1. Heterogeneous Reaction Engineering: Theory and Case Studies
Module 4
Analysis of Local Transport Effects in Gas-Liquid-Solid Systems
P.A. Ramachandran

2. Outline Transport Effects Diagnostic plots for slurry systems
Partial wetting and implications
Slurries containing fine particles

3. Heterogeneous Liquid-Phase Reaction Phenomena
Bulk liquid
Liquid
film
Vapor ci T
catalyst Ni E
Bulk vapor
Challenges: 1. Identifying reaction(s) and their location(s)
2. Accounting for internal and external catalyst
wetting / holdup phenomena

4. Mass Transfer Resistances in Gas-Liquid-Solid Systems

5. Local Rate of Reaction for Gas-Liquid-Solid Catalyzed Systems
A (g) + b B (l) P (l)
Gas-Liquid Mass Transfer:
RA = kLaB (A* - AL )
Liquid-Solid Mass Transfer for A:
RA = ksap (AL - As )
Liquid-Solid Mass Transfer for B:
RB = ksap (BL - Bs )
Intra particle Diffusion with Reaction:
RA = wc(As, Bs)kmnAsmBsn

6. Intraparticle Diffusion Limitations
Solution of the reaction-diffusion equations in the catalyst particle for some simple reactions results in effectiveness factor-Thiele modulus relationship similar to that represented by the enhancement factor-Hatta number relationship for gas-liquid reactions
Other details: Froment & Bischoff (1979)

7. Observed Rate - 1st Order Reaction in a Gas-Liquid-Solid System
For linear kinetics and the slow reaction regime, an overall resistance can
be defined that includes the gas-liquid and liquid-solid mass transfer
and reaction terms, including intraparticle diffusion limitations -1 w

8. Diagnostic Plots: First Order Case
1/w
A*/RA
1/w
A*/RA
Gas-Liquid Mass Transfer Controls the Process
Negligible Gas-Liquid Resistance
1/w
A*/RA
Slope = rcr
Intercept = rb
Intermediate Case

9. Diagnostic Plots (contd)
1/w
A*/RA
A*/RA
Increasing resistance
to gas absorption
Decreasing Particle Size
1/w
m > 1
m = 1
m < 1
A*/RA
m = 0
1/w
Schematic Plots for other Higher Orders

10. Commonly-Used Kinetic Models for Gas-Liquid-Solid Systems
A (g) + b B (liq) P (liq)
Mechanism
Rate Form
1. Single site adsorption of dissolved gas
2. Dissociative adsorption of dissolved gas
3. Adsorption of both A & B on single sites
4. General single site adsorption for N species

11. Overall Effectiveness Factor for a (m,n) order Reaction
= f(sA , fo)
(1)
where:
(2)
(3)

12. Overall Effectiveness Factor for a Single-Site L-H Rate Form
Example: Glucose Hydrogenation
Ramachandran & Chaudhari, 1983

13. Analysis of External Mass Transport Resistance
Overall mass transfer of H2 (gas) to catalyst surface is :
Rgas = MA(A*-As), A* - gas concentration in the liquid phase (using Henry’s Constant)
Gas consumption by all reactions:
Considering As = 0 , we have
If LHS > > RHS, then no mass transfer resistance !

14. Analysis of Internal Resistance (within the Catalyst Pellet)
n = reaction order, taken as unity
robs = net rate of consumption of limiting
Reactant (initial rate)
Cb = concentration of limiting reactant in liquid
Deff = effective diffusivity = DABp/τ
p= particle porosity ~ 0.5
τ = totuosity = 2
DAB = binary diffusivity (Wilke Chang correlation
L = (characteristic length) Vp/Sp
Weisz-Prater criterion is used
Internal Resistance is considered negligible if
We0.5 < 0.2

15. Parameter Estimation Method
Step-by-step approach
Start with a temperature data set
Identify the reactions
Identify the reaction form (reaction rate):
Where,
Aoj and Ej are estimated !

