CFD simulation of thermal runaway reaction of styrene polymerization

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Cite This: Org. Process Res. Dev. XXXX, XXX, XXX−XXX

Computational Fluid Dynamics Simulation of Thermal Runaway Reaction of Styrene Polymerization Jiawei Cui,†,‡,§ Lei Ni,*,†,‡ Juncheng Jiang,*,†,‡ Yong Pan,†,‡ Hao Wu,†,‡ and Qiang Chen†,‡ †

College of Safety Science and Engineering, Nanjing Tech University, Nanjing 211816, Jiangsu, China Jiangsu Key Laboratory of Hazardous Chemicals Safety and Control, Nanjing 211816, Jiangsu, China

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‡

ABSTRACT: Thermal polymerization of styrene in a lab-scale batch reactor was simulated using computational fluid dynamics (CFD). The corresponding hydrodynamic model of thermal polymerization of styrene was combined with the fluid−solid coupling model of a simulated heat exchanger by using the CFD method to construct the corresponding reactor model. The effects of stirring rate, cooling temperature, and cooling flow rate were investigated under the runaway conditions of thermal polymerization of styrene. The results showed that the increase in temperature during the reaction was sensitive to different runaway conditions. The stirring rate and cooling flow rate greatly influenced the increase in temperature during the reaction. Based on the temperature distribution inside the reactor, the optimal location of the temperature monitor was determined by employing the divergence (DIV) criterion. KEYWORDS: batch reactor, styrene polymerization, thermal runaway reaction, computational fluid dynamics (CFD) and Bosch, Kerr, and Snee7 proposed that in batch and semibatch reactors, online monitoring can be achieved by arranging only one temperature sensor, provided that the appropriate sensor location is determined. However, in the studies of the thermal runaway of polymerization, most researchers have ignored heat transfer across the reactor wall and the cooling flow field in the cooling jacket. Moreover, there are few studies on determination of the cooling flow rate and location of the heat transfer barrier region. In the present work, the thermal runaway reaction of styrene polymerization is studied. We employ the CFD method to combine a kinetic model of the thermal polymerization in bulk polymerization of styrene and the fluid−solid coupling model of the simulated heat exchanger to construct the corresponding reactor model.8,9 The multireference frame method (MRF) is employed to solve the problem of rotation of the stirring paddle, and the component-transport equation source term and the energy equation source term are added via user-defined functions (UDF). Considering the influence of material viscosity on the reaction system, CFD simulation analyses of the cooling and the stirring out-of-control scenarios are performed to investigate the exothermic temperature rise of the reactor and determine the area that hinders heat transfer. Moreover, the divergence (DIV) criterion is employed to determine the optimal location of the temperature detector in the reactor to provide a technical reference for reactor safety design and emergency control.

1. INTRODUCTION Plastics, resins, and other products produced by polymerization are widely used in the automotive industry and in household appliances, electronics, packaging, and building materials because of their favorable characteristics such as low specific gravity, easy processing, impact resistance, and good electrical insulation. However, because polymerization is typically a strongly exothermic reaction and the heat of polymerization cannot be removed quickly, the viscosity of the entire reaction system increases rapidly during the reaction, leading to uneven temperature distribution. This causes the occurrence of thermal runaway accidents. Accidents due to thermal runaway of polymerization account for one-third of all runaway reaction accidents.1 Computational fluid dynamics (CFD) is used widely to simulate the thermal runaway behavior of polymerization because large-scale experiments of the process would be extremely dangerous. Given the high viscosity in the polymerization reaction and the uneven temperature distribution in the reactor, many scholars have studied the mixing characteristics of fluids in various stirred tanks and the position of the temperature sensor in the reactor. For instance, Aubin et al.2 pointed out that in a high-viscosity fluid system, the mixing effect achieved using a multilayer oblique 45° Intermig-type impeller is better than that achieved using a 90° impeller. Milewska et al.3 and Milewska et al.4 used CFD to simulate the thermal runaway behavior of a reactor during agitation failure and used online divergence to predict the thermal runaway behavior of the reaction. The results showed that the location of the temperature sensor significantly influenced the accuracy of thermal runaway behavior prediction. Jiang et al.5 employed CFD to simulate the styrene polymerization reaction by studying the effect of viscosity changes in the system on temperature distribution and determined the optimal temperature monitoring point and the optimal inhibitor injection position during stirring. In addition, Bosch, Strozzi, and Lister6 © XXXX American Chemical Society

