- Email: [email protected]
Transient Behavior Of an Industrial Acetylene Converter
Reaction Kinetics and the Developmentof Catalytic Processes G.F. Froment and K.C. Waugh (Editors) 9 1999 Elsevier Science B.V. All rights reserved.
141
T R A N S I E N T B E H A V I O R O F AN I N D U S T R I A L A C E T Y L E N E C O N V E R T E R Noemi S. Schbib, Alberto F. Errazu and Jos6 A. Porras 12 de octubre 1842, 8000 Bahia Blanca, Argentina e- mail: [email protected] FAX. 54-91-861600
Abstract The dynamic behavior of an industrial acetylene converter is discussed in the present work. The reactor is used to remove unwanted unsaturated hydrocarbons by means of a hydrogenation. This exothermic reaction is carried out in an adiabatic fixed bed reactor train in series (using a Pd/A1208 catalyst). Undesirable reactions accompany the main one. Therefore, the selectivity of the catalyst is very important. It is necessary to maintain stable operation while meeting product specifications for extremely low acetylene concentrations (<1 ppm). A computer simulation program for the industrial acetylene converter was developed. The steady states estimated by simulation are in good agreement with those found in industry. Besides, the simulated dynamic behavior of the converter shows the same general trends as those exhibited by industrial equipment. 1. INTRODUCTION The selective hydrogenation of acetylene in the presence of large amounts of ethylene is an important step in the ethylene manufacturing process. Most commercial installations manage to reduce the acetylene impurity to the desired specification effectively. In practice, this unit may have control problems when the undesirable hydrogenation of ethylene becomes important, leading to a runaway effect. In industry the acetylene converter can be located at different points in the purification section of an ethylene plant [1]. In one disposition the converter is placed after the conversion section (front-end). Another alternative involves the hydrogenation of the stream taken from the top of the de-ethanizer (tail-end). A great deal of research on acetylene hydrogenation has been undertaken. Most of it refers to kinetic studies under conditions similar to those at the taft-end and only a few papers study front-end conditions [2, 3]. Only some works analyze the steady-sate or dynamic simulations of the industrial process in particular. Sughrue et al. [4] have studied the dynamic behavior of a reactor with tail-end arrangement using Speedup software (Aspen Technology) for the dynamic simulation. Brown et al. [5] carry out the control and economic optimization of the taft-end hydrogenation process. They assume pseudo steady states for the mathematical model of the reactor. Hobbs [6] has analyzed the dynamic behavior and control of the front-end disposition. He simulated the reactor with lumped parameter model. In this work, the dynamic behavior of an industrial converter with front-end disposition is presented. It is based on the mathematical modeling of each unit of the converter (i.e. the condenser, the fixed beds and the heat exchangers). The main features of the feed of the front-end are: the high H2/C2H2 ratio @ 100) and the presence of several acetylenic, olefinic and diolefinic by-products as well as carbon monoxide. The CO is produced in the cracking furnaces and constitutes the main inhibitor of the hydrogenation reactions.
142 Figure 1 shows the scheme of the industrial converter simulated in this work, which includes a condenser (I1) and three adiabatic beds (R1, R2, R3) with intermediate cooling (12, I3). T2e Feed Fg
Ti e wt I y-,,i
~
"
T~ U
T2s
(
t
I
Tls T~
water Produet
F i g u r e 1: Scheme of the industrial acetylene converter
2. MATHEMATICAL MODEL The hydrogenation process can be described appropriately by the reaction scheme shown in table 1. The kinetic model for the C2H2 and C2H4 T a b l e 1: Reaction mechanism hydrogenation was previously obtained for a C2H2 + H2 --->C2H4 commercial Pd/a-A1203 catalyst, under conditions similar to those at the front-end industrial C2H4 + tt2-->C2H6 hydrogenation process [2]. The conversions of C4H6 C3H4 +H2-'-~C3H6 and C3H4 are calculated by using an empirical C4H6 + H 2 - + C 4 H 8 model, that allow their estimation as a function of the acetylene conversion. Each stage of the acetylene converter consists of a short adiabatic fixed-bed reactor. The transient behavior of the three reactors (R1, R2, R3) has been simulated by a onedimensional pseudo-homogeneous model. The dynamic models for the condenser (I1) and the heat exchangers (12, 13) are first-order interactive systems, which result from the thermal balances at both, the process side and heating/cooling medium: M o d e l f o r reactors R1, R2 and R3 Kinetic M o d e l
M a s s Balances:
aci c~t
Z ( - ri )PL
~ a(,,ci ) e
8z
_
1
c
- r~ =
a+~C~Cn
[I+(KHCH)'/2 +K+
(1)
_1
(3)
i=A, E
j = 1,2... NC Energy balance:
z.
