Simple Approach to Designing Safe and Productive Operation of

Article Cite This: Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Simple Approach to Designing Safe and Productive Operation of Homogeneous Semibatch Reactors Involving Autocatalytic Reactions Zichao Guo,† Wei Feng,‡ Liping Chen,† and Wanghua Chen*,† †

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Department of Safety Engineering, School of Chemical Engineering, Nanjing University of Science and Technology, Nanjing, Jiangsu 210094, China ‡ Xi’an Modern Chemistry Research Institute, Xi’an 710065, China S Supporting Information *

ABSTRACT: In the fine chemical and pharmaceutical industries, design of the safe and productive operating conditions for isoperibolic semibatch reactors(SBRs) involving exothermic autocatalytic reactions is an essential topic. Since determination of the detailed kinetic parameters is a time-consuming process, development of kineticparameter-free approach for the above purpose is greatly desirable. In this work, an insight into the desirable QFS (Quick onset, Fair conversion and Smooth temperature profile) operations in isoperibolic SBRs involving autocatalytic reactions is first provided. Then by comparing the thermal performances of SBRs involving autocatalytic reactions in both isothermal and isoperibolic mode, we found that if the MTSR increases with the reaction temperature in isothermal SBRs, the corresponding isoperibolic SBRs with initial temperature equal to the reaction temperature of the isothermal SBRs must be in the QFS region. On the basis of this finding, a facile approach with no requirement of the information on the kinetic parameters is developed to design safe and productive operating conditions for isoperibolic SBRs involving exothermic autocatalytic reactions.

1. INTRODUCTION Semibatch reactors (SBRs) are commonly used in the fine chemical and pharmaceutical industries. When conducting highly exothermic reactions in SBRs, the prevention of runaway reactions is an essential issue that has been deeply investigated in the last decades. Once the incidents of runaway reactions occur, loss of property and even human lives may be triggered. In general, the accumulation of the dosed component at too low a temperature is considered as the main cause of the runaway reactions in SBRs. The ideal behavior of the SBRs is considered as that the dosing components immediately react with other reactants, implying that absolutely no accumulation occurs. However, a great portion of reactions do not present the ideal behavior, which means that the accumulation is unavoidable. Alternatively, researchers focus on searching for the reasonable criterion to distinguish between safe and runaway operating regions in a safety diagram representing a two parameter field with reactivity and cooling intensity as parameters. Hugo and co-workers1,2 first developed a semiempirical criterion for homogeneous SBRs that as long as the Damköhler number (Da) was smaller than the modified Stanton number (St), which has been renamed as the Westerterp number (Wt) in 2010,3 the SBRs are considered to be operated in the safe situation. Westerterp and co-workers together extended the cases to heterogeneous liquid−liquid reactions.4,5 They © XXXX American Chemical Society

proposed a clear criterion to define the acceptable accumulation in SBRs through introducing a target temperature−time profile. Consequently, by comparing the reaction mixture temperature with the target temperature, three operation regions in isoperibolic SBRs can be identified: no ignition, thermal runaway and QFS(Quick onset, Fair conversion and Smooth temperature profiles). These three regions are discriminated in a dimensionless boundary diagrams. The validation of the safety criterion and boundary diagrams have been experimentally verified by van Woezik and Westerterp through conducting the isoperibolic calorimetry tests of nitric oxidation of 2-octanol.6,7 Then Maestri and Rota8,9 found that the reaction orders had intense influences on the topologies of boundary diagrams and, as a result, the operating conditions determined by second-order based boundary diagrams are not always safe. Therefore, they extended the boundary diagrams to the cases of arbitrary reaction orders. Recently, Bai and coworkers10 found that for QFS and no ignition regions, the maximum temperature of synthesis reaction under adiabatic conditions (MTSR) must appear at the stoichiometric point of dosing period while for thermal runaway scenarios, MTSR occurred before this point. On the basis of this finding, they Received: Revised: Accepted: Published: A

September 22, 2018 December 2, 2018 December 5, 2018 December 5, 2018 DOI: 10.1021/acs.iecr.8b04644 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research

