1. BASIC DESIGN EQUATIONS FOR MULTIPHASE REACTORS

2. Starting Reference
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, , , (1996)
3. Trambouze, P., H. Van Landeghem, J.-P. Wauquier, “Chemical Reactors: Design, Engineering, Operation”, Technip, (2004)

3. Objectives 1. Review microkinetic and macrokinetic processes that
occur 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 ideal
flow patterns for the various phases.
4. Introduce non-ideal fluid mixing models.
5. Illustrate concepts through use of case studies.

4. Types of Multiphase Reactions
Reaction Type
Degree of Difficulty
• Gas-liquid without catalyst
• Gas-liquid with soluble catalyst
• Gas-liquid with solid catalyst
• Gas-liquid-liquid with soluble
or solid catalyst
or solid catalyst (two liquid phases)
Straightforward
Complex

5. Hierarchy of Multiphase Reactor Models
Model Type
Implementation
Insight
Empirical
Ideal Flow Patterns
Phenomenological
Volume-Averaged
Conservation Laws
Pointwise Conservation
Laws
Straightforward
Very little
Very Difficult
or Impossible
Significant

6. 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
Reactor
Model
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,…)

7. Macrokinetic Processes in Fixed-Bed Reactors
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
Reactor
Model
Heat transfer phenomena
- Liquid evaporation & condensation
- Fluid-to-wall, fluid-to-internal coils, etc.
Energy dissipation
- Pressure drop
(e.g., stirrers, fluid-fluid interactions,…)

8. 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
heat transfer
• Catalyst particle wetting
• Flow patterns for the
gas, liquid, and solids
• Hydrodynamics of the
• Macro distributions of
the gas, liquid and solid
• Heat exchange
• Other types of transport
phenomena

9. Reactor Design Variables
Qout
Tout
Cout
Qin
Tin
Cin
Reactor
Product
Feed
Reactor Process Reaction Flow
= f
Performance Variables Rates Patterns
• Conversion • Flow rates • Kinetics • Macro
• Selectivity • Inlet C & T • Transport • Micro
• Activity • Heat exchange

10. Ideal Flow Patterns for Single-Phase Systems
Q (m3/s)
Q (m3/s)
a. Plug-Flow
Q (m3/s)
Q (m3/s)
b. Backmixed Flow

11. Impulse Tracer Response
MT t
y(t)
x(t) t t
Q (m3/s)
Reactor System
Q (m3/s)
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:

12. Fluid-Phase Mixing: Single Phase, Plug FlowQ
(m3/s)

13. Fluid-Phase Mixing: Single Phase, BackmixedQ
(m3/s)
Mi = Mass of tracer injected (kmol)

14. Idealized Mixing Models for Multiphase Reactors
Model Gas-Phase Liquid Phase Solid-Phase Reactor Type
Plug-flow Plug-flow Fixed Trickle-Bed
Flooded-Bed
Backmixed Backmixed Backmixed Mechanically
agitated
Plug-Flow Backmixed Backmixed Bubble column
Ebullated - bed
Gas-Lift & Loop

15. Ideal Flow Patterns in Multiphase Reactors Example: Mechanically Agitated Reactors
VR = vG + VL + VC
1 = G + L + C or

16. First Absolute Moment of the Tracer Response for Multiphase Systems
For a single mobile phase in contact with p stagnant phases:
For p mobile phases in contact with p - 1 mobile phases:
is the partition coefficient of the tracer
between phase 1 and j

17. 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:
Hp(kc) = pdf for the stagnant phase

18. Illustrations of Ideal-Mixing Models for Multiphase Reactors
Stirred tank
Bubble Column 
Trickle - Bed
Flooded - Bed z z G L G L
• Plug-flow of gas
• Backmixed liquid & catalyst
• Batch catalyst
• Catalyst is fully wetted
• Plug-flow of gas
• Plug-flow of liquid
• Fixed-bed of catalyst
• Catalyst is fully wetted

19. Intrinsic Reaction Rates
Reaction Scheme: A (g) + vB (l)  C (l)

20. Gas Limiting and Plug-Flow of Liquid
Key Assumptions
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 z G L

21. Gas Limiting and Plug flow of liquid
Constant gas phase concentration  valid for pure gas at high flow rate
Concentration or Axial Height
Relative distance from catalyst particle
(Net input by convection)
(Input by Gas-Liquid Transport)
(Loss by Liquid-solid Transport) + -
= 0
(1)
(2)
Dividing by Ar.dz and taking limit dz  
(3)
(4)

22. Gas Limiting and Plug flow of liquid

23. Gas Limiting and Plug flow of liquid Solving the Model Equations

24. Concept of Reactor Efficiency
Rate of rxn in the Entire Reactor with Transport Effects
Maximum Possible Rate

25. Conversion of Reactant B (in terms of Reactor Efficiency)

26. Gas Limiting and Backmixed Liquid
Key Assumptions
Stirred Tank
Bubble Column 
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 z G L

27. Gas Limiting and Backmixed Liquid
Concentration or Axial Height
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

28. Gas Limiting and Backmixed Liquid
A at the catalyst surface:
For Reactant B:
(Net input by flow)
(Rate of rxn of B at the catalyst surface) =
(Note: No transport to gas since B is non-volatile)

29. Gas Limiting and Backmixed Liquid Solving the Model Equations

30. Flow Patterns Concepts for Multiphase SystemsB
A 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

31. Flow Patterns Concepts for Multiphase Systems
C, 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 E C D

32. Axial Dispersion Model (Single Phase)
Basis: Plug flow with superimposed “diffusional” transport in the direction of flow
@ z = L
@ z = 0
Let
@  = 1
@  = 0