Fixed-Bed Reactors with Regenerative Cooling George R. Gavalas Chemical Engineering Laboratory, California Institute of Technology, Pasadena, Calif. 91109
A regeneratively cooled fixed-bed reactor system was studied theoretically. It consists of two sections which alternate roles as reactor and heat regenerator by periodic flow reversals. Calculations were performed for a single exothermic reaction using a forward cell model. The temperature profiles can be maintained within preassigned limits by a suitable choice of operating conditions and by diluting the catalyst with an inert solid. Because of the facility of heat removal and the favorable temperature profiles, the regenerative system can be used for strongly exothermic reactions such as partial hydrocarbon oxidations.
Exothermic catalytic reactions, such as the partial oxidation of ethylene, ljuteiie, o-xylene, aiid naphthalene, requirc the control of temperature within narrow limits. The lower temperature limit is imposed by the requirement of reahonable conversioii. whereas the higher limit ix dictated by the requireiiieiit- of selectivity aiid the prevention of catalyst deactivatioii. I T ~ u a l l ythe yield of an intermediate product, a c h a> ethylene oxide, must be maxiniized in the preseiice of consecutive and 1)arallel reaction>. leading to wast,eful total oxid:ition. The Iroblerii of determining the optimum temperature pofiles for such reactions has been solved theoretically (*iris, 1961). Such optimal profiles are difficult and expensive to implement, and industrial reactors employ the followiiig Imctical alternatives, singly or in combination. Oiie i i a heat exchanger-reactor huch as the amnionia coiiverter. . h o t h e r ii the dilution of the feed with an inert like iteani. .serviiig a i n heat siiik. Interhtage cooling or mixing with freih feed is also w e d . Yet another alternative is the fluidized bed. 111tliiz work we investigated the temperature regulation of aii exothermic reaction by using the catalyst bed itself as the cooling medium. This allows adiabatic operation hut obviouily requires thermal regeneration. h catalytic system with thermal regeneration involves a combination of two or more fixed beds with alternating roleh as reactors aiid heat regenerator,s. As the temperature in a reacting section reaches the higher limit, the flow is reversed and this section is brought back t o the lower temperature limit b y passing a cooler gas through it. The cooling gas can actually be one of the reactants -e.g., air-which is thus preheated and allows autothermal operation. In the prejent work we have chosen a geometrical configuration and carried out a numerical study of the effect of various parameters on the temperature profiles for the case of a single irreversible exothermic reaction. The emphasis has been on ascertaining the possibility of maintaining the temperature within an admissible range and st'ill obtaining reasonably high conversion. Future work will include the optimization of such systems by proper choice of configuration, heat capacity distribution, flow rates and temperatures of certain critical streams, and frequency of flow reversals. Optimization problems of similar mathematical structure have been treated (Ogunye aiid Ray, 1969) relative to fixed-bed reactors with catalyst' deactivation. .Isfar as we know, this is the first study of regenerative cooling for carrying out exothermic reactions. Regenerative
operation ha. been u\ed in the Iin>t t o coiiduct ciidothertiiic reaction.: requiriiig very high tenil)er:iture-. T h e reactioiis take place during the fir3t part of the cycle 1)y bringing the reactants in direct contact with hot refractory material. During the second l m t of the cycle. the i,efixc.tor>-riinterial is lireheated ivith combustioil gii*eb. Oiie huch 1)loce-h is the Kulf procesi (Bognrd and Loiiy, 1962) for the l)>-roly,&of hydrocarhow to ethylene and acetylene. . h o t h e r ib the Wiicoiibiii process for nitrogen fixation (Kirk aiid Othnirr, 1952). Reactor System
Figure 1 s h o w the reactor iystem unitlei coiisideratioii. -\ir is preheated in the regeiieratilig heetioii. mised with hydrocarbon, and introduced iii the reactilia section. 1)uring a given cycle, the regenerating section is cooled and the reacting section is heated. The direction of flow is then reversed and the two sections interchange fuiictioiis. The recycling, 1, is necessary to obtain a relatively uiiiforin temperature profile along the regenerator. This profile will be the initial profile of the react,or for the succeeding cycle. Part of the air from the regenerator, 6, is vented in order to regulate the temperature of the stream, 11. entering the reactor. If iieceshary, additional cold air can be introduced by st'reani 9. The temperatures aiid flow rat,es in the various streanis can he programmed as functioii.: of t,ime,to optimize the operation. Mathematical Description
The simlile forward cell model-Le., a >cries of htirred tanks-is used as computationally simpler thaii the 1)lug fion or the axial dispersion model. For a si~igleexothermic reaction, the temperature and concentration T,(m,t), c , ( m , t ) iii the i t h cell of the reacting rection mid the temperature p 7 ( m j t )in the i t h cell of the regenerating section duriiig the mth cycle or period satisfy the equations
Ind. Eng. Chem. Fundom., Vol. 10, No. 1 , 1971
71
CYCLE M AIR I
- 2
REGENERATING
CYCLE M i l
01 =
Figure 1.
s
-
8
Regeneratively cooled fixed-bed reactor system
with initial conditions
i
=
1 , . .).V, m = l j 2 , . , .
