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CHEMICAL ENGINEERING SCIENCE
GENIE CHIMIQUE
VOL.
I
JULY 1952
NO. 4
Application of the Temkin kinetic equation to ammonia synthesis in large scale reactors
D.
ANNARLE
Bese8mh Depertment, Imperi8l Ohem~al Industnes Lmuted, Bdlmghsm Division
(Reuwed 1 March 1952)
Summrry-The rate of re8otlon in 8n industrial, high pressure ammom synthesis reactor ls expressed in
terms of the km&lo equation formulated by TEAKKINand PYZHEV. An estunate of cetalyst activity is
derived, effordmg a meane of comp8rmg tiferent cat8lysts, and of measurmg cetalyst deterioration.
Optmuun temper8tures gmmg maximum rates of reaction 8re e&mated for certam conditions of catalyst
ectlvlty and mtml ges composltlon.
A reasoneble 8pproach to optimum conditions ls calculated for 8 partrxrhu design of catctlyat bed, fitted
with 8 me8ns of removmg some of the he8t of re8ctlon. Incorporation of the design m a plent reactor showed
th8t the best operatmg conditions conformed closely to those calculated
RBsumB-La vltesse
de r&&ion d8ns un convertrsseur mdustnel pour 18 synth&ee de I’ammonlac sous
haute pressron, est exprun6e sous I8 forme de 1’6quation conetique de TEMKIN et PYZHEV On obtlent
une estlmatlon de l’ctctlvlt6 catalytique, fourmssant un moyen de comparer divers catalyseurs et de
mesurer la b8mm d’actunte d’un catalyseur.
On obtient une veleur approxun8ttlve des temp6r8tures optun8, dormant les plus gr8ndes vltesses
de r&x&on, pour dee conditions don&es d’activlt6 catalytlque et de composition mltmle des gaz.
Une 8pproxmWlon nrlsonnable des comhttlons optun8 8 et+5c8lcuMe pour une disposition partlcuhere
du ht de cetQseu.r, comportant un moyen d’evacuer une partie des cctlories fourmes psr 18 rt ctlon.
L’mtroduotion de ce duxxxitlf d8ns un convertlsseur mdustriel a montr6 aue les mellleures comhtions
op6r8toues coincident fort bien 8vec oelles p&us
INTRODUCTION
TEMEINand PYZEEV [l] formulated s, kinetic equation
for ammonia synthesis assuming that the rate determ-
ining step was the process of activated adsorption of
nitrogen. A formula for the latter was postulated on
a semi-empirical basis, and the equation for ammonia
synthesis m a static system given as:
where
NNS
= no. of mole. of
N,,
per unit vol. of catalyst
after time of contact
t
hours.
P
NH,9 PN? PH.
= partial pressures of NH,, N,,
H, after tnne t.
kl
and
k, are
the reactron velocity constants for
ammoma synthesis and decomposition, respectively
At pressures above atmospheric, the perfect gas
laws are assumed to hold. kl and k, are related to the
equihbrium constant l&, thus =
Ki As Kp is
known accumtely [2] over a wide rkge of temperature
*
TEMKW ormtted the fector 2 between the rate of NC
adsorptron and NB, synthesis, and neglected the change. 8t
con&& pressure, of the tot.81 volume of gas with reaction
[see eq (21 =d (311.
par
le calcul
and pressure, experimental reaotlon data can be used
to determine values of the reaction velocity constants.
k2 is
the constant usually calculated, probably because
experimenters, such as WINTER [3], first concentrated
on the kinetics of rtmmomla decomposition. k2 should
obey the Arrhenius equation
where
k, = b, e- %c/RT
E
dCC
=
apparent activation energy for ammonia de-
composition cals/mol N, reacting.
R = gas constant.
27 = absolute temperature “K.
b, = frequency factor.
