- Email: [email protected]
Modelling of spatiotemporal patterns in a sequence of catalytic monolith reactors
Pergamon
Chemical Engineering Science, Vol. 51, No. 11, pp. 3157-3162, 1996 Copyright 1~ 1996Eht~i~ Sci~ce Ltd Printed in Great Britain. All ri~ts 0009-2509/96 $15.00 + 0.00
sooog.2sog(96)oo213-8
MODELLING OF SPATIOTEMPORAL PATTERNS IN A SEQUENCE OF CATALYTIC MONOLITH REACTORS PAVEL PINKAS, DALIMIL SNITA, MILAN KUBICEK and MILOS MAREK Prague Institute of Chemical Chemical Technology, Technick~ 5, 166 28 Prague 6, Czech Republic A b s t r a c t - System of monolith metallic (M) and ceramic (C) catalytic reactors described by two-phase model with axial dispersion is studied for CO oxidation. Values of kinetic and transport parameters are fitted to experimental ignition data. Periodic flow reversal is shown to stabilize temperature fronts in the C-M-C and M-C-M combination of monoliths. Existence of unsymmetric spatial temperature regimes and the possibility of adaptive control of flow direction switching are demonstrated. INTRODUCTION Metallic and ceramic catalytic monolith reactors are used for control of volatile hydrocarbon emissions (VOC) of low and moderate concentrations both in mobile and stationary sources. The exhaust flow rates are often determined by the process conditions. Hence transient behaviour of monolith reactors has become the subject of continuous research. The aim is to find systems with a lower light-off temperature and faster ignition with a minimum necessary external heat supply. The heat recovery and maintenance of operating (ignited) state of the reactor system under transient conditions and low content of combustibles are other interesting aspects of the control of such reactors (Barresi et al., 1992, Pfefferle and Pfefferle, 1987, Dvorak et al., 1994). The dynamic light-off performance can be influenced by the choice of low thermal mass high thermal conductivity metallic monoliths (Andersson and Sch55n, 1993; Pinkas et al., 1994). Metallic electrically heated monoliths combined with conventional ceramic ones are considered as a proper control strategy for meeting cold start and overall new stringent emission limits by automobile manufacturers (Cooper, 1994; Oh et al., 1994). The combination of a short metallic catalytic preheater with a ceramic monolith catalyst is the mostly considered arrangement in catalytic car afterburners (Oh et al., 1993, 1994; Pinkas et al., 1994). The periodic flow reversal is often considered for applications in VOC control in situations where the recovery of reaction heat is critical. In the standard configuration (Matros, 1989, Eigenberger and Nieken, 1988, Vanden Bussche et al., 1993) the front and end parts of the catalyst bed (monolith) act as regenerative heat exchangers for feed and effluent allowing even weakly exothermic reactions to be operated nearly autothermally at high reaction temperature. The heat is usually recovered at the center of the reactor. The combination of ceramic and metallic monoliths studied in this paper can have better dynamic properties from the point of view of not only the ignition at the startup but also of the heat recovery in the reverse flow operation. TWO PHASE AXIAL DISPERSION MODEL The model used in this paper considers variations of concentrations and temperature in the solid phase of the catalytic monolith and in the fluid (gas) phase containing combustible and inert components. We use as an experimental and modelling example a single reaction of the type A + B ~ C, i. e., CO + ½ 02 ---*COs. The spatially one-dimensional model with axial heat and mass transport in the fluid phase and axial heat conduction in the solid phase was found to be appropriate from the point of view of comparison of experimental and modelled data (Pinkas et al., 1994 ). The model equations are in the form: Fluid phase mass balance
Oc
O~c
- ~ = o . ~o~
~
a
(vc) - k c - i ( c - c*).
(1)
3157
3158
R PINKA$et al.
Fluid phase heat balance
or=
0v
O-T
(2)
: Ox---7 - vpep-~z
Mass balance on the monolith solid phase
e . -Oc* -~
=
k
c . - ~a_ e ( c - c * ) - T C ( c * , T *
).
(3)
Heat balance in the monolith solid phase
*c* OT* P P Ot
=
+
02T * "V~'O-~'x2+(-AHR)7~(c*'T*)+
.v27_" ( r - r ' ) -
- rw)
(4)
Boundary conditions are in the form
Oe voco = v(O,t)c(O,t)- n=-~x (O,t),
(5)
povo%To = po(O, t)vo(O, t)%T(O, t) - ,~ _~x (O,
(6)
OT L t OT* OOTx * ( o , t ) = -~x OC'L,t) ( = -~x ( , ) = --~-x ( L , t) = O.
