Venting Design for Di-tert-butyl Peroxide Runaway Reaction Based on Accelerating Rate Calorimeter Test

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1 PROESS SYSTEMS ENINEERIN AND PROESS SAFETY hinese Journal o hemical Engineering, 0(4) (01) Venting Design or Di-tert-butyl Peroxide Runaway Reaction Based on Accelerating Rate alorimeter Test WEI Tongtong ( 魏彤彤 ) and JIAN Huiling ( 蒋慧灵 ) Department o Fire Protection Engineering, hinese People s Armed Police Force Academy, Langang , hina Abstract In order to design the relie system size o di-tert-butyl peroxide (DTBP) storage tanks, the runaway reaction o DTBP was simulated by accelerating rate calorimeter (AR). The results indicated that under adiabatic conditions the initial exothermic temperature was 10.6, the maximum sel-heating rate was min, the maximum sel-heating temperature was 375.9, and the pressure produced by unit mass was 4.51 MPa g. Judged by AR test, the emergency relie system or DTBP was a hybrid system. Based on Design Institute or Emergency Relie System (DIERS) method, the releasing mass low rate W was determined by Leung methods, and the mass velocity was calculated by two modiied Omega methods. The two relie sizes calculated by monograph Omega method and arithmetic Omega method are close, with only 0.63% relative error. The monograph Omega method is more convenient to apply. Keywords di-tert-butyl peroxide, accelerating rate calorimeter, runaway reaction, venting size 1 INTRODUTION Di-tert-butyl peroxide (DTBP) is widely used as reaction initiator and cross-linking agent in high polymer synthesis industry, but its thermal instability and oxidizability makes it very easy to decompose and release large volume o gas, which may lead to explosion accident because o high pressure in the storage and transport tanks. Thus it is necessary to design an appropriate emergency relie system or DTBP tanks. In hina, the criterions o emergency relie systems or reactive liquids are not perect [1]. In this study, Design Institute or Emergency Relie System (DIERS) method is introduced to calculate the relie system size. The accelerating rate calorimeter (AR) is used, which is highly adiabatic, allows a small amount o testing sample, and the results can be extrapolated to any size. Thermal and pressure hazard parameters can be derived rom the data, including onset temperature, adiabatic temperature rise, pressure generation rate, time needed to reach the maximum rate, and temperature o no return. The thermodynamic and kinetic inormation or runaway reactions can be acquired to investigate the cause o explosion and provide the most serious conditions or relie system size design []. slope sensitivity. Once an exothermic reaction is detected, the data o time, temperature, sel-heating rate and pressure are collected until the reaction inishes. The sample DTBP is in chemical pure. The mass o sample m is g. Its speciic heat c is.1 kj kg K. The volume o sample bomb V e is 8.75 cm 3. Its mass m b is g and its speciic heat c b is 0.53 kj kg K. Thermal inertia actor φ =.865, which is calculated by Eq. (1) [3]. mc + mc b b φ = (1) mc 3 TESTIN RESULTS AND MODIFIATION OF DATA The test results o DTBP by AR are shown in Figs. 1-4 and the second column in Table 1. EXPERIMENTAL The apparatus is provided by Department o Fire Protection Engineering o hinese People s Armed Police Forces Academy. A typical test employs a titanium bomb loaded under kpa (1 atm). The bomb is kept in a nearly perect adiabatic environment, and the sample is heated by a ixed increment o temperature, searching or exothermic reaction and checking i the sel-heating rate o sample exceeds the Figure 1 Temperature and pressure vs. time 3.1 Adiabatic modiication Because the test system is not absolutely adiabatic, Received , accepted To whom correspondence should be addressed. wei_tongtong@16.com

