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PERFORMANCE STUDIES OF TRICKLE BED REACTORS
Mohan R. Khadilkar
Thesis Advisors: M. P. Dudukovic and M. H. Al-Dahhan
Chemical Reaction Engineering Laboratory
Department of Chemical Engineering
Washington University
St. Louis, Missouri
CREL
Trickle Bed Reactors
Cocurrent Downflow of Gas and Liquid
on a Fixed Catalyst Bed
Catalyst Wetting Conditions in Trickle Bed Reactor
...
......
........ ......
Operating Pressures up to 20 MPa
Operating Flow Ranges:
High Liquid Mass Velocity (Fully Wetted Catalyst)
(Suitable for Liquid Limited Reactions)
Low Liquid Mass Velocity (Partially Wetted Catalyst)
(Suitable for Gas Limited Reactions)
.......
L i q u id F il m
o r R i v u le
L i q u id F il le d p o r e s
D r y P e lle t
C a p ill a r y
Limiting Reactant criterion:
DeB C Bi
1
DeAC A*
D C
  eB Bi
1
DeA C A*
 
Gas limited reaction if
L IQ U ID
G AS
C o n d e n s a ti
Liquid limited reaction if
Flow Map (Fukushima et al., 1977)
10000
C AT AL Y S T
SPRAY
B ED
Re(Gas)
WAVY
G AS
1000
PULSE
TRICKLE
100
DISP .
BUBBLE
10
1
L IQ U ID
10
100
1000
Re (Liquid)
CREL
FLOW REGIMES AND CATALYST WETTING EFFECTS
DOWNFLOW (TRICKLE BED REACTOR)
UPFLOW (PACKED BUBBLE COLUMN)
PARTIAL WETTING
COMPLETE WETTING
CATALYST
LIQUID
GAS
(Trickle Flow Regime)
(Bubble Flow Regime)
CREL
Motivation

A clear understanding of the differences between the two modes
of operation is needed, particularly for high pressure operation.
Are upflow reactors indicative of trickle bed performance under
different reaction conditions?

To understand the effects of bed dilution with fines on reactor
performance

To develop guidelines regarding the preferred mode of operation
for scale-up/scale-down of reactors for gas or liquid reactant
limited reactions
Objectives

Experimentally investigate the performance of DOWNFLOW
(Trickle Bed) and UPFLOW (Packed Bubble Column) reactors
for a test HYDROGENATION reaction

Study the effects of PRESSURE, FEED CONCENTRATION and
GAS VELOCITY on the performance of both modes of
operation

Study the effect of FINES on the performance of the two modes
at different feed concentrations and pressures

Compare MODEL PREDICTIONS with experimental data at
different pressures
Reaction Scheme:
CH3
C
CH2
+ H2
Catalyst : 2.5 % Pd on Alumina
(cylindrical 0.13 cm dia.)
Fines
: Silicon carbide 0.02 cm
CH3
HC CH3
Pd/Alumina
Alpha-methylstyrene
B (l) + A(g)
cumene
P(l)
Range of Experimentation :
• Superficial Liquid Velocity (Mass Velocity) : 0.09 - 0.5 cm/s (0.63-3.85 kg/m2s)
• Superficial Gas Velocity (Mass Velocity) : 3.8 -14.4 cm/s (3.3x10-3-12.8x10-3 kg/m2s)
• Feed Concentration
• Operating Pressure
• Feed Temperature
: 3.1 - 7.8 % (230-600 mol/m3)
: 30 - 200 psig (3-15 atm)
: 24 oC
Limiting Reactant criterion:
Gas limited reaction if
 