TEMKIN and PYZHEV [l] and EMMETTand KUBX-
MER [4] have apphed the kmetm equation to experr-
mental data at pressures up to 100 atm for various
space velocities, H,/N, ratios and degrees of approach
to equilibrium. The data were obtamed at three
temperatures, 370,400 and 450” C. The equation was
found to interpret the date satmfaotorrly, except that
k2 decreased with inoreasmg pressure, and some van&-
tion. 40000 to 55000-was observed m
Edeo**.
*+
See Tables 4 and 6
2 Chem
Esz 9ci Vol
145
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The present paper describes the flttmg of the
equation to approximate plant data, to fmd a measure
of catalyst activity and a means of estimating the best
practical reaction conditions The data were obtained
at 245 and 300 atm pressure, and covered a temperature
range of 370 to 550” C
TREATMENTOF DATA
EXPERIMENTAL
The plant reactor, from which the data at 245 atm
were obtained, was an upright cylmdncal forgmg,
contammg a smgle vertical catalyst bed The basket
holdmg the catalyst was lagged and measurements
showed the heat loss from the converter to be only
about 2% of the total heat evolved The catalyst
bed was therefore considered as adiabatic
As the catalyst beds were a&abatlc, various slmph-
fymg assumptions could be made. Radial conduction of
heat was taken to be neghgble, so that catalyst temper-
atures over any cross-section were considered uniform
Gm and catalyst temperatures were aasumed equivalent
and- longitudinal conduction of heat was neglected
In the case of the smgle bed reactor, for the pur-
poses of analysis, the catalyet bed, of total depth
13 ft, was consldered as a series of small horizontal
sections, of depth 6” or 1 ft, such that there were
temperature measurements at the begmnmg and end
of each se&on
Gas at 245 atm pressure, and of constant (imtlal)
gas composltlon flowed contmuously mto the reactor
After bemg heated to reactlon temperature, the gas
passed down over the catalyst bed, where It was
partially converted to ammonia, mth a nse m tempera-
ture due to the heat of reactlon Condltlons were
steady, and the pressure constant, so that at each
level m the catalyst bed, there was a constant tempe-
rature and also a constant ammonia concentration,
both quantities mcreasmg with the amount of catalyst
traversed
After leavmg the catalyst, the gas gave up some
of its heat to the mcommg gas, before flowmg out of
the reactor
The vanables measured were the pressure, the inlet
gas rate and composltlon, the concentration of am-
monia m the exit gas, and temperatures taken at short
intervals through the catalyst bed by a thermocouple
which could be moved m a vertical sheath near the
axis of the reactor
Except for a more comprehensive exploration of
temperature m the catalyst bed, the measurements
were the normal plant readmgs, and no great accuracy
for them is clanned
Smce all the heat of reactlon appeared as Increased
heat content of the reaction gas, the amount of reactlon
in each of the above sectlons could be found from the
rise m temperature of the gas over the se&on, usmg
spectilc heat and heat of reaction data The calculation
was commenced at the top sectlon, as the rate and com-
posltlon of the gas were known only at the inlet of the
bed The result for the top section provided mlet gas
data for the second section Repeatmg the calculation
for successive sections gave a senes of amounts of am-
monia synthesised, the sum of which should agree urlth
the total ammonia made m the reactor, as given by the
gas rate and the inlet and exit ammonia analyses The
agreement actually obtamed was usually wlthm &6%
In the case of the multi-bed reactor, each bed was
considered as one catalyst section The amounts of
reaction and the gas concentrations were calculated
by the same method as above, makmg allowance for
the extra gas added before each bed The mltlal reac-
tion temperatures m the beds subsequent to the first
were calculated from the exit temperatures of the
precedmg beds and the amounts of coohng produced
by the added coId gaE The agreement between the
calculated amount of ammoma made m the reactor
and the total amount measured was usually between
0 and -7%
The kmetlc equation was adapted to the contmuous
flow system and became
The data at 300 atm were obtamed from a reactor
slmllar to the above, but contaming several adiabatic
beds m senes, between each of which was provlsion
for addmg cold unconverted gas The measurements
used were the pressure, the lmtlal gas composltlon,
the amounts and temperatures of the gas added be-
fore each bed, the total amount of ammonia made
m the reactor, and the temperatures at the exit of
each bed
Direction of gas flow
& -1 J &
Entry to
---_M3---
catalyst
-----
~- A kg mols/hr NH, -
----_-
,----1-zJ- & - J --
- _ - ~~ -
+-dW
_ _ - _._ - -
146
(2)
D ANNABUG' Apphce;tionof the Temkin km&c equation to ammonia synthesis111arge-ecdereactors
~ngi~&? %enoe
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Vol
I
No 4 - 1062
D.ANNAJ.WZ: pplmatlonf he emku~ uwtlc quationo ammoxua syutheslsi arge-scaleeaotore
where A = flow of ammoma m kg mols/hr after the
gs,s has traversed w, Me of catalyst.