8T
a 8T
Z (-Atr--Ii)(-r+)PL i
8t
6T 8 z
6T
(2)
= 1 - ( 1 - z~) ~"
y
z,, = 1 - ( 1 - z~) ~
(4)
143 Model for the condenser 11 Energy balance for the process side: p g VgC pg t i T ; : Fg2Cpg (Tge- T; ) + Q dt
Mass balance for the condensed fluid:
(5)
dh pcS ---~= Wv - FcPM
(6)
Energy balance for the heating fluid (steam):
(7) Models of the heat exchangers 12 and 13 Energy balance for the process side:
Energy balance for the cooling stream (wateO : (7/tCpwPw + MsCps) a ~w~ = FwCpw(Twe - Two)+p
(9)
To solve the steady-state model, the time derivatives of equations 1 to 9 set in zero. Steady-state results obtained from the solution of this mathematical model showed good agreement with industrial steady-state data [7].
3. RESULTS AND DISCUSSION
The dynamics of each fixed bed and of the whole converter was studied for different step disturbances at the inlet of each unit. Starting from the initial steady state, individual step changes in inlet flow-rate, temperature, CO concentration and C2H2 concentration were carried out. The progress of the disturbances throughout the process can be explained by means of three types of waves: a "pressure wave", which is practically instantaneous; a "convective wave", which depends on residence time and is, therefore, fast Oust few seconds) because industrial flow-rate are high; and "thermal wave", which depends on the all thermal capacities (fluid + catalyst + reactor) and is relatively slow. Although these three waves have different propagation velocities, the time taken to reach the final steady-states is similar for different disturbances due to the relationship between temperature and concentration represented by reaction rate expressions. This effect complicates the study of the dynamic responses of the individual bed and the whole converter. 3.1. D y n a m i c S i m u l a t i o n s o f the Bed For the dynamic simulations, the axial coordinate (z) (eqs. 1 and 2) was discretized using finite differences. A "Gear routine" [8] was used to solve the system of ordinary differential equations. The behavior of each bed under the disturbances listed above was analyzed. In the following sections, the dynamic responses of the first bed under two of those disturbances, are explained in detail.
3.1.1. Disturbance in the feed temperature for the first bed (R1) The first bed was simulated under a +8% step in the feed temperature. The axial profiles for the temperature and concentrations of C2H2 and C2H4, at six different times are shown in figs. 2 to 4. The axial temperature profile in the final steady-state (t---~) is higher than the initial one (t=0) (fig. 2). Due to the higher reaction rate, this evolution is accompanied by a drop in the acetylene concentration profile (fig. 3). At the same time, a maximum
144 appears at the final ethylene concentration profile (t=oo) (fig.4) because this is an intermediate compound in the following series of reactions: C2H 2 rA ) C2H4 rE ) C2H6. The t e m p e r a t u r e profile changes gradually since it is related to the slow propagation rate of the "thermal wave". A quick change of the concentration profiles simultaneously occurs (figs. 3 and 4). These different propagation rates cause the inverse response exhibited by the outlet temperature (fig. 5). This effect, called "wrong-way behavior", has been observed before by other authors [9, 10] 100
0.5 t=
9O
0.4 t=0 s s
60
U' ,o
1
t'q 0.3 O 0.2
80
o~
70
0.1 60
,
30
,
,
60
f
r
,
,
90 120 z [cm]
,
,
150
r
180
Figure 2" Axial temperature profiles in R1. Disturbance in the feed to R1 (To = 69.5 75~
0.0 0
30
60
90 120 150 180 z [em] Figure 3: Axial profiles for C2H2 in R1 Disturbance in the feed to R1 (To = 69.5 75~ 100
52.0 t=_Qo ~51.9 r
95
P
~51.8
/
/
/
90
51.7
85 0
30
60
90 120 z [cm]
150
180
Figure 4: Axial profiles for C2H4 in R1. Disturbance in the feed to R1 (To = 69.5 75~
,
0
,
50
,
r
i
f
,
,
f
,
100 150 200 250 time [s]
r
300
Figure 5: Outlet temp. for bed R1 (z=180em). Disturbance in the feed to R1 (Te = 69.5 --~ 75~
3.1.2. Disturbance in the acetylene concentration in the feed The dynamic responses of the first bed under concentration changes were analyzed. For example, when the feed concentration CAe changes from 0.47 to 0.40 %wt the internal amounts of C2H2 and C2H4 drop immediately. The corresponding axial profiles for five different times are shown in figures 6 and 7. The final steady-state t e m p e r a t u r e profile (t=oo) is under the initial one (t-0). This is due to the lower rate of heat generation associated to the smaller concentration of the reactant (C~Hg. In contrast with the concentration profiles, the temperature remains unchanged during the first few seconds.
