A GENERAL CRITERION TO DEFINE RUNAWAY LIMITS IN CHEMICAL REACTORS. AWARD PROJECT (Advanced Warning And Runaway Disposal) (Growth Project G1RD-CT-2000-00499)

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EUROPEAN COMMISSION
JOINT RESEARCH CENTRE
Institute for Environment and Sustainability
Inland and Marine Waters Unit
1-21020 Ispra (VA) Italy
A GENERAL CRITERION TO DEFINE RUNAWAY LIMITS IN
CHEMICAL REACTORS
AWARD PROJECT (Advanced Warning And Runaway Disposal)
(Growth Project G1RD-CT-2000-00499)
PlotmaU) a01-\ > 335
320325-"u
Temperature (K)
/. M. Zaldivar,J. Canot, Μ. A. Alóst, J. Semperet, R. Nomen*, D. Lister*, G.
Maschio*, J. Boschtand F. Strozzi*
European Commission, Joint Research Centre, Institute for Environment and Sustainability,
Ispra, Italy
¡Institut Químic de Sarriá-URL,Chemical Engineering Department,
Barcelona, Spain
Dipartimento di Chimica Industriale ed Ingegneria dei Materiali, Università di Messina,
Messina, Italy
tCarlo Cattaneo University, Engineering Department, Quantitative Methods Group
Castellanza, Italy
2002 EUR 20250 EN EUROPEAN COMMISSION
JOINT RESEARCH CENTRE
Institute for Environment and Sustainability
Inland and Marine Waters Unit
1-21020 Ispra (VA) Italy
A GENERAL CRITERION TO DEFINE RUNAWAY LIMITS IN
CHEMICAL REACTORS
AWARD PROJECT (Advanced Warning And Runaway Disposal)
(Growth Project G1RD-CT-2000-00499)
0.012 A
360 365 370
i-e 340 345 [Ilo (mo«) gu-i 330 3J5
320 325
Temperature (K)
J. M. Zaldívar,J. Cano*, M. A. Alósf, J. Semperef, R. Nomen*, D. Lister*, G.
Maschio*, J. Bosch* and F. Strozzi*
European Commission, Joint Research Centre, Institute for Environment and Sustainability,
Ispra, Italy
Tinstitut Químic de Sarriá-URL,Chemical Engineering Department,
Barcelona, Spain
*'Dipartimento di Chimica Industriale ed Ingegneria dei Materiali, Università di Messina,
Messina, Italy
*Carlo Cattaneo University, Engineering Department, Quantitative Methods Group
Castellanza, Italy
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Printed in Italy AWARD (Advanced Warning And Runaway Disposal) Project
(Growth Project G1RD-CT-2000-00499)
Deliverable: Final report on the theoretical verification of the divergence criterion (D12. Task 2.1.).
Objective: The objective of Task 2.1 was to extend the validity of the runaway criterion, div >0,
and to compare it with other existing criteria. We recall that the divergence, div, is a scalar quantity
defined at each point as the sum of the partial derivatives of the mass and energy balances with
relation to the correspondent variables -temperature and conversions-, i.e.
d(dT I dt) I dT + Σ d(dz¡ Idt) ' &, ■
i
Abstract
A general runaway criterion valid for single as well as for multiple reaction types, and for several
types of reactors, i.e. batch (BR), semibatch (SBR) and continuous stirred tank reactor (CSTR) has
been developed. The criterion says that we are in a runaway situation when the divergence of the
system becomes positive (div >0) on a segment of the reaction path. We recall that the divergence
is an scalar quantity defined at each point as the sum of the partial derivatives of the mass and
energy balances with respect to the correspondent state variables. Only conversions that contribute
to the heat balance should be included in the calculation. The application of the runaway criterion is
illustrated for several kinetic schemes, between them: consecutive, parallel, equilibrium, mixed
kinetics and polymerisation reactions. Furthermore, different types of reactors, i.e. BR, SBR, and
CSTR; and operating conditions, i.e. isoperibolic and isothermal, have been analysed. The runaway
limits (or parametric sensitive regions) have been compared with previous criteria. The results show
that this is a general runaway criterion than can be used to calculate the runaway limits for chemical
reactors. A considerable advantage, over existing criteria, is that it can be calculated on-line based
only on temperature measurements and, hence, it constitutes the core of an early warning runaway
detection system we are developing.
