- Email: [email protected]
New concept of cold feed injection in RFR
European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.
953
New Concept of Cold Feed Injection in RFR J. Thullie and M. Kurpas Silesian University of Technology, Department of Chemical and Process Engineering, Strzody 7,44-100 Gliwice, Poland, tel/fax +48 32 237 1266, [email protected]
Abstract A model of a reverse flow reactor with an injection of cold feed was investigated. The injection caused a decrease in maximum temperature and conversion. However the decrease in maximum temperature of catalyst bed is lower than in minimum conversion especially for small cycling time.
1. Introduction Reverse flow operation is a conmion practice nowadays. Such operation involves existence of large differences in temperature along the catalytic bed and in time as well (Matros, 1989; Matros and Bunimovich, 1996; Eigenberger and Niken, 1994). This was caused by the fact that due to heat coupling between the catalytic bed and reacting gas a wandering temperature profile exists inside the catalytic bed. The movement of this profile is of crucial importance for the process. Sometimes the temperature gradients are so high that a damage to the catalytic bed may be done. It takes place when inlet conditions have been changed. When such a situation takes place will be one of the objectives of this work. The maximum of temperature gradient inside the reactor is related (Thullie and Kurpas, 2002) to the maximum temperature of the catalyst bed. This temperature may be kept within some limits when an injection of cold gas is used. There are two problems connected with such operation. First sintering or deactivating of the catalyst may be done because of high temperature. The second one the carrier may be cracked because of temperature gradient. A simple remedy to these problems is to divide the bed in two parts and inject a cold reacting gas between them. However this kind of action will decrease the final conversion. The problem is what part of the total stream of inlet gas should be directed as an cold injection and where it should be placed when a limit of maximum temperature is imposed. The reactor investigated is shown in Figure 1. The inlet mass stream G is divided into a main inlet stream Gj and an injection stream G2. The injection stream is placed in the middle of the catalytic bed. However when different position of injection stream is investigated, to fulfil symmetry requirements two injection points should be used. When the first is placed in the distance Ax from the entrance to the reactor, the second one should be placed in position L-Ax (where L is the length of the catalytic bed). RFR is working perpetually in nonstationary state forced by the reversion of the flow through the reactor. It was revealed by numerical simulation and was confirmed by the experiments (Matros, 1985) that after each reversion of the flow reaction zone is formed. The reaction zone has much higher temperature than the rest of the bed and
954 wanders through the catalytic bed in the direction of the flow. The velocity of this wandering is much slower than the velocity of reacting gas passing through the reactor (Thullie J. et al. 2001). Cold gas, injected between the catalyst bed is mixed together with the main stream of much higher temperature. When two injection points are present, a change in direction of the flow through the reactor demands immediate change of the injection position to have always the same distance of injection point from the feed point. Of course when central injection is used the position is always the same.
Figure 1. Scheme of a switch-flow reactor with inter-stage injection. Such operation of the reactor requires a proper selection of reactor parameters (Thullie and Burghardt, 1995). When the cycling time is properly determined according to mass flow rate of the main stream a special attention should be given to mass flow rate of the injection. When it is too high in comparison to the main stream the reactor may be cooled down and the reaction on the catalyst surface will be stopped.
2. Mathematical Background To specify a working point of the reactor one should determine main flow rate, cycling time, starting temperature of the catalyst bed, inlet gas temperature inlet concentration and a share of injection in the main stream. To investigate dependencies among these parameters some basic assumptions should be made. At first a simple first order reaction A—>B is assumed and first order rate expression r^ = /:Q introduced. All parameters are assumed constant. A homogeneous model according to mass transport and a heterogeneous model according to heat transport is considered. Under these assumptions the set of governing equations (Thullie J. et al. 2001) is: f dz
Da exp
\ 1 (l-.)
(1)
955
'l = s,(e,-e)
(2)
az
r 11 Y -y
dr 3^,
Initial conditions are:
— 1
(i-n)
(3)
And boundary conditions are: i9 (z,0) = ??o
The conditions of a change in flow direction after
i?(0,r) = ??o
cycling time
z
is:
i^i^iz.T^) = i9f^\^-z,T~), where: r^ and r~ denote right hand side limit and left hand side limit at the time moment r^. A new temperature after the mixing point is calculated according to equation: ^m = ( G ^ I ^ I + < ^ o ^ . )/G
"»
^11
(4)
2 2/
The assumption of ideal mixing at the injection point was done. A standard finite difference method was used to solve the set of equations (1-3).