The above equations involve the following assumptions mid simplifications. The heat and mass transfer betweeii the bulk of t,he gas and the catalyst is fast relative to the reaction, so t.hat the concentration and teniperatures in the bulk of t,he gas are t'lie same as on the esteriial hurface of the catalyst pellets. A characteristic time for changing the catalyst temperature is ( p s c p s ~ p Q c p Q )which 8, is much larger than the residence time, 8. Therefore, the concent,ration,ci,adjusts very rapidly t o a value very near the steady-state corresponding to T i . Moreover, the heat capacity of the gas in the interparticle space is neglected as being much smaller than the solid heat capacity. The reaction is fint-order, wit,h its rate expressed per unit pellet volume. The effectiveness factor is unity. Because of the recycling around the regenerator, S < 8 ; neverthelees the same nuiiiber of cells are used for both sections. This simplification is innocuous, since the temperature gradients along the regeiierat,or a t the eiid of each period are small. The iiilet coiidit,ioiis 4 are taken as constant. for simplicity. In the case of multiple periodic solut'ioiis the initial conditions 7 determine which of the st'able peiiodic solut,ioiis the system will settle to. By choosing T , and T , sufficient,ly high, the system reaches a st,eady periodic operation with reasonably high conversion within a few cycles from start,up.
The solution of the regenerator equatioii is easily obtained as
The solutions of the reactor equations were obtuiiied on a digital computer sequentially for V I = 1 (i = 1,. , . ,.V), 2(i = 1,. . , &V)>. . . The reaction choheii \vab CO 1,'202 -,CO, on a ViOjSi02 cataly-t. Calculations were performed for rhe followiiig vahies of p h y h d con;taiits :tnd parameters:
+
T,
=
Fa =
T,
=
c, = 1.692 X po =
45OoC
g mole
0.4906 X
c111-~
g
c p o = 0.258 cal g-l "C-'
Int'roducing now the dimensioiilees variables,
ps =
1.0 g c m U a
c p s = 0.2 cal g-l
"C-I
e = 0.4
k 72 Ind. Eng. Chem. Fundom., Vol. 10, No. 1, 1971
AH
=
-6.7 X lo4 cal g mole-'
E
=
3.0 X lo4 cal g mole-'
=
7.8 X lo7 sec-l, 3.9 X lo7 sec-'
1
I
I
i
l40c
"I
II 3 0
I
I
5
--
20
15
IO
25
CELL
30
35
40
I
I
I
I N.50 k = 7.8 x IO' SEC-'
1I i 1
45
NUMBER
Figure 2. Final temperature profiles in reactor a t successive cycles
4
" 5 0
e/t7= 4 yo(rn,rl=I O 1
k = 7 8 x IO' S E C - ' X = 0 4 5 5 0.4
Figure 5.
06 CONVERSION
Maximum temperature vs. conversion
I
N 5
15
IO
20
25
CELL
Figure cycle
3.
30
35
40
45
NUMBER
1
N = 75
e/&= 6 Y&rn,r)= 1 04 kX =. 03498 3x IO' S E C - '
~~~
;I O 8
T, =723'K
7;
LL
w
I
I
qZ.6
1
k =3.9x IO7 S E C - '
t
I04 -
2
0S t f 0
i
c w
O.* IO
Figure 4. cycle
1
= 75
Evolution of reactor temperature profile in one
I20
2
0,71
08
20
30 40 50 CELL N U M B E R
60
t
70
Evolution of reactor temperature profile in one
6=
0.0125 hec, 0.00833 iec
s=
50, 7 5
t, = 296.26 iec = 118.5 ( X 0 ) Discussion of Numerical Results and Conclusions
The numerical results are presented i t i Figures 2 to 6. In all ca-ex, stead!- iieriodic operation was attained within 10 cycle>, anti a tyljical approach to the final periodic profile is shown in Figure 2. O m way of controlling the temperature withiii liarrower limits is the use of a lower activity catalyst, or equivaleiitly the dilution of the catalyst b y an inert solid material (Figures 3 and 3 ) . Although this requires a somewhat
6.
