Ind. Eng. Chem. Res. 2004, 43, 7019-7024
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PROCESS DESIGN AND CONTROL Runaway Detection in a Pilot-Plant Facility J. Bosch,†,‡ D. C. Kerr,§ T. J. Snee,§ F. Strozzi,| and J. M. Zaldı´var*,† European Commission, Joint Research Centre, Institute for Environment and Sustainability, TP272, 21020 Ispra (VA), Italy, Health and Safety Laboratory, Harpur Hill, Buxton, Derbyshire SK17 9JN, U.K., and Quantitative Methods Group, Engineering Department, Carlo Cattaneo University, Castellanza (VA), Italy
The divergence criterion allows detection in advance runaway initiation. When divergence (div) is greater than zero, this indicates that the reactor is moving to a dangerous state. In this work, a series of experiments have been carried out in a pilot-plant reactor, using the esterification reaction between 2-propanol and propionic anhydride, in order to assess the performances of a developed algorithm to calculate div online using temperature or pressure data. Furthermore, the model developed for this process allows a comparison between simulated and experimentally reconstructed divergences. The results show that a good agreement is obtained for the runaway experiments, whereas for near-runaway conditions, the presence of “noise” in the data shows the necessity to establish a limit value for the divergence, i.e., div > lim. In any case, we show that this methodology can be applied online to detect anomalous behavior in chemical reactors. 1. Introduction An essential task in chemical manufacturing processes consists of the maintenance of a high product quality. During recent years, because of market globalization, this has become more important in order to keep the competitive edge. The economic impact of abnormal situations on safety and product quality is enormous.1 For this reason, continuous monitoring of process variables is essential for the diagnosis of process malfunctions as well as for the rapid provision of corrective measures. In chemical reactor operation, temperature and pressure data frequently provide the basis for quality monitoring, evaluation, and control. An important step toward a better understanding of the behavior of the process is through the extraction of the salient features encapsulated in these data sets. In a series of recent works,2,3 a new online algorithm to calculate the divergence in chemical reactors has been developed. This algorithm can be implemented by only measuring reactor and jacket temperatures, and it uses state-space reconstruction techniques4,5 to calculate the divergence, which is a local property of the dynamics of the system. As was shown in refs 6-8, the divergence provides information on the safety status; i.e., div > 0 indicates a dangerous situation. Furthermore, as was shown in ref 9, the divergence may be obtained from several other measured variables, e.g., pressure, pro* To whom correspondence should be addressed. Tel.: +390332-789202. Fax: +39-0332-789328. E-mail:
[email protected]. † Institute for Environment and Sustainability. ‡ E-mail:
[email protected]. § Health and Safety Laboratory. Tel.: +44-114-289 2154. Fax: +44-114-289 2160. E-mail:
[email protected]. | Carlo Cattaneo University. Tel.: +39-0331-572364. Fax: +39-0331-480746. E-mail:
[email protected].
vided that they properly reflect the behavior of the chemical reactor. In this work, we have compared the analytical (calculated using a model) and reconstructed (calculated using only temperature or pressure measurements) divergences using a series of experiments conducted in the pilot plant at the Health and Safety Laboratory in Buxton, U.K.,10 which is a scale closer to industrial application than the calorimetric experiments2,3 and also interesting from the point of view of assessing the impact of process noise on the sensitivity of the calculation of the divergence. The selected reaction was the esterification between 2-propanol and propionic anhydride. The reaction was selected because it is a wellknown reaction and is moderately exothermic with no danger of decomposition reactions and for which accurate kinetics exist; the reaction exhibits second-order kinetics when no strong acid is present and a kind of autocatalytic behavior when the acid is introduced. We have found that early detection of runaway initiation is possible. Furthermore, by comparison of analytical and reconstructed divergence, it is shown that state-space reconstruction techniques using temperature and pressure perform correctly for runaway experiments, whereas for the limit case (between runaway and nonrunaway), reconstruction is more problematical because of the low values of state-space volume and, hence, in the divergence. The differences in signal-tonoise ratios in pressure versus temperature measurements are reflected in the quality of the reconstructed divergence. 2. Experimental Section 2.1. Pilot-Plant Installation. The pilot-scale facility for investigating runaway reactions10 is based around a 250-L (total capacity ) 340 L), jacketed, glass-lined reactor equipped with two glass feed vessels and con-
10.1021/ie049540l CCC: $27.50 © 2004 American Chemical Society Published on Web 10/02/2004
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Figure 1. Pilot plant. Instrumentation diagram.