3. Results The use of cold gas injections gives a significant decrease in maximum catalyst temperature and a moderate decrease in conversion. At the very beginning of the start up procedure the temperature and conversion profiles are similar for both processes regardless the injection, because the initial catalyst bed temperature dominates (Figures 2-3). When the injection point has a central position (the catalyst bed was divisible into two equal parts and the injection is situated between them) the significant decrease in maximum catalyst temperature was observed in comparison to standard operation. The simultaneous decrease in conversion was not so significant especially for short cycling times (Figure 2). A decrease of Tk^ of about 30% caused 23% decrease in conversion (Figures 2-3). The results of calculations suggest that in the case of the operation limit to maximum catalyst temperature, a cold gas injection is a useful solution. The injection point should be placed in the middle of catalytic bed, with exception of the case when the limit is so high that there is no possibility to reach cycling steady state (Figure 4). For this case the of injection should be placed near the entrance to the reactor (Figure 5). This results in higher rjmin in comparison to standard conditions. The points along the curves in Figure 5 are give for different positions of injection points with injection point equal to Vi L at the edge.
956
0.8
injection 1/2 L - cycle 2 injection 1/2 L - cycle 82 no injection - cycle 2 no injection - cycle 82 0.6
0,8
injection 1/2 L - cycle 2 • injection 1/2 L - cycle 82 no injection - cycle 2 no injectbn - cycle 82
" ^
1
Figure 2. Gas temperature profiles along the reactor when inter-stage injection is applied and in standard operation (St = 20, Da = 0.0496, O) = 0,1, ^ = 1, i&ko=2,eo = l, G2=107cGi).
y
-
0,2
0.4
0,6
0,8
Figure 3. Conversion profiles reactor when inter-stage is applied and in standard (St = 20, Da = 0.0496, co = 1^0 =2,1^0= 1, G2=10%Gi).
/
1
along the injection operation 0.1, J3 = 1,
It J"^^^^ ,
^^jc^^!^^^
— M — Injection 1/4 L ^
L
^
"*
^*"-
J H
- — E j e c t i o n 1/2 L 1
a
y
—A—injection 3/4 L X — • — no injection
1 ^
J
. . . X - - . injection 1/4 L ^
1 }
. . ^ . . . injection 1/2 L 1 -.-A-.-injection 3/4 L
[
. . . e . . - n o injection
J
10% Gi
- ^ T =4
c
1
Figure 4. Comparison of r]mm = / (^kmax) for Figure 5. Comparison of rimm = / ( ^ m J different location of injection points, and two for different cycling times (St = 20, injection flow rates (St = 20, Da=0.0496, Da=0.0496, CO = 0.1, /? = 7, ?%o= 2, (0 ^0.1, P=l, i^o= 2,1^0=1 G2 =5%Gi). 1^0=1 G2 =5%Gi).
When the cycling time is increasing, regardless the location of injection point, the number of cycles which gives pseudo-steady state operation decreases (Figure 6). This means that one should perform a lot of short cycles or not so many long cycles. The most profound decrease in maximum temperature with comparatively small decrease of minimum conversion is observed for small cycling times.
957 For small mass flow rate of injection gas no influence on to the start up time is observed.
ooo222fififi9fififlfiAA*A*f*****A^*^f
080000000
^i o •
3,5
•
o
AA^^^^^^^^T•
•
AA
ddddAAAAA^AAAAAAAAfii
••••••••
QpnaanDiiiDDDaannnaipaaaaaaaaaijiaaaaaaaaail] • injection -1/2 ' A injection - 3/4
^Tc=3
• no injection
2.5
D injecti(Mi -1/2 A injection - 3/4 f
1>- ^ = 6
o no injection
10
20
40
30
50 number of cycling
Figure 6. Comparison of catalyst maximum temperature for different cycling times for the case with cold gas injection and standard operation (with no injection) (St = 20, Da = 0.0744, co=0.l J3= 7, i^o= 2, i9o== I G2 = 10% d).
4. Conclusions 1. The results of calculations suggest that the use of cold gas injections gives the significant decrease in maximum catalyst temperature and moderate decrease in conversion. 2. The best position of the injection point is usually the middle of the catalyst bed. However when the temperature limit is so high that PSS is not achieved the flow rate of the injection should be lowered. If it is not possible the place of the injection should be moved in the direction of the reactor inlet. 3. When cold gas injection is used the most profound decrease in maximum temperature with comparatively small decrease of minimum conversion is observed for small cycling times.
