gas – liquid and gas- liquid –solid...
TRANSCRIPT
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: Governing equations, problem complexities
• Examples and Illustrative Results
• Solution Algorithm (computational concepts)
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 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 Concept W.G. Whitman, Chem. & Met. Eng., 29 147 (1923).
Bulk Liquid Bulk Gas
pA pAi
CAi
•
•
CAb
x = 0
x
x + ∆∆∆∆x
δδδδL
Liquid Film Gas Film
x = δδδδL x = δδδδG
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
= - kmn CA
m CB
n
Closed form solutions only possible for linear kinetics
or when linear approximations are introduced
B & P are nonvolatile
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 B
dx dx
δ
δ
+ →
= = = = =
= = = = =
• 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 n
mn
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
−
=
= = + =
• Diffusion - reaction equations for a
single reaction in the liquid film are:
AA
AA R
x
CD
t
C+
∂∂
=∂
∂2
2
BB
BB R
x
CD
t
C+
∂∂
=∂
∂2
2
Penetration Theory Model
Comparison Between Theories
• Film theory: – kL∝ D, δ - film thickness
• Penetration theory: – kL∝ D1/2
Higbie model
t* - life of surface liquid element
Danckwerts model s - average rate of
surface renewal
'
*
A
L
R Dk
C C δ=
−
'
* *2A
L
R Dk
C C tπ=
−
'
*
AL
Rk Ds
C C=
−
=
=
=
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 ( ) ( ) ( )ll PbgA =+ β
The rate in the composition region of interest can usually be approximated as
nB
mAA CCk
sm
AmolkR =
−
3
Where BA CC , are dissolved A concentration and concentration of liquid reactant B in the liquid.
Reaction rate constant k is a function of dissolved catalyst concentration when catalyst is involved.
For reactions that are extremely fast compared to rate of mass transfer form gas to liquid one
evaluates the enhancement of the absorption rate due to reaction.
( ) ( ) LAALLA HpEakRgo
ε=−
For not so fast reactions the rate is
( ) LnB
m
A
A
A CH
pkR g εη
=−
Where η effectiveness factor yields the slow down due to transport resistances.
S30
Gas Absorption Accompanied by Reaction in the Liquid
Assume: - 2nd order rate
Hatta Number :
Ei Number:
Enhancement Factor:
HkkK gLL
111+=
S31
S32
In this notation ( )smAmolkNA2&=ϕ
is the gas to liquid flux
( )( )( )sreactormmolkRR
sliquidmmolkaNR
ALA
AA
3'
3'
−=−
=−
ε
&
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 ( ) ( ) ( )ll 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
Lgεβ
S29
Gas- liquid – solid systems
Gas-Liquid-Solid Reactions
Let us consider: EBA ECatalyst νν →+
Reaction occurring in the pores of the catalyst particles and is gas reactant limited
A Reactant in the gas phase
B Non-volatile reaction in the liquid phase
Number of steps:
• Transport of A from bulk gas phase to gas-liquid interface
• Transport of A from gas-liquid interface to bulk liquid
• Transport of A&B from bulk liquid to catalyst surface
• Intraparticle diffusion in the pores
• Adsorption of the reactants on the catalyst surface
• Surface reaction to yield product
The overall local rate of reaction is given as
1
2
* 111−
++=
lcpsA
BkwakakAR
Lη
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
ηε
εη
εη
−++
=−=
−
−
−
Ω=
1
1111
:. RATE (APPARENT) OVERALL
k:solid-Liquid -
K:liquid-Gas -
lumereactor vounit per
. RATE TRANSPORT
lumereactor vounit per
.1 : CATALYST IN RATE
olumecatalyst vunit per
.: RATE KINETIC
3
s
11
3
3
3
S21
Gas – Liquid Solid Catalyzed Reaction A(g)+B(l)=P(l)
Dependence of Apparent Rate Constant (kapp) on
Transport (kls, ηηηηp) and Kinetic Parameters (kv)
( ) ( ) ( )
( )
( )( )
( ) ( )sreactmmolaBBk
sreactmmolBk
scatmmolBk
lPlBgA
pslls
Bspv
v
.:lume)reactor vounit (per
rateTransport
.1:lume)reactor vounit (per
catalystin Rate
.:olume)catalyst vunit (per
rate Kinetic
catalyst wettedcompletely of Case - le)(nonvolatireactant limiting Liquid
:Reaction
3
3
3
−
−
=+
εη
( )( )
( )Bvppls
LLappBvp
kak
BBkBk
sreactmmol
εη
εη
−+
=−−
1
111
. rate (apparent) Overall
1
3
Liquid limiting reactant (nonvolatile) – Case of completely wetted catalyst
LIQUID FILM
BULK
LIQUID
CATALYST
S-L FILM SOLID
PHASE
rp 0
Bs
Bl
GAS
Clearly is determined by transport limitations and by
reactor type and flow regime.
