Gas – Liquid
and
Gas- Liquid –Solid Reactions
A. Gas –Liquid Systems
Proper Approach to Gas-Liquid Reactions
References
•Mass Transfer theories
• Gas-liquid reaction regimes
• Multiphase reactors and selection criterion
• Film model:
complexities
Governing
equations,
• Examples and Illustrative Results
• Solution Algorithm (computational concepts)
problem
Theories for Analysis of Transport
Effects in Gas-Liquid Reactions
Two-film theory
1. W.G. Whitman, Chem. & Met. Eng., 29 147 (1923).
2. W. K. Lewis & W. G. Whitman, Ind. Eng. Chem., 16, 215 (1924).
Penetration theory
P. V. Danckwerts, Trans. Faraday Soc., 46 300 (1950).
P. V. Danckwerts, Trans. Faraday Soc., 47 300 (1951).
P. V. Danckwerts, Gas-Liquid Reactions, McGraw-Hill, NY (1970).
R. Higbie, Trans. Am. Inst. Chem. Engrs., 31 365 (1935).
Surface renewal theory
P. V. Danckwerts, Ind. Eng. Chem., 43 1460 (1951).
Rigorous multicomponent diffusion theory
R. Taylor and R. Krishna, Multicomponent Mass Transfer,
Wiley, New York, 1993.
Two-film Theory Assumptions
1. A stagnant layer exists in both the gas and the
liquid phases.
2. The stagnant layers or films have negligible
capacitance and hence a local steady-state exists.
3. Concentration gradients in the film are onedimensional.
4. Local equilibrium exists between the the gas and
liquid phases as the gas-liquid interface
5. Local concentration gradients beyond the films are
absent due to turbulence.
Two-Film Theory Concept
W.G. Whitman, Chem. & Met. Eng., 29 147 (1923).
pA
pAi
Bulk Gas
pAi = HA CAi
•
Gas Film Liquid Film
• CAi
Bulk Liquid
CAb
x
x + x
L
x = G
x=0
x = L
Two-Film Theory
- Single Reaction in the Liquid Film -
A (g)
+
b B (liq)
P (liq)
B & P are nonvolatile
 kg -moles A 
m
n
RA
=
k
C
C
mn A
B
3


m
liquid
s


Closed form solutions only possible for linear kinetics
or when linear approximations are introduced
Film Theory Model for a Single Nonvolatile
Gas-Liquid Reaction
• Diffusion - reaction equations for a single reaction in the liquid film are:
A( g )  bB(l )  P(l )
d2A
DA 2  r
dx
d 2B
DB 2  br
dx
at x  0 A  A* at x   A  AL
dB
at x  0
 0 at x   B  BL
dx
• In dimensionless form, the equations become dependent on two
dimensionless parameters, the Hatta number Ha and q*:
For r  kmn Am B n
1/ 2
tD  2

* m 1
Ha =  
DA kmn  A  BLn 
tR  m  1

q* 
BL DB
bA* DA
Penetration Theory Model
C A
 2C A
 DA
 RA
2
t
x
C B
 2C B
 DB
 RB
2
t
x
• Diffusion - reaction equations for a
single reaction in the liquid film are:
Comparison Between Theories
• Film theory:
– kL D,  - film thickness
• Penetration
theory:
– kL D1/2
Higbie model
RA'
D
kL = *

C C 
kL
=
t* - life of surface liquid
element
Danckwerts model
s - average rate of
surface renewal
kL
=
RA'
D
2
*
*
C C
t
'
A
R
 Ds
*
C C
Gas-Liquid Reaction Regimes
Instantaneous
Fast (m, n)
Instantaneous & Surface
General (m,n) or Intermediate
Rapid pseudo
1st or mth order
Slow Diffusional
Very Slow
Characteristic Diffusion &
Reaction Times
• Diffusion time
• Reaction time
• Mass transfer time
D
tD  2
kL
C  CE
tR 
r
1
tM 
k L aB
Reaction-Diffusion Regimes Defined
by Characteristic Times
• Slow reaction regime
tD<<tR kL=kL0
– Slow reaction-diffusion regime:
tD<<tR<<tM
– Slow reaction kinetic regime:
tD<<tM<<tR
• Fast reaction regime:
– Instantaneous reaction regime:
tD>>tR kL=EA kL0>kL0
kL= EA kL0
For reaction of a gas reactant in the liquid with liquid reactant with/without assistance of a
dissolved catalyst
A g   b     P 
The rate in the composition region of interest can usually be approximated as
 k mol A 
m
n

