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Simulation and optimization of a set of catalytic reactors used for dehydrogenation of butene into butadiene
Computers them. Engng Vol. 19, Suppl., PD. S345-S350, 1995
Pergamon
009%1354(95)00097-6
Copyright 8-i99Sm&evier Science Ltd Printed in Great Britain. All rinhts reserved 0098-1354/95 39.50 + 0.00
SIMULATION AND OPTIMIZATION OF A SET OF CATALYTIC REACTORS USED FOR DEHYDROGENATION OF BUTENE INTO BUTADIENE D. 0. BORIO, N.S. SCHBIB Planta Pilot0 de Ingenieria Quimica (UNS-CONKET) 12 de octubre 1842- 8000 Bahia Blanca-ARGENTINA
ABSTRACT The simulation and optimization of a set of industrial fixed bed catalytic reactors is presatted. The reactors are operating in deactivation-regeneration cycles. Dynamic mathematical models for the four stages of the process are included, i.e. dehydrogenation (deactivation by coking), steam purge, oxidative regeneration and evacuation. An iterative method was used to simulate an autothermal process, which is common in the industrial practice. To prevent the permanent loss of the catalyst activity by s&ring, an upper limit of temperature has been imposed. The cycle time, temperature and composition of the feed during the regeneration stage are selected as optimization variables. Under autothermal conditions, the four stages of the cycle start with markedly non-uniform thermal profiles in the catalytic bed, which have considerable influence on the maximum temperature of the cycle. In this way, the production rate of butadiene has been substantially improved as both the maximum allowable temperature and the inertcatalyst ratio increase. The higher the oxygen molar fraction at the regeneration stage, the shorter is the optimal duration ofthe cycle. KEYWORDS:
Fixed bed reactor, catalytic dehydrogenation, butadiene, cyclic operation optimization INTRODUCTION In the industrial practice, the dehydrogenation of l-butene (or butane-butene mixtures) takes place under adiabatic conditions, with temperatures ranging from 550 to 650 C and pressures from 0.1 to 0.25 atm. The process operates cyclically and after 6 to 8 minutes the feed is switched to another catalytic bed. The first bed is purged with steam for a few minutes and then the coke deposited on the catalyst is burned off by combustion in air or mixtures with low oxygen concentration, leading to a temperature rise within the reactor. When the regeneration has been completed, the air stream is shut off and a fuel-gas mixture is admitted to bum off the residual oxygen and pretreat the catalyst under reducing conditions (Rielly, 1977; Craig and Dufallo, 1979). In order to have continuous flows of the major reactant streams, at least three reactors in parallel must be used (see Fig. 1). The catalyst beds are diluted with inert particles. n 0,s. OLOIlD “IL”. w “LL”#
Dumez and Froment (1976) studied the optimization of an industrial reactor for the dehydrogenation of 1-butene to 1,3butadiene over a CrsOs/AlsOs catalyst. In this work, a Fig. 1: Scheme of the process rigorous transient simulation of the production stage was carried out, whereas the simulation of the regeneration step was avoided by assuming a linear relationship between the average coke concentration in the bed and the duration of the decoking process. s345
European Symposium on Computer Aided Process Engineering-5
S346
Recently, an optimization study of the dehydrogenation of 1-b-e in a fixed bed reactor subjected to maximum temperature constraints was perf&med (Borio et al., 1992), where a detailed regeneration model was included to predict the transient temperature profiles developed at this stage. The temperature changes during the purge and evacuation stages (PS and ES) had been neglected, and constant temperature profiles had been assumed at the begin&g of both the dehydrogenation and regeneration stages (DS and RS). This is a suitable assumption provided the intermediate stages are long because the bed temperature becomes homogeneous. However, as it will be shown, this hypothesis may be unrealistic under industrial operating conditions. Unlike previous studies, the transient models for the four stages of the process, i.e. dehydrogenation, steam purge, regeneration and evacuation, are included in the present work. Since the simulation modules operate in series, the coke and temperature axial profiles at the beginning of each stage are already known from the previous one. MATHEMATICAL MODEL Dehydrogenation stage @IS): The simulation has been developed using the kinetic scheme proposed by Dumez and Froment (1976). The values of the parameters and operating conditions employed in the simulation have been presented previously (Borio et al., 1992). at t=O:
(1)
C,,forz=O cB(o,z)
=
0
forz#
0
(2) aCH_ E---
a z(uc”)+
(3)
Pb.dHe
at --dCc
T(O,z) = _ cl
+
0
at z=O, for any time: dT
Pb.TCp,s
T;“(z) forz#
(4)
rc2
at
vforz=O
x
=
-
a(up,c,,~T) az
+
Pb,oal(-AHR)
rHe
(5)
cB(t,o)
=
cB,
C,(t,0)
=
C,(t,0)
=
0
T(t,O) = T,d”” Purge and Evacuation stages (PS - ES): Due to the short duration of the purge and evacuation periods, the changes in the catalyst activity have been neglected. Therefore, only the heat transfer process between gas and solid has been considered.