5. Symbols j)a =
k^L-exp
5/ = ^ ^ : ^ ^ P-S*"o
(-y)
_ Damkohler number, - Stanton number,
k
- rate constant, 1/s
koo - frequency coefficient, 1/s
958 X
- dimensionless space variable,
L
- length of reactor, m
- dimensionless adiabatic temperature rise,
r^
- ration rate, kmol/m s
- dimensionless activation energy,
T
- temperature, K
L AO
fi = E y =
•
- dimensionless gas temperature, TQ
t? = -
'0
- dimensionless temperature of catalyst, • dimensionless time.
S'L
{^•^)pk-^pk
- ratio of heat capacities of gas to catalyst. ,2/^3
- inlet temperature, K - catalyst temperature, K
UQ
- lineary velocity, m/s
X
- space variable, m
Gy
- specific surface area, m /m"
a^
- heat transfer coefficient, J/m^Ks
^^'
- concentration of reference component, kmol/m^
e
- void fraction, m^/m^
Cp
- specific heat, J/kg K
p
- density, kg/m^
E
~ ration activation energy, kJ/kmol
T]
- conversion of component A
G
- flow rate of gas, kmol/s
R
- g a s constans, kJ/kmol K
AH
- heat of reaction, kJ/kmol
t
- time, s
6. References Eigenberger, G. and Niken, V., 1994, Internal. Chem. Eng. 34,4-16. Matros, Yu., 1989, Studies in surface science and catalysis, vol. 43. Utrecht The Netherlands. Matros, Yu., 1985, Elsevier, Amsterdam. Matros, Yu., and Bunimovich, G., 1996, Catal. Rev. Sci. Eng. 38, 1. ThuUie, J. and Burghardt, A., 1995, Chem. Eng. Sci. 50, 2299-2309. Thullie, J. and Kurpas, M., 2002, Inz. Chem. Proc. 23, 309-324 (in Polish). Thullie, J., Kurpas, M., Bodzek, M., 2001, Inz. Chem. Proc. 22, 3E, 1405 (in Polish).
953
New Concept of Cold Feed Injection in RFR J. Thullie and M. Kurpas Silesian University of Technology, Department of Chemical and Process Engineering, Strzody 7,44-100 Gliwice, Poland, tel/fax +48 32 237 1266, [email protected]
Abstract A model of a reverse flow reactor with an injection of cold feed was investigated. The injection caused a decrease in maximum temperature and conversion. However the decrease in maximum temperature of catalyst bed is lower than in minimum conversion especially for small cycling time.
1. Introduction Reverse flow operation is a conmion practice nowadays. Such operation involves existence of large differences in temperature along the catalytic bed and in time as well (Matros, 1989; Matros and Bunimovich, 1996; Eigenberger and Niken, 1994). This was caused by the fact that due to heat coupling between the catalytic bed and reacting gas a wandering temperature profile exists inside the catalytic bed. The movement of this profile is of crucial importance for the process. Sometimes the temperature gradients are so high that a damage to the catalytic bed may be done. It takes place when inlet conditions have been changed. When such a situation takes place will be one of the objectives of this work. The maximum of temperature gradient inside the reactor is related (Thullie and Kurpas, 2002) to the maximum temperature of the catalyst bed. This temperature may be kept within some limits when an injection of cold gas is used. There are two problems connected with such operation. First sintering or deactivating of the catalyst may be done because of high temperature. The second one the carrier may be cracked because of temperature gradient. A simple remedy to these problems is to divide the bed in two parts and inject a cold reacting gas between them. However this kind of action will decrease the final conversion. The problem is what part of the total stream of inlet gas should be directed as an cold injection and where it should be placed when a limit of maximum temperature is imposed. The reactor investigated is shown in Figure 1. The inlet mass stream G is divided into a main inlet stream Gj and an injection stream G2. The injection stream is placed in the middle of the catalytic bed. However when different position of injection stream is investigated, to fulfil symmetry requirements two injection points should be used. When the first is placed in the distance Ax from the entrance to the reactor, the second one should be placed in position L-Ax (where L is the length of the catalytic bed). RFR is working perpetually in nonstationary state forced by the reversion of the flow through the reactor. It was revealed by numerical simulation and was confirmed by the experiments (Matros, 1985) that after each reversion of the flow reaction zone is formed. The reaction zone has much higher temperature than the rest of the bed and
954 wanders through the catalytic bed in the direction of the flow. The velocity of this wandering is much slower than the velocity of reacting gas passing through the reactor (Thullie J. et al. 2001). Cold gas, injected between the catalyst bed is mixed together with the main stream of much higher temperature. When two injection points are present, a change in direction of the flow through the reactor demands immediate change of the injection position to have always the same distance of injection point from the feed point. Of course when central injection is used the position is always the same.