16. Kinetic Parameter Estimation (contd.)
Non-linear Optimization Problem
Identify and select the for the objective function
Identify the species adsorbed, if any (C1 to C5 here, as an example)
Develop parameter estimation program and the autoclave model / Slurry reactor model
Autoclave model predicts the species concentration at every instant (for the operating conditions) – set of differential equations can be solved by VODE routine from NETLIB libraries
Levenberg-Marquardt algorithm for parameter estimation – UNLSF routine from IMSL libraries

17. Trickle-Bed Reactors

18. Fixed-Bed Multiphase Reactors
(a) Trickle - Bed (b) Trickle - Bed (c) Packed - Bubble Flow
Cocurrent Countercurrent Cocurrent
downflow flow upflow
Semi-Batch or Continuous Operation; Inert or Catalytic Solid Packing

19. Trickle-Bed Reactors - Pros and Cons -
Plug-flow high conversion
Low liquid holdup less homogeneous reactions
High specific reaction rate
Temperature control possible by liquid vaporization
High pressure operation possible
Minimal catalyst handling issues
Process flexibility, reasonable throughput limitations
Lower capital & operating costs
Intraparticle diffusion resistance
Incomplete contacting/wetting
High pressure drop
Temperature control problems
hot spots
Scale-up and design is complex
Attrition and crush resistant catalyst is required
Dirty process streams cannot be used plugged or fouled bed
Catalyst loading is complicated

20. Fundamental Phenomena in Trickle Bed Reactors
Macroscale
Microscale
Axial & radial RTD’s
Flow regime
Pressure drop
Liquid holdup
Liquid flashing
Interphase transport
Liquid distribution
Heat transfer
Energy dissipation
LocaL texture of liquid flow (films, rivulets, stagnant pockets)
Local irrigation and wetting
Liquid holdup in pores
Local transport between gas and flowing and stagnant liquid, and solid
Local transport between flowing liquid, stagnant liquid, and solid
Local transport between gas and vapor-filled pores

21. Classification of TBR Processes Based on Volatility
1. Nonvolatile liquid reactant
• Rate limiting reactant
- Liquid
- Gas
- Both
2. Volatile liquid reactant
Reaction occurs only on wetted catalyst
Reaction occurs both on wet and dry catalyst

22. Key TBR Design Parameters
• Flow regime
• Pressure drop
• Liquid holdup
• Liquid - solid contacting
• Interphase transport coefficients
• Intraparticle diffusion
• Extent of liquid volatilization
• Reaction kinetics
• Thermo - physical constants

23. Flow Regime Structures for Gas-Liquid Flow in Fixed-Beds
Trickle-Flow
Pulse-Flow
Spray-Flow
Bubble-Flow
Mewes, Loser, and Millies (1999)

24. Affecting Flow Regimes
Three Key Factors
Affecting Flow Regimes
1. Throughput of gas and liquid
L - liquid mass velocity
G - gas mass velocity
L / G - ratio of mass velocities
2. Physical properties of the gas and liquid
- viscosity
- surface tension
- density
3. Foaming or non-foaming characteristics of
the liquid

25. Factors Affecting Choice of L / G
• Stoichiometry of the reaction
• Pressure drop limitations
• Establishment of desired flow regime
• Foaming characteristics of liquid
• Heat removal requirement
• Maximum allowed Tad

26. Flow Regime Map for Gas-Liquid Flow in Fixed-Beds
Gianetto, Baldi, Specchia and Sicardi, AIChEJ (1978)

27. Flow Regimes for Commercial and Pilot - Plant TBR’s
Fukushima & Kusaka, J Che Eng Japan (1977)

28. Effect of Bed Prewetting and Hysteresis Effects
CCD Video Imagesof
Liquid Flow in 2-D Beds
This slide demonstrates the effect of particle prewetting on liquid distribution.
The right two images show the differences of liquid distribution in prewetted bed and non-prewetted bed. (We used colored water !)
If you look at the intensity profiles at specific axial position, you will get the results as shown in the left plot.
More liquid spreading was occurred in the case of prewetted packed bed whereas the channel flow was dominate in the non-prewetted bed.
This is just cold flow experiment. The question will be if we have reaction happened in both cases, we will be the difference of reactor performance?
Recently, people really did this kind of experiments for oxidation of SO2 with active carbon as catalyst particles.
channel flow
film flow
L = 3.52 Kg/m2.s