Improving only improves if we are not already transport
limited.
Our task in catalytic reactor selection, scale-up and design is to
either maximize volumetric productivity, selectivity or product
concentration or an objective function of all of the above. The key
to our success is the catalyst. For each reactor type considered
we can plot feasible operating points on a plot of volumetric productivity versus catalyst concentration.
vm&
aS
vm&
maxvm&
maxx x
maxxmaxvm&
aS
ionconcentratcatalyst
activity specific
3=
=
reactorm
catkgx
hcatkg
PkgSa
S38
Chemists or biochemists need to improve Sa and together with engineers work on increasing maxx .
Engineers by manipulation of flow patterns affect
maxvm& .
In Kinetically Controlled Regime
vm& aSx,∝
maxx limited by catalyst and support or matrix loading capacity for cells or
enzymes
In Transport Limited Regime
vm& pp
a xS ,∝
2/10 ≤≤ p
Mass transfer between gas-liquid, liquid-solid etc. entirely limit vm& and set maxvm& .
Changes in ,aS do not help; alternating flow regime or contact pattern may help!
∴ Important to know the regime of operation
S39
Key Multiphase 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
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
1. P. A. Ramachandran and R. V. Chaudhari, Three-Phase Catalytic Reactors, Gordon and Breach Publishers, New York, (1983). 2. Nigam, K.D.P. and Schumpe, A., “Three-phase sparged reactors”, Topics in chemical engineering, 8, 11-112, 679-739, (1996) 3. Trambouze, P., H. Van Landeghem, J.-P. Wauquier, “Chemical Reactors: Design, Engineering, Operation”, Technip, (2004) 4. Dudukovic, Mills and Ramachandran, Course Notes (1990s and 2000s)
Types of Multiphase Reactions
• Gas-liquid without catalyst
• Gas-liquid with soluble catalyst
• Gas-liquid with solid catalyst
• Gas-liquid-liquid with soluble
or solid catalyst
• Gas-liquid-liquid with soluble
or solid catalyst (two liquid phases)
Straightforward
Complex
Reaction Type Degree of Difficulty
Hierarchy of Multiphase Reactor Models
Empirical
Ideal Flow Patterns
Phenomenological
Volume-Averaged
Conservation Laws
Point-wise Conservation Laws
Straightforward
Implementation Insight
Very little
Very Difficult
or Impossible
Significant
Model Type
Basic Reactor Types for Systems With Solid
Catalyst ( three or four phase systems)
• Systems with moving catalysts
- stirred tank slurry systems
- slurry bubble columns
- loop slurry reactors
- three phase fluidized beds (ebulated beds)
• Systems with stagnant catalysts
-packed beds with two phase flow: down flow, up flow, counter-current flow
- monoliths and structured packing
- rotating packed beds
Phenomena Affecting Slurry Reactor Performance
Flow dynamics of the multi-phase dispersion
- Fluid holdups & holdup distribution
- Fluid and particle specific interfacial areas
- Bubble size & catalyst size distributions
Fluid macro-mixing
- PDF’s of RTDs for the various phases
Fluid micro-mixing
- Bubble coalescence & breakage
- Catalyst particle agglomeration & attrition
Heat transfer phenomena
- Liquid evaporation & condensation
- Fluid-to-wall, fluid-to-internal coils, etc.