145 0.5
52.0 r
~-
0.4 51.9
~0.3
r
t'q
~9 0.2
~51.8 t---- OO
0.1
--Os
0.0
'
0
I
30
'
I
~
I
'
I
'
I
'
60
90 120 150 180 z [cm] Figure 6: Axial profiles for CzI-Ig. in R1. Disturbance in CAe=0.47 -~ 0.40 %wt
51.7
I
0
30
'
I
'
I
'
I
'
I
'
60
90 120 150 180 z [era] Figure 7: Axial profiles for CzH4 in R1. Disturbance in CAe=0.47 -~ 0.40 %wt
3.2. D y n a m i c s o f t h e w h o l e c o n v e r t e r
The disturbances enter the converter through the condenser (I1). To perform the simulation, the differential equations (1) to (9) must be solved. With the help of this model, the dynamic responses for temperature and conversions of C9H2 and C9H4 in each bed (R1, R2 and R3) were obtained, as well as the temperature profiles for the streams leaving the condenser and the heat exchangers. The "push-forward" interactive effect, that generates a variety of disturbances throughout the units, was also analyzed. 3.2.1. Disturbance in the feed temperature The behavior of the whole converter under a +5~ step change in the temperature of the feed entering I 1 was studied. This disturbance causes an increase in the outlet temperature for the condenser. This change moves upstream, affecting the first bed. In Figure 8 the dynamic evolution of the temperature leaving each bed (at z=180 cm.) is shown. An inverse response, similar to those described for the first bed (item 3.1.1) was found for all the beds. This effect is magnified and delayed for beds R2 and R3. The dynamic profiles for C2H2 and C2H4 at the outlet of the third catalyst bed (R3) were plotted in Figure 9. It is easy to note that the temperature increase in each bed produces lower C2H2 and C2H4 concentrations at the final steady state in comparison with the initial one. 3.2.2. Disturbance in the inlet CO concentration The carbon monoxide is produced in the cracking furnace according to the water-gas shift reaction. Its concentration is related to the amount of coke deposited during the pyrolysis process. It is known that, in addition to the conversion and cracker operating conditions, the sulfur additives have influence on the coke and CO formation [11]. As regards stability, the variations in CO concentration are the most dangerous disturbances. A small step change in the amount of CO at the inlet (Cco= 0.04 -~ 0.03 %wt), rises the temperature in all the beds (see fig. 10). In consequence, as it can be observed in figure 11, the outlet C2H4 concentration decreases almost 1% with respect to the initial steady-state value, while the C2H2 practically disappears. Another feasible situation during plant operation is that the CO concentration decreases beneath its normal value. A high negative step change (e.g. -60%) causes runaway conditions in the second and/or the third beds (see fig. 13). In this respect, our simulation results agree with industrial practice. A lower level of CO leads to higher hydrogenation rates with a sudden drop in the acetylene and ethylene concentrations. This effect is shown in figure 13, where the dynamic outlet concentrations for the third bed (R3) have been represented.
146
100
R1
f
/
96
%wt C2H2 8E-6
%wt C2H4 51.3
/
~51.2
R3
o~ 92 415-6
88
51.1
/
84 80 I 0
,
I , 400 600 800 time [s] F i g u r e 8: Outlet temperature of the reactors. Disturbance in the condenser (To: 35 ~ 40~
200
0
,
, 51.0 400 600 800 time [s] F i g u r e 9: Outlet concentrations for R3. Disturbance in the condenser (To: 35 ~ 40~ 0
200
% w t C2H4 51.2
% w t C2H2 4E-6 96 R3
51.0 2E-6
1
50.8
88
84 0
200
400 time [s]
600
800
F i g u r e 10: Outlet temperature of the reactors Disturbance in Cco =0.04 ~ 0.03 %wt
120
50.6 400 600 800 time [s] F i g u r e 11: Outlet concentrations for R3 Disturbance in Cco: 0.04 -~ 0.03 %wt 0
0
200
%wt C2H2 4E-6
%wt C2H4 52
112 ~ ' 104 o
R2
R
f 2E-6
48
96 88 0
40
80 time [s]
120
160
F i g u r e 12: Outlet temperature for the reactors Disturbance in Cco: 0.04 -~ 0.015 %wt
0
44 80 120 160 time [s] F i g u r e 13: Outlet concentrations for R3 Disturbance in Cco: 0.04 ~ 0.015 %wt 0
40
3.2.3. D i s t u r b a n c e in t h e inlet C2H2 c o n c e n t r a t i o n T h e c h a n g e in c o n c e n t r a t i o n t r a v e l s t h r o u g h t h e r e a c t o r s w i t h t h e s a m e velocity as t h e g a s flow. T h e r e f o r e , w h e n t h e C2H2 c o n c e n t r a t i o n drops from CAe =0.47 to 0.4 %wt, t h e
147 temperature of the first reactor (R1) diminishes. The temperature of the other reactors (R2 and R3) suffers the same effect but it is delayed, as a consequence of the dynamic effects of the preceding heat exchangers and the catalyst beds (see fig. 14). %wt C2H2 4E-5 -
90 l ~ 87 ~
RI
~"
~
84 ~
R3
200
. . . . 400 600 time [s]
-
51.20
-
51.15
2E-5 -
R2
81 0
