CFD simulation of accidents in industrial batch stirred tank reactors

CFD simulation of accidents in industrial batch stirred tank reactors

Chemical Engineering Science 62 (2007) 4920 – 4925 www.elsevier.com/locate/ces CFD simulation of accidents in industrial batch stirred tank reactors ...

382KB Sizes 5 Downloads 59 Views

Recommend Documents

No documents
Chemical Engineering Science 62 (2007) 4920 – 4925 www.elsevier.com/locate/ces

CFD simulation of accidents in industrial batch stirred tank reactors A. Milewska, E.J. Molga ∗ Chemical and Process Engineering Department, Warsaw University of Technology, Wary´nskiego 1, 00-645 Warsaw, Poland Received 14 June 2006; received in revised form 17 November 2006; accepted 17 December 2006 Available online 30 December 2006

Abstract In this work, we have analyzed the application of CFD (computational fluid dynamics) to simulate consequences of stirrer failures, which can lead to reactor thermal runaway. For a typical industrial batch reactor, several “CFD computational experiments” have been carried out to explore runaway and non-runaway situations. Then the results of the CFD simulations, supported by an on-line divergence criterion, have been used to detect a dangerous reactor behavior. It has been found out, that even for the reactor operated at potentially safe conditions a failure of the stirring system can lead to serious thermal runaways. A significance of a proper location of temperature probe for an early runaway detection has also been discussed. A modification of the applied divergence criterion to avoid false alarms has been proposed and tested. 䉷 2007 Elsevier Ltd. All rights reserved. Keywords: Batch reactor; Thermal runaway; Reactor safety; Reactor modelling; Computational fluid dynamics (CFD)

1. Introduction

2. Divergence criteria

A loss of temperature control (thermal runaway) in batch and semibatch chemical reactors occurs for exothermic reactions, when for some reasons the rate of heat generation by chemical reaction exceeds that of heat removal by cooling. Then, an increase in the reaction rate, hence further increase of the heat generation rate, is provoked and this auto-acceleration effect can bring the reactor temperature to such a high value, that dangerous side and decomposition reactions may be triggered off. Despite of significant improvement in the safety predictions and countermeasures, still a lot of serious runaways occur in batch and semibatch industrial reactors (Westerterp and Molga, 2004). This paper presents a discussion of results obtained with the CFD (computational fluid dynamics) model developed for a batch stirred tank reactor, in which a strongly exothermic homogeneous reaction takes place in the liquid phase. The consequences of stirrer failures are simulated and discussed from the safety point of view.

A numerous off- and on-line safety criteria help to prevent thermal runaway by predicting safe or even inherently safe operating conditions. The problems of robustness and accuracy of these criteria are widely discussed in the literature—e.g. see Westerterp and Molga (2006). One of these criteria based on the chaos theory techniques has been proposed by Strozzi and Zaldivar (1994) and Strozzi et al. (1999), then developed further by Bosch et al. (2004c) and Zaldivar et al. (2005). This criterion states that the reactor is under runaway conditions, when the divergence of the system is positive on a segment of the reaction path. This divergence is a scalar defined as

∗ Corresponding author. Tel.: +48 22 6606293; fax: +48 22 8251440.

E-mail addresses: [email protected] (A. Milewska), [email protected] (E.J. Molga). 0009-2509/$ - see front matter 䉷 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2006.12.036

div {F[x(t)]} =

F1 [x(t)] F2 [x(t)] Fn [x(t)] + + ··· + , x1 x2 xn (1)

where Fi [x(t)] = xi /t for i = 1, 2, . . . , n is a continuous dynamic system of the ordinary differential equations. For chemical reactors, the divergence is defined at each time point as the sum of the partial derivatives of the mass and energy balances with respect to the corresponding variables: the conversion () and the reactor temperature (Tr ), respectively. The above definition can be used analytically only if we can

A. Milewska, E.J. Molga / Chemical Engineering Science 62 (2007) 4920 – 4925

define the differential balance equations of the system, i.e., if the reaction kinetics is known. If the explicit reactor model cannot be formulated, the divergence can be calculated on-line by the reconstruction of a state space from the time series of measurements—e.g. temperature measurements. Based on the Liouville’s theorem which states that:  t  Vps (t) = Vps (0) exp div {F[x()]} d (2) 0

after several transformations, the following expression can be obtained (Bosch et al., 2004c): div [J (x)] =

Vps (t) 1 dVps (t) ≈ , Vps (t) dt Vps (t)

