Microsoft Word - 1.docx CHEMICAL ENGINEERING TRANSACTIONS VOL. 77, 2019 A publication of The Italian Association of Chemical Engineering Online at www.cetjournal.it Guest Editors: Genserik Reniers, Bruno Fabiano Copyright © 2019, AIDIC Servizi S.r.l. ISBN 978-88-95608-74-7; ISSN 2283-9216 Computer Aided Design of Thermally Safe Operating Conditions for Heterogeneous Semibatch Reactors Zichao Guo*, Liping Chen, Wanghua Chen Department of Safety Engineering, School of Chemical Engineering, Nanjing University of Science and Technology, Nanjing, Jiangsu, 210094, China gzc319@njust.edu.cn Semibatch reactors (SBRs) are widely used to control the heat generation rate of exothermic reaction by tuning the dosing rate. To avoid the undesirable thermal runaway accidents, designing thermally safe operating conditions for SBRs is of high importance. In this work, a new simple computer aided method is developed to facilitate the process of designing safe conditions for liquid-liquid reactions that occur in the continuous phase following a slow reaction regime. The information required to design the safe operation parameters of dosing time (tD) and jacket coolant temperature (Tj) just include ε, RH, ∆τad,0 and MAT, which can be simply obtained from the reaction recipes or calorimetry tests. This method is developed on the basis of a deep insight into the thermal behaviors for isoperibolic SBRs. Two cases are conducted to verify the validity of the developed approach in this article. 1. Introduction In the fine chemical and pharmaceutical industries, semibatch reactors (SBRs) are widely used to control the heat generation during the reaction process. To prevent the undesirable thermal runaway accidents, designing thermally safe operating conditions for SBRs is of high importance. In the last decades, a number of works have been reported concerning this issue. Hugo and Steinbach (1985) are the first who observed that an accumulation of the reactants at low reactor temperature was the main cause of the thermal runaway in homogeneous SBRs. Steensma and Westerterp (1990,1991) developed the boundary diagrams for liquid-liquid reaction systems that followed second order kinetics to assist designing thermal safe operating conditions for SBRs. Recently, Bai et al. (2017) constructed a new set of boundary diagrams for homogeneous semibatch reactions on the basis of their finding that, with respect to QFS and no ignition scenarios, the maximum temperature of systhesis reaction under adiabatic conditions (MTSR) appeared at the stoichiometric point of dosing period, whereas MTSR always occurred before this time point for thermal runaway scenario. Applying the above methods to design safe operating conditions requires knowledge on the kinetic parameters, at least, the apparent kinetic parameters. However, determination of the kinetic parameters in realistic cases requires professional expertise, especially in the cases of heterogeneous reaction systems, which strongly restricts the application of the above method. Therefore, it is desirable to develop approaches without requirement of kinetic parameters and solubility of reactants to design thermally safe operating conditions. In this sense, Maestri et al. (2017, 2018) developed an integrated criterion aiming to simply monitor SBRs. Guo et al. (2017) recently developed the practical procedures to design thermally safe operating conditions for SBRs without kinetic parameters. Although a great progress in this research field has been reached, the ambition to develop more reliable and simple approaches to design thermally safe operating conditions for SBRs is perpetual. In this work, a new simple method is developed to facilitate the process of designing safe conditions for liquid-liquid reactions that occur in the continuous phase following a slow reaction regime. This method is developed on the basis of the deep insights into the thermal behaviors of QFS operating conditions for isoperibolic SBRs. The validity of this method will also be verified by two case studies. DOI: 10.3303/CET1977094 Paper Received: 25 February 2019; Revised: 15 April 2019; Accepted: 27 June 2019 Please cite this article as: Guo Z., Chen L., Chen W., 2019, Computer aided design of thermally safe operating conditions for heterogeneous semibatch reactors, Chemical Engineering Transactions, 77, 559-564 DOI:10.3303/CET1977094 559 2. Dimensionless mathematic model for kinetically controlled liquid-liquid semibatch reactions that occur in the continuous phase Let’s first assume that a single bimolecular kinetically