%~ C2H4 51.25
r
800
0
I
0
Figure 14: Outlet temperature for the reactors. Disturbance in CAe:0.47 --~ 0.40
200
i
400 time [s]
,
600
51.10
,
800
Figure 15: Outlet concentrations for R3. Disturbance in CAe:0.47 ~ 0.40
When the acetylene concentration diminishes at the inlet to the converter, the simulator predicts (as commented in section 3.1.2) a drop in the outlet concentrations of C2H2 and C2H4 in the first bed (see figs. 6 y 7). However, the lower temperature in each bed (fig. 14) leads to an increase in the final values for the C2H2 and C2H4 concentrations at the outlet to the converter, with respect to the initial ones (fig. 15). 3.2.4. Disturbance in the flow-rate The flow-rate change affects all units of the converter, practically at the same time since it moves along the converter following the "pressure wave". The dynamic response of the outlet temperature condenser (i.e. inlet to the first catalyst bed) for this disturbance is shown in figure 16. Then, two disturbances enter RI: an increase in the flow-rate and a decrease in the inlet temperature. The addition of both effects lowers the C2H2 conversion. Three disturbances enter R2: an increase in flow-rate and in the C2H2 concentration and a decrease in the temperature at the outlet of R1. Similar effects are produced in reactor R3. These disturbances lead to an increase in C2H2 and C2H4 at the outlet of R3 (fig. 17)
%wt C2H2 5E-5
70 1
%wt C2H4 51.35
/#
4E-5 t r..) o 69
3E-5
51.30 51.25
2E-5 51.20
1E-5
r
68 l . . . . 0
200
400 time [s]
600
800
Figure 16: Outlet temperature for I1. Disturbance in Fg: 72000 ~ 75000 NmS/h.
0
200
400
600
51.15
800
time [s] Figure 17: Outlet concentrations for R3 Disturbance in Fs: 72000 --} 75000 Nm3/h.
148
4. C O N C L U S I O N S The m a t h e m a t i c a l model presented here allows the simulation of an industrial converter. The steady states obtained by simulation are in good agreement with those found in industry. The axial t e m p e r a t u r e and conversion profiles can be obtained as a function of time, after applying changes in the feed concentration of C9.H2 and CO and/or in the inlet flow rate and temperature. The dynamic behavior of the converter estimated by simulation exhibits the same general trends as those found in industrial practice. The t r a n s i e n t t e m p e r a t u r e profiles obtained for each bed when, for example, a t e m p e r a t u r e disturbance enters the condenser, indicate t h a t the inverse responses are several times greater t h a n those found from the independent studies of the dynamic responses of each mdividual bed. This fact m a k e s the dynamic model of the whole converter a powerful tool to predict t r a n s i e n t system behavior. 5. N O M E N C L A T U R E Cj concentration of j-th component in the gas phase, kmol/m 8 A CD~ti specific heat, J/kmol/K heat of reaction, J/kmol F flowrate, kg/s ki Arrhenius type rate constant of component i Ki equilibrium constant of component i NC number of components PM molecular weight Q rate of heat transfer, kcaYs S cross section of the condenser, m e ri rate of reaction of component i, mol/kgca t s t time, s T temperature, K T" by-pass temperature, K u average velocity of the fluid through the bed, m/s V volume, m s Wvt steam flowrate, kg/s wt weight fraction z reactor length coordinate, m
Subscripts A B c CO E Et g H e o P s v w
acetylene butadiene condensed carbon monoxide ethylene ethane gas hydrogen input output propadiene solid steam water
s pL p a
void fraction of packed bed bed density, kg/m 3 fluid density deactivation factor
Greek symbols
6. R E F E R E N C E S 1. Derrien M.L., "Catalytic Hydrogenation", Cerveny (Ed.), Elsevier Science, Amsterdam, (1986). 2. Schbib N. S., M. Garcia, C. Gigola and A. Errazu. Ind. Eng. Chem. Res. (1996) Vol 35, No. 5, 1496. 3. Schbib, N.S. "Din~maica y Control de un Convertidor Industrial de Acetileno". Tesis Doctoral, UNS. March (1998). 4. Sughrue E.L., R.L. Hair and R.J. CaUejas. AIChE Meeting, March (1995), 19-23. 5. Brown M.W., A_ Penlidis and G.R. Sullivan. The Can. J. of Chem. Engn. (1991) 69, 152. 5. Hobbs J.W., "Computer Control of an Acetylene Hydrogenation Process". Ind. Proc. Control Proc. Workshop, (1979). 7. Schbib N.S., &F. Errazu, J./~ Romagnoli, J.& Porras. Computers Chem. Engn. (1994), Vol 18, $355. 3. Gear C.W., "Numerical Initial Value Problems in Ordinary Differential Equations". Prentice Hall, Englewood Cliffs, N.S., (1971). 9. Van Doesburg H. and W.A, Jong, Chemical Engineering Science, (1976) 31, 45. 10. Gatica J. E, J.A_ Porras, A. F. Errazu and J. A Romagnoli. Chem. Engng. Comm. (1989) 78, 73-96. 11. Santiago J . ~ , Francesconi J.D. and N.L.Moretti. O/l Gas J. (1982) 81(39), 78-82.