2. MATHEMATICAL MODEL With respect to homogeneous SBRs involving autocatalytic reactions, it is generally considered that the product can catalyze the reaction. Thus, we can assume the following autocatalytic reaction scheme (1) A + B → 2B + C It is further assumed that component B is loaded into the SBRs first and then component A is dosed into the SBRs at a constant rate. A number of reacting systems that show an autocatalytic behavior can be described through the scheme in eq 1. The typical reactions that exhibit the autocatalytic behavior following the scheme in eq 1 are oxidation of organic compound by nitric acid.6,21,22 The reaction rate can be described using a power law type function as follows

constructed a new set of boundary diagrams for homogeneous SBRs. In addition, to guarantee safe operation of SBRs, another important safety constraint must be followed: the maximum allowable temperature (MAT) must not be exceeded during normal or during upset conditions. Herein, the MAT refers to the temperature at which no highly exothermic secondary reaction will be triggered in 24 h. For this reason, Ni and coworkers11,12 recently developed the modified boundary diagrams that allow reading the maximum reaction temperature in SBRs. Maestri and Rota13 also developed a new typology of diagrams (namely temperature diagrams), which allow the prediction of the maximum temperature increase with respect to the initial temperature. It is worthwhile to note that all of the above methods require detailed reaction kinetics, at least the apparent kinetics. However, it is well-known that determination of the detailed kinetic model and kinetic parameters is a time-consuming and process and the determined kinetic parameters may even deviate from the real values, which strongly restrict the application of the above methods. For these reasons, development of facile approaches to design safe operating conditions without requirement of kinetic parameters is desirable. For this purpose, Copelli and co-workers14−16 have introduced the theoretical topology tool, which requires the information on Tmax/Tj vs conversion in SBRs. Recently, Maestri and Rota17,18 developed a kinetic free SBR monitoring method to allow for online detection of the runaway accidents and designing the safe operating conditions for SBRs. In our recent work, we developed a simple approach for isoperibolic homogeneous SBRs, which was developed on the basis of the phenomenon that the MTSR vs reaction temperature profiles for isothermal exothermal reactions presented an “S” shape.19 However, this approach was developed on the basis of the assumption of nonautocatalytic reaction systems. With respect to autocatalytic reactions, though Maestri and Rota20 have proposed a safety criterion based on the boundary and temperature diagrams previously proposed for nonautocatalytic reactions, their approach still requires the detail kinetic parameters. As mentioned previously, determination of the accurate kinetic parameters is a time-consuming and tedious work. Hence, development of a simple kinetic-parameter-free approach for autocatalytic reaction systems is really fascinating. For these reasons, this work aim to develop a facile kineticparameter-free approach to design safe and productive operating conditions for SBRs involving autocatalytic reactions. This approach will be developed on the basis of the deep insights into the relationship between isothermal and isoperibolic operation of SBRs involving autocatalytic reactions. This approach allows one to design safe and productive operating conditions for isoperibolic homogeneous autocatalytic SBRs by conducting several isothermal calorimetry tests in laboratory. Because conducting the laboratory-scale isothermal tests by reaction calorimeters like RC1 produced by METTLER TOLEDO is considered to be convenient and safe, the approach developed in this work allows for the prediction of the behavior of an isoperibolic SBR based on safe isothermal RC1 experiments.

r = kn , mCAn C Bm

(2)

where r is the reaction rate, k is the reaction rate constant, and n and m are the kinetic order to components A and B, respectively. 2.1. Mathematical Model for Isothermal SBRs. For rigorously isothermal SBRs, the reaction temperature is constant. Consequently, the heat balance equation for isothermal SBRs is not necessary to be formed. We develop the mass balance equation for isothermal SRBs in the following. We can easily write the concentration of component A (CA) and component B (CB) during the dosing period in the form as follows CA =

NAt(θ − XA ) Vr,0(1 + εθ )

(3)

CB =

NAt (M + XA ) Vr,0(1 + εθ )

(4)

where θ = t/tD is the dimensionless time, tD is the dosing time, ε = VD/Vr,0 is the relative volume increase at the end of the dosing period, M = NB0/NAt is the molar ratio of component B to component A, Vr,0 is the initial reaction volume, XA=(NAtNA)/NAt is the molar fraction of component A, VD is the total volume of the dosing stream, NB0 is the initial molar amount of component B in the SBRs and NAt is the total molar amount of component A added into the SBRs. The molar conversion rate of component A can be written as −

dNA = Vrkn , mCAn C Bm dt

(5)