nected, via a vent line, to a 2500-L stainless steel catch tank. Figure 1 is a schematic diagram of the pilot plant and catch tank, respectively. The reactor and catch tank have a maximum working pressure of 6 bar. The vent line between the reactor and catch tank is fitted with either a restricting orifice plate or a short nozzle and an actuated valve. The valve is linked to a pressure controller and is opened automatically when the pressure reaches a preselected value. The catch tank is fitted with a 75-mm vent direct to the atmosphere. Heattransfer fluid is circulated to the reactor jacket and to heating coils in the feed vessels. The temperature of each vessel can be independently controlled. Interconnecting chemical transfer pipework is fitted with remotely operated actuated valves. The pilot plant can be controlled and monitored remotely from a control room 100 m from the reactor building. 2.2. Experiment Design. A set of three experiments were carried out in the pilot-scale chemical plant at the Health and Safety Laboratory in Buxton, U.K., to evaluate the performance of the EWDS prototype. The selected reaction was the uncatalyzed esterification between 2-propanol and propionic anhydride. The stoichiometric scheme is given in eq 1. This reaction is interesting for our objectives because it is a moderately exothermic reaction with no danger of side or decomposition reactions. In addition, this reaction has been extensively studied in the past and accurate kinetics have been developed.
Figure 2. Maximum analytical divergence as a function of the jacket temperature (Tw) obtained for the esterification reaction and divergence criterion runaway boundary, div > 0. Table 1. Operating Conditions for the Esterification Experiments mass of 2-propanol mass of propionic anhydride stirrer speed jacket flow pressure vent set
Table 2. Kinetic Constants and Physicochemical Parameters of the Esterification Reaction A ) 4.3 × 108 s-1 n ) 2.1 CA0 ) 4.81 mol‚L-1 V0 ) 200 L
dx ) Ae-E/RT(1 - x)n dt dT dx 1 -∆HCA0V0 ) - US(T - Tw) dt FCpV0 dt
[
(2)
]
(3)
with initial conditions at t ) 0 s, CA0 ) CB0 ) 4.81
E/R ) 9900 K ∆H ) 66.641 kJ‚mol-1 US ) 305.8 W‚K-1 FCp ) 2432 J‚L-1‚K-1
mol‚L-1, V0 ) 200 L, and T ) Tw - 15 (to take into account endothermic mixing). The values of the kinetic constants, as well as the physicochemical properties of the system, are given in Table 2 (see also the Notoation section). The analytical divergence is defined as the trace of the Jacobian matrix, J, of the system, i.e.
[
∂(dx/dt) ∂(dx/dt) ∂x ∂T J) ∂(dT/dt) ∂(dT/dt) ∂x ∂T
(CH3)2CHOH + (CH3CH2CO)2O f CH3CH2COOH + CH3CH2COOCH(CH3)2 (1) The reactor was operated under isoperibolic conditions (constant jacket temperature), and the experiments were conducted batchwise using the parameters and operating conditions listed in Table 1. The only parameter that changed between experiments was the jacket temperature. The experiments were designed by applying the divergence criterion calculated from the mass and energy balances given by
58.7 kg 127.1 kg 25 rpm 20 kg‚min-1 1.5 bar
]
(4)
which means the sum of the diagonal elements
div ) j11 + j22
(5)
j11 ) -nAe-E/RT(1 - x)n-1
(6)
( )
]
where
j22 )
[
1 E -∆HCA0V0 Ae-E/RT(1 - x)n - US 2 FCpV0 RT (7)
The runaway criterion6 states that when divergence is greater than zero on a segment of the reaction path, the system is under runaway conditions.
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Figure 3. Experimental and simulated (venting not simulated) reactor temperatures for the batchwise uncatalyzed esterification reaction between 2-propanol and propionic anhydride at several jacket temperatures, i.e., 348.16 K (Exp1), 343.16 K (Exp2), and 333.16 K (Exp3).
Figure 2 shows the maximum divergence value obtained for the parameters contained in Tables 1 and 2 as a function of the jacket temperature. As can be seen, the maximum divergence value increases as the jacket temperature increases, crossing the criterion boundary when the divergence is zero at 331.59 K. From these results, it was decided to set the jacket temperature for Exp1, Exp2, and Exp3 at 348.16, 343.16, and 333.16 K, respectively. These temperatures were selected in order to change the system characteristics from a runaway scenario to a nonrunaway scenario (limit case, between ignition and nonignition) while still being able to perform the experiments in a reasonable amount of time. 2.3. Experimental Procedure. The esterification experiments have been carried out following the procedure summarized below: (i) 2-Propanol (reactant B) was weighed and loaded into a feed vessel. (ii) Propionic anhydride (reactant A) was weighed and loaded into the reactor. (iii) Reactor and feed vessel temperatures were set at the desired temperature. (iv) Once both the feed vessel and reactor had reached the set-point temperature, 2-propanol was added to the reactor from the feed vessel. (v) When the reaction had finished, the reactor contents, and the catch tank (if the reactor had been vented), were discharged. Figures 3 and 4 show the experimental and simulated temperature profiles and the experimental pressure profiles, respectively. In the first two experiments, the reactor pressure reached the pressure vent set point of 1.5 bar, causing the vent valve to open. This is noticeable by the sudden decrease in the reactor temperature at 1810 and 2504 s, respectively, and by the corresponding pressure drop in Exp1 in Figure 4. Because of problems with the pressure transducer, no pressure data are available for Exp2. On the contrary, the third experiment presents a clear, but slower, exothermic effect without autoacceleration behavior or venting of the reactor contents.