(7)
The reaction rate expression of the Langmuir-Hinshelwood type was used in the modelling of experiments with CO combustion C02 [1 + K ( T ' ) . c'] ~"
~(c*,T*)= k(T*) c* •
"
(8)
The above axial dispersion model can be used also for short reactors where entrance effects and axial dispersion are important. NUMERICAL SIMULATIONS For numerical simulations of the system of parabolic PDE's (1) - (7) we used the Crank-Nicolson difference method with such approximations of terms on the old time step profile that the problem became decomposed. This procedure then enables one to obtain the profile at the new time step subsequently for T*, T, c and c* using three subsequent factorizations (solutions of the system of linear equations with three-diagonal matrix) for T*, T and c; the profile of c* values is then determined by means of quasilinearisation technique. The undecomposed problem would require the solutions of the systems with band matrices. A modular approach similar to flow-sheeting in CAD of chemical plant systems was used for the modelling of sequence of monolith reactors. The role of the individual module is played by the simulation of a single new time profile in the given reactor. The sequence of calling of individual modules (corresponds to the studied schema of coupling of monolith reactors) and the transfer of information between the modules is contained for each system in the master program (it determines only the sequence of calls of the the subroutines in the considered cycle). The simulation of the flow reversal is organized in a similar way. After the chosen reversal at half-period a symmetric exchange of variables with respect to the center of each reactor is made and the calling sequence is reversed for the next flow reversal half-period. FITTING OF KINETIC AND TRANSPORT PARAMETERS The most important phenomena in the description of the transient behaviour of combustion of VOC are ignition and extinction of combustion fronts. The values of reaction and transport parameters further used in simulations were adjusted to fit experimentally determined ignition and extinction temperature profiles on the system consisting of the metallic and ceramic monolith similarly, as it was made earlier for single ceramic monolith, cf. Pinkas et al. (1994), where the properties of catalytic monoliths and experimental arrangement are described. The coexistence of stationary states (hysteresis) limited by ignition and extinction curves was observed also in the sequence of single metallic and single ceramic monoliths at higher values of inlet CO concentrations. Its use for fitting of reaction and transport parameters is illustrated in Fig. 1. In experiments with the cascade of monoliths we followed the dependence of the outlet conversion from the last monolith on the temperature of the gas entering the first monolith. The inlet temperature
3159
A sequence of catalytic monolith reactors
v
0.0525
Tw
298
c~,me,az,ic
0.46 A;,,ne~au~c 11.5 P~ne,amc 7220 ~rnetamc 0.6836 AHR 2.78 x 105 ~e,v < 0 ; 1600>
[K] [J k g - ' K -1] [J m -1 s -1 K -1] [k9 m -s] [1]
[J tool -1]
2.5
[m s -1]
a 540 c; . . . . . . ic 0.94 A*,eerami¢ 0.18
[m -1] [J kg -1 g -1] [J m -1 s -1 g -1]
p; . . . . ~¢ c .... mi¢ En
2500
[kg m -a]
0.6836 1.01×105
[1] [J tool -1]
[Win -2K -l] Table 1: Values of parameters
a
0.~
l
b,
F
0.8
0.6
I
t
0.4
0.6
~
0.4
°-]
0.2 0
"i
d$.,,,~..A2[,h
,,o
oo
,
Figure 1: Comparison of a) measured and b) simulated hysteresis curves, MC sequence of monoliths, 2% CO
was increased in small steps to reach the stationary state at a given inlet temperature between practically zero conversion and complete outlet conversion. The procedure was then reversed and the inlet temperature was decreased. The difference between the ignition and extinction temperature then determines the width of the hysteresis region. The fitting of simulated conversion - inlet temperature profiles is used for adjustment of model parameters. Ignition occurs in experiments for 2% CO at the inlet approximately at 140°C, extinction at 100°C. In the simulations is ignition temperature equal to 135°C and extinction temperature is again approximately equal to 100°C. Similar agreement between measured and simulated ignition curves were obtained for 1% CO (here no hysteresis exists) and 3% at the inlet. Simulations of dynamic behaviour of different arrangements of sequences of monoliths was then made on the basis of the values of parameters determined from the above comparison of measured and modelled ignition and extinction phenomena for an inlet concentration of CO equal 2.5%. Characteristic values of chosen parameters used in simulations are given in Table 1. TRANSIENT BEHAVIOUR OF SEQUENCE OF MONOLITHS The metallic converter has comparatively a high thermal conductivity and a low thermal capacity. The ceramic converter has just the opposite properties. These properties and their dynamic consequences can be utilized in the sequence of converters. Thermal response of the metallic converter is faster