TVA Reactor Haber-Bosch Process (1965)

Chemical Engineering Science, 1965, Vol. 20, pp. 281-292. Pergamon Press Ltd., Oxford. Printed in Great Britain.

Steady-state simulation of an ammonia synthesis converter

R. F. BADDOUR, P. L. T. BRIAN, B. A. L~~E.-wJ, and 1. P. EYMERY

Department of Chemical Engineering, Massachusetts Institute of Technology

(Received in revised form 28 September 1964)

Abstract-A simple one-dimensional model of a T.V.A. ammonia synthesis converter approximates closely the ammonia production rate and the catalyst bed temperature profile of an industrial reactor. Using this simulation, the effects of space velocity, feed gas ammonia and inert contents, reactor heat conductance, and catalyst activity upon reactor stability, ammonia production rate, and catalyst bed temperature profile have been determined.

THE AMMONIA synthesis as it is performed in a Haber-Bosch reactor belongs to the category of autothermic processes. This term has been intro- duced by VAN HEERDEN [l] to describe an exothermic chemical reaction for which the temperature is maintained by the heat of reaction alone. In order to achieve this condition, gas flow and heat exchange are arranged to reduce the increase in temperature associated with the exothermic reaction and to suppress the need for an external source of heat once the reaction is started. The Tennessee Valley Authority reactor (T.V.A. reactor), which is a particular design of the Haber- Bosch reactor, has been described elsewhere [2,3,4,] and a simplified diagram of it is shown in Fig. 1. In the catalyst section the preheated gas flows up inside a large number of small tubes. There it absorbs part of the heat generated by the chemical reaction on the catalyst. At the top of the reactor (C) the synthesis gas, now brought to a sufficient temperature, reverses its direction and flows down the catalyst bed where the reaction occurs.

The operating characteristics of a T.V.A. reactor have been described by SLACK, ALLGOOD and MAW [4]. The process variables they reported are: temperature of the feed, pressure, space velocity (equivalent to the feed rate of gas), ammonia and inert content of the feed gas, and hydrogen to nitrogen ratio in the feed. They reported the existence of an optimum feed temperature, which maximizes the production of ammonia and the existence for each condition of operation of a maximum in the temperature profile, called

the hot spot or peak temperature. Both the optimum feed temperature and the hot spot temperature were found to vary with the process variables and the catalyst activity. SLACK, ALL- GOOD and MAUNE [4] reported that as the space velocity increases the stability of the reactor decreases. The reactor tends to blow off, causing the temperature and the ammonia mole fraction to decrease monotonically. As the catalyst ages

SHELL COOLING GASES F

CATALYST BED

SECTlON

HEAT

Es%FR

GASES

.c

CATALYST

-G

-D

-B

ENTRANCE n

BY PASS INLET

FIG. 1. Simplified diagram of a T.V.A. reactor.

281

R. F. BAJXXXJR, P. L. T. BRIAN, B. A. LOGEAIS and J. P. EYMERY

an increase in the average feed temperature is necessary to avoid instability and keep the ammonia production up.

To investigate the steady state behavior of such a reactor, VAN HEERDEN [l], ANNABLE [5], BEUTLER and ROBERTS [6], and KJAER [7] have derived mathematical models of Haber-Bosch type reactors. VAN HEERDEN, ANNABLE, BEUTLER and ROBERTS derived one-dimensional models allowing for temperature and composition variations in the longitudinal direction only. Even though their results approximated experimental results, none investigated the effect of operating and design variables on the production, stability and temperature profiles in the reactor. KJAERS model took into account the variations in temperature in both the longitudinal and radial directions. His mathematical model consisted of three partial differential equations which were solved by hand computation using a double step integration technique, The temperature and composition profiles in the reactor were computed for only one set of operating conditions. The agreement of the computed production rate and average bed temperatures with plant data was very good. However, the KJAER model could not explain the radial temperature gradient reported by SLACK, ALLGOOD and MAUNE. KJAER gave a qualitative explanation of this discrepancy based on the location of the various thermocouple wells with respect to the cooling tubes in the catalyst bed. The work already published on the T.V.A. reactor still leaves the following important areas to be investigated. The effect of operating and design variables on:

(1) the optimum feed temperature, (2) the stability of the reactor, (3) the temperature profiles in the reactor.