Figure 1. Scheme of a switch-flow reactor with inter-stage injection. Such operation of the reactor requires a proper selection of reactor parameters (Thullie and Burghardt, 1995). When the cycling time is properly determined according to mass flow rate of the main stream a special attention should be given to mass flow rate of the injection. When it is too high in comparison to the main stream the reactor may be cooled down and the reaction on the catalyst surface will be stopped.
2. Mathematical Background To specify a working point of the reactor one should determine main flow rate, cycling time, starting temperature of the catalyst bed, inlet gas temperature inlet concentration and a share of injection in the main stream. To investigate dependencies among these parameters some basic assumptions should be made. At first a simple first order reaction A—>B is assumed and first order rate expression r^ = /:Q introduced. All parameters are assumed constant. A homogeneous model according to mass transport and a heterogeneous model according to heat transport is considered. Under these assumptions the set of governing equations (Thullie J. et al. 2001) is: f dz
Da exp
\ 1 (l-.)
(1)
955
'l = s,(e,-e)
(2)
az
r 11 Y -y
dr 3^,
Initial conditions are:
— 1
(i-n)
(3)
And boundary conditions are: i9 (z,0) = ??o
The conditions of a change in flow direction after
i?(0,r) = ??o
cycling time
z
is:
i^i^iz.T^) = i9f^\^-z,T~), where: r^ and r~ denote right hand side limit and left hand side limit at the time moment r^. A new temperature after the mixing point is calculated according to equation: ^m = ( G ^ I ^ I + < ^ o ^ . )/G
"»
^11
(4)
2 2/
The assumption of ideal mixing at the injection point was done. A standard finite difference method was used to solve the set of equations (1-3).
3. Results The use of cold gas injections gives a significant decrease in maximum catalyst temperature and a moderate decrease in conversion. At the very beginning of the start up procedure the temperature and conversion profiles are similar for both processes regardless the injection, because the initial catalyst bed temperature dominates (Figures 2-3). When the injection point has a central position (the catalyst bed was divisible into two equal parts and the injection is situated between them) the significant decrease in maximum catalyst temperature was observed in comparison to standard operation. The simultaneous decrease in conversion was not so significant especially for short cycling times (Figure 2). A decrease of Tk^ of about 30% caused 23% decrease in conversion (Figures 2-3). The results of calculations suggest that in the case of the operation limit to maximum catalyst temperature, a cold gas injection is a useful solution. The injection point should be placed in the middle of catalytic bed, with exception of the case when the limit is so high that there is no possibility to reach cycling steady state (Figure 4). For this case the of injection should be placed near the entrance to the reactor (Figure 5). This results in higher rjmin in comparison to standard conditions. The points along the curves in Figure 5 are give for different positions of injection points with injection point equal to Vi L at the edge.
956
0.8
injection 1/2 L - cycle 2 injection 1/2 L - cycle 82 no injection - cycle 2 no injection - cycle 82 0.6
0,8
injection 1/2 L - cycle 2 • injection 1/2 L - cycle 82 no injection - cycle 2 no injectbn - cycle 82
" ^
1
Figure 2. Gas temperature profiles along the reactor when inter-stage injection is applied and in standard operation (St = 20, Da = 0.0496, O) = 0,1, ^ = 1, i&ko=2,eo = l, G2=107cGi).
y
-
0,2
0.4
0,6
0,8
Figure 3. Conversion profiles reactor when inter-stage is applied and in standard (St = 20, Da = 0.0496, co = 1^0 =2,1^0= 1, G2=10%Gi).