and thus it can be conveniently used for preheating or heat removal. In the following we shall illustrate the dynamic behaviour of the system consisting of three converters in the arrangements C-M-C and M-C-M and then we shall discuss the effects of introducing flow reversals. The above symmetric arrangements were chosen with regard to the use of flow reversal as otherwise the M-C arrangement has mostly better transient characteristics. In both systems we shall consider the heat removal from metallic monoliths (ceramic monoliths will be considered adiabatic). The overall mass of the converters will be the same as that of the M-C system studied earlier (Pinkas et al., 1994). We shall follow the effect of the amount of removed heat on the operating stability of the system. An example of the ignition and propagation of combustion fronts in the C-M-C system with all catalytic monoliths taken as adiabatic is shown in Figs 2a,b. We can observe in Fig 2a, where spatial temperature profiles are presented in 5 s intervals, that under the used conditions the propagating temperature front initiated at the center metallic converter is propagating at first into the following ceramic monolith and is then subsequently blown out from the last ceramic monolith. This is connected with the decrease of the outlet conversion leading finally to total extinction of the reaction (cf. Fig. 2b). The change of the
3160
P. P1NKASet al. a 700
'C
M
C
waveFtol~g~iou
6OO
I
'
I
0.6
500
0.4 400
300 0.05
C
700
'C
0.1 0.15 axial coordinate [m]
M
0
0.2
,
i
200
250
300
~*me [s]
C
'
1
'f
0.8 /
6OO 150
i|
0.6 500 0.4 400 0.2 OS
300 0.05
0.1 0,15 axial coordinate [m]
0 0.2
,
i
100
200
300 lime (s]
I
I
400
500
600
Figure 2: Ignition and propagation of combustion fronts in C-M-C system of monoliths; a) sequence of temperature profiles in 5 s intervals without flow reversal; initial temperatures ceramic monoliths 298 K metallic monolith 773 K; fluid inlet temperature 393 K. b) outlet conversion without flow reversal, c) spatial temperature patterns with flow reversal (TR = 75 s), d) outlet conversion with flow reversal.
direction of propagating front can be achieved by the introduction of the inlet flow into the last reactor and is then maintained by repeated (e.g., periodic or controlled according to chosen control algorithm) flow reversal. Typical spatiotemporal patterns after introduction of periodic flow reversal are shown in Fig. 2c. The propagating temperature front is after 300 s stabilized in the center part of the monolith system. The time course of the outlet conversion, depicted in Fig. 2d, illustrates fast transition to nearly complete outlet conversion within several periods of flow reversal. The vertical lines in the figure correspond to times of flow reversals where parts of the unburned CO are blown out from the reactor system. Comparison of C-M-C and M-C-M systems Example of results of two parametric comparative study of the stabilized time averaged conversion in C-M-C and M-C-M systems are shown in Figs 3a,b. Ceramic monoliths were considered adiabatic. Two studied parameters were the coefficient of external heat transfer from the metallic monolith acw (effective value) and the length of the flow reversal half- period TR. Metallic monoliths were initially heated up to the same temperature and transient simulations were used to determine whether the regime with high conversion or extinction regime is reached. Parametric plane acw vs TR in Fig. 3 is divided into high conversion and extinction regions. We can observe that the high conversion regime in the C-M-C sequence (Fig. 3a) is reached whenever the heat removal from the metallic converter is not too high or the flow reversal half-period TR not too long. Hence TR is only limited from above. If TR is high and the propagating temperature wave already starts to leave the last monolith, then the system becomes extinguished. The residence time of propagating wave depends on the initial temperature of the metallic converter, inlet CO concentration and temperature and on the lengths of monoliths. Example of stationary catalyst temperature profiles for TR = 10s is illustrated in Fig. 4a. Here the full line corresponds to the flow from the left and the dotted line to the flow from the right both at the end of the half period. The profile is mirror symmetric with respect to flow reversal. In the M-C-M system the range of flow reversal periods for the high conversion regime is limited both from below and above, cf. Fig. 3b. U n s y m m e t r i c s t a t i o n a r y spatial t e m p e r a t u r e p a t t e r n s in C - M - C s y s t e m If a high amount of heat is withdrawn from the metallic converter in the C-M-C system and the flow reversal half-period is sufficiently low, so that the high conversion regime is still maintained, we can observe that
3161
A sequence of catalytic monofith reactors
~Cw
Ofeto
1400 1200 1000 800
extinction ......... . + . - ' " ' " ' - + . . . . . . . . . .. -.° . . . . . . . . . . . . . -..°..
