9.1 - Gas–liquid and gas-liquid-solid reactions (1)

7/28/2019 9.1 - Gasliquid and gas-liquid-solid reactions (1)

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Gas Liquid

and

Gas- LiquidSolid Reactions

A. GasLiquid Systems


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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, problemcomplexities

Examples and Illustrative Results

Solution Algorithm (computational concepts)


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Theories for Analysis of TransportEffects in Gas-Liquid Reactions

Two-film theory1.W.G. Whitman, Chem. & Met. Eng., 29 147 (1923).2. W. K. Lewis & W. G. Whitman, Ind. Eng. Chem., 16, 215 (1924).

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

Rigorous multicomponent diffusion theoryR. Taylor and R. Krishna, Multicomponent Mass Transfer,Wiley, New York, 1993.


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Two-film Theory Assumptions

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

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

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

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

5. Local concentration gradients beyond the films are

absent due to turbulence.


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Two-Film Theory ConceptW.G. Whitman, Chem. & Met. Eng., 29 147 (1923).

Bulk LiquidBulk Gas

pA pAi

CAi

CAb

x = 0

xx + x

L

Liquid FilmGas Film

x = Lx = G

pAi = HA CAi


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Two-Film Theory- Single Reaction in the Liquid Film -

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

RA kg -moles A

m3 liquid - s

= - kmn CA

mCB

n

Closed form solutions only possible for linear kinetics

or when linear approximations are introduced

B & P are nonvolatile


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Film Theory Model for a Single Nonvolatile

Gas-Liquid Reaction

2*

2

2

2

( ) ( ) ( )

0

0 0

A L

B L

A g bB l P l

d AD r at x A A at x A A

dx

d B dBD br at x at x B Bdx dx

Diffusion - reaction equations for a single reaction in the liquid film are:

In dimensionless form, the equations become dependent on two

dimensionless parameters, the Hatta number Ha and q*:

1/ 2

1* *

*

2

1

m nmn

mnD L B

A mn L

R A

For r k A B

t B DHa D k A B q

t m bA D

=


8/100

Diffusion - reaction equations for a

single reaction in the liquid film are:

AA

AA R

xCD

tC

2

2

BB

BB R

xCD

tC

2

2

Penetration Theory Model


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Comparison Between Theories

Film theory: kL D, - film thickness

Penetration

theory: kL D

1/2

Higbie model

t* - life of surface liquid

element

Danckwerts models - average rate of

surface renewal

'

*

AL

R Dk

C C

'

* *2AL

R Dk

C C t

'

*

AL

Rk Ds

C C

=

=

=


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Gas-Liquid Reaction Regimes

Very Slow

Rapid pseudo

1st or mth order

Instantaneous Fast (m, n)

General (m,n) or Intermediate Slow Diffusional

Instantaneous & Surface


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Characteristic Diffusion &Reaction Times

Diffusion time

Reaction time

Mass transfer time

2D

L

Dt

k

ER

C Ct

r

1M

L B

tk a


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Reaction-Diffusion Regimes Definedby Characteristic Times

Slow reaction regime tD


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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 involve

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 HpEakR go

For not so fast reactions the rate is

Ln

B

m

A

A

A CH

pkR

g

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

S30


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Gas Absorption Accompanied by Reaction in the Liquid

Assume: - 2nd order rate

Hatta Number:

Ei Number:

Enhancement Factor:

HkkK gLL

111

S31


15/100S32


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In this notation smAmolkNA 2 is the gas to liquid flux

sreactormmolkRRsliquidmmolkaNR

ALA

AA3'

3'

S33


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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.

S35


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M i diff fil d l l


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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

S38


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- 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 thepower (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 thesolubility of the gas reactant


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Key Issues

Evaluate possible mechanisms and identify reaction pathways, keyintermediates and rate parameters

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

best reactor typeAssess reactor flow pattern and flow regime on the rateSelect best reactor, flow regime and catalyst concentration

Approximately for 2nd

order reaction PBbgA

reactorinfractinvolumeliquidlocalreactor

liquid

factortenhancemenessdimensionl

ly.respectivefilm,liquidandgasfortcoefficientransfermassvolumetric1,

AforconstantsHenry'

phasegasin theAofpressurepartiallocal

reactorofeunit volumperratereactionlocalobserved

111

3

3

3

3

m

mE

E

sakHak

Amolk

liquidmatmH

atmp

sm

AmolkR

CkEakHak

HPR

L

L

AAA

A

A

A

LLAAA

AAA

Lg

Lg

S29


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Gas- liquid solid systems

G Li id S lid R i


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Gas-Liquid-Solid Reactions

Let us consider: EBA ECatalyst

Reaction occurring in the pores of the catalyst particles and is gas reactant limitedA Reactant in the gas phase

