Article Cite This: Ind. Eng. Chem. Res. 2017, 56, 14771−14780
pubs.acs.org/IECR
Development of Adiabatic Criterion for Runaway Detection and Safe Operating Condition Designing in Semibatch Reactors Zichao Guo,* Liping Chen, and Wanghua Chen Department of Safety Engineering, School of Chemical Engineering, Nanjing University of Science and Technology, Nanjing, Jiangsu 210094, China S Supporting Information *
ABSTRACT: To prevent the occurrence of thermal runaway accidents in semibatch reactors (SBRs), it is desirable and practicable to develop criteria that can distinguish between the safe and runaway operating regions. In this article a new safety criterion, namely, the adiabatic criterion, has been developed for SBRs in which liquid homogeneous as well as liquid−liquid heterogeneous reactions with arbitrary reaction orders occur. It states that an SBR is operated in the potential runaway situation if the value of the adiabatic criterion exceeds zero at a segment of the reaction path. Numerical results show that the adiabatic criterion is more conservative than the two other criteria (divergence criterion and target temperature criterion). However, the adiabatic criterion is not suitable to reactions with autocatalytic behaviors. Also knowledge of activation energies and reaction enthalpies is necessary to utilize the adiabatic criterion.
1. INTRODUCTION In the fine chemical and pharmaceutical industries, exothermic reactions are usually conducted in the semibatch reactors (SBRs) to prevent the occurrence of thermal runaway events. By tuning the dosing rate of reactants, the heat release rate can be controlled to match the cooling capacity of reactor jackets or coils. However, incidents of loss of temperature control in SBRs still occur from time to time, mainly resulting from improper design of the operating conditions or maloperation. To prevent thermal runaway incidents in SBRs, designing the right operating conditions should be considered first.1 In the last decades, many works have been devoted to this issue. The pioneers are Hugo and Steinbach2 who observed that an accumulation of the dosed component at too low reactor temperature was the cause of the runaway in homogeneous SBRs. The ideal safe behavior of SBRs can be identified as that the dosed reactant immediately reacts with the component initially present in the SBRs, indicating that completely no accumulation can be observed. However, it is not possible to avoid accumulation completely in a realistic case. As an alternative solution, it is desirable and practicable to develop criteria to distinguish between the safe and runaway operating regions. Hugo and Steinbach3 determined empirically from their calculations that as long as the Damköhler number Da = kcB0tdos was smaller than the modified Stanton number St = (UAtdos/ VCpρ), which was renamed as the Westerterp number in 2010,4 the SBRs could be considered to be performed in a safe way. Steensma and Westerterp5,6 stated that resulting from comparison of the reaction mass temperature profile with a © 2017 American Chemical Society
target temperature profile, three operation scenarios in isoperibolic SBRs, namely, no ignition, thermal runaway, and QFS, could be observed. The accumulation of the dosed component in QFS scenario could be identified as harmless because the temperature profile of the reaction mass was smooth. On the basis of this consideration, they developed a series of boundary diagrams to help designing thermally safe operating conditions for isoperibolic SBRs.5,6 However, these boundary diagrams did not include the information on the triggering of the second reactions. To solve this problem, Ni and co-workers7,8 developed the modified boundary diagrams in their recent series of works, in which the information on the maximum allowable temperature had been included. In addition, another important sort of safety criterion9,10 was developed on the basis of parametric sensitivity. This criterion predicted a parametrically sensitive or runaway region, which might be called “generalized” because the maximum temperature became simultaneously sensitive to small changes to any of the model inputs. In a practical SBR, a basic safety principle is that MTSR (the maximum temperature of synthesis reaction) should be lower than a maximum allowable temperature (MAT), which generally refers to the onset decomposition temperature of reaction mixture (TD) or the maximum temperature for technical reason (MTT).11,12 This basic safety principle has Received: Revised: Accepted: Published: 14771
October 8, 2017 November 27, 2017 November 27, 2017 November 27, 2017 DOI: 10.1021/acs.iecr.7b04181 Ind. Eng. Chem. Res. 2017, 56, 14771−14780
Article
Industrial & Engineering Chemistry Research
Table 1. Expression of the Reactivity Enhancement Factor, RE, and of the Function, f, for Homogeneous and Heterogeneous SBRs in Which Slow or Fast Reactions Occur in the Dispersed or Continuous Phase Homogeneous SBRs RE f
(vB/vA)1−n (θ − X)n(1 − X)m/(1 + εθ)n+m−1 Heterogeneous Liquid−Liquid SBRs reactions in the dispersed (d) phase