+.°..
high conversion 10
extinction
400 2O0
I
I
I
I
I
I
20
30
40
50
60
70
80
600 40O 200 0
600
"'°-+ +
I
1400 1200 1000 800
I
90 100 TR Is]
, .,----... . . . . . . . . . . . . . . . . . . . . ,..+ •":
0
high
conversion
" ........ ,
'-.
i
l
I
I
50
100
150
200
I
250 TR [s]
Figure 3: Conversion as a function of heat removal rate and flow reversal half-period; a) C-M-C system; b) M-C-M system.
b
380
s+o
,
,
,
!~---.~
,
560 540
|
|
/"
520
.-"+
500
..../+ +
i ".,
480 460 440 42O
420 ~
400 0
0.02
0.04
0.06 0.08 axial coordinate Ira]
0.1
0.02
0.12
0.04
0.06 0.08 axial coordinate Ira]
0.1
0.12
Figure 4: Spatial temperature profiles, flow-rate reversal, C-M-C system; a) symmetric profile; b) unsymmetric profile.
I
b
i
0.9
0.9 -
0.8
oO+, oo+ l I IIIIII]llI!llll
0.7 0.6 0.5 0.4 0.3
0.3 i 0.2
0.2
0.1 -
0.1 0
-0.1
0
'
too
'
2oo
'
3oo
'
4oo
'
5oo
~e
-0d
tOO
200
300
400
500
60<3
[sl
Figure 5: C-M-C system with flow reversal adaptive control; a) flow reversal period stabilization via control, b) blow out under improper control.
3162
P. I~NKASet a£
the reaction front is not crossing the region of lower temperature on the metallic monolith and spatially unsymmetric temperature profiles arise. The highest temperature is reached in the last ceramic segment (counted at the start of the system simulation). An example of such stabilized profiles is given in Fig. 4b. The profile is unsymmetric with respect to flow reversal. Evidently, spatially mirror image profiles also exist; they can be reached by starting the flow into the last reactor. A d a p t i v e flow reversal c o n t r o l Adaptive control of flow reversal in the C-M-C system can be, for example, realized in such a way that two thermocouples are located at two ends of the system, i.e. at x = XL in the left ceramic monolith and at x = xR in the right ceramic monolith. If we denote the corresponding limit temperatures T~ and T~, respectively, we can apply the following adaptive control algorithm: a) if the flow is from the left to the right and T*(xR) > T~, then the flow direction is reversed b) if the flow is from the right to the left and T*(XL) > T~, then the flow direction is reversed. Fast transition to the high conversion regime then occurs for proper choice of XL, xR, T~, T/~. An example of such a choice is shown in Fig. 5a where the stabilized flow reversal half-period TR - 6. Improper choice of values of T~, R can lead either to blow out (T~,R too high, cf Fig 5b) or to trivial satisfaction of both switching conditions (T~, R too low). CONCLUSIONS Combination of monoliths with the same catalyst on metallic and ceramic carriers with the use of flow reversal can be used to stabilize different types of temperature regimes in the system. Even richer possibilities are available if catalysts of different types (possibly with different activities) are used in multiple reaction systems. The same CAD - type software can also be used for the simulation of a combination of monolith catalysts with regenerating self - cleaning particle traps and filters currently studied for the control of emissions from diesel motor vehicles. Notation: TR - - flow reversal half-period, ZL, xR, T~ and T~ are defined in the text, other symbols see Pinkas et al., 1994.