This information is necessary to determine the conditions of maximum production. The objective of this paper is to present the results of calculations using a computer simulation of a T.V.A. reactor. The operating variables investigated were : space velocity, ammonia and inert content of the feed, and catalyst activity. The design variable was the heat conductance per unit volume of reactor between the reacting gas and the gas in the cooling tube. The pressure was kept constant, and the hydrogen to nitrogen ratio was equal to 3.0.

Table 1. Parameters and their range of variation

Lower Upper limit Standard limit

Space Velocity, VO Ammonia mole fraction in

the feed, y* Inert mole fraction in

the feed, ant Catalyst activity, f Total heat conductance, US

9000 13,800 18,000

0.01 0.05 0.10

0.0 0.08 0.15 0.4 . f 30,000 :&IO &IOO

The range of parameters investigated appears in Table 1.

MATHEMATICAL MODEL

A one-dimensional model was used, neglecting the temperature and concentration gradients in the radial direction. The temperature of the gas flowing through the catalyst at each location was assumed equal to the temperature of the catalyst particles. With these assumptions the T.V.A. reactor can be lumped radially into two sections as shown in Fig. 2. The empty tube section repre- sents the gas inside the cooling tubes, and the catalyst section includes the catalyst particles and the gas flowing through them. The temperatures TT and I, vary longitudinally in both sections. The reaction rate expression used is that of TEM- KIN and PYZHEV [S] with constants obtained by

T TOP

CATALYST

SECTON T Tc TT Y l--L 1 I T INLET

EMPTY TUBE

sEcnm

FIG. 2. Lumped model of T.V.A. reactor

282


fitting [3] this expression to SmOROV'S experimental results[9] measured at the same pressure (300 atm) and over the same range of temperature and space velocities considered in this investigation. In this equation the ?eaction rate is a unique function of temperature and gas composition, neglecting mass transfer and pore diffusional resistances.

In this model, both heat and mass diffusion in the longitudinal direction have been neglected. It was also assumed that the heat capacity of the gas is independent of temperature and that the effect of pressure on enthalpy is negligible. The pressure drop along the reactor was neglected. The validity of the major assumptions will be discussed in a later section.

A material balance written around a differential slice of the catalyst section and enthalpy balances in the empty tube section and in the catalyst section completely characterize the steady state behavior of the T.V.A. reactor with the assumptions presented before. These three equations are presented in dimensionless form.

(a) Material balance

fA 1 -20,300 1 m = m exp , ~ . d~

X {[ (K~P)2'~(~ -- y)1.5(c~ _ y)

Y

:.l (1 + Y) t (a~ - y )15] 1 + y* J

(b)

(e)

(1)

Energy balance in the empty tube section

dTr / US \ /AC\ T.

Energy balance in the catalyst section

[1 (AC~(y - y*~] dT c + -- [Cpo] \ 1 + y / J

I US \ /AC\ T +

r ( -AHo) -- T~AC -L +

y*,,dy,

In equations (1), (2), and (3) the temperature is normalized with respect to the temperature at the top of the reactor where the gas reverses its direction to enter the catalyst section.

The boundary conditions associated with this mathematical model are specified at the top of the reactor by

Atg=O, To=l , T r= l , y=y* (4)

The numerical values of thermodynamic constants in the dimensionless groups are reported in Table 2.

Solution of the mathematical model

This system of ordinary differential equations was solved on an I.B.M. 704 digital computer using the Runge Kutta formulas. The details of the computation are in reference [3]. Increment sizes used in the computation were:

A~=0.05 for 0

R. F. BADDOUII, P. L. T. BRIAN, B. A. LOGEAIS and J. P. KYMERY

top REACTOR LENGTH, (ft ) bottom

FIG. 3. Typical temperature profiles.

coefficient which yielded a value of 57,300 Btu/(hr) (F) for US. The calculated ammonia production rate of 142 tons/day was 19 % higher than the plant value. This discrepancy is discussed later.