 RA 

k
C
C
A
B
3

 m s 
Where C A , C B 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.
 RA   kLa EL
o
p
Ag

HA L
For not so fast reactions the rate is
m
 p Ag 
 RA    k   CBn  L
 HA 
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:
1
1
1


K L kL k g H
S31
S32

In this notation   N A k mol A m2s
is the gas to liquid flux

 R A'  N A a k mol m 3 liquid s



 R A   L  R A' k mol m 3 reactor s


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.
D.
Rapid second order reaction in the film. No unreacted A penetrates into
bulk liquid
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 Limiting Reaction-Diffusion Regimes
Slow reaction kinetic regime
•
•
Rate proportional to liquid holdup and reaction rate and influenced by the
overall concentration driving force
Rate independent of klaB and overall concentration driving force
Slow reaction-diffusion regime
•
•
Rate proportional to klaB and overall concentration driving force
Rate independent of liquid holdup and often of reaction rate
Fast reaction regime
•
•
Rate proportional to aB,square root of reaction rate and driving force to the
power (n+1)/2 (nth order reaction)
Rate independent of kl and liquid holdup
Instantaneous reaction regime
•
•
Rate proportional to kL and aB
Rate independent of liquid holdup, reaction rate and is a week function of the
solubility of the gas reactant
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 Ag   b B   P 
 RA 
k Ag
PA H A
1
1
1


a H A k AL a EL k C  L
 k mol A 
 RA 
  observed local reaction rate per unit volum e of reactor
 m3 s 
p A atm  local partial pressure of A in the gas phase
 atm m3 liquid
H A 
 k mol A
k Ag a H A , k AL a1

  Henry' s constant for A


s   volumetric mass transfer coefficien t for gas and liquid film, respective ly.
EL  dimensionl ess enhancemen t factor
 m3 liquid 
  local liquid volume fractin in reactor
EL  3

 m reactor 
S29
Gas- liquid – solid systems
Gas-Liquid-Solid Reactions
Let us consider:
A  B 
 E E
Catalyst
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

1
1
RA  A* 



k
a
k
a

w
k
B
s p
c
2 l
 L

1
S45
Gas – Liquid Solid Catalyzed Reaction A(g)+B(l)=P(l)
Gas Limiting Reactant (Completely Wetted Catalyst)


KINET ICRAT E : k v A m ol m 3 cat.s   A
per unit catalyst volume

RAT E IN CAT ALYST: k v  p 1   B  As m ol m 3 react. s
per unit reactor volume

T RANSP ORTRAT E m ol m 3 react. s
per unit reactor volume
 Ag

: K 1 a B 
 A1 
 Ha

- Liquid - solid : k s a p  Al  As 


- Gas - liquid


OVERALL (AP P ARENT RAT
)
E m ol m 3 react.s :
Ag
Ag
HA
R A   o k v 1   B  H A 
1
1
1


K l a B k s a p 1   B  k v p
S21
Dependence of Apparent Rate Constant (kapp) on
Transport (kls, p) and Kinetic Parameters (kv)
Reaction: Ag   Bl   Pl 
Liquid limiting
reactant(nonvolati
le) -–Case
limiting reactant
(nonvolatile)
Caseofofcompletely
completely wetted
wettedcatalyst
catalyst

Kineticrate
: kv B m ol m3 cat.s
(per unit catalyst volume)





Rate in catalyst
: kv p Bs 1   B  m ol m3 react.s
(per unit reactor volume)
T ransportrate
: kls Bl  Bs a p m ol m3 react.s
(per unit reactor volume)
CATALYST