Acknowledgment: This work was partially supported by the grant No. 104/94/0649, Czech Grant Agency, and EU COST grant CIPA-CT92-4021. REFERENCES
Andersson, S. L. and Sch55n, N. H., 1993, Ind. Engng Chem. 32, 1081. Barresi, A. A., Hung, S. L. and Pfefferle, L. D., 1992, Chem. Engng J. 50 123. Cooper, B. J., 1994, Platinum Metals Rev. 38, 2. Dvof£k, L., Pinkas, P. and Marek, M., 1994, Catalysis Today 20 , 449. Eigenberger, G. and Nieken, U., 1988, Chem. Engng Sci. 42, 2109. Matros, Y. S., 1989, Studies in Surface Sci. and Catalysis 43 Oh, S. H., Bissett E. J., and Battiston, P. A., 1993, Ind. Engng Chem. Res. 32 1560. Oh, S. H. and Bisset, E. J., 1994, I. E. C. Res. 33, 3086. Pfefferle, L. D. and Pfefferle, W. C., 1987, Catal. Rev. - Sci. Engng 29, 219. Pinkas, P., Snita, D., Kubitek, M. and Marek, M., 1994, Chem. Engng Sci. 49, 5347. l~eh£tek, J., Kubitek, M., and Marek, M., 1992, Chem. Engng Sci. 47, 2897. Vanden Bussche, K. M., Neophytides, S. N., Zolotarskii, I. A. and Froment, G. F, 1993, Chem. Engng Sci. 48, 3335. Young, L. C. and Finlayson, B. A., 1976, A.I.Ch.E.J. 22 331 & 343.
Chemical Engineering Science, Vol. 51, No. 11, pp. 3157-3162, 1996 Copyright 1~ 1996Eht~i~ Sci~ce Ltd Printed in Great Britain. All ri~ts 0009-2509/96 $15.00 + 0.00
sooog.2sog(96)oo213-8
MODELLING OF SPATIOTEMPORAL PATTERNS IN A SEQUENCE OF CATALYTIC MONOLITH REACTORS PAVEL PINKAS, DALIMIL SNITA, MILAN KUBICEK and MILOS MAREK Prague Institute of Chemical Chemical Technology, Technick~ 5, 166 28 Prague 6, Czech Republic A b s t r a c t - System of monolith metallic (M) and ceramic (C) catalytic reactors described by two-phase model with axial dispersion is studied for CO oxidation. Values of kinetic and transport parameters are fitted to experimental ignition data. Periodic flow reversal is shown to stabilize temperature fronts in the C-M-C and M-C-M combination of monoliths. Existence of unsymmetric spatial temperature regimes and the possibility of adaptive control of flow direction switching are demonstrated. INTRODUCTION Metallic and ceramic catalytic monolith reactors are used for control of volatile hydrocarbon emissions (VOC) of low and moderate concentrations both in mobile and stationary sources. The exhaust flow rates are often determined by the process conditions. Hence transient behaviour of monolith reactors has become the subject of continuous research. The aim is to find systems with a lower light-off temperature and faster ignition with a minimum necessary external heat supply. The heat recovery and maintenance of operating (ignited) state of the reactor system under transient conditions and low content of combustibles are other interesting aspects of the control of such reactors (Barresi et al., 1992, Pfefferle and Pfefferle, 1987, Dvorak et al., 1994). The dynamic light-off performance can be influenced by the choice of low thermal mass high thermal conductivity metallic monoliths (Andersson and Sch55n, 1993; Pinkas et al., 1994). Metallic electrically heated monoliths combined with conventional ceramic ones are considered as a proper control strategy for meeting cold start and overall new stringent emission limits by automobile manufacturers (Cooper, 1994; Oh et al., 1994). The combination of a short metallic catalytic preheater with a ceramic monolith catalyst is the mostly considered arrangement in catalytic car afterburners (Oh et al., 1993, 1994; Pinkas et al., 1994). The periodic flow reversal is often considered for applications in VOC control in situations where the recovery of reaction heat is critical. In the standard configuration (Matros, 1989, Eigenberger and Nieken, 1988, Vanden Bussche et al., 1993) the front and end parts of the catalyst bed (monolith) act as regenerative heat exchangers for feed and effluent allowing even weakly exothermic reactions to be operated nearly autothermally at high reaction temperature. The heat is usually recovered at the center of the reactor. The combination of ceramic and metallic monoliths studied in this paper can have better dynamic properties from the point of view of not only the ignition at the startup but also of the heat recovery in the reverse flow operation. TWO PHASE AXIAL DISPERSION MODEL The model used in this paper considers variations of concentrations and temperature in the solid phase of the catalytic monolith and in the fluid (gas) phase containing combustible and inert components. We use as an experimental and modelling example a single reaction of the type A + B ~ C, i. e., CO + ½ 02 ---*COs. The spatially one-dimensional model with axial heat and mass transport in the fluid phase and axial heat conduction in the solid phase was found to be appropriate from the point of view of comparison of experimental and modelled data (Pinkas et al., 1994 ). The model equations are in the form: Fluid phase mass balance
Oc
O~c
- ~ = o . ~o~
~
a
(vc) - k c - i ( c - c*).