Figure 4. Pressure data recorded temperatures for the batchwise uncatalyzed esterification reaction between 2-propanol and propionic anhydride at several jacket temperatures, i.e., 348.16 K (Exp1), upper layer, and 333.16 K (Exp3), lower layer.
Figure 5. Analytical divergence, eq 5, and divergence criterion limit (div > 0) obtained from simulation of the batchwise esterification reaction between 2-propanol and propionic anhydride at several jacket temperatures, i.e., 348.16 K (Exp1), 343.16 K (Exp2), and 333.16 K (Exp3).
As shown in Figure 3, simulations are in good agreement with the experimental results during the reaction while the vent valve is closed, presenting slight differences in the profile in the ignition region in Exp1 and Exp2, where the simulated experiments show a higher heating rate. This is due to the characteristically high sensitivity of the system (Morbidelli and Varma, 1999) under these conditions. Regarding the reactor contents venting, the performed simulations do not take this scenario into account and, therefore, the simulated results differ from the experimental results after the vent valve is opened. The analytical divergence for the three experiments is shown in Figure 5. As can be seen in the upper layers, these cases correspond to a runaway situation, whereas the lower layer corresponds to a limit case between ignition and nonignition behavior where the divergence is close to the zero line.
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3. State-Space Reconstruction of the Divergence Using Temperature and Pressure Experimental Data To calculate the divergence online without the need to know the differential equations of the system, we have used the theory of embedding. The theory of embedding is a way to move from a temporal time series of measurements to a state space similar, in a topological sense, to that of the underlying dynamical system we are interested in analyzing. Techniques of statespace reconstruction were introduced in refs 4 and 5, in which it is shown that it is possible to address this problem using measurements of a time series of the dynamical system of interest. The extension of this theory for the case of batch and semibatch chemical reactors is complicated by the dynamic nature (nonstationarity) of the system, which implies that the embedding parameters, i.e., time delay, ∆t (the lag between data when reconstructing the state space), and the embedding dimension, dE (the dimension of the space required to unfold the dynamics), are changing during the process. However, as was discussed in ref 2, an appropriate value for these parameters can be chosen to allow state-space reconstruction. Furthermore, several methods of reconstruction of state spaces time delay embedding vectors, derivative coordinates, and integral coordinatessmay be used.2 However, in our experience, the method more robust to noise in the data is the one based on delayed vectors, i.e., {T(t), T(t-∆t), ...} or {P(t), P(t-∆t), ...}, and for the cases studied, an embedding dimension of 2 is sufficient to reconstruct the divergence.2,3 Concerning time delay, a value between 50 and 150 s produces similar results in the reconstruction of the divergence; lower or higher values increase the noise or produce shorter in advance detection times, respectively. The divergence gives the rate of expansion or contraction of the phase space volume, VPS, of a dynamical system, and as was shown in ref 6, it may be calculated as
div ) V˙ PS(t)/VPS(t)
(8)
whereas the phase space volume (area) at time t may be calculated using the determinant between close points in state space from a series of temperature or pressure measurements as
[
VPS(t) ) |det
]
T(t) - T(t-∆t) 0 | T(t-∆t) - T(t-2∆t) 0 (9)
Because of the volume contraction in state space, characteristic of dissipative systems, VPS(t) will rapidly tend to zero (computer precision) and produce artifacts when introduced as the denominator in eq 8.2 However, by definition, the volume is always positive and, hence, div > 0 is equivalent to checking if
∆VPS(t) > 0
(10)
where ∆VPS(t) is an infinitesimal state-space volume variation. This eliminates the need to divide two small numbers, thus producing an increase in the numerical errors. Even though the values of ∆VPS(t) are, in principle, not preserved under state-space reconstruc-
Figure 6. Comparison between the analytical and reconstructed divergences using {T(t), T(t-∆t)} as the state space and dE ) 2 and ∆t ) 50 s as reconstruction parameters, for the batchwise esterification experiments.