Energy dissipation
- Power input from various sources
(e.g., stirrers, fluid-fluid interactions,F)
Reactor
Model
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,F)
Reactor
Model
Phenomena Affecting Fixed-Bed Reactor Performance
Elements of the Reactor Model
Micro or Local Analysis Macro or Global Analysis
• Gas - liquid mass transfer
• Liquid - solid mass transfer
• Interparticle and inter-phase
mass transfer
• Intraparticle and intra-phase
diffusion
• Intraparticle and intra-phase heat transfer
• Catalyst particle wetting
• Flow patterns for the
gas, liquid, and solids
• Dynamics of gas, liquid, and solids flows
• Macro distributions of
the gas, liquid and solids
• Heat exchange
• Other types of transport
phenomena
Reactor Design Variables
Reactor Process Reaction Flow
= f
Performance Variables Rates Patterns
• Conversion • Flow rates • Kinetics • Macro
• Selectivity • Inlet C & T • Transport • Micro
• Activity • Heat exchange
Feed Reactor Qin
Tin
Cin
Product
Qout
Tout
Cout
Idealized Mixing Models for Multi-
phase ( Three Phase) Reactors
Model Gas-Phase Liquid Phase Solid-Phase Reactor Type
1 Plug-flow Plug-flow Fixed Trickle-Bed
Flooded-Bed
2 Back mixed Back mixed Back mixed Mechanically
agitated
3 Plug-Flow Back mixed Back mixed Bubble column
Ebullated - bed
Gas-Lift & Loop
Ideal Flow Patterns in Multiphase Reactors Example: Mechanically Agitated Reactors
t
XG(t)
0
δ δ δ δ (t)
t
XL(t)
0
δ δ δ δ (t)
t
EG(t)
0
δ δ δ δ (t-ττττg)
ττττg
t
EL(t)
- t / ττττLe
ττττL
0
H
QL
QG
QL
QG
τε ε
Lr G L
L
V
Q=
− −( )1τε
Gr G
G
V
Q=
VR = vG + VL + VC
1 = εG + εL + εC or
First Absolute Moment of the
Tracer Response for Multi-phase Systems
For a single mobile phase in contact with p stagnant phases:
µ1 =
V1 + K1j V jj = 2
p
∑Q1
For p mobile phases in contact with p - 1 mobile phases:
µ1 =
V1 + K1j V j
j = 2
p
∑
Q1 + K1j Qj
j = 2
p
∑
K1j = Cj
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:
∫∞
0
H -A
pe = X - dt )t(E 1 extt )(k c
∫∞
0
( -e = dt )t(E ext
t )Q/Wk 1W
Hp(kc) = pdf for the stagnant phase
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
Reaction Scheme: A (g) + vB (l) C (l)
∆∆∆∆z
G L
Gas Limiting Reactant and Plug-Flow of Liquid
1. Gaseous reactant is limiting
2. First-order reaction wrt dissolved gas
3. Constant gas-phase concentration
4. Plug-flow of liquid
5. Isothermal operation
6. Liquid is nonvolatile
7. Catalyst concentration is constant
8. Finite gas-liquid, liquid-solid,
and intraparticle gradients
Key Assumptions Reaction Scheme: A (g) + vB (l) C (l)
1/0
>>lAB CC 1/ >>
lLL AABB CDCD ν
Gas Reactant Limiting and Plug Flow of Liquid
Constant gas phase concentration
valid for pure gas at high flow rate
Concentration or Axial H
eight
Relative distance from catalyst particle
( ) ( ) 0dz= AAAadz- kAAAakAQAQrslpsrl
*
Bldzzllzll−−+−
+
(Net input by
convection)
(Input by Gas-
Liquid Transport) (Loss by Liquid-
solid Transport) + - = 0 (1)
(2)
(3)
(4)
Dividing by Ar.dz and taking limit dz ∞
Gas Reactant Limiting and Plug Flow of Liquid
Gas Reactant Limiting and Plug Flow of Liquid Solving the Model Equations
Concept of Reactor Efficiency
=Rη Rate of rxn in the Entire Reactor with Transport Effects
Maximum Possible Rate
Conversion of Reactant B (in terms of Reactor Efficiency)
Gas Reactant Limiting and Backmixed Liquid
∆∆∆∆z
G L
1. Gaseous reactant is limiting
2. First-order reaction wrt dissolved gas
