Chapter 5 Performance of Catalytic Processes in the Formation and Propagation of an Heat Wave

217

Chapter 5

PERFORMANCE OF CATALYTIC PROCESSES n~ THE FORMATION AND PROPAGATION OF AN HEAT WAVE

5.1

DESCRIPTION OF VARIOUS TECHNOLOGICAL SCHEMES

Chapter 3 considered in detail the major properties of the heat front inside a fixed catalyst bed. It was shown, in particular, that the time of formation of the heat wave is largely dependent on the initial conditions. The term "heat wave" will now be applied to the non-steady-state temperature field. Let us now describe several technological schemes enabling non-steady-state regimes with an heat wave phenomenon. Scheme 1. I denote this scheme "the rocker" (refs. 1, 2) (see Fig. 5.1). It was discussed earlier in Chapter 4. The periodic regimes via this scheme are attained owing to a cyclic reversal of the reaction mixture filtration through the catalyst bed. The direction of filtration is indicated in fig. 5.1 by solid arrowheads. Valves 1 are opened while valves 2 are closed. The incoming mixture with a low inlet temperature is warmed inside the catalyst bed to a temperature sufficient for the reaction to start and as the result an heat wave a is propagated along the bed. After some time equalling the semi-cycle (t c/2), heat wave a will occupy position a2. At the moment of time corresponding to t c/2, valves 1 and 2 are quickly and simultaneously switched to the opposite direction and so the direction of the reaction mixture filtration will be changed thereby. Hence, the reaction zone will move in the opposite direction. In addition, there is a zone in the catalyst body in front of the heat wave moving in the direction of filtration and which is cooled to the temperature of the initial mixture. In time t c/2, front a2 will occupy position a1 and then the whole cycle is repeated, providing continuous output of the converted reaction mixture from the catalyst bed. The temperature at the bed outlet increases in the course of the semi-cycle from Tin to Tout.

218

2

L

- ....t 2

Fig. 5.1. Technological scheme to perform a process with a periodic reversal of the inlet and outlet of the reaction mixture (lithe rocker tl ) . 1, 2 = the valves; A = catalyst bed; a1, a2 = heat waves in the bed.

Scheme 2. The phenomenon of reaction mixture overshoot past the catalyst bed due to a slow action or loose fitting of the valves is the shortcoming of Scheme 1. This may reduce the extent of conversion at the reactor outlet averaged over the cycle. This shortcoming can be avoided by using an additional catalyst bed, A2, placed behind the main bed A1 (Fig. 5.2) so that the initial substance which escaped conversion in bed A1 can also be transformed. This is how Scheme 2 works. Cool reaction mixture is introduced onto the preliminarily warmed catalyst bed, (A1), where, as a result, a moving heat wave is created. As it propagates in the direction of filtration, the heat from bed A1 will be siphoned away to bed A2. Thus, in time, a portion of bed A2 is warmed (wave c1, Fig. 5.2). The wave in bed A1 occupies position a1. Meantime, the direction of the reaction mixture filtration in bed A1 is reversed. During the reversal, valves and 2 stay open for a while and the initial reaction mixture is fed to the preliminarily warmed bed 2, avoiding bed A1. Within

219

2

-

a)

;';'-

6)

:::: " -A2

...... .... '.0. ", ; :.~.

I ~

~

l

t . : . : ',.:.: al -

. ' ..

.. : .... = :

"

~

':;. '.'

;,

;,

.::..::

52

c)

Fig. 5.2. Technological scheme to perform a non-steady-state process in two catalyst beds, A1 and A2. The direction of the reaction mixture filtration is periodically varied in bed Al. 1 - 4 = valves; a1, a2, b1, b2 = heat waves; a, b, c = positions of the heat waves at various moment of time.

this time, wave c1 will change its position to c2 (bed A2, Fig. 5.2c). Once the reversal is completed, almost all the reacting mixture is introduced into bed A1. Heat front al will propagate in the direction of filtration until it reaches position a2 (Fig. 5.2c). Thus bed A2 is heated. The gas flow is then reversed and the reaction mixture is converted in bed A2 and the cycle is repeated. Note that the second catalyst bed, A2, operates under conditions of periodically varied inlet temperature, concentration and load. Scheme 3. This scheme is denoted "the torus" (ref. 3) (see Fig. 5.3). The reaction mixture is fed to the contact zone in one direction. The bed of catalyst is devided into two identical portions, A1 and A2, and the reaction heat wave periodically migrates from position a1 to a2 and back. A displacement of the wave is performed through the use of switches (valves) 1-6

220

at

a2

At

Ai

Fig. 5.3. Technological scheme to perform a non-steady-state process with switch of the reaction mixture inlet into one of the two identical parts of the catalyst bed. 1-6 = valves; A1, A2 = bed of catalyst; a1, a2 = heat waves.

functioning in turn. The converted mixture is removed from the catalyst bed in the direction indicated by the arrowheads. For example, the initial low-temperature reaction mixture is introduced onto the part of the catalyst bed, preliminarily heated to an high temperature. Valves 1, 3, 5 are opened while valves 2, 4, 6 are closed. The heat wave begins to creep from position a1 to position a2. After a semi-cycle, the high-temperature reaction zone is transported to bed A1. At this instant valves 1 and 3 simultaneously close while valve 2 is opened and the initial reaction mixture at low temperature is fed into the portion of bed, A2. Once valves 1 and 3 are closed and valve 2 is open, valves 4, 5 and 6 commence operation (valves 4 and 6 are open, valve 5 is closed). During this time

221

-

--

a)

b)

::

.

.:: . :.~: : ........ . " ""::: :.:. ,I.'.:

-

a2.

.