controlled liquid-liquid reaction is carried out in SBRs. A B Dv A v B C v D+ → + (1) where vi is the stoichiometric coefficient of the reactant. Component C is assumed to be the product, accordingly the value of vi with respect to component C can be set to 1. In addition, we assume that reactant B is loaded into the reactor initially and reactant A is dosed at a constant rate until the stoichiometric amount of A is added. The micro-kinetic rate expression can be described by a generic power law expression: A Br kC C= (2) where r is the reaction rate, k is the reaction rate constant, Ci is the molecular concentration of reactant i. To deduce the dimensionless mathematic model, more assumptions should be made. These assumptions could be found elsewhere.(Maestri et al., 2005; Guo et al., 2017) The mass and energy balances for isoperibolic SBRs involving kinetically controlled liquid-liquid reactions that occur in the continuous phase can be written in a dimensionless form as follows: ,0 1 ( ( (1 )( ) ( ))) 1 B A B ad j H D H dX v DaRE f d dXd Wt R d R d κ θ τ τ ε εθ τ τ τ τ θ ε θ θ  = ⋅ ⋅   = Δ − + − + − + (3) 3. Theoretical tools to design thermally safe operating conditions for isoperibolic SBRs involving kinetically controlled liquid-liquid reactions that occur in the continuous phase It is well known that there are three operation regions in isoperibolic SBRs: no ignition(NI), thermal runaway(TR), and QFS(quick onset, fast conversation, smooth temperature profile), which are defined as a result of comparison of the reaction temperature profile with a so-called “target temperature” (Tta) profiles. QFS operating conditions are usually considered as the desirable one in practice. (Steensma and Westerterp, 1990) Six dimensionless parameters are present in the dimensionless model of isoperibolic SBRs: vADaRE, ε, γ, RH, ∆τad,0 and Wt. If we set the values of ε, RH, ∆τad,0as RH=1, ε=0.4, ∆τad,0=0.7, then a safety boundary diagram that separate the three scenarios by the so-called Ry (reactivity number) vs Ex (exothermicity number) lines can be constructed following the procedure developed by Steensma and Westerterp, (1990) as shown in Figure.1. Herein, the expressions of Wt, Ry and Ex are 0 0 0 ( ) ( ) D p UA t Wt c Vε ρ = (4) | ( ) jA H v DaRE Ry R Wt τκ ε ⋅ = + (5) ,0 2 ( ) ad j H Ex R Wt τγ τ ε Δ  =  +  (6) Table 1: The corresponding Wtmin to different sets of ε, RH and ∆τad,0 ε RH=0.5 RH =1 RH =2 0.2 42 41 39 0.3 26 25 22.5 ∆τad,0=0.5 0.4 19 18 15 0.5 14 13 10.5 0.6 11 10 7.5 0.2 19.5 18 14 0.3 11.5 9.5 <5 ∆τad,0=0.3 0.4 7.5 7 <5 0.5 5.5 <5 <5 0.6 <5 <5 <5 560 0 5 10 15 20 25 30 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 Wt=1.5 Wt=3 Wt=5 Wt=10 Wt=15 R y Ex Figure 1: Boundary diagrams for isoperibolic liquid-liquid SBRs in which kinetically controlled reactions occur in the continuous phase. RH=1, ε=0.4, ∆τad,0=0.7, 0.025Rymin, the isoperibolic SBRs must be in the QFS scenario. Herein, Rymin refers to the maximum value of Ry with respect to each Ry vs Ex line in Figure.1. In addition, it is obvious that when the value of Wt is higher than a critical point, for example Wt=3, both the values of Rymin and the numbers of Ry vs Ex points rapidly decrease. This tendency indicates that the required Rymin will decrease with Wt increasing up to be higher than the critical point. We find that when the value of Wt increases up to 28, the Ry vs Ex points in Figure.1 completely disappear, indicating that no thermal runaway will occur as long as Wt≥28 for this case. In fact, different sets of ε, RH, ∆τad,0 correspond to different values of such critical Wt, which will be denoted to Wtmin in the following. Table 1 show the corresponding Wtmin to different sets of ε, RH, ∆τad,0. This table provides a simple approach to design safe operating conditions for isoperibolic semibatch liquid-liquid reactions reactions that occur in the continuous phase following a slow reaction regime. Once the values ofε, RH, ∆τad,0 had been determined, thermal runaway operating conditions can be avoided as long as Wt is higher than the corresponding Wtmin 3.1 Effect of reaction order It should be kept in mind that the values of Wtcri in Table 1 are developed on the basis of second-order kinetics assumption. Since most of organic reactions may not rigorously obey second order kinetics, discussion of the effect of reaction order on Wtcri is essential. For this purpose, the values of ε, RH and ∆τad,0 are set to be constant and the effects of reaction orders of n and m are investigated separately. One typical example of ε=0.3, RH=1 and ∆τad,0=0.5 is shown in Figure.2. 