Then substituting eqs 3 and 4 into eq 5 gives the dimensionless mass balance equation component A

dXA = Dafκ dθ

(6) n+m−1

where Da = kn,m,RtD(NAt/Vr,0) is the Damköhler number involving the physical information about the chemical kinetics and the dosing time, f = [(θ − XA)n(M + XA)m]/(1 + εθ)n+m−1 reflects the mechanism of the autocatalytic reactions over the dosing period. After the dosing period, the term of f in eq 6 should be described as f=[(1 − XA)n(M + XA)m]/(1 + ε)n+m−1. κ=exp[γ(1 − 1/τ)] is the dimensionless reaction rate constant, in which γ = E/RTR is the dimensionless activation energy and τ = T/TR is the dimensionless temperature. TR is the reference B

DOI: 10.1021/acs.iecr.8b04644 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Article

Industrial & Engineering Chemistry Research temperature, which is supposed to be 300 K in this work. E is the activation energy of the reactions. R is the ideal gas constant. 2.2. Mathematical Model for Isoperibolic SBRs. For isoperibolic SBRs, the coolant temperature in the jacket is supposed to be constant and the reaction mixture temperature varies. Furthermore, the initial temperature in isoperibolic SBRs are assumed to be equal to the coolant temperature. The mathematical model for isoperibolic SBRs should include mass and heat balance equations. The mass balance equation for isoperibolic SBRs has the same form as that for isothermal SBRs, namely eq 6. The heat balance equation for isoperibolic SBRs has been developed elsewhere.3,20 Therefore, the heat balance equation is briefly introduced as follows l dX dτ 1 o = Δτad,0 A − ε[Wt(1 + εθ )(τ − τj) m o dθ 1 + εRHθ n dθ | o + RH(τ − τD)]} o (7) ~

Figure 1. Influence of the initial temperature on the dimensionless temperature (τ) and maximum dimensionless temperature (τmax) in the isoperibolic SBRs involving autocatalytic reactions. n = 1, m = 1, Da = 1, γ = 35, RH = 1, ε = 0.3, Δτad,0 = 0.5, Wt = 10, M = 1, τD = τj.

where RH = (ρcp)D/(ρcp)0 is the ratio of the volumetric heat capacities between the dosing stream and the initial reaction mass in SBRs, Δτad,0 = (−ΔHr)NAt/[(ρCp)0Vr,0TR)] is the dimensionless initial adiabatic temperature rise and Wt = (UA)0tD/[ε(ρCp)0Vr,0] represents the Westerterp number that accounts for the cooling efficiency of the SBRs. It should be kept in mind that eq 7 is valid only in the dosing period, namely θ ≤ 1. After the dosing period, namely θ > 1, eq 7 should be rewritten as

coolant temperatures in the jacket (τj) by the fourth-order Runge−Kutta method. The initial temperature is supposed to be equal to τj. The calculated temperature profiles are shown in Figure 1. One can see that the temperature profiles in the initial temperature range of 0.93−0.98 present significant temperature jumps, which correspond to the thermal runaway event. The blue line in Figure 1 represents the maximum dimensionless reaction temperature (τmax) at different initial temperatures. One can see that when the initial temperature increases from 0.925 to 0.95, the values of τmax significantly increase as the initial temperature increases. When the initial temperature increases to 1, τmax is reached at the earliest time. The generalized criterion developed by Alós23 states that the start of the QFS operation is defined at the condition where τmax is reached at the earliest time. Accordingly, the QFS operations in Figure 1 start from the initial temperature equal to 1. To better understand the tendency of τmax, the curve of τmax−τj is shown in Figure 2. It is apparent that for the no ignition and QFS operations, τmax is almost linearly dependent on τj. This is in agreement with the derivative of τmax to τj in Figure 2. Specifically, the values of derivative of τmax to τj (namely dτmax//dτj) keep constant in no ignition and QFS scenarios. With respect to the thermal runaway region, the corresponding curve τmax−τj looks like a hump, which indicates that τmax is highly sensitive to τj in the thermal runaway region. From the above discussion, one can find that the generalized criterion developed by Alós23 is actually one sort of the wellknown sensitivity criterions for defining thermal runaway boundaries. 3.2. Comparison of the Two Criterion for QFS Identification. According to the Tta criterion developed by Hugo,1,2 for the no ignition and QFS operations, the mixture temperature profiles must be underneath the target temperature profiles. By introducing a 5% overestimation of the temperature difference, the dimensionless target temperature (τta = Tta/TR) can be calculated by24