Table 3. Operating Conditioh

Parameter Actual

Converter Model

HB Mole fraction in feed 0.65 O-6375 Na Mole fraction in feed 0.219 O-2125 NHs Mole fraction in feed O-052 0.050 Inert Mole fraction in feed 0.079 O-08 Space velocity, (hr)-l 13,800 13,800 Pressure, atm 286 300 Catalyst volume, ft8 144 144

The temperature profiles are shown in Fig. 3. At the outlet of the converter the model temperature is 12C higher than the plant outlet temperature; the hot point for the model is 1 ft lower and the maximum temperature is 4C. higher than in the plant reactor. Figure 3 also indicates the computed temperature profile inside the tubes where the synthesis gases are heated from 228C to 421C. No experimental data are available for comparison with these temperatures.

RESULTS AND DISCUSSION

Before discussing the agreement between the computed and the experimental results, each of the major assumptions made about the model will be considered. As mentioned previously, ~AER [71 explained qualitatively the difference between the temperatures reported by the center thermocouple and by the outer thermocouple as due to the rela- tive positions of the thermocouple wells and the cooling tubes. As shown in Fig. 4, the center thermocouple well replaces a cooling tube, while each of the off-center wells is located in the middle

COOLING TUBES

0 THERMOCOUPLE WELL

OUTER THERMCCOlJP,_E

FIG. 4. Thermocouple arrangement.

284


of the equilateral triangle formed by 3 cooling tubes. The same hexagonal area (hatched area on Fig. 4) is cooled by two cooling tubes in the case of the center thermocouple and by three cooling tubes in the case of the off-center thermocouple. For this reason the measured center temperature prolYe should correspond approximately to a heat transfer area decreased by one third, i.e., to a value of US equal to 37,000.

In order to examine this explanation, the effect of heat conductance on the temperature profile was computed, and the results are shown in Fig. 5. It can be seen that a conductance of 55,000 gives a good fit with the profiles measured by the south and north thermocouples when the experimentally determined top temperature is used for each profile. On the other hand, a conductance of 37,000 is the value which gives a good fit with the center thermocouple experimental temperature profile. The results in Fig. 5 show that the difference in area available for heat transfer accounts quantita- tively for the higher readings of the center thermocouple as reported by SLACK, ALLGWD and MAUNE [4]. Thus the computations performed by KJAER appear to be reasonable, and they support the choice of a one-dimensional model.

The difference in temperature between the catalyst particle and the gas flowing past it has been estimated by KJAER [7] and EYMERY [2] for the synthesis of ammonia using the same type of catalyst. The maximum temperature difference

has been computed to be 2~3C at the top of the reactor where the rate of reaction is a maximum. This difference decreases as the gas proceeds down the reactor to a value of 0.6C. near the middle and 0.4C. at the outlet. These small temperature differences justify the assumption that the particle temperature is equal to the temperature of the gas with which it is in contact.

The effect of longitudinal diffusion of enthalpy in the T.V.A. reactor has been estimated by EYMERY [2]. A mathematical model taking into account the axial diffusion of enthalpy by Taylor diffusion has been derived and solved on a digital computer. The inclusion of the longitudinal dis- persion term altered the steady-state temperature profile by less than 0.6C. This effect is considered to be negligibly small.

In addition to the assumptions discussed above, the catalyst activity was assumed to be uniform and constant with time. When a catalyst activity factor of O-7 was used, the plant production of 120 tons/day could be obtained but with a temperature profile unlike any of those measured.

Finally, the converter was operated at a lower pressure than that used for the model, and the hydrogen-nitrogen ratio in the plant was not exactly 3. Because of both these factors, the model should give a higher production rate. Also, the data used in the rate expression were taken from Russian experiments made using a catalyst different from that in the T.V.A. reactor.

- MODEL ----- PLANT DATA

0 5 IO I5 top REACTOR L~~oTH, (ft 1 bottom

Fm, 5. Comparison of mode.1 with plant operation Y. = 13,800, y* = 0.05, y; = O-08, f = I.

285

225

2001 I I I I 300 400 500

TOP TEMPERATURE, (C)

FIG. 6. Relationship between inlet and top temperatures.

In view of these differences, agreement between actual and calculated production rates within 20 % corresponds to a reasonable fit. Furthermore, it is possible to explain the difference between measured and calculated profiles in the upper part of the converter in terms of a decrease in catalyst activity in that region. For the first 3ft of reactor length the experimental curves in Fig. 3 correspond to computed curves for a catalyst activity reduced by about 50%. For the next 3ft the temperature rise in the actual converter is faster than in the model, but this might be explained by the fact that the gas mixture entering this section is farther away from equilibrium because of the lower catalyst activity in the upper part of the bed.

