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KINETICS, CATALYSIS, AND REACTION ENGINEERING Model To Obtain the True Parameters of Decomposition of Volatile Liquids Such as Acrylonitrile and Nitromethane M. Surianarayanan,* B. V. Bharat Ram,† and R. Vijayaraghavan Cell for Industrial Safety and Risk Analysis (CISRA), Central Leather Research Institute (CLRI), Adyar, Chennai 600 020, India
The heat flow data of a decomposable volatile liquid obtained by a microcalorimetric technique denote the combined effect of two competing processes, viz., vaporization and decomposition. A model, therefore, is needed to evaluate the true decomposition parameters such as onset temperature, peak temperature, and enthalpy of decomposition. Such an exercise was carried out for the highly volatile and decomposable liquids such as nitromethane and acrylonitrile, using high-pressure differential calorimetry (HPDSC). A model has been proposed further under conditions where vaporization was suppressed as in HPDSC. On the basis of the experimental data, a mass-transfer coefficient was derived at low pressures (where only vaporization took place). This was employed for the prediction of the decomposition parameters at higher pressures. The predicted data agreed well with the experimental results carried out at higher pressures. It is believed that the results are useful in reaction systems in plants where chemicals such as the ones considered here are subjected to higher pressures. Introduction Thermal decomposition of reactants and products during processing and handling causes hazardous situations in the chemical process industry.1 The consequences of such accidents are severe, serious, and devastating. Microcalorimetric techniques have been successfully employed to identify and quantify exothermicity in chemical processes and products. Process optimization and safety considerations at the plant level based on the test results of microcalorimetry have been in practice in recent times. However, there are difficulties in the scale-up of the microcalorimetric data to the chemical plants because of an incomplete understanding of certain chemical and physical transformations taking place during thermal runaway processes. One of the problems in the interpretation of microcalorimetric test results of any decomposable volatile liquid sample is the inadequacy of obtaining the true decomposition parameters, such as the onset temperature, peak temperature, and self-heat rate. Heat loss occurs in the measurement as a result of the thermal inertia (φ) of the reaction vessel. So, φ corrections have been recommended to determine the true decomposition parameters to ensure a closer approximation of the runaway reaction in a commercial reactor. Past studies have not offered satisfactory results to correct the effects of the thermal inertia of the reaction vessel. Though φ correction is sensible to the heat loss of the container, heat can often be lost * To whom correspondence should be addressed. E-mail:
[email protected]. † Current address: Department of Chemical Engineering and Biotechnology, St. Joseph’s College of Engineering, Chennai 600 119, India.
through physical and complex chemical transformations, for example, vaporization of solvents, reagents, gaseous products, or competing endothermic processes. Vaporization effects can be more significant with increasing vapor space and become more complex at higher decomposition temperatures. Consequently, the calculated molar heat of reaction carries an error in its value. Using these results in runaway simulation and reactor design can definitely lead to failure at a critical juncture. When a decomposable sample is heated to a higher temperature, two processes, vaporization and decomposition,2 occur simultaneously. Vaporization is endothermic, while decomposition may be exothermic or endothermic. As the temperature increases, the rate of decomposition increases. In exothermic decompositions, the effects of vaporization can be suppressed by carrying out the experiments at relatively high pressure to ensure that the decomposition temperature is lower than the corresponding boiling point of the sample. However, under these conditions, the data obtained are only indicative and not absolute because vaporization is not eliminated but only suppressed (also applicable under closed conditions). Thus, the heat flow data are obtained as the combined effect of two competing processes, viz., heat liberation due to decomposition and heat absorption due to vaporization. It is difficult to find exactly the pressure at which liquids can exhibit decomposition. Hence, the applied pressure is usually kept higher than the saturated vapor pressure of the compound at the expected decomposition temperature regions and can be ascertained from a prior knowledge of P-T correlations3 only. Thus, the heat flow data obtained from microcalorimetric techniques do not give the true decomposition characteristics but are just the sum
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of the effects of two competing processes, viz., vaporization and decomposition. Therefore, it becomes necessary to develop a method to evaluate the true decomposition parameters while at the same time accounting for the vaporization losses. This paper deals further with our earlier reported model2 for vaporization effects during decomposition and seeks to account for the combined effects of vaporization and decomposition to predict the true decomposition parameters from high-pressure differential calorimetry (HPDSC) experimental data obtained at a relatively low pressure (where decomposition is insignificant). The model was verified for the decomposition of acrylonitrile (AN) and nitromethane (NM). Experimental Work In this study, TA Instruments 2910 thermal analysis system was used in conjunction with HPDSC. DSC was widely used for first-level thermal hazard evaluation in view of its simplicity of operation and approach. The basic principle of DSC was to measure the heat flow (temperatures of transitions) as a function of the temperature or time, achieved by measuring the difference in power required to maintain the temperatures of the reference and sample. The data of heat flow obtained by DSC gave an indication of the sensitivity (onset temperature) and severity (heat of decomposition) of chemical compounds to thermal hazards. The principles of operation and equipment details of HPDSC have been adequately reported in the literature.3 HPDSC experiments were carried out to study the decomposition characteristics of AN and NM at 0.1, 0.69, 2.62, 3.44, and 4.83 MPa nitrogen pressures. Higher pressure was applied to suppress the vaporization of AN and NM and to ensure that the decomposition temperature (Td) was lower than the corresponding boiling point. A 5 mg sample size at a 5 K/min heat rate was employed for the DSC studies. The thermal data obtained from HPDSC were the sum of the effects of two competing processes, viz., heat liberation due to thermal decomposition and heat absorption due to sample vaporization.