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 10 15 20 25 30 35 40 W t c ri value of n a 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 15 20 25 30 b W t c ri value of m Figure. 2: Effect of kinetic order of (a)n and (b)m on the values of Wtcri for the reactions with ε=0.3, RH=1, ∆τad,0=0.5 One can see from Figure.2 that the values of Wtcri decrease with the reaction orders increasing, indicating that, for reactions with kinetic orders of n>1 and m>1, no thermal runaway will occur as long as the practical Wt is higher than the Wtcri in Table 1. 561 For reactions with orders of n<1 or m<1, the Wtcri in Table 1 can’t guarantee that thermal runaway event must be avoided. In fact, the values of Wtcri in Table 1 can also be applied to reactions of an order lower than 2. When the second-order reactions are in QFS situation, the reactions of an order lower than 2 must be also in QFS situation. This can be ascribed to the fact that, when the reactant concentrations are identical, the reaction rates for the reactions of an order lower than 2 are faster than that for the second-order reactions. In short, though the values of Wtcri in Table 1 are determined on the basis of second-order reactions, they can also be applied to reaction of other kinetic order. In other words, the applicability of the Wtcri in Table 1 is independent on the reaction orders. However, we have to highlight that, when coming crossing the autocatalytic reactions, the Wtcri in Table 1 cannot be applied because autocatalytic reactions show a completely different behavior. 4. The facile approach for designing thermally safe operating conditions Thermally safe operating conditions also require that the undesirable exothermic side or decomposition reactions, usually companied with strong heat and gas generation, are not triggered. Hence, the thermal stability of reactants, products and/or reactive mixtures should be investigated. This can be achieved by carrying out dynamic DSC (differential scanning calorimetry) and ARC (adiabatic rate calorimeter) tests. These thermal analysis techniques can offer the MAT (maximum allowable temperature) parameter, which is defined to prevent the triggering of dangerous decompositions or strongly exothermic side reactions. Then information on ∆τad,0, RH and ε should be obtained first. With respect to ∆τad,0, at least one effective reaction calorimetry (RC1) tests should be conducted to determine the heat of reaction. Then ∆τad,0 can be calculated by the following expression ,0 ,0 0 0 ( ) ( ) r B ad R p H n T c V τ ρ −Δ Δ = (7) In fact, RC1 tests can also provide information on heat capacity (cp) of the reaction mass through a calibration procedure, as a result, RH can be easily obtained. As for the information on ε, it can directly be determined from the specific reaction recipes. Now that information on ∆τad,0, ε and RH have been determined, Wtmin can be obtained from Table 1. Then the minimum value of dosing period, tD,min can be calculated from Eq. 4, namely min 0 0 ,min 0 ( ) ( ) p D Wt c V t UA ε ρ⋅ = (8) Then one can reasonably expect that regardless of the value of Tj, as long as tD>tD,min, no thermal runaway events will occur in the isoperibolic SBRs. Now that tD,min has been determined, then the other important operating constraint, namely Tj,max, which means the maximum allowable jacket coolant temperature, should be determined. This can be achieved on the basis of the fact that the maximum of reaction mixture temperature, Tmax, should be lower than MAT. With respect to no ignition and QFS operations in isoperibolic SBRs, the value of Tmax must be lower than the maximum value of Tta, namely Tta,max, which refers to the target temperature occurs at the initial period. Hence, the above constraint of TmaxtD,min and Eq.10 are confirmed, thermally safe operating conditions can be ensured. However this still can’t ensure that the operations correspond to QFS situation. To obtain QFS operations, operating condition with relatively high values of Tj or tD can be reasonably considered and then at least one isoperibolic reaction calorimetry test needs to be conduct.. 