B Non-volatile reaction in the liquid phase

umber 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

lcps

ABkwakak

AR

L

S45

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


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Gas Limiting Reactant (Completely Wetted Catalyst)

pvBpsBl

A

g

H

g

BvoA

slp

a

g

B

sBpv

Av

kakaK

HA

AkR

sreactmmol

AAa

AH

Aa

sreactmmol

sreactmmolAk

scatmmolAk

A

1

1111

:.RATE(APPARENT)OVERALL

k:solid-Liquid-

K:liquid-Gas-

lumereactor vounitper

.RATETRANSPORT

lumereactor vounitper

.1:CATALYSTINRATE

olumecatalyst vunitper

.:RATEKINETIC

3

s

11

3

3

3

S21

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

Dependence of Apparent Rate Constant (k ) on


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Dependence of Apparent Rate Constant (kapp) on

Transport (kls, p) and Kinetic Parameters (kv)

sreactmmolaBBk

sreactmmolBk

scatmmolBk

lPlBgA

pslls

Bspv

v

.:lume)reactor vounit(per

rateTransport

.1:lume)reactor vounit(per

catalystinRate

.:olume)catalyst vunit(per

rateKinetic

catalystwettedcompletelyofCase-le)(nonvolatireactantlimitingLiquid

:Reaction

3

3

3

Bvppls

LLappBvp

kak

BBkBk

sreactmmol

1

111

.rate(apparent)Overall

1

3

Liquid limiting reactant (nonvolatile)

Case of completely wetted catalyst

LIQUIDFILM

BULK

LIQUID

CATALYST

S-LFILM S

OLID

PHASE

rp 0

BsBl

GAS

O t k i t l ti t l ti l d d i i t


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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

activityspecific

3

reactorm

catkgx

hcatkg

Pkg

Sa

S38

Ch i t bi h i t d t i S d t th ith i k


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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 affectmaxv

m .

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 ma xvm .

Changes in ,aS do not help; alternating flow regime or contact pattern may help!

Important to know the regime of operationS39


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Key Multiphase Reactors


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Bubble Column in different modes


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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


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Depending on the reaction regime one should select reactor type

For slow reactions with or without transport limitations choose reactor with largeliquid holdup e.g. bubble columns or stirred tanks

Then create flow pattern of liquid well mixed or plug flow (by staging) depending onthe reaction pathway demands

This has not been done systematically

Stirred tanks

Stirred tanks in seriesBubble 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 anddecrease gas liquid resistance.

Not explained in terms of basic reaction pathways.

Unknown transport resistances.

S39


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2-10

40-100

10-10010-50

4000-104

150-800

S40


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S41


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Multiphase Reactor Types for Chemical,

Specialty, and Petroleum Processes

S42


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3. Basic Design Equations for

Multiphase Reactors

P.A. Ramachandran, P. L. Mills and M. P. Dudukovic

[email protected]; [email protected]

Chemical Reaction Engineering Laboratory

Multiphase Reaction Engineering:

Starting References
mailto:[email protected]:[email protected]


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Starting References

1. P. A. Ramachandran and R. V. Chaudhari, Three-Phase

Catalytic Reactors, Gordon and Breach Publishers, New York,(1983).

2. Nigam, K.D.P. and Schumpe, A., Three-phase spargedreactors, Topics in chemical engineering, 8, 11-112, 679-

739, (1996)

3. Trambouze, P., H. Van Landeghem, J.-P. Wauquier,Chemical Reactors: Design, Engineering, Operation,Technip, (2004)

4. Dudukovic, Mills and Ramachandran, Course Notes (1990sand 2000s)

T f M lti h R ti


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Types of Multiphase Reactions

Gas-liquid without catalyst

Gas-liquid with soluble catalyst

Gas-liquid with solid catalyst

Gas-liquid-liquid with soluble

orsolid catalyst

Gas-liquid-liquid with soluble

orsolid catalyst (two liquid phases)

Straightforward

Complex

Reaction Type Degree of Difficulty

Hi h f M lti h R t M d l


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Hierarchy of Multiphase Reactor Models