141
T R A N S I E N T B E H A V I O R O F AN I N D U S T R I A L A C E T Y L E N E C O N V E R T E R Noemi S. Schbib, Alberto F. Errazu and Jos6 A. Porras 12 de octubre 1842, 8000 Bahia Blanca, Argentina e- mail: [email protected] FAX. 54-91-861600
Abstract The dynamic behavior of an industrial acetylene converter is discussed in the present work. The reactor is used to remove unwanted unsaturated hydrocarbons by means of a hydrogenation. This exothermic reaction is carried out in an adiabatic fixed bed reactor train in series (using a Pd/A1208 catalyst). Undesirable reactions accompany the main one. Therefore, the selectivity of the catalyst is very important. It is necessary to maintain stable operation while meeting product specifications for extremely low acetylene concentrations (<1 ppm). A computer simulation program for the industrial acetylene converter was developed. The steady states estimated by simulation are in good agreement with those found in industry. Besides, the simulated dynamic behavior of the converter shows the same general trends as those exhibited by industrial equipment. 1. INTRODUCTION The selective hydrogenation of acetylene in the presence of large amounts of ethylene is an important step in the ethylene manufacturing process. Most commercial installations manage to reduce the acetylene impurity to the desired specification effectively. In practice, this unit may have control problems when the undesirable hydrogenation of ethylene becomes important, leading to a runaway effect. In industry the acetylene converter can be located at different points in the purification section of an ethylene plant [1]. In one disposition the converter is placed after the conversion section (front-end). Another alternative involves the hydrogenation of the stream taken from the top of the de-ethanizer (tail-end). A great deal of research on acetylene hydrogenation has been undertaken. Most of it refers to kinetic studies under conditions similar to those at the taft-end and only a few papers study front-end conditions [2, 3]. Only some works analyze the steady-sate or dynamic simulations of the industrial process in particular. Sughrue et al. [4] have studied the dynamic behavior of a reactor with tail-end arrangement using Speedup software (Aspen Technology) for the dynamic simulation. Brown et al. [5] carry out the control and economic optimization of the taft-end hydrogenation process. They assume pseudo steady states for the mathematical model of the reactor. Hobbs [6] has analyzed the dynamic behavior and control of the front-end disposition. He simulated the reactor with lumped parameter model. In this work, the dynamic behavior of an industrial converter with front-end disposition is presented. It is based on the mathematical modeling of each unit of the converter (i.e. the condenser, the fixed beds and the heat exchangers). The main features of the feed of the front-end are: the high H2/C2H2 ratio @ 100) and the presence of several acetylenic, olefinic and diolefinic by-products as well as carbon monoxide. The CO is produced in the cracking furnaces and constitutes the main inhibitor of the hydrogenation reactions.
142 Figure 1 shows the scheme of the industrial converter simulated in this work, which includes a condenser (I1) and three adiabatic beds (R1, R2, R3) with intermediate cooling (12, I3). T2e Feed Fg
Ti e wt I y-,,i
~
"
T~ U
T2s
(
t
I
Tls T~
water Produet
F i g u r e 1: Scheme of the industrial acetylene converter
2. MATHEMATICAL MODEL The hydrogenation process can be described appropriately by the reaction scheme shown in table 1. The kinetic model for the C2H2 and C2H4 T a b l e 1: Reaction mechanism hydrogenation was previously obtained for a C2H2 + H2 --->C2H4 commercial Pd/a-A1203 catalyst, under conditions similar to those at the front-end industrial C2H4 + tt2-->C2H6 hydrogenation process [2]. The conversions of C4H6 C3H4 +H2-'-~C3H6 and C3H4 are calculated by using an empirical C4H6 + H 2 - + C 4 H 8 model, that allow their estimation as a function of the acetylene conversion. Each stage of the acetylene converter consists of a short adiabatic fixed-bed reactor. The transient behavior of the three reactors (R1, R2, R3) has been simulated by a onedimensional pseudo-homogeneous model. The dynamic models for the condenser (I1) and the heat exchangers (12, 13) are first-order interactive systems, which result from the thermal balances at both, the process side and heating/cooling medium: M o d e l f o r reactors R1, R2 and R3 Kinetic M o d e l
M a s s Balances:
aci c~t
Z ( - ri )PL
~ a(,,ci ) e
8z
_
1
c
- r~ =
a+~C~Cn
[I+(KHCH)'/2 +K+
(1)
_1
(3)
i=A, E
j = 1,2... NC Energy balance:
z.