(3)

where Vps =

Vps (t + t2 ) − Vps (t) dVps (t) ≈ . dt t2

So, because the state space volume is always positive, therefore the runaway criterion div > 0 is equivalent to Vps > 0. A crucial factor for the efficient application of this criterion is the method of the phase space reconstruction, i.e., the type of coordinates (delay, divergence, integral, mixed), embedding dimension and time delay that provides useful results for a given purpose—see Bosch et al. (2004b). For the experimental data the reconstruction parameters found by Bosch et al. (2004a) are: delay coordinates {Tr (t), Tr (t − t)}, embedding dimension dE = 2 and time delay t = 100 s. To avoid false alarms lim = 10−3 . If the variation of the the limit value was set as: Vps reconstructed phase space volume exceeds the limit value, the warning alarm is set.

4921

Schematic diagram of the reactor vessel is shown in Fig. 1, where a location of three hypothetical temperature probes is also indicated. The considered reactor is equipped with a jacket and a pitched-blade stirrer and no baffles are provided. The vessel diameter is 0.680 m, height 0.755 m, stirrer diameter 0.477 m located at 0.052 m from the bottom. A CFD reactor model has been formulated. The commercial grid-generation tools (MIXSIM 2.0 and GAMBIT 2.1 of Fluent Inc.) have been used to model the geometry and to generate the body-fitted grids. About 340k computational cells have been applied for the simulation. It should be pointed out that an adequate number of cells is crucial for the accuracy of CFD calculations. It has been established, based on our previous experience and several trials, that the grid consisting of 340k cells is sufficient for our model. The “Reynolds stresses” appearing in a momentum balance equation have been modelled by employing the Bussinesq hypothesis and the standard k– turbulent model has been used, e.g. see Wilcox (1998). For the wall function, two-layer model for enhanced wall treatment with thermal effects has been applied. A stirrer movement has been modelled using “multiple reference frame” (MRF) approach—for details see Fluent 6.2, User’s guide, 2002. For the considered esterification reaction, the source term in the species balance equations (due to a progress of the chemical reaction) has been evaluated with the kinetic expressions developed by Bosch et al. (2004a) and for purpose of this study implemented in the user defined function (UDF). The finite volume method has been employed and CFD simulations have been executed using a commercial code Fluent 6.2 by Fluent Inc. A good convergence of calculations has been obtained with a time step equal to 0.1 s.

4. Consequences of stirrer failures—CFD simulations 3. CFD reactor model CFD is a method of predicting fluid flow, heat and mass transfer, chemical reactions and other related phenomena (e.g. as boiling, crystallization) by solving a set of the appropriate mathematical equations that describe these processes—such as mass, momentum, energy and species balances. CFD allows to analyze the fluid motion and performance of process equipment at its different geometrical configurations, operating conditions and scale. Such kind of “computational experiments” can supply important information on the process performance, its reliability and safety, product consistency and productivity. CFD simulations are very useful for modelling and designing of the process, particularly in industrial scale. Among others, CFD is applied to many areas of chemical reaction engineering—e.g. see Kuipers and van Swaaij (1998) and Ranade (2002). The reactor model elaborated in this study is based on a geometry of the pilot-scale reactor (250 1) at the Health and Safety Laboratory in Buxton, UK—see Bosch et al. (2004b). In that reactor the esterification reaction between propionic anhydride and 2-propanol was carried out. The reactor was operated at isoperibolic conditions, i.e., at a constant jacket temperature.

It has been found that even for processes carried out along a safe temperature trajectory the thermal runaway is still possible due to unexpected events such as failures of stirring and/or cooling systems. Particularly, a failure of the stirring system is very dangerous. For polymerization reactions, when during the reaction progress the product viscosity increases significantly as well as for other reactions local “hot spots” caused by inefficient mixing can lead to a global thermal runaway, triggering off dangerous side or decomposition reactions. Runaway events are difficult and dangerous for experimental investigation, particularly in industrial scale reactors. In this case, the CFD simulations (“computational experimentation”) can be extremely useful. Four CFD simulations have been carried out—see Table 1. The first two simulations indicate a typical runaway (run HSL1) as well as non-runaway (run HSL3) behavior of the reactor. Using the latter run carried out at potentially safe operating conditions two stirrer failures have been considered. In the first case, after 8000 s of a normal work, the stirrer speed has been significantly slowed down to R = 5 rpm. In the second one, after the same 8000 s of a normal work, the stirrer has been completely stopped.