Purge stage
att=O:
Evacuation stage T(O,z) =
T,p”forz=O q!“(z)
at z=O, any time:
for z z 0
T( t,O) = T,”
att=O:
T(O,z) =
T,”
forz=O
T,%(z) forz# at z=O, any time:
0
T( t,O) = T,”
Regeneration Stage (RS): To simulate the regeneration stage, the following assumptions have been made: (i) A sharp interface model was chosen for the catalyst particle (Borio et al ., 1992). (ii) External (gas-solid) resistances to mass and heat transfer were considered. The internal temperature gradients in the catalyst particle were neglected. (iii) The catalyst and inert particles were assumed to be at the same temperature.
European Symposium
s347
on Computer Aided Process Engineering-5
(iv) The kinetic parameters reported by Mickley et al. (1965) for coke combustion over a CrzOs/Al203 catalyst were selected. (v) Plug flow and adiabatic operation were considered.
c7)
$ =(-AH,)
rv + ah(T - T,) (14)
,%,+ps where:
Pb,T
= Pb.cat
(15)
+Pb.I
(8)
at t=O:
- !%I = 4Rrzk(T,)CAp dt
c, =
(9)
'A(',')=
l+!!p(!$k&(l3-1 (10)
Ao
T(0, z) =
ax
c
Pb.Tcc,i MC(l
C-
--
dt
(11)
kc -
Pb,TCC,iVp
T,‘% for z= 0 T:“‘(z) forz#
clr,=%W dt
r, (0,~)= rp
C,(O,z) = c;(z);
dNA
‘) (
(12)
TJO,z) = T,p”(z) at z=O, any time:
dt
‘&‘)
dT -=-ucpgpa UP&?%!
g-ah(~-T,)
at
0
T(t,O) = Td”
= c,,;
(13)
In order to solve the dynamic models, the spatial coordinate was discretized using finite differences. Jntegration in time was performed by means of a Gear algorithm. Jn practice, the complete cycle was desigoed to satisfy the closure of the overall heat and mass balances (autothermal operation). Therefore, the coke and temperature profiles resulting from the ES had to coincide with the initial profiles of the DS (Borio and Schbib, 1994). The solution is reached iteratively, by means of simulations of the entire cycle. A hybrid method that combines successive-substitutions and Quasi-Newton algorithms were used to attain convergence of the tear stream. Process Optimization:
The optimization problem studied in this work consists in the maximization of the butadiene production per unit mass of catalyst in a given cycle, subjected to a maximum temperature constraint to avoid the catalyst sintering. The objective function can be expressed as PD %bj
s.t. T_
= Wcat(fdeb
+$m
+%,
5 Tm
;
where:
PD= I;” Fn(t)dt
+‘ev)
(16) Three operating parameters: cycle duration (t& oxygen molar fraction (y& and feed temperature during regeneration (TB) have been selected as optimization variables. Purge and evacuation times (t,, t,) were assumed to be constant and equal to 2 minutes each. The optimization problem was solved by means of a variable metric projection method (VMP) for nonlinear programming, using penalty functions to account for the temperature restrictions. The method requires the simulation of the entire cycle at each step. RESULTS AND DISCUSSION All the results satisfied the following operating constraint, which is necessary to have a continuous flow (for three reactors in parallel). of the I-butene stream: 2 t,, = t,, + t, + t, A start up policy: The evolution of the different variables towards an autothermal cycle is presented in Figs. 2 to 4. At the
beginning of the first cycle, the catalytic bed was assumed to be exempt of coke deposits, with a uniform
European Symposium on Computer Aided Process Engineering-5
S348
temperature of 823 K. Table 1 shows the operating conditions for each stage, which were always kept constant. The coke and temperature profiles at the end of each cycle were assumed to be the initial conditions for the following cycle. As a result, a progressive accumulation of coke and Table 1: Operating Conditions of the different stages heat occurs in the bed (Figs. 2 & 3). Once the autorhermal process has been achieved, the heat production during the RS is approximately equal to the heatconsumption during the DS . The production per cycle reaches a maximum after five cycles, and then decreases towards lower values than
920 900 660 660 640 0.00
8 0.0
8 0.2
r 0.4
=
Cm1
I 0.6
0.6
“2%.b 2
Fig. 2: Evolution towards the autothermal cycle. Coke profiles after regeneration.