| l dX dτ 1 o o = Δτad,0 A − ε[Wt(1 + ε)(τ − τj)]} m o o dθ 1 + εR H n dθ ~

(8)

From the above model, there are nine dimensionless model parameters: Da, M, ε, n, m, γ, Δτad,0, Wt, and RH. From eq 1, one can directly expect that component B can catalyze the reaction. Thus, we can reasonably predict that the amount of component B initially loaded in the reactor has a significant influence on the reaction rate and temperature profiles in isoperibolic SBRs. This is the main difference between nonautocatalytic and autocatalytic reactions. In addition, it should be emphasized that the compound B must be preloaded. An inversion would lead to a runaway reaction.

3. QFS OPERATIONS IN ISOPERIBOLIC HOMOGENEOUS SBRS INVOLVING AUTOCATALYTIC REACTIONS 3.1. Identification of the QFS Operation. In general, the operations of isoperibolic SBRs could be divided into three regions: no ignition, thermal runaway and QFS.4,5 Herein, QFS operation is the desirable one due to the low accumulation and smooth temperature profiles. Two criteria, namely, the target temperature (Tta) criterion developed by Hugo1,2 and the generalized criterion developed by Alós,23 are present to identify QFS operations, so far. In the following, we mainly employ the generalized criterion to illustrate the QFS operation for isoperibolic SBRs involving autocatalytic reactions. For better understanding, we arbitrarily assume a set of the dimensionless parameters for isoperibolic SBRs as shown in the caption of Figure 1. The corresponding model of isoperibolic SBRs is then numerically calculated at different C


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Figure 2. Effect of the jacket temperature (τj) on the maximum dimensionless temperature (τmax) and the derivative of τmax to τj (namely dτmax/dτj) in the isoperibolic SBRs involving autocatalytic reactions. n = 1, m = 1, Da = 1, γ = 35, RH = 1, ε = 0.3, Δτad,0 = 0.5, Wt = 10, M = 1, τD = τj.

l Wt(1 + εθ )τj + RHτD o o o o θ≤1 o o Wt(1 + εθ ) + RH o o o o Δτad,0 o o o o o + 1.05 ε(Wt(1 + εθ ) + R ) o o H o τta = m o o Wt(1 + ε)τj + RHτD o o o o θ>1 o o Wt(1 + ε) + RH o o o o Δτad,0 o o o + 1.05 o o o ε(Wt(1 + ε) + RH) n

(9)

Then one can directly deduce that for the no ignition and QFS operations τmax must be lower than the maximum value of τta (τta,max). τta,max can be calculated by τta,max =

Wtτj + RHτD Wt + RH

+ 1.05

Δτad,0 ε(Wt + RH)

(10)

Figure 3. Comparison of the τmax−j and τta,max−τj profile in the isoperibolic SBRs involving autocatalytic reactions. n = 1, m = 1, Da = 1, γ = 35, RH = 1, ε = 0.3, Δτad,0 = 0.5, Wt = 10, M = 1, τD = τj.

For the QFS operation defined by the generalized criterion,23 the corresponding τmax is also lower than τta,max. For better understanding, one typical example with the τmax−τj and τta,max−τj curves are shown in Figure 3. It is obvious that the values of τta,max are higher than that of τmax in the QFS scenario.

where Xac,max is the maximum accumulation of the unconverted coreactant. The term of ΔTad in eq 11 can be calculated by

4. THERMAL PERFORMANCES OF ISOTHERMAL AND ISOPERIBOLIC SBRS INVOLVING AUTOCATALYTIC REACTIONS Recently, we reported a facile approach to design thermally safe operating conditions for isoperibolic homogeneous SBRs involving nonautocatalytic reactions, which is developed on the basis of the deep insights into the relationship between isothermal and isoperibolic homogeneous SBRs.19 This approach states that as long as the values of MTSR increase with the reaction temperature in isothermal mode, the corresponding isoperibolic homogeneous SBRs must be in QFS region, regardless of the values of Wt. Herein, the MTSR in the isothermal SBRs can be calculated by the following expression MTSR = T + XaC,max ΔTaD