8T
a 8T
Z (-Atr--Ii)(-r+)PL i
8t
6T 8 z
6T
(2)
= 1 - ( 1 - z~) ~"
y
z,, = 1 - ( 1 - z~) ~
(4)
143 Model for the condenser 11 Energy balance for the process side: p g VgC pg t i T ; : Fg2Cpg (Tge- T; ) + Q dt
Mass balance for the condensed fluid:
(5)
dh pcS ---~= Wv - FcPM
(6)
Energy balance for the heating fluid (steam):
(7) Models of the heat exchangers 12 and 13 Energy balance for the process side:
Energy balance for the cooling stream (wateO : (7/tCpwPw + MsCps) a ~w~ = FwCpw(Twe - Two)+p
(9)
To solve the steady-state model, the time derivatives of equations 1 to 9 set in zero. Steady-state results obtained from the solution of this mathematical model showed good agreement with industrial steady-state data [7].
3. RESULTS AND DISCUSSION
The dynamics of each fixed bed and of the whole converter was studied for different step disturbances at the inlet of each unit. Starting from the initial steady state, individual step changes in inlet flow-rate, temperature, CO concentration and C2H2 concentration were carried out. The progress of the disturbances throughout the process can be explained by means of three types of waves: a "pressure wave", which is practically instantaneous; a "convective wave", which depends on residence time and is, therefore, fast Oust few seconds) because industrial flow-rate are high; and "thermal wave", which depends on the all thermal capacities (fluid + catalyst + reactor) and is relatively slow. Although these three waves have different propagation velocities, the time taken to reach the final steady-states is similar for different disturbances due to the relationship between temperature and concentration represented by reaction rate expressions. This effect complicates the study of the dynamic responses of the individual bed and the whole converter. 3.1. D y n a m i c S i m u l a t i o n s o f the Bed For the dynamic simulations, the axial coordinate (z) (eqs. 1 and 2) was discretized using finite differences. A "Gear routine" [8] was used to solve the system of ordinary differential equations. The behavior of each bed under the disturbances listed above was analyzed. In the following sections, the dynamic responses of the first bed under two of those disturbances, are explained in detail.
3.1.1. Disturbance in the feed temperature for the first bed (R1) The first bed was simulated under a +8% step in the feed temperature. The axial profiles for the temperature and concentrations of C2H2 and C2H4, at six different times are shown in figs. 2 to 4. The axial temperature profile in the final steady-state (t---~) is higher than the initial one (t=0) (fig. 2). Due to the higher reaction rate, this evolution is accompanied by a drop in the acetylene concentration profile (fig. 3). At the same time, a maximum
144 appears at the final ethylene concentration profile (t=oo) (fig.4) because this is an intermediate compound in the following series of reactions: C2H 2 rA ) C2H4 rE ) C2H6. The t e m p e r a t u r e profile changes gradually since it is related to the slow propagation rate of the "thermal wave". A quick change of the concentration profiles simultaneously occurs (figs. 3 and 4). These different propagation rates cause the inverse response exhibited by the outlet temperature (fig. 5). This effect, called "wrong-way behavior", has been observed before by other authors [9, 10] 100
0.5 t=
9O
0.4 t=0 s s
60
U' ,o
1
t'q 0.3 O 0.2
80
o~
70
0.1 60
,
30
,
,
60
f
r
,
,
90 120 z [cm]
,
,
150
r
180
Figure 2" Axial temperature profiles in R1. Disturbance in the feed to R1 (To = 69.5 75~
0.0 0
30
60
90 120 150 180 z [em] Figure 3: Axial profiles for C2H2 in R1 Disturbance in the feed to R1 (To = 69.5 75~ 100
52.0 t=_Qo ~51.9 r
95
P
~51.8
/
/
/
90
51.7
85 0
30
60
90 120 z [cm]
150
180
Figure 4: Axial profiles for C2H4 in R1. Disturbance in the feed to R1 (To = 69.5 75~
,
0
,
50
,
r
i
f
,
,
f
,
100 150 200 250 time [s]
r
300
Figure 5: Outlet temp. for bed R1 (z=180em). Disturbance in the feed to R1 (Te = 69.5 --~ 75~
3.1.2. Disturbance in the acetylene concentration in the feed The dynamic responses of the first bed under concentration changes were analyzed. For example, when the feed concentration CAe changes from 0.47 to 0.40 %wt the internal amounts of C2H2 and C2H4 drop immediately. The corresponding axial profiles for five different times are shown in figures 6 and 7. The final steady-state t e m p e r a t u r e profile (t=oo) is under the initial one (t-0). This is due to the lower rate of heat generation associated to the smaller concentration of the reactant (C~Hg. In contrast with the concentration profiles, the temperature remains unchanged during the first few seconds.