29. Models for Trickling to Pulsing Flow Regime Transition
Macroscopic model - balance of inertial and capillary forces
Grosser, Carbonell & Sundaresan, AIChE J (1988)
Attou & Ferschneider, CES (1999)
Microscopic model - pore blockage by balance of inertial and capillary forces
Ka Ng, AIChE Jnl (1986)
Microscopic model - wave formation on surface of liquid film
Holub, Dudukovic & Ramachandran, AIChE J (1993)

30. Estimation of Pressure Drop for Two-phase Flow in Packed-Beds
Various empirical correlations based on:
• Lockhart -Martinelli parameter
• Two - phase friction factor
• Energy dissipation parameter
• Relative permeability parameter
• Other dimensionless parameters

31. Key Pressure Drop Equation Parameters
• Single - phase pressure drop
• Lockhart -Martinelli parameter
• Two - phase friction factor
Validity:
• Low and high Interaction regimes
• Non-foaming and foaming systems

32. Pressure Drop - Summary
Correlations based on single-phase gas and liquid DP (Ergun equation)
Lockhart-Martinelli (1949), Larkins et al. (1961), Specchia & Baldi (1974) - separate for low and high interaction, Kan & Greenfield (1978) - hysteresis effect on DP
Flow models
Relative permeability model: Saez & Carbonell, AIChE J (1985); Levec, Saez & Carbonell, AIChE J (1985); Saez, Levec & Carbonell, AIChE J (1985)
Slit model: Holub, Dudukovic & Ramachandran, CES (1992); AIChE J (1993); Al-Dahhan, Khadilkar, Wu, & Dudukovic IEC Res. (1998); Iliuta & Larachi, CES (1999)
Fluid- fluid interface model: Attou, Boyer & Ferschneider, CES (1999), Attou & Ferschneider, CES (1999)

33. Liquid Holdup - Key Definitions
• Liquid holdup (HL , L ) is the fraction of reactor volume
that is occupied by liquid (m3 liquid / m3 reactor).
L = VL / VR
• Liquid saturation (L , L ) is the fraction of external
bed voidage (B ) occupied by liquid (m3 liquid / m3 voids).
L = L / B
• Fractional pore fill-up (Fi) is the fraction of catalyst pore
volume occupied by liquid (m3 liquid / m3 pore volume).

34. Key Liquid Holdup Relationships
Total Bed Voidage = External Voidage + Internal Voidage
t = B p ( 1 - B )
Total Liquid Holdup = External Holdup Internal Holdup
L = LE L
Internal Holdup for Liquid-Filled Catalyst Pores (Fi = 1)
LI = F i p ( 1 - B )
External Liquid Holdup = Dynamic Holdup + Static Holdup
LE = LD LS

35. Typical External Holdup Values
External Liquid Holdup = Dynamic Holdup + Static Holdup
LE = LD LS
0.1 < LE < ( or higher at high L / G )

36. Liquid Holdup - Summary
Contributions to the overall liquid holdup
Internal liquid holdup (inside particle) ~ equal to particle porosity
External liquid holdup
dynamic (flowing liquid) - depends on flow regime and is determined
by viscous, gravity and inertial forces
static - volume fraction of liquid retained when a pre-wetted bed is drained, from balance of gravity and surface tension forces
HL= HLD + HLSe+ HLi = HLD + HLSe+ ip(1- B)
HL, HLD & HLe correlations for low & high interaction regime
Separate correlations for low and high interaction regimes
Empirical: Larachi et al. (1991), Lara-Marquez et al. (1992)
Phenomenological: Holub et al. (1992, 1993);
Al-Dahhan & Dudukovic (1994)

37. Pressure Drop and Liquid Holdup Correlations
MARE (%)* eL DP / L
Iliuta & Larachi (1999)
Ellman et al. (1988, 1990)
Saez et al. (1985)
Al-Dahhan & Dudukovic (‘95, ‘96)
Larachi et al. (1991)
*Mean Absolute Relative Error
Carbonell, O&G Sci & Tech, vol 55 (4) (2000)