4922

A. Milewska, E.J. Molga / Chemical Engineering Science 62 (2007) 4920 – 4925

Fig. 1. Results of the CFD simulation obtained for the run HSL3-f2, see Table 1. Local temperature inside the reactor vessel after stirrer failure at t = 8200 s. Stirrer stopped at t = 8000 s.

Table 1 Operating conditions for the simulated runs Run

Tj (◦ C)

R (rpm)

Stirrer failure

Runawaya

HSL1 HSL3 HSL3-f1 HSL3-f2

75 60 60 60

25 25 25 25

Non Non After t = 8000 (s) stirrer slowed down at R = 5 (rpm) After t = 8000 (s) stirrer stopped

Yes Non Non (false alarm) Yes

a Detected

with the divergence criterion taking calculated volume-averaged temperature—Tavg .

5. Results and discussion Spatial temperature profiles inside the reactor, obtained from the elaborated CFD model after a stirrer failure, are shown in Fig. 1. Such results can be used to design a runaway detection system integrated with an effective quenching system. After the alarm is set, a suitable inhibitor can be added or other countermeasures (e.g. venting) taken to stop the reaction progress and prevent the accident. However, as the stirrer does not work properly, a method of inhibitor addition must be carefully selected (Dakshinamoorthy et al., 2004). Safety considerations are summarized in Fig. 2, where for each simulated run the local temperatures (at points indicated in Fig. 1) as well as the volume-averaged temperatures are plotted as a function of the reaction time. In Fig. 2, also results obtained

with application of the divergence criterion are shown—i.e., the values of Vps determined with the use of temperature profiles obtained from the elaborated CFD reactor model. For the runs HSL1 and HSL3 (runaway and non-runaway case, respectively, and no stirrer failure), due to a sufficiently good mixing of the reactor content, no influence of the location of temperature probes on a detection of runaway or safe reactor performance is noticed. However, due to a steep temperature trajectory caused by the runaway, a slight spatial temperature distribution inside the reactor can be observed for run HSL1. For run HSL3-f1, in which no runaway operating conditions as those in run HSL3 are applied, but after t = 8000 s a significant slow down of stirrer occurs, only a very slight temperature distribution inside the reactor is noticed. However, even such a small disturbance in reactor operation causes the set of

A. Milewska, E.J. Molga / Chemical Engineering Science 62 (2007) 4920 – 4925

4923

HSL1 1

ΔVps

T [°C]

150

100

50

0.5

0 0

2000

4000

0

6000

2000

t [s]

4000

6000

t [s] HSL3

80

20

x 10−4

15 ΔVps

T [°C]

70 60

10 5 0

50 0

2000

4000

6000 t [s]

8000

10000

−5

12000

0

2000

4000

6000 t [s]

8000

10000

12000

x 10−3

HSL3−f1 100

80

ΔVps

T [°C]

4

2

60 0 0

2000

4000

6000 t [s]

8000

10000

8000

12000

10000 t [s]

11000

12000

9000 t [s]

9500

10000

x 10−3

HSL3−f2 4

ΔVps

150 T [°C]

9000

100

2

0

50 0

2000

4000

6000 t [s]

8000

10000

12000

8000

8500

Fig. 2. Results of the CFD simulations and runaway detection. Left column: temperature vs. time profiles: local temperatures profiles (at points T1, T2, T3—see Fig. 1) and the volume-averaged temperatures profiles (Tavg ) for each simulated run—see Table 1. Right column: variation of reconstructed phase space volume Vps estimated with use of the local temperatures (T1–T3) and the volume-average temperature (Tavg ) from CFD simulations. Dashed lines lim = 10−3 . Legend: —— T , - - - T1, · · · · · · T2, —·— T3. show the limit value Vps avg

4924

A. Milewska, E.J. Molga / Chemical Engineering Science 62 (2007) 4920 – 4925

Table 2 Runaway detection with the results of CFD simulations and the divergence criterion Run

HSL1 HSL3 HSL3-f1 HSL3-f2

Temperature sensor

Tavg Tavg Tavg Tavg T1 T2 T3

Divergence criterion talarm (s)

Tr,alarm ( C)

talarm (s)

Tr,alarm (◦ C)

881 No alarm 8168 8280 8240 8260 8220

66.3

1121 No alarm No false alarm 8420 8780 8720 8360

69.2

77.5 77.6 77.7 77.8 78.0

alarm, while the maximum reactor temperature is about 98 ◦ C. Such a warning system behavior can be classified as the “false alarm”. To prevent such situations an additional condition has been proposed: the runaway alarm is set when the time during lim exceeds the limit value t lim . which Vps > Vps lim t (Vps > Vps ) > t lim .