[m]
.
0.8
Fig 3 : Evolution towards the autothermal cycle. Temperature profiles after regeneration.
o.1e8 m----l
90.160 3
0.152
c) pI 0.144 0.136
LimllJ 1
11
Cycle
21
31
number
41
Fig. 4: Butadiene production per cycle during the evolution towards the autothermal conditions.
615
0.0
0.2
0.6
0
3
Fig. 5: Thermal profiles at the end of each stage (autothermal cycle).
those corresponding to the first cycle, (see Fig. 4), because of the increase in the average coke concentration in the bed (Fig. 2). Once the. autothermal conditions have been reached, each cycle is equivalent to the previous one, and the butadiene production becomes constant (Fig 4). Obviously, the evolution of the system towards the autothermal cycle depends on the initial conditions selected at the start of cycle 1. However, the final steady state (autothermal cycle) is not a function of the initial conditions employed. Simulation of the autothermal operation:
For the conditions of Table 1, Fig. 5 shows the temperature profiles at the end of the four stages, after the autothermal operation has been achieved. It should be noted that each stage begins with a markedly nonuniform thermal profile due to both the strong heat effects involved in the chemical reactions and the short duration of the PS and ES. Therefore, the assumption of constant bed temperature at the start of both the DS and RS is unrealistic and non-conservative under industrial operating conditions, where short purge and evacuation periods are usually employed to maximize the production rate. The temperature maxima appearing in the bed can be explained considering the behaviour of the oxygen conversion and the temperature profiles during the RS (Figs. 6 and 7). Due to the high coke combustion rate, at the beginnmg of the RS the oxygen is completely consumed in the first zone of the bed, where a temperature raise is observed. As the regeneration proceeds, the coke depletion near the entrance allow the oxygen to
EuropeanSymposiumon ComputerAided Process Engineering-5
s349
advance in the reach
(see Fig. 6), which is accompanied with a thermal increase. Thus, the high amount of coke present in the last zone ofthe bed causes a temperature maximum near 2=0.4 m. This maximum moves dawnstream, but it can not reach the reactor outlet because of the short duration of the stage (t, = 6 min.). 016
000 884 860 852 83% 820
Cm1
z
0.0
0.2
0.4
=
Fig. 6: Evolution of the oxygen profiles during Fig. 7: Temperature (autothermal cycle). the JXS(autothermal cycle).
cm1
0.6
evolution
0-a
during the
Rs
Optimization of the autothermal operation: The optimal values for FM as a function of the cycle time are shown in Fig. 8. All the results correspond inert-catalyst ratios. to the same total mass of solid (pb,~_1300 kg,olidm3 of reactor), for three differAn upper limit of TM= 923 K is imposed for the maximum temperature of the cycle, the optimization variable being the molar fraction in the RS (y,&. A substantial improvement in the objeaive function is achieved as the bed dilution increases. The influence of TM upon the optimal values for F4 is shown in Fig. 9. The optimization variable is again yA0,for an inert-catalyst ratio of 3110. Under these conditions, the optimal production rate depends slightly on the cycle time. Conversely, the objective function augments strongly as Tm increases. In fact, the higher the TM, the higher is the optimal oxygen level in the RS and the more active catalysts result at the beginning of the DS. However, the e&momic value associated to an increase in the butadiene production per cycle may be offset by the permanent loss of catalyst activity connected with the simering (Bono et al.. 1992). 2.30
-
2.18
-
“0
-+ 2.02 34 zl.B8 0 k 1.74 1.80
-
inert/cat.=3/10 T =923K h44
ineticat.=5/8 -
- . 6
I 10
I t,
I 18
1.51 5
10
20
250 I
[gin]
Fig. 8: Optimal values for the production rate of butadiene, for different inert-catalyst ratios.