A.z

-

Fig. 5.4. Technological scheme of a reactor operated at variable temperature of the reaction mixture prior to the main bed of catalyst, A2. A1 is the catalyst bed creating a variable inlet temperature prior to bed A2. a1, a2, b1, b2 = heat waves in the beds; 1, 2, 3 = valves. a) and b) show direction of mixture feeding in the first and the second semi-cycle.

the converting mixture from A2 is transported to A1 and then out off the bed (section-lined). Upon repeated switching of valves 1-6, a continuous motion of the heat wave is obtained according to the pattern: a1 - a2 - a1 - a2, etc., in one direction. The inlets and the outlets of the reaction mixture are interchanged. Migration of the heat wave in accordance with this scheme gives the impression of circulation through a torus. Scheme 4. An appropriate name for this scheme seems to be "the match" (Fig. 5.4) (ref. 4). The process is performed in a catalyst bed divided into two unequal parts, A1 and A2. One part of the bed (A1) is used for periodic heating of the other (A2). For example, an initial reaction mixture at low temperature is fed into the catalyst bed, A1 and A2 preliminarily heated to an high temperature through valve 3. The direction of the reaction mixture filtration is indicated by the arrowheads (Fig. 5.4a).In every portion of the bed (inA1 and inA2) one heat wave is created

222

(a1 and b1) which propagates in the direction of the mixture filtration. Valve 1 is closed, valve 3 is open and valve 2 is partly open controlling the velocity of filtration. Consequently, valve 2 controls the rate of propagation of the heat wave in bed A1. In a while, the waves will occupy positions a2 and b2 (Fig. 5.4b) and then valve 1 is opened allowing the reaction mixture to pass through bed A1 and then bed A2 in the direction indicated by the arrowheads. Some time later, the heat wave b2 will occupy the position shown in Fig. 5.4a. At this moment, the reaction mixture is introduced into the area between beds A1 and A2 by switching of valves 1, 2, 3: valve 1 is closed, valve 3 is opened and valve 2 is partly open thus controlling the velocity of the mixture filtration and consequently the rate of wave b1 in bed A1. This causes formation of two waves, a1 and b1. The cycle is repeated. So, bed A1 serves for periodic heating of a part of bed A2 where conversion of the initial reaction mixture is later performed. Scheme 5. This is denoted lithe wings" (ref. 5). The bed of catalyst is divided into three portions (Fig. 5.5). The non-steady-state regimes are realized by introduction of a low-temperature reaction mixture through valves 1 and 2 in turn. The start of the reactor operation is as follows. The initial reaction mixture at low temperature is fed into the preliminarily heated catalyst bed through valve 2 while valve 1 is closed. In the middle section of bed A1 and in the periphery section A2, heat waves a1 and b1 emerge. These waves move in the direction of the reaction mixture filtration. The direction of the gas flows in the sections of the bed is indicated by the solid arrowheads (Fig. 5.5a). After some time (the time of the semi-cycle), wave a1 will reach position a2 and wave b1 position b2 (Fig. 5.5b). At this time, valve 1 is opened while valve 2 is closed. This brings about separation of the heat peak of a2 into two heat waves. One of them will propagate through the central part of bed A1, the second through the periphery of bed A3. The directions of propagation of the heat waves coincide with the directions of the mixture filtration in the beds and are indicated by arrowheads in Fig. 5.5b. After the time for a semi-cycle, heat wave a2 will occupy position a1 again (Fig. 5.5a) and the cycle is repeated. The central part of the bed operates

223

.... . ' .- .' . . .... =. ~'. :~ .... '. '

,

00,

•

•

'.:.

:J ;

Fig. 5.5. Technological scheme to perform a non-steady-state process in a reactor with a catalyst bed in three pieces. (a) introduction of the reaction mixture through valve 2; (b) through valve 1. A1, A2, A3 = .beds of the catalyst; a1, b1, c 1, a 2, b2 = heat waves. in the regime of variant directions of the reaction mixture filtration and the heat abstracted in this area is used to warm beds A2 and A3 in turn. The peripheral sections of the bed periodically operate in the regime of warming or formation and displacement of the heat wave. After several switches the periodically reiterating temperature and concentration fields are established in all sections of the bed. Let us now consider various technological schemes which can realize a non-steady-state process in the regime of a forming and moving heat front (heat wave). Further, the results of numerical analysis of the behaviour of a three-bed technological scheme and the results of experiments will be examined in more detail.

224

5.2

INVESTIGATION OF THE THREE-BED TECHNOLOGICAL SCHEME "THE WINGS"

5.2.1 A mathematical model The mathematical simulation of this technological scheme was completed on the basis of numerical analysis of the following description

dT cx,(T-T)=C arr: j3 (xc
=

(5.1)

dx

d7:

x=o;

rr:=0:

(5.2) rr;=rc

c

where

e

'[;=- ;

U

J.dTc =D drc

_ A e;

J.-

C U2

P

7:

C

L

=-

LU

~ is the conventional time of contact; A ; is the effective e longitudinal heat conductivity of the catalyst bed frame; Cp ' Cc are the specific heat capacities of the gas and the catalyst pellet, respectively; u is the mixture filtration velocity; ~o, Po are the coefficients of external heat and mass exchange, respectively; Ssp is the specific external surface area of the catalyst pellet; 1, L are the current coordinate and the length of the catalyst bed, respectively; T, Tc are the temperatures

225

of the gas and the catalyst, respectively; x, x c are the extents of conversion in the gas phase and on the catalyst pellet, respectively; A Tad is the adiabatic mixture heating; Tin is the reactor inlet temperature. The expression for W is as follows

The computation was done with the following values of the parameters: r = 400; ~ =fl = 35 s-1; K(Tb) = 10 s-1; Tb = 400°C; J. = 5 ·10- 3s. An example of the calculated temperature fields in the established steady-state cyclic regime is shown in Fig. 5.6. The operational conditions of the central and peripheral sections are considerably different in that the high-temperature regimes in bed I are provided by a partial "heat lock" while in beds II' and II" they are due to a periodic heating of the inlet section to sufficiently high temperatures. First, the question of the range of adiabatic heating which would allow steady-state high-temperature regimes in all sections of the bed was to be solved. Numerical results permitting evaluation of this range are shown in Fig. 5.7. With an increase in the adiabatic heating, the extent of conversion in the middle section of the bed is almost unchanged (curve 1), but it is noticeably increased in the peripheral sections II' and II" (curve 3). This is explained by the increase in the high-potency heat accumulation in beds II' and II" periodically given off from the centre. With adiabatic heating of 75-90 oC, the peripheral sections allow realization of the high-temperature periodic regimes. One can attain a reduction in the time required for the heat wave formation in the peripheral portions of the bed displacing the maximum amount of heat from the central part. At the same time this allows a decrease in the volume of the catalyst. However, the danger that the process may be extinguished in the central part of the catalyst bed is quite real under the circumstances. The influence of the semi-cycle time on the average conversion extent is shown in Fig. 5.8. At small times of the semi-cycles, the temperature at the central bed outlet will