ΔTad =

Q tot (mc p)f

(12)

Where Qtot is the total heat generated by the autocatalytic reactions, m is the reaction mass, cp is the heat capacity of the reaction mixture, and the subscript f refers to the finial reaction mixture. With respect to isothermal homogeneous SBRs involving autocatalytic reactions, the corresponding MTSR0−τ profiles may also present an ‘S’ shape for highly exothermic reactions. Herein, MTSR0 = MTSR/TR refers to the dimensionless form of MTSR. For better understanding, two examples are illustrated in Figure 4. The difference between the two MTSR0−τ curves in Figure 4 is the Δτad,0 and the other model parameters are identical. Obviously, for lowly exothermic autocatalytic reactions, MTSR0 always increases with τ

(11) D


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namely Wt and M, are shown in Figures 6 and 7, respectively. The influences of other model parameters can be found in the Supporting Information profiles. From Figures S1−S7 and Figures 6 and 7, one can see that the variation of all nine model parameters did not influence the finding stated in the above paragraph. This finding opens a new way to design QFS operations in isoperibolic SBRs involving autocatalytic reactions. This will be discussed in detail in the next section. With respect to homogeneous reaction, the mass transfer characters during the scale-up process can be neglected. Thus, only heat transfer characters needs to be considered.21 Provided that the three key operating parameters (namely the dosing stream temperature, the jacket temperature and the dosing time) for isoperibolic SBRs keep identical during the scale-up process, the other eight model parameters except Wt keep constant and the Wt number decreases from the laboratory scale to the pilot/industrial scale. In Figure 6, one can see that the finding in Figure 5a is feasible regardless of the values of Wt. Accordingly, we can reasonably expect that as long as the reaction temperature at isothermal mode locates after the valley point of MTSR0−τ curve in Figure 5a, the isoperibolic SBRs involving autocatalytic reactions in pilot/ industrial plants must be in QFS scenario. With respect to the autocatalytic reactions in eq 1, because the component B acts as both reactant and catalyst, one can reasonably expect that the initial amount of component B has a significant influence on the thermal behavior of the isoperibolic SBRs involving autocatalytic reactions. Therefore, it is essential to investigate the influence of M on the QFS operation in isoperibolic SBRs. For this purpose, the τmax−τj profiles at different M are shown in Figure 8. Obviously, as the value of M increases, the critical τj corresponding to the valley points on the τmax−τj curves significantly shift to the low values, which can be ascribed to the fact that the more amount of component B can accelerate the reaction rate. Accordingly, we can reasonably expect that the reduction of the amount of component B may transfer the isoperibolic SBRs involving autocatalytic reactions from the QFS region to the thermal runaway region. Therefore, in realistic cases, the amount of component B loaded into the SBRs should be paid intensive attention. As a rule of thumb, loading an enough amount of component B into the SBRs is necessary.

Figure 4. Dimensionless MTSR vs reaction temperature profiles in the isothermal SBRs involving autocatalytic reactions. n = 1, m = 1, Da = 1, γ = 35, ε = 0.3, M = 1.

increasing while for highly exothermic autocatalytic reactions, MTSR0-τ curves may present an ‘S’ shape. To illustrate the relationship between isothermal and isoperibolic SBRs involving autocatalytic reactions, the comparison of the τmax−τj profile in the isoperibolic mode and the MTSR0−τ profile in the isothermal mode is shown in Figure 5. The value of Δτad,0 in Figure 5a is 0.5 and that in Figure 5b is 0.13. One can see that for lowly exothermic autocatalytic reactions, the values of τmax are always lower than the values of τta,max, which indicates that if the autocatalytic reactions are lowly exothermic, thermal runaway operation will hardly happen.20 This phenomenon is in agreement with the nonautocatalytic reactions.19 For highly exothermic autocatalytic reactions in Figure 5a, we can see that if the reaction temperature in the isothermal mode is located after the valley point, the corresponding isoperibolic SBRs with τj equal to the reaction temperature of the isothermal SBRs must be in QFS region. Furthermore, if the isoperibolic SBRs are in the no ignition region, the corresponding values of MTSR0 in the isothermal mode must increase as the reaction temperature increases. To validate the universality of the finding stated in the above paragraph, it is necessary to study the influence of all the nine model parameters on the phenomenon in Figure 5a. Herein, to conserve the space, the influence of only two-model parameter,