GAS
rp
SOLID
PHASE
Bs
S-L FILM

BULK
LIQUID
LIQUID FILM
Bl

Overall(apparent)rate m ol m3 react.s
BL
 p kv 1   B B1  k app BL 
1
1

kls a p  p kv 1   B 
0
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.
m vmax
m v
 kg P 
  specific activity
S a 
 kg cat h 
 kg cat 
x 3
  catalyst concentrat ion
 m reactor 
Sa
xmax
x
 vmax is determined by transport limitations and xmax by
Clearly m
reactor type and flow regime.
Improving
limited.
S a only improves
m v if we are not already transport
S38
Chemists or biochemists need to improve Sa and together with engineers work on
increasing xmax .
Engineers by manipulation of flow patterns affect
In Kinetically Controlled Regime
m v

x,
m vmax .
Sa
xmax limited by catalyst and support or matrix loading capacity for cells or
enzymes
In Transport Limited Regime
m v

p
Sa , x p
0  p  1/ 2
Mass transfer between gas-liquid, liquid-solid etc. entirely limit m v and set m vmax .
Changes in S a , do not help; alternating flow regime or contact pattern may help!

Important to know the regime of operation
S39
Key Multiphase Reactors
Bubble Column in different modes
Key Multiphase Reactor Parameters
Trambouze P. et al., “Chemical Reactors – From Design to
Operation”, Technip publications, (2004)
Depending on the reaction regime one should select reactor type
 For slow reactions with or without transport limitations choose reactor with large
liquid holdup e.g. bubble columns or stirred tanks
 Then create flow pattern of liquid well mixed or plug flow (by staging) depending on
the reaction pathway demands
This has not been done systematically




Stirred tanks
Stirred tanks in series
Bubble columns &
Staged bubble columns
Have been used (e.g. cyclohexane oxidation).
One attempts to keep gas and liquid in plug flow, use small gas bubbles to increase a and
decrease gas liquid resistance.
Not explained in terms of basic reaction pathways.
Unknown transport resistances.
S39
2-10
40-100
10-100
10-50
4000-104
150-800
S40
S41
Multiphase Reactor Types for Chemical,
Specialty, and Petroleum Processes
S42
Multiphase Reaction Engineering:
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
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, 679739, (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
Reaction Type
Degree of Difficulty
• Gas-liquid without catalyst
Straightforward
• 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)
Complex
Hierarchy of Multiphase Reactor Models
Model Type
Empirical
Implementation
Insight
Straightforward
Very little
Ideal Flow Patterns
Phenomenological
Volume-Averaged
Conservation Laws
Point-wise Conservation Very Difficult
or Impossible
Laws
Significant
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,…)
Reactor
Model
Phenomena Affecting Fixed-Bed Reactor Performance
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,…)
Reactor
Model
Elements of the Reactor Model
Micro or Local Analysis
• Gas - liquid mass transfer
Macro or Global Analysis
• Liquid - solid mass transfer
• Flow patterns for the
gas, liquid, and solids
• Interparticle and inter-phase
mass transfer
• Dynamics of gas, liquid,
and solids flows
• Intraparticle and intra-phase
diffusion
• Macro distributions of
the gas, liquid and solids
• Intraparticle and intra-phase
heat transfer
• Heat exchange
• Catalyst particle wetting
• Other types of transport
phenomena
Reactor Design Variables
Feed
Qin
Tin
Cin
Qout
Tout Product
Cout
Reactor
Reactor
Process
Reaction
Flow
Performance
Variables
Rates
• Conversion
• Flow rates
• Kinetics
• Selectivity
• Inlet C & T
• Transport • Micro
• Activity
• Heat exchange
=f
Patterns
• Macro
Idealized Mixing Models for Multiphase ( Three Phase) Reactors
Model Gas-Phase
Liquid Phase
Solid-Phase
Plug-flow
Fixed
Reactor Type
1
Plug-flow
2
Back mixed Back mixed
Back mixed
Mechanically
agitated
3
Plug-Flow
Back mixed
Bubble column
Ebullated - bed
Gas-Lift & Loop
Back mixed
Trickle-Bed
Flooded-Bed
Ideal Flow Patterns in Multiphase Reactors
Example: Mechanically Agitated Reactors
or
VR = vG + VL + VC
1 = G + L + C
G 
Vr G
QG
L 
Vr (1   G   L )
QL
First Absolute Moment of the
Tracer Response for Multi-phase Systems
For a single mobile phase in contact with p stagnant phases:
p
V1 +
 K1j Vj
j=2
1 =
Q1
For p mobile phases in contact with p - 1 mobile phases:
p
V1 +
 K1j Vj
j= 2
p
1 =
Q1 +
 K 1j Qj
j= 2
K1j
C j 
=  
C1 equil.
is the partition coefficient of the tracer
between 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 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:
 - H (k ) t
p
c
1 - XA =  e
Hp(kc) = pdf for the stagnant phase
0