226

T(OC) '100 300 200

a)

faa

T(oc) 'faa

300 200

B)

100

Fig. 5.6.Reached temperature profiles along the catalyst beds at various moments of time, t in the non-steady-state process. (a) the f~rst semi-cy?lej ~b) the seco~d semi-cycle. t = .3 min (1), 10 nun (2), 16 man ~3). LlT ad = 90 C, u = 0.4 mis, L =1.1 m, 1 L2=1.3 m.I=middle part of the bed A1; II' and II" = side beds A2 and A.3 (see Fig. 5.5).

always remain low enough that a low-temperature regime is established in the peripheral beds after a few reversals. Only the central part of the catalyst body is effecient. The extent of conversion at the reactor outlet averaged over the cycle in this situation is close to 50%. At 28 min ~ t c ~ 42 min, an high-temperature periodic regime in the peripheral sections is possible. If the semi-cycle exceeds 42 min, the process in the central part of the bed ceases and, consequently, a temperature equalling that of the inlet temperature is established in the entire reactor. Thus, high-temperature regimes are realized all over the bed with values of parameter t c between 28 and 42 min. The average conVersion extent is slightly dependent on the time of the semi-cycle.

227

80

60

20

o

so

Fig. 5.7. Dependence of the average (over the time) conversion extent, x, on the value of the adiabatic heating of the mixture, ~ T d' 1 = x at the outlet of bed 1; 2 = averaged at the outlet of a the apparatus; 3 = at the outlet of bed II' (II"). E = 32700 J/mol.

The reaction mixture filtration velocity produces a noticeable effect on the average extent of conversion (at fixed contact time, ~c). An increase in the filtration velocity causes an increase in the heat and mass exchange between the surface of the catalyst pellets and the flow of gas. This, in turn, brings about an increase in the maximum temperature in the heat wave and the heat capacity of the bed is also increased. As a result, the amount of the high-potency heat transported from the centre of the bed to its periphery is also increased. The extent of conversion in remote sections of the bed increases as does the average extent of conversion in the apparatus. The plot in Fig. 5.9 shows that an increase in the filtration velocity from 0.2 m/s to 0.7 m/s (total time of contact in the reactor is 3.9 s) leads to an increase in the conversion extent from 75% to 97%. At ~ Tad = 90°C, the maximum temperature is elevated from 340°C to 440°C.

228

Fig. 5.8. Extents of conversion averaged over the c¥cle at the outlet from the central part of the catalyst bed (1), from the contact apparatus as a whole (2) and at the outlet of beds II' and II" (3) as a function of the cycle duration in the three-bed soheme "the wings" operating in the non-steady-state regime. ~ Tad = SooC; E = 32700 J/mol.

x(%)

=

fOO

90

80 70

0.2.

0.3

0."

0.5

0.6

0.7

0.8

u. (m/$)

Fig. 5..9. Reached extents of conversion averaged OVer a cycle at the outlet of the apparatus operating according to the scheme "the wings" as a function of the filtration velocity, u. (1) 6 Tad = 150°C, '7:'c = 2.4 s; (2) 6 Tad = 120°C, '7:'c = 3..5 s; (,3) 6 Tad = 90°C, '"Cc= 3.9 s ,

229

x ("!.) fOO

90

80

70

20

5'0

70

100

120

Fig. 5.10. Reached extents of conversion averaged over a cycle at the outlet from the central part of the bed (1), at the outlet of the apparatus (2) and at the outlet from the side bed II' (II" ) (3) as a function of the initial temperature of the mixture at the apparatus inlet.

V(hen performing heterogeneous catalytic reactions under non-steady-state conditions according to periodic variation of the direction of the reaction mixture filtration, the inlet temperature as a rule does not seriously influence the conversion extent at the outlet (curve 1, Fig. 5.10). The peripheral sections of the bed operate in the regime of periodic variation of the inlet temperature and conversion extent. The time required for formation of a heat wave in these sections is determined both by the initial heat reserve in the bed (the heat transported from the centre and by the temperature of the reaction mixture applied to the catalyst. The larger the heat storage and the higher the inlet temperature, the quicker is the heat wave formation and the higher is the extent of conversion averaged over the cycle in the peripheral sectors of the bed. The calculations illustrated in Fig. 5.10 show that an increase in the inlet temperature from 50°C to 100°C leads to an increase in the peripheral conversion extent from 78% to 95% (curve 3) and as a result, the "apparatus" extent of conversion as a whole increases from 86% to 97% (curve 2).

230

A theoretical analysis revealed the following peculiarities of the non-steady-state regimes carried out according to the three-bed scheme: (1) Organization of an high-temperature periodic regime is possible in all parts of the catalyst bed with adiab'atic heatings over 70-90 oC. These regimes provide an high average conversion extent of the reaction mixture at the apparatus outlet. (2) The temperature at the apparatus outlet is slightly altered by a temporary shift (by the value of the semi-cycle) between the temperature profiles in beds II' and II" • At the same time, when the temperature at the outlet of the bed II almost equals that of the inlet, it reaches its maximum at the outlet of bed II" •

5.2.2

Experimental research

The research was performed on the reaction of butene oxidation on copper chromite/AL20). Some of the experiments connected with determination of the operational range of the adiabatic heating were performed on a propane-butene mixture. The apparatus is shown in Fig. 5.11. It consists of two tube-shaped reactors 0.175 mm in diameter and 2.8 m high placed vertically. The tickness of the catalyst beds in both reactors is 2-2.4 m. The catalyst pellets are cylindrically shaped: 4-6 mm long. Twelve quick response thermocouples are placed along each catalyst bed. The reaction mixture temperature is recorded at the outlet of the first bed and at the inlet of the second. The out-going air is measured by a rotameter. Butene is injected through a flow-meter then mixed with air. An heater is used for initial warming of the catalyst bed in the reactor P1 and a chromatograph is used for the analysis of the butene content in the mixture. A cyclic regime of operation can be realized by means of opening and closing valves B), B4, B7. Regime A: B) is open, B4 and B7 are closed. Regime B: B) is closed while B4 and B7 are open.