tion, its sign, which is the sign of the divergence and, hence, its identification criterion, is preserved. However, because of noise in the signal, a limit value greater than zero needs to be defined. In this case, we have used the limit case, Exp3, to define a suitable value to distinguish between runaway and nonrunaway situations. 3.1. ∆VPS and div for Esterification Experiments Using Temperature Measurements. Even though the divergence reconstruction sometimes presents numerical problems due to division by a small number, the reconstructed divergences using reactor temperature data in Exp1, Exp2, and Exp3 and their corresponding analytical divergences are displayed in Figure 6 using a time delay of 50 s and an embedding dimension, dE, of 2. Because the model does not consider the venting process, the comparison between reconstructed and analytical divergences is only valid from the addition of 2-propanol to the venting of the reactor contents in Exp1 and Exp2 and until the end of the reaction in Exp3. As can be seen, because of the small values of VPS, sometimes is not possible to calculate the divergence, and in this case, its value is set equal to zero. This happens during the venting in Exp1 and Exp2 and during the last part of the reaction in Exp3. Furthermore, because four sampling points are necessary for the calculation of ∆VPS (see eq 9), during the first 200 s (4∆t), its calculation is not possible. Analytical and reconstructed divergences have been calculated using eqs 5 and 8, respectively. To avoid numerical errors due to division by a small number in eq 8, the reconstructed divergence has only been calculated when volume values were bigger than a limit value. As can be seen, the reconstructed divergence presents a good agreement with the analytical divergence, especially in the first two experiments. In the third experiment, the reconstructed divergence shows an oscillating profile close to the analytical divergence that improves as the time delay increases (results are not shown). This behavior is produced because of the volume contraction in the state space typical of dissipative systems such as chemical reactors. This means that VPS tends to zero and, hence, when introduced as a denominator in eq 8, produces numerical errors by
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Figure 7. ∆VPS values obtained using {T(t), T(t-∆t)} as the state space. Reconstruction parameters: ∆t ) 100 s and dE ) 2. ∆Vlim PS ) 1 × 10-3 for alarm.
increasing the noise level. On the other hand, the presented results show that it is possible to calculate the divergence satisfactorily using a reconstructed state space. To avoid the numerical errors and noise increase when the volume tends to zero, we may just evaluate ∆VPS as stated previously. As can be seen in Figure 7 from Exp1, Exp2, and Exp3, ∆VPS values exceed the alarm limit, ∆Vlim PS (this value was obtained using Exp3 and heating/cooling ramps not shown), in the first two cases presenting an increasing profile, whereas in the third case, i.e., the nonrunaway case, ∆VPS values remain oscillating around zero. In particular, alarms are triggered off at 584 s in Exp1 and at 797 s in Exp2, i.e., 1226 and 1707 s before the reactor venting, respectively. In general, ∆VPS produces a larger segregation among nonrunaway and runaway conditions than the reconstructed divergence (see Figure 6), which is an important feature to avoid false alarms. For these reasons, we use ∆VPS in our algorithm for early warning detection of runaway initiation rather than using the reconstructed divergence. Furthermore, the uncatalyzed esterification reaction between 2-propanol and propionic anhydride represents a moderately exothermic reaction with long induction periods and, hence, the values of div are relatively small when compared with those of faster and more exothermic reactions.2,3,9 3.2. ∆VPS and div for Esterification Experiments Using Pressure Measurements. One of the usually monitored variables in process plants is pressure. Pressure may be a direct measure of a state variable in gassy systems or related to the state variables in vapor systems. In either case, the theory of embedding ensures that state-space reconstruction is possible under these conditions and, hence, divergence may be calculated as well. Following the same procedure, VPS, ∆VPS, and the reconstructed divergence have been calculated for Exp1 and Exp3 and the reconstructed divergence is compared with the analytical one in Figure 8. Because of the high levels of noise contained, as can be seen in Figure 4, pressure data have been filtered using an 11-pointcentered moving-average technique before the reconstruction of the state space. As shown in Figure 8, the reconstructed divergence in Exp1 first oscillates around
Figure 8. (a) State-space volume, VPS. (b) Variation of the statespace volume, ∆VPS. (c) Comparison between the analytical, eq 5, and the reconstructed divergence values obtained using {P(t), P(t∆t)} as the state space for Exp1. Reconstruction parameters are ∆t ) 100 s and dE ) 2. The limit value for runaway detection was -6 obtained from Exp3, ∆Vlim PS ) 3 × 10 , whereas the minimum value of the state-space volume for reconstruction is in this case VPS,min ) 2 × 10-4.