DeB CBi
 1
DeA C*A
Liquid limited reaction if
 
DeB CBi
 1
DeA C*A
CREL
Experimental Setup
PC
Timer
High Pressure
Gas Supply
PC
Distributor
Rotameter
Damper
TT
High Pressure
Gas Supply
LT
LT
LT
Cooling
Jacket
Saturators
Feed Tank
DPT
Reactor
Vent
Solvent
PC
Vent
TT
High Pressure
Diaphragm Pump
PT
TT
PT
PC
PC
Rotameter
LT
LC
Demister
Waste Tank
Gas-Liquid
Separator
PC
PC
Gas
Chromatograph
Computer
CREL
Downflow and Upflow Experimental Results at Low Pressure
(Gas limited Reaction) without Fines
1
UPFLOW
Conversion(X)
0.8
DOWNFLOW
CBi=7.8%v/v, P=30psig
0.6
Gas Limited 8.8
0.4
0.2
0
0
100
200
300
Space time , s
400
DOWNFLOW OUTPERFORMS UPFLOW DUE TO PARTIAL EXTERNAL WETTING
LEADING TO IMPROVED GAS REACTANT ACCESS TO PARTICLES
CREL
Conversion(X)
Downflow and Upflow Experimental Results at High Pressure
(Liquid limited Reaction) without Fines
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
DOWNFLOW
UPFLOW
CBi=3.1(v/v)%,P=200psig
Liquid Limited 0.8
0
50
100
Space time, s
150
200
UPFLOW OUTPERFORMS DOWNFLOW DUE TO MORE COMPLETE EXTERNAL WETTING
LEADING TO
BETTER TRANSPORT OF LIQUID REACTANT TO THE CATALYST
CREL
Conversion(X)
Downflow and Upflow Experimental Results at Low Pressure
(Gas limited Reaction) with Fines
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
DOWNFLOW
UPFLOW
CBi=6.7 %(v/v), P=30 psig
7.5
0
50
100
Space time,s
150
200
ABOUT EQUAL PERFORMANCE DUE TO COMPLETE WETTING
Fines Packing Procedure: Vol. of Fines ~Void volume (Al-Dahhan et al. 1995)
CREL
Conversion(X)
Downflow and Upflow Experimental Results at High Pressure
(Liquid limited Reaction) with Fines
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
DOWNFLOW
UPFLOW
CBi=3.18%(v/v), P=200 psig.
0.8
0
50
100
150
200
Space time,s
SAME PERFORMANCE DUE TO COMPLETE WETTING
Fines Packing Procedure: Vol. of Fines ~Void volume (Al-Dahhan et al. 1995)
CREL
Effect of Pressure on Downflow Performance
Conversion(X)
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
p=100psig
2.4
p=200 psig
6.2
p=30psig
1.3
0.2
0.1
0
Ug=3.8cm/s, CBi=4.8%v/v
0
50
100
150
200
250
Space time,s
CREL
Effect of Pressure (as transition to liquid limitation occurs) on
Upflow Reactor Performance.
1
Conversion(X)
p=30psig
4.0
0.8
p=100psig 1.5
0.6
CBi=3.1%,Ug=3.8 cm/s
p=200psig 0.8
0.4
0.2
0
0
50
100
150
Space time,s
200
CREL
Conversion(X)
Slurry Kinetics
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
# 1 p =3 0 p s ig , C B i=3 . 9 %
# 2 p =1 0 0 p s ig , C B i=3 . 9 9 %
# 3 p =2 0 0 p s ig , C B i=4 %
# 4 p =3 0 0 p s ig , C B i=3 . 4 5 %
0
100
200
300
Time (min)
LHHW FORM
r
kvsCams Ch2
( 1  K1Cams  K2Ccume )
Pressure (psig)
kvs
3
(m iq./m3cat./s)
*(mol/m3 liq)r-1
K1
K2