2 hin. J. hem. Eng., Vol. 0, No. 4, August Table 1 Measured and modiied thermal decomposition characteristic data o DTBP (φ =.865) haracteristic parameters Original data Modiied data initial exothermic temperature/ T 0,s = 110. T 0 = 10.6 inal exothermic temperature/ T end,s = 05.6 T end = adiabatic temperature rise/ ΔT ad,s = 95.4 ΔT ad = 73.3 initial sel-heating rate/ min (dt/dt) 0,s = (dt/dt) 0 = maximum sel-heating rate/ min (dt/dt) max,s = 149 (dt/dt) max = temperature at maximum sel-heating rate/ T max,s = 05.6 T max = time to maximum sel-heating rate/min t max,s = 85 t max = 73.8 maximum pressure rate/mpa min maximum pressure/mpa pressure produced by unit mass/mpa g p m,s = 4.51 Figure Rise rates o pressure and temperature vs. temperature during exothermal stage Figure 3 Exothermal curve o temperature vs. pressure Then the adiabatic temperature rise ΔT ad, the initial temperature T 0, the inal temperature Tend and the time needed to reach the maximum sel-heating rate t max can be modiied by thermal inertia actor rom Eqs. ()-(7) [5], as shown in the third column o Table 1. Δ T = φδ T () ad ad,s Figure 4 urves o temperature vs. pressure in order to investigate the explosion under the worst condition, it is necessary to modiy the tested data with thermal inertia actor. The kinetic parameters such as apparent activation energy E a and pre-exponential actor A o the thermal decomposition are calculated by pseudo-inverse matrix method with the results o n = 1, E a = kj mol, and A = [4]. 1 R T0 = + lnφ T0,s E a 0 s 0,s (3) T = T + φ T T (4) ( d T /dt) = φ ( d T /dt) (5) 0 0,s Ea Ea d T /dt max = φ exp ( d T /dt) RTmax,s RT max t max T0 t max,s T0,s max,s (6) = (7) where R is the gas constant, subscript s reers to the

3 71 hin. J. hem. Eng., Vol. 0, No. 4, August 01 reaction parameters including sample and sample bomb. From Table 1, it can be seen that under adiabatic condition, the onset exothermic temperature is 10.6 and ater 85 min, the reaction is the most drastic with the maximum sel-heating rate o min, and the reaction reaches the maximum temperature 375.9, which is also the inal temperature. The adiabatic temperature rise, inal temperature, the maximum sel-heat rate and maximum sel heat rate temperature are higher under adiabatic condition than those under test condition, but the onset exothermic temperature is lower. The lower the thermal inertia φ, the more easily the runaway reaction will take place. I reactant is excessive or the released heat cannot disperse in time, the reaction will be runaway and the emergency relie system should start, otherwise ire or explosion accident will take place. In order to reduce the damage rom runaway reaction, the venting size should be suitable or emergency relie. 3. Pressure mapping Pressure mapping is necessary or two reasons. Firstly, whether a vessel is in the relie state depends on the working pressure. I the working pressure reaches the designed relie pressure, the relie device will work, so parameters (temperature, sel-heating rate, pressure rising rate) at relie state are crucial to the design o relie size. Secondly, because o the dierence between experimental and industrial storage, the thermodynamic parameters (such as temperature and sel-heating rate) under industrial conditions are much dierent rom experimental data even at the same pressure. One way to solve these problems is to ind a relationship between the experimental pressure and the designed relie pressure as in Eqs. (8) and (9) [6]. me αv pe = pr m r V (8) e mr α = 1 (9) ρv where p is the pressure, MPa; m is the mass, kg; ρ is the liquid density, kg m 3 ; V is the volume, m 3 ; α is the void raction, subscripts r and e reer to industry condition and test condition, respectively. A storage tank o 5 m 3 loaded with 000 kg DTBP has a design pressure p r =. MPa and a maximum accumulated pressure p m = 3. MPa. From Eq. (8), p r = 0.37 MPa and p m = 0.54 MPa under AR experimental conditions (α = 0.497). The modiied physical parameters o DTBP are listed in Table. 