145 0.5
52.0 r
~-
0.4 51.9
~0.3
r
t'q
~9 0.2
~51.8 t---- OO
0.1
--Os
0.0
'
0
I
30
'
I
~
I
'
I
'
I
'
60
90 120 150 180 z [cm] Figure 6: Axial profiles for CzI-Ig. in R1. Disturbance in CAe=0.47 -~ 0.40 %wt
51.7
I
0
30
'
I
'
I
'
I
'
I
'
60
90 120 150 180 z [era] Figure 7: Axial profiles for CzH4 in R1. Disturbance in CAe=0.47 -~ 0.40 %wt
3.2. D y n a m i c s o f t h e w h o l e c o n v e r t e r
The disturbances enter the converter through the condenser (I1). To perform the simulation, the differential equations (1) to (9) must be solved. With the help of this model, the dynamic responses for temperature and conversions of C9H2 and C9H4 in each bed (R1, R2 and R3) were obtained, as well as the temperature profiles for the streams leaving the condenser and the heat exchangers. The "push-forward" interactive effect, that generates a variety of disturbances throughout the units, was also analyzed. 3.2.1. Disturbance in the feed temperature The behavior of the whole converter under a +5~ step change in the temperature of the feed entering I 1 was studied. This disturbance causes an increase in the outlet temperature for the condenser. This change moves upstream, affecting the first bed. In Figure 8 the dynamic evolution of the temperature leaving each bed (at z=180 cm.) is shown. An inverse response, similar to those described for the first bed (item 3.1.1) was found for all the beds. This effect is magnified and delayed for beds R2 and R3. The dynamic profiles for C2H2 and C2H4 at the outlet of the third catalyst bed (R3) were plotted in Figure 9. It is easy to note that the temperature increase in each bed produces lower C2H2 and C2H4 concentrations at the final steady state in comparison with the initial one. 3.2.2. Disturbance in the inlet CO concentration The carbon monoxide is produced in the cracking furnace according to the water-gas shift reaction. Its concentration is related to the amount of coke deposited during the pyrolysis process. It is known that, in addition to the conversion and cracker operating conditions, the sulfur additives have influence on the coke and CO formation [11]. As regards stability, the variations in CO concentration are the most dangerous disturbances. A small step change in the amount of CO at the inlet (Cco= 0.04 -~ 0.03 %wt), rises the temperature in all the beds (see fig. 10). In consequence, as it can be observed in figure 11, the outlet C2H4 concentration decreases almost 1% with respect to the initial steady-state value, while the C2H2 practically disappears. Another feasible situation during plant operation is that the CO concentration decreases beneath its normal value. A high negative step change (e.g. -60%) causes runaway conditions in the second and/or the third beds (see fig. 13). In this respect, our simulation results agree with industrial practice. A lower level of CO leads to higher hydrogenation rates with a sudden drop in the acetylene and ethylene concentrations. This effect is shown in figure 13, where the dynamic outlet concentrations for the third bed (R3) have been represented.
146
100
R1
f
/
96
%wt C2H2 8E-6
%wt C2H4 51.3
/
~51.2
R3
o~ 92 415-6
88
51.1
/
84 80 I 0
,
I , 400 600 800 time [s] F i g u r e 8: Outlet temperature of the reactors. Disturbance in the condenser (To: 35 ~ 40~
200
0
,
, 51.0 400 600 800 time [s] F i g u r e 9: Outlet concentrations for R3. Disturbance in the condenser (To: 35 ~ 40~ 0
200
% w t C2H4 51.2
% w t C2H2 4E-6 96 R3
51.0 2E-6
1
50.8
88
84 0
200
400 time [s]
600
800
F i g u r e 10: Outlet temperature of the reactors Disturbance in Cco =0.04 ~ 0.03 %wt
120
50.6 400 600 800 time [s] F i g u r e 11: Outlet concentrations for R3 Disturbance in Cco: 0.04 -~ 0.03 %wt 0
0
200
%wt C2H2 4E-6
%wt C2H4 52
112 ~ ' 104 o
R2
R
f 2E-6
48
96 88 0
40
80 time [s]
120
160
F i g u r e 12: Outlet temperature for the reactors Disturbance in Cco: 0.04 -~ 0.015 %wt
0
44 80 120 160 time [s] F i g u r e 13: Outlet concentrations for R3 Disturbance in Cco: 0.04 ~ 0.015 %wt 0
40
3.2.3. D i s t u r b a n c e in t h e inlet C2H2 c o n c e n t r a t i o n T h e c h a n g e in c o n c e n t r a t i o n t r a v e l s t h r o u g h t h e r e a c t o r s w i t h t h e s a m e velocity as t h e g a s flow. T h e r e f o r e , w h e n t h e C2H2 c o n c e n t r a t i o n drops from CAe =0.47 to 0.4 %wt, t h e
147 temperature of the first reactor (R1) diminishes. The temperature of the other reactors (R2 and R3) suffers the same effect but it is delayed, as a consequence of the dynamic effects of the preceding heat exchangers and the catalyst beds (see fig. 14). %wt C2H2 4E-5 -
90 l ~ 87 ~
RI
~"
~
84 ~
R3
200
. . . . 400 600 time [s]
-
51.20
-
51.15
2E-5 -
R2
81 0
%~ C2H4 51.25
r
800
0
I
0
Figure 14: Outlet temperature for the reactors. Disturbance in CAe:0.47 --~ 0.40
200
i
400 time [s]
,
600
51.10
,
800
Figure 15: Outlet concentrations for R3. Disturbance in CAe:0.47 ~ 0.40
When the acetylene concentration diminishes at the inlet to the converter, the simulator predicts (as commented in section 3.1.2) a drop in the outlet concentrations of C2H2 and C2H4 in the first bed (see figs. 6 y 7). However, the lower temperature in each bed (fig. 14) leads to an increase in the final values for the C2H2 and C2H4 concentrations at the outlet to the converter, with respect to the initial ones (fig. 15). 3.2.4. Disturbance in the flow-rate The flow-rate change affects all units of the converter, practically at the same time since it moves along the converter following the "pressure wave". The dynamic response of the outlet temperature condenser (i.e. inlet to the first catalyst bed) for this disturbance is shown in figure 16. Then, two disturbances enter RI: an increase in the flow-rate and a decrease in the inlet temperature. The addition of both effects lowers the C2H2 conversion. Three disturbances enter R2: an increase in flow-rate and in the C2H2 concentration and a decrease in the temperature at the outlet of R1. Similar effects are produced in reactor R3. These disturbances lead to an increase in C2H2 and C2H4 at the outlet of R3 (fig. 17)
%wt C2H2 5E-5
70 1
%wt C2H4 51.35
/#
4E-5 t r..) o 69
3E-5
51.30 51.25
2E-5 51.20
1E-5
r
68 l . . . . 0
200
400 time [s]
600
800
Figure 16: Outlet temperature for I1. Disturbance in Fg: 72000 ~ 75000 NmS/h.