Empirical

Ideal Flow Patterns

Phenomenological

Volume-Averaged

Conservation Laws

Point-wise Conservation

Laws

Straightforward

Implementation Insight

Very little

Very Difficult

or Impossible

Significant

Model Type


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Basic Reactor Types for Systems With Solid

Catalyst ( three or four phase systems)

Systems with moving catalysts- stirred tank slurry systems

- slurry bubble columns

- loop slurry reactors- three phase fluidized beds (ebulated beds)

Systems with stagnant catalysts

-packed beds with two phase flow: down flow,up flow, counter-current flow

- monoliths and structured packing

- rotating packed beds

Phenomena Affecting Slurry Reactor Performance


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Phenomena Affecting Slurry Reactor Performance

Flow dynamics of the multi-phase dispersion

- Fluid holdups & holdup distribution

- Fluid and particle specific interfacial areas

- Bubble size & catalyst size distributions

Fluid macro-mixing

- PDFs of RTDs for the various phases

Fluid micro-mixing

- Bubble coalescence & breakage

- Catalyst particle agglomeration & attrition

Heat transfer phenomena

- Liquid evaporation & condensation- Fluid-to-wall, fluid-to-internal coils, etc.

Energy dissipation

- Power input from various sources

(e.g., stirrers, fluid-fluid interactions,)

Reactor

Model

Phenomena Affecting Fixed-Bed Reactor Performance


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Fluid dynamics of the multi-phase flows

- Flow regimes & pressure drop- Fluid holdups & holdup distribution

- Fluid-fluid & fluid-particle specific interfacial areas

- Fluid distribution

Fluid macro-mixing- PDFs of RTDs for the various phases

Heat transfer phenomena

- Liquid evaporation & condensation

- Fluid-to-wall, fluid-to-internal coils, etc.

Energy dissipation

- Pressure drop

(e.g., stirrers, fluid-fluid interactions,)

Reactor

Model

Phenomena Affecting Fixed Bed Reactor Performance

Elements of the Reactor Model


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Elements of the Reactor Model

Micro or Local Analysis Macro or Global Analysis

Gas - liquid mass transfer

Liquid - solid mass transfer

Interparticle and inter-phase

mass transfer

Intraparticle and intra-phase

diffusion

Intraparticle and intra-phase

heat transfer

Catalyst particle wetting

Flow patterns for the

gas, liquid, and solids

Dynamics of gas, liquid,and solids flows

Macro distributions of

the gas, liquid and solids

Heat exchange

Other types of transport

phenomena


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Reactor Design Variables

Reactor Process Reaction Flow

= fPerformance Variables Rates Patterns

Conversion Flow rates Kinetics Macro

Selectivity Inlet C & T Transport Micro

Activity Heat exchange

Feed ReactorQ

in

Tin

Cin

Product

Qout

Tout

Cout

Id li d Mi i M d l f M lti


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Idealized Mixing Models for Multi-

phase ( Three Phase) Reactors

Model Gas-Phase Liquid Phase Solid-Phase Reactor Type

1 Plug-flow Plug-flow Fixed Trickle-Bed

Flooded-Bed

2 Back mixed Back mixed Back mixed Mechanically

agitated

3 Plug-Flow Back mixed Back mixed Bubble columnEbullated - bed

Gas-Lift & Loop

Ideal Flow Patterns in Multiphase Reactors


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Ideal Flow Patterns in Multiphase ReactorsExample: Mechanically Agitated Reactors

L

r G L

L

V

Q

( )1

G

r G

G

V

Q

VR= vG + VL + VC

1 = G + L + Cor

First Absolute Moment of the


47/100

First Absolute Moment of the

Tracer Response for Multi-phase Systems

For a single mobi le phase in contact w ith p s tagnant ph ases:

1 =

V1 + K1j V jj = 2

p

Q1

For p mobi le phases in contact with p - 1 mobi le phases:

1 =

V1 + K1j V jj = 2

p

Q1 + K1j Q jj = 2

p

K1j =C j

C1

equil.

is the partition coefficient of the tracer

between phase 1 and j

Relating the PDF of the Tracer Impulse


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Relating the PDF of the Tracer Impulse

Response to Reactor Performance

Forany system where the covariance of sojourn times is zero(i.e., when the tracer leaves and re-enters the flowing stream at

the same spatial position), the PDF of sojourn times in the reaction

environment can be obtained from the exit-age PDF for a

non-adsorbing tracer that remains confined to the flowing phase

external to other phases present in the system.