4 RELIEF SYSTEM DESIN 4.1 lassiication o relie system The reacting system may be vapor, gas or hybrid (tempered and non-tempered), depending on which luid has dominant contribution to pressure rising. The type o reacting system can be determined by AR tests. AR test is carried out until the end o exothermal reaction and then cooled with all data recorded. By analyzing lgp vs. (1/T) curve, i the pressure alls to the original value due to cooling o compressible gases, it reveals a vapor system. I the pressure shows little reduction due to cooling o incompressible gases, it reveals a gassy system. I the pressure reduces to intermediate between the two systems, it reveals a hybrid system. When the pressure o vapor is lower than 10% o the total pressure, the system is non-tempered, otherwise it is tempered [7]. The DTBP reacting system is a hybrid system. In the AR test, the vapor pressure is in direct proportion to vapor generating rate Q V and gas pressure is in direct proportion to gas generating rate Q. Q V and Q can be calculated by Eqs. (10) and (11) [8]. Since p / p = Q / Q + Q = 0.31 > 0.1 V V V the system is tempered. mr c dt QV = ρ h dt (10) Q V V dp V dt T m = g e e m,e r pm dt m Tm dt m T e m,r me 4. alculation o relie system size (11) The relie size A o tempered hybrid systems can be obtained rom W/, where W is the mass low rate released and is the mass low rate per unit area. W can be calculated by Leung method as shown in Eq. (1) [9, 10], where q is the average heat release rate per unit mass o reacting mixture, depending on the absolute overpressure ( p m p r )/ p r. Δt B in Eq. (13) is called Boyle time which means the time taken or the pressure to rise rom the relie pressure to the maximum accumulated pressure. In this emergency relie circumstance, the absolute overpressure is 0.31, so q = W kg. ΔT H is the temperature change as Table Physical property o DTBP under experimental conditions p/mpa T/K ρ /kg m 3 c /kj kg K Latent heat, h g /kj kg Vapor density, ρ V /kg m 3 (dt/dt)/k min at p r state at p m state average value

4 hin. J. hem. Eng., Vol. 0, No. 4, August the pressure rises rom p m to p r and the detailed calculation equations can be ound in reerence [11]. The inal calculation result or W is kg s. mq r W = VT m T p 0.5 dpv pv + Δ H r d ( c T ) dt dt p p q = ΔT p p c > Δt m r 0.5 c +, 0.5 dt r dt m pr 0.5 m r, 0.5 B pr (1) (13) can be obtained by omega () method, which includes a series o simpliication assumptions but is convenient to apply because it does not require a complex computer code or its evaluation and is a dimensionless parameter criterion or compressibility o two-phase mixture, whose deinition equation can be ound in reerence [1]. When <1, it is a non-lashing two-phase system; when = 1, it is an incompressible gas single-phase system; when >1, it is a lashing two-phase system. In the omega method, the calculation o or hybrid system consists o two main steps: obtain the mass velocity or gas relie system assuming that the system consists o non-lashing liquid and permanent gas, and obtain the mass low velocity V or vapor system assuming that the system consists o only lashing liquid. can be calculated as ollows. ( 1 ) = y + y (14) V V V where y V is the mole raction o vapor in the gas/vapor phase under stagnation condition at the inlet to the relie line, y V = p V /p. Based on method, there are two calculation methods or and V, which are monograph and arithmetic calculation. In the monograph method, three main correction actors (dimensionless mass lux, riction correction actor 1, and back pressure correction actor ) are determined by the empirical graphs. Then and V can be calculated as ollows. pr = 1 (15) pv V = 1 (16) where = V / mr. The calculation results are listed in Tables 3 and 4. Under ideal condition, y V = p V / p = 0.31, so = 1498 kg m. In the arithmetic calculation method, the critical pressure ratio η is determined rom Eq. (17) by iteration [13]. When η>η, the relie low is in sub-critical state, or V is calculated by Eq. (18). I the relie low is in critical state, or V is calculated by Eq. Parameter Table 3 (19). By trial and error method, the critical pressure ratio or incompressible gas system and vapor system are obtained as 0.4 and 0.88, respectively. Form Eq. (19), the inal results are = 1473 kg m and V = 916 kg m. From Eq. (14), = 1563 kg m. η + 1 η + lnη + 1 η = 0 (17) [ η η ] 0 ln + (1 ) p = η (18) = p0 / η (19) As a result the relie size A o the storage tank in this case is m rom monograph method and m rom arithmetic method. The relative error is only 0.63%, so the two methods give similar results. From Eq. (6), it can be inerred that i cooling systems work well, the relie size will be smaller, so it is very important to make cooling systems in good condition in industry. 