temperature Td in an atmosphere of vapor B, the stoichiometric equation can be expressed as B
A 98 ν1C + ν2D
(3)
The number of moles of A, nA,liq in the liquid phase at a given time t is given by eq 4, where k is the rate
nA,liq ) nA0e-KtR
(4)
constant, nA0 is the number of moles of A initially present in the liquid phase, and R is defined by eq 5.
R ) Wi/Wi0
(5)
The weight of the sample Wi remaining in the liquid phase at a given time t is given by eq 6.
Wi ) nA,liqMA
(6)
The fraction of the weight Wi of the sample at any time to its initial weight Wi0 at time t ) 0 is represented by the term R. The number of moles of A remaining in the vapor phase, nA,vap, can be determined from eq 7. Thus, the
nA,vap ) nA0 - nA,liq
(7)
volume of the sample VA at a given time is given by
VA ) Wi/FA
(8)
The vapor volumes of A-D can be estimated as
VA,vap ) nA,vapMA/FA,vap
(9)
VC,vap ) ν1nC,vapMC/FC,vap
(10)
VD,vap ) ν2nA,vapMD/FD,vap
(11)
Similarly,
The Model The model deals with vaporization effects and cumulative effects of vaporization and decomposition. Vaporization Effects. The model previously reported2 by us accounts for the thermal loses due to vaporization according to eqs 1 and 2.
where Fi,vap is the vapor-phase density of compound i in the vapor phase. The volume of gas B, VB,vap, at any given time is obtained by subtracting the volume occupied by the sample in the vapor and liquid phases from the total volume
Pi β Vg dZ dVg Vg dPi Pi dMe ) ARNi + Vg + P dt ZRT T Z dt dt Pi dt (1)
VB,vap ) Vcell - VA - VA,vap - VC,vap - VD,vap (12)
[
]
dQ + ∆HdKdR ) CpiWiβ + λKgAR(fi - fg)/RT (2) dt In the present study, the above model is extended to determine the decomposition parameters at the onset temperature by calculating (a) the rate of partial pressure change and volume of vapors generated and (b) the film thickness and mass-transfer coefficient for the vaporization process. Finally, the vaporization effects are subtracted from the combined effects of vaporization and decomposition to obtain the true decomposition parameters. Mass and Energy Balances Assuming that 1 mol of sample A decomposed to form ν1 and ν2 moles of products C and D, respectively, at
where Vcell ) 250 µL. The value of VA can be obtained from eq 8. The values of VA,vap, VC,vap, and VD,vap were obtained from eqs 9-11, respectively. Thus, the total number of moles of B, nB,vap, was related to VB,vap by the eq 13.
nB,vap ) VB,vapFB,vap/MB
(13)
Using the Peng-Robinson equation of state,4 the number of moles of compounds A-D at a given time t, the mole fractions of the compounds, and the liquid- and gas-phase fugacities can be calculated,
fg ) (Z - 1) - ln(Z - B) -
[
]
Z + (1 + x2)B A ln 2x2b Z + (1 - x2)B (14)
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fl ) fg,sat(T,Psat) eV[(P-P
sat)/RT ] r
(15)
where A and B are defined as
A ) aP/(RT)2
(16)
B ) bP/RT
(17)
where
a ) y12a1 + y22a2 + y32a3 + y42a4 + 2y1y2xa1a2 + 2y1y3xa1a3 + 2y1y4xa1a4 + 2y2y3xa2a3 +
2y2y4xa2a4 + 2y3y4xa3a4 (18)
and
b ) y1b1 + y2b2 + y3b3 + y4b4
(19)
The terms ai and bi are defined as
ai )
Figure 1. AN decomposition at 0.69 MPa N2 pressure.
