4. DEMand tangential component of F and F
Normal (discrete element method) or collision wall
F n = k n D x n - h n dx n
dt
DPM m(distinct particle
Ft = Fn x t method) m
Ft > Fn
x t Demo
Numerical x - h dxera coming
Ft = k tD t
simulation t Ft m Fn
t
dt
soon?
h = 2 g km g = ( ln e ) 2
What is it providing us? ( ln e ) 2 + p 2
SAFIRE (Horio et al.,1998~)
Rupture joint h c
Attractive force Fc Surface/bridge force
(Non-linear spring)
kn Normal dumping h n w/wo Normal Lubrication
Normal elasticity
No tension joint Tangential dumping h t
Tangential elasticity k t
SAFIRE is an extended Tsuji-Tanaka model
developed by TUAT Horio group
Friction slider m
w/wo Tangential Lubrication
Soft Sphere Model with Cohesive Interactions
5. Plan of my Talk
1. Introduction
Nature of suspensions/beds and the effect
of Walls that we design
2. Scaling Issues
Derivations and validations
3. Agglomerating Fluidization
Progresses in Binderless Agglomeration
6. Phenomenology and Design
Nature and Art (wall effect)
Fluidlike
nature of
suspension:
no need of
walls but Plant
appreciated design:
the wall trying to get
most out of
the wall
effect
Fluidization
science: high Confusions
potential in in
developing the definitions
knowledge on etc.
suspension
nature
15. Fast fluidized beds = super-
critical state of G/S systems
A phase diagram of particle
suspensions (w/ Dr. Hirama data by Horio)
Nature
16. Hydrodynamics
Particle
behavior
Heat &
Mass
transfer
Chemistry
Mechanisms
&
Scale-up issues
Kinetics
Good performance
Good performance
Hydrodynamics
Chemistry
Heat &
Heat &
Mass Mechanis
ms &
Boundary Particle Mass
Transfer
Kinetics
Conditions behavior
+ Nature
Good performance ?
17. Three Previous Approaches
to the Scaling Law
1. Dimensional analysis
Fitzgerald (1982)
2. Dimensionless parameters in
differential equations
which do not contain Dt as an explicit parameter
Glicksman (1982?, 84……)
3. Integrated relationships,
phenomenology and correlations
Horio et al. (1982, 84, 86)
Note: Differential Eqs., boundary conditions and
integration gives solutions !
18. ub=[gDb]1/2 ub [ gmDbo]1/2
ubb=u0-umf
= m 1/2 ubo
ub= ubo [gDbo]1/2 Db=mDbo
Dbo m times
Dt=Dto
Dt=mDto
bshould remain same
A simple thought experiment (‘82)
19. Thought Expmt:
Dc/Db=(b+2)/(b-1)
ub=[gDb]1/2
Db: Bubble diam.
Dc: Cloud diam.
b= ub/(umf/mf)
umf/mf
ub=[gDb]1/2
xm
umf/mf
Gas flow in emulsion phase
20. Horio’s Scaling Law
1) For Geldart Group B powders, the bubble
fraction, bubble size distribution, solids
circulation and mixing can be made similar
among different scale models if the following
condition is satisfied:
May allow to use
U 0 - U mf = m(U 0 - U mf ) (98) the same solids!
o
2) Fluidization behavior of Group A powders,
both bubble distribution and interstitial gas flow
can be made similar if Equation (96b) is
satisfied, in addition to Equation (98).
U mf = m U mf (96b)
22. CFB: Area fraction of annulus
Extended Capes model by Horio et al. (‘89)
1/ 2
1 C
1 - = ** **
2
2 p (1 - C )(1 - A ) ** ( usl ,C - usl )
** **
(60)
C - A uT ,C
usl: gas-solid slip velocity
Suffix C: core
Horio’sScaling Law
23. Anderson-Jackson (’66) model
Equation of continuity for gas:
+ ( u) = 0 (1)
What happens if t
we start from Equation of motion for gas:
u
the governing f + ( u )u = f g - p - R (2)
t
equations ? Equation of continuity for solid particles:
(1 - )
+ (1 - )v = 0 (3)
t
Equation of motion for solids:
v
p (1 - ) + ( v )v = (1 - ) p g - (1 - )p + R + Ps (4)
t
where R denotes
D( u - v )
R = ( u - v) + (1 - ) M f
Dt (5)
with
n-1
β= ( p - f ) g(1 - ) / uT
(mf ≪≦ 1, Richardson and Zaki, 1954 ) (6a)
1- 150(1 - )m
+ 175 f u - v
.