5 ONLUSIONS From AR tests, the DTBP runaway reaction is easy to occur because under adiabatic conditions the initial exothermic temperature o DTBP is 10.6, and the operating temperature in production cell is much higher. The sel-accelerating decomposition is rather ast because the time needed to reach the maximum rate is only 73.8 min. The decomposition reaction o DTBP is very drastic, which can be inerred rom the maximum sel-heating rate ( min ) and maximum pressure rising rate (14.76 MPa min ). The lgp vs. (1/T) curve during heating and cooling reveals that DTBP runaway involves a hybrid system. Based on DIERS method, the relie sizes o DTBP runaway system calculated by monograph Omega method and arithmetic Omega method are close, with only 0.63% relative error. From the view o application, the monograph Omega method is more convenient. NOMENLATURE A relie size, m alculation results or 1 η /kg m result Parameter Table 4 alculation results or V 1 η V /kg m result

5 714 hin. J. hem. Eng., Vol. 0, No. 4, August 01 A c E a 1 h g pre-exponential actor speciic heat, kj kg K apparent activation energy, kj mol mass low rate per unit area, kg m dimensionless mass lux riction correction actor back pressure correction actor latent heat, kj kg m mass, g n reaction order p pressure, MPa Q vapor or gas generating rate, m 3 s q average heat release rate per unit mass o reacting mixture, W kg R gas constant T temperature, t time, min W mass low rate at releasing, kg s V volume, m 3 y mole riction α void raction volume/mass ratio ( = V/m r ), m 3 kg η pressure ratio ρ density, kg m 3 φ thermal inertia actor dimensionless parameter criterion Subscripts ad b e end m max r s V adiabatic bomb critical experimental condition inal exothermic sample gas maximum accumulated pressure maximum sel-heating rate industry condition reaction parameter including sample and sample bomb vapor 0 initial exothermic REFERENES 1 Jiang, H.L., Qiang, X.M., Fu, Z.M., Review o emergency relie system or runaway reaction, Journal o Saety and Environment, 4 (), (004). (in hinese) Jiang, H.L., Zang, N., Qian, X.M., Fu, Z.M., Thermal stability o potassium supersulphate and sodium supersulphate, Journal o hemical Industry and Engineering (hina), 57 (1), (006). (in hinese) 3 Townsend, D.I., Tou, J.., Thermal hazard evaluation by an accelerating rate calorimeter, Thermochimica Acta, 37 (1), 1-30 (1980). 4 Zhu, H.Q., Qian, X.M., Fu, Z.M., Pseudo-inverse metric method-a new method to deal with the adiabatic test data, hinese Journal o Explosives & Propellants, 6 (1), (003). (in hinese) 5 Fu, Z.M., Evaluating thermal stability or reactive chemical by accelerating rate calorimeter, Ph. D. Thesis, Beijing Institute o Technology, Beijing (00). (in hinese) 6 Hu, J.E., Emergency venting requirements, Plant/Operation Progress, 1 (4), 11-9 (198). 7 Singh, J., Vent sizing or gas-generating runaway reaction, Journal o Prevention in the Process Industries, 7 (6), (1994). 8 Leung, J.., Simpliied vent sizing equations or emergency relie requirements in reactors and storage vessels, AIhE J., 3 (10), (1986). 9 Leung, J.., Fauske, H.K., Runaway system characterization and vent sizing based on DIERS technology, Plant/Operations Progress, 6 (), (1987). 10 Fisher, H.., Emergency Relie System Design Using DIERS Technology Appendix VI-17(Leung Analytical method II), DIERS/AIHE, USA (199). 11 Leung, J.., The Omega method or discharge rate evaluation, In: International Symposium on Runaway Reaction and Pressure Relie Design, AIHE, Denver, USA, (1995). 1 Mcintosh, R.D., Nolan, P.F., Review o the selection and design o mitigation systems or runaway chemical reactions, Journal o Loss Prevention in the Process Industries, 14 (), 7-4 (001). 13 erald, W.B., Emergency relie system (ERS) design: An integrated approach using DIERS methodology, Process Saety Process, 14 (), (1995).