Keywords. Nonlinear dynamics, safety, batch, reaction engineering, dynamic simulation CONTENTS
1. INTRODUCTION 5
2. DEFINITION OF THE RUNAWAY CRITERION 7
3. KINETIC SCHEMES 9
3.1. Consecutive reactions 10
3.2. Parallel reactions4
3.3. Equilibrium reactions7
3.4. Mixed kinetic schemes 2
3.5. Case study: Methylmethacrylate Polymerization 23
4. BATCH, SEMIBATCH AND CSTR REACTORS 32
5. THE INFLUENCE OF THE CONTROL SYSTEM 4
5.1. Two proportional control loops0
5.2. PI control 46
6. CONCLUSIONS8
NOTATION9
REFERENCES 51 1. INTRODUCTION
It is well-known that for certain values of the parameters in the mass and energy balance equations
that represent the dynamic behaviour of chemical reactors the system becomes very sensitive to the
values of the initial conditions and the parameters of the system (Varma et αϊ., 1999). Parametric
sensitivity in this context describes the situation in which a small change in the inlet conditions, as
well as to any of the other physicochemical parameters of the system, induces a large change in the
temperature profile of the reactor.
There have been many runaway/parametric sensitivity studies in chemical reactors (Wilson,
1946; Barkelew, 1959; Thomas, 1961; Adler and Enig, 1964; van Welsenaere and Froment, 1970;
Rajadhyaksha et ah, 1975; Westerterp and Ptasinski K., 1984a,b; Westerterp and Overtoom, 1985;
Morbidelli and Varma, 1986, 1987, 1988; Hagan et al, 1987, 1988a,b; Westerink and Westerterp,
1988; Balakotaiah, 1989; Westerterp and Westerink, 1990; Steensma and Westerterp, 1990, 1991;
Vajda and Rabitz, 1992; Strozzi and Zaldivar, 1994; Balakotaiah et al, 1995; Alós et al, 1996,
1998; Wu et al, 1998) aiming to derive runaway boundaries for different types of reactions and
different types of reactors. For a general overview see Varma et al, (1999). At the beginning, since
numerical calculations were difficult, these criteria were based on some geometrical property in the
temperature profile versus time or conversion (for example Adler and Enig, 1964). Although some
of them give fundamentally correct descriptions of thermal runaway, they do not give any measure
of its extent or intensity (Varma et al, 1999). Moreover, some of them were too conservative or
were derived separately for each type of reactor and kinetic scheme. In order to overcome these
limitations, a new series of criteria were developed based on the concept of parametric sensitivity
(Morbidelli and Varma 1986, 1987, 1988; Vajda and Rabitz, 1992; etc.). However, these new
criteria require a significant amount of computation and they are implicit and, hence, it is not
possible to extent them on-line. Finally, in despite of all these studies, there are still few criteria
derived for predicting runaway boundaries that can be used for several types of reactors or for
systems with multiple reactions. For example, general criteria that have been applied to different
processes and to multiple reactions are the MV criterion (Morbidelli and Varma, 1987) based on
the concept of parametric sensitivity and the Balakotaiah et al (1995) criterion based on the
analysis of reaction paths in the temperature-conversion plane.
Sensitivity to initial conditions is a well-known characteristic of chaotic phenomena. To study
such systems, researchers have developed powerful methods of extracting physical quantities from
theoretically or experimentally obtained signals (Abarbanel, 1996; Kantz and Schreiber 1997). In a series of studies carried out previously (Strozzi and Zaldivar, 1994; Alós et al, 1996), it was
shown, theoretically and experimentally, that some of the chaos theory techniques, developed to
measure the parametric sensitivity in strange attractors could be used to identify critical regions in
which thermal runaway can occur. The advantage of this approach is that, in principle, a runaway
criterion based on one invariant of the system may be calculated on-line using only temperature
measurements by applying state space embedding reconstruction techniques (Abarbanel, 1996).
Hence, firstly, we defined an appropriate early warning detection criterion, based on an invariant
property under phase space reconstruction. The criterion says that we are in a runaway situation
when the divergence of the system becomes positive (div >0) on a segment of the reaction path
(Strozzi et al, 1998 and 1999). We recall that the divergence is an scalar quantity defined at each
point as the sum of the partial derivatives of the mass and energy balances with relation to the
correspondent variables - temperature and conversions -, i.e. d(dTIdt)ldT + ^¡d(dzi/dt)/dz¡ ■
i
The criterion was compared with several existing criteria for the case of a first order and an
autocatalytic reaction carried out in an isoperibolic (constant jacket temperatur