday Soc., 46 300 (1950).

P. V. Danckwerts, Trans. Faraday Soc., 47 300 (1951).

P. V. Danckwerts, Gas-Liquid Reactions, McGraw-Hill, NY (1970).

R. Higbie, Trans. Am. Inst. Chem. Engrs., 31 365 (1935).

Surface renewal theory

P. V. Danckwerts, Ind. Eng. Chem., 43 1460 (1951).

Rigorous multicomponent diffusion theory

R. Taylor and R. Krishna, Multicomponent Mass Transfer,

Wiley, New York, 1993.

two film theory assumptions
Two-film Theory Assumptions

1. A stagnant layer exists in both the gas and the liquid phases.

2. The stagnant layers or films have negligible capacitance and hence a local steady-state exists.

3. Concentration gradients in the film are one-dimensional.

4. Local equilibrium exists between the the gas and liquid phases as the gas-liquid interface

5. Local concentration gradients beyond the films are absent due to turbulence.

two film theory concept w g whitman chem met eng 29 147 1923
Two-Film Theory ConceptW.G. Whitman, Chem. & Met. Eng., 29 147 (1923).



pAi = HA CAi

Bulk Gas

Gas Film

Liquid Film

Bulk Liquid




x + x


x = G

x = 0

x = L

two film theory single reaction in the liquid film
Two-Film Theory- Single Reaction in the Liquid Film -

A (g) + b B (liq) P (liq)

B & P are nonvolatile

Closed form solutions only possible for linear kinetics

or when linear approximations are introduced


Gas-Liquid Reaction Regimes


Fast (m, n)

Rapid pseudo

1st or mth order

Instantaneous & Surface

General (m,n) or Intermediate

Slow Diffusional

Very Slow

characteristic diffusion reaction times
Characteristic Diffusion & Reaction Times
  • Diffusion time
  • Reaction time
  • Mass transfer time
reaction diffusion regimes defined by characteristic times
Reaction-Diffusion Regimes Defined by Characteristic Times
  • Slow reaction regimetD<<tR kL=kL0
    • Slow reaction-diffusion regime: tD<<tR<<tM
    • Slow reaction kinetic regime: tD<<tM<<tR
  • Fast reaction regime: tD>>tR kL=EA kL0>kL0
    • Instantaneous reaction regime: kL= EAkL0
comparison between theories
Comparison Between Theories
  • Film theory:
    • kL D,  - film thickness
  • Penetration theory:
    • kL D1/2

Higbie model

t* - life of surface liquid element

Danckwerts model

s - average rate of surface renewal





Gas Absorption Accompanied by Reaction in the Liquid


- 2nd order rate

Hatta Number:

Ei Number:

Enhancement Factor:



Eight (A – H) regimes can be distinguished:

A. Instantaneous reaction occurs in the liquid film

B. Instantaneous reaction occurs at gas-liquid interface

  • High gas-liquid interfacial area desired
  • Non-isothermal effects likely



C. Rapid second order reaction in the film. No unreacted A penetrates into bulk liquid

D. Pseudo first order reaction in film; same Ha number range as C.

Absorption rate proportional to gas-liquid area. Non-isothermal effects still possible.



Maximum temperature difference across film develops at complete mass transfer limitations

Temperature difference for liquid film with reaction

Trial and error required. Nonisothermality severe for fast reactions.

e.g. Chlorination of toluene


summary limiting reaction diffusion regimes
- Summary -Limiting Reaction-Diffusion Regimes

Slow reaction kinetic regime

  • Rate proportional to liquid holdup and reaction rate and influenced by the overall concentration driving force
  • Rate independent of klaB and overall concentration driving force

Slow reaction-diffusion regime

  • Rate proportional to klaB and overall concentration driving force
  • Rate independent of liquid holdup and often of reaction rate

Fast reaction regime

  • Rate proportional to aB,square root of reaction rate and driving force to the power (n+1)/2 (nth order reaction)
  • Rate independent of kl and liquid holdup

Instantaneous reaction regime

  • Rate proportional to kL and aB
  • Rate independent of liquid holdup, reaction rate and is a week function of the solubility of the gas reactant

Gas – Liquid Solid Catalyzed Reaction A(g)+B(l)=P(l)

Gas Limiting Reactant (Completely Wetted Catalyst)



Our task in catalytic reactor selection, scale-up and design is to either maximize volumetric productivity, selectivity or product concentration or an objective function of all of the above. The key to our success is the catalyst. For each reactor type considered we can plot feasible operating points on a plot of volumetric productivity versus catalyst concentration.

Clearly is determined by transport limitations and by reactor type and flow regime.Improving only improves if we are not already transport limited.


key multiphase reactor types
Key Multiphase Reactor Types

• Mechanically agitated tanks

• Multistage agitated columns

• Bubble columns

• Draft-tube reactors

• Loop reactors

Soluble catalysts


Powdered catalysts

• Packed columns

• Trickle-beds

• Packed bubble columns

• Ebullated-bed reactors

Soluble catalysts


Tableted catalysts

classification of multiphase gas liquid solid catalyzed reactors
Classification of Multiphase Gas-Liquid-Solid Catalyzed Reactors

1. Slurry Reactors

Catalyst powder is suspended in the liquid

phase to form a slurry.

2. Fixed-Bed Reactors

Catalyst pellets are maintained in place as

a fixed-bed or packed-bed.

K. Ostergaard, Adv. Chem. Engng., Vol. 7 (1968)

modification of the classification for gas liquid soluble catalyst reactors
Modification of the Classification for Gas-Liquid Soluble Catalyst Reactors

1. Catalyst complex is dissolved in the liquid

phase to form a homogeneous phase.

2. Random inert or structured packing, if used,

provides interfacial area for gas-liquid contacting.


Key Multiphase Reactor Parameters

Trambouze P. et al., “Chemical Reactors – From Design to Operation”, Technip publications, (2004)