Gas – Liquid and

Gas- Liquid –Solid Reactions

A. Gas –Liquid Systems

Proper Approach to Gas-Liquid Proper Approach to Gas-Liquid ReactionsReactions

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 Theories for Analysis of Transport Effects in Gas-Liquid Transport Effects in Gas-Liquid

ReactionsReactionsTwo-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 AssumptionsTwo-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 ConceptTwo-Film Theory Concept W.G. Whitman, Chem. & Met. Eng., 29 147 (1923).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 TheoryTwo-Film Theory- Single Reaction in the Liquid - Single Reaction in the Liquid

Film -Film -

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

RA kg -moles A

m3 liquid - s

= - kmn CA

m CBn

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

B & P are nonvolatile

Film Theory Model for a Single Film Theory Model for a Single

Nonvolatile Gas-Liquid ReactionNonvolatile 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 B

dx 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

m nD L BA mn L

R A

For r k A B

t B DHa D k A B q

t m bA D

=

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

AA

AA R

x

CD

t

C

2

2

BB

BB R

x

CD

t

C

2

2

Penetration Theory ModelPenetration Theory Model

Comparison Between Comparison Between Theories 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-Liquid Reaction RegimesGas-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 & Characteristic Diffusion & Reaction TimesReaction Times

• Diffusion time

• Reaction time

• Mass transfer time

2DL

Dt

k

ER

C Ct

r

1M

L B

tk a

Reaction-Diffusion Regimes Reaction-Diffusion Regimes Defined by Characteristic TimesDefined 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.

S30

Gas Absorption Accompanied by Reaction in the Liquid

Assume: - 2nd order rate

Hatta Number :

Ei Number:

Enhancement Factor:

HkkK gLL

111

S31

S32

In this notation smAmolkN A2

is the gas to liquid flux

sreactormmolkRR

sliquidmmolkaNR

ALA

AA

3'

3'

S33

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

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

S36

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 -- Summary -Limiting Reaction-Diffusion Limiting Reaction-Diffusion

RegimesRegimesSlow 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

S29

Gas- liquid – solid systems

Gas-Liquid-Solid Reactions

Let us consider: EBA ECatalyst

Reaction occurring in the pores of the catalyst particles and is gas reactant limited 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

S45

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

S21

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

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

catalystin Rate

.:olume)catalyst vunit (per

rate Kinetic

catalyst wettedcompletely of Case - le)(nonvolatireactant limiting Liquid

:Reaction

3

3

3

Bvppls

LLappBvp

kak

BBkBk

sreactmmol

111

1

. rate (apparent) Overall

1

3

Liquid limiting reactant (nonvolatile) – Case of completely wetted catalyst

LIQ

UID

FIL

M

BU

LK

L

IQU

ID

CATALYST

S-L

FIL

M SO

LID

P

HA

SE

rp 0

Bs

Bl

GAS

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

S38

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

S39

Key Multiphase ReactorsKey Multiphase Reactors

Bubble Column in different Bubble Column in different modesmodes

Key Multiphase Reactor Key Multiphase Reactor ParametersParameters

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.

S39

2-1040-10010-10010-504000-104

150-800

S40

S41

Multiphase Reactor Types for Chemical, Specialty, and Petroleum Processes

S42

3. Basic Design Equations for Multiphase Reactors

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

rama@wustl.edu; dudu@wustl.edu

Chemical Reaction Engineering Laboratory

Multiphase Reaction Engineering:Multiphase Reaction Engineering:

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 sparged reactors”, 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 (1990s and 2000s)

Types of Multiphase Reactions

• Gas-liquid without catalyst

• Gas-liquid with soluble catalyst

• Gas-liquid with solid catalyst

• Gas-liquid-liquid with soluble

or solid catalyst

• Gas-liquid-liquid with soluble

or solid catalyst (two liquid phases)

Straightforward

Complex

Reaction Type Degree of Difficulty

Hierarchy of Multiphase Reactor Models

Empirical

Ideal Flow Patterns

Phenomenological

Volume-AveragedConservation Laws

Point-wise ConservationLaws

Straightforward

Implementation Insight

Very little

Very Difficultor Impossible

Significant

Model Type

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

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- PDF’s 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,…)