Figure 5. Comparison of the τmax−τj, τta,max−τj, and MTSR0−τj profiles in the SBRs involving autocatalytic reactions. (a) Δτad,0 = 0.5; (b) Δτad,0 = 0.13. n = 1, m = 1, Da = 1, γ = 35, RH = 1, ε = 0.3, Wt = 10, M = 1, τD = τj. E


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Figure 6. Influence of Wt on the τmax−τj, τta,max−τj, and MTSR0−τj profiles in the SBRs involving autocatalytic reactions. (a)Wt = 6; (b)Wt = 10; (c) Wt = 20; (d) Wt = 40. n = 1, m = 1, Da = 1, γ = 35, RH = 1, ε = 0.3, M = 1, Δτad,0 = 0.5 τD = τj.

5. DESIGN OF SAFE AND PRODUCTIVE OPERATING CONDITIONS FOR ISOPERIBOLIC HOMOGENEOUS SBRS INVOLVING AUTOCATALYTIC REACTIONS In general, to design safe and productive operations of isoperibolic homogeneous SBRs involving autocatalytic reactions, two constraints should be fulfilled:

To better understand the above procedure, let us assume that the isothermal SBRs are conducted at two different temperature (T2>T1) and MTSR2 at temperature T2 is higher than MTSR1 at temperature T1. This assumption implies that at temperature T2, MTSR increases with the reaction temperature increasing. Accordingly, the isoperibolic SBRs involving autocatalytic reactions at the initial temperature of T2 must be not in the thermal runaway scenario, regardless of the values of Wt. However, when employing the above procedure to design QFS operating conditions, it should be kept in mind that when the isoperibolic SBRs are in a no ignition region, the MTSR also increases with increasing reaction temperature in the isothermal mode, as shown in Figure 5a. This indicates that only employing the MTSR criterion cannot distinguish between the no ignition and QFS regions. Thanks to the fact that the accumulation in no ignition region is much higher than that in QFS scenario, even close to 100%, we can distinguish the QFS operation from the no ignition operation. When the reaction temperature in isothermal mode where the values of MTSR increase with the reaction temperature increasing has been found, the accumulation should be checked. If the accumulation is reasonably low, then one can expect the corresponding isoperibolic operation will be in QFS scenario. With respect to the lowly exothermic reactions, because the thermal runaway events hardly occur, more attentions should be paid to designing the productive operation rather than the prevention of the thermal runaway events. To achieve the productive operation, it is desirable to conduct the isoperibolic

(1) Under normal operating conditions, the temperature profile must be rigorously controlled, i.e., the heat exchange system must be able to cope with the heat produced by the reaction. In this case, the operation of SBRs in isoperibolic mode should be in QFS region. (2) The accumulation of nonconverted reactants should not trigger the secondary reactions even in case of cooling failure. As mentioned previously, determination of the detailed kinetic parameters is a time-consuming process, especially for the autocatalytic reactions. Therefore, it is desirable to develop a kinetic-parameter-free approach to design safe and productive operating conditions for SBRs involving autocatalytic reactions. To design QFS operating conditions, the following procedure can be followed: first, empirically set the dosing time; second, conduct isothermal calorimetry tests at different reaction temperatures and select a reaction temperature where the values of MTSR increase with the reaction temperature increasing; third, assign such a reaction temperature in the isothermal mode to the initial temperature in the isoperibolic mode and conduct the isoperibolic calorimetry test in laboratory scale to verify the QFS operation. F


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Figure 7. Influence of M on the τmax−τj, τta,max−τ, and MTSR0−τj profiles in the SBRs involving autocatalytic reactions. (a) M = 0.1; (b) M = 0.5; (c) M = 1; (d) M = 1.5. n = 1, m = 1, Da = 1, γ = 35, RH = 1, ε = 0.3, Wt = 10, Δτad,0 = 0.5 τD = τj.