38. Key Transport Resistances
• Gaseous reactant resistances
1 - Gas-to-liquid resistance
2 - Liquid-to-solid resistance
3 - Intraparticle diffusion and kinetic resistances
• Liquid reactant resistances
1 - Liquid-to-solid resistance
2 - Intraparticle diffusion and kinetic resistances
• Heat transfer resistances
1 - Bulk gas-to-particle
2 - Bulk liquid-to-particle
3 - Intraparticle

39. Transport Parameter Correlations
kLaB - Gas to liquid ( liquid - side )
volumetric mass transfer coefficient
kSL Liquid to actively wetted solid mass transfer
coefficient
kSg Gas to dry solid mass transfer coefficient
h Overall heat transfer coefficient
e Effective conductivity of particles

40. Interphase Mass Transfer Correlations - Summary
Liquid side of gas-to-liquid mass transfer
Separate correlations for low and high interaction regimes
Wild et al. (1992); Larachi (1991); Cassanello et al. (1996)
Gas side of gas-to-liquid mass transfer
For most situations negligible resistance
Gotto et al. (1977); Fukushima & Kusaka (1978)
Liquid-to-solid mass transfer
Some have separate correlations for low and high interaction regimes
Goto & Smith (1975), Satterfield et al. (1978), Specchia et al. (1978)

41. Liquid - Solid Contacting in TBR’s
• Incomplete liquid - solid contacting can occur due to:
1. Reactor- scale (gross liquid maldistribution)
2. Particle - scale (local catalyst incomplete wetting)
• Internal particle incomplete contacting is unlikely in the
absence of highly exothermic reactions
• External particle incomplete contacting is likely in the
trickle - flow regime when Lm < 5 kg / m2 - s

42. External Contacting Efficiency Low Gas-Liquid Interaction Regime
where: D = Dynamic liquid saturation

43. Liquid-Solid Contacting - Summary
Combining flow pattern deviations from ideal liquid plug flow, and incomplete catalyst wetting:
Liquid not in plug flow and there is no radial mixing, but all catalyst is wetted
Liquid not in plug flow and extensive radial mixing, and all catalyst is wetted
Partial external wetting of catalyst
Partial internal wetting of catalyst
Correlations for liquid-solid contacting:
Ruecker & Agkerman (1987), Ring & Missen (1991), Al-Dahhan & Dudukovic (1995)

44. Intraparticle Diffusion Resistance
Conventional Thiele-modulus/effectiveness factor approach needs to be modified to account for partial external and intraparticle wetting:
Mills & Dudukovic (1980) solved the diffusion-reaction equations for partial external wetting for slab, cylinder and sphere-shaped particles
The numerical solution can be approximated by weighted average of effectiveness factor of totally wetted and totally dry particles, the weighting factor being the contacting efficiency
TB = CE W + (1- CE) NW
Internal wetting effects have been largely ignored

45. Catalyst Effectiveness Factor
for a Differential TBR
• Assume:
(1) Gas-limiting or volatile liquid-limiting reactant
(2) First-order reaction
(3) Incomplete external wetting, complete internal wetting
• Approximate solution only possible for large modulus p

46. Overall Effectiveness Factor for a
Trickle-Bed Reactor (limiting reactant in
Gas phase), hO
Increasing ηCE decreases conversion !
LHSV based scale-up alone is not suitable !
CE = external liquid-solid contacting efficiency
CE < 1 for cocurrent downflow; CE = 1 for upflow

47. Overall Effectiveness Factor for a
Trickle-Bed Reactor, (limiting reactant
in liquid phase) hO
Increasing ηCE increases conversion !
LHSV based scale-up is suitable !