β= s d p sd p
2
(≪1, Ergun, 1952 ) (6b)
24. Dimensionless expressions
f u
$
$ $ )u + gl + p + l u - v0 v÷ 0
÷ + ( u $ $$ $ ÷ = $ (86)
÷ t 2
p $ U0 pU 0 U 0
U v$ U 0 gl
2
l U 0 v0
2
(1 - ) 0 ÷ + ( v )v + ÷ 2 -
$ $ $ ÷ u - ÷÷ 0 (87)
$ v =
$
v0 t
$ v0 U 0 pU 0 v0 U 0
where
$ $ $ $
t$ t / ( l / U 0 ), u u / U 0 , v v / v0 , p p / pU 0 and l .
2
The representative length should be the plant
scale.
25. Are you trying to
make everything
similar? NO!
Remember: We are using same
molecules!
Scaling law should tell us in what
scale level and how much we can
sacrifice the similarity: Plant scale flow
pattern?; bubble/cluster scale?; particle scale?.
26. When f /p≪1,
$ p + l ( u - v) = 0
$ $ $
pU 0
= (1 - )p g / uT (mf≪≦1)
= (1 - mf ) p g / Umf (mf≦≪1)
l gl U 0
= 2 (1 - ) (mf≪≦1)
pU 0 U 0 uT
l gl U 0
= 2 (1 - mf ) (mf≦≪1)
pU 0 U 0 U mf
27. The flow field in a unit of length scale l, which is
geometrically similar to a reference unit (denoted by
superscript °), can be made similar, if the following four
conditions are satisfied:
l / U02 = l / U02 (91)
U0 / uT = U0 / uT (mf≪? ≦1) (92a)
U 0 / U mf = U 0 / U mf
(mf ≦ ≪1) (92b)
v0 / U0 = v0 / U0 (93)
f / p = f / p (94)
28. Ret=Ar/18 (Ar<104), Remf=Ar/1650 (Ar<1.9x104)
U 0 / U 0 = v0 / v0 = m (95)
uT = m uT (mf≪? ≦1) (96a)
U mf = m U mf (mf≦≪? ) (96b)
1/ 2
dp - m
=m
- m
p f
(Ar≦104)
1/ 4
(97a)
dp p
o
f
dp p - f f
=m (105≦Ar) (97b)
dp p - f f
29. Prof. Glicksman’s guideline ?
As noted above, the judgment of the dominant
mechanism can be done based on the Archimedes
number Ar. The guideline of Glicksman (1988),
Rep<4
i.e. for the viscosity-dominant regime, can be
disregarded if fluidizing gas velocity U0 is
considered as not being related to the criterion for
particle size selection. In other words, Equations
(97) can be used regardless of the fluidizing gas
velocity.
35. Straight column
l/Dt=1/15 Straight column
Straight column
l/Dt=2/15 Tapered column
Tapered column
l/Dt=1/15 radial position [-] PE pellet
concentration [%]
Transient response
Tapered column
l/Dt=2/15 t*=t/[Dt/g]1/2
Validation of scaling
radial position [-] PE pellet concentration [%] law
Radial and axial PE
t*=16.2 ; ○: bed A Dt=0.6m,
▽:bed B Dt=0.3m, △:bed C Dt=0.15m pellet distribution
42. lcl: cluster length Voidage in cluster
Similarity in Mesoscale flow structure
43. Scaling Hydrodynamics,
Experiments Erosion etc.
PLAN & IDEAS REAL PLANT
down CFD up
Reactor Model
Experiments
Scale down using the same Key points:
the imagined materials and Reaction,Heat Reduce risks
plant and conditions as & mass
expected for the but save
organize transfer, money &
real plant
sure tests distributor time
elements etc.
44. Agglomerating Fluidization
■Introduction
◇ Agglomerating Fluidization
◇ Previous thoughts and models
◇ Why binderless granulation?