231

7

B

Butene air from the

neturor-tc

8J

Fig. 5.11. Pilot apparatus for investigation of the non-steady-state process carried out according to the scheme "the wings". B1, B), B4, B7 = valves; P1, P2 = reactors; 1, 4 = temperature recorders; 2, 3, 5 = temperature indication devices; 6 = heater; 7,8 = rotameters.

The pilot apparatus imitated operation in the central part of the bed (reactor P1) and in one of the peripheral parts (reactor P2). The temperature and concentration profiles in the peripheral sectors of the bed (II' and II ff ) are displaced in relation to one another by the value of the semi-cycle 0.5 t c• So, to learn the function of the scheme as a whole, it is enough to investigate the periodic regimes in the central part of the bed and in one of the peripheral sections. The cyclic regime with periodically reiterating temperature profiles is steady after 5-10 switches. The time for one experiment was 20-30 h. Fig. 5.12 contains the temperature profiles along the axis of the catalyst bed at different times in the periodic regime established under the following conditions: u = 0.4 mis, ~c = 5 s, t c / 2 = 75 min, Cin = 0.2%. The variation of the temperature and conversion extent vs. time for different reactor areas is schown in Fig. 5.13.

232

noc) 600 400

200

a

Fig. 5.12. Temperature profiles obtained in the experiment with a non-steady-state process in "the wingstf regime along the catalyst body length, ; ~ Tad = 205°C, t: 1-5 min, 2-30 min, 3-70 min.

r(oc) 500

1(00

500

200

too

10

20

30

I{O

50

60

o.stc (min)

Fig. 5. 13. Experimental data on temperature variations at the outlet from the central part of the catalyst bed (1) and at the inlet to the periphery (2) during the semi-cycle of a non-steady-state process in "the wingsll regime. ~ Tad = 205°0.

233

5.3

COMPARISON OF TECHNOLOGICAL SCHEbffiS THE CYCLIC NON-STEADY-STATE PROCESS

REALIZn~G

Let us single out a number o£ general characteristics inherent to all discussed schemes. (1) The possibility to convert inlet mixtures at low temperatures at which the reaction cannot usually be carried out. This allows one to avoid heating o£ huge volumes of gas and thus to save considerable amounts of energy conventionally used for preliminary heating of the mixture to the reaction temperature. (2) The catalyst is used not only for acceleration of the reaction but also as the heat regenerator. (3) Short-time oscillations of the flow and concentration of the converting substance do not cause operational deviations because of the large heat capacity of the bed. Let us point out the major parameters suitable for comparison: (a) characteristics o£ the valves in respect of speed of responce and leak-proofness; (b) temperature variation vs. time at the outlet of the contact apparatus; (c) minimum adiabatic heatings of the processed mixture allowing for an efficient operation. The comparison is

shown in Table 5.1.

Scheme 1. This allows for processing of the mixture with minimum adiabatic heating. The calculation and experiment showed that this scheme is good for processing of mixtures with adiabatic heating between 10 and 15°C. To process mixtures with a low adiabatic heating, less catalyst is reqUired owing to the packing of the bed's faces with an inert material. The features complicating industrial application of this scheme are the necessity to use quick response leak-proof valves, sharp temperature variations in pipes and valves during the the reversals of the filtration direction. Scheme 2. One can use conventional locking valves to switch the flow of the gas. However, this results in an increase in the adiabatic heating of the mixtures suitable for processing

234

according to this scheme. Variable temperature fields in pipes and valves at the moment of change of the filtration direction are not effected. An increase in the catalyst amount leads to an increase in the hydraulic resistance of the reactor unit. Scheme 3. The advantage of this scheme is the possibility to use conventional locking accessories. In addition, considerable temperature gradients in the areas where valves are placed (except valves 3 and 4) can be avoided. Another advantage is the fact that both parts of the bed function under conditions of constant direction of the reaction mixture filtration. However, complicated piping and application of six (instead of four) valves increases the hydraulic resistance and heat losses in the reactor unit. Scheme 4. This allows for reduction of the number of valves to three and operation at constant inlet temperature. However, either the inlet temperature elevation or operation with mixtures requiring a larger adiabatic heating is necessary for high conversion extent. Scheme 5. This represents a logical continuation of the preceding scheme. The number of valves is reduced to two. The outlet temperature remains practically constant during the semicycle. Still, an efficient operation (as compared to scheme 1) is possible only with a considerable heating of the processed mixture and with larger contact times. It is of note that Schemes 1 and 3 permit realization of a decreasing temperature profile along the catalyst bed (with increasing conversion extent). This meets the requirement of the theoretical optimum regime for reversible reactions and allows one to obtain an additional rise in the conversion extent in the region of decreasing temperature profile. Except for areas with decreasing temperature along the bed (on the faces of bed A2 in Schemes 2 and 4 and of beds A2 and A3 in Scheme 5) there will exist sections with high temperatures. This complicates the performance of the reversible exothermic reactions carried out according to Schemes 1, 4 and 5. That is why the comparison of the technological schemes was done for the case of irreversible exothermic reactions.

S

Lf

j

2.

1

Jf

W

~

~

~

00

Scheme

J

1!.