Thus, while the proposed model is only an approximation to the actual reactor, it appears to give a fairly good prediction of the ammonia production rate and the catalyst bed temperature profile. The results obtained from this model concerning the effects of operating and design variables on production, stability and temperature profiles in a T.V.A. reactor are considered to be reliable.

R. F. BADDOUR, P. L. T. BRIAN, B. A. LOGEAIS and J. P. BYMERY

Existence of Several Steady States

For the operating conditions in Table 3, Fig. 6 presents the relationship between the top tempcra- ture (computed at location C in Fig. 1) and the inlet temperature (location G). Figure 6 shows that there is a minimum inlet temperature called blow-out feed temperature below which stable operation of the reactor is not possible. For each inlet temperature higher than the blow-out feed temperature there are two top temperatures, an example of which is shown by the upper dotted line in Fig. 6. Likewise there are two different temperature and composition profiles which satisfy the steady state equations and which correspond to the same value of the inlet temperature. VAN HIZERDEN [I] explained that the lower of the two top temperatures corresponds to an unstable point. Although the steady state equations are satisfied at this point, a small perturbation would result in either reactor blow-out or reactor heat-up and change-over to the stable operating point for that inlet temperature. Thus in Fig. 6 only the branch of the curve to the right of the minimum corresponds to stable operation of the reactor.

Efects of parameters on production

The effect of top temperature on ammonia production rate is shown in Fig. 7. The middle curve corresponds to the standard conditions of operation with a space velocity of 13,800. Figure 7 reveals the existence of an optimum top temperature equal to 425C for the standard conditions of operation. As space velocity is varied, the optimum top temperature changes as shown in Fig. 7. When the space velocity increases from 9,000 to 18,000, production rate increases as expected, but the production rate near the maximum becomes more and more sensitive to a change in the top temperature. A deviation from the optimum top temperature affects the production rate more strongly at higher space velocity.

An analogous result is found when the ammonia content of the feed gas decreases. The production rate of the T.V.A. reactor is quite sensitive to changes in ammonia mole fraction in the feed gas but much less sensitive to changes in the inert content of the feed gas. A decrease in catalyst

286


350 400 450

TOP TEhtPEFfATLRE, (=C)

FIG. 7. Effect of top temperature on production rate y* = O-05, g = 0.08, f= 1.0.

activity decreases the production rate and requires that the reactor be operated at higher temperatures. Furthermore, at low catalyst activity, the production rate is more sensitive to changes in top temperature. The heat conductance has been found to have a small effect on production. Although there is a value which maximizes the production (US = 60,000), the maximum is very flat.

Figure 8 presents the effects of the parameters on the maximum production rate. For each set of parameters the converter is operating at the optimum top temperature. Around the reference conditions the changes in operating variables reported in Table 4 result in a decrease in production rate by 5 tons/day.

Efects of parameters on stability

It was shown previously that for each set of parameters there is a minimum inlet temperature below which the reactor cannot be operated. On Fig. 9 the relationship between the top and the inlet temperatures is shown for three values of the

I 11 11 11 1 1 l0,000 15,000

, I, f I 81 8 I I

0 0.05 0.10

I$,, ,,,II,llllllll 0 0.05 0.10 0.15

I I 1 , t 0.5 1.0 1

I I I, 1 I I I I I I,

3QOoO 50,000 l30,ooo

0

Y'

Y;

f

US

FIG. 8. Effect of parameters on maximum production rate.

287

400 I I I I Table 5. Changes in parameters resulting in a

v. = SWCE VELOCITY +lOC change in the blow-ofl inlet temperature

50[ 300 350 450 500 550

TOP TEMPERATURE (C)

FIG. 9. Effect of space velocity on stability.