as τmax is lower than the dimensionless MAT (MAT0 =MAT/ TR), the secondary reaction can be avoided under normal operating conditions. The value of τmax can be easily determined by carrying out the laboratory-scale isoperibolic calorimetry test. From the inherent safety point of view, the secondary reactions should not be triggered even in case of the cooling failure. This goal can be reached as long as the accumulation of nonconverted reactants will not trigger the secondary reactions in case of cooling failure. In other words, MTSR of the QFS isoperibolic SBRs should be lower than MAT. This constraint condition can be confirmed by carried out the isoperibolic calorimetry test in laboratory scale. If MTSR > MAT, the dosing rate should be lowered until MTSR < MAT. After lowering the dosing rate, the QFS operation is still in the QFS region. In this stage, safe and productive operations of isoperibolic SBRs involving autocatalytic reactions has been designed following the above approach. For better understanding, a feasible procedure to illustrate the approach is shown in Figure 9. The most outstanding merit of the approach in Figure 9 is that the approach does not require information on the kinetic parameters of the autocatalytic reactions at all. In our previous work,19 we proposed a procedure to design the safe operating conditions of isoperibolic SBRs for nonautocatalytic reactions. That procedure is similar to the procedure in this work. The main difference between these two procedures are that (1) MTSR for nonautocatalytic reactions in isothermal mode always occurs at the time when the stoichiometric amount of reactant A is added while MTSR for autocatalytic reactions may occur at any time; (2) with respect

Figure 8. Influence of M on the τmax− τj profiles in the isoperibolic SBRs involving autocatalytic reactions.

SBRs at relatively high temperatures and quick dosing rates but should not trigger possible secondary reactions. In general, to avoid triggering the possible secondary reaction, the thermal stability of reactants, products and reacting mixture should be experimentally determined. This can be achieved by carrying out dynamic differential scanning calorimetry (DSC) tests and/or adiabatic rate calorimetry (ARC) tests. Subsequently, maximum allowable temperature (MAT) in the isoperibolic homogeneous SBRs can be identified as the temperature at which no highly exothermic decomposition will be triggered in 24 h, namely TD24. As long G


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Figures S1−S7, influence of the variation in the seven other model parameters on the finding in Figure 5a (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +86 025 84315526. Fax: +86 025 84315526. ORCID

Wanghua Chen: 0000-0002-2716-7674 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work has been financially supported by National Key R&D Program of China (2017YFC0804701-4) and the Fundamental Research Funds for the Central Universities (30917011312).

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NOMENCLATURE A = heat exchange area, m2 C = concentration, mol m−3 cp = specific heat capacity, J g−1 K−1 Da = Damköhler number, Da = kn,m,RtD(NAt/Vr,0)n+m−1 E = activation energy, J mol−1 f = the mechanism of the autocatalytic reactions k = kinetic rate constant, m3 mol−1 s−1 MAT = maximum allowable temperature MAT0 = dimensionless form of MAT MTSR = maximum temperature of synthesis reactions under adiabatic condition MTSR0 = dimensionless form of MTSR Q = heat generated by the reactions m = mass M = the molar ratio of reactant B to reactant A in eq 1, N = mole amount, mol r = reaction rate, mol/(m3 s) R = the ideal gas constant RH = ratio of the volumetric heat capacities between the dosing stream and the initial reaction mass in SBR SBR = semibatch reactor St = Stanton number t = time, s T = temperature, K Tta = the target temperature, K TR = reference temperature, 300 K U = overall heat transfer coefficient, W m−2 K−1 V = volume, m3 Wt = Westerterp number, Wt = (UA)0tD/(ε(ρCp)0V0) X = conversion

Figure 9. Flowchart to design the safe and productive operations of the homogeneous isoperibolic SBRs involving autocatalytic reactions.

to autocatalytic reactions, adding more of reactant B can be considered as a measure to design QFS operation. It is worthwhile to note that the procedure is developed on the assumption that the physical heat, for example the mixing heat, can be neglected relative to the reaction heat.