Fig. 9: Optimal values
for the production rate of butadiene and yA0,for different Tm
Optimal values for F~bj are shown in Fig. 10 as a function ofthe cycle duration. In this case, T,JJ was "0 2.40 chosen as the optimization variable, for three 1 different values of yA@ A con&ant value of x 2.20 Tm=923 K was selected. The curve for y,,$&=9% 32.00 c4" presents a maximum near & = 10 min, whereas the 1.80 maxima of the CurveS corresponding to y/,0= 6.5 % and 3% are located near k= 12 and 24 min, l.Oo t, [min] respectively. Therefore, the optimal duration of the Fig. 10 Optimal values for the production rate of cycle decreases substantially as mixtures with higher butadiene, for different oxygen levels. oxygen concentrations are admiUed.
European Symposium on Computer Aided Process Engineering-5
s350
CONCLUSIONS By means of a detailed modeling of the four stages of the process, the cyclic operation of a set of three fixed-bed catalytic reactors has been simulated. Since the simulation modules operate in series, it is possible to follow the behavior of the process along the cycles starting from any initial condition of the bed, until the overall mass and heat balances are satisfied. Once the autothennal cycle uniform. These gradients temperature reached during tolerated without exceeding
has been achieved, the temperature profiles along the beds are markedly nonin the solid temperature have a considerable influence on the maximum the regeneration, and strongly restrict the oxygen wncentrations that can be the maximum allowable temperature.
The production rates of butadiene per mass of catalyst are improved significantly by the dilution of the catalyst bed with inert solid. In fact, more severe regenerations are admitted in diluted beds for the same TF~IA,due to a higher thermal inertia. Besides, the optimal duration of the cycle increases as mixtures of lower oxygen concentrations
are fed at the RS, provided
an optima1 selection of T,“p has been made.
NOMENCLATURE a = external surface of catalyst, m2/m3 CA = corm. of 02, gas phase, kmol/m3 CAc= wnc. of 02, unreacted core, kmol/m3 CH = concentration of butene, gas phase, kmol/m3 Cc = wncentration of coke, kg coke/kg catalyst CH = concentration of butadiene, gas phase, kmol/m3 CH = wncentration of hydrogen gas phase, kmol/m3 crs = specific heat of the solid, W/(&cd K) cr,a = specific heat of the gas, kJ/(kg K) D, = effective diffusivity of oxygen, m2/s Fn = outlet molar flow of butadiwe, kmol/h Fobj = objective function, kmolD/(k9c,t h) h = heat transfer wefflcient, kJ/(m%K) AHR = heat of reaction, kJ/kmol k = kinetic constant for coke wmbustion, m/s b= external mass transfer wefficient, m/s L = reactor length, m Mi = molecular weight, component I, kg/km01 PD = butadiene production per cycle, km01 r, = radius of the unreacted core, m rcl, rc2 = reaction rates for coke formation from butene and butadiene, respectively., kmol/(b h) rH = reaction rate for dehydrogenation, kmol/(& h) reaction rate, kmol/(kgc,l h) rHe = n rH; effective rr = particle radius, m.
= reaction Zrol/(m$ t= time,h
rate
for
4
wnsumptig
tdeh, tpur, tregr tev’ dehydrogenation purge, regeneration and evacuation periods, h b= duration of the cycle, h T = temperature, K Tmsx= max. temperature of the cycle, K Tm = max. allowable temperature, K T, = temperature of the solid phase, K u = linear gas velocity, m/h V, = volume of the catalyst particle, m3 coke conversion Xc = yA0 = 02 molar fraction, reactor feed. z = axial position, m E= void fraction in the reactor e&ctiveness factor n= pb,cat’ catalyst bulk density, kg,&m3 pbJ = inert bulk density, b&m3 m3 pb,T = solid bulk density, kg&k& 2 ps= density of the gas phase, kg/m \vcH = coke yield factor, k&&kg,ti,, YCD= coke yield factor, kgmk$kgbutadiene Subscripts 0 = at axial position, z=O f = at the end of the stage
REFERENCES Borio D. O., M. Menwdez, and J. Santamaria (1992). Ind. Eng. Chem. Res., 3_l, 2699-2707. Borio D. O., N. S. Schbib (1994). XIV Simp. Iberoam. de Camlisis, Concepcion (Chile). Vol. 3, 12831288. Craig R. G. and J. M. Dufallo (1979), Chem. Eng. Prog., Feb., 62-65. Dumez F. J., G. F. Froment (1976). Ind. Eng. Chem. Process Des. Dev., l5,291-301. Mickley H. S., J.W. Nestor, L. A. Gould (1965). The Can. J. Chem. Eng., 61-68. Rielly T. (1977). Butadiwe, General, In: Encyclopedia of Chem. Process. and Des., (J. JMcKetta ed.), Vol. 5, pp. 110-170, Marcel Dekker.