1 ~
1
I
I
IO1
102
103
REGENERATOR
Figure
0 = 0.05 'ec
Tr=723'K
I 1.04
I
I
I05
I N L E T TEMPERATURE,
7,/Tr
Effect of regenerator inlet temperature
higher initial temperature, the maxiniutn tem1)erature for ii given conversioii is well below the undiluted ca\e (Figure 5 ) . The temperature, go, of stream 2 in Figure 1 determines the final temperat'ure profile in the regenerator-Le., the initial profile in the reactor. Hence, go is the most important variable relative to conversion and maximum temperature. A s Figure 6 s h o w , an increase of 29°C i n go iiicrease* the conversion from 0.217 to 0.575. On the other hand, the inlet temperature to the reactor yo has a very small effect-e.g., a decrease of 14°C decreases the conversioii by only 0.0025 (S = 75, 0'6 = 6, k = 3.9 x lo7 5ec-1). Thehe effect., hiiggest a relatively easy control of the total ol)eratioii, since the regenerator temperature a t the elid of the le can be controlled nccurately. Finally, period T , has little effect as loiig as it does llot become too high-for example, when T , variez in the range 7 Ind. Eng. Chem. Fundam., Vol. 10,
No. 1 , 1971
73
to 15, the conversion varie:: 1)). 0.013 and the iiiaximurii temperature hy 6 . 5 T (S = 7 5 , fl,8 = 6. h. = 3.9 X 10' ,5ec-l). .I11 coiiverbioiis reported repre>eiit average* over a cyclc, whereah the inasimum temperature i- taken with respect to both space aiitl time. 1%othvariables refer to the steady lieriodic operatioii. Iluriiig startup, hlightly higher temperatures may sometimes occur (Figure 2 ) . The regenerative s p t e m htutlied here seem. t o have some important advantages over the steady-state reactor with wall cooling or dilution: the ease of heat removal uiitl the favorable shalw of teniperature profile.. 111 coiitraht with the n-allcooled reactor, the regeneratively cooled reactor ha3 no radial temperature gradient. which caii oiily iiiipair selectivity. The tli,+atlvaiitages oi the rcgeiierative system are the comIilesity in the pi1)iiig :ind valves and the time-varying product compo,*itioii. Tht. latter can he minimized hy using surge tank; or mow thaii (me renctor i i i I)nrnllel. Further ~ o r kwill inclutlc the ->-nteniatic o1)timizutioii of the temperature lrofile- for the c.:ihe of consecutive reactionse.#., liaitial oridutioiib. Thc key control variable> for this optiniizatioii oultl lie the tli.+tiil)utioiiof iiicrt holid and cata1y.t aloiig the heti : l i d the teiii1)er;iture j,,(ni,t). Esl)erimental W C J I , ~ i- also ini1)ortant hecause oi the uncertainties involved in the kinetic and transport model.+wed iii the calculatioiib.
c i ( m , tj
=
t)
= = = = =
concentration in ith cell of reactor, g moles c1iir3
co
('P Y cp,
E k
?ti
74 Ind.
R t ff
Tdm, 0
T d m , 2)
Tdm, t ) To(%, t ) To!T,, T o , T, xtjm,
T)
yt(t)1,
7)
s
udm, 7 ) Ydm,
7)
uo(nl, 7)
= = = = = = =
= = = = = = = = =
tot'al number of cells gas constant, cal g mole-' "C-1 time, see length of a cycle, see temperature in ith cell of react,or, 'Ei inlet temperature to reactor, OK temperature in ith cell of regenerator, "I( inlet temperature to regenerator. OK constant temperatures the reference temperature dimensionles. c i ( v , t) average coiivercioii, dimensionles,< dimensionless T i ( m ,t ) dinleiisionless T o ( m ,t ) dimensionless T i ( m ,t ) dimensionless T,(rn,T )
GREEKLETTERS Po,
PI, P?
Y LEI E
0
e Ps. P g 7
T/
dimensionless constants defined in Equation 8 = dimeiisioiiless activation energy = heat of reaction = bed porosity = residence time in each reactor cell = residence time iii each regenerator cell = densities of catalyst and of gas = dimensionless time = dimensionless length of cycle
=
literature Cited
Nomenclature
Co(t?1.
N
inlet conceiitratioii to reactor, g moles cm+ constant' concentration, g moles cn1-3 heat capacity of gas, cal g-1 "C-1 heat capacity of solid, cal g-1 '(2-1 activation energy, cal g mole-' = frequency factor of rate constant, sec-1 = indicates the cycle number
Eng. Chem. Fundarn., Vol. 10,
No. 1, 1971
Ari>, R., "Optimal Design of Chemical Reactor>," p. 142, Academic Prehb, New York, 1961. Bogard, JI. J. P., Long, R . H., Chem. Eng. Proyr. 58(7), 90 11962)). Kirk, R'.E., Othmer, 11. F., eds., "Encyclopedia of Chemical Technology," Vol. 9, p. 339, Interscience, Xew York, 1952. Ogiuiye, A . F., Ray, W. H., A.I.Ch.E., 62nd Aiinual lleeting, Washington, D.C., Xovember 1969.
RECEIVED for review Sovember 28, 1969 ACCEPTEDSeptember 8, 1970
