Gas- Liquid and Gas –Liquid –
Solid Reactions
Basic Concepts
Proper Approach to Gas-Liquid Reactions
References
•Mass Transfer theories
• Gas-liquid reaction regimes
• Multiphase reactors and selection criterion
• Film model:
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
RA
 kg - moles A
3

m
liquid


- s 

=
- k mn C A
m
CB
n
Closed form solutions only possible for linear kinetics
or when linear approximations are introduced
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
tD 
tR 
tM 
D
2
L
k
C  CE
r
1
kLaB
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 
  k C Am C B n
 RA
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.
 R A  
kLa EL
o
p
Ag

H A L
For not so fast reactions the rate is
 p Ag
  R A    k 
 HA




m
CB  L
n
Where  effectiveness factor yields the slow down due to transport resistances.
S30
Comparison Between Theories
• Film theory:
– kL D,  - film thickness
• Penetration
theory:
'
kL =
– kL D1/2
Higbie model
s - average rate of
surface renewal
C C
*

D

'
kL =
t* - life of surface liquid
element
Danckwerts model
RA
kL =
RA
C C
*
R
'
A
C C
*
2

D
t
Ds
*
Gas Absorption Accompanied by Reaction in the Liquid
Assume:
- 2nd order rate
Hatta Number :
Ei Number:
Enhancement Factor:
1
KL

1
kL

1
kg H
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S32
In this notation   N A k
is the gas to liquid flux
mol A m s


'
 R A  N
A
a k mol

 RA   L  RA
'
2
3
m liquid s
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
 RA 
1
kA
g

a H
A
PA H
1
A
kA a EL
L
A  g   b B    P  

1
k C  L
 k mol A 
 RA 
  observed local reaction rate per unit volum e of reactor
3
 m s 
p A  atm   local partial pressure of A in the gas phase
 atm m 3 liquid
H A

k mol A


  Henry' s constant for A


k A a H A , k A a 1 s   volumetric
g
L
mass transfer coefficien t for gas and liquid film, respective ly.
E L  dimensionl ess enhancemen t factor
 m 3 liquid
EL  3
 m reactor


  local liquid volume fractin in reactor


S29
Gas-Liquid-Solid Reactions
Catalyst
Let us consider:
A   B      E E
Reaction occurring at the surface of the catalyst
A Reactant in the gas phase
B Non-volatile reaction in the liquid phase
Number of steps:
 Transport of A from bulk gas phase to gas-liquid interface
 Transport of A from gas-liquid interface to bulk liquid
 Transport of A&B from bulk liquid to catalyst surface
 Intraparticle diffusion in the pores
 Adsorption of the reactants on the catalyst surface
 Surface reaction to yield product
The overall local rate of reaction is given as
RA
 1

1
1
*
 A 



k
a
k
a

w
k
B
 L
s
p
c
2
l 

1
S45
Gas – Liquid Solid Catalyzed Reaction A(g)+B(l)=P(l)
Gas Limiting Reactant (Completely Wetted Catalyst)
KINETIC
 per
RATE

: k v A mol m
: k v  p 1   B
RATE IN CATALYST
unit reactor vo lume
TRANSPORT
 per
mol
RATE
unit reactor vo lume
- Gas - liquid
- Liquid
OVERALL
- solid
A

unit catalyst v olume
 per

cat . s  
3
mol
 As
m
3
react . s


m
3
react . s


 Ag

: K 1 a B 
 A1 
Ha

:ks ap
 Al
(APPARENT)
 As 
RATE
mol
m
3

react . s :
Ag
R A   o k v 1   B

Ag
H
A

H
1
K laB

1
ksa p
A

1
1   B  k v p
S21
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 v m ax
m v
 kg P 
  specific activity
S a 
 kg cat h 
Sa
 kg cat

x 3
  catalyst concentrat ion
 m reactor 
x m ax
x
Clearly m v max is determined by transport limitations and x max by
reactor type and flow regime.
Improving S a only improves m v if we are not already transport
limited.
S38
Chemists or biochemists need to improve Sa and together with engineers work on
increasing x .
max
Engineers by manipulation of flow patterns affect
m v max
.
In Kinetically Controlled Regime
m v

x,
Sa
x max
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 v .
Changes in S a , do not help; alternating flow regime or contact pattern may help!
max