48. Trickle-Bed Reactor Catalyst Effectiveness Factors Overall effectiveness factor, hO
• Both external and internal transport resistances
are included

49. Comparison of Effectiveness Factors Calculated
From Previous approximate Solution and Actual Numerical
Simulation

50. Rigorous Multicomponent Diffusion Modeling - Gas Liquid Interphase Function Vector -
Khadilkar et al., 1998
CREL

51. General Geometry
Discuss MFS use here
See muthana. Eusebio paper

52. Level III TBR Model -Catalyst Scale Equations-
Externally Half Wetted,
Partially Liquid Filled Pellet
Liquid Filled Zone
Gas Filled Zone
Intra-catalyst G-L Interface
Continuity of temperature,
mass and energy fluxes,
and equilibrium relations
for all species
Khadilkar et al., 1998
CREL

53. Methods of Determining Contacting Efficiency
Tracer Method
Chemical Reaction Method

54. Prediction of TBR Multiplicity Effects
Hysteresis Effects Predicted
Two Distinct Rate Branches Predicted
(as Observed by Hanika, 1975)
Branch Continuation, Ignition and
Extinction Points
Wet Branch Conversion (~30 %)
Dry Branch Conversion (> 95 %)
Continuation of the dry branch
Thermal conductivity - L II model
Intracatalyst interface location-LIII model
System: Cyclohexene hydrogenation
CREL

55. Three Types of Catalyst for Highly Exothermic Reactions

56. Nonvolatile Liquid-Limiting Reactant Completely Wetted Catalyst ( hce = F i =1 )
Reaction : A (gas) + B (liquid) = P (liquid)
• Kinetic rate : kVBS ( mol / m3 catalyst - s )
( per unit catalyst volume )
• Rate in catalyst : kvPBS ( 1- B ) ( mol / m3 reactor - s )
( per unit reactor volume )
• Transport rate : kLS ap BL - BS ) ( mol / m3 reactor - s )

57. Overall or Apparent Reaction Rate
Liquid-Limiting Reactant ( mol / m3 reactor - s )

58. Plug-Flow Model for Scale - Up
Nonvolatile liquid, 1st order reaction
where:
Using : • Same catalyst activity
• Same size particles
• Same packing procedure ( B )
• Same feed
• Same Temperature

59. Gaseous-Limiting Reactant Completely Wetted Catalyst ( ce = F i =1 )
Reaction : A (gas) + B (liquid) = P (liquid)
• Kinetic rate : kVAS ( mol / m3 cat - s )
( per unit catalyst volume )
• Rate in catalyst : kv ( 1- B )PAS ( mol / m3 reactor - s )
( per unit reactor volume )
• Transport rate : ( mol / m3 reactor - s )
1. Gas - liquid KLaB ( AG /HA - AL)
2. Liquid-solid kLS aP AL - AS )

60. Overall or Apparent Reaction Rate
Gas Limiting Reactant (mol / m3 reactor - s )

61. Reactor Performance for a Gas-Limiting
Reaction with First-order Reaction
A (gas) +  B (liquid)
P (liquid)
where:
An increase in CE may decrease kapp so that equal LHSV for
scale-up may not work, i.e., if kapp decreases as uL increases.

62. Scale-up Methodology for a Gas-Limiting Reaction
• Keep same liquid hourly space velocity (LHSV)
• Keep same ratio of liquid to gas mass velocities (L / G )
• Keep same packed-bed length (i.e., same L (uL) )
These criteria are often impractical to implement.
Hence, a fundamental reactor model that captures the
key phenomena is needed for scale-up or scale-down.

63. TBR Scale - Up for Aldehyde Hydrogenation Scale - up done based on equal LHSV with disastrous results
Data Plant Laboratory
Height (m)
Diameter (m)
LHSV (h-1)
UL (LHSV) (mh-1)
H2 flow (STD) (m3h-1)
GHSV
Pressure (bar)
Temperature (oC)
Bed porosity
Catalyst tablets 3 / 16 “ x 1 /8 “ (Vp / SP = cm )
Conversion (XB)

64. Scale-up & Scale-down from Pilot Plant to Commercial Reactor
Catalyst orientation (flat surface preferred)
Addition of fines in pilot plant to simulate good liquid distribution and absence of wall effects
Reactor internals
- Inlet distribution
- Quench zones with redistribution
- Outlet collector geometry