0
200
400
600
51.15
800
time [s] Figure 17: Outlet concentrations for R3 Disturbance in Fs: 72000 --} 75000 Nm3/h.
148
4. C O N C L U S I O N S The m a t h e m a t i c a l model presented here allows the simulation of an industrial converter. The steady states obtained by simulation are in good agreement with those found in industry. The axial t e m p e r a t u r e and conversion profiles can be obtained as a function of time, after applying changes in the feed concentration of C9.H2 and CO and/or in the inlet flow rate and temperature. The dynamic behavior of the converter estimated by simulation exhibits the same general trends as those found in industrial practice. The t r a n s i e n t t e m p e r a t u r e profiles obtained for each bed when, for example, a t e m p e r a t u r e disturbance enters the condenser, indicate t h a t the inverse responses are several times greater t h a n those found from the independent studies of the dynamic responses of each mdividual bed. This fact m a k e s the dynamic model of the whole converter a powerful tool to predict t r a n s i e n t system behavior. 5. N O M E N C L A T U R E Cj concentration of j-th component in the gas phase, kmol/m 8 A CD~ti specific heat, J/kmol/K heat of reaction, J/kmol F flowrate, kg/s ki Arrhenius type rate constant of component i Ki equilibrium constant of component i NC number of components PM molecular weight Q rate of heat transfer, kcaYs S cross section of the condenser, m e ri rate of reaction of component i, mol/kgca t s t time, s T temperature, K T" by-pass temperature, K u average velocity of the fluid through the bed, m/s V volume, m s Wvt steam flowrate, kg/s wt weight fraction z reactor length coordinate, m
Subscripts A B c CO E Et g H e o P s v w
acetylene butadiene condensed carbon monoxide ethylene ethane gas hydrogen input output propadiene solid steam water
s pL p a
void fraction of packed bed bed density, kg/m 3 fluid density deactivation factor
Greek symbols
6. R E F E R E N C E S 1. Derrien M.L., "Catalytic Hydrogenation", Cerveny (Ed.), Elsevier Science, Amsterdam, (1986). 2. Schbib N. S., M. Garcia, C. Gigola and A. Errazu. Ind. Eng. Chem. Res. (1996) Vol 35, No. 5, 1496. 3. Schbib, N.S. "Din~maica y Control de un Convertidor Industrial de Acetileno". Tesis Doctoral, UNS. March (1998). 4. Sughrue E.L., R.L. Hair and R.J. CaUejas. AIChE Meeting, March (1995), 19-23. 5. Brown M.W., A_ Penlidis and G.R. Sullivan. The Can. J. of Chem. Engn. (1991) 69, 152. 5. Hobbs J.W., "Computer Control of an Acetylene Hydrogenation Process". Ind. Proc. Control Proc. Workshop, (1979). 7. Schbib N.S., &F. Errazu, J./~ Romagnoli, J.& Porras. Computers Chem. Engn. (1994), Vol 18, $355. 3. Gear C.W., "Numerical Initial Value Problems in Ordinary Differential Equations". Prentice Hall, Englewood Cliffs, N.S., (1971). 9. Van Doesburg H. and W.A, Jong, Chemical Engineering Science, (1976) 31, 45. 10. Gatica J. E, J.A_ Porras, A. F. Errazu and J. A Romagnoli. Chem. Engng. Comm. (1989) 78, 73-96. 11. Santiago J . ~ , Francesconi J.D. and N.L.Moretti. O/l Gas J. (1982) 81(39), 78-82.