chemical engineering science volume 1 issue 4 1952 [doi 10.1016%2f0009-2509%2852%2987011-3] d....

8/18/2019 Chemical Engineering Science Volume 1 Issue 4 1952 [Doi 10.1016%2F0009-2509%2852%2987011-3] D. Annable …

http://slidepdf.com/reader/full/chemical-engineering-science-volume-1-issue-4-1952-doi-1010162f0009-250928522987011-3 1/10

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



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



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



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



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



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



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



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



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

chemical engineering science volume 1 issue 4 1952 [doi 10.1016%2f0009-2509%2852%2987011-3] d....

Documents