■ Characteristics of PSG and PSG granules
◇ Granules appearance, structure, strength, size and
density, operating factors, scale effect
◇ Co-agglomeration and coating
■ Model predictions
■ Applications
◇ Hard metal cutting tool manufacturing
◇ Dry Particle Inhalation
■ Concluding remarks
45. “Agglomerating Fluidization”
“Agglomerating fluidization is a common mode of fluidization popular
in beds of Geldart group C powders, spray granulation, coating or
polymerization, metal powder processing at elevated temperatures
and combustion or gasification with sticky ash or sorbent particles.
However, in such a variety of cases their differences are only in
types of cohesiveness, their order of magnitude, the rate of
development and the elastic/plastic characteristics of necks between
particles. Once interaction forces are properly expressed, it should
be possible to mechanistically describe any different kinds of
agglomerating fluidization.”
Iwadate and Horio, Fluidization IX, Durango (1998)
Cited by Prof. J.C. Chen of Lehigh U. for a quiz at 10th
ceremony of Fluidization X, Beijin, May 2001.
47. Starting
cast shot
Fines
taken up
1500F 87% reduction 1600F 87% reduction
Experimental data from self nucleation tests
Wt pct Wt pct Wt pct
first cycle second cycle third cycle
Size, mesh Starter Final Final Starter Final Final Starter Final Final
US std bed bed bed less beda bed bed less bedb bed bed less
oversize oversize oversize
+20 32.1 42.3 44.6
-20+30 18.2 33.6 49.4 55.6 38.1 66.0 67.0 36.2 65.4
-30+40 45.1 18.3 27.0 30.0 12.5 21.7 22.0 10.1 18.2
-40 36.7 16.0 23.6 14.4 7.1 12.3 11.0 9.1 16.4
Iron particle growth by sintering
Langston and Stephens (1960)
48. g(p -ff) 2 n2F
umf= dp + 3pm dp
18m
Umf
increase
for fine
u [cm/sec]
powders
[cm/sec]
Data by Sugihara(1966)
and
umfmf
correlation by Jimbo (1966)
[ Along with their efforts for
establishing Soc. Powder
CaCO3 Tech. Japan]
dp mm]
49. Chronology of Group C issues
Green letters: fundamentals
1961 Davidson’s Bubble
1966 Jimbo, Sugihara’s umf issue left a question at least to Japanese
1973 Geldart’s Powder classification and ‘Group C’ for cohesive ones
197X Donsi-Massimila(75), Masters-Rietema(77): Cohesion force and
fluidized bed behavior
1985 Chaouki et al., Group C fluidization and agglomerate size (da)
prediction
1987 Kono et al.: Measurement of force acting on particles
1988 Morooka et al.: Energy balance model for da
1990 Pacek-Nienow: Fine & dense hardmetal powder fluidization
1991 Campbell-Wang: Particle pressure in a FB
1992 Nishii et al.: Pressure Swing Granulation
1993 Tsuji, Kawaguchi & Tanaka: DEM for Fluidized Bed
1998 Mikami, Kamiya & Horio: Numerical simulation of agglomerating FB
(SAFIRE)
Iwadate-Horio: Particle pressure / Force balance model to predict da
50. Very slow liquid layer flow
small
contact angle
droplet
liquid bridge
particle collision
liquid bridge
large
contact angle
particle collision
Liquid Bridge formation (SAFIRE model)
51. u0=1.2m/s, dp=1.0mm, p=2650kg/m3
(a) Dry particles
1 2 3 4 5
6 (b) Wet particles (water: 0.54wt%)
7 8 9 10
Fluidized bed behavior of dry and wet particles
(SAFIRE simulation, Mikami et al., 1998)
52. Spray Granulation: Pre Granulation is needed to avoid
dusting, sticking to walls & non-stoichiometric charging
(a) (b)
50mm 50mm
(a) before binder removal (b) after binder removal
Trace of original granules in alumina compacts
before and after binder removal
Uematsu, Uchida and Zhang (1994)
53. Potential of binderless
granulation (1)
Agglomeration: Reduces troubles associated with cohesiveness of
fines (dusting, sticking & poor chemical accuracy);
Increases uniformity of chemical composition of
product granules by decreasing segregation;
Binders: So far necessary to agglomerate but
Provide unnecessary strength to products;
Leave unwanted binder-originated species even
after the de-binder-ing operation;
Binderless ? Yes, because-------
54. Potential of binderless
granulation (2)
Because It gives weak products;
--Many processes do not need too much strength.--
Contamination-free;
Weaker granules provide higher green densities,
higher composition uniformity and not severe
defluidization;
Possible to granulate hydrophorbic powders / water
sensitive powders;
Well controlled granulation by Pressure Swing
Granulation (PSG; Dalton Ltd. / Fuji Paudal);
Probably possible to make layered structure.