2. CFD MODEL 2.1. Reactor Model and Boundary Condition. A CFD model of the styrene polymerization reaction was established by using a reaction calorimeter (RC1) (Mettler Toledo) as the model. The reactor geometry was generated by using the Design Received: January 4, 2019 Published: February 26, 2019 A

DOI: 10.1021/acs.oprd.9b00005 Org. Process Res. Dev. XXXX, XXX, XXX−XXX

Organic Process Research & Development

Article

Model (Ansys Workbench, Inc.) software package and another software package called Mesh (Ansys Workbench, Inc.) to build and mesh the geometry models required for CFD. The reactor specifications used in the model simulations are listed in Table 1.

Transfer: KP

R r· + M → R r·+ 1 , K tc

R r· + R s· → Pr + s ,

Parameter

Values

Parameter

Values

2115 mm 55 mm 245 mm 4

Liquid level Impeller diameter Impeller elevation Impeller type

80.02 mm 60 mm 20 mm 30° pitched blade

(3)

r, s ≥ 1

(4)

Termination:

Table 1. Reactor Specifications Reactor inner diameter Inner wall thickness Reactor height No. of blades

r≥1

where M, R·r, and P, respectively, represent styrene monomer, radical, and polystyrene. The subscripts r and s represent the length of the polymer chain. The rate constants of the aforementioned three reactions are Kth, Kp, and Ktc, respectively. The styrene polymerization rate R is expressed as follows:

From the interior to the exterior, the reactor consists of four parts, namely, a four-bladed inclined stirring paddle, reaction liquid system, inner wall, and cooling jacket. To study the mixing characteristics of the stirring paddle, we assumed the reaction liquid as a completely mixed flow (CMF), used the multireference system model to solve the stirring problem, and used the standard k−ε turbulence model to solve the flow field problem. We adopted fluid−solid coupling boundary conditions at the vessel wall, there was no heat source inside, and the remaining walls were adiabatic boundaries. The grid of the entire reactor was a polyhedral mesh, and the boundary layer was set to encrypt the grid in the fluid−solid coupling boundary region, which consisted of 14,75040 cells (Figure 1).

R = K p[M ][R·] = K p[M ]

2K th[M ]3 K tc

(5)

Because the styrene concentration [M] in the mixture is related to the styrene density ρ, (Wm is the mass fraction of styrene and Mn is the molecular mass of styrene), we have the following equation: [M ] =

ρWm Mn

(6)

Therefore, the polymerization rate can be expressed as follows: ÄÅ ÉÑ2.5 2K th ÅÅÅ ρWm ÑÑÑ Å ÑÑ R = Kp Å K tc ÅÅÅÇ Mn ÑÑÑÖ (7) 13 The kinetic parameters are listed in Table 2. Table 2. Kinetic Parameter Values Parameter

Values/m3·kmol−1·s−1

Parameter

Values/j·mol−1

Ath Ap Ato

2.190 × 105 2.170 × 107 8.200 × 109

Eth Ep Eto

1.147 × 105 3.243 × 107 1.145 × 109

Figure 1. Reactor model.