REslow,c/d REfast,c/d fslow,c/d f fast,c/d
reactions in the continuous (c) phase
(vB/vA) mmB (6/db,0)mB(m+1)/2CB,0(1−n−m)/2(vB/vA)(1−n)/2[2DL,B/((m n m n−1
(vB/vA) mmA (6/db,0)mA(n+1)/2CB,0(1n−m)/2(vB/vA)(1−)/2[2DL,A/((n + 1)k)]1/2 (θ − X)n(1 − X)m/(εθ)n [(θ − X)(n+1)/2(1 − X)m/2(εθ)(1−n)/2]/[1 + 2.5εθ/(1 + εθ)]
1−n
1−n
+ 1)k)]1/2
(θ − X) (1 − X) /(εθ) [(θ − X)n/2(1 − X)(m+1)/2(εθ)n−1]/[1 + 2.5εθ/(1+εθ)]
been widely utilized in chemical industries.13,14 Along this line, Maestri and Rota developed the temperature diagrams to predict the maximum temperature reached for the isoperibolic SBRs.15 Online monitoring the SBRs is another important way to ensure safety in SBRs. Hub and Jones16 proposed a simple criterion, which stated that the SBRs were in a runaway situation once the first and second derivatives of the reactor ́ temperature were positive simultaneously. Zaldivar. and coworkers17,18 proposed a more advanced divergence criterion, which was derived from characterization of chaotic attractors in dynamical systems. This divergence criterion states that when the divergence of the dissipative reactive systems exceeds zero at a segment of the reaction path, the reaction is under a potential risk of thermal runaway. Recently, Maestri and Rota19−21 proposed a kinetic-free SBR monitoring method based on the concept of X number that did not require any kinetic characterization of the system, but only the much more straightforward estimation of the reaction heat. They have successfully applied their kinetic-free method to both single and consecutive side reactions. In addition, we recently developed an adiabatic criterion for runaway detection in SBRs in which homogeneous exothermic reactions were handled.22 This adiabatic criterion states that if the value of adiabatic criterion is lower than zero, then both the second derivatives of conversion and reaction temperature to time are lower than zero even in the undesirable case of complete cooling failure. Regretfully, the previous work only took into account the homogeneous reactions. It is well-known that many strongly exothermic reactions belong to liquid− liquid reaction systems, such as nitration, oxidation, sulfonation, and so forth. Hence, it is necessary to extend the adiabatic criterion to liquid−liquid situations. Moreover, how to employ this criterion to design thermally safe operating conditions for SBRs will be discussed in this work.
In general, when a thermal runaway event occurs, qr(t) must have been higher than qex(t); consequently, the reaction temperature increases and then promotes the heat generation rate in return. With respect to qex, though it always increases with reaction temperature increasing, its rising rate cannot keep pace with the rising rate of qr when thermal runaway occurs. From the above analysis, it can be reasonably expected that SBRs can be remained in stable state if the first derivative of qex to time is always higher than that of qr at any instant, namely
dqr dt
(1)
Tcf (t ) ≤ MAT
(2)
dqex dt
(3)
As mentioned previously, qex will increase before thermal runaway occurs, in other words, dqex/dt must be positive. We can reasonably expect that if the value of dqr/dt is negative over the entire reaction course, the reaction temperature can be certainly controlled and no runaway event occurs. Before deducing the expression of dqr/dt, let us assume that a single exothermic reaction is performed in a stirred SBR equipped with the cooling jacket: vA A + vB B → C + vDD
(4)
where A and B are the reactants, C is the desirable product, and D is the side product, vi is the stoichiometric coefficient of the components. The number of vi for C is assumed to be equal to 1. In addition, reactant B is supposed to be loaded into the reactor initially and reactant A is dosed at a constant rate until the stoichiometric amount of A is added. Before we proceed the discussion, some assumptions can be stated as follows: (1) The reaction mass is perfectly macromixed. (2) The influence of the chemical reaction on the reaction volume is negligible. (3) No phase inversions occur during the reaction duration for liquid−liquid reactions. (4) The chemical reaction takes place only in one of the two liquid phase: this situation is very common in industrial processes (such as nitration and oxidations), in which the catalyst (typically a strong acid) is present only in one phase. (5) Heat dissipation by the agitator or mixing effect is negligible relative to the reaction heat; consequently, the heat effects are only associated with the chemical reaction. (6) The physicochemical properties of all the components are constant and additive during the whole reaction. On the basis of the above assumptions, for SBRs in which strongly exothermic liquid homogeneous or liquid−liquid
2. DEVELOPMENT OF THE ADIABATIC CRITERION For SBRs in which single-step liquid homogeneous or liquid− liquid heterogeneous exothermic reactions occur, to prevent the occurrence of thermal runaway, two safety constraints should be fulfilled generally:23 qr(t ) ≤ qex,max (t )