(1)
3157
3158
R PINKA$et al.
Fluid phase heat balance
or=
0v
O-T
(2)
: Ox---7 - vpep-~z
Mass balance on the monolith solid phase
e . -Oc* -~
=
k
c . - ~a_ e ( c - c * ) - T C ( c * , T *
).
(3)
Heat balance in the monolith solid phase
*c* OT* P P Ot
=
+
02T * "V~'O-~'x2+(-AHR)7~(c*'T*)+
.v27_" ( r - r ' ) -
- rw)
(4)
Boundary conditions are in the form
Oe voco = v(O,t)c(O,t)- n=-~x (O,t),
(5)
povo%To = po(O, t)vo(O, t)%T(O, t) - ,~ _~x (O,
(6)
OT L t OT* OOTx * ( o , t ) = -~x OC'L,t) ( = -~x ( , ) = --~-x ( L , t) = O.
(7)
The reaction rate expression of the Langmuir-Hinshelwood type was used in the modelling of experiments with CO combustion C02 [1 + K ( T ' ) . c'] ~"
~(c*,T*)= k(T*) c* •
"
(8)
The above axial dispersion model can be used also for short reactors where entrance effects and axial dispersion are important. NUMERICAL SIMULATIONS For numerical simulations of the system of parabolic PDE's (1) - (7) we used the Crank-Nicolson difference method with such approximations of terms on the old time step profile that the problem became decomposed. This procedure then enables one to obtain the profile at the new time step subsequently for T*, T, c and c* using three subsequent factorizations (solutions of the system of linear equations with three-diagonal matrix) for T*, T and c; the profile of c* values is then determined by means of quasilinearisation technique. The undecomposed problem would require the solutions of the systems with band matrices. A modular approach similar to flow-sheeting in CAD of chemical plant systems was used for the modelling of sequence of monolith reactors. The role of the individual module is played by the simulation of a single new time profile in the given reactor. The sequence of calling of individual modules (corresponds to the studied schema of coupling of monolith reactors) and the transfer of information between the modules is contained for each system in the master program (it determines only the sequence of calls of the the subroutines in the considered cycle). The simulation of the flow reversal is organized in a similar way. After the chosen reversal at half-period a symmetric exchange of variables with respect to the center of each reactor is made and the calling sequence is reversed for the next flow reversal half-period. FITTING OF KINETIC AND TRANSPORT PARAMETERS The most important phenomena in the description of the transient behaviour of combustion of VOC are ignition and extinction of combustion fronts. The values of reaction and transport parameters further used in simulations were adjusted to fit experimentally determined ignition and extinction temperature profiles on the system consisting of the metallic and ceramic monolith similarly, as it was made earlier for single ceramic monolith, cf. Pinkas et al. (1994), where the properties of catalytic monoliths and experimental arrangement are described. The coexistence of stationary states (hysteresis) limited by ignition and extinction curves was observed also in the sequence of single metallic and single ceramic monoliths at higher values of inlet CO concentrations. Its use for fitting of reaction and transport parameters is illustrated in Fig. 1. In experiments with the cascade of monoliths we followed the dependence of the outlet conversion from the last monolith on the temperature of the gas entering the first monolith. The inlet temperature
3159
A sequence of catalytic monolith reactors
v
0.0525
Tw
298
c~,me,az,ic
0.46 A;,,ne~au~c 11.5 P~ne,amc 7220 ~rnetamc 0.6836 AHR 2.78 x 105 ~e,v < 0 ; 1600>
[K] [J k g - ' K -1] [J m -1 s -1 K -1] [k9 m -s] [1]
[J tool -1]
2.5
[m s -1]
a 540 c; . . . . . . ic 0.94 A*,eerami¢ 0.18
[m -1] [J kg -1 g -1] [J m -1 s -1 g -1]
p; . . . . ~¢ c .... mi¢ En
2500
[kg m -a]
0.6836 1.01×105
[1] [J tool -1]
[Win -2K -l] Table 1: Values of parameters