3. Constant gas-phase concentration
4. Liquid and catalyst are backmixed
5. Isothermal operation
6. Liquid is nonvolatile
7. Catalyst concentration is constant
8. Finite gas-liquid, liquid-solid,
and intraparticle gradients
Stirred Tank
Bubble Column
Key Assumptions
Gas Reactant Limiting and Backmixed Liquid Concentration or Axial H
eight
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: (Note: No transport to gas
since B is non-volatile) (Net input by
flow)
(Rate of rxn of B at
the catalyst surface) =
Gas Reactant Limiting and Backmixed Liquid Solving the Model Equations
Flow Pattern Concepts
for Various Multiphase Systems
A B 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
Flow Pattern Concepts
for Various Multiphase Systems
C D E 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
Strategies for Multiphase Reactor Selection
• Strategy level I: Catalyst design strategy – gas-solid systems: catalyst particle size, shape, porous structure,
distribution of active material
– gas-liquid systems: choice of gas-dispersed or liquid-dispersed systems, ratio between liquid-phase bulk volume and liquid-phase
diffusion layer volume
• Strategy level II: Injection and dispersion strategies – (a) reactant and energy injection: batch, continuous, pulsed,
staged, flow reversal
– (b) state of mixedness of concentrations and temperature: well-mixed or plug flow
– (c) separation of product or energy in situ
– (d) contacting flow pattern: co-, counter-, cross-current
• Strategy level III: Choice of hydrodynamic flow regime – e.g., packed bed, bubbly flow, churn-turbulent regime, dense-
phase or dilute-phase riser transport
Strategies for Multiphase Reactor Selection
R. Krishna and S.T. Sie, CES, 49, p. 4029 (1994)
)J(T),j(C ggi 11 −−−−−−−−
Gas Film Liquid Bulk
)J(T),j(Cgg
i )J(T),j(C LLi
)J(T),j(C LLi 11 −−−−−−−−
Gas Bulk
∑=
∆−=NR
j
R
f
j
f
HRdx
Td
12
2
)(κ
∑=
−=NR
j
f
jji
f
ii R
dx
CdD
12
2
υ
Liquid Film
Cell Jth 0====X
f)j(,i
N1====X
f)j(,i
N
1====X
f)j(,iq
0)(, =X
f
jiq
mδhδ
Two-Film Theory: Mass and Heat Transfer
Heat Film
Gas-Liquid Film Model: Mass Transfer
j
NR
j
ji
f
ii R
dZ
CdD ∑
=
−=1
2
2
υ
)( 0,
0, g
zi
g
ig
f
zi
i CCkdZ
dCD =
= −−=B.C.1
f
zi
f
i
g
ziCHC
0,0, == =
mZZZ δ=→= 0
Gas Film f
ZiN 0, =
Liquid Film
f
Zim
N δ=,
igp ,
g
Zig
p0
, =
f
ZiC 0, = b
i
f
ZiCC
m
==δ,
Bulk Liquid
( )f
ref
ref
f
Z
Siref
i
f
i hHTTR
HHH 0
0
)11
(exp ==
=
−
∆−= ξθ
Solubility or Violability
( )[ ]0
00
*
,,
=
==−=−
ξ
ξξ ξθ
d
dchccBi
f
if
i
f
iigim
i
irefgm
imD
HkBi
,
,
δ=
irefiref
ig
igCH
pc
,,
,*
, =
B.C.2: Dirichlet conditions
∑=
∆−=
NR
j
jjr
f
L RHdZ
Td
1
,2
2
))((λ
B.C.1
B.C.2
( )01
,0
0
)()(
===
=
−∆−+−=− ∑Z
f
ii
NS
i
is
f
z
g
outg
Z
f
LdZ
dCDHTTh
dZ
dTλ
( )mh
f
Z
L
L
Z
f
Lm
h
TT
dZ
dT
δδλλ δ
δ−
−−=− =
=
)(
gT
fT
g
AC
g
BC f
BC
f
AC
hδ
b
AC
b
BC
Z
Gas Film Liquid Film Liquid Bulk
Heat Transfer Film
Mass Transfer Film
bT
mδ
Gas-Liquid film
Gas-Liquid Film Model: Heat Transfer
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 in series-parallel combination Exchange between Upward and downward moving liquid
Liquid Gas Liquid Gas
Cell 1
Cell N
Cell j
Cells in series: G plug flow, L mixed flow
Prototype cell
Mixing Cell Model for gas-liquid systems
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
• Interfacial region modeled using film theory and solved using integral formulation of the Boundary Element Method (BEM)