ReactorModel

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- PDF’s 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,…)

ReactorModel

Phenomena Affecting Fixed-Bed Reactor Performance

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

Reactor Design Variables

Reactor Process Reaction Flow = f

Performance Variables Rates Patterns

• Conversion • Flow rates • Kinetics • Macro

• Selectivity • Inlet C & T • Transport • Micro

• Activity • Heat exchange

Feed ReactorQin

Tin

Cin

ProductQout

Tout

Cout

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 column Ebullated - bed Gas-Lift & Loop

Ideal Flow Patterns in Multiphase ReactorsExample: Mechanically Agitated Reactors

t

XG(t)

0

(t)

t

XL(t)

0

(t)

t

EG(t)

0

(t-g)

g

t

EL(t)

- t / Le

L

0

H

QL

QG

QL

QG

Lr G L

L

V

Q

( )1

Gr G

G

V

Q

VR = vG + VL + VC

1 = G + L + C

or

First Absolute Moment of theTracer Response for Multi-phase Systems

For a single mobile phase in contact with p stagnant phases:

1 =

V1 + K1j Vjj = 2

p

Q1

For p mobile phases in contact with p - 1 mobile phases:

1 =

V1 + K1j Vjj = 2

p

Q1 + K1j Qjj = 2

p

K1j = C j

C1

equil.

is the partition coefficient of the tracerbetween phase 1 and j

Relating the PDF of the Tracer Impulse Response to Reactor Performance

“For any system where the covariance of sojourn times is zero(i.e., when the tracer leaves and re-enters the flowing stream atthe same spatial position), the PDF of sojourn times in the reactionenvironment can be obtained from the exit-age PDF for a non-adsorbing tracer that remains confined to the flowing phaseexternal to other phases present in the system.”

For a first-order process:

0

H -A

pe = X - dt )t(E 1 extt )(k c

0

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

Hp(kc) = pdf for the stagnant phase

Illustrations of Ideal-Mixing Modelsfor 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 ColumnTrickle - Bed

Flooded - Bed

Limiting Forms of Intrinsic Reaction Rates

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

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

1/0

lAB CC 1/

lLL AABB CDCD

Gas Reactant Limiting and Plug Flow of Liquid

Constant gas phase concentration valid for pure gas at high flow rate

Conce

ntr

ati

on o

r A

xia

l H

eig

ht

Relative distance from catalyst particle

0dz= AAAadz- kAAAakAQAQ rslpsrl*

Bldzzllzll

(Net input by

convection)

(Input by Gas-Liquid

Transport)

(Loss by Liquid-solid

Transport)

+ - = 0 (1)

(2)

(3)

(4)

Dividing by Ar.dz and taking limit dz

Gas Reactant Limiting and Plug Flow of Liquid

Gas Reactant Limiting and Plug Flow of Liquid Solving the Model Equations

Concept of Reactor Efficiency

R Rate of rxn in the Entire Reactor with Transport Effects

Maximum Possible Rate

Conversion of Reactant B(in terms of Reactor Efficiency)

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 Assumptions

Gas Reactant Limiting and Backmixed LiquidC

once

ntr

ati

on o

r A

xia

l H

eig

ht

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

Gas Reactant Limiting and Backmixed Liquid

A at the catalyst surface:A at the catalyst surface:

For Reactant B:For Reactant B:(Note: No transport to

gas since B is non-volatile)

(Net input by flow)

(Rate of rxn of B at the catalyst

surface)

=

Gas Reactant Limiting and Backmixed Liquid

Solving the Model Equations

Flow Pattern Concepts for Various Multiphase Systems

A BA - Single plug flow phase flow of gas or liquid with exchange between the mobile phase and stagnant phase.