30
100
200
0.0814
1.14
0.022
0
4.41
0.0273
0
11.48
0.021
0
1
2
CREL
El- Hisnawi (1982) model
REACTOR SCALE
•Reactor scale plug flow equations
L
G
Liquid phase gas reactant concentration
Direct Access
.
Access of Gas
of gas
.
.
.
.
.
.
.
.
.
via Liquid .....................to Dry Areas
...................
..............................
. ....................
.....................
.
•Constant effectiveness factor
Modified by external contacting efficiency
•Allowance for rate enhancement on
externally dry catalyst
Direct access of gas on inactively wetted pellets.
Liquid Dry
Film
L
G
CREL
Beaudry (1987) model
• Pellet scale reaction diffusion equations
DRY
HALF-WET
FULLY WET
For fully wetted and partially wetted slabs
d 2C ' A
 (1   ) 2  A2C ' A  0, 0  x  1;
2
dx
d 2C ' A
  A2C ' A  0, 0  y  1
2
dy
• Effectiveness factor weighted based on
contacting efficiency
Catalyst Pellet
Flowing Liquid
• Overall effectiveness factor changes along
the bed length
Evaluation of overall effectiveness with change in
concentration and contacting
Overall Effectiveness factor at any location
o  ( 1  ce )2 od  2 ce ( 1  ce )odw  2ce ow
CA
CB
CB
CA
2V/S
0
1
x
0
0
y
1
CREL
Conversion(X)
Upflow and Downflow Performance at Low Pressure
(Gas Limited Condition)
Experimental Data and Model Predictions
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
down,El-Hisnawi
upflow,El-Hisnawi
downflow,Beaudry
upflow,Beaudryi
downflow,exp
upflow,exp
Ug=4.4cm/s,Co=7.6%(v/v),p=30psig
0
100
200
300
400
Space time(s)
CREL
Conversion(X)
Upflow and Downflow Performance at High Pressure
(Liquid Limited Conditions):
Experimental Data and Model Predictions
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Ug=3.8cm/s,Co=3.1%(v/v),p=200psig
down,El-Hisnawi
up, El-Hisnawi
down, Beaudry
up, Beaudry
downflow,exp
upflow,exp
0
50
100
150
200
250
space time(s)
CREL
Summary

DOWNFLOW PERFORMS BETTER AT LOW PRESSURE.
(Hydrogenation of alpha-methylstyrene is a gas limited reaction.
Partial wetting is helpful in this situation.)

UPFLOW PERFORMS BETTER AT HIGH PRESSURE.
(Hydrogenation of alpha-methylstyrene becomes a liquid limited
reaction. Complete wetting is beneficial to this situation.)

THE PREFERRED MODE FOR SCALE-UP (UPFLOW OR DOWNFLOW)
DEPENDS ON THE TYPE OF REACTION SYSTEM AS WELL AS ON THE
RANGE OF OPERATING CONDITIONS THAT AFFECT CATALYST WETTING.

FINES NEUTRALIZE PERFORMANCE DIFFERENCES DUE TO MODE OF
OPERATION AND REACTION SYSTEM TYPE , DECOUPLE
HYDRODYNAMICS AND KINETICS, AND HENCE ARE TO BE PREFERRED
AS SCALE-UP TOOLS.

THE TESTED MODELS PREDICT PERFORMANCE WELL
(although improvements in mass transfer correlations are necessary)
CREL
Unsteady State Operation in Trickle Bed Reactors
“Modulation of input variables or parameters to create unsteady
state conditions to achieve performance better than that attainable
with steady state operation”
Motivation




Performance enhancement in existing reactors
Design and operation of new reactors
Lack of systematic experimental or rigorous modeling studies in
lab reactors necessary for industrial application
Two Scenarios
– Gas Limited Reactions
– Liquid Limited Reactions
CREL
Objectives

To experimentally investigate trickle bed performance under
unsteady state operation (flow modulation) for gas and liquid
limited conditions for a test hydrogenation system

To develop model equations for unsteady state phenomena
occurring in trickle-bed reactors

To simulate unsteady state transport processes in trickle-bed
reactors including bulk and interphase momentum, mass, and
energy transport for the test reaction system
CREL
Strategies for Unsteady State Operation

Flow Modulation
(Gupta, 1985; Haure, 1990; Lee and Silveston, 1995)
– Liquid or Gas Flow
– Isothermal/Non-Isothermal
– Adiabatic

Composition Modulation
(Lange, 1993)
– Pure or Diluted Liquid/Gas
– Isothermal/Non-Isothermal
– Adiabatic

Activity Modulation
(Chanchlani, 1994; Haure, 1994)
– Enhance activity due to pulsed component
– Removal of product from catalyst site
– Catalyst regeneration due to pulse
CREL
Possible Advantages of Unsteady State Operation
Gas Limited Reactions

Partial Wetting of Catalyst Pellets -Desirable
– Internal wetting of catalyst
– Externally dry pellets for direct access of gas
– Replenishment of reactant and periodic product removal
– Catalyst reactivation
Liquid Limited Reactions