In addition, the CFD simulation software calculation process requires the source terms of the component-transport equation and the energy equation, as follows:

2.2. Mathematical Model. 2.2.1. Governing Equations. For incompressible−finite volume reactions occurring in a homogeneous liquid phase, the continuity equation, momentum equation, energy equation, and component-transport equation for the styrene thermal initiation bulk polymerization reactor can be expressed by the following general equation10 (1):

∂(ρUiϕ) ∂(ρϕ) ∂ jij ∂ϕ zyz + = jΓϕ z + Sϕ ∂t ∂xi ∂xi jjk ∂xi zz{ (1) where ϕ is the system variable; ρ is the fluid density; t is the time; Ui is the velocity of the fluid along the x, y, and z directions; Γϕ is the general diffusion coefficient; and Sϕ is the source term. 2.2.2. Source Term. Styrene is one of the few monomers that can initiate bulk polymerization under the application of heat. Domestic and foreign scholars have researched extensively the mechanism of thermal initiation of bulk polymerization. In the present work, we employ a three-molecule initiation mechanism, which mainly includes chain initiation, transfer, and termination.11,12 The simplified kinetic equation is as follows: Initiation: K th

3M ⎯→ ⎯ 2R1·

S⌀ = −Mn × R

(8)

S⌀ = ΔH × R

(9)

where ΔH is reaction enthalpy.12 2.2.3. System Viscosity and Density Calculation. Owing to changes in viscosity of the entire reaction system during the polymerization reaction, the flow characteristics of the fluid in the reactor are significantly affected. Therefore, in the present study, we consider the influence of material viscosity on the reaction system. Thus, the viscosity of the mixture was calculated using the following equation:14 μ=

μ

0 1.2

(1 + μ0 γ /35000)0.6

(10)

where γ is the shear rate. The zero shear viscosity of the reaction mass was estimated using the empirical correlation reported by Kim and Nauman:14

(2) B


Organic Process Research & Development ÄÅ ÅÅ 1109 0.1413Å ÅÅ12.032W ln(μ0 ) = −11.091 + + MP ÅÅ p ÅÅ T ÅÇ ÉÑ ( −1327Wp + 1359W p2 + 3597WP3) ÑÑÑ ÑÑ + ÑÑ ÑÑ T ÑÖ

Article

− 19.501W p2 + 2.92W p3

(11)

where Mp is the average molecular weight of the polymer, WP is the polymer mass fraction in the mixture, and T is the reaction temperature. The density of the mixture was calculated using the correlation reported by Soliman et al.:15 ρ = (1174.7 − 0.918T )(1 − Wp) + (1250.0 − 0.605T ) WP

(12)

Finally, we input each parameter and equation into UDF (User Defined Function) and imported UDF into the CFD solver. 2.2.4. Critical Criteria of Thermal Runaway. In the past, many scholars have focused on the critical criteria for thermal runaway, and the critieria were systematically summarized by Jiang Jun-Cheng et al.16 A critical criterion for thermal runaway based on the Chaos theory is widely used.17 Based on temperature data, this method can accurately predict the thermal runaway situation and help realize the purpose of online monitoring. Zaldivar et al.18 defined system divergence as the trace of the Jacobian matrix: ÉÑ ÄÅ ÅÅÅ ∂(∂ξ /∂t ) ∂(∂ξ /∂t ) ÑÑÑ ÑÑ ÅÄÅ j j ÑÉÑ ÅÅÅ ÑÑ ÅÅ 11 12 ÑÑ ÅÅ ∂ξ ∂T ÑÑ Å Å Ñ Ñ Ñ = ÅÅ J = ÅÅ Ñ ÅÅ j j ÑÑ ÅÅ ∂(∂T /∂t ) ∂(∂T /∂t ) ÑÑÑ ÑÑ ÅÅÇ 21 22 ÑÑÖ ÅÅ ÑÑ ÅÅ ÑÑ ÅÅ T ∂ ∂ ξ (13) ÑÖ ÅÇ

Figure 2. Temperature curves for styrene polymerization reaction simulated by different models at the initial temperature of 150 °C.

Table 3. Time Interval for a 30 °C Temperature Increase at the Initial Temperature of 150 °C in Styrene Polymerization Reaction Simulated by Different Models Models Hui−Hamiele model Weickert model Marten−Hamielec model CFD model

Time interval of a 30 °C temperature increase from 150 to 180 °C (s) 254 263 297 306

where T is the reactor temperature and ξ is the conversion rate of the reactants. Therefore, div = j11 + j22

(14)

When div > 0, the reaction can be considered out of control. Therefore, so long as the temperature monitor is positioned appropriately in the reactor, its readout represents the temperature of the entire reaction system, and the value of system divergence can be calculated online. Thus, online monitoring of the uncontrolled reaction can be realized.