= e
0
Eext ( t ) dt
- (k W W / Q1 ) t
Eext ( t ) dt
Illustrations of Ideal-Mixing Models
for Multiphase Reactors
Stirred tank
Trickle - Bed
Bubble Column







z
Flooded - Bed













z






G


L
• Plug-flow of gas
• Backmixed liquid & catalyst
• Batch catalyst
• Catalyst is fully wetted
G
L
• Plug-flow of gas
• Plug-flow of liquid
• Fixed-bed of catalyst
• Catalyst is fully wetted
Limiting Forms of Intrinsic Reaction Rates
Reaction Scheme: A (g) + vB (l)  C (l)
Gas Limiting Reactant and Plug-Flow of Liquid
Reaction Scheme: A (g) + vB (l)  C (l)
Key Assumptions
1. Gaseous reactant is limiting
2. First-order reaction wrt dissolved gas
3. Constant gas-phase concentration
z
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
G
L
CB0 / CAl  1
DBL C B /D AL C Al  1
Concentration or Axial Height
Gas Reactant Limiting and Plug Flow of Liquid
Constant gas phase concentration 
valid for pure gas at high flow rate
Relative distance from catalyst particle
(Net input by
(Input by Gas- +
convection)
Liquid Transport)
Ql Al z  Ql Al


(Loss by Liquidsolid Transport)
=0
*

k
a
A
 Al Ar dz- ks a p Al  As Ar dz= 0
l B
z dz
(1)
(2)
Dividing by Ar.dz and taking limit dz  
(3)
(4)
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
Key Assumptions
Stirred Tank
Bubble Column
1. Gaseous reactant is limiting







z
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


G


L
7. Catalyst concentration is constant
8. Finite gas-liquid, liquid-solid,
and intraparticle gradients
Concentration or Axial Height
Gas Reactant Limiting and Backmixed Liquid
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
A at the catalyst surface:
For Reactant B:
(Net input by
(Rate of rxn of B at
=
flow)
the catalyst surface)
(Note: No transport to gas
since B is non-volatile)
Gas Reactant Limiting and Backmixed Liquid
Solving the Model Equations
Flow Pattern Concepts
for Various Multiphase Systems
A
A - 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
B
Flow Pattern Concepts
for Various Multiphase Systems
C
D
C, 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 of
which has strong internal
recirculation.
Empty bubble columns and
fluidized beds
E
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: wellmixed 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, densephase or dilute-phase riser transport
Strategies for Multiphase Reactor Selection
R. Krishna and S.T. Sie, CES, 49, p. 4029 (1994)
Two-Film Theory: Mass and Heat Transfer
C ig ( j ), T g ( J )
Gas Bulk
C iL ( j ), T L ( J )
Gas Film
N if,( j )
qif,( j )
Liquid Film
Cell Jth
X 0
N if,( j )
NR
d 2Ci f
f
Di



R

ji j
dx 2
j 1
d 2T f NR f

  R j (H R )
2
dx
j 1
X 1
qif,( j )
X 0
m
Cig ( j  1 ), T g ( J  1 )
Liquid Bulk
Heat
Film
X 1
h
CiL ( j  1 ), T L ( J  1 )
Gas-Liquid Film Model: Mass Transfer
Gas Film Liquid Film Bulk Liquid
N
p g ,i
p g ,i
f
i , Z 0
C if,Z 0
g
N
NR
d 2Ci f
Di
  ji R j
2
dZ
j 1
f
i ,Z  m
C if,Z   Cib
m
Z 0
Z  0 Z  Z  m
f
i , z 0
B.C.1 D dC
i
dZ
 k g (C  C
g
i
g
i , z 0