The psrtial pressures of the gases were expressed
m terms of total pressure
P
atm, and z the mol fraction
of NH, in the gas after flowing over w, M* of catalyst,
and the equatron was rearranged exphcitly m k,, vm.
k = P4a16V
z(l-bz)‘6
2
___--
48
* (3)
(l+z)[L*(l-bbz) -za]
w
where, after traversing w, Ma of catalyst, the gas rate
is
V,
MS/hr, measured at 1 stm and 20” C, the tempera-
ture IS T” K and the composition m mol fraction is
z of NH,,
a(1 --bz) of H,, and
(l -
bz) of N,
L = (1 ::Gq)z
where zes is the equilibrium mol fraction of NH8 at
pressure
P
atm, and temperature
T”
K. a and b are
constants determmed from the initial gas composition.
As mtegration of the equation for an admbatic
system, where z is a function of
T,
would be extremely
complex, the followmg approximation was adopted.
The average reaction velocity over each catalyst sec-
tion, given by
A z/A w, was
assumed equal to the actual
velocity
d z/d w at
the erithmetmal average temperature
of the section, for the concentrations of reactants and
products correspondmg to that temperature.
The errors thus involved were, for the c&se of the
smgle bed reactor, generally less than 1 or 2” C m
temperature, and 0901 m the mol fraction of am-
monia, and were within the errors of measurement
In the calculation of k2, except for conditions near
eqmhbrium, an error of 2” C in temperature will cause
an error of about 9 % in i&, whilst an error of 0 001 m
the mol fraction of ammoma wdl affect the msgmtude
of ka by less than 10%.
As
the errors act m opposite
directions, the final maccuracy of k , should not be
more than 10%. Errors of measurement may easily
c&use an additional error of the same order in the
k, values.
The reaction velocity constant has not been cal-
culated for conditions very near equlhbrium, for the
errors produced by errors of measurement are then
very large
Using the approxnnatlon_to apply the kmetm equa-
tion to the data of the multi-bed reactor may mvolve
greater errors, because of the more scanty mformation
on catalyst temperatures It le estimated that m the
malority of the examples, the error mcurred m the
k,
value should not be greater than 16%
With regard to the poor s.ucuracy, It LB ornted out
that the purpose of this work was to find out how much
use could be made of the plant data as measured,
without mtroducing more elaborate
ma rumentation
f
to improve the accuracy end frequency1 of measure-
ment
I
Table .
Expersmenti data fw tAe
detewns
iola
f k,
Pressure
245 tm. Temperatureange
4Ok5
6'C. Efffr-
csency ange. 09 to 090.
1
ma?
metron
Repreaentattve rnhu.? gas unnpo ton
NH
0021
H,
0674
K
0225
CH,\ 0048
A' 0032
N-
1000
Temp.