• Model validity over a wide range of dimensionless numbers like Hatta, Arrhenius, solubility parameter, Biot, Damkohler
• Application to oxidation reactions like cyclohexane, p-xylene, etc. in stirred tank and stirred tank in series
(Ruthiya et al. under progress)
(Kongto, Comp.&Chem.Eng., 2005)
Prototype Gas Cell
Prototype Liquid Cell
Non-Dimensionalized parameters
Variables
Reaction based
refi
f
if
ig
refi
g
ig
iC
Ccand
C
Cc
,,
==
refi
g
refirefi HCC ,,, /=
r
L
ref
LcellgL
Au
kaV=α refref,ii CC=ω
ref
j
ref
L
mLcellj R
CQ
aVM
)( δε −=
ref
aj
jRT
E=γ
ref
L
pLL DCLe ρλ=
ref
L
pL
refj,r
jTC
CHB
ρ
∆−=
refref
2
m
ref
j2
jCD
RHa
δ=
i
grefim
iMD
kHBi
,
,
δ=
Mass transfer based
refL
refrefjr
jT
CDH
λβ
)( ,∆−=
L
mg
H
hBi
λ
δ=
refL
refiiiS
iST
CDH
λβ ,,
,
)( ∆−=
refi
g
ref
L
ref
fiHu
u
,
=γ
ref
i
iD
Ds =
gpmg
Lcellglg
Cm
VaS
,δ
λ=
mLpL
LcellglL
Cm
VaS
δ
λ
,
=
Heat transfer based
Gas-Liquid Reactor Model
m
Z
δξ =
g
ref
gg
Q
Qf =
ref
LL
T
T=θ
ref
gg
T
T=θ
Heat of reaction parameter
Bulk reaction number Hatta number Arrhenius number
Heat of reaction parameter
Damkohler number Biot number
Biot number Heat of solution parameter
Liquid heat transfer number
Gas heat transfer number
Lewis number
Diffusivities ratio
Effective G/L ratio
- Vas Bhat R.D., van Swaaij W.P.M., Kuipers, J.A.M., Versteeg,G.F., “Mass transfer with
complex chemical reaction in gas-liquid ”, Chem. Eng. Sci., 54, 121-136, (1999)
- Vas Bhat R.D., van Swaaij W.P.M., Kuipers, J.A.M., Versteeg,G.F., “Mass transfer with complex chemical reaction in gas-liquid ”, Chem. Eng. Sci., 54, 137-147, (1999)
- Al-Ubaidi B.H. and Selim M.H. (1992), “ Role of Liquid Reactant Volatility in Gas Absorption with an Exothermic Reaction”, AIChE J., 38, 363-375, (1992)
- Bhattacharya, A., Gholap, R.V., Chaudhari, R.V., “Gas absorption with exothermic bimolecular (1,1 order) reaction”, AIChE J., 33(9), 1507-1513, (1987)
- Pangarkar V.G., Sharma, M.M., “Consecutive reactions: Role of Mass Transfer
factors”, 29, 561-569, (1974)
- Pangarkar V.G., Sharma, M.M., “Simultaneous absorption and reaction of two
gases”, 29, 2297-2306, (1974)
- Ramachandran, P.A., Sharma, M.M., Trans.Inst.Chem.Eng.,49, 253,(1971)
Studies for Complex Gas-Liquid Reactions
Types of Heat Generation
1. Heat of solution (∆Hs), which is generated at the gas-liquid interface due to the physical process of gas dissolution
2 Heat of vaporization (∆Hv), of volatile reactants due to
evaporative 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-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
GL second order reaction
BAkdx
AdDA 22
2
=
AD
BkHa 02
22 δ
=
Non-dimensionlizing
δx
y =
Reaction Scheme: A + vB C
BAvkdx
BdDB 22
2
=
baHady
ad 2
2
2
= abq
Ha
dy
bd2
2
2
= where *
0
AzD
BDq
A
B=
2
2
2
2
dy
bdq
dy
ad=
( )Ha
HaE
tanh= For no depletion of B (interface concentration= bulk,
first order reaction
( )i
i
bHa
bHaE
tanh= For depletion of B
−+=
)tan(1
1
i
i
ibHa
bHaq
qb
A
i
D
BkHa 2
22 δ
=
Case 1: Single non-isothermal reaction
Dimensionless Film Thickness
Dim
en
sion
less
Con
cen
tra
tion
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 .035
1 .040
1 .045
1 .050
1 .055
Dim
ensi
on
less
Tem
pera
ture
Non-volatility (Bim=0)
Volatility (Bim=1.5)
การกระจายของความเขมขนและอณหภมในฟลมของเหลวสาหรบการถายโอนมวลของปฏกรยาเด rยวแบบ ผนกลบไมไดสาหรบระบบท rม การระเหย (Bim=1.5) และ ไมมการระเหย (Bim=0)
Temp.