For a first-order process:

0

H-A pe=X- dt)t(E1 ext

t)(kc

0

(-e= dt)t(Eextt)Q/Wk 1W

Hp(kc) = pdf for the stagnant phase

Illustrations of Ideal Mixing Models


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Illustrations of Ideal-Mixing Models

for Multiphase Reactors

z

G L Plug-flow of gas

Backmixed liquid & catalyst

Batch catalyst Catalyst is fully wetted

z

G L Plug-flow of gas

Plug-flow of liquid

Fixed-bed of catalyst Catalyst is fully wetted

Stirred tank

Bubble Column

Trickle - Bed

Flooded - Bed

Limiting Forms of Intrinsic Reaction Rates


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Limiting Forms of Intrinsic Reaction Rates

Reaction Scheme: A (g) + vB (l) C (l)

Gas Limiting Reactant and Plug Flow of Liquid


51/100

z

G L

Gas Limiting Reactant and Plug-Flow of Liquid

1. Gaseous reactant is limiting

2. First-order reaction wrt dissolved gas

3. Constant gas-phase concentration

4. Plug-flow of liquid

5. Isothermal operation

6. Liquid is nonvolatile

7. Catalyst concentration is constant

8. Finite gas-liquid, liquid-solid,and intraparticle gradients

Key Assump t ionsReaction Scheme: A (g) + vB (l) C (l)

1/0

l

ABCC 1/

lLLAABB CDCD

Gas Reactant Limiting and Plug Flow of Liquid


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Constant gas phase concentration

valid for pure gas at high flow rate

Co

ncentration

orAxialHeight

Relative distance from catalyst particle

0dz=AAAadz- kAAAakAQAQ

rslpsrl

*

Bldzzllzll

(Net input byconvection)

(Input by Gas-Liquid Transport)

(Loss by Liquid-solid Transport)

+ - = 0 (1)

(2)

(3)

(4)

Dividing by Ar.dz and taking limit dz



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g g qSolving the Model Equations

Concept of Reactor Efficiency


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Concept of Reactor Efficiency

RRate of rxn in the Entire Reactor with Transport Effects

Maximum Possible Rate

Conversion of Reactant B


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(in terms of Reactor Efficiency)

G R i i i d B k i d i id


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Gas Reactant Limiting and Backmixed Liquid

z

G L

1. Gaseous reactant is limiting

2. First-order reaction wrt dissolved gas

3. Constant gas-phase concentration

4. Liquid and catalyst are backmixed

5. Isothermal operation

6. Liquid is nonvolatile

7. Catalyst concentration is constant

8. Finite gas-liquid, liquid-solid,and intraparticle gradients

Stirred Tank

Bubble Column

Key Assump t ions



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Co

ncentration

orAxialHeight

Relative distance from catalyst particle

-Concentration of dissolved gas in the liquid bulk is constant [f(z)] [=Al,0]-Concentration of liquid reactant in the liquid bulk is constant [f(z)] [=Bl,0]

A in liquid bulk: Analysis is similar to the previous case



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A at the catalyst surface:

For Reactant B:

(Note: No transport to gassince B is non-volatile)

(Net input byflow)

(Rate of rxn of B atthe catalyst surface)

=

Gas Reactant Limiting and Backmixed LiquidS l i h M d l E i


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Solving the Model Equations

Flow Pattern Concepts


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p

for Various Multiphase Systems

A BA - Single plug flow phase flow ofgas or liquid with exchange between

the mobile phase and stagnant phase.

Fixed beds, Trick le-beds , packed

bubb le columns

B - Single phase flow of gas or

liquid with exchange between a

partially backmixed stagnant phase.

Sem i-batch slur r ies, f luid ized-beds ,ebul lated beds

Flow Pattern Concepts


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p

for Various Multiphase Systems

C D EC, D - Co current orcountercurrent two-phase

flow (plug flow or dispersed

flow) with exchange

between the phases and

stagnant phase.Trick le-beds, packed or

emp ty bubble columns

E - Exchange between twoflowing phases, one of

which has strong internal

recirculation.