2
Effu:
OC
?wl
fmc
4%
Az/Aw
404 00321
009
0096
404 00263 0.07 0096
414 0.0286
008
0.106
414 0.0339 010 0093
416
00247
007
0093
420 0.0368 011 0066
423 OG439 0.13 0.106
432 00354 012 0.133
433 00408
0.13 0.203
437 00476 016
0138
444 00690 021 0162
448
0.0622
0.19
0209
462 00484
0.18 0.176
463
00630 020 0230
469 00666 028
0182
472 00761 0.32 0137
476
00631
027
0163
476 00687 030 0281
484
00743 036 0.164
496
00922 0 47 0136
498 00833 043
0214
502 0.0876 046 0176
506 00842
046
0194
612 00919
0.52
0134
618 0.1088 064 0146
528
00993 062 0126
629
01050 067 0174
530 01054 068 0126
638
01067 073 0126
547
0.1164 0.86
0030
550 01149 0 86 0076
565 01234 096 0062
&f'/
c
---T
344
34.2
238
289
31.1'
33.8
340~
3091
23
286
3361
33 1
30 ~
232~
28 i
33.0'
30.11
2291
3221
32.6
22.6'
27.6
296
317
321
290
22.3
271
288
267
286
21.7
k,
170
13.1
152
19.7
16.6
20.4
43.7
62.8
762
998
161
209
166
191
368
417
381
662
614
983
966
1112
1410
1360
2460
2140
2626
2481
3630
3360
6440
11760
12~
Chem.Eng.Sai.ol 1
147
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D
ANNABLE Apphcatlon of the Ten-dun km&o equation to ammoma synthe+w
m large-scale reactors
Cl1cmirXXl
E~neering Science
RESULTS
Tables 1 and
2 gwe the valuee of k, determined by the
above methods The values of log, 4
are
plotted wd,h
reciprocal temperature in Figs 1 and 2
Table
2.
Experzmental data
for the
determcnatzon
of
k,
Preesure 300
atm.
Temperature range 37449Q” C. Effc-
ctency range 0 19 to 0 76.
mol
fractcon
Represent&we znetial gas
wmpoestwn NH, 0060
H*
0 678
N*
0
192
CH,
0045
A 0 126
x
Temp
OC
T
--
2
mol
frac
-
-
374 0 076 0 19
376 0 131
0.34
379 0 120 0 31
386 O-081 0 22
387 0 078 0 21
391 0 145
040
396
0 088
0.26
395 0 076 021
396 0 107 0 30
396
0 087 0 26
397
0 074
0.21
403 0 152
045
404
0 074 0 22
406
o-157 0 47
410
0 082
026
412
0 079
0.26
413
0100 031
415
0,148 047
420 0,113
0 37
421
0 090
0 30
422
0 143
0 47
426 0 123
0 41
430 0 134
046
432
0 097 o-34
438
0164 0 69
446 0 161 0.62
448
O-099 0 38
451 0 109 0 43
463
0 147 0 63
471 0 124
0 66
487 0 131 0 66
496 0 142 o-74
499 0140 0 75
0 008 46 2
0 008 64.1
0011 61 0
0 015
46 0
0 016 42.2
0007 64 5
0 016
46 7
0 013
50 4
0 016
46 1
0 015
618
0 021
32.2
0 008 67 4
0017 33 4
0006 66 6
0.049 320
0049 33.3
0 014 51 9
0 014 616
0 015 52 7
0064
31 7
0016
60 1
0 021 64.9
0 016 66 1
0054 31.6
0 010 66 5
0 010 65 3
0 034 33 2
0 082
313
0 027 68 1
0 071
30 8
0 072 318
0 083 306
0 062 316
Gas
mate
kM8/hr
4
155
446
6.68
6 07
4 82
7 84
790
6
10
908
848
6 62
16.1
6 97
13.1
22.0
23 8
16 4
36 7
26 0
38 2
43 4
49 1
47 3
69.0
67.1
87 6
60 7
174
292
332
603
1120
893
JO
80-
70-
I
60 -
*
w
H
50.