the analytical one and, only at the end, shows a good agreement with that calculated analytically. When div could not be calculated, its default value was set to zero. This fact is due to the initial low values of VPS that have a low signal-to-noise ratio, as has already been observed in the former reconstruction. On the other hand, it is not possible to calculate the reconstructed divergence for Exp3 because the VPS values are below the limit value fixed to avoid numerical errors. However, it is still possible to evaluate ∆VPS to define the alarm limit for Exp1. In this case, also because of noise in the signal, ∆VPS could not always be calculated and, hence, it was fixed arbitrarily to -1 × 10-5. In this case, the alarm limit is exceeded at 1471 s, 245 s later than when using temperature measurements. 4. Conclusions The comparison between analytical and reconstructed divergences using only temperature or pressure measurements results has shown that the temperature reconstruction is able to detect runaway situations without producing false alarms. In addition, the reconstructed divergence using temperature is in good agreement with the analytical one, which confirms the accuracy of the reconstruction. However, numerical errors, produced during the calculation of the reconstructed divergence, point to ∆VPS as the best parameter for early warning detection of runaway initiation. Again, using pressure measurements, it is also possible to see that the divergence can be reconstructed and that pressure may be used for early detection. However, the detection occurs later than when using temperature measurements because of in this case the larger noiseto-signal ratio in the pressure data. Acknowledgment This research has been supported by the EU funded project AWARD (Advanced Warning and Runaway
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Disposal; Contract G1RD-CT-2001-00499) in the GROWTH program of the European Commission. Notation A ) Arrhenius parameter Cp ) mean specific heat of the reaction mixture, kJ‚K-1‚kg-1 C ) concentration of the reactant, kmol‚m-3 dE ) embedding dimension E ) activation energy, kJ‚mol-1 n ) reaction order R ) universal gas constant, kJ‚mol-1‚K-1 S ) heat-exchange surface area, m2 t ) time, s T ) temperature, K Tw ) jacket temperature, K U ) heat-transfer coefficient, J‚m-2‚K-1‚s-1 V ) volume of reaction, L VPS ) phase space volume x ) conversion, x ) 1 - (CA/CA0) Greek Symbols ∆H ) heat of the reaction, kJ‚mol-1 ∆t ) time delay, s F ) density of the mixture, kg‚L-1
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isoperibolic batch reactors: Simulated and experimental results. Comput. Chem. Eng. 2004, 28, 527. (3) Zaldı´var, J. M.; Bosch, J.; Strozzi, F.; Zbilut, J. P. Early warning detection of runaway initiation using chaos-like features. Commun. Nonlinear Sci. Numer. Simul. 2004 (in press, available online at sciencedirect). (4) Packard, N.; Crutchfield, J.; Farmer, D.; Shaw, R. Geometry from a time series. Phys. Rev. Lett. 1980, 45, 712. (5) Takens, F. Detecting strange attractors in fluid turbulence. Dynamical Systems and Turbulence; Springer: Berlin, 1981; pp 366-381. (6) Strozzi, F.; Zaldı´var, J. M.; Kronberg, A.; Westerterp, K. R. On-line runaway prevention in chemical reactors using chaos theory techniques. AIChE J. 1999, 45, 2394. (7) Zaldı´var, J. M.; Cano, J.; Alo´s, M. A.; Sempere, J.; Nomen, R.; Lister, D.; Maschio, G.; Obertopp, T.; Gilles, E. D.; Bosch, J.; Strozzi, F. A general criterion to define runaway limits in chemical reactors. J. Loss Prev. Process Ind. 2003, 16, 187. (8) Bosch, J.; Strozzi, F.; Lister, D.; Maschio, G.; Zaldı´var, J. M. Sensitivity Analysis in Polymerization Reactions using the Divergence Criterion. Process Saf. Environ. Prot. 2004, 82, 18. (9) Bosch, J.; Strozzi, F.; Snee, T. J.; Hare, J. A.; Zaldı´var, J. M. A comparative ana´lisis between temperature and pressure measurements for early detection of runaway initiation. J. Loss Prev. Process Ind. 2004, 17, 389. (10) Snee, T. J.; Hare, J. A. Development and application of a pilot scale facility for studying runaway exothermic reactions. J. Loss Prev. Process Ind. 1992, 5, 46. (11) Varma, A.; Morbidelli, M.; Wu, H. Parametric Sensitivity in Chemical Systems; Cambridge University Press: Cambridge, U.K., 1999.
Received for review May 28, 2004 Revised manuscript received July 26, 2004 Accepted August 25, 2004 IE049540L