Partial Wetting of Catalyst Pellets-Undesirable
– Achievement of complete catalyst wetting
– Controlled temperature rise and hotspot removal
CREL
Test Reaction and Operating Conditions
Alpha-methylstyrene hydrogenation to isopropyl benzene (cumene)
CH3
C
CH3
HC CH3
CH2
+ H
Pd/Alumina
2
Operating Conditions
• Superficial Liquid Mass Velocity : 0.1-3.0 kg/m2s
• Superficial Gas Mass Velocity : 3.3x10-3-15x10-3 kg/m2
• Feed Concentration
: 2 .7 - 20 % (200-1500 mol/m3)
• Cycle time (Total Period)
: 40-900 s
• Cycle split (ON Flow Fraction) : 0.1-0.6
• Max. Allowed temperature rise : 25 oC
• Operating Pressure
: 30 -200 psig (3-15 atm)
• Feed Temperature
: 20-35 oC
CREL
Experimental Results
1
0.45
0.9
0.4
0.8
0.35
Conversion (X)
Conversion(X)
0.7
0.6
0.5
0.4
0.3
0.3
0.25
0.2
0.15
0.1
0.2
Steady State
0.1
Unsteady State (Cycle = 60s, S=0.5)
Unsteady State (Cycle=60s, S=0.5)
Steady State
0.05
0
0
0
200
400
600
800
0
Space time (s)
100
200
300
Space time (s)
400
500
Liquid Limited Conditions ( = 2)
Gas Limited Conditions ( = 20)
High Pressure,
Low Liquid Feed Concentration
Low Pressure,
High Liquid Feed Concentration
D C
  eB Bi
DeA C A*
CREL
Effect of Cycle Split on Performance Enhancement
0.4
0.35
Conversion (X)
0.3
0.25
Steady
State
0.2
0.15
0.1
0.05
0
0
0.2
0.4
0.6
0.8
Cycle Split (ON time/Total Cycle Time)
1
Gas Limited Conditions ( = 20)
Operating Conditions : Pressure=30 psig
Liquid Reactant Feed Concentration= 1484 mol/m3
Cycle Split (St)= Liquid ON Period/Total Cycle Period(T)
CREL
Phenomena occurring under unsteady state operation
with flow modulation in a trickle-bed reactor
LIQ UID PULSE ON
Catalyst (Internally and Externally wetted)
Liquid Full (Holdup=Bed voidage)
Temperature, Low (=Feed Temperature)
(a)
LIQ UID PULSE TRANSITON ZONE
Catalyst (Internally wet, externally partially wet)
Liquid films (Holdup = dynamic +static)
Gas accesing liquid and dry catalyst
(b)
Temperature, Rise (>Feed Temperature)
(Only Scenario II)
LIQ UID PULSE OFF
Catalyst (Internally wet, externally dry)
Liquid films (Holdup = only static)
Gas Accesing dry catalyst
(c)
Temperature, High (>Feed Temperature)
(Only Scenario II)
time,t
GOAL: To Predict Velocity, Holdup, Concentration and Temperature Profiles
CREL
The Model Structure
Bulk Phase Equations
SOLID
GAS
z=0
C1G
C2G
.
.
CnG
NiGS
EGS
NiGL
EGL
NiGSEGS
NiGL
EGL
NiLS
LIQUID
ELS
NiLS
ELS
C1L
C2L
.
.
CnL
Species


(  G CiG )  u IG  G CiG    N iGL a GL  N iGS a GS
t
z


(  L CiL )  u IL  L CiL   N iGL a GL  N iLS a LS
t
z
Energy
( L  L E L ) (  L u IL  L H L )

 E GL a GL  E LS a SL
t
z
( G  G E G ) (  G u IG  G H G )

  E GL a GL  E GS a GS
t
z
 c (1   B ) E CP
 2 TCP
 (1   B ) k e
  E LS a LS  E GS a GS
t
z 2
z=L
CREL
Advantages of Maxwell-Stefan Multicomponent
Transport Equations over Conventional Models




Multicomponent effects are considered for individual component
transport
[k]’s are matrices
Bulk transport across the interface is considered
Nt coupled to energy balance (non zero)
Transport coefficients are corrected for high fluxes
[k] corrected to [ko] = [k][F] [exp([F])-[I]]-1
Concentration effects and individual pair binary mass transfer
coefficients considered
Dij  Dij