2

2-

1

A2,A'j-constant

At- uariaJCe

A 1- consiani

A2- varia8te

Both. 8eds

2

3

6

Lf

At- uariaste A2- constant Consiard: for

'-I

VariaJte

c0r1o-

Eorure ni ional

torure ntionat

Conarerctioruu;

Co rurerdionar

Guicli- response eeaff, -prOOf

Characteristics for comparison Bed Values lfumBer Operation J{um6er Requirem.etits of lions relaiiue oj parts jietration reaersat uatues

--

Constant temperature

uariatJee gradients Constant temperature smooth Change

gradients

VarialJCe

gradients

irariaste

gradients

VariaBee graaients irarcaste grad.i8Tbts Varia6te

Temperature Gate values irvlet lout let

Constant temperature smoothCIw.Ti11fl

ChoJLfle

smooin:

change

Smooth.

stee!? gradzents Smooth chan-(Je smooth change

(on the tome)

Sleep gradientstf.//(;, //7,e steep gradients Steep gradient

Gas pipes inlet jouttet

conditions

Table 5.1 Comparison of various technological schemes realizing an non-steady-state cyclic process in a fixed catalyst bed

1/

-so 160- 110

50

50 -80 v' - - - BA2 At

'-10-50

20 --

50 - 80

2.0 -3D

15"

---

cote. us.exp.

Minimum Use of mixture inert heaiinu(OC) pacl1iTLf

01

""co

236

The use of the heat abstracted in the reaction progress makes Schemes 1 and 3 utterly different. The same goes for Schemes 2, 4 and 5. In Schemes 1 and 3 the heat is "locked" in the catalyst bed, while in Schemes 2,4 and 5 the necessary condition is that a portion of the heat is expelled to warm other sections of the bed (section A2 or in the case of Scheme 5, sections A2 and A3). This leads to an increase in the adiabatic heating at which an efficient operation of technological Schemes 2, 4 and 5 is possible (in comparison with Schemes 1 and 3). A theoretical analysis of the quantitative comparison of various technological schemes was done on model 5.1-5.2 with irreversible reaction, A--- B, as the example. Two values for the activation energy were compared: 32700 J/mol and 50300 J/mol, and K(Tb) = 10 s-1 (T b = 400°C). The calculations took account of three values for the adiabatic heating: 90, 120 and 150°C which correspond, for example, to volume concentrations of 0.9, 1.2 and 1.5% of carbon oxide in the initial mixture. Tin = 50°C. A conversion extent x ~ 99% of the initial mixture was assigned to compare the technological schemes. This extent was provided by a proper selection of the operational conditions. The time between switches was chosen to be not less than 5 min. The minimum contact time was determined for every adiabatic heating to provide the assigned conversion extent averaged over the cycle, x ~ 0.99. In Schemes 1 and 3 at the minimum time of the semi-cycle, the contact time was successively reduced unitil the extent of conversion was equal to its prescribed value. Except for the determination of the minimum contact time, the investigation of the catalyst distribution between the sections was done for Schemes 2, 4 and 5. If with a variation of the catalyst distribution a decrease in the conversion extent was observed, the volume of the catalyst found was regarded as minimal. Two more degrees of freedom appear for Scheme 4: the distribution of the mixture between sections of the bed and the relationship between the semi-cycle times. It appeared that the variation by means of the gas flow distribution in this scheme did not cause any noticeable reduction of the contact time. The relationship of the semi-cycle times affected the stability of the high-temperature periodic regimes but its influence on the

237

conversion extent at the outlet of the contact apparatus was insignificant. The contact time for every scheme was calculated through the following formulae Scheme 1: reC = L1/u1; Scheme 2: rec = (L 1 + L2)/u1; Scheme 3: = 2L1/u1; Scheme 4: 1:[; = (L 1 + L2)/u1; Scheme 5: 1:c = (L 1 + 2L2)/(u1 + u 2), where L1 and L2 are the lengths of the catalyst beds; u 1 and u 2 are the filtration velocities of the mixtures in the catalyst beds. '6c

Fig. 5.14 shows computed dependences of the contact time upon the adiabatic heating. With a limitation the minimum time of the semi-cycle and an increase in the adiabatic heating of the mixture under conversion, the contact time required to attain the preset extents of conversion is reduced. The reduction of the contact time in Schemes 2, 4 and 5 occurs faster than in Schemes 1 and 3. With an increase in the adiabatic heating from 90 to 150°C the contact time is reduced 2.5 times (Schemes 2, 4, 3, 5), while in Scheme 1 it is reduced 1.5 times.

rc (S) 8

7 6 S t{

.3

Z

70

150

180

<1Ta d (oc)

Fig. 5.14. Dependence of the required contact time of the reaction mixture, rtc ' on the adiabatic heating Ll Tad in various Schemes 1-5 (see Table 5.1) realizing the non-steady-state cyclic regime. (x ~ 99%, E = 32700 J/mol).

238

An important technological feature is the maximum temperature in the bed. Oscillations of the maximum temperature in different schemes appeared to be insignificant. In schemes where the beds with varied direction of the mixture filtration are used, the temperature can reach its crest value (as in Scheme 1 or in the central part of the catalyst bed in Scheme 5). This can be explained by temperature overshoot at the moment of the change in filtration direction. In Scheme 3 where the heat wave does not change its shape in the process of its propagation along the bed, a dynamic overshoot is impossible. The maximum temperature in this case will be somewhat lower. The schemes were compared in relation to two values of the activation energy. An increase in the activation energy leads to an increase in the maximum temperature in the bed. In addition, with an increase in activation energy the contact time is prolonged, which is necessary to attain the preset extent of conversion. The greater part of the gain in the catalyst volume falls on peripheral parts A2 and A3 in Scheme 5, while in Schemes 2 and 4 it is in part A2. Deviation of the values for the average conversion extent relative to x ~ 99% did not exceed

0.3%. The comparison of various technological schemes allowing for performance of the catalytic processes under non-steady-state conditions permit one to single out several characteristic features. With a limitation on the minimum semi-cycle time and with an increase in the adiabatic heating of the reaction mixture, a certain similarity of all schemes is observed in respect of the contact time reqUired to attain the assigned value of the conversion extent. With an increase in the activation energy, as was stated earlier, the maximum temperature and the contact time are also increased. The latter is provided by an extended time of formation of the heat wave on a preliminarily warmed catalyst bed, which results in the scheme's characteristic convergency (in respect of the contact time at higher values of the adiabatic heating. Reduction of the minimum allowed time of the semi-cycle and of the reaction rate constant will produce a similar effect. The contact times in different schemes appear to become closer at higher values of the adiabatic heating.