Pergamon
009%1354(95)00097-6
Copyright 8-i99Sm&evier Science Ltd Printed in Great Britain. All rinhts reserved 0098-1354/95 39.50 + 0.00
SIMULATION AND OPTIMIZATION OF A SET OF CATALYTIC REACTORS USED FOR DEHYDROGENATION OF BUTENE INTO BUTADIENE D. 0. BORIO, N.S. SCHBIB Planta Pilot0 de Ingenieria Quimica (UNS-CONKET) 12 de octubre 1842- 8000 Bahia Blanca-ARGENTINA
ABSTRACT The simulation and optimization of a set of industrial fixed bed catalytic reactors is presatted. The reactors are operating in deactivation-regeneration cycles. Dynamic mathematical models for the four stages of the process are included, i.e. dehydrogenation (deactivation by coking), steam purge, oxidative regeneration and evacuation. An iterative method was used to simulate an autothermal process, which is common in the industrial practice. To prevent the permanent loss of the catalyst activity by s&ring, an upper limit of temperature has been imposed. The cycle time, temperature and composition of the feed during the regeneration stage are selected as optimization variables. Under autothermal conditions, the four stages of the cycle start with markedly non-uniform thermal profiles in the catalytic bed, which have considerable influence on the maximum temperature of the cycle. In this way, the production rate of butadiene has been substantially improved as both the maximum allowable temperature and the inertcatalyst ratio increase. The higher the oxygen molar fraction at the regeneration stage, the shorter is the optimal duration ofthe cycle. KEYWORDS:
Fixed bed reactor, catalytic dehydrogenation, butadiene, cyclic operation optimization INTRODUCTION In the industrial practice, the dehydrogenation of l-butene (or butane-butene mixtures) takes place under adiabatic conditions, with temperatures ranging from 550 to 650 C and pressures from 0.1 to 0.25 atm. The process operates cyclically and after 6 to 8 minutes the feed is switched to another catalytic bed. The first bed is purged with steam for a few minutes and then the coke deposited on the catalyst is burned off by combustion in air or mixtures with low oxygen concentration, leading to a temperature rise within the reactor. When the regeneration has been completed, the air stream is shut off and a fuel-gas mixture is admitted to bum off the residual oxygen and pretreat the catalyst under reducing conditions (Rielly, 1977; Craig and Dufallo, 1979). In order to have continuous flows of the major reactant streams, at least three reactors in parallel must be used (see Fig. 1). The catalyst beds are diluted with inert particles. n 0,s. OLOIlD “IL”. w “LL”#
Dumez and Froment (1976) studied the optimization of an industrial reactor for the dehydrogenation of 1-butene to 1,3butadiene over a CrsOs/AlsOs catalyst. In this work, a Fig. 1: Scheme of the process rigorous transient simulation of the production stage was carried out, whereas the simulation of the regeneration step was avoided by assuming a linear relationship between the average coke concentration in the bed and the duration of the decoking process. s345
European Symposium on Computer Aided Process Engineering-5
S346
Recently, an optimization study of the dehydrogenation of 1-b-e in a fixed bed reactor subjected to maximum temperature constraints was perf&med (Borio et al., 1992), where a detailed regeneration model was included to predict the transient temperature profiles developed at this stage. The temperature changes during the purge and evacuation stages (PS and ES) had been neglected, and constant temperature profiles had been assumed at the begin&g of both the dehydrogenation and regeneration stages (DS and RS). This is a suitable assumption provided the intermediate stages are long because the bed temperature becomes homogeneous. However, as it will be shown, this hypothesis may be unrealistic under industrial operating conditions. Unlike previous studies, the transient models for the four stages of the process, i.e. dehydrogenation, steam purge, regeneration and evacuation, are included in the present work. Since the simulation modules operate in series, the coke and temperature axial profiles at the beginning of each stage are already known from the previous one. MATHEMATICAL MODEL Dehydrogenation stage @IS): The simulation has been developed using the kinetic scheme proposed by Dumez and Froment (1976). The values of the parameters and operating conditions employed in the simulation have been presented previously (Borio et al., 1992). at t=O:
(1)
C,,forz=O cB(o,z)
=
0
forz#
0
(2) aCH_ E---
a z(uc”)+
(3)
Pb.dHe
at --dCc
T(O,z) = _ cl
+
0
at z=O, for any time: dT
Pb.TCp,s
T;“(z) forz#
(4)
rc2
at
vforz=O
x
=
-
a(up,c,,~T) az
+
Pb,oal(-AHR)
rHe
(5)
cB(t,o)
=
cB,
C,(t,0)
=
C,(t,0)
=
0
T(t,O) = T,d”” Purge and Evacuation stages (PS - ES): Due to the short duration of the purge and evacuation periods, the changes in the catalyst activity have been neglected. Therefore, only the heat transfer process between gas and solid has been considered.