Conc.
Case 1: Single non-isothermal reaction Reaction Scheme: A + vB C
Ha = 10, q = 0.05, γ = 22, γs = -7.5, γvap = 2, βs=0.001, βvap = -0.005, BiHg= 1
No vaporization
Vaporization of B
6.713.0Enhancement
0.310.42Product (C)
0.330.58Reactant (B)
0.760.70Gas (A)
VolatileNon-volatile
6.713.0Enhancement
0.310.42Product (C)
0.330.58Reactant (B)
0.760.70Gas (A)
VolatileNon-volatile
BiHg = 0.75
BiHg = 1.5
BiHg = 10
Ha
Dim
ensi
on
less
T
em
pera
ture
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
δ
κ=
BiHg ↑ → Temp ↓
A
b
Bmref
D
CkHa
2
2δ
=
Ha ↑ → Rxn ↑ → Temp. ↑
Case 1: Single non-isothermal reaction
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)
Basis: Plug flow with superimposed “diffusional” or “eddy” transport in
the direction of flow
Rdz
Cu
z
CD
t
Cax +
∂−
∂∂
=∂∂
2
2
@ z = 0 z
CDuCCu
ax ∂∂
−=00
@ z = L 0=∂∂
z
C
Let
L
zη =
ax
axD
uLPe =
u
Lτ =
Rτηd
C
η
C
Pet
Cτ
ax
+∂
−∂∂
=∂∂
2
21
@ η = 0 η
C
PeCC
ax∂∂
−=1
0@ η = 1 0=
∂∂
η
C
Axial Dispersion Model
Rτηd
C
η
C
Pet
Cτ
ax
+∂
−∂∂
=∂∂
2
21
@ η = 0 η
C
PeCC
ax∂∂
−=1
0@ η = 1 0=
∂∂
η
C
Axial Dispersion Model for the Liquid with
Constant Gas-Phase Concentration - 1
Mass Balance of A in the liquid phase
(Net input by
convection)
(Net input by
axial dispersion)
(Loss by Liquid-
solid Transport) + + = 0
(input by gas-
liquid transport) -
<Al> = mean X-sectional area occupied by liquid at z
Axial Dispersion Model for the Liquid with
Constant Gas-Phase Concentration - 2
Axial Dispersion Model for the Liquid with
Constant Gas-Phase Concentration - 3
ADM Model: Boundary Conditions
Axial Dispersion Model - Summary
( ) ( )slpsl
*
Bll
ll
ax AAakAAakdz
dAu
dz
AdD −=−+−
2
2
( )scslps
wAkηAAak1
=−
@ z = 0 dz
dADAuAu l
axlllil −=
@ z = L 0=dz
dAl
Comments regarding axial dispersion model
(ADM)
• The model is very popular because it has only a single
parameter, axial dispersion coefficient, Dax, the value of
which allows one to represent RTDs between that of a
stirred tank and of a plug flow. The reactor model is usually
written in dimensionless form where the Peclet number for axial dispersion is defined as:
timeconvection sticcharacteri
timedispersion axial sticcharacteri
/
//
2
===UL
DLDLUPe ax
axax
Peax →∞ plug flow
Peax→0 complete back mixing
ADM comments continued-1
• Use of ADM was popularized by the work of Danckwerts, Levenspiel, Bischoff, j. Smith and many others in the 1960s through 1970s.
• Since Dax encompasses the effects of the convective flow pattern, eddy as well as molecular diffusion, prediction of the Axial Peclet Number with scale –up is extremely difficult as a theoretical basis exists only for laminar and turbulent single phase flows in pipes.
• Moreover use of ADM as a model for the reactor is only advisable for systems of Peclet larger than 5 (preferably 10).