239

Now we come to formulate the recommendations on how to use the above schemes. (I) Schemes 1 and J with adiabatic heating over 100°0 differ in respect of the contact time by as much as a factor of 1.3-1.4. So, to perform exothermic processes with values A Tad = 80-120°0, Scheme 3 is recommended. The possibility to use conventional accessories is the advantage of this scheme. (II) One may prefer Scheme 5 to Schemes 2 or 4 for mixtures with adiabatic heating over 100°0. It requires fewer valves and about the same catalyst volume as in Scheme 2 and 4. This scheme can be recommended for large amounts of exhaust gases over the catalyst with high activity and catalytic reactions with optimum temperature profiles close to those which were shown in Fig. 5.6. (III) Scheme 1 is the most efficient to process mixtures with adiabatic heating between 30 and 80°0 under non-steady-state conditions. It provides a minimum contact time and allows for processing of mixtures with a low content of combustibles. An inert backfill can be packed at the faces of the bed to reduce the contact time and to play the role of recuperative heat exchangers. Of course, the preference of this or that scheme should be accompanied by a detailed technical-economical analysis. 5.4

AIVIMONIA SYNTHESIS VIA "THE MATOH" SOHEME

In this part of the chapter the results of the mathematical simulation of ammonia synthesis in the non-steady-state regime and their comparison with the characteristics of the process carried out in the traditional and the steady-state regime will be described. Fig. 5.4 showed the converter consisting of two catalyst beds, the main bed, A2 with length, L1 and cross-section, F1 and the auxiliary bed A1 (L 2, F2). The operational cycle is formed by two unequal time intervals

t~ and t~. In the first part of the period, t~, the gas is introduced into the space between the beds (see Fig. 5.4a). A o lesser position of the gas, Q1' passes through the auxiliary bed while the larger portion, Q~, passes through the main one. During the second part of the period, t~, which is much smaller than the first, the gas flows according to the

240

scheme shown in Fig. 5.4b. Within this time the gas passes through the auxiliary bed A1. Mathematical description 5.1-5.2 was the basis of calculation. The rate of chemical transformation was determined by means of the Temkin-Pyzhov equation. Internal-diffusion resistance was taken into account for catalyst pellets of various size. The model of the observable rate of the synthesis was not changed under the circumstances, but the values of the observable activation energy and the preexponential suffered alteration. For example. on the catalyst pellet 5-10- 3 m in diameter at a pressure 3-10 7 Pa, the rate constant, K, at T 450°C was 0.26 s-1, while at T = 500°C it was 1.26 s-1. The following values of the parameters were used in comparison: pressure, P = 3.10 7 Pa; adiabatic heating at complete conversion, b. Tad = 1802°C; heat conductivity of the gas, .Ie = 1.9.10- 1 W/moK; dynamic viscosity of the gas, Z = 0.378 -10- 4 Pa-s; specific gas weight, p = 43 kg/m3 ; specific heat capacity of the gas, Cp = 1.34-10 5 J/m 3 - 3 ; diameter of the pellet, d = (5-12.5)-10-3 m; specific external surface area of the catalyst,

Ssp = 240-600 m; catalyst porosity, 8 = 0.5-0.6; specific heat capacity of the catalyst, Cc = 4.35-10 6 J/m 3· K; coefficient for rating volume velocity in terms of normal conditions, Q/Qo = 10-2•

The variable technological parameters of the calculation are: L1, L2,m is the length of the auxiliary and the main bed, respectively; F1, F2, m2 is the cross-sectional area of the auxiliary and the main bed, respectively; Q1' Q2 (m3/s) is the flow of gas in the auxiliary and in the main bed in the second part of the semi-cycle; t 1c' t 2, s is the duration of the first c o o and the second part of the cycle; 7/c = (F 1L1 + F2L2)/(Q1 + Q2) is the general conventional contact time; Zin is the mole fraction of ammonia in the initial mixture; Tin' K is the temperature of the gas fed into the reactor. The ammonia concentration at the outlet of the reactor averaged over the cycle can be calculated through the expression

241

-

where Z1 2 is the average ammonia concentration at the outlet of , the main bed in the first part of the period; Z2,1 is the average ammonia concentration at the outlet of the auxiliary bed in the second part of the period; Z2 , 2 is the average ammonia concentration at the outlet of the second bed. Now let us consider a typical calculation at a pressure, P = 3.10 7 Pa, initial mixture composition, Zin = 2% of ammonia and i = 10% of the inert mass. The technological parameters are: 2; L1 = 0.2 m; L2 = 0.8 m; F1 = F2 = 1 m Q~ = 2.67 m3/s; Q~ = 0.66 m3/s; d 1 = d 2 = 5·10 m. The temparature of the gas applied to the reactor is 185°C. The total time of the cycle, t c = 300s. The duration of the first part of the cycle is t~ = 240 s, while of the second part, t 2c = 60 s.