Thermodynamic non-idealities are considered by activity correction of
transport coefficients
 ln  i
[ij ]   ij  xi
x j
Holdups and velocities are affected by interphase mass transport and
corrected while solving continuity and momentum equations
Flow Model Equations
Momentum
L L
u IL
u
P
  L  L u IL IL   L  L g   L
t
z
z
G  G
 FD, Liq  K (u IG  uIL )  u IL ( N iGL aGL M i   N iLS a LS M i )
L
uIG
u
P
 G  G uIG IG   GG g   G
 FD,Gas  K (uIL  uIG )  uIG ( NiGL aGL Mi   NiGS aGS Mi )
t
z
z G
u ,u
iL
Continuity
L
iG
u IL  L 
 L
 L
  N iGL aGL M i   N iLS a LS M i
t
z
G  G G uIG  G 

  N iGL aGL Mi   N iGS aGS Mi
t
z
Pressure
*
1
1
( L uiL* ) ( G uiG
)
  (p) 
 N (    )  z  z  t z  c z 
G
L
L,G,P
Z
Staggered 1-D Grid
CREL
Stefan-Maxwell Flux Equations for Interphase
Mass and Energy Transport
Gas-Liquid Fluxes
n
q
Ni  J  xi   k J  xi
x
k 1
E L  hL. (TI  TL )   N iL HiL (TL )
q
N  J  yi   k J  yi
y
k 1
E  h (TG  TI )   N iV HiV (TG )
n 1
L
L
i
L
k
i 1
n 1
V
i
V
i
n
V
V
k
Liquid-Solid and Gas-Solid Fluxes
 N LS   ct [LS ][k LS. ] x
 N   ct [GS ][k
GS
.
GS
.
V
i 1
n
.
E LS  hLS
(TL  TILS )   N iLS HiL (TL )
i 1
n
] x
E
GS
 h (TG  TIGS )   N iGS HiG (TG )
.
GS
i 1
Bootstrap Condition for Multicomponent Transport
• Interphase Energy Flux for the Gas-Liquid Transport and Bulk to Catalyst
Interface Transport [ ]    y 
 ik  ( k   nc ) /  y
i ,k G
ik
i
k
,
 y   yi  i
i
,
:
 i  yi ( HiV (@ TG )  HiL (@ TL ))
• Net Zero Volumetric Flux for Liquid-Solid and Gas-Liquid Interface for
Intracatalyst Flux
[i , k ]CP   ik  xci  k
k  (
:
Mk
M
 nc ) /  mx
k
 nc
 mx   x ci
and
i
Mi
i
CREL
Catalyst Level Equations
Approach I: Rigorous Single Pellet Solution of Intrapellet Profiles
along with Liquid-Solid and Gas-Solid Equations
ctCP
xint,nc1  xint,nc
dt
  {[][ B] [  ]}1, j
1
j
( x ntj ,nc11  2 x ntj ,nc1  x ntj ,nc11 )
( xc) 2
 1 Rncnt 1  0
G
CiCP
L
xc
Approach II: Apparent Rate Multipellet Model Solution of Liquid-Solid
and Gas-Solid Equations
ctCP
L
xint 1  xint
nt 1
  NiLS a jLS   NiGS a GS
j  1 RApp  0
dt
j 1a ,1b
j 1a ,1b
CiCP
L
Type I: Both Sides
Externally Wetted
G
CiCP
L
Type II: Half Wetted
G
CiCP
G
Type III: Both Sides
Externally Dry
CREL
Holdup and Liquid Velocity Profiles
0.06
z=0.0
0.09
z=0.25
0.08
z=0.45
z=0.0
Liquid Velocity (m/s) …..
Liquid Holdup ...
0.1
z=0.65
0.07
z=0.85
0.06
0.05
z=1.0
0.04
0.03
0.02
0.01
z=0.25
0.05
z=0.45
z=0.65
0.04
z=0.85
z=1.0
0.03
0.02
0.01
0
0
0
0
10
20
time (s)
30
40
10
20
30
40
time (s)
Operating Conditions: Liquid ON time= 15 s, OFF time=65 s
Liquid ON Mass Velocity : 1.4 kg/m2s
Liquid OFF Mass Velocity: 0.067 kg/m2s
Gas Mass Velocity
: 0.0192 kg/m2s
CREL
Pseudo-Transient Simulation Results
Alpha-methylstyrene Concentration Profiles
time,s
Alpha-methylstyrene Concentration buildup in the reactor to steady state or
during ON cycle of flow modulation
Feed Concentration : 200 mol/m3
Pressure
: 1 atm.
Reaction Conditions : Gas Limited ( = 10)