Empty bubble columns and

fluid ized beds

Strategies for Multiphase Reactor Selection


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Strategy level I: Catalyst design strategy

gas-solid systems: catalyst particle size, shape, porous structure,distribution of active material

gas-liquid systems: choice of gas-dispersed or liquid-dispersedsystems, ratio between liquid-phase bulk volume and liquid-phasediffusion layer volume

Strategy level II: Injection and dispersion strategies (a) reactant and energy injection: batch, continuous, pulsed,

staged, flow reversal

(b) state of mixedness of concentrations and temperature: well-mixed or plug flow

(c) separation of product or energy in situ (d) contacting flow pattern: co-, counter-, cross-current

Strategy level III: Choice of hydrodynamic flow regime

e.g., packed bed, bubbly flow, churn-turbulent regime, dense-phase or dilute-phase riser transport



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R. Krishna and S.T. Sie, CES, 49, p. 4029 (1994)

Two-Film Theory: Mass and Heat Transfer


65/100

)J(T),j(C

gg

i 11

Gas Film Liquid Bulk

)J(T),j(Cgg

i )J(T),j(CLL

i

)J(T),j(C

LL

i11

Gas Bulk

NR

j

R

f

j

f

HRdx

Td

12

2

)(

NR

j

f

jji

fi

i Rdx

CdD

12

2

Liquid Film

Cell Jth0X

f

)j(,i

N1X

f

)j(,i

N

1X

f)j(,iq

0)(, X

fjiq

mh

Two Film Theory: Mass and Heat Transfer

HeatFilm

Gas-Liquid Film Model: Mass Transfer


66/100

j

NR

j ji

f

i

i

RdZ

CdD

12

2

)( 0,0, g

zi

g

ig

f

zi

i CCkdZ

dCD

B.C.1

f

zi

f

i

g

zi

CHC0,0,

mZZZ

0

Gas Film

f

ZiN

0,

Liquid Film

f

Zim

N

,

igp

,

g

Zig

p0

,

f

ZiC

0, bi

f

ZiCC

m

,

Bulk Liquid

frefref

f

Z

Siref

i

f

i hH

TTR

HHH 0

0

)11

(exp

Solubility or Violability

0

00

*

,,

d

dchccBi

f

if

i

f

iigim

i

irefgm

im

D

HkBi

,

,

irefiref

ig

ig

CH

pc

,,

,*

,

B.C.2: Dirichlet conditions

Gas-Liquid Film Model: Heat Transfer


67/100

NR

j

jjr

f

L RHdZ

Td

1

,2

2

))((

B.C.1

B.C.2

01 ,00)()(

Zf

i

i

NS

i is

f

z

g

outgZ

f

L dZ

dCDHTTh

dZ

dT

mh

f

Z

L

L

Z

f

Lm

h

TT

dZ

dT

)(

gT

fT

g

AC

g

BC fB

C

f

AC

h

b

AC

b

BC

Z

Gas Film Liquid Film Liquid Bulk

Heat Transfer Film

Mass Transfer Film

bT

m

Gas-Liquid film

Bubble Column Mixing Cell Model


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Bubble Column Mixing Cell Model

- Cells arranged in different modes to simulate the averaged flow patterns

- These averaged flow patterns can be obtained from the CFD simulations

Cells in series:G and L mixed flow

Cells inseries-parallel

combination

ExchangebetweenUpward anddownward

moving liquid

Liquid GasLiquid Gas

Cell 1

Cell N

Cell j

Cells in series:G plug flow, L mixed flow

Prototype cell

Mixing Cell Model for gas-liquid systems


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Mixing Cell Model for gas liquid systems

Novel features

Non-isothermal effects in the gas-liquid filmand in the bulk liquid

Effect of volatility of the liquid phasereactant on the interfacial properties

Interfacial region modeled using film theory

and solved using integral formulation of theBoundary Element Method (BEM)

Model validity over a wide range ofdimensionless numbers like Hatta, Arrhenius,solubility parameter, Biot, Damkohler

Application to oxidation reactions likecyclohexane, p-xylene, etc. in stirred tank andstirred tank in series

(Ruthiya et al. under progress)

(Kongto, Comp.&Chem.Eng., 2005)

Prototype Gas Cell

Prototype Liquid Cell

Gas-Liquid Reactor Model


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Non-Dimensionalized parameters