ADM comments continued -2
• However, ADM leads to the boundary value
problem for calculation of reactor performance
with inlet boundary conditions which are needed
to preserve the mass balance but unrealistic for
actual systems. Since at large Peclet numbers
for axial dispersion the RTD is narrow, reactor
performance can be calculated more effectively
by a tanks in series model or segregated flow
model.
ADM comments continued -3 • ADM is not suitable for packed beds, since there is
really never any dispersion upstream of the point of
injection (Hiby showed this conclusively in the
1960s); a parabolic equation does not describe the
physics of flow in packed beds well. A hyperbolic
equation approach (wave model) should be used as
shown recently by Westerterp and coworkers (AICHE
Journal in the 1990s).
• ADM is not suitable for bubble column flows as the
physics of flow requires at least a two dimensional
convection- eddy diffusion model for both the liquid
and gas phase (Degaleesan and Dudukovic, AICHEJ
in 1990s).
• ADM is clearly unsuitable for multiphase stirred tanks
Final Comments • To improve predictability of multiphase reactor
models and reduce the risk of scale-up, they
should be increasingly developed based on
proper physical description of hydrodynamics in
these systems.
• Improved reactor scale descriptions coupled
with advances on molecular and single eddy
(single particle) scale will facilitate the
implementation of novel environmentally benign
technologies by reducing the risk of such
implementations.
Return to Systems Approach in
selecting best reactor for the task
• Expansion in capacity of a ‘best selling’
herbicide provides an opportunity to
assess the current reactor and suggest a
better solution
• Detailed chemistry is kept proprietary
Reaction System
S46
Disadvantages of Semi-Batch Slurry Reactor
• Batch nature – variable product
• Low volumetric productivity (due to low catalyst loading
and limited pressure)
• Pressure limitation (shaft seal)
• High power consumption
• Poor selectivity (due to high liquid to catalyst volume
ratio and undesirable homogeneous reactions)
• Catalyst filtration time consuming
• Catalyst make-up required
• Oxygen mass transfer limitations
S47
Potential Advantages of Fixed Bed System
S48
Slurry vs Fixed Bed • With proper design of catalyst particles a packed-bed
reactor with co-current down-flow of gas and liquid both
in partial wetting regime and in induced pulsing regime
can far surpass the volumetric productivity and
selectivity of the slurry system, yet require an order of magnitude less of the active catalyst component.
• Undesirable homogenous reactions are suppressed in
the fixed bed reactor due to much higher catalyst to
liquid volume ratio
• Father advantage is accomplished in fixed beds by
operation at higher pressure (no moving shafts to seal).
• Fixed bed operation requires long term catalyst stability or ease of in situ regeneration .
S49
References
1. Suresh, A.K., Sharma, M.M., Sridhar, T., “Engineering
Aspects of Liquid-Phase Air Oxidation of
Hydrocarbons”, Ind. Eng. Chem. Research, 39, 3958-
3997 (2000).
2. Froment, G.F. and Bischoff, K.B., Chemical Reactor Analysis and Design, Wiley (1990).
3. Levenspiel, O., Chemical Reaction Engineering, Wiley,
3rd Edition (1999).
S50
References
1. Dudukovic, M.P., Larachi, F., Mills, P.L., “Multiphase Reactors – Revisited”, Chem. Eng. Science, 541, 1975-1995 (1999).
2. Dudukovic, M.P., Larachi, F., Mills, P.L., “Multiphase Catalytic Reactors: A Perspective on Current Knowledge and Future Trends”, Catalysis Reviews, 44(11), 123-246 (2002).
3. Levenspiel, Octave, Chemical Reaction Engineering, 3rd Edition, Wiley, 1999.
4. Trambouze, P., Euzen, J.P., “Chemical Reactors – From Design to Operation”, IFP Publications, Editions TECHNIP, Paris, France (2002).
S45
For any process chemistry involving more
than one phase one should :
• Select the best reactor flow pattern based on the kinetic scheme and mass and heat transfer requirements of the system,
• Assess the magnitude of heat and mass transfer effects on the kinetic rate
• Assess whether design requirements can be met based on ideal flow assumptions
• Develop scale-up and scale-down relations
• Quantify flow field changes with scale if needed for proper assessment of reactor performance
• Couple physically based flow and phase contacting model with kinetics