/
1
along the injection operation 0.1, J3 = 1,
It J"^^^^ ,
^^jc^^!^^^
— M — Injection 1/4 L ^
L
^
"*
^*"-
J H
- — E j e c t i o n 1/2 L 1
a
y
—A—injection 3/4 L X — • — no injection
1 ^
J
. . . X - - . injection 1/4 L ^
1 }
. . ^ . . . injection 1/2 L 1 -.-A-.-injection 3/4 L
[
. . . e . . - n o injection
J
10% Gi
- ^ T =4
c
1
Figure 4. Comparison of r]mm = / (^kmax) for Figure 5. Comparison of rimm = / ( ^ m J different location of injection points, and two for different cycling times (St = 20, injection flow rates (St = 20, Da=0.0496, Da=0.0496, CO = 0.1, /? = 7, ?%o= 2, (0 ^0.1, P=l, i^o= 2,1^0=1 G2 =5%Gi). 1^0=1 G2 =5%Gi).
When the cycling time is increasing, regardless the location of injection point, the number of cycles which gives pseudo-steady state operation decreases (Figure 6). This means that one should perform a lot of short cycles or not so many long cycles. The most profound decrease in maximum temperature with comparatively small decrease of minimum conversion is observed for small cycling times.
957 For small mass flow rate of injection gas no influence on to the start up time is observed.
ooo222fififi9fififlfiAA*A*f*****A^*^f
080000000
^i o •
3,5
•
o
AA^^^^^^^^T•
•
AA
ddddAAAAA^AAAAAAAAfii
••••••••
QpnaanDiiiDDDaannnaipaaaaaaaaaijiaaaaaaaaail] • injection -1/2 ' A injection - 3/4
^Tc=3
• no injection
2.5
D injecti(Mi -1/2 A injection - 3/4 f
1>- ^ = 6
o no injection
10
20
40
30
50 number of cycling
Figure 6. Comparison of catalyst maximum temperature for different cycling times for the case with cold gas injection and standard operation (with no injection) (St = 20, Da = 0.0744, co=0.l J3= 7, i^o= 2, i9o== I G2 = 10% d).
4. Conclusions 1. The results of calculations suggest that the use of cold gas injections gives the significant decrease in maximum catalyst temperature and moderate decrease in conversion. 2. The best position of the injection point is usually the middle of the catalyst bed. However when the temperature limit is so high that PSS is not achieved the flow rate of the injection should be lowered. If it is not possible the place of the injection should be moved in the direction of the reactor inlet. 3. When cold gas injection is used the most profound decrease in maximum temperature with comparatively small decrease of minimum conversion is observed for small cycling times.
5. Symbols j)a =
k^L-exp
5/ = ^ ^ : ^ ^ P-S*"o
(-y)
_ Damkohler number, - Stanton number,
k
- rate constant, 1/s
koo - frequency coefficient, 1/s
958 X
- dimensionless space variable,
L
- length of reactor, m
- dimensionless adiabatic temperature rise,
r^
- ration rate, kmol/m s
- dimensionless activation energy,
T
- temperature, K
L AO
fi = E y =
•
- dimensionless gas temperature, TQ
t? = -
'0
- dimensionless temperature of catalyst, • dimensionless time.
S'L
{^•^)pk-^pk
- ratio of heat capacities of gas to catalyst. ,2/^3
- inlet temperature, K - catalyst temperature, K
UQ
- lineary velocity, m/s
X
- space variable, m
Gy
- specific surface area, m /m"
a^
- heat transfer coefficient, J/m^Ks
^^'
- concentration of reference component, kmol/m^
e
- void fraction, m^/m^
Cp
- specific heat, J/kg K
p
- density, kg/m^
E
~ ration activation energy, kJ/kmol
T]
- conversion of component A
G
- flow rate of gas, kmol/s
R
- g a s constans, kJ/kmol K
AH
- heat of reaction, kJ/kmol
t
- time, s
6. References Eigenberger, G. and Niken, V., 1994, Internal. Chem. Eng. 34,4-16. Matros, Yu., 1989, Studies in surface science and catalysis, vol. 43. Utrecht The Netherlands. Matros, Yu., 1985, Elsevier, Amsterdam. Matros, Yu., and Bunimovich, G., 1996, Catal. Rev. Sci. Eng. 38, 1. ThuUie, J. and Burghardt, A., 1995, Chem. Eng. Sci. 50, 2299-2309. Thullie, J. and Kurpas, M., 2002, Inz. Chem. Proc. 23, 309-324 (in Polish). Thullie, J., Kurpas, M., Bodzek, M., 2001, Inz. Chem. Proc. 22, 3E, 1405 (in Polish).