(Intrinsic Rate Zero order w.r.t. Alpha-MS)
CREL
Pseudo-Transient Cumene and Hydrogen
Concentration Profiles
Liq. Phase Hydrogen Conc (mol.m )
0.75
25
20
8.124
14.004
21.084
15
29.814
34.254
10
16
-3
4.044
-3
Cumene concentration (mol.m)
1.644
44.034
5
0
14
z=0
12
z=0.1
10
z=0.2
z=0.3
8
z=0.4
z=0.5
6
z=0.6
z=0.7
4
z=0.8
2
z=1
0
0
0.2
0.4
0.6
Axial Position (m)
0.8
1
0
5
10
15
20
time (s)
Profiles show build up of Cumene and Hydrogen profiles to steady state
or during ON part of the pulse
CREL
Alpha-methylstyrene and Cumene Concentration
Profiles During Flow Modulation
40
160
30
120
20
80
40
0.9
Axial Location, m
0.7
0.5
0.3
0
37.225
34.725
29.831
25.313
20.433
15.852
10.156
time, s
5.353
0.227
10
39.455
0
29.291
Cumene Conc., mol/m3
200
0.1
Alpha-MS conc., mol/m3
50
0.5
20.644
0.4
10.479
time, s
0.3
0.2
0.341
Axial Location, m
0.1
Supply and Consumption of AMS and Corresponding Rise in Cumene Concentration
Operating Conditions: Cycle period=40 sec, Split=0.5 (Liquid ON=20 s)
Liquid ON Mass Velocity : 1.01 kg/m2s
Liquid OFF Mass Velocity: 0.05 kg/m2s
Gas Mass Velocity
: 0.0172 kg/m2s
CREL
Catalyst Level Hydrogen and Alpha-methylstyrene
Concentration Profiles During Flow Modulation
160
Concentration of Hydrogen during Liquid ON
(1:20s, Wetted Catalyst ) and Liquid OFF(20:40 s,
Dry catalyst) for negligible reaction test case
40
1
0.9
0.8
20
0.7
0.2
0.1
35.0302
30.1751
0.3
21.0159
0.4
15.1737
Axial Location, m
24.9087
0.5
39.7204
0
0.6
10.3263
Hydrogen
Concentration,
mol/m3
0.9
Axial Position, m
80
60
5.0781
0.1
0.035
120
100
0.035
5.0781
0.3
time,s
0.5
35.0302
30.1751
25.4597
20.0057
15.1737
0.7
14
12
10
8
6
4
2
0
Alpha-MS concentration,
mol/m3
140
time,s
Concentration of Alpha-MS in previously dry
pellets during Liquid ON
(1:20s, Wetted Catalyst ) and Liquid
OFF(20:40 s, Dry catalyst)
CREL
Conclusions
• Performance enhancement under unsteady state operation is demonstrated to be
significantly dependent on reaction and operating conditions
• Rigorous modeling of mass and energy transport by Maxwell-Stefan equations
and solution of momentum equations needed to simulate unsteady state flow,
transport and reaction occurring in a trickle bed reactor has been accomplished.
This algorithm can be used as a generalized simulator for any multicomponent,
multi-reaction system and converted to a multidimensional code for large scale
industrial reactors.
• Pseudo-transient and transient operation is simulated for the case of liquid flow
modulation to demonstrate performance enhancement under unsteady state
conditions. Product formation rate is enhanced due to increased supply of liquid
reactant to dry pellets (during ON cycle) and gaseous reactant to previously
wetted pellets (during OFF cycle). Exothermic enhancement and higher
hydrogen solubility can also be taken advantage of in the OFF cycle due to
systematic quenching during the ON cycle.
CREL