Table 4. Changes in operating variables resulting in a 5 tons/day decrease in production rate

Operating variable Reference Change value

R. F. BADDOUR, P. L. T. BRIAN, B. A. LOGEAIS and J. P. EYMERY

Operating variable Reference Change value

Space velocity, VO Ammonia mole fraction, y* Inert mole fraction, yc* Catalyst activity, f

13,800 +600 0.05 +oGN3 0.08 $0.024 1.0 -0.05

The stability of the reactor can also be expressed in terms of changes of the top temperature corresponding to the blow-off inlet temperature. Figure 11 shows the effects of these same parameters on the blow-off top temperature. It can be seen that while the effect of space velocity and ammonia mole fraction on the blow-off inlet temperature is relatively large, the corresponding effect on the blow-off top temperature is much smaller. On the other hand the catalyst activity a&&s the blow- off top temperature more strongly. The heat transfer coefficient per unit volume affects the blow- off inlet and top temperatures in opposite directions: an increase in heat transfer coefficient allows a lower blow-off inlet temperature but increases the blow-off top temperature.

Eflect of parameters on temperature profire

Space velocity, VO. Ammonia mole fraction, y* Inert mole fraction, yr Catalyst activity, f

13,800 -700 0.05 +0.01x 0.08 +0.02x 1.0 -10%

space velocity V,. The blow-off inlet temperature corresponds to the minimum of the curve, and this temperature can be seen to increase as the space velocity increases. Figure 10 presents the effects of the parameters upon the blow-off inlet temperature. Increasing the ammonia or the inert mole fraction in the feed increases the blow-off inlet temperature. Increasing the catalyst activity or the heat transfer conductance decreases the blow-off inlet temperature. The changes in operating variables reported in Table 5 result in a 10C increase in the blow-off inlet temperature around the reference condition.

Rather than study the effects of the various parameters for a fixed value of the inlet temperature, the catalyst bed temperature profile corresponding to each set of operating conditions has been computed for the inlet temperature which maximizes the ammonia production rate. These proties are presented in reference [3]; they will be described qualitatively here.

An increase in space velocity shifts the hot spot downward with only a small increase in the hot spot temperature. A larger increase in the outlet temperature results, and the average temperature of the bed increases. The amount of ammonia in the feed gas influences greatly the location and the magnitude of the hot spot. As the ammonia mole fraction in the feed increases, the profile becomes flatter, the hot spot shifting downstream and becoming cooler. The average temperature of the bed remains approximately constant. A variation in inert content of the feed gas has little effect

288


I_ f 100 - Y 01 I 1 1 1 1

10,000 15,000

YK P I

Y; 0.05 0.10 III! IIII ,!!I III)

0 0.05 0.10 0.15

f I I I I I { 05 1.0

US I, I I I I I I I I I 30.000 54000 00,000

FIG. 10. Effect of parameters on blow-off inlet temperature.

I- 0 0.05 0.10 0.15

I I I I I I I II 11 30,000 50,000 00,000

"0

Y' Y;

f

us

0

Y-

Y;

f

us

FIG. 11. Effect of parameters on blow-off top temperature.

289

R. F. BADDOUR, P. L. T. BRIAN, B. A. LOOEAIS and J. P. EYMERY

0 I I I I I II I II

l0,000 15,000 "0

YS 0

I I I I 1 I I I Y 0.05 0.10

Yi* CO

, I I I I I IS I I I I f I I1 11 0.05 0.10 0.15

y;

f. I f 0.5 I .o I I I I I I I I 11 1

us 30,000 50,000 80,000 us

FIG. 12. Effect of parameters on peak temperature.

bottom

I I, ! I I II,,, 10,000 15,000

IO I I I I 1 I

0.05 0.10

0 I, I I I I ,,,I I I I I I I I I \

0.05 0.10 0.15 I I I I I

0.5 1.0 I I I I I * I I I I I

30,000 50,000 80,OO

FIG. 13. Effect of parameters on hot spot location.

290

0

Y'

Yi*

f

Us


on the temperature profile; the hot spot does not move and its temperature varies little. A decrease in the activity of the catalyst results in an increase in the temperature at every location in the catalyst bed. The heat transfer coefficient per unit volume affects both the location and the magnitude of the hot spot, but the average bed temperature does not vary very much. High values of the heat transfer coefficient give higher hot spot temperatures located nearer the top of the reactor. The effects of the parameters on the magnitude and the location of the hot spot are presented graphically in Figs. 12 and 13.

CONCLUSIONS

A simple mathematical model of a T.V.A. ammonia synthesis reactor has been developed which approximates within 15 to 20% the temperature profiles and the ammonia production rates of an industrial reactor. With this model the effects of design and operating parameters upon reactor stability, ammonia production rate, and catalyst bed temperature profile have been studied.