Modified divergence criterion ◦

(4)

For the considered pilot-plant scale reactor t lim = 240 s. Using such a modified divergence criterion the false alarms can be avoided. For run HSL3-f2, in which no runaway operating conditions as those in run HSL3 are applied, but after t = 8000 s the stirrer is stopped, a significant temperature non-homogeneity inside the reactor should be taken into account. In this case, a proper localization of a single temperature probe can be crucial for an early detection of runaway. As can be concluded from the diagrams of Fig. 2 as well as from data collected in Table 2, the time needed to trigger off the alarm, talarm , significantly depends on localization of the temperature probe. In a considered case, to detect a thermal runaway as early as possible the temperature sensor should be placed at the upper and central part of the reactor vessel—e.g. as the sensor T3 in Fig. 1. 6. Conclusions The elaborated CFD model has been used to simulate an operation of the pilot-scale reactor at both: normal operation and operation after stirrer failure. For the obtained results the divergence criterion was applied to detect a thermal runaway in advance. To avoid false alarms a modification of this criterion has been proposed, which is based on an additional condition for the time of lasting warning signal. It has been found, that even for the reactor operated following potentially safe conditions the failure of the stirring system can lead to thermal runaway. The results presented in this paper can be useful for extending the application of CFD for preventing thermal runaway. Presented approach (method of modelling, application of divergence criterion) can be generalized for different reacting systems, although specific conclusions—as the value of t lim —depend on properties of the system under consideration.

78.2 81.5 80.7 78.6

Notation J R talarm t lim Tr Tj V Vps lim Vps 

Jacobian matrix stirrer rotation speed, rpm time of runaway detection, s limit value of time (Eq. (4)), s reactor temperature, ◦ C jacket temperature, ◦ C state space volume, m3 variation of reconstructed phase space volume, m3 limit value of variation of reconstructed phase space volume, m3 conversion

Acknowledgments This study has been supported by the State Committee for Scientific Research (KBN) within a frame of the Grant no. l T09C 024 30. References Bosch, J., Kerr, D., Snee, T., Strozzi, F., Zaldivar, J., 2004a. Runaway detection in a pilot-plant facility. Industrial & Engineering Chemistry Research 43, 7019–7024. Bosch, J., Strozzi, F., Snee, T., Hare, J., Zaldivar, J., 2004b. A comparative analysis between temperature and pressure measurements for early detection of runaway initiation. Journal of Loss Prevention in the Process Industries 17, 389–395. Bosch, J., Strozzi, F., Zbilut, J., Zaldivar, J., 2004c. On-line runaway detection in isoperibolic batch and semibatch reactors using the divergence criterion. Computers and Chemical Engineering 28, 527–544. Dakshinamoorthy, D., Khopkar, A., Louvar, J., Ranade, V., 2004. CFD simulations to study shortstopping runaway reactions in a stirred vessel. Journal of Loss Prevention in the Process Industries 17, 355–364. Fluent 6.2, User’s guide, 2002, Fluent Inc., USA. Kuipers, J., van Swaaij, W., 1998. Computational fluid dynamics applied to chemical reaction engineering. Advances in Chemical Engineering, vol. 24. Academic Press, USA. Ranade, V., 2002. Computational flow modeling for chemical reactor engineering. Process Systems Engineering, vol. 5. Academic Press, New York. Strozzi, F., Zaldivar, J., 1994. A general method for assessing the thermal stability of batch chemical reactors by sensitivity calculations based on Lyapunov exponents. Chemical Engineering Science 49, 2681–2688.

A. Milewska, E.J. Molga / Chemical Engineering Science 62 (2007) 4920 – 4925 Strozzi, F., Zaldivar, J., Kronberg, A., Westerterp, K., 1999. On-line runaway prevention in chemical reactors using chaos theory techniques. A.I.Ch.E. Journal 45, 2429–2443. Westerterp, K., Molga, E., 2006. Safety and runaway prevention in batch and semibatch reactors—a review. Transactions of the Institution of Chemical Engineers, Part-A, Chemical Engineering Research and Design 84, 543–552.

4925

Westerterp, K.R., Molga, E.J., 2004. No more runaways in fine chemical reactors. Industrial & Engineering Chemistry Research 43, 4585–4594. Wilcox, D.C., 1998. Turbulence Modeling for CFD. second ed. DCW Industries. Zaldivar, J., Bosch, J., Strozzi, F., Zbilut, J., 2005. Early warning detection of runaway initiation using non-linear approaches. Communications in Nonlinear Science and Numerical Simulations 10, 299–311.