3. RESULTS AND DISCUSSION Thermal polymerization of styrene in a batch-scale reactor with a cooling jacket under isoperibolic operating conditions and 150 °C as the initiation temperature was conducted to explore the effect of reaction safety under several runaway conditions, such as stirring runaway, fluctuation of cooling temperature, and reduction of cooling rate. Temperature profiles are used to analyze the scenario of the polymerization runaway reaction, and the corresponding temperature profile is volume-average temperature (Tavg). 3.1. Validation of Models. The thermal runaway reaction of styrene polymerization is very dangerous. At present, there are few experimental studies on the thermal runaway reaction of styrene polymerization. More studies investigated the effect of temperature, catalyst, and polymerization inhibitor on the

Figure 3. Time−volume average temperature curve for scenario of stirring out of control.

conversion rate. The Hui−Hamielec model, Weickert model, and Marten−Hamielec model were studied in comparison by Hungenberg et al.19 They found that the three models showed good agreement with the experimental results of styrene polymerization. In this paper, the three models are chosen for the comparison with the CFD model. Figure 2 shows the temperature curves with 150 °C as initial temperature. The comparative results indicate that the temperature curves of the CFD model coincide with the predicted temperature curves of the other three models. As a parameter for comparison, the time C



Article

Figure 6. Temperature vs time plot for four cooling temperatures.

Figure 4. Time−maximum temperature curve for scenario of stirring out of control.

Figure 5. Temperature profile of the y-axis section at stirring speeds of 150 r/min and 0 r/min.

Figure 7. Cooling flow field speed vector.

Table 4. Effects of Stirring Rate on Runaway Time and Temperature Stirring rate/ (r·min−1)

Time to reach maximum reaction temperature (s)

Maximum reaction volume average temperature (°C)

Maximum temperature rise rate (°C·s−1)

150 100 50 0

674 571 536 480.5

338.4 363.2 379.1 329.1

2.21 3.57 5.90 8.49

interval of a 30 °C temperature increase is shown in Table 3. It reveals that the time interval for a 30 °C temperature increase differs by less than 15% between the models.5 Obviously, the temperature curve of the CFD model is between the Weickert model and the Marten−Hamielec model in Figure 2. Therefore, the CFD model in this paper can be used for simulation styrene polymerization reaction. 3.2. Effect of the Stirring Speed. Stirring runaway is one of the most dangerous runaway scenarios. Milewska et al.20 showed that stirring has a significant effect on internal component diffusion and the convective heat transfer coefficient. Stirring runaway can cause uneven heat exchange between the reaction system and the reactor wall, which decreases the heat exchange efficiency. Figure 3 shows a time−volume average temperature curve under stirring runaway. As the stirring speed decreases from 150 r/min to 50 r/min, the maximum volume−average temperature of the entire reaction system increases. However, when the stirring was stopped, the maximum volume−average

Figure 8. Temperature vs time for different cooling velocities.

temperature was the lowest compared with those in the three other scenarios shown in Figure 3, which cannot indicate the risk of reaction depression. To explain this situation, the time− maximum temperature curve is shown in Figure 4. As shown in Figure 4, when the stirring speed is 0 r/min, the maximum temperature of the reaction system reaches 468.84 °C, which is very high and dangerous, as well as in conflict with the result in Figure 3. To further illustrate this situation, the temperature D