Applications Dry ceramic process, Powder metallurgy, Drugs etc.
56. ①Fluidization
Bag filter interval
15s
②Compaction 1s
Group C interval
powder 0 time[s] 7200
Gas tank
Nature
Compressor
0.41m
0.108m
Compressor ①Fluidization ②Compaction
interval interval
+ Wall Effect (b) operation
(a) apparatus
Pressure Swing Granulation: PSG
Nishii et al., U.S. Patent No. 5124100 (1992)
Nishii, Itoh, Kawakami,Horio, Powd. Tech., 74, 1 (1993)
57. Al2O3 Lactose
Typical examples of PSG
granules
58. original
PSG
granules
Cumulative weight [%]
PSG
granules slide
500mm
from ZnO gate
dp=0.57mm
after
1st fall
2nd fall
3rd fall
Particle size [10-6m]
PSG granules: weak but strong enough!
Change in PSD of PSG granules in realistic
conditions
59. Cumulative size distribution [v%] 100
80 d p,sv [ mm]
No. 2 7.48
60 No. 3 4.95
No. 4 4.79
40 No. 5 4.14
No. 6 3.71
20 No. 7 2.58
0
0 10 20 30 40 50
Primary particle size [ mm]
PSG from lactose
Fig. 4 Size distributions of primary particles
Original powders of Lactose
(Takano et al. (2001))
60. 1mm 1mm 1mm
No. 2 No. 3 No. 4
1mm 1mm 1mm
No. 5 No. 6 No. 7
PSG from
Fig. 6 Microphotographs of PSG granules of lactose
lactose
61. #30-2 #30-2 #16-2 #16-2
#30-1 #30-1 #16-1 #16-1
ZnO
#30-2 #30-1 #16-2 #16-1
500mm
Structure of PSG granules
Granules split by a needle show a core/shell structure.
(Horio et al., Fluidization X (2001))
62. 1000
Median diameter [m10-6]
500
E
150
0.1 0.5 1.0
Superficial gas velocity [m/s]
Effect of fluidizing gas
velocity on da
63. 1.2
Bulk density of granules [kg/m3]
w=0.4kg
1.0 0.2kg
with
gas velocity,
0.8 solids charge
and
compaction
chamber
0.6 pressure
0 2.0 4.0 6.0
Maximum pressure difference for compaction [Pa104]
Factors affecting PSG
granule density
64. DQ labo
ρ(bulk)=3710kg/m3
angle of repose=34º
DQ200
ρ(bulk)=3800kg/m3
angle of repose=33º
DQ350
ρ(bulk)=3760kg/m3
angle of repose=35º
DQ 500 series
Scale up -
65. ① bubbling period: pulse (in reverse flow period)
Bed expansion de- ① ②
agglomerates and
compaction, attrition
and solids revolution
make grains spherical. cake
Fines are separated
and re compacted on
the filter.
fines‘ entrainement
② filter cleaning &
bed expansion reverse flow period:
Cakes and fines are
bubbling returned to the bed
cleaning-up the filter, and
bed is compacted
distributor promoting
compaction agglomerates’ growth
and attrition and consolidation.
air (in bubbling period)
What happens in
66. Gas velocity: linear increase from 0-0.25 m/s within t=0.1s, holding for 0.039s and linear decrease within 1.011s
Ha=0.39x10-19 J, dp=1mm, p=30 kg/m3 0.0546m
Ha=4.0x10-19 J
Numerical simulation of agglomerating fluidization
Iwadate-Horio (Fluidization IX, 1998)
67. Comparison of previous model concepts
Authors Model External force/energy Cohesion force/energy Comments
FGa Fpp
Chaouki
[ ]
FGa = Fpp No bubble
FGa = p d a3
hwd p
hw
et al. Fpp =
2 1+ 8 2 3 hydrodynamic
ag
6 16 p
effects included.