0.45724[RTc,i]2 [1 + fw,i(1 - xTr)]2 Pc,i
(20)
bi ) 0.0778RTc,i/Pc,i
(21)
fw,i ) 0.37464 + 1.54226ωi - 0.26992ωi2
(22)
where
The liquid volume V′ was estimated by the Hankinson-Brobst-Thomson method5
V′ ) Vr0[1 - ωVri]Vc
(23)
with
Vr0 ) 1 + c5[1 - Tr]1/3 + c6[1 - Tr]2/3 + c7[1 - Tr] + c8[1 - Tr]4/3 (24) and
Vri )
c9 + c10Tr + c11Tr2 + c12Tr3 Tr
(25)
The fugacities obtained were substituted in eq 2. The mass-transfer coefficient kg in eq 2 is calculated using eq 26.
Kg ) Deff/δ
(26)
The effective diffusivity Deff can be obtained from eq 27,6,7
y2 y3 y4 1 ) + + Deff DAB DAC DAD
(27)
where
DA,i )
0.00143T1.75 2MAMB 1/2 1/3 P [v + vi1/3]2 M A + MB
[
]
(28)
The film thickness δ can be calculated from the DSC data by substituting the experimental dQ/dt and T data in eq 2 and equating ∆Hd to 0 (because decomposition
Figure 2. AN decomposition at 3.44 MPa N2 pressure.
was negligible) at atmospheric pressure for most of the chemicals. The film thickness was a weak function of the temperature and was accordingly assumed to be constant. With all other factors in eq 2 being known, the quantity dQ/dt for high pressures (conditions wherein decomposition cannot be neglected) can be calculated from the same film thickness δ as was calculated by the above method. The model outputs of HPDSC data for AN and NM at various pressures are shown in Figures 1-4. Results and Discussion NM (MA ) 61.041) and AN (MA ) 53.06) were subjected to HPDSC runs at various pressures. At 0.1 MPa applied pressure, a broad endothermic peak (vaporization curve in Figures 1-4) was recorded nearer to their respective boiling points of AN and NM. However, upon an increase of the applied pressure to 0.69 and 3.44 MPa for AN and 2.62 and 4.83 MPa for NM, the liquids exhibited decomposition as shown in Figures 1-4 (experimental curves). Although AN and NM were known to undergo exothermic decomposition,8,9 the experimental curves given in Figures 1-4 did not exhibit exothermic behavior because of the effects of vaporization as discussed before. The rate of partial pressure change and volume of vapors generated
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underwent an increase owing to nucleate boiling causing bubble formation. However, the generation of the decomposition characteristics and, hence, the kinetic data for the early part of the decomposition was appropriate in order to plan for emergencies. Thus, the model explained the heat flow characteristics for all temperatures up to the boiling point of the sample. The model could also be used for decomposition reactions that were endothermic in nature. The only change needed was a reversal of the sign of the ∆Hd term in the energy balance equation. However, for reactions with unknown kinetics, high-pressure thermogravimetric analysis (HPTGA) at conditions where decomposition was predominant provided the timevariant weight change data at different applied pressures. From the HPTGA data, the mole fractions of the compounds could be calculated. Figure 3. NM decomposition at 2.62 MPa N2 pressure.
Summary The thermal responses of a volatile liquid were due to the net effects of two competing processes, viz., vaporization and decomposition. Mass and energy balances for the two processes were defined mathematically. By using the rate of change of the partial pressure and volume of vapors generated, the true decomposition parameters were determined from the HPDSC data for AN and NM decompositions. The model predictions were satisfactory up to the onset of thermal decomposition. Limitations in the Decomposition Model
Figure 4. NM decomposition at 4.83 MPa N2 pressure.