VO-
so-
Fig 1 Log,
k, versus I/T
for five batches of new cata-
lyst Different symbols denote different batches of
catalyst.
Fig
2 Log,
k, versus I/T for one batch of catalyst
operatmg at various temperatures and effmlencles.
148
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Vol. I
Ho. 4 - 1962
D; &~ABLB: Application of the Temkin kinetic equation to ammonia synthesis in large-so& reactors.
All the data applied to new catalyst, which was
multi-promoted iron oxide. Poisons (oxygen contain-
ing compounds and sulphur) were
probabIy present
n
very small quantities in every example. Measurements
of them were not undertaken, but their concentration
is regarded as being fairly steady between the experi-
mental runs. The actual small variations which oc-
curred will increase the so-called experimental error.
Table 1 and Fig. 1 include data at 245 atm from
five charges of catalyst. Initial gas composition was
very similar from one run to another, and as there
was not much variation in initial reaction temperature,
the adiabatic nature of the reaction has resulted in
some interdependence of temperature and efficiency,
where efficiency = z/z,,.
Fig. 2 and Table 2 present the data at 300 atm press-
ure from a single batch of catalyst spread between
the series of adiabatic beds. Although initial gas
composition was again fairly constant, it was possible
to obtain some variation of temperature which was
independent from the variation in efficiency, thus pro-
viding a more comprehensive test of the Temkin
equation.
In Table 3 are summarised values of k, and E,,
obtained from the two sets of data by calculating the
best straight line for the relation log, k, versus l/T.
Table 3
Data
k, at
420” C ) 470” C
Edec
I
Table 1 . . . .
Table 2 . . . .
DISCUSSIONOF RESULTS
Fig. 2 and
Table
2 show that, over the experimental
range of ammonia concentrations, efficiencies and total
rates of flow, the Temkin equation gave values of the
reaction velocity constant, k,, which conformed well
with the Arrhenius equation.
Fig. 1 and Table 1 prove that reproducible results
could be obtained with different batches of catalyst,
-and show that the Arrhenius equation was obeyed
under different sets of reaction conditions and wider
ranges of efficiencies than in the case of
Table
2.
The values of E,,
obtained at 245 aCm and
300 atm are similar. The small difference between
the k, values is approximately that expected, if the
empirical relation between the reaction velocity con-
stant and pressure, mentioned in the subsequent sec-
tion, is correct, and the concentration of poisons in the
reaction gas is similar for the two sets of measurements.
The experimental scatter in the data is consider-
able, amounting to a coefficient of variation in k, of
29% for the fimt set of data, and 31% for the second.
Neverthel&, the results are good enough to de-
monstrate that the Temkin equation in conjunction
with the Arrhenius equation give a good interpretation
of the ammonia synthesis reaction in the plant reac-
tors, making possible the measurement of catalyst
activity n terms of the reaction velocity constant k, ,
and the apparent activation energy for ammonia de-
composition : E,, .
The large experimental scatter will make impos-
sible the detection of real small differences in the reac-
tion velocity constant, and will render approximate any
calculations on reactor operation.
AGREEMENTOF k, AND EdeC
wrrn 0TnEn Po~Lrsnxn
RESULTS
The values for Edec,
the apparent activation energy
for ammonia decomposition, accord well with estim-
ates found by other workers (see Table 4).
As the reaction velocity constant varies with press-
ure, it is difficult to compare our results at 245 and
300 atm with others at pressures of 106 atm and less,
(see Table 5). Moreover, as k, is very sensitive to the
concentration of poisons in the reaction gas, it is not
justifiable to compare different estimates without
a knowledge of the gas purity.
Nevertheless it is interesting to note that our results
can be correlated fairly well with those of EMMETT nd
Table
4. Gknwpa~iem~of
v&m for 2,
kc
@-m arious 8ource.s
of
data
Tsnxm ond PYZEEV . .