Force balance Hr
van der Waals force
gravity force ≒drag force
between primary particles
No bubble
v=u mf Etotal =(Ekin+Elam ) Esplit
hydrodynamic
Etotal=(Ekin+Elam ) h w (1- a)d a2
Morooka Elaminer =3pmu mfd a2 Esplit =
effects included.
=Esplit shear
322 If 3m umf <hw (1-a)
et al. Ekinetic =mu mf 2/2 Etotal ad p /(32pd p a),
Energy balance energy required to negative d a is
laminar shear + kinetic force
break an agglomerate obtained.
expansion Fcoh,rup
Fexp = Fcoh,rup exp = - Ps Bed expansion
force caused by
p Db ag(-Ps)d a2 Had a(1- a)
bubble Fexp = Fcoh,rup = bubbles is
Iwadate-Horio 2n k 242 equated with
Force balance cohesive rupture
force.
bed expansion force cohesive rupture force
68. (a) example force balance and (b) Limiting size of agglomerates
two solutions
The critical condition
stable point unstable point
1E-4
1E-4
1E-5
^
pDbag(-Ps)d a2 B 1E-5
Fexp= 2nk
1E-6
A easy to 1E-6
C
log F[N]
log F[N]
1E-7
defluidize 1E-7
fluidized
1E-8 1E-8
saddle point
Hada(1- a)
Fcoh,rup=
1E-9 1E-9
24 2
1E-10
1E-10
1E-6 3E-6 1E-5 3E-5 1E-4 3E-4 1E-3 3E-3
1E-6 3E-6 1E-5 3E-5 1E-4 3E-4 1E-3 3E-3
log d a[m] log da[m]
defluidization due to u0=umfa
Force balance of I-H model (Powder Technol., 1988)
and the critical solution
69. 3
2.5
Ff
Grain compression test
Load [mPa]
2
1.5
1 and typical force
0.5
0
0 50 100 150
Displacement [mm]
200 displacement responses
(a) Example of fr actur e tensile str ength mesur ement
A : Elastic and plastic
deformation
Ff
B : Elastic brittle fracture
Ff
C :Plastic deformation
Ff
(b) Types of mesur ements
70. 1,000 0.1
500
Chaouki et al.
300
Iwadate-Horio 0.05
da [mm] Bubble size
Da [mm]
200 0.03
(IHM)
100 0.02
50 bubbling
Morooka et al. 0.01 fixed bed
30 bed
20 u0=umf
u0=0.5m/s
2,000
0.005
10 0.01 0.03 0.1 0.3 1 3
0.01 0.03 0.1 0.3 1 3 10 30 100 1,000
dp [mm] 500
IHM
(a) Effect of primary particle size 200
da [mm]
100
5,000 50
Chaouki et al.
2,000 Morooka et al.
20
1,000 IHM
da [mm]
10
500 0.01 0.03 0.1 0.3 1 3
200 u [m/s]
0
100
50 Chaouki et al. (c) Effect of u0
20 Morooka et al.
u0=0.5m/s
10
0.3 0.5 1 2 3 5
Ha [J]
Iwadate-Horio (1998)
(b) Effect of Hamaker const.
Comparison of model
performances
71. 1E-3 1E-3
No. 4 No. 5
Fex p
1E-4 1E-4
Fex p
Fcoh,r up
Fcoh,r up
F[N]
Fexp and Fcoh,rup [N]
F[N]
1E-5 1E-5
1
0
h=
=h .039
7
=h .057
1
h=
cr
0
cr
ri =
0
1E-6
h=
1E-6
hc
d ob s=677mm d ob s=788mm
d calc=621mm d calc=723mm
1E-7 1E-7
1 10 100 1000 10000 1 10 100 1000 10000
d a[mm] d a[mm]
1E-3 1E-3
No. 6 No. 7
Fex p Fex p
1E-4 1E-4 Fc oh,r up
Fc oh,r up
F[N]
F[N]
1E-5 1E-5
1
8
h=
=h .080
=h .152
cr
cr
i =0
0
1
i=
h=
hcr
hcr
1E-6 1E-6
d ob s=607mm d ob s=373mm
d calc=726mm d calc=667mm
1E-7 1E-7
1 10 100 1000 10000 1 10 100 1000 10000
d a[mm] d a[mm]
Fig. 13 Agglomerate size determination (PSG:2hr, pre-sieving by 16mesh)
Agglomerate size determination by I-H
model (Takano et al. Powd. Tech.,accepted,2001; Lactose;
72. 1.4E-3
1.2E-3
Lactose
1E-3 ZnO
da,calc [m] L:E=7:3
8E-4 L:E=1:1
L:E=3:7
6E-4
4E-4
2E-4
0E+0
0E+0 4E-4 8E-4 1.2E-3
2E-4 6E-4 1E-3 1.4E-3
da,obs[m]
Comparison of model predictions with observed data
Model (IHM)
works !