Article

°C. Overall, as the stirring speed decreased, the runaway time advanced, resulting in shorter emergency time and higher risk of reaction. When the stirring failed completely, runaway occurred 193.5 s earlier than it did when the stirring speed was 150 r/min, as given in Table 4. 3.3. Fluctuation of Cooling Temperature. Fluctuations in cooling temperature are among the most common out-ofcontrol situations in chemical production processes. During the reaction, the cooling temperature is very likely to fluctuate by around 3 °C. The simulation results of reactions proceeding at different cooling temperatures are shown in Figure 6. As shown in the graph, as the cooling temperature increases slightly, the reaction safety is affected adversely, and the out-of-control time is about 57 s ahead of the previous average, which makes it more difficult to predict the out-of-control time. Moreover, the emergency response time is shortened, which increases the accident occurrence probability. 3.4. Cooling Flow Rate Failure. In the runaway scenario, a decrease in the cooling flow rate is a dangerous situation. The main mode of heat transfer in a batch reactor is through the cooling system. In actual industrial production, partial blockage of the cooling system or failure of the refrigeration cycle pump occurs often. Figure 7 shows the cooling flow speed vector corresponding to the cooling flow rate of 3 m/s. After the cooling flow enters the jacket, it winds upward along the clockwise facing wall for about half a week and then flows out from the upper port. It can be seen from Figure 7 that uneven distribution of the external cooling flow field creates a heat exchange obstacle zone at the bottom of the reactor away from the inlet region. This heat exchange dead zone is formed at the bottom of the reactor, and the lowest local cooling flow rate is 0 m/s. Figure 8 shows the reaction time−temperature curve when the refrigeration cycle pump fails, causing the global cooling flow rate to decrease. The maximum temperature rise rate, maximum temperature, and corresponding time are given in Table 5. As the cooling flow rate decreases, the maximum temperature change of the reaction system is not significant, but the time of reaction runaway is advanced significantly. When the refrigeration cycle pump stops working (cooling flow velocity is 0 m/s) and the cooling fluid in the jacket is stagnant, the reaction system exchanges heat only with the stagnant coolant. Therefore, runaway occurs 151 s ahead when it occurs for the cooling flow rate of 3 m/s, and the maximum temperature is increased by 26 °C. When the cooling flow rate is 0 m/s, the comprehensive convective heat transfer coefficient of the reactor wall throughout the reaction is considerably lower than that when the cooling flow rate is 3 m/s, as shown in Figure 9. This causes the heat of the reaction system to accumulate within a short period, and the reaction goes out of control. 3.5. Selection of Temperature Sensor Position. In an actual production process, selection of temperature-monitoring points is crucial because it directly affects the determination of early warning and emergency time. Considering the nonuniformity of the temperature distribution, the setting of the temperature monitoring point is considered from the same horizontal direction and the vertical direction, respectively. Therefore, we selected four points, namely, a, b, c, and d, as monitoring points at the bottom, middle, and top of the reactor, respectively. The specific positions are shown in Figure 1. Figure 10 shows the temperature profiles at different detection positions during reaction runaway at the stirring speed of 150 r/min and cooling flow rate of 3 m/s. Figure 10 shows that in the

Table 5. Effects of Cooling Velocity on Runaway Time and Temperature Cooling velocity (m/s)

Time to reach maximum reaction temperature (s)

Maximum reaction volume average temperature (°C)

Maximum temperature rise rate (°C·s−1)

3 2 1 0

674 661 645 523

338.39 337.9 342.2 361.9

2.2104 2.2118 2.2259 2.6006

Figure 9. Wall-integrated heat transfer coefficient vs time for low cooling velocity.

Figure 10. Temperature profiles at different detection positions during reaction runaway.

profile of the y-axis section at the stirring speeds of 150 r/min and 0 r/min when the volume−average temperature of the reaction peaks is shown in Figure 5. It can be seen from Figure 5 that the temperature distribution of the entire reaction volume is relatively uniform at the stirring speed of 150 r/min, whereas the temperature is severely stratified when the stirring speed is 0 r/ min. This is because when the stirring was completely runaway, the entire reaction system was laminar and the viscosity of the system changed greatly as the reaction progressed. Therefore, the uneven temperature distribution results in the volume average temperature decreasing at 0 r/min but the maximum temperature anywhere in reaction system is highest up to 468.84 E



Article

Figure 11. Divergence of simulation results under experimental conditions.