Important to know the regime of operation
S39
Comparison Between Gas-Solid and Gas-Liquid-Solid Catalytic Converters
Category
Gas-Solid Catalytic
Gas-Liquid-Solid Catalytic
Design and engineering
Simple
More elaborate
Material
Often expensive material can be used
Corrosion problems can be critical
Catalyst
Possible poisoning by non-volatile
byproducts
Resistance to corrosion is required
Thermal control
Low thermal stability and low heat
capacity require internal heat exchange or
low conversion
Better stability and higher heat capacity;
partial vaporization is possible; better heat
exchange coefficient
Reactant recycling
Often important
Stoichiometric ratio can generally be
achieved; hydrodynamics can require gas
recycling
Safety
Temperature run-away and ignition can
occur. Gas mixture must lie outside the
explosive range
Better stability
Dissipated power
Higher pressure drop
Low pressure drop but sometimes stirring
is required
Reactant preheating
Always important
Less important or unnecessary
Heat recovery
Generally at a high level but low heat
transfer rate
At a lower level but high heat transfer
rate; high efficiency
Operation within the inflammability or
explosion limits sometimes possible
Key Multiphase Reactor Types
•
•
•
•
•
Mechanically agitated tanks
Multistage agitated columns
Bubble columns
Draft-tube reactors
Loop reactors
•
•
•
•
Packed columns
Trickle-beds
Packed bubble columns
Ebullated-bed reactors
Soluble catalysts
&
Powdered
catalysts
Soluble catalysts
&
Tableted catalysts
Classification of Multiphase
Gas-Liquid-Solid Catalyzed Reactors
1. Slurry Reactors
Catalyst powder is suspended in the liquid
phase to form a slurry.
2. Fixed-Bed Reactors
Catalyst pellets are maintained in place as
a fixed-bed or packed-bed.
K. Ostergaard, Adv. Chem. Engng., Vol. 7 (1968)
Modification of the Classification for
Gas-Liquid Soluble Catalyst Reactors
1. Catalyst complex is dissolved in the liquid
phase to form a homogeneous phase.
2. Random inert or structured packing, if used,
provides interfacial area for gas-liquid contacting.
Multiphase Reactor Types for Chemical,
Specialty, and Petroleum Processes
S42
Multiphase Reactor Types at a Glance
Middleton (1992)
Key Multiphase Reactor
Comparison Between Slurry and Fixed-Bed Gas-Liquid-Solid Catalytic Converters
Category
Slurry Reactors
Trickle-Bed Reactors
Specific reaction rate
High or fast reactions
Rel. high for slow reactions
Catalyst
Highly active
Supported; high crushing strength, good
thermal stability and long working life
needed
Homogeneous side reactions
Poor selectivity
Good selectivity
Residence time distribution
Perfect mixing
Plug flow
Pressure drop
Low or medium
Low except for small particles
Temperature control
Isothermal operation
Adiabatic operation
Heat recovery
Easy
Less easy
Catalyst handling
Technical difficulties
None
Maximum volume
50 m3
300 m3
Maximum working pressure
100 bar
high pressure possible
Process flexibility
Batch or continuous
Continuous
Investment costs
High
Low
Operating costs
High
Low
Reactor design and
extrapolation
Well known
difficult
Bubble Column in different modes
Slurry and Fixed Bed Three Phase Catalytic Reactors
Typical Properties
Slurry
Trickle-bed
Flooded bed
Catalyst loading
0.01
0.5
0.5
Liquid hold-up
0.8
0.05-0.25
0.4
Gas hold-up
0.2
0.25-0.45
0.1
Particle diameter
0.1 mm
1 – 5 mm
1 – 5 mm
External catalyst area 500 m-1
1000 m-1
1000 m-1
Catalyst
effectiveness
1
<1
<1
G/L Interfacial area
400 m-1
200 m-1
200 m-1
Dissipated power
1000 Wm-3
100 Wm-3
100 Wm-3
Key Multiphase Reactor Parameters
Trambouze P. et al., “Chemical Reactors – From Design to
Operation”, Technip publications, (2004)
Depending on the reaction regime one should select reactor type
 For slow reactions with or without transport limitations choose reactor with large
liquid holdup e.g. bubble columns or stirred tanks
 Then create flow pattern of liquid well mixed or plug flow (by staging) depending on
the reaction pathway demands
This has not been done systematically




Stirred tanks
Stirred tanks in series
Bubble columns &
Staged bubble columns
Have been used (e.g. cyclohexane oxidation).
One attempts to keep gas and liquid in plug flow, use small gas bubbles to increase a and
decrease gas liquid resistance.
Not explained in terms of basic reaction pathways.
Unknown transport resistances.
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2-10
40-100
10-100
10-50
4000-104
150-800
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S41