T&xm and PyZEEVB caku-
l&ions on WINTERS re-
sults , . . . . . . . .
LARSON and TOUR. . . .
.LARSONand TOUR . . . .
EMMETT . . . . . . . .
EMMETT . . . . . . . .
EMXE~ . . . . . . . .
Em&r a . . . . . . .
I.C.I. . . . . . . . . .
I.C.I. . . . . . . . . .
i
I
resswe
tm
1
4oooo
1
46600
10
436oa
31-6
46600
33.3
45ooo
66.6
46 600
100
48900
100
53000
246 46 800.
300
47900
-
Edcc
References
111
PI end [31
Cll.~nd161
PI and PI
II41
II41
141
141
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D.
ANNABLE:
Apphcatlon of the Temkm kmetm equatzon to ammonm synthe& m large-tie reactors
Chemical
Englnedng Boienoe
Table 5. &nqwwon
o
k, vdua from vmww wwc
Te?np
“C
sfnkrce
of
data
300
460
420
400
370
I C I
LARSON and
Tow
.
&?dE’FT . . .
I.C
I. . .
LARSON
and TOUR
I.C.I. . . . .
E-m. . . .
I.C.I. . . . .
EMMETT . . . . .
127
30.1
10.7
2 02
Preaeure (am)
245
100 666
33 3 316
135
424-613 781-915
196-212 237-292 34-17
33.9
223-208
12 6
16.2-216 24 l-30.8 37.2-47 4
-
1 27-2.91 3 194.96 7.33-8 96
LAIWON and TOTJR, by an empirical relationship
k, cc P-0 ‘=, whmh
is very similar to that found by
EMMETT,k, bcPo5 see Fq. 3).
IO-
1=/Cl
E-
Emme ft
I = hson 8 row
O
20
30
I O
50
a - 0
l og
-D
Fig 3 Varmtlon of k, with pressure
USE OF k, AS A MEASUXE OF CATALYSTAUTJJ-ITY
Two examples are mentioned of this use of the reaction
velocity constant Fig 4 presents data for five charges
of new catalyst which operated in a g&s system con-
-
-
10
714-91s
248
tammg a heavier concentration of poisons than that
appertammg to the data for Fig. 1
Although similar
catalyst of similar age was used in both cases, the
IIW 1200
1300 I400
1
loft
1
Fig
4.
Effect of po~som on actmty of new catalyst
Different symbols denote Uferent batches of catalyst
activity of the catalyst subject to the greater amount
of poisons 1s only about one third of that operatmg
under the more favourable condrtlons. This rapid
poisonmg effect, at least partly due to oxygen-contain-
mg compounds, IS to be expected from the experimen-
tal results of ALMQUIST nd BL~OK [6], on the poison-
ing of ammonia catalyst by carbon monoxide and
water-vapour .
150
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Vol. I
No 4- 1962
D. ANXABLE: Apphcatlon of the Temkin kmetio equation to ammoma synthesu 111 arge-soak maators
The change m activation energy due to the iucreas-
where Earn
= apparent activation energy for am-
ed poisonmg is obscured by the fact that the slope of
monia synthesis in cal/mol N, reactmg
the line correlatmg log, k, w&h l/T IS mflueneed by
The above expression gives
the greater poisoning of those layers of the c&al-&t bed
which operate at the lower temperatures
k
P
r-
Eaec
Fig. 5 demonstrates the tiference in activity which
ka -i -a
was observed for two catalysts of different manufact-
which reduces to
ure operatmg under smular condltlons
(4)
Fig. 6 Comparison of two catalysts
and gas composition. Hence the optimum tempera-
ture T, correspondmg to z, can be deduced. For the
example quoted, a pressure of 245 atm was chosen,
with an mltlal gas composltlon
t LOJLATION
OF &‘TllWM CONDITIONS
The most useful apphcation of the Temkin equation 1s
to calculate optimum reactlon con&tlons, and then
to find how nearly these may be achieved m a plant
reactor
The determination of optimum reaction conditions
1s a wide problem, but m the example gven below, the
vanables of catalyst activity, total pressure and initial
gas composition were fixed
Maximum reactlon velocity for a gven gas compo-
sltlon, is attamed at a temperature where the dtieren-
tial coefficient of reaction velocity with respect to
temperature 18 zero.