they indicate that the reaction runaway may occur at the red point, where the divergence value increases abruptly. Table 6 shows alarm schedules for different runaway scenarios, with the warning time tavg corresponding to the volume−average temperature (Tavg) as the reference, and the overall trend is ta > tb > tavg > tc ≅ td. Points c and d better

horizontal direction, the temperature of the bottom near the cooling inlet monitoring point a is lower than that at monitoring point b, which is at the same height away from the inlet; that is, Ta < Tb. In the vertical direction, as the height increases, the temperature increases gradually as Td > Tc > Tb > Ta. The div values at different detection points are shown in Figure 11, and F



Article

Table 6. Alarm Schedules for Different Runaway Scenarios Runaway scenarios Cooling velocity (m/s)

Cooling temperature (°C)

Stirring speed (r·min−1)

tavg (s)

ta (s)

tb (s)

tc (s)

td (s)

3 0 3 3

150 150 153 150

150 150 150 50

576 300.5 489 335.5

648 515.5 574 448

634.5 496.5 557.5 423.5

576.5 301 488.5 335.5

576 300.5 488 333

Author Contributions

represent the overall temperature, so the monitor sets at those points can be used to provide early warning to avoid accidents.

§

(J.C.) First author.

Notes

4. CONCLUSION By using CFD models, herein, we discussed the thermal runaway reaction of styrene polymerization under different failure scenarios. Our conclusions are as follows: 1 CFD simulation can help predict the exothermic behavior of batch polymerization in different situations accurately, thus helping improve intrinsically safe designs and runaway risk assessments of reactors. 2 The established CFD coupling model was applied to a batch polymerization reactor. Parameter sensitivity analysis was carried out for a reactor with stirring runaway and uncontrolled cooling, and the temperature data of the reaction under different uncontrolled conditions were simulated. It was concluded that the batch reactor is parameter sensitive. For example, stirring runaway was found to significantly influence the rise in reaction temperature; for example, under total failure of stirring, reaction runaway occurred 193.5 s before it did when the stirring speed was 150 r/min, and the maximum temperature of the reaction system reached 468.84 °C. The cooling system was found to influence reaction safety. As the cooling flow rate decreased, the reaction runaway time advanced, and a heat transfer obstacle zone was formed at the reactor bottom. 3 The combination of the chaos out-of-control criterion with the CFD coupling model can help predict out-ofcontrol reactions accurately and provide a numerical reference for setting reactor temperature detection points. In a reactor, the critical times corresponding to different monitoring points under different runaway situations were obtained by calculating the DIV criterion, and the overall trend was ta > tb > tavg > tc ≅ td. Based on the critical times, the temperature detector should be installed inside the reaction liquid system away from the cooling inlet, at a position 1/3 or more from the liquid surface. 4 Uncontrolled polymerization scenario analysis is the basis for reactor safety design. On this basis, a method for related cooling suppression after a polymerization reaction is out of control and its influencing factors will be our focus in future works.

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The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors are grateful for the support provided under Jiangsu National Science Foundation of China (BK20171004) and for the support of the key project of National Science Foundation of China under Grant No. 21436006. This manuscript was edited by Wallace Academic Editing.

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NOMENCLATURE Φ System variable ρ Density, kg·m−3 Ui Fluid velocity along x, y, and z directions, m/s Γϕ Diffusion coefficient Source term Sϕ Kth, Kp, Ktc Reaction constant ξ Conversion rate Ath, Ap, Ato Pre-exponential factor, m3·kmol−1s−1 Eth, Ep, Eto Activation energy, J·mol−1 Wm Mass fraction Mn Molecular mass R Reaction speed ΔH Reaction enthalpy μ Dynamic viscosity, Pa·s γ Shear rate μ0 Zero shear viscosity Mp Average molecular weight Tavg Volume-temperatures of reaction mixture, °C t Time [M] Styrene concentration Wp Polymer mass fraction

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REFERENCES

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Lei Ni: 0000-0001-5941-6156 Juncheng Jiang: 0000-0001-7018-2709 Yong Pan: 0000-0002-2516-9799 G



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CFD simulation of thermal runaway reaction of styrene polymerization

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