Variables

Reaction based

refi

f

ifig

refi

g

igi

CCcand

CCc

,,

refi

g

refirefi HCC ,,, /r

L

re f

LcellgL

Au

kaV re fre f,ii

CC

ref

j

ref

L

mLcellj R

CQ

aVM

)(

ref

aj

jRT

E

ref

L

pLL DCLe

ref

L

pL

refj,r

jTC

CHB

refref

2

m

ref

j2

jCD

RHa

i

grefim

iMD

kHBi

,

,

Mass transfer based

refL

refrefjr

jT

CDH

)( ,

L

mg

H

hBi

refL

refiiiS

iST

CDH

,,

,

)(

refi

g

ref

L

reffi

Hu

u

,

re f

ii

D

Ds

gpmg

Lcellglg

Cm

VaS

,

mLpL

LcellglL

Cm

VaS

,

Heat transfer based

m

Z

gref

g

g

QQf

ref

L

L

TT

ref

g

g

TT

Heat of reaction

parameterBulk reaction number Hatta number Arrhenius

numberHeat of reactionparameter

Damkohler number Biot number

Biot numberHeat of solutionparameter

Liquid heat

transfer number

Gas heat

transfer number

Lewis number

Diffusivitiesratio

Effective G/L ratio

Studies for Complex Gas-Liquid Reactions


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- Vas Bhat R.D., van Swaaij W.P.M., Kuipers, J.A.M., Versteeg,G.F.,Mass transfer withcomplex chemical reaction in gas-liquid , Chem. Eng. Sci., 54, 121-136, (1999)

-Vas Bhat R.D., van Swaaij W.P.M., Kuipers, J.A.M., Versteeg,G.F., Mass transfer withcomplex chemical reaction in gas-liquid , Chem. Eng. Sci., 54, 137-147, (1999)

-Al-Ubaidi B.H. and Selim M.H. (1992), Role of Liquid Reactant Volatility in GasAbsorption with an Exothermic Reaction, AIChE J., 38, 363-375, (1992)

-Bhattacharya, A., Gholap, R.V., Chaudhari, R.V., Gas absorption with exothermicbimolecular (1,1 order) reaction, AIChE J., 33(9), 1507-1513, (1987)

- Pangarkar V.G., Sharma, M.M., Consecutive reactions: Role of Mass Transferfactors, 29, 561-569, (1974)

- Pangarkar V.G., Sharma, M.M., Simultaneous absorption and reaction of twogases, 29, 2297-2306, (1974)

- Ramachandran, P.A., Sharma, M.M., Trans.Inst.Chem.Eng.,49, 253,(1971)

Types of Heat Generation


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Types of Heat Generation

1. Heat of solution(Hs), which is generated at the gas-liquidinterface due to the physical process of gas dissolution

2 Heat of vaporization(Hv), of volatile reactants due toevaporative cooling in oxidation reaction

3. Heat of reaction(Hr), which is generated in the film near the

gas-liquid interface (for fast reactions), or in the bulk liquid(for slow reactions).

Uncontrolled heat generation can lead to:1. Undesired production of by-products2. Thermally-induced product decomposition3. Increased rate of catalyst deactivation4. Local hot spots and excess vapor generation5. Reactor runaway and unsafe operation

Modeling of simultaneous mass and heat transport effects in

the film is necessary for accurate predictions

How Heat Generation Can Affect Mass


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Transfer Rates in Gas-Liquid Reactions

1. Physical, transport, and thermodynamicproperties of the reaction medium exhibitvarious degrees of temperature dependence

2. Kinetic parameters exhibit exponentialdependence on the local temperature

3. Instabilities at the gas-liquid reactioninterface that are driven by surface tension effects

(Marangoni effect) and density effects

Typical Systems with Notable Heat Effects


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Typical Systems with Notable Heat Effects

Shah & Bhattacharjee, in RecentAdvances, 1984.

Properties and Interfacial Temperature


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p pRise for Some Practical Systems

Shah & Bhattacharjee, in Recent Advances in the Engineering Analysis

of Multiphase Reacting Systems, Wiley Eastern, 1984.

Laboratory Reactors for


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Laboratory Reactors forGas - Liquid Reaction Kinetics

Case 1: Single non-isothermal reaction


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GL second order reaction

BAkdx

Ad

DA 22

2

A

D

BkHa 02

22

Non-dimensionlizing

xy

Reaction Scheme: A + vB C

BAvkdx

Bd

DB 22

2

baHa

dy

ad 22

2

ab

q

Ha

dy

bd 2

2

2

where *0

AzD

BDq

A

B

2

2

2

2

dy

bdq

dy

ad

HaHa

Etanh

For no depletion of B (interface concentration= bulk,first order reaction

ii

bHa

bHaE

tanh For depletion of B

)tan(1

1

i

i

ibHa

bHaq

qb

A

i

D

BkHa 2

22



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Dimensionless Film Thickness

Dimensionles

sConcentration

Ac

Bc

Pc

0.0

0.2

0.4

0.6

0.8

1.0

0 0.2 0.4 0.6 0.8 1

1 .03 5

1 .04 0

1 .04 5

1.