Dfiferentlatmg eq. (2), under optimum condltlons
o=&(g)
E,, w&8 taken as 47400, and the function k, such
that its value at 470’ C was 325. A value of 20800
was taken for Esyn, ~1etermined from the relation
E
wn
- E,, = Q,
the heat of reaction pr mol N,
reacting. With this information, the optimum tempe-
rature correspondmg to any mol fraction of NH, could
be calculated. Fig 6 gives the relation obtained be-
tween these two quantltles, and Fig 7 the correspondmg
This equation gives L, for any z
L, being related to the equihbrmm constant, IS an
accuraQly known function of pressure, temperature
0
0 I 020
MO/
racfton
of
NH -
Fig 6 Relation between optunum temperature
and ammoma conoentratxon
mol fraction
0 016
.
0686
0 228
0 036
0 034
Total. ..I000
151
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D
ANNABLE
Apphcation of the Temkm km&o equation to
ammonia
synthesla m h@-s0a~0 rfxwtora
Engin ~~?eience
maximum reaction velocities. It is of interest that
the reaction velocities, whilst they are high and de-
crease rapidly at low ammoma concentrations, are
Mot thcf~on of Ii3 L
low and relatively constant
for high ammonia ooncen-
trations
Integration of the syn-
thesis equation makes pos-
sable the construction of
the ideal temperature and
ammonia concentratiPm gra-
dients through a catalyst
bed The equation me mte-
grated m a stepwise manner
commencmg wrth the nntial
reaction conditions of gas
rate, composition and pres-
sure. For a small increment
d z m the mol fraction
of ammonia, the optimum
temperature is calculated,
for the arithmetical aver-
age z m the interval, from
eq (4) The increment of
Fig 7 Maximum reaction velocltles at optimum
condltlons
catalyst volume
A w 1s
then found by substituting the
average values of V, z, and T 111 q. (3) ucz
dw= P6a15V
48
(I+t);:(lIIE&_*t] (I%*
A z 1sorigmally chosen small enough for the approxuna-
tion to be apphed g = g at the average conditions.
Subsequent increments A w are calculated m a similar
manner until the whole catalyst bed has been taken
mto account
The resultmg ideal gradients of ammoma concen-
tration and temperature are given m Fig 8
The unit
of the abcissae la volume of catalyst traversed/imtlal
reaction gas rate, chosen so that results cantbe easily
computed for various gas rates
THEBESTOPERATINGCONDITIONSINAF'LANTREACTOR
Attainment of ideal condltlons m a plant reactor would
be a complex practmal problem mvolvmg removal of
the heat of reaction from the catalyst bed at a rate
decreasmg with catalyst age, and varymg through the
bed from a high figure at the beginnmg of the reaction
to a low figure at the end of the reaction. Moreover,
the first part of the bed would be operated at such a
high temperature that the activity of the catalyst
there would probably be quickly impaired
A reactor had been designed, however, to grve a par-
tial approach to the ideal condrkons, by transferring
some of the heat of reaction to partially heated gas
which flowed m a counter-current direction to the
reaction gas, through vertical tubes mserted m the
catalyst bed
The rate of removal of the heat of reac-
tion could be vaned by altering
the rate of flow of the cooling gas,
or its initial temperature, but the
coolmg of particular sections of
catalyst could not be varied in-
_--
‘\
L, fd, l
femperofufe
--__
--__
1
.
