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 Examples and Illustrative Results Solution Algorithm (computational concepts)

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 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 pA pAi pAi = HA CAi • Bulk Gas Gas Film Liquid Film Bulk Liquid CAi • CAb x x + x L x = G x = 0 x = L

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 Instantaneous Fast (m, n) Rapid pseudo 1st or mth order Instantaneous & Surface General (m,n) or Intermediate Slow Diffusional Very Slow

Characteristic Diffusion & Reaction Times Diffusion time Reaction time Mass transfer time

Reaction-Diffusion Regimes Defined by Characteristic Times Slow reaction regime tD<<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

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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 Assume: - 2nd order rate Hatta Number : Ei Number: Enhancement Factor: S31

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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 S34

D. Pseudo first order reaction in film; same Ha number range as C. 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. S35

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Temperature difference for liquid film with reaction 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 S38

- 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

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Gas Limiting Reactant (Completely Wetted Catalyst) Gas – Liquid Solid Catalyzed Reaction A(g)+B(l)=P(l) Gas Limiting Reactant (Completely Wetted Catalyst) S21

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. S38

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Comparison Between Gas-Solid and Gas-Liquid-Solid Catalytic Converters Category Gas-Solid Catalytic Gas-Liquid-Solid Catalytic Design and engineering Simple More elaborate Material Often expensive material can be used Corrosion problems can be critical Catalyst Possible poisoning by non-volatile byproducts Resistance to corrosion is required Thermal control Low thermal stability and low heat capacity require internal heat exchange or low conversion Better stability and higher heat capacity; partial vaporization is possible; better heat exchange coefficient Reactant recycling Often important Stoichiometric ratio can generally be achieved; hydrodynamics can require gas recycling Safety Temperature run-away and ignition can occur. Gas mixture must lie outside the explosive range Better stability Operation within the inflammability or explosion limits sometimes possible Dissipated power Higher pressure drop Low pressure drop but sometimes stirring is required Reactant preheating Always important Less important or unnecessary Heat recovery Generally at a high level but low heat transfer rate At a lower level but high heat transfer rate; high efficiency

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 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 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.

Multiphase Reactor Types for Chemical, Specialty, and Petroleum Processes

Multiphase Reactor Types at a Glance Middleton (1992)

Key Multiphase Reactor

Comparison Between Slurry and Fixed-Bed Gas-Liquid-Solid Catalytic Converters Category Slurry Reactors Trickle-Bed Reactors Specific reaction rate High or fast reactions Rel. high for slow reactions Catalyst Highly active Supported; high crushing strength, good thermal stability and long working life needed Homogeneous side reactions Poor selectivity Good selectivity Residence time distribution Perfect mixing Plug flow Pressure drop Low or medium Low except for small particles Temperature control Isothermal operation Adiabatic operation Heat recovery Easy Less easy Catalyst handling Technical difficulties None Maximum volume 50 m3 300 m3 Maximum working pressure 100 bar high pressure possible Process flexibility Batch or continuous Continuous Investment costs High Low Operating costs Reactor design and extrapolation Well known difficult

Bubble Column in different modes

Slurry and Fixed Bed Three Phase Catalytic Reactors Typical Properties Slurry Trickle-bed Flooded bed Catalyst loading 0.01 0.5 Liquid hold-up 0.8 0.05-0.25 0.4 Gas hold-up 0.2 0.25-0.45 0.1 Particle diameter 0.1 mm 1 – 5 mm External catalyst area 500 m-1 1000 m-1 Catalyst effectiveness 1 <1 G/L Interfacial area 400 m-1 200 m-1 Dissipated power 1000 Wm-3 100 Wm-3

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

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2-10 40-100 10-100 10-50 4000-104 150-800 S40

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