basic design equations for multiphase reactors · 2018. 3. 20. · 3 objectives 1. review...
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BASIC DESIGN EQUATIONS FOR MULTIPHASE REACTORS
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Starting Reference
1. P. A. Ramachandran and R. V. Chaudhari, Three-PhaseCatalytic Reactors, Gordon and Breach Publishers, New York,(1983).
2. Nigam, K.D.P. and Schumpe, A., “Three-phase spargedreactors”, Topics in chemical engineering, 8, 11-112, 679-739, (1996)
3. Trambouze, P., H. Van Landeghem, J.-P. Wauquier,“Chemical Reactors: Design, Engineering, Operation”,Technip, (2004)
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Objectives
1. Review microkinetic and macrokinetic processes thatoccur in soluble and solid-catalyzed systems.
2. Review ideal flow patterns for homogeneous systems as a precursor for application to multiphase systems.
3. Derive basic reactor performance equations using idealflow patterns for the various phases.
4. Introduce non-ideal fluid mixing models.
5. Illustrate concepts through use of case studies.
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Types of Multiphase Reactions
• Gas-liquid without catalyst
• Gas-liquid with soluble catalyst
• Gas-liquid with solid catalyst
• Gas-liquid-liquid with soluble
or solid catalyst
• Gas-liquid-liquid with soluble
or solid catalyst (two liquid phases)
Straightforward
Complex
Reaction Type Degree of Difficulty
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Hierarchy of Multiphase Reactor Models
Empirical
Ideal Flow Patterns
Phenomenological
Volume-Averaged
Conservation Laws
Pointwise Conservation
Laws
Straightforward
Implementation Insight
Very little
Very Difficult
or Impossible
Significant
Model Type
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Macrokinetic Processes in Slurry Reactors
Hydrodynamics of the multi-phase dispersion
- Fluid holdups & holdup distribution
- Fluid and particle specific interfacial areas
- Bubble size & catalyst size distributions
Fluid macromixing
- PDF’s of the various phases
Fluid micromixing
- 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 variouis sources
(e.g., stirrers, fluid-fluid interactions,…)
Reactor
Model
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Hydrodynamics of the multi-phase flows
- Flow regimes & pressure drop
- Fluid holdups & holdup distribution
- Fluid-fluid & fluid-particle specific interfacial areas
- Fluid distribution
Fluid macromixing
- PDF’s of 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
Macrokinetic Processes in Fixed-Bed Reactors
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Elements of the Reactor Model
Micro or Local Analysis Macro or Global Analysis
• Gas - liquid mass transfer
• Liquid - solid mass transfer
• Interparticle and interphase
mass transfer
• Intraparticle and intraphase
diffusion
• Intraparticle and intraphase
heat transfer
• Catalyst particle wetting
• Flow patterns for the
gas, liquid, and solids
• Hydrodynamics of the
gas, liquid, and solids
• Macro distributions of
the gas, liquid and solid
• Heat exchange
• Other types of transport
phenomena
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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 ReactorQin
Tin
Cin
Product
Qout
Tout
Cout
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Ideal Flow Patterns
for Single-Phase Systems
Q (m3/s) Q (m3/s)
Q (m3/s) Q (m3/s)
a. Plug-Flow
b. Backmixed Flow
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Impulse Tracer Response
Q (m3/s) Q (m3/s)Reactor System
t
x(t) MT t
t
y(t)
Fraction of the outflow with a
residence time between t and t + dt
E(t) is the P.D.F. of the residence time distribution
Tracer mass balance requirement:
oT dt y(t) Q M
Q /M
dt y(t) dt )t(E
T
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Fluid-Phase Mixing: Single Phase, Plug Flow
Q (m3/s)
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Fluid-Phase Mixing: Single Phase, Backmixed
Q (m3/s)
Mi = Mass of tracer injected (kmol)
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Idealized Mixing Models for
Multiphase Reactors
Model Gas-Phase Liquid Phase Solid-Phase Reactor Type
1 Plug-flow Plug-flow Fixed Trickle-Bed
Flooded-Bed
2 Backmixed Backmixed Backmixed Mechanically
agitated
3 Plug-Flow Backmixed Backmixed Bubble column
Ebullated - bed
Gas-Lift & Loop
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Ideal Flow Patterns in Multiphase ReactorsExample: Mechanically Agitated Reactors
L
r G L
L
V
Q
( )1
G
r G
G
V
Q
VR = vG + VL + VC
1 = G + L + C
or
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First Absolute Moment of the
Tracer Response for Multiphase Systems
For a single mobile phase in contact with p stagnant phases:
1 =
V1 + K1j Vj
j = 2
p
Q1
For p mobile phases in contact with p - 1 mobile phases:
1 =
V1 + K1j Vj
j = 2
p
Q1 + K1j Qj
j = 2
p
K1j = C j
C1
equil.
is the partition coefficient of the tracer
between phase 1 and j
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Relating the PDF 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
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Illustrations of Ideal-Mixing Models
for Multiphase Reactors
z
G L• Plug-flow of gas
• Backmixed liquid & catalyst
• Batch catalyst
• Catalyst is fully wetted
z
G L• Plug-flow of gas
• Plug-flow of liquid
• Fixed-bed of catalyst
• Catalyst is fully wetted
Stirred tank
Bubble Column
Trickle - Bed
Flooded - Bed
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Intrinsic Reaction Rates
Reaction Scheme: A (g) + vB (l) C (l)
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z
G L
Gas Limiting 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
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Gas Limiting and Plug flow of liquid
Constant gas phase concentration
valid for pure gas at high flow rate
Conce
ntr
ation o
r Axia
l H
eig
ht
Relative distance from catalyst particle
0dz= AAAadz- kAAAakAQAQ rslpsrl
*
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
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Gas Limiting and Plug flow of liquid
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Gas Limiting and Plug flow of liquid Solving the Model Equations
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Concept of Reactor Efficiency
RRate of rxn in the Entire Reactor with Transport Effects
Maximum Possible Rate
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Conversion of Reactant B(in terms of Reactor Efficiency)
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Gas 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
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Gas Limiting and Backmixed LiquidConce
ntr
ation o
r Axia
l H
eig
ht
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
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Gas Limiting and Backmixed LiquidA 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)
=
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Gas Limiting and Backmixed LiquidSolving the Model Equations
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Flow Patterns Concepts
for Multiphase Systems
A BA - Single 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
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Flow Patterns Concepts
for Multiphase Systems
C D EC, D - Cocurrent or
countercurrent two-phase
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
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Axial Dispersion Model (Single Phase)
Basis: Plug flow with superimposed “diffusional” transport in the
direction of flow
Rdz
Cu
z
CD
t
Cax
2
2
@ z = 0z
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
@ = 0 η
C
PeCC
ax
10
@ = 1 0
η
C