Fixed beds, Trickle-beds, packed bubble columns

B - Single phase flow of gas or liquid with exchange between a

partially backmixed stagnant phase.Semi-batch slurries, fluidized-beds,

ebullated beds

Flow Pattern Concepts for Various Multiphase Systems

C D EC, D - Co current or countercurrent two-phase flow (plug flow or dispersed flow) with exchange between the phases and stagnant phase.Trickle-beds, packed or empty bubble columns

E - Exchange between two flowing phases, one ofwhich has strong internal recirculation.Empty bubble columns and fluidized beds

Strategies for Multiphase Reactor Selection

• 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-dispersed

systems, ratio between liquid-phase bulk volume and liquid-phase diffusion 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

Strategies for Multiphase Reactor Selection

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

)J(T),j(C ggi 11

Gas Film Liquid Bulk

)J(T),j(C ggi )J(T),j(C LL

i

)J(T),j(C LLi 11

Gas Bulk

NR

jR

fj

f

HRdx

Td

12

2

)(

NR

j

fjji

fi

i Rdx

CdD

12

2

Liquid Film

Cell Jth

0X

f)j(,iN

1X

f)j(,iN

1X

f)j(,iq

0)(, X

fjiq

mh

Two-Film Theory: Mass and Heat Two-Film Theory: Mass and Heat TransferTransfer

Heat Film

Gas-Liquid Film Model: Mass Transfer

j

NR

jji

fi

i RdZ

CdD

1

2

2

)( 0,0, g

zigig

fzi

i CCkdZ

dCD

B.C.1

fzi

fi

gzi CHC 0,0,

mZZZ 0

Gas FilmfZiN 0,

Liquid Film

fZi m

N ,

igp,g

Zigp 0,

fZiC 0, b

ifZi CC

m,

Bulk Liquid

fref

reff

Z

Sirefi

fi hH

TTR

HHH 0

0

)11

(exp

Solubility or Violability

0

00

*,,

d

dchccBi

fif

if

iigim

i

irefgmim D

HkBi ,

,

irefiref

igig CH

pc

,,

,*,

B.C.2: Dirichlet conditions

NR

jjjr

f

L RHdZ

Td

1,2

2

))((

B.C.1

B.C.2

01

,0

0

)()(

Z

fi

i

NS

iis

fz

goutg

Z

f

L dZ

dCDHTTh

dZ

dT

mh

fZ

L

L

Z

f

Lm

h

TT

dZ

dT

)(

gT

fT

gAC

gBC

fBC

fAC

h

bAC

bBC

Z

Gas Film Liquid Film Liquid Bulk

Heat Transfer Film

Mass Transfer Film

bT

m

Gas-Liquid film

Gas-Liquid Film Model: Heat Transfer

Bubble Column Mixing Cell ModelBubble 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 in series-parallel combination

Exchange betweenUpward and downward moving liquid

Liquid Gas Liquid Gas

Cell 1

Cell N

Cell j

Cells in series: G plug flow, L mixed flow

Prototype cell

Mixing Cell Model for gas-liquid Mixing Cell Model for gas-liquid systemssystemsNovel features• Non-isothermal effects in the gas-liquid film and in the bulk liquid

• Effect of volatility of the liquid phase reactant on the interfacial properties

• Interfacial region modeled using film theory and solved using integral formulation of the Boundary Element Method (BEM)

• Model validity over a wide range of dimensionless numbers like Hatta, Arrhenius, solubility parameter, Biot, Damkohler

• Application to oxidation reactions like cyclohexane, p-xylene, etc. in stirred tank and stirred tank in series

(Ruthiya et al. under progress)

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

Prototype Gas Cell

Prototype Liquid Cell

Non-Dimensionalized parameters

Variables

Reaction based

refi

fif

igrefi

gig

i C

Ccand

C

Cc

,,

refigrefirefi HCC ,,, /

rLref

LcellgL Au

kaV refref,ii CC

refj

refL

mLcellj R

CQ

aVM

)(

ref

ajj RT

E

refLpLL DCLe

refLpL

refj,rj TC

CHB

refref

2m

refj2

j CD

RHa

i

grefimiM D

kHBi ,

,

Mass transfer based

refL

refrefjr

j T

CDH

)( ,

L

mgH

hBi

refL

refiiiSiS T

CDH

,,

,

)(

refigref

Lref

fi Hu

u

,

ref

ii D

Ds

gpmg

Lcellglg

Cm

VaS

,

mLpL

LcellglL

Cm

VaS

,

Heat transfer based

Gas-Liquid Reactor Model

m

Z

gref

gg

Q

Qf

ref

LL

T

T

ref

gg

T

T

Heat of reaction parameter

Bulk reaction number Hatta number Arrhenius number

Heat of reaction parameter

Damkohler number Biot number

Biot number Heat of solution parameter

Liquid heat transfer number

Gas heat transfer number

Lewis number

Diffusivities ratio

Effective G/L ratio

- Vas Bhat R.D., van Swaaij W.P.M., Kuipers, J.A.M., Versteeg,G.F., “Mass transfer with complex 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 with complex 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 Gas Absorption with an Exothermic Reaction”, AIChE J., 38, 363-375, (1992)