a
0.~
l
b,
F
0.8
0.6
I
t
0.4
0.6
~
0.4
°-]
0.2 0
"i
d$.,,,~..A2[,h
,,o
oo
,
Figure 1: Comparison of a) measured and b) simulated hysteresis curves, MC sequence of monoliths, 2% CO
was increased in small steps to reach the stationary state at a given inlet temperature between practically zero conversion and complete outlet conversion. The procedure was then reversed and the inlet temperature was decreased. The difference between the ignition and extinction temperature then determines the width of the hysteresis region. The fitting of simulated conversion - inlet temperature profiles is used for adjustment of model parameters. Ignition occurs in experiments for 2% CO at the inlet approximately at 140°C, extinction at 100°C. In the simulations is ignition temperature equal to 135°C and extinction temperature is again approximately equal to 100°C. Similar agreement between measured and simulated ignition curves were obtained for 1% CO (here no hysteresis exists) and 3% at the inlet. Simulations of dynamic behaviour of different arrangements of sequences of monoliths was then made on the basis of the values of parameters determined from the above comparison of measured and modelled ignition and extinction phenomena for an inlet concentration of CO equal 2.5%. Characteristic values of chosen parameters used in simulations are given in Table 1. TRANSIENT BEHAVIOUR OF SEQUENCE OF MONOLITHS The metallic converter has comparatively a high thermal conductivity and a low thermal capacity. The ceramic converter has just the opposite properties. These properties and their dynamic consequences can be utilized in the sequence of converters. Thermal response of the metallic converter is faster and thus it can be conveniently used for preheating or heat removal. In the following we shall illustrate the dynamic behaviour of the system consisting of three converters in the arrangements C-M-C and M-C-M and then we shall discuss the effects of introducing flow reversals. The above symmetric arrangements were chosen with regard to the use of flow reversal as otherwise the M-C arrangement has mostly better transient characteristics. In both systems we shall consider the heat removal from metallic monoliths (ceramic monoliths will be considered adiabatic). The overall mass of the converters will be the same as that of the M-C system studied earlier (Pinkas et al., 1994). We shall follow the effect of the amount of removed heat on the operating stability of the system. An example of the ignition and propagation of combustion fronts in the C-M-C system with all catalytic monoliths taken as adiabatic is shown in Figs 2a,b. We can observe in Fig 2a, where spatial temperature profiles are presented in 5 s intervals, that under the used conditions the propagating temperature front initiated at the center metallic converter is propagating at first into the following ceramic monolith and is then subsequently blown out from the last ceramic monolith. This is connected with the decrease of the outlet conversion leading finally to total extinction of the reaction (cf. Fig. 2b). The change of the
3160
P. P1NKASet al. a 700
'C
M
C
waveFtol~g~iou
6OO
I
'
I
0.6
500
0.4 400
300 0.05
C
700
'C
0.1 0.15 axial coordinate [m]
M
0
0.2
,
i
200
250
300
~*me [s]
C
'
1
'f
0.8 /
6OO 150
i|
0.6 500 0.4 400 0.2 OS
300 0.05
0.1 0,15 axial coordinate [m]
0 0.2
,
i
100
200
300 lime (s]
I
I
400
500
600
Figure 2: Ignition and propagation of combustion fronts in C-M-C system of monoliths; a) sequence of temperature profiles in 5 s intervals without flow reversal; initial temperatures ceramic monoliths 298 K metallic monolith 773 K; fluid inlet temperature 393 K. b) outlet conversion without flow reversal, c) spatial temperature patterns with flow reversal (TR = 75 s), d) outlet conversion with flow reversal.
