Heterogeneous Reaction Engineering: Theory and Case Studies

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

• Transport Effects
• Diagnostic plots for slurry systems
• Partial wetting and implications
• Slurries containing fine particles

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Heterogeneous Liquid-Phase Reaction Phenomena
Challenges 1. Identifying reaction(s) and their
location(s) 2. Accounting for internal and
external catalyst wetting / holdup phenomena
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Mass Transfer Resistances in Gas-Liquid-Solid
Systems
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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
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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)
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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
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Diagnostic Plots First Order Case
Gas-Liquid Mass Transfer Controls the Process
Negligible Gas-Liquid Resistance
Slope rcr
Intercept rb
Intermediate Case
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Diagnostic Plots (contd)
A/RA
Increasing resistance to gas absorption
Decreasing Particle Size
1/w
m gt 1
m 1
m lt 1
m 0
A/RA
1/w
Schematic Plots for other Higher Orders
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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
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Overall Effectiveness Factorfor a (m,n) order
Reaction
f(sA , fo)
(1)
where
(2)
(3)
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Overall Effectiveness Factorfor a Single-Site
L-H Rate Form
Example Glucose Hydrogenation
Ramachandran Chaudhari, 1983
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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 Henrys Constant)
• Gas consumption by all reactions
• Considering As 0 , we have

If LHS gt gt RHS, then no mass transfer resistance !
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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/t ?p particle porosity 0.5 t 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 lt 0.2
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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 !
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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

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Trickle-Bed Reactors
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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
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Trickle-Bed Reactors - Pros and Cons -
Pros
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

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Fundamental Phenomena in Trickle Bed Reactors
Macroscale
Microscale

• Axial radial RTDs
• 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

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

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Flow Regime Structures for Gas-Liquid Flow in
Fixed-Beds
Trickle-Flow
Pulse-Flow
Bubble-Flow
Spray-Flow
Mewes, Loser, and Millies (1999)
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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
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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
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Flow Regime Map for Gas-Liquid Flow in
Fixed-Beds
Gianetto, Baldi, Specchia and Sicardi, AIChEJ
(1978)
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Flow Regimes for Commercial and Pilot - Plant
TBRs
Fukushima Kusaka, J Che Eng Japan (1977)
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Effect of Bed Prewetting and Hysteresis Effects
CCD Video Imagesof Liquid Flow in 2-D Beds
channel flow
film flow
L 3.52 Kg/m2.s
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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)

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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
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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
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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)

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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).
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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
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Typical External Holdup Values
External Liquid Holdup Dynamic Holdup Static
Holdup ?LE ?LD ?LS
0.1 lt ?LE lt 0.25 ( or higher at high L / G )
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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)

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Pressure Drop and Liquid Holdup Correlations
MARE () eL DP / L Iliuta Larachi
(1999) 18 27 Ellman et al. (1988,
1990) 23 54 Saez et al. (1985) 22 41 Al-Dah
han Dudukovic (95, 96) 17 32 Larachi et al.
(1991) 22 73 Mean Absolute Relative Error
Carbonell, OG Sci Tech, vol 55 (4) (2000)
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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
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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
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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)

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Liquid - Solid Contacting in TBRs
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 lt
5 kg / m2 - s
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External Contacting EfficiencyLow Gas-Liquid
Interaction Regime
where ?D Dynamic liquid saturation
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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)

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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

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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
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Overall Effectiveness Factor for a Trickle-Bed
Reactor (limiting reactant in Gas phase), hO
Increasing ?CE decreases conversion ! LHSV based
scale-up alone is not suitable !
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Overall Effectiveness Factor for a Trickle-Bed
Reactor, (limiting reactant in liquid phase) hO
Increasing ?CE increases conversion ! LHSV based
scale-up is suitable !
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Trickle-Bed ReactorCatalyst Effectiveness
FactorsOverall effectiveness factor, hO
Both external and internal transport
resistances are included
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Comparison of Effectiveness Factors
Calculated From Previous approximate Solution and
Actual Numerical Simulation
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Rigorous Multicomponent Diffusion Modeling- Gas
Liquid Interphase Function Vector -
Khadilkar et al., 1998
CREL
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General Geometry

• Discuss MFS use here
• See muthana. Eusebio paper

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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
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Methods of Determining Contacting Efficiency

• Tracer Method
• Chemical Reaction Method

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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 (gt 95 )
• Continuation of the dry branch
• Thermal conductivity - L II model
• Intracatalyst interface location-LIII model

System Cyclohexene hydrogenation
CREL
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Three Types of Catalyst for Highly Exothermic
Reactions
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Nonvolatile Liquid-Limiting ReactantCompletely
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 ) ( per unit reactor
volume )
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Overall or Apparent Reaction Rate
Liquid-Limiting Reactant ( mol / m3 reactor - s )
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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
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Gaseous-Limiting ReactantCompletely 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 ) ( per unit reactor volume ) 1. Gas -
liquid KLaB ( AG /HA - AL) 2. Liquid-solid
kLS aP ??AL - AS )
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Overall or Apparent Reaction Rate Gas Limiting
Reactant (mol / m3 reactor - s )
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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.
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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.
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TBR Scale - Up for Aldehyde HydrogenationScale -
up done based on equal LHSV with disastrous
results
Data Plant Laboratory Height
(m) 19.4 0.235 Diameter (m) 0.455 0.0341
LHSV (h-1) 1.3 1.3 UL (LHSV)
(mh-1) 26 0.26 H2 flow (STD)
(m3h-1) 1000 - GHSV - 312 Pressure
(bar) 65 - 80 70 Temperature
(oC) 110 110 Bed porosity 0.425 0.425 Cat
alyst tablets 3 / 16 x 1 /8 (Vp / SP
0.31 cm ) Conversion (XB) 0.40 0.90
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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