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

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

- Pangarkar V.G., Sharma, M.M., “Simultaneous absorption and reaction of two gases”, 29, 2297-2306, (1974)

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

Studies for Complex Gas-Liquid Reactions

Types of Heat GenerationTypes of Heat Generation

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

2 Heat of vaporization (ΔHv), of volatile reactants due to evaporative cooling in oxidation reaction

3. Heat of reaction (ΔHr), 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 How Heat Generation Can Affect Mass Transfer Rates in Gas-Liquid Mass Transfer Rates in Gas-Liquid

ReactionsReactions

1. Physical, transport, and thermodynamic properties of the reaction medium exhibit various degrees of temperature dependence

2. Kinetic parameters exhibit exponential dependence on the local temperature

3. Instabilities at the gas-liquid reaction interface that are driven by surface tension

effects (Marangoni effect) and density effects

Typical Systems with Notable Heat Typical Systems with Notable Heat EffectsEffects

Shah & Bhattacharjee, in “RecentAdvances…”, 1984.

Properties and Interfacial Properties and Interfacial Temperature Rise for Some Temperature Rise for Some

Practical SystemsPractical Systems

Shah & Bhattacharjee, in “Recent Advances in the Engineering Analysisof Multiphase Reacting Systems,” Wiley Eastern, 1984.

Laboratory Reactors forLaboratory Reactors forGas - Liquid Reaction Gas - Liquid Reaction

KineticsKinetics

GL second order reaction

BAkdx

AdDA 22

2

AD

BkHa 02

22

Non-dimensionlizing

x

y

Reaction Scheme: A + vB C

BAvkdx

BdDB 22

2

baHady

ad 22

2

abq

Ha

dy

bd 2

2

2

where*

0

AzD

BDq

A

B

2

2

2

2

dy

bdq

dy

ad

Ha

HaE

tanh For no depletion of B (interface concentration=

bulk, first order reaction

i

i

bHa

bHaE

tanh For depletion of B

)tan(1

1

i

ii

bHa

bHaq

qb

A

i

D

BkHa 2

22

Case 1: Single non-isothermal reactionCase 1: Single non-isothermal reaction

Dimensionless Film Thickness

Dim

ensi

onle

ss C

once

ntr

atio

n

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 .0 3 5

1 .0 4 0

1 .0 4 5

1 .0 5 0

1 .0 5 5

Dim

ensi

onle

ss T

emp

erat

ure

Non-volatility (Bim=0)

Volatility (Bim=1.5)

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การระเหย (Bim=1.5) และ ไม!ม&การระเหย (Bim=0)

Temp.

Conc.

Case 1: Single non-isothermal reactionCase 1: Single non-isothermal reactionReaction 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

BiHg = 0.75

BiHg = 1.5 BiHg = 10

Ha

Dim

ensi

onle

ss T

emp

erat

ure

1 .0 0

1 .0 2

1 .0 4

1 .0 6

1 .0 8

1 .1 0

1 .1 2

1 .1 4

1 .1 6

0 5 1 0 1 5 2 0 2 5 3 0 3 5

m gHg

hBi

BiHg ↑ → Temp ↓

A

bBmref

D

CkHa

22

Ha ↑ → Rxn ↑ → Temp. ↑

Case 1: Single non-isothermal reactionCase 1: Single non-isothermal reaction

Case 2: Local Supersaturation in the filmCase 2: Local Supersaturation in the film

No C reaction here

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

Axial Dispersion Model (Single Phase)