direction of propagating front can be achieved by the introduction of the inlet flow into the last reactor and is then maintained by repeated (e.g., periodic or controlled according to chosen control algorithm) flow reversal. Typical spatiotemporal patterns after introduction of periodic flow reversal are shown in Fig. 2c. The propagating temperature front is after 300 s stabilized in the center part of the monolith system. The time course of the outlet conversion, depicted in Fig. 2d, illustrates fast transition to nearly complete outlet conversion within several periods of flow reversal. The vertical lines in the figure correspond to times of flow reversals where parts of the unburned CO are blown out from the reactor system. Comparison of C-M-C and M-C-M systems Example of results of two parametric comparative study of the stabilized time averaged conversion in C-M-C and M-C-M systems are shown in Figs 3a,b. Ceramic monoliths were considered adiabatic. Two studied parameters were the coefficient of external heat transfer from the metallic monolith acw (effective value) and the length of the flow reversal half- period TR. Metallic monoliths were initially heated up to the same temperature and transient simulations were used to determine whether the regime with high conversion or extinction regime is reached. Parametric plane acw vs TR in Fig. 3 is divided into high conversion and extinction regions. We can observe that the high conversion regime in the C-M-C sequence (Fig. 3a) is reached whenever the heat removal from the metallic converter is not too high or the flow reversal half-period TR not too long. Hence TR is only limited from above. If TR is high and the propagating temperature wave already starts to leave the last monolith, then the system becomes extinguished. The residence time of propagating wave depends on the initial temperature of the metallic converter, inlet CO concentration and temperature and on the lengths of monoliths. Example of stationary catalyst temperature profiles for TR = 10s is illustrated in Fig. 4a. Here the full line corresponds to the flow from the left and the dotted line to the flow from the right both at the end of the half period. The profile is mirror symmetric with respect to flow reversal. In the M-C-M system the range of flow reversal periods for the high conversion regime is limited both from below and above, cf. Fig. 3b. U n s y m m e t r i c s t a t i o n a r y spatial t e m p e r a t u r e p a t t e r n s in C - M - C s y s t e m If a high amount of heat is withdrawn from the metallic converter in the C-M-C system and the flow reversal half-period is sufficiently low, so that the high conversion regime is still maintained, we can observe that
3161
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l
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150
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Figure 3: Conversion as a function of heat removal rate and flow reversal half-period; a) C-M-C system; b) M-C-M system.
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Figure 4: Spatial temperature profiles, flow-rate reversal, C-M-C system; a) symmetric profile; b) unsymmetric profile.
I
b
i
0.9
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Figure 5: C-M-C system with flow reversal adaptive control; a) flow reversal period stabilization via control, b) blow out under improper control.
3162
P. I~NKASet a£
the reaction front is not crossing the region of lower temperature on the metallic monolith and spatially unsymmetric temperature profiles arise. The highest temperature is reached in the last ceramic segment (counted at the start of the system simulation). An example of such stabilized profiles is given in Fig. 4b. The profile is unsymmetric with respect to flow reversal. Evidently, spatially mirror image profiles also exist; they can be reached by starting the flow into the last reactor. A d a p t i v e flow reversal c o n t r o l Adaptive control of flow reversal in the C-M-C system can be, for example, realized in such a way that two thermocouples are located at two ends of the system, i.e. at x = XL in the left ceramic monolith and at x = xR in the right ceramic monolith. If we denote the corresponding limit temperatures T~ and T~, respectively, we can apply the following adaptive control algorithm: a) if the flow is from the left to the right and T*(xR) > T~, then the flow direction is reversed b) if the flow is from the right to the left and T*(XL) > T~, then the flow direction is reversed. Fast transition to the high conversion regime then occurs for proper choice of XL, xR, T~, T/~. An example of such a choice is shown in Fig. 5a where the stabilized flow reversal half-period TR - 6. Improper choice of values of T~, R can lead either to blow out (T~,R too high, cf Fig 5b) or to trivial satisfaction of both switching conditions (T~, R too low). CONCLUSIONS Combination of monoliths with the same catalyst on metallic and ceramic carriers with the use of flow reversal can be used to stabilize different types of temperature regimes in the system. Even richer possibilities are available if catalysts of different types (possibly with different activities) are used in multiple reaction systems. The same CAD - type software can also be used for the simulation of a combination of monolith catalysts with regenerating self - cleaning particle traps and filters currently studied for the control of emissions from diesel motor vehicles. Notation: TR - - flow reversal half-period, ZL, xR, T~ and T~ are defined in the text, other symbols see Pinkas et al., 1994.
Acknowledgment: This work was partially supported by the grant No. 104/94/0649, Czech Grant Agency, and EU COST grant CIPA-CT92-4021. REFERENCES
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