Bim ,i c
)
*
g ,i
Bim,i
C
 Hi C
f
f
i , z 0
 0

hi 
f
 0
 m k g H ref ,i c* 

g ,i
Di

dcif

d
p g ,i
H ref ,i Cref ,i
Solubility or Violability
B.C.2: Dirichlet conditions
g
i , z 0
 ci
f
Hi  H
f
ref
i
  H Si
1
1 
exp
( f 
)  H ref h f0
TZ 0 Tref 
 R


 0
Gas-Liquid Film Model: Heat Transfer
Gas Film
Liquid Film
T
Liquid Bulk
f
Tb
Tg
C Ag
C Af
Gas-Liquid film
C Ab
C Bb
CBg
CBf
 d 2T f
L 
2
dZ

 NR
   (H r , j )(R j )
 j 1
m
Z
h
Mass Transfer Film
Heat Transfer Film
B.C.1
dT f
 L
dZ
dT f
B.C.2  L
dZ

 hg T
g
out
T
Z 0
  L
Z  h
(T L  TZf m )
 h   m 
f
z 0

dCi f
  (H s ,i )( Di )
dZ
i 1
NS
Z 0
Bubble Column Mixing Cell Model
Cells in series:
G plug flow, L mixed flow
Cells in series:
G and L mixed flow
Cell N
Cell j
Cells in
series-parallel
combination
Exchange
between
Upward and
downward
moving liquid
Cell 1
Liquid
Gas
Liquid
Gas
Prototype cell
- Cells arranged in different modes to simulate the averaged flow patterns
- These averaged flow patterns can be obtained from the CFD simulations
Mixing Cell Model for gas-liquid systems
Prototype Gas Cell
Novel 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
Prototype Liquid Cell
• 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)
Gas-Liquid Reactor Model
Non-Dimensionalized parameters
Variables
Cig
c  g
Ci ,ref
g
i
Ci f
and ci 
Ci ,ref
f

Z
TL
 
Tref
Tg
 
Tref
L
g
m
f
g
Qg
 g
Q ref
 fi 
L
u ref
g
u ref
H i ,ref
Effective G/L ratio
Reaction based
Bj  
V (  a m ) ref
M j  cell LL
Rj
Q Cref
H r , j C ref
 L CpL Tref
Heat of reaction
parameter
Ha 
2
j
2
R ref
j m
j 
j 
RTref
Arrhenius
number
D ref C ref
Hatta number
Bulk reaction number
Eaj
(  H r , j ) Dref Cref
LTref
Heat of reaction
parameter
Mass transfer based
 gL
aV k
 Lcell L
u ref A r
BiM ,i 
Damkohler number
 m H i ,ref k g
i  Ci,ref Cref
Ci,ref  Cig,ref / H i,ref
Di
Biot number
si 
Di
D ref
Diffusivities
ratio
Heat transfer based
BiH 
hg m
L
Biot number
 S ,i 
(H S ,i ) Di Ci ,ref
LTref
Heat of solution
parameter
S 
L
aglVcellL
mLC p , L m
Liquid heat
transfer number
S 
g
aglVcellL
mg mC p , g
Gas heat
transfer number
Le  L LC pL Dref
Lewis number
Studies for Complex Gas-Liquid Reactions
- 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)
Types 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-products
2. Thermally-induced product decomposition
3. Increased rate of catalyst deactivation
4. Local hot spots and excess vapor generation
5. 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
Transfer Rates in Gas-Liquid Reactions
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 Effects
Shah & Bhattacharjee, in “Recent
Advances…”, 1984.
Properties and Interfacial Temperature
Rise for Some Practical Systems
Shah & Bhattacharjee, in “Recent Advances in the Engineering Analysis
of Multiphase Reacting Systems,” Wiley Eastern, 1984.
Laboratory Reactors for
Gas - Liquid Reaction Kinetics
Case 1: Single non-isothermal reaction
Reaction Scheme: A + vB  C
GL second order reaction
d 2B
d2A
 vk2 A B
DA
 k 2 A B DB
2
2
dx
dx
Non-dimensionlizing
2
2
2
d b Ha