Initially, both catalyst beds were heated to T = 500°C (curve 1 in Fig. 5.15a and b). At time t = 0 the amount of the gas equalling Q~ +Q~ is fed into the auxiliary bed. After time t = 30 s (curve 2) an high-temperature reaction zone is created in this bed and the hot gas then goes to the main bed. At time t = 60 s (curve 3) a switch is performed. During the interval between 60 and 300 s, the heat wave in the auxiliary bed propagates to the beginning of the bed (curves 4-6, Fig. 5.15). As long as the amount of gas, QO, is considerably smaller than the sum of Q~ and Q~, the rate of propagation of the high-temperature zone in the opposite direction is much lower than that in the first part of the period.Simultaneously,the cool gas is fed into the main bed in amount Q~ and the inlet sections of this bed are gradually cooled (curves 4-6, Fig. 5.15). Curve 6 in Fig. 5.15a and b corresponds to the temperature profile at the final moment of the period, t = 300 s. After several periods a periodic regime is found to be established in the reactor with the corresponding temperature profiles shown in Fig. 5.15e, f, g and h. Thus, the regime established in the auxiliary bed is characterized by the propagation of an high-temperature wave in different (reversed) directions whereas a temperature variation at the inlet of the bed occurs in the main bed. By selecting an appropriate duration of the cycle in the main bed, one can attenuate the temperature oscillations as they approach the end of the bed (see Fig. 5.15f and h).

242

a)

8)

C)

7ft. 6oiJr----------.

"

fiOO

K"

500 300

d)

7fc,

r- - - - - - - - -

f

200

o

OJ 0.2

0.2 O.S 0.'1

elm)

as 0.6 0.7 0.$ 0.9'

e)

elm)

t(m)

0.2 0.3

o.«

O.!J 0.6 0.7 0.8 0.9

f

e(m)

h)

-,

600

0.1 0.2

0.' 0.2

f)

If'c,rr----

o

0

elm)

Tf'.~---_ _----.

500

0.2 0.' OJ! 0.5 0.6 0.7 0.8 0.9

,

tIm-)

o

0.1 0.2

elm)

0.2 0.' 0."1

0.' 0.6

0.7 0.8 0.9 f

e{nv)

Fig. 5.15. Temperature profiles in the auxiliary (a, b, c, f) and in the main bed (c, d, g, h) at the reactor actuation (a, b, c, d). ( 1) t = o· (2) t = 30 s; (3) t = 60 s; ( 4) t = 120 s; (5) t = 180 s; (6) t = 300 s and in the steady-state cyclic regime (e , f, g J h) [( 1) t = 0; (2) t = 30 s; (3) t = 60 s; (4) t = 120 s; ~5) t = 180 s; (6) t = 300 s},

The average ammonia concentration at the reactor outlet in the regime established is 17.5%. The maximum catalyst temperature in the main bed equals 566°C and in the auxiliary bed it can reach 601°C. Tables 5.2 and 5.3 contain the main calculational results for ammonia synthesis with various technological parameters. The calculations were done with account of two values for the conventional contact time, ~c = 0.3 s (Table 5.2) and ~c = 0.2 s (Table 5.3). The numerical experiments allowed for variations of the duration of the period, the relation bet,ween the period's parts, ~, and ~z' the temperature of the gas fed into the reactor (Tin)' In some instances the geometric characteristics

243

of the auxiliary bed (without changing the volume) or pellet size in the same bed were varied. Parameters which differ from the basic values are cited as "notes" in a separate column. As a result of the computation, the concentrations at the outlet from different beds averaged over the cycle were found for the first and the second parts of the period, which allowed estimation of the average ammonia concentration at the reactor outlet and the maximum temperatures in the catalyst. The data in Table 5.2 demonstrate that if other technological parameters are fixed, the average ammonia concentration at the reactor outlet has the maximum in dependence of the period duration and of the temperature of the gas, introduced into the reactor. With the values of the parameters listed at the head of Table 5.2, the optimum duration of the cycle is about 300 seconds and the optimum inlet temperature is 185°C. The maximum concentration at the reactor outlet is 17.5%. Special attention should be paid to the maximum temperature of the catalyst. In calculations 1-11 its value exceeds the temperature allowed by the conditions of the heat resistance for an industrial catalyst. Though such an high temperature occurs only in the auxiliary bed and, consequently, does not produce any effect on the catalyst operation in the main bed, it nevertheless seems expedient to reduce it. Earlier, in Chapter 3 it was shown that an increase in the effective heat conductivity and/or a decrease in the inter-phase convective heat exchange leads to a reduction of the maximum temperature of the creeping reaction front. To demonstrate this, calculations 12-15 were done where the cross-section of the auxiliary bed was varied. Variations 16-21 where the catalyst pellet size was changed were also performed with this idea in mind. The calculations showed that the second method was more efficient. Application of large pellets with diameter, d = 10-12.5°10-3 m in the auxiliary bed yields maximum temperatures, Tmax' in the range 540-545°0. Similar results were obtained for the contact time, ~c =0.2 s. In this case, application of pellets with diameter, d = 10- 2 m was quite enough. The data in Table 5.3 show that the optimum

=

1

m

2

125

150

150

165

175

175

175

2

3

4

5

6

7

8

Tin (oe)

=

50

~

1

N°

FI

P = .]. /0 7 Pa ,

;

=

72

48

60

60

72

60

72

72

~f (e )

rtf

=

228

252

240

240

228

240

228

228

1:2 (e )

-~

TTl,

3/s;

15.5

-

-

17 .5

15.5

15.5

15.6

15.3

15.8

15.6

17.7

17.8

17 .1

15.8

14.0

9.7

Z1.2 (%) Z2.1 (%)

m.

2 %; Q(0 = 2. 67

d 2 = 5' to

i = to % ; Z in,

fl

0

= 0.66

16.8

-

17.8

17.5

16.4

15.1

14.7

5.4

Z2.2 (%)

2

TTl,

:

16.7

-

17.4

17.2

16.4

15.3

14.7

7.9

Z (%)

3/ s

L(

Table 5.2 The results of numerical simulation of the ammonia synthesis under the forced non-steady-state conditions (~c = 0.3 s) = 7T(,;

592

175

603

601

593

603

587

T (oe) max 585

O. 8 L2

0.8 rru;

Notes

=

s

""......