05 0

1 .05 5

D

imensionlessTeme

rature

Non-volatility(Bim=0)

Volatility (Bim=1.5)

(Bim=1.5)

(Bim=0)

Temp.

Conc.

Reaction Scheme:A + vB CHa = 10, q = 0.05, = 22,s = -7.5, vap = 2, s=0.001,vap = -0.005, BiHg= 1

No vaporization

Vaporization of B

6.713.0Enhancement

0.310.42Product (C)

0.330.58Reactant (B)

0.760.70Gas (A)

VolatileNon-

volatile

6.713.0Enhancement

0.310.42Product (C)

0.330.58Reactant (B)

0.760.70Gas (A)

VolatileNon-

volatile



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BiH g= 0.75

BiH g= 1.5

BiH g= 10

H a

DimensionlessTem

erat

ure

1.00

1.02

1.04

1.06

1.08

1.10

1.12

1.14

1.16

0 5 10 15 20 25 30 35

m g

Hg

hBi

BiHg Temp

A

b

Bmref

D

CkHa

2

2

HaRxn Temp.

Case 2: Local Supersaturation in the film


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No C reaction here

Shah, Y.T., Pangarkar, V.G. and Sharma, M.M., Criterion for supersaturation in gas-liquid reactionsinvolving a volatile product, Chem. Eng. Sci., 29, 1601-1612, (1974)

Axial Dispersion Model (Single Phase)


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p ( g )

Basis: Plug flow with superimposeddiffusional or eddy transport in

the direction of flow

Rdz

Cu

z

CD

t

Cax

2

2

@ z = 0 z

C

DuCCu ax

00

@ z = L

0

z

C

Let

L

z

ax

axD

uLPe

u

L

Rd

C

C

Pet

C

ax

2

21

@ = 0

C

PeCC

ax

10

@ = 1 0

C

Axial Dispersion Model


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R

d

C

C

Pet

C

ax

2

21

@ = 0

C

PeCC

ax

10

@ = 1 0

C

Axial Dispersion Model for the Liquid withConstant Gas-Phase Concentration - 1


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Constant Gas-Phase Concentration - 1

Mass Balance of A in the liquid phase

(Net input byconvection)

(Net input byaxial dispersion)

(Loss by Liquid-solid Transport)+ + = 0

(input by gas-

liquid transport) -

= mean X-sectional area occupied by liquid at z



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Constant Gas Phase Concentration 2



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Constant Gas Phase Concentration 3

ADM Model: Boundary Conditions


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Axial Dispersion Model - Summary


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slpsl*Bllllax AAakAAakdz

dAu

dz

AdD

2

2

scslps wAkAAak 1

@ z = 0dz

dADAuAu laxlllil

@ z = L 0dz

dAl

Comments regarding axial dispersion model


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Comments regarding axial dispersion model

(ADM)

The model is very popular because it has only a singleparameter, axial dispersion coefficient, Dax, the value of

which allows one to represent RTDs between that of a

stirred tank and of a plug flow. The reactor model is usually

written in dimensionless form where the Peclet number foraxial dispersion is defined as:

timeconvectionsticcharacteri

timedispersionaxialsticcharacteri

/

//

2

UL

DLDLUPe ax

axax

Peax plug flow

Peax

0 complete back mixing

ADM comments continued-1


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Use of ADM was popularized by the work of

Danckwerts, Levenspiel, Bischoff, j. Smith andmany others in the 1960s through 1970s.

Since Dax encompasses the effects of theconvective flow pattern, eddy as well as

molecular diffusion, prediction of the Axial PecletNumber with scaleup is extremely difficult as atheoretical basis exists only for laminar andturbulent single phase flows in pipes.

Moreover use of ADM as a model for the reactoris only advisable for systems of Peclet largerthan 5 (preferably 10).