ab
2
dy
q
d a
2

Ha
ab
2
dy
where y  x

D B
q  B 0*
zDA A
Ha 
2
 2 k2 B0
DA
d 2a
d 2b
q 2
2
dy
dy
E
Ha
t anhHa
E
Ha bi

t anh Ha bi

For no depletion of B (interface concentration= bulk,
first order reaction
2

k2 Bi
Ha bi 
1 
2

Ha 
For depletion of B bi  q  q  1 

DA
tan(Ha bi ) 

Nonvolatile
Volatile
Gas (A)
0.70
0.76
Reactant (B)
0.58
0.33
Product (C)
0.42
0.31
Enhancement
13.0
6.7
การกระจายของความเข้มข้น
และอุณหภูมใิ นฟิ ล์มของเหลว
สาหร ับการถ่ายโอนมวลของ
ปฏิกริ ย
ิ าเดีย
่ วแบบ
 ผ ันกล ับไม่ได้สาหร ับระบบทีม
่ ี
การระเหย (Bim=1.5) และ ไม่
มีการระเหย (Bim=0)
Dimensionless Concentration
Reaction Scheme:
A + vB  C
Ha = 10, q = 0.05,  = 22,
s = -7.5, vap = 2, s=0.001,
vap = -0.005, BiHg= 1
Dimensionless Temperature
Case 1: Single non-isothermal reaction
Temp.
1 .055
No vaporization
1 .050
1 .045
Vaporization of B
1 .040
1 .035
Conc.
1 .0
0 .8
cB
0 .6
Non-volatility (Bim=0)
0 .4
cP
0 .2
Volatility (Bim=1.5)
cA
0 .0
0
0 .2
0 .4
0 .6
Dimensionless Film Thickness
0 .8
1
Case 1: Single non-isothermal reaction
Dimensionless Temperature
1 .16
1 .14
BiHg = 0.75
1 .12
BiHg = 1.5
BiHg = 10
1 .10
1 .08
BiHg ↑
→ Temp ↓
Ha ↑ → Rxn ↑ → Temp. ↑
1 .06
1 .04
1 .02
1 .00
0
BiHg
5
10
15 Ha 20
2 b
k

 m hg
ref m C B
2
Ha 

DA

25
30
35
Case 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)
C
 2C
C
 Dax
u
R
2
t
z
dz
@z=0
Let
C
u0C0  uC  Dax
z
z
η
L
Peax 
uL
Dax
Basis: Plug flow with superimposed
“diffusional” or “eddy” transport in
the direction of flow
@z=L
C
0
z
L
τ
u
C
1  2C C
τ


 τR
2
t
Peax η
dη
@  = 0
1 C
C0  C 
Peax η
@  = 1
C
0
η
Axial Dispersion Model
C
1  2C C
τ


 τR
2
t
Peax η
dη
@  = 0
1 C
C0  C 
Peax η
@  = 1
C
0
η
Axial Dispersion Model for the Liquid with
Constant Gas-Phase Concentration - 1
Mass Balance of A in the liquid phase
(Net input by
(Net input by +
+
convection)
axial dispersion)
(input by gas(Loss by Liquid- = 0
liquid transport)
solid 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


d 2 Al
dAl
*
Dax

u

k
a
A
 Al  k s a p  Al  As 
l
l B
2
dz
dz
ks a p  Al  As   ηc k1wAs
@z=0
dAl
ul Ali  ul Al  Dax
dz
@z=L
dAl
0
dz
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:
2
L / Dax characteri stic axial dispersion time
Peax  U L / Dax 

L /U
characteri stic convection time
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, 39583997 (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
1.
Dudukovic, M.P., Larachi, F., Mills, P.L., “Multiphase
Reactors – Revisited”, Chem. Eng. Science, 541, 19751995 (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