9.1 - Gas–liquid and gas-liquid-solid reactions (1)
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Transcript of 9.1 - Gas–liquid 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
=
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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.
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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
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In this notation smAmolkNA 2 is the gas to liquid flux
sreactormmolkRRsliquidmmolkaNR
ALA
AA3'
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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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
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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
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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
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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
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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.
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2-10
40-100
10-10010-50
4000-104
150-800
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Multiphase Reactor Types for Chemical,
Specialty, and Petroleum Processes
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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
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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
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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
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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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Gas Reactant Limiting and Plug Flow of Liquid
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
Gas Reactant Limiting and Plug Flow of Liquid
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Gas Reactant Limiting and Plug Flow of Liquid
Gas Reactant Limiting and Plug Flow of Liquid
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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
Gas Reactant Limiting and Backmixed Liquid
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Gas Reactant Limiting and Backmixed Liquid
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
Gas Reactant Limiting and Backmixed Liquid
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Gas Reactant Limiting and Backmixed Liquid
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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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-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
Strategies for Multiphase Reactor Selection
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Strategies for Multiphase Reactor Selection
R. Krishna and S.T. Sie, CES, 49, p. 4029 (1994)
Two-Film Theory: Mass and Heat Transfer
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)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
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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
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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
Case 1: Single non-isothermal reaction
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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
Case 1: Single non-isothermal reaction
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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
Axial Dispersion Model for the Liquid withConstant Gas-Phase Concentration - 2
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Constant Gas Phase Concentration 2
Axial Dispersion Model for the Liquid withConstant Gas-Phase Concentration - 3
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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
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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
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y
S46
Disadvantages of Semi-Batch Slurry Reactor
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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
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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
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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