Purge stage
att=O:
Evacuation stage T(O,z) =
T,p”forz=O q!“(z)
at z=O, any time:
for z z 0
T( t,O) = T,”
att=O:
T(O,z) =
T,”
forz=O
T,%(z) forz# at z=O, any time:
0
T( t,O) = T,”
Regeneration Stage (RS): To simulate the regeneration stage, the following assumptions have been made: (i) A sharp interface model was chosen for the catalyst particle (Borio et al ., 1992). (ii) External (gas-solid) resistances to mass and heat transfer were considered. The internal temperature gradients in the catalyst particle were neglected. (iii) The catalyst and inert particles were assumed to be at the same temperature.
European Symposium
s347
on Computer Aided Process Engineering-5
(iv) The kinetic parameters reported by Mickley et al. (1965) for coke combustion over a CrzOs/Al203 catalyst were selected. (v) Plug flow and adiabatic operation were considered.
c7)
$ =(-AH,)
rv + ah(T - T,) (14)
,%,+ps where:
Pb,T
= Pb.cat
(15)
+Pb.I
(8)
at t=O:
- !%I = 4Rrzk(T,)CAp dt
c, =
(9)
'A(',')=
l+!!p(!$k&(l3-1 (10)
Ao
T(0, z) =
ax
c
Pb.Tcc,i MC(l
C-
--
dt
(11)
kc -
Pb,TCC,iVp
T,‘% for z= 0 T:“‘(z) forz#
clr,=%W dt
r, (0,~)= rp
C,(O,z) = c;(z);
dNA
‘) (
(12)
TJO,z) = T,p”(z) at z=O, any time:
dt
‘&‘)
dT -=-ucpgpa UP&?%!
g-ah(~-T,)
at
0
T(t,O) = Td”
= c,,;
(13)
In order to solve the dynamic models, the spatial coordinate was discretized using finite differences. Jntegration in time was performed by means of a Gear algorithm. Jn practice, the complete cycle was desigoed to satisfy the closure of the overall heat and mass balances (autothermal operation). Therefore, the coke and temperature profiles resulting from the ES had to coincide with the initial profiles of the DS (Borio and Schbib, 1994). The solution is reached iteratively, by means of simulations of the entire cycle. A hybrid method that combines successive-substitutions and Quasi-Newton algorithms were used to attain convergence of the tear stream. Process Optimization:
The optimization problem studied in this work consists in the maximization of the butadiene production per unit mass of catalyst in a given cycle, subjected to a maximum temperature constraint to avoid the catalyst sintering. The objective function can be expressed as PD %bj
s.t. T_
= Wcat(fdeb
+$m
+%,
5 Tm
;
where:
PD= I;” Fn(t)dt
+‘ev)
(16) Three operating parameters: cycle duration (t& oxygen molar fraction (y& and feed temperature during regeneration (TB) have been selected as optimization variables. Purge and evacuation times (t,, t,) were assumed to be constant and equal to 2 minutes each. The optimization problem was solved by means of a variable metric projection method (VMP) for nonlinear programming, using penalty functions to account for the temperature restrictions. The method requires the simulation of the entire cycle at each step. RESULTS AND DISCUSSION All the results satisfied the following operating constraint, which is necessary to have a continuous flow (for three reactors in parallel). of the I-butene stream: 2 t,, = t,, + t, + t, A start up policy: The evolution of the different variables towards an autothermal cycle is presented in Figs. 2 to 4. At the
beginning of the first cycle, the catalytic bed was assumed to be exempt of coke deposits, with a uniform
European Symposium on Computer Aided Process Engineering-5
S348
temperature of 823 K. Table 1 shows the operating conditions for each stage, which were always kept constant. The coke and temperature profiles at the end of each cycle were assumed to be the initial conditions for the following cycle. As a result, a progressive accumulation of coke and Table 1: Operating Conditions of the different stages heat occurs in the bed (Figs. 2 & 3). Once the autorhermal process has been achieved, the heat production during the RS is approximately equal to the heatconsumption during the DS . The production per cycle reaches a maximum after five cycles, and then decreases towards lower values than
920 900 660 660 640 0.00
8 0.0
8 0.2
r 0.4
=
Cm1
I 0.6
0.6
“2%.b 2
Fig. 2: Evolution towards the autothermal cycle. Coke profiles after regeneration.