60

54

195

175

185

185

185

175

185

185

185

195

195

11

12

13

14

15

16

17

18

19

20

21

60

54

66

60

60

60

60

60

60

60

185

10

78

175

9

240

216

264

240

216

240

240

240

240

240

240

240

222

18.5

18.3

18.5

18.3

18.9

17.7

17.8

18.2

18.2

17.3

18.1

18.2

17.7

18.0

17.8

17.8

17.7

17.9

18.0

17.4

17.2

17.6

17.1

15.5

15.5

16.1

17.7

17.9

17.5

17.9

18.0

17.7

16.2

16.5

16.8

15.5

17.6

17.8

17.0

17.9

17.9

17.7

17.9

18.1

17.7

16.7

16.9

17.0

16.1

17.4

17.5

17.0

541

546

546

544

544

541

558

565

576

566

602

601

590

= 0.067

mj F1

=3

m~

d 1 = 12.5-10-3 m

L1 = 0.1 mj F1 = 2 m2 L1 = 0.67 mj F1 = 3 m2 L1 = 0.05 mj F1 = 4 m2

L1

>l>01

""

246

duration of the cycle is 120 s shorter and the corresponding optimum temperature is 50°C higher than in the reactor with contact time, ~c = 0.3 s. Let us look at these data in the light of the results of optimization of the traditional four-bed reactor with a cool bypass between the beds as reported in ref. 6 and shown in Table 5.4. The ammonia concentration at the outlet of the steady-state four-bed apparatus is 1.5% higher than in the non-steady-state apparatus at an identical contact time, ~c = 0.2 s. Consequently, the catalyst productivity in the former apparatus is alittlehigherthanin the latter. This is no wonder because in the steady-state multi-bed reactor the temperature profile is well approximated to the optimum. However, the temperature of the reaction mixture fed into the first bed is 377°C. To warm the nitrogen-hydrogen mixture to this temperature one has to install a large heat exchanger which would normally occupy 30-40% of the volume of the high-pressure apparatus. At the same time, the initial temperature of the reaction mixture in the non-steady-state regime is 235°C at 7:'c = 0.2 s and 185°C at 'tc = 0.3 s. The main advantage of the non-steady-state technology is the reduction of the dimensions of the preliminary heat exchanger or its complete elimination in cases where some technological scheme involves introduction of the reaction mixture into the reactor at temperature 160-180 oC. Moreover, there is no need for the intermediate heat removal between the beds. All this indicates a decrease in reactor volume. The unoccupied reactor volume could be filled with an additional portion of catalyst, which can step up the productivity of the reactor per unit volume. The heat extracted in the course of the reaction can be used for production of high-pressure steam (P = 1-1.5-10 7 Pa) which also improves the process' heat power characteristics. Performance of processes according to non-steady-state technology requires application of a reliable automatic system to switch the mixture flow. In addition-measures schould be taken to prevent overheating of the catalyst in the auxiliary bed.

42

36

36

36

33

36

39

33

205

215

225

235

235

235

245

3

4

5

6

7

8

9

36

7:, (n)

d., = d,p

185

2;

2

1 rri

185

==

1

F2

i=10%;

Tin(OC)

==

7pa;

N°

F,

P=J·'0

t : 10-

132

156

144

132

144

144

144

168

144

7:g (a)

==

lTU.

16.4

16.8

16.6

16.5

16.4

15.4

13.3

9.9

10.6

16.9

17.0

16.9

17.0

17.0

16.9

16.8

14.5

15.5

Z2 t1(%)

16.2

16.3

16.3

16.3

16.1

15.2

12.9

8.4

8.9

1

16.3

16.5

16.5

16.5

16.3

15.3

13.6

9.5

10.3

543

539

540

539

535

531

524

493

502

Notes

L == O. f 5 m ; L

Z (%) Tmax(OC)

fl 2o = O. 66 m 3 / s ;

Z2 t2(%)

a/==2.67771,3/s ;

Z2 t1(%)

2

lin=2%;

Table 5.3 The results of numerical simulation of the ammonia synthesis under forced non-steady-state conditions ( r:c = 0.2 s ) 2==O.5'-/rn;

-l

...""

419

423

424

8.5

11.5

13.5

3

4

388

2

Zin

= 2%;

Tin' i (oC)

= 10%;

2

7 Pa; i

1

010

Zin' i (%)

=3

N°

P

18.0

15.5

13.5

10.4

Zout' i (%)

= 40 oC;

506

497

511

541

Tout, i (oC)

bypass temperature, T~

Table 5.4 The result of steady-state optimization with four adiabatic catalyst beds and a cool bypass ( ~c = 0.2 s)

d 010-

1

0.85

0.7

0.53

Qio/Qo

=5 3 m

0.47

0.24

0.18

0.11

Li/L

...r;p ""

249

The method discussed above for ammonia synthesis allows for a productivity increase per reactor unit volume and a simplification of the apparatus construction, since heat exchangers are no longer necessary. The optimum shape of the catalyst pellets and perfection of the proposed scheme are thought to be routes to creation of an highly efficient industrial apparatus for ammonia synthesis under non-steady-state conditions.

REFERENCES

2

3

4

5

6

G.K. Boreskov, Yu.Sh. Matros, V.Yu. Volkov and A.A. Ivanov, Method for S02 Oxidation into S03' USSR Application Priority N°994400; Bull. Izobr.,5(1983) G.K. Boreskov, Yu.Sh. Matros and V.I. Lugovskoy, Method for Purification of Effluent Gases, USSR Application Priority N°849594; Bull. Izobr., 14(1982) G.K. Boreskov, V.S. Lakhmostov and Yu.Sh. Matros, Method for S03 Production, USSR Application Priority N°811551; Bull. Izobr., 46(1982) G.K. Boreskov, V.S. Lakhmostov and Yu.Sh. Matros, Method for S02 Oxidation into Sulphur Anhydride, USSR Application Priority N°1002233; Bull. Izobr., 9(1983) A.S. Noskov, V.S. Lakhmostov and Yu.Sh. Matros, in Unsteady Processes in Chemical Reactors, Institute of Catalysis, Novosibirsk, 1982, pp. 75-79 P. Valko and Yu.Sh. Matros, Dokl. Akad. Nauk SSSR, 248, 4(1979) 912-915