It has been shown that an increase in space velocity increases ammonia production rate but decreases reactor stability and requires that the converter be operated at a higher temperature level. Any increase in ammonia or inert content of the feed gas was found to decrease both production rate and stability but not to affect the aver- average temperature of the bed. The use of a less active catalyst was shown to decrease both production rate and stability and to necessitate operation at a higher temperature level. The heat transfer coefficient per unit volume of catalyst was found to have a small effect on the production rate and the average bed temperature but a marked influence on stability, a high coefficient increasing stability and lowering the inlet temperature of the reactor. The optimum temperature profiles were found to be relatively insensitive to operating parameter variations. However, the use of a high coefficient

of heat transfer increased local overheating of the catalyst.

The reactor was shown to be sensitive to changes in the operating parameters. Since under most conditions the difference between the optimum feed temperature and the blow off feed temperature is very small (5C or less), the stability prob- lems associated with small perturbations in the feed condition should be investigated from a dynamic point of view. The results of such an investigation appear in an accompanying paper.

Acknowledgement-The machine computations were performed at the Massachusetts Institute of Technology Computation Center. H. Y. ALLGOOD supplied the operating data, for which the authors are appreciative.

NOMENCLATURE

(359) (1.75 x 1016) (P-0.5) (1.5 - Yl*,2)1.5(03 - Y;,)/(i + y*)2,5

(Y$, + 1*5y*)l(1*5 - Y * a) (YNa) + @5Y*)/(@5 - YN2) molal heat capacity of the feed gas, Btu/(lb mole) (F) (1 + Y*)l(1*5 - Y&P5 molal feed rate lb mole/hr catalyst activity factor equilibrium constant (atm)-1 length of reactor ft total pressure atm. total heat transfer area fP top temperature R catalyst temperature R empty tube section temperature, R base temperature for enthalpy datum = 537R normalized catalyst temperature TC P&p normalized empty tube section temperature T$/T&,, normalized base temperature heat transfer coefficient

T,*I%, Btu/(hr)(ftz)(F)

space velocity = (359)(F)/v reactor volume ammonia mole fraction

W-1 fts

NHa mole fraction in the feed gas Ha mole fraction in the feed gas N2 mole fraction in the feed gas inerts mole fraction in the feed distance from the top of the reactor, ft normalized distance = z/L decrease in heat capacity resulting from the formation of one mole of ammonia Btu/(lb mole)(oF) heat of formation of ammonia Btu/lb mole

291

R. F. BADDOUR, P. L. T. BRIAN, B. A. LOGEAIS and J. P. EYMERY

&iFERENCES

[l] VAN HEERDEN C., Zndustr. Engng. Chem., 45, 1242, 1953. [2] EYMERY J. P., Clrem. Engng. Sc.D. thesis, M.I.T., 1964. [3] LOOEAIS B., Chem. Engw. M.S. thesis, M.I.T., 1959. [4] SLACK A. V., ALLGOOD N. Y. and MAIJNE H. E., Chem. Engng. Progr., 49, 393, 1953. [5] ANNABLE D., Chem. Engng. Sci., 1, 145, 1952. [6] BEU~SR, J. A. and ROBWTS, J. B., Chem. Engng. Progr., 52,69, 1956. [7j KJAER J., Measurements and Calculations of Temperature and Conversion in Fixed Bed Catalytic Reactors, Jul.

Gjellerups Forlag, Copenhaeon, 1958. [8] TEMKIN M. I. and PYZHEV V., Phys. Chem. Acta USSR, 12, 327, 1940. [9] Smo~ov I. P. and Lxvsnrrs V. D., J. Phys. Chem., USSR, 21, 1177, 1947.

[lo] ALLGOOD H. Y., Private communication, Div. of Chemical Operation, Tennessee Valley Authority, Wilson Dam, Alabama.

RtiLEn se basant sur un modele uni-dimensionnel du r&acteur T.V.A. pour la synth&se de lammoniaque on a calcule leffet de la v&cite spatiale, de la composition de lalimentation, de la con- ductibilit6 thermique du lit et de lactivite du catalyseur sur la stabilitt du reacteur, la production et les profils de temperature.

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Documents

TVA Reactor Haber-Bosch Process (1965)