[m]
.
0.8
Fig 3 : Evolution towards the autothermal cycle. Temperature profiles after regeneration.
o.1e8 m----l
90.160 3
0.152
c) pI 0.144 0.136
LimllJ 1
11
Cycle
21
31
number
41
Fig. 4: Butadiene production per cycle during the evolution towards the autothermal conditions.
615
0.0
0.2
0.6
0
3
Fig. 5: Thermal profiles at the end of each stage (autothermal cycle).
those corresponding to the first cycle, (see Fig. 4), because of the increase in the average coke concentration in the bed (Fig. 2). Once the. autothermal conditions have been reached, each cycle is equivalent to the previous one, and the butadiene production becomes constant (Fig 4). Obviously, the evolution of the system towards the autothermal cycle depends on the initial conditions selected at the start of cycle 1. However, the final steady state (autothermal cycle) is not a function of the initial conditions employed. Simulation of the autothermal operation:
For the conditions of Table 1, Fig. 5 shows the temperature profiles at the end of the four stages, after the autothermal operation has been achieved. It should be noted that each stage begins with a markedly nonuniform thermal profile due to both the strong heat effects involved in the chemical reactions and the short duration of the PS and ES. Therefore, the assumption of constant bed temperature at the start of both the DS and RS is unrealistic and non-conservative under industrial operating conditions, where short purge and evacuation periods are usually employed to maximize the production rate. The temperature maxima appearing in the bed can be explained considering the behaviour of the oxygen conversion and the temperature profiles during the RS (Figs. 6 and 7). Due to the high coke combustion rate, at the beginnmg of the RS the oxygen is completely consumed in the first zone of the bed, where a temperature raise is observed. As the regeneration proceeds, the coke depletion near the entrance allow the oxygen to
EuropeanSymposiumon ComputerAided Process Engineering-5
s349
advance in the reach
(see Fig. 6), which is accompanied with a thermal increase. Thus, the high amount of coke present in the last zone ofthe bed causes a temperature maximum near 2=0.4 m. This maximum moves dawnstream, but it can not reach the reactor outlet because of the short duration of the stage (t, = 6 min.). 016
000 884 860 852 83% 820
Cm1
z
0.0
0.2
0.4
=
Fig. 6: Evolution of the oxygen profiles during Fig. 7: Temperature (autothermal cycle). the JXS(autothermal cycle).
cm1
0.6
evolution
0-a
during the
Rs
Optimization of the autothermal operation: The optimal values for FM as a function of the cycle time are shown in Fig. 8. All the results correspond inert-catalyst ratios. to the same total mass of solid (pb,~_1300 kg,olidm3 of reactor), for three differAn upper limit of TM= 923 K is imposed for the maximum temperature of the cycle, the optimization variable being the molar fraction in the RS (y,&. A substantial improvement in the objeaive function is achieved as the bed dilution increases. The influence of TM upon the optimal values for F4 is shown in Fig. 9. The optimization variable is again yA0,for an inert-catalyst ratio of 3110. Under these conditions, the optimal production rate depends slightly on the cycle time. Conversely, the objective function augments strongly as Tm increases. In fact, the higher the TM, the higher is the optimal oxygen level in the RS and the more active catalysts result at the beginning of the DS. However, the e&momic value associated to an increase in the butadiene production per cycle may be offset by the permanent loss of catalyst activity connected with the simering (Bono et al.. 1992). 2.30
-
2.18
-
“0
-+ 2.02 34 zl.B8 0 k 1.74 1.80
-
inert/cat.=3/10 T =923K h44
ineticat.=5/8 -
- . 6
I 10
I t,
I 18
1.51 5
10
20
250 I
[gin]
Fig. 8: Optimal values for the production rate of butadiene, for different inert-catalyst ratios.
Fig. 9: Optimal values
for the production rate of butadiene and yA0,for different Tm
Optimal values for F~bj are shown in Fig. 10 as a function ofthe cycle duration. In this case, T,JJ was "0 2.40 chosen as the optimization variable, for three 1 different values of yA@ A con&ant value of x 2.20 Tm=923 K was selected. The curve for y,,$&=9% 32.00 c4" presents a maximum near & = 10 min, whereas the 1.80 maxima of the CurveS corresponding to y/,0= 6.5 % and 3% are located near k= 12 and 24 min, l.Oo t, [min] respectively. Therefore, the optimal duration of the Fig. 10 Optimal values for the production rate of cycle decreases substantially as mixtures with higher butadiene, for different oxygen levels. oxygen concentrations are admiUed.
