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

ReactionsTwo-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., 29 147 (1923).

Bulk LiquidBulk Gas

pA pAi

CAi

•

•

CAb

x = 0

x

x + x

L

Liquid FilmGas Film

x = Lx = G

pAi = HA CAi

Two-Film Theory- Single Reaction in the Liquid

Film -

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

RA kg -moles A

m3 liquid - s

= - k mn CA

m CBn

Closed form solutions only possible for linear kinetics or when linear approximations are introduced

B & P are nonvolatile

Gas-Liquid Reaction Regimes

Very Slow

Rapid pseudo1st or mth order

Instantaneous Fast (m, n)

General (m,n) or Intermediate Slow Diffusional

Instantaneous & Surface

Characteristic Diffusion & Reaction Times

• Diffusion time

• Reaction time

• Mass transfer time

2DL

Dt

k

ER

C Ct

r

1M

L B

tk a

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>kL

0

– Instantaneous reaction regime: kL= EA kL0

For reaction of a gas reactant in the liquid with liquid reactant with/without assistance of a dissolved catalyst

PbgA The rate in the composition region of interest can usually be approximated as

nB

mAA CCk

sm

AmolkR

3

Where BA CC , are dissolved A concentration and concentration of liquid reactant B in the liquid. Reaction rate constant k is a function of dissolved catalyst concentration when catalyst is involved. For reactions that are extremely fast compared to rate of mass transfer form gas to liquid one evaluates the enhancement of the absorption rate due to reaction.

LAALLA HpEakRgo

For not so fast reactions the rate is

LnB

m

A

AA C

H

pkR g

Where effectiveness factor yields the slow down due to transport resistances.

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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

'

*A

L

R Dk

C C

'

* *2A

L

R Dk

C C t

'

*A

L

Rk Ds

C C

=

=

=

Gas Absorption Accompanied by Reaction in the Liquid

Assume: - 2nd order rate

Hatta Number :

Ei Number:

Enhancement Factor:

HkkK gLL

111

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In this notation smAmolkNA2

is the gas to liquid flux

sreactormmolkRR

sliquidmmolkaNR

ALA

AA

3'

3'

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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

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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.

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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

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- Summary -Limiting Reaction-Diffusion

RegimesSlow 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

Key Issues Evaluate possible mechanisms and identify reaction pathways, key

intermediates and rate parameters Evaluate the reaction regime and transport parameters on the rate and assess

best reactor type Assess reactor flow pattern and flow regime on the rate Select best reactor, flow regime and catalyst concentration

Approximately for 2nd order reaction PBbgA

reactorin fractin volumeliquid local reactor

liquid

factort enhancemen essdimensionl

ly.respective film, liquid and gasfor t coefficien transfer mass volumetric1,

Afor constant sHenry'

phase gas in theA of pressure partial local

reactor of eunit volumper ratereaction local observed

111

3

3

3

3

m

mE

E

sakHak

Amolk

liquidmatmH

atmpsm

AmolkR

CkEakHak

HPR

L

L

AAA

A

A

A

LLAAA

AAA

Lg

Lg

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Gas-Liquid-Solid Reactions

Let us consider: EBA ECatalyst

Reaction occurring at the surface of the catalyst A Reactant in the gas phase B Non-volatile reaction in the liquid phase

Number of steps: Transport of A from bulk gas phase to gas-liquid interface

Transport of A from gas-liquid interface to bulk liquid

Transport of A&B from bulk liquid to catalyst surface

Intraparticle diffusion in the pores

Adsorption of the reactants on the catalyst surface

Surface reaction to yield product

The overall local rate of reaction is given as 1

2

* 111

lcpsA Bkwakak

ARL

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Gas Limiting Reactant (Completely Wetted Catalyst)

pvBpsBl

A

g

H

gBvoA

slp

a

gB

sBpv

Av

kakaK

H

A

AkR

sreactmmol

AAa

AH

Aa

sreactmmol

sreactmmolAk

scatmmolAk

A

1

1111

:. RATE (APPARENT) OVERALL

k:solid-Liquid -

K:liquid-Gas -

lumereactor vounit per

. RATE TRANSPORT

lumereactor vounit per

.1 : CATALYST IN RATE

olumecatalyst vunit per

.: RATE KINETIC

3

s

11

3

3

3

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

Clearly is determined by transport limitations and by reactor type and flow regime.

Improving only improves if we are not already transport limited.

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.

vm

aS vm

maxvm

maxx x

maxxmaxvm

aS

ionconcentratcatalyst

activity specific

3

reactorm

catkgx

hcatkg

PkgSa

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Chemists or biochemists need to improve Sa and together with engineers work on increasing maxx . Engineers by manipulation of flow patterns affect

maxvm . In Kinetically Controlled Regime

vm aSx,

maxx limited by catalyst and support or matrix loading capacity for cells or enzymes In Transport Limited Regime

vm pp

a xS , 2/10 p

Mass transfer between gas-liquid, liquid-solid etc. entirely limit vm and set maxvm .

Changes in ,aS do not help; alternating flow regime or contact pattern may help! Important to know the regime of operation

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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

Soluble catalysts&

Tableted catalysts

• Packed columns

• Trickle-beds

• Packed bubble columns

• Ebullated-bed 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

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

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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 High Low

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 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 1 – 5 mm

External catalyst area 500 m-1 1000 m-1 1000 m-1

Catalyst effectiveness

1 <1 <1

G/L Interfacial area 400 m-1 200 m-1 200 m-1

Dissipated power 1000 Wm-3 100 Wm-3 100 Wm-3

Key Multiphase Reactor Parameters

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

Depending on the reaction regime one should select reactor type For slow reactions with or without transport limitations choose reactor with large

liquid holdup e.g. bubble columns or stirred tanks Then create flow pattern of liquid well mixed or plug flow (by staging) depending on

the reaction pathway demands

This has not been done systematically Stirred tanks Stirred tanks in series Bubble columns & Staged bubble columns

Have been used (e.g. cyclohexane oxidation).

One attempts to keep gas and liquid in plug flow, use small gas bubbles to increase a and decrease gas liquid resistance. Not explained in terms of basic reaction pathways. Unknown transport resistances.

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2-1040-10010-10010-504000-104

150-800

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