500
I
-----a__
I
0
5
IO
Vof cafa&f fmvemed/Imtlf/o/yas rafe -W
Fig 8 Ideal temperature and NH, oonoentratlon gradients
- 706
C
- 50
dependently from one another.
The kinetic data and methods
described above were apphed to
forecast the output and the best
operatmg conditions of this re-
actor, by calculatmg the optimum
nntial synthesis temperature and
the optimum degree of cooling
The same catalyst activity and
initial gas composition were as-
sumed as 111 he calculation of the
ideal gradients.
152
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Vol I
No
4-l Q. 62
D.
ANNABLE
Apphcatlon of the Temkm kin&o equation to emmome synthwa m large-scale reaotore
The catalyst bed was considered in small seetfons, the commencement of the reaction, and the cooling
and the kmetic equation was used to give, for each of one section of catalyst cannot be adJusted independ-
sectlon, the maximum possrble reaction which was
ently from another
These limltatlons stall, however,
consistent wrth a heat balance between the heat permrt of a fair correspondence between the practical
Vof ata d tr aversed/hfl a/gas rai e -
I
I
and ideal condltlons over the last 80%
of the catalyst bed (see Frg 9). The
divergence occurs where the optimum
temperatures are higher than 550’ C so
that operation at the lower temper-
atures has the compensation of pre-
serving the life of the catalyst This
feature, together wrth Frg 9 demonstrate
that m future developments of the de-
sign of reactor, the arm should be to
improve still further the correspondence
between practical and ideal condrtrons
m the region of the peak temperature
and subsequently
mar
I I
I I
002 00.5 0 10 045 m 021
MO/ i acf /on of ti n,
Fig 9 Comperlson of practlcel and ideal condltlons.
of reaction, the change in heat content of the re-
action gas, and the heat transferred to the coohng
medium.
The best operating conditions, calculated by the
above method, gave an output of ammonra from the
reactor, equivalent to an exrt mol fraction of 0 21, or
a conversron .
(exit mol fraction-inlet mol fractron) X 100, of
19 4% (see Frg 9)
Thus compared with a maximum ammonra con-
versron of 22 0%) calculated for the Ideal operatmg
conditrons, and a figure of 19 0% which was the maxi-
mum conversion actually achieved m the running of
the plant reactor
The agreement between the calculated and achrev-
ed practical condrtions 1s good, considering the large
coeffroient of variation (30%) in the original k, values,
from which the k, function was determmed The actual
catalyst temperature gradient was quite close to that
calculated, as was the amount of heat transfer from
the bed.
The best practmal condltrons also represent quite
a reasonable approach to the ideal The maxrmum
further improvement in the design and operation of
the catalyst bed would only mcrease the output by
less than 14%) although wrth the present arrangement,
the rate of heat removal is least instead of greatest at
AUKNOWLEtiUEMENT
The author wuthes to thank the staff of
Ammonza Works for provrdmg most of
the experimental data, and the staff of Technical
Department ad Research Department for helpful advme
NOTATION
a = mol fraction of H, m the reaction gas,
correspondmg to zero NH, content
A = kg mols/hr NH,
b =
constant, such that a (1
-bz) 1s
the mol
frctctlon of H, m the reactlon gas corree-
pondmg to a mol fraction z of NH,
b, =
frequency factor m the Arrhenms’ equa-
tion for
k,,
the reectlon velocity constant
for ammoma decomposltlon
E
deo = apparent activation energy for ammomla
decomposltlon
E
8Yn
=
apparent activation energy for ctmmoma
synthesis
k l = reaction velocity constant for ammoma
synthesis
L
k, =
reaction velocity constant for ammonw
decomposltlon
Kp = eqmhbnum constant for ammoma eynthesls
N = number of kilo mols of ammoms
P =
total preseure atm
PNK,, PN,, PE, = p d pressuresm atm of NEE,, Np, and
H, respeotlvely
& = heat of reactron, c&/gm mol N, reactmg
R = gae
constant cals/deg., gm mol
153
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