European Symposium on Computer Aided Process Engineering-5
s350
CONCLUSIONS By means of a detailed modeling of the four stages of the process, the cyclic operation of a set of three fixed-bed catalytic reactors has been simulated. Since the simulation modules operate in series, it is possible to follow the behavior of the process along the cycles starting from any initial condition of the bed, until the overall mass and heat balances are satisfied. Once the autothennal cycle uniform. These gradients temperature reached during tolerated without exceeding
has been achieved, the temperature profiles along the beds are markedly nonin the solid temperature have a considerable influence on the maximum the regeneration, and strongly restrict the oxygen wncentrations that can be the maximum allowable temperature.
The production rates of butadiene per mass of catalyst are improved significantly by the dilution of the catalyst bed with inert solid. In fact, more severe regenerations are admitted in diluted beds for the same TF~IA,due to a higher thermal inertia. Besides, the optimal duration of the cycle increases as mixtures of lower oxygen concentrations
are fed at the RS, provided
an optima1 selection of T,“p has been made.
NOMENCLATURE a = external surface of catalyst, m2/m3 CA = corm. of 02, gas phase, kmol/m3 CAc= wnc. of 02, unreacted core, kmol/m3 CH = concentration of butene, gas phase, kmol/m3 Cc = wncentration of coke, kg coke/kg catalyst CH = concentration of butadiene, gas phase, kmol/m3 CH = wncentration of hydrogen gas phase, kmol/m3 crs = specific heat of the solid, W/(&cd K) cr,a = specific heat of the gas, kJ/(kg K) D, = effective diffusivity of oxygen, m2/s Fn = outlet molar flow of butadiwe, kmol/h Fobj = objective function, kmolD/(k9c,t h) h = heat transfer wefflcient, kJ/(m%K) AHR = heat of reaction, kJ/kmol k = kinetic constant for coke wmbustion, m/s b= external mass transfer wefficient, m/s L = reactor length, m Mi = molecular weight, component I, kg/km01 PD = butadiene production per cycle, km01 r, = radius of the unreacted core, m rcl, rc2 = reaction rates for coke formation from butene and butadiene, respectively., kmol/(b h) rH = reaction rate for dehydrogenation, kmol/(& h) reaction rate, kmol/(kgc,l h) rHe = n rH; effective rr = particle radius, m.
= reaction Zrol/(m$ t= time,h
rate
for
4
wnsumptig
tdeh, tpur, tregr tev’ dehydrogenation purge, regeneration and evacuation periods, h b= duration of the cycle, h T = temperature, K Tmsx= max. temperature of the cycle, K Tm = max. allowable temperature, K T, = temperature of the solid phase, K u = linear gas velocity, m/h V, = volume of the catalyst particle, m3 coke conversion Xc = yA0 = 02 molar fraction, reactor feed. z = axial position, m E= void fraction in the reactor e&ctiveness factor n= pb,cat’ catalyst bulk density, kg,&m3 pbJ = inert bulk density, b&m3 m3 pb,T = solid bulk density, kg&k& 2 ps= density of the gas phase, kg/m \vcH = coke yield factor, k&&kg,ti,, YCD= coke yield factor, kgmk$kgbutadiene Subscripts 0 = at axial position, z=O f = at the end of the stage
REFERENCES Borio D. O., M. Menwdez, and J. Santamaria (1992). Ind. Eng. Chem. Res., 3_l, 2699-2707. Borio D. O., N. S. Schbib (1994). XIV Simp. Iberoam. de Camlisis, Concepcion (Chile). Vol. 3, 12831288. Craig R. G. and J. M. Dufallo (1979), Chem. Eng. Prog., Feb., 62-65. Dumez F. J., G. F. Froment (1976). Ind. Eng. Chem. Process Des. Dev., l5,291-301. Mickley H. S., J.W. Nestor, L. A. Gould (1965). The Can. J. Chem. Eng., 61-68. Rielly T. (1977). Butadiwe, General, In: Encyclopedia of Chem. Process. and Des., (J. JMcKetta ed.), Vol. 5, pp. 110-170, Marcel Dekker.