Basis: Plug flow with superimposed “diffusional” or

“eddy” transport in the direction of flow

Rdz

Cu

z

CD

t

Cax

2

2

@ z = 0z

CDuCCu ax

00

@ z = L 0

z

C

Let

L

zη

axax D

uLPe

u

Lτ

Rτηd

C

η

C

Pet

Cτ

ax

2

21

@ = 0 η

C

PeCC

ax

1

0 @ = 1 0

η

C

Axial Dispersion Model

Rτηd

C

η

C

Pet

Cτ

ax

2

21

@ = 0 η

C

PeCC

ax

1

0 @ = 1 0

η

C

Axial Dispersion Model for the Liquid with Constant Gas-Phase Concentration - 1

Mass Balance of A in the liquid phase

(Net input by

convection)

(Net input by axial

dispersion)

(Loss by Liquid-solid

Transport)

+ + = 0(input by gas-

liquid transport)

-

<Al> = mean X-sectional area occupied by liquid at z

Axial Dispersion Model for the Liquid with Constant Gas-Phase Concentration - 2

Axial Dispersion Model for the Liquid with Constant Gas-Phase Concentration - 3

ADM Model: Boundary Conditions

Axial Dispersion Model - Summary

slpsl*

Bll

ll

ax AAakAAakdz

dAu

dz

AdD

2

2

scslps wAkηAAak 1

@ z = 0dz

dADAuAu l

axlllil

@ z = L 0dz

dAl

Comments regarding axial dispersion model (ADM)

• The model is very popular because it has only a single parameter, 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 for axial dispersion is defined as:

timeconvection sticcharacteri timedispersion axial sticcharacteri

//

/2

ULDL

DLUPe ax

axax

Peax →∞ plug flow

Peax→0 complete back mixing

ADM comments continued-1

• Use of ADM was popularized by the work of Danckwerts, Levenspiel, Bischoff, j. Smith and many others in the 1960s through 1970s.

• Since Dax encompasses the effects of the convective flow pattern, eddy as well as molecular diffusion, prediction of the Axial Peclet Number with scale –up is extremely difficult as a theoretical basis exists only for laminar and turbulent single phase flows in pipes.

• Moreover use of ADM as a model for the reactor is only advisable for systems of Peclet larger than 5 (preferably 10).

ADM comments continued -2

• However, ADM leads to the boundary value problem 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 numbers for 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

really never any dispersion upstream of the point of injection (Hiby showed this conclusively in the 1960s); 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 (AICHE Journal 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• 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 benign technologies by reducing the risk of such implementations.

Return to Systems Approach in selecting best reactor for the task

• Expansion in capacity of a ‘best selling’ herbicide provides an opportunity to assess the current reactor and suggest a better solution

• Detailed chemistry is kept proprietary

Reaction System

S46

Disadvantages of Semi-Batch Slurry Reactor

• 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

S48

Slurry vs Fixed Bed • 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 in the fixed bed reactor due to much higher catalyst to liquid volume ratio

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

• Fixed bed operation requires long term catalyst stability or ease of in situ regeneration .

S49

References

1. Suresh, A.K., Sharma, M.M., Sridhar, T., “Engineering Aspects of Liquid-Phase Air Oxidation of Hydrocarbons”, 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

References1. Dudukovic, M.P., Larachi, F., Mills, P.L., “Multiphase

Reactors – Revisited”, Chem. Eng. Science, 541, 1975-1995 (1999).

2. Dudukovic, M.P., Larachi, F., Mills, P.L., “Multiphase Catalytic Reactors: A Perspective on Current Knowledge and Future Trends”, Catalysis Reviews, 44(11), 123-246 (2002).

3. Levenspiel, Octave, Chemical Reaction Engineering, 3rd Edition, Wiley, 1999.

4. Trambouze, P., Euzen, J.P., “Chemical Reactors – From Design to Operation”, IFP Publications, Editions TECHNIP, Paris, France (2002).

S45

For any process chemistry involving more than one phase one should :

• Select the best reactor flow pattern based on the kinetic scheme and mass and heat transfer requirements of the system,

• Assess the magnitude of heat and mass transfer effects on the kinetic rate

• Assess whether design requirements can be met based on ideal flow assumptions

• Develop scale-up and scale-down relations• Quantify flow field changes with scale if needed

for proper assessment of reactor performance• Couple physically based flow and phase

contacting model with kinetics