73. Possibility of size control by
surface modification
by
vacuum drying, CH2OH or
NH4OH adsoption
Nishii and Horio (1996)
74. 500
Median diameter [10-6m] Median diameter [10- 600
Median diameter [10-
adsorption at: 293K, 293K,
p(adsorbate): 4kPa 4kPa
400 500
No effect: desorbed
during PSG
6m]
6m]
300 400
0 3 6 9 12 0 3 6 9 12 Notes: At 573K all
Absorption time [h] Absorption time [h] hydroxyl groups
Median diameter [10-6m]
500 on TiO2 are
500 eliminated
573K, 573K, (Morimoto, et al.,
13.3kPa 13.3kPa Bull. Chem. Soc.
400 JPN, 21, 41(1988).
400 Highest heat of
immersion at 573K
300 (Wade &
No effect ?? Hackerman, Adv.
Chem. Ser., 43, 222,
200 300 (1964))
0 3 6 9 12 0 3 6 9 12
Absorption time Absorption time [h]
[h] heat treatment:at p<13.3Pa
(a) C2H5OH (b) NH4OH 523K, for 6 hrs
adsorption:
Mean size of PSG granules from TiO2 (0.27x10 m) -6 bed= 150x10mm
in a 0.03m3 vacuum
after heat treatment and surface modification dryer
PSG: charge=0.0333 kg
Nishii & Horio 50%
u0=0.55 m/s RH: 40-
fluidiz.:15 s comp.: 1 s
(Fluidization VIII, 1996) total cycles=450
76. feed compositions
powd. dp(WC) WC Co wax*
x10-6m %wt %wt %wt
1 1.5 93.0 7.0 0.5
2 6.0 85.0 15.0 0.5
Powder 1 Powder 2 Powder 3 3 9.0 77.0 23.0 0.5
dp(cobalt)=1.3-1.5x10-6m
*) Tmp(wax)=330K
preparation:
1. grinding 2.5hr
2. vacuum drying
PSG:
Agglomerate 1 Agglomerate 2 Agglomerate 3 Dt=44mm
charge=150g
Hard Metal Application u0=0.548 m/s
SEM images of feeds and P(TANK)=0.157 MPa
total cylces=64
product granules
Nishii et al., JJSocPPM(1994)
77. Transverse rupture strength [N/mm2]
PSG
method
PSG
method
convent-
ional
method
Co content [wt%] Co content [wt%]
Application to hard metal industry
(Nishii et al., JJSPPM(1994))
Improved strength of sintered
bodies
78. Co-agglomeration
of lactose and ethensamide
CH3
CH2OH O C O
H O H
C-NH2 HN
CH2OH H
OH H OCH2CH3
OH O O OH
H H OH
OH H
H H
H OH ・H2O
OH
Lactose Ethenzamide Acetaminophen
Molecular structures
79. 500mm 500mm 500mm 500mm 500mm
L : E=0 : 1 L : E=3 : 7 L : E=1 : 1 L : E=7 : 3 L : E=1 : 0
10mm 10mm 10mm 10mm 10mm
L : E=0 : 1 L : E=3 : 7 L : E=1 : 1 L : E=7 : 3 L : E=1 : 0
top: PSG granules; second line: surface of agglomerate
(SEM)
Co-agglomeration of lactose
and ethensamide
80. 100
Concentration of Ethenzamide 1000mm
Granule Sample : 10mg
in Product Granules [%]
80 500mm
60
250mm
40
UV
20 absorbance:
300nm
0
0 20 40 60 80 100
Average Mass Concentration of
Ethenzamide in Feed [%]
Chemical Uniformity of PSG
granules
86. Concluding remarks
Knowing the nature of both
suspension and suspension-
wall interactions and
governing them to get good
products should be the role
of fluidization engineers.