5. Case study In this case, pure 4-chloro benzotrifluoride (BTF) is dosed into an anhydrous mixture of sulfuric and nitric acid at 9% w/w of nitric acid. 562 The reaction occurs in the continuous acid phase. Maestri et al. (2009,2016) has experimentally demonstrated that this aromatic nitration is kinetically controlled and reported the reaction rate expression as follows 12 , , 87260[J / mol] 3.228 10 exp( ) A A d B cr m C CRT = × − (11) where CA,d and CB,c are the concentrations of 4-chloro BTF in the dispersed phase and of nitric acid in the continuous phase, respectively, and mA=0.01 is the distribution coefficient of 4-chloro BTF, which is the ratio of the concentrations in the continuous and in the dispersed phases). The initial concentrations of 4-chloro BTF in the dispersed phase and HNO3 in the continuous phase are 7.495 kmol/m 3 and 2.623 kmol/m3, respectively. The reaction temperature must be limited within 80 oC, because above this temperature an undesired second nitration of the reaction product could partially take place. If the reaction temperature doesn’t exceed this threshold value, the overnitration of the product by nitric acid is kinetically negligible even with a large excess of mixed acids. Table 2: Geometry and operating conditions of the RC1 reactor Parameters Value Volume of the reactor 1.2 L Volume of continuous phase, Vc 382.9 cm 3 Volume of dispersed phase, Vd 134 cm 3 Mass of mixture acid, mc 688.05 g Mass of 4-chloro BTF, md 181.3 g Specific heat capacity of mixture acid, cp,c 1.477 J/(g· oC) Specific heat capacity of 4-chloro BTF, cp,d 1.257 J/(g· oC) Initial UA 3.15 W/K Final UA 4.25 W/K 0 1000 2000 3000 4000 12 14 16 18 20 22 24 26 28 30 T T ta X ac a time,s te m p e ra tu re ,o C 0.0 0.2 0.4 0.6 0.8 1.0 X a c 0 1000 2000 3000 4000 20 22 24 26 28 30 32 34 36 38 time, s te m p e ra tu re ,o C b 0.0 0.2 0.4 0.6 0.8 1.0 X a c 0 1000 2000 3000 4000 38 40 42 44 46 48 50 52 54 56 c time, s te m p e ra tu re ,o C 0.0 0.2 0.4 0.6 0.8 1.0 X a c 0 1000 2000 3000 4000 58 60 62 64 66 68 70 72 74 76 78 d time,s te m p e ra tu re ,o C 0.0 0.2 0.4 0.6 0.8 1.0 X a c Figure 3: Temperature, target temperature and accumulation profiles of nitration of 4-chloro benzotrifluoride. ε=0.35, γ=35, RH=0.6444, vADaRE=0.986, ∆τad,0=0.43, Tj=TD. (a)Tj =11.85 oC; (b)Tj=20.85 oC; (c)Tj=38.85 oC; (d)Tj=60 oC. 563 The reaction is conducted at a laboratory scale calorimetric reactor, that is RC1. The geometry and operating conditions of RC1 are listed in Table 2. The reaction heat is equal to -123 kJ/mol. The initial adiabatic temperature rise can be calculated as follows 4 chloro BTF ,0 ( ) 129 ( ) r ad p c H n T mc −−Δ ×Δ = = ℃ (12) According to the above knowledge, the dimensionless parameters are: ε=0.35, γ=35, ∆τad,0=0.43, RH=0.644. For the sake of conservation, substitute the values of ε=0.35, RH=0.5 and ∆τad,0=0.5 into Table 1 and give Wtmin=21.5. Accordingly, the minimum dosing time (tD,min) can be calculated to be 2427 s. Then the value of vADaRE can be calculated to be 0.986. In addition, substituting MAT=80 oC into Eq.10 gives the corresponding value of Tj,max= 62.52 oC. The temperature, target temperature and accumulation profiles of nitration of 4-chloro benzotrifluoride at dosing time (tD=2427 s) and four different Tj are shown in Figure.3. It is obvious that none of all the temperature profiles is in the thermal runaway situations. As the value of Tj,max increases, the accumulation decreases. Particularly, the profiles in Figures.3d can be considered as the QFS operation. The maximum reaction temperature Tmax in Figure.3d is equal to 77.2 oC, which is lower than the MAT=80 oC. 6. Conclusion In summary, a facile approach is developed in this article to design thermally safe operating conditions for liquid-liquid reactions that occur in the continuous phase following a slow reaction regime. The information required for this purpose just include ε, RH and ∆τad,0, which can be simply obtained from the reaction recipes or an isothermal RC1 test. By substituting these three parameters into Table 1, the value of Wtmin can be determined and the value of tD,min can also be calculated by Eq.8. To avoid the triggering of the second side or decomposition reaction, the maximum temperature of jacket coolant Tj,max can be derived from Eq.10. In addition, two cases are conducted, which clearly verify the validity of the developed approach in this article. To the end, we would like to underline that the approach in this article are developed on the basis of the kinetics of second order. Acknowledgments This work has been financially supported by the Fundamental Research Funds for the Central Universities and National Key R&D Program of China. References Bai W., Hao L., Guo Z., Liu Y., Wang R., Wei H., 2017, A new criterion to identify safe operating conditions for isoperibolic homogeneous semi-batch reactions, Chemical Engineering Journal, 308, 8-17. 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