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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: Governing equations, problemcomplexities
• Examples and Illustrative Results
• Solution Algorithm (computational concepts)
Theories for Analysis of Transport Effects 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.
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 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 ConceptW.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 Theory- Single Reaction in the Liquid Film -
A (g) + b B (liq) P (liq)
RA kg -moles A
m3 liquid - s
= - k mn CA
m CB
n
Closed form solutions only possible for linear kinetics
or when linear approximations are introduced
B & P are nonvolatile
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
Characteristic Diffusion & Reaction Times
• Diffusion time
• Reaction time
• Mass transfer time
2D
L
Dt
k
ER
C Ct
r
1M
L B
tk a
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: 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 HpEakR
go
For not so fast reactions the rate is
LnB
m
A
A
A CH
pkR
g
Where effectiveness factor yields the slow down due to transport resistances.
S30
Comparison Between Theories
• Film theory:– kL D, - film thickness
• Penetration theory:– kL D1/2
Higbie model
t* - life of surface liquid element
Danckwerts models - average rate of
surface renewal
'
*
AL
R Dk
C C
'
* *2A
L
R Dk
C C t
'
*
AL
Rk Ds
C C
=
=
=
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 smAmolkNA2
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 -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 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
atmp
sm
AmolkR
CkEakHak
HPR
L
L
AAA
A
A
A
LLAAA
AAA
Lg
Lg
S29
Gas-Liquid-Solid Reactions
Let us consider: EBA ECatalyst
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
1
2
* 111
lcpsA
BkwakakAR
L
S45
Gas Limiting Reactant (Completely Wetted Catalyst)
pvBpsBl
A
g
H
g
BvoA
slp
a
g
B
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)
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
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
Operation within the inflammability or
explosion limits sometimes possible
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
Key Multiphase Reactor Types
• Mechanically agitated tanks
• Multistage agitated columns
• Bubble columns
• Draft-tube reactors
• Loop reactors
Soluble catalysts
&
Powdered
catalysts
Soluble catalysts
&
Tableted catalysts
• Packed columns
• Trickle-beds
• Packed bubble columns
• Ebullated-bed reactors
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.
S39
2-10
40-100
10-100
10-50
4000-104
150-800
S40
S41