during decomposition were obtained by mass and energy balance modeling calculations as discussed previously. After subtraction of the effects of vaporization from the experimental curve, the true decomposition curves for AN and NM were obtained (as shown in Figures 1-4). By employment of the literature value4,5 of the heat of decomposition (AN ) 7.35 kcal mol-1 and NM ) 57 kcal mol-1) and the film thickness obtained from the HPDSC run at 0.1 MPa (where decomposition was negligible) for NM and AN, the HPDSC curves for the remaining pressures were predicted. There was good agreement with the experimental results (Figures 1-4). HPDSC runs were made at different heating rates of 5, 10, 15, and 20 K min-1, and it was found that the effects of heating rates at different applied pressures were insignificant. In certain cases, the curves deviated slightly from the experimental curves. This deviation was attributed to the fact that initial heating caused the volume of the liquid to expand slightly. In addition, there would have been a significant baseline change,4 which occurred primarily because of the differences in the heat capacities of the sample and reference. Because the heat capacity is directly related to weight, an endothermic shift indicated that the reference pan was too light to offset the sample weight. These differences were neglected in the model because the resulting error was nil. As the boiling point of the sample was approached, the area of cross section of the sample
The present model did not take into account the nucleate boiling and bubble formation to predict the HPDSC data in the vicinity and beyond the boiling point of the sample at an applied pressure. The model also cannot explain the complex decomposition reactions such as double decomposition reactions and the second or third order in nature. The model also ignored the volume expansion that the sample underwent during initial heating. Acknowledgment The authors are thankful to Poojari Yadagiri, Scientist, Chemical Engineering Department of CLRI, for verifying the calculations and G. Swaminathan, Head, Chemical Engineering Department of CLRI, for useful discussions. The authors are also thankful to the Director of CLRI for kind permission to publish this paper. List of Symbols AR ) area of cross section of the sample pan, cm2 Af ) frequency factor of the reaction, s-1 Cp ) specific heat capacity of the sample, J mol-1 K-1 Dai ) diffusivity of compound i with respect to the sample, cm2 s-1 Deff ) fugacity of the sample, bar fg ) vapor-phase fugacity of the sample, bar k ) rate constant, s-1 kg ) mass-transfer coefficient, cm s-1 Mi ) molecular weight of compound i Ni,liq ) number of moles of compound i in the liquid phase Ni,vap ) number of moles of compound i in the vapor phase P ) pressure, bar Pc ) critical pressure, bar Pr ) reduced pressure (P/Pc) dQ/dt ) heat flow, W/g
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R ) universal gas constant, J mol-1 K-1 T ) pan temperature, K Tc ) critical temperature, K Tr ) reduced temperature (T/Tc) vi ) molecular volume of compound i, cm3 mol-1 Vi,liq ) volume of compound i in the liquid phase, cm3 Vi,vap ) volume of compound i in the vapor phase, cm3 Z ) gas-phase compressibility factor Greek Symbols R ) ratio of the weight change at a given time t to the initial weight β ) heating rate, °C s-1 δ ) film thickness, cm ω ) accentric factor Fi,vap ) vapor density of compound i Fi,liq ) liquid density of compound i
Literature Cited (1) Berthrick, L. Handbook for reactive chemical hazards, 2nd ed.; Butterworths: London, 1987; pp 15-39. (2) Panduranga, R. S.; Vivek, P.; Surianarayanan, M.; Mallikarjunan, M. M. Vaporization effects in evaluation of decomposi-
tion kinetic parameters by high-pressure DSC. Thermochim. Acta 1996, 282, 1-9. (3) Thomas, L. C. Specialty applications of thermal analysis. Am. Lab. (Shelton, Conn.) 1987, Jan, 1-6. (4) Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases and Liquids, 5th ed.; McGraw-Hill: New York, 1988. (5) Thomson, G. H.; Brobst, K. R.; Hankinson, R. W. An improved correlation for densities of compressed liquids and liquid mixtures. AIChE J. 1982, 28, 671-676. (6) Wilke, C. R. Correlation of diffusion coefficients in dilute solutions. AIChE J. 1955, 1, 264-272. (7) Fuller, E. N.; Schettler, P. D.; Giddings, J. C. A new method for the prediction of binary gas-phase diffusion coefficients. Ind. Eng. Chem. Res. 1966, 58, 18-24. (8) Surianarayanan, M.; Panduranga, R. S. P.; Vijayaraghavan, R.; Raghavan, K. V. Thermal behaviour of acrylonitrile polymerization and polyacrylonitrile decomposition. J. Hazard. Mater. 1998, 62, 187-197. (9) Koshy, A.; Surianarayanan, M.; Raghavan, K. V. Thermochemical analysis of 1-methylamino-1-methylthio-2-nitroethene synthesis. J. Hazard. Mater. 1995, 42, 215-223.
Received for review May 19, 2004 Revised manuscript received September 23, 2004 Accepted November 2, 2004 IE049576D