6. CONCLUSION Design safe and productive operating conditions for isoperibolic SBRs involving autocatalytic reactions is an essential issue in the fine chemical and pharmaceutical industries. Since determination of the reaction kinetics is time-consuming, a kinetic-parameter-free approach to designing the safe and productive operating conditions for the isoperibolic homogeneous SBRs involving autocatalytic reactions is desirable. Such an approach in this work is developed on the basis of the finding that if the values of MTSR increase with the reaction temperature increasing in the isothermal mode and the accumulation is significantly smaller than 1, the corresponding isoperibolic SBRs involving autocatalytic reactions must be not in the thermal runaway scenario regardless of the values of Wt. To follow this procedure, we should first conduct several isothermal calorimetry tests to determine the safe operating parameters for the isoperibolic homogeneous SBRs involving autocatalytic reactions. In the end, it should be kept in mind that the approach is developed on the basis of the reaction scheme in eq 1. With respect to other kind of autocatalytic reactions, one should carry out the calculations like in this article to make sure the same results can be obtained. Also, the approach developed is based on the assumption that the physical heat, like mixing heat, can be neglected relative to the reaction heat.

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GREEK SYMBOLS γ =dimensionless activation energy, γ = E/RTR ε =relative volume increase at the end of the dosing period θ =dimensionless time, θ = t/tD κ =dimensionless reaction rate constant, κ = exp(γ(1 − 1/ τ)) ρ =density, kg m−3 τ =dimensionless temperature, τ = T/TR ΔHr =reaction enthalpy, J mol−1 ΔTad =adiabatic temperature rise Δτad,0 =dimensionless initial adiabatic temperature rise

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S Supporting Information *

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Processes Using Topology Tools. Comput. Chem. Eng. 2013, 56, 114− 127. (17) Maestri, F.; Rota, R. Kinetic-Free Safe Operation of Fine Chemical Runaway Reactions: A General Criterion. Ind. Eng. Chem. Res. 2016, 55, 925−933. (18) Maestri, F.; Rota, R. Kinetic-Free Safe Optimization of a Semibatch Runaway Reaction: Nitration of 4-Chloro Benzotrifluoride. Ind. Eng. Chem. Res. 2016, 55, 12786−12794. (19) Guo, Z.; Feng, W.; Li, S.; Zhou, P.; Chen, L.; Chen, W. Facile Approach to Design Thermally Safe Operating Conditions for Isoperibolic Homogeneous Semibatch Reactors Involving Exothermic Reactions. Ind. Eng. Chem. Res. 2018, 57, 10866−10875. (20) Maestri, F.; Rota, R. Safe and Productive Operation of Homogeneous Semibatch Reactors Involving Autocatalytic Reactions with Arbitrary Reaction Order. Ind. Eng. Chem. Res. 2007, 46, 5333− 5339. (21) Joshi, S. R.; Kataria, K. L.; Sawant, S. B.; Joshi, J. B. Kinetics of Oxidation of Benzyl Alcohol with Dilute Nitric Acid. Ind. Eng. Chem. Res. 2005, 44, 325−333. (22) Xi, H.; Gao, Z.; Wang, J. Kinetics of Oxidative Decarboxylation of 3,4-Methylenedioxymandelic Acid to Piperonal with Dilute Nitric Acid. Ind. Eng. Chem. Res. 2009, 48, 10425−10430. (23) Alós, M. A.; Nomen, R.; Sempere, J. M.; Strozzi, F.; Zaldívar, J. M. Generalized Criteria for Boundary Safe Conditions in Semi-batch Processes: Simulated Analysis and Experimental Results. Chem. Eng. Process. 1998, 37, 405−421. (24) Steensma, M.; Westerterp, K. R. Thermally Safe Operation of a Cooled Semi-batch Reactor. Slow Liquid-Liquid Reactions. Chem. Eng. Sci. 1988, 43, 2125−2132.

SUBSCRIPTS AND SUPERSCRIPTS A =reactant A in eq 1 ac =accumulation B =reactant B in eq 1 D =dosing 0 =initial f =final j =jacket m =kinetic order toward reactant B in eq 1 max =maximum n =kinetic order toward reactant A in eq 1 r =reaction R =reference ta =the target temperature t =total

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Simple Approach to Designing Safe and Productive Operation of

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