ADM comments continued -2


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ADM comments continued 2

However, ADM leads to the boundary valueproblem for calculation of reactor performance

with inlet boundary conditions which are needed

to preserve the mass balance but unrealistic for

actual systems. Since at large Peclet numbersfor axial dispersion the RTD is narrow, reactor

performance can be calculated more effectively

by a tanks in series model or segregated flow

model.

ADM comments continued -3 ADM is not suitable for packed beds since there is


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ADM is not suitable for packed beds, since there is

really never any dispersion upstream of the point of

injection (Hiby showed this conclusively in the1960s); a parabolic equation does not describe the

physics of flow in packed beds well. A hyperbolic

equation approach (wave model) should be used as

shown recently by Westerterp and coworkers (AICHEJournal in the 1990s).

ADM is not suitable for bubble column flows as the

physics of flow requires at least a two dimensional

convection- eddy diffusion model for both the liquid

and gas phase (Degaleesan and Dudukovic, AICHEJ

in 1990s).

ADM is clearly unsuitable for multiphase stirred tanks

Final Comments


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Final Comments To improve predictability of multiphase reactor

models and reduce the risk of scale-up, they

should be increasingly developed based on

proper physical description of hydrodynamics in

these systems. Improved reactor scale descriptions coupled

with advances on molecular and single eddy

(single particle) scale will facilitate the

implementation of novel environmentally benigntechnologies by reducing the risk of such

implementations.

Return to Systems Approach in


93/100

y pp

selecting best reactor for the task

Expansion in capacity of a best sellingherbicide provides an opportunity to

assess the current reactor and suggest a

better solution Detailed chemistry is kept proprietary

Reaction System


94/100

y

S46

Disadvantages of Semi-Batch Slurry Reactor


95/100

g y

Batch nature variable product

Low volumetric productivity (due to low catalyst loading

and limited pressure)

Pressure limitation (shaft seal)

High power consumption

Poor selectivity (due to high liquid to catalyst volume

ratio and undesirable homogeneous reactions)

Catalyst filtration time consuming

Catalyst make-up required

Oxygen mass transfer limitations

S47

Potential Advantages of Fixed Bed System


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g y

S48

Slurry vs Fixed Bed With proper design of catalyst particles a packed bed


97/100

With proper design of catalyst particles a packed-bed

reactor with co-current down-flow of gas and liquid both

in partial wetting regime and in induced pulsing regime

can far surpass the volumetric productivity and

selectivity of the slurry system, yet require an order of

magnitude less of the active catalyst component.

Undesirable homogenous reactions are suppressed inthe fixed bed reactor due to much higher catalyst to

liquid volume ratio

Father advantage is accomplished in fixed beds byoperation at higher pressure (no moving shafts to seal).

Fixed bed operation requires long term catalyst stability

or ease of in situ regeneration .S49

References


98/100

1. Suresh, A.K., Sharma, M.M., Sridhar, T., Engineering

Aspects of Liquid-Phase Air Oxidation ofHydrocarbons, Ind. Eng. Chem. Research, 39, 3958-

3997 (2000).

2. Froment, G.F. and Bischoff, K.B., Chemical Reactor

Analysis and Design, Wiley (1990).3. Levenspiel, O., Chemical Reaction Engineering, Wiley,

3rd Edition (1999).

S50

References


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1. Dudukovic, M.P., Larachi, F., Mills, P.L., MultiphaseReactorsRevisited, Chem. Eng. Science, 541, 1975-

1995 (1999).

2. Dudukovic, M.P., Larachi, F., Mills, P.L., MultiphaseCatalytic Reactors: A Perspective on Current Knowledgeand Future Trends, Catalysis Reviews, 44(11), 123-246(2002).

3. Levenspiel, Octave, Chemical Reaction Engineering, 3rdEdition, Wiley, 1999.

4. Trambouze, P., Euzen, J.P., Chemical Reactors FromDesign to Operation, IFP Publications, Editions TECHNIP,Paris, France (2002).

S45

For any process chemistry involving morethan one phase one should :


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than one phase one should :

Select the best reactor flow pattern based on the

kinetic scheme and mass and heat transferrequirements of the system,

Assess the magnitude of heat and mass transfereffects on the kinetic rate

Assess whether design requirements can be metbased on ideal flow assumptions

Develop scale-up and scale-down relations

Quantify flow field changes with scale if neededfor proper assessment of reactor performance

Couple physically based flow and phasecontacting model with kinetics

Documents

9.1 - Gas–liquid and gas-liquid-solid reactions (1)