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Ind. Eng. Chem. Fundam. 1982,21 186-188
Levenspiel, 0. "Chemical Reaction Engineering"; Wiley: New York, 1962; Chapter 9. Levenspiel, 0.; Smith, W. K. Cbem. Eng. Sci. 1957 6,227. Michell, R. W.; Furzer, I. A. Trans. Inst. Chem. Eng. 1972,5 0 , 334. Michell, R. W.; Furzer, I . A. Chem. Eng. J . 1972,4 , 53. Morsi, E. I.; Laurent, A.; Midoux, N.; Charpentier, J. C. Cbem. Eng. sei. lB80,35, 1467. Otake, T.; Kunugita, E. Chem. Eng. Jpn. 1958, 22, 145. Sater, V. E.; Levenspiel, 0. Ind. Eng. Cbem. Fundam. 1986,5,86. SatterfieM, C. N.; Van Eek, M. w.; Bliss, G. s. AIchE J . 1978,2 4 , 709. Schwartz, J. G.; Dudukovic, M. P. AICh€ J. 1976,22,953. Schwartz, J. G.; Roberts, G. W. Ind. Eng. Chem. Process Des. Dev. 1973, 12, 262.
Sicardl, S., et ai, Chem. Eng. Sci. 1981,36, 226. Van Swaaij, W. P.: Charpentler, J. C.; Villermaux, J. Chem. Eng. Sci. lB6B, 2 4 , 1083. Weekman, V. W. Ph.D. Thesis, Purdue University, 1963.
Engineering Technology Laboratory Engineering R&D Division E . I. d u Pont de Nemours & Co., Inc. Wilmington, Delaware 19898
G u r a y Tosun
Received for review August 17, 1981 Accepted November 25, 1981
Flash Points of Flammable Liquid Mixtures Using UNIFAC Flash points are used to classify liquids containing combustible components according to their relative flammability. Such a classification is important for the safe handling of flammable liquids such as organic solvents and solvent mixtures. The UNIFAC group-contribution method is shown to be applicable for the prediction of flash points of binary and multicomponent liquid mixtures. The predictions are reliable for mixtures constituted alone from combustible substances and for mixtures also containing noncombustibles such as water.
Introduction Flash points are used to classify combustible liquids according to their relative flammability. Regulations for the safe handling, transportation, and storage of such substances are dependent on this classification, and flash points are therefore of great importance in the chemical industry. It is the purpose of this paper to show how the UNIFAC group-contribution method can be used to predict flash points of liquid mixtures containing combustible components.
able to propagate from an ignition source. The ambient temperature of the gas-air mixture is T. If the partial pressure is lower than Li the combustible compound i will burn around the ignition source. The liberated heat, however, will not be so large that the combustion of any one layer will ignite the neighboring layer of unburned gas, and the mixture will not be capable of self-propagation of flames. The flash point for a pure combustible liquid i can thus be written as the temperature TFfor which
Flash Point A flash point is not a fundamental physical property and its value will to some extent depend on the apparatus and method used for its measurement. The experimental procedures have, however, been standardized in many countries, thus allowing for reproducibility and comparison between flash points measured in different laboratories. In principle the measurements are carried out in the following way: a small liquid sample is placed in the bottom of a cup. The temperature of the cup is slowly increased and the vapors from the liquid surface will mix with air in the space above. The flash point temperature is reached when a flame will propagate from an ignition source through the whole vapor-air mixture. A flash is observed. The cup may be open to the atmosphere (Open Cup Tester) or closed, which will confine a given amount of air (Closed Cup Tester). The closed cup tester is usually applied today and all calculations here are based on this type of tester. Lance et al. (1979) have in a recent review described in detail the apparatus and the procedures used for the measurement of flash points. Theory A flash point is defined as the lowest temperature for which vapors above a liquid form a flammable mixture with air at a pressure of 101.325 kPa. For a pure combustible component i the flash point may thus be estimated as the temperature for which the vapor pressure, Pi",equals the partial pressure at the lower flammability limit, Li. This is illustrated in Figure 1. A lower flammability limit Li in a homogeneous gas-air mixture at temperature T corresponds to such a partial pressure of the combustible compound in air that a flame will just be
P,"/Li = 1 (1) Le Chatelier (1891) has presented an analogous equation for binary and multicomponent mixtures containing N combustible compounds. i = 1, 2, ..., N cPi/Li= 1 (2) i
In this equation Pi is the actual partial pressure of component i in a vapor-air mixture which is in equilibrium with the liquid mixture. Li is the partial pressure in a gas-air mixture with a composition correspbnding to the lower flammability limit of pure component i. The lower flammability limit Li is a function of the temperature and of the heat of combustion AHci. The pressure has negligible influence on Li at pressures around atmospheric pressure (Coward and Jones, 1952). The heat of combustion is the net A H d since the reactants and the combustion products all are in the gaseous state. Over moderate ranges of temperature there are only small changes in Li. Zabetakis (1965) accounted for the temperature effect for various types of substances by means of an expression which may be written as L;(t) = Li(25) - 0.182(t - 25)/AH& (3) LJt) and Li(25) (in kPa) are the lower flammability limits at t "C and 25 OC, respectively; AHci is the net heat of combination in kJ/mol. Equation 3 has also been used by Wu and Finkelman (1978). Tables with values of Li(25) may, for example, be found in Coward and Jones (1952) and Zabetakis (1965). Zabetakis also indicates how Li(25) values may be estimated when no experimental data are available. Since Jensen et al. (1981) have described a method for the prediction of pure component vapor
0196-4313/82/1021-0186$01.25/0 0 1982 American Chemical Society
Ind. Eng. Chem. Fundam., Vol. 21, No. 2, 1982 p' and Li
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I -T
TF
Figure 1. Estimation of flash temperature TFfor a pure substance i. Pi'is the partial pressure in air correspondingto the vapor pressure. Liis the partial pressure correspondingto the lower flammability limit. T is the temperature.
pressures, it is possible to predict approximate values of the flame point temperatures TFfor pure substances. The partial pressures Pi corresponding to vapor-liquid equilibrium VLE at temperature T may be calculated using the following equation in which it is assumed that the vapor-air mixture behaves like an ideal gas
Pi = xiyipi" (4) x i is the mole fraction of component i, yi is the activity coefficient, and Pi" is the vapor pressure of component i a t temperature T. The pure component vapor pressures Pi" may be calculated by means of the Antoine equation log Pi" = Ai - Bi/(t
+ Ci)
(5)
The constanta Ai, Bj,and Ci may be found for many substances in Gmehling et al. (1977). Ellis (1976) used values of the activity coefficients y i calculated from experimental VLE data. In general, the activity coefficients may be calculated from a model describing the liquid phase nonideality. Wu and Finkelman (1978) used, for example, the van Laar equation for binary mixtures and the Wilson equation for multicomponent mixtures, and De Micheli and Delogu (1980) used the NRTL equation. The use of such models requires a knowledge of the necessary parameters. Parameters for some commonly applied models and for many different types of mixtures can be found in Gmehling et al. (1977). Quite often one cannot find the parameters for all the pairs of components in a mixture and one has to rely on a predictive method for the estimation of the activity coefficients. UNIFAC is a fast and reliable method for the prediction of activity coefficients in nonelectrolyte liquid mixtures. The method is based on the solution of groups concept. The groups are structural units such as CH3, OH, and others which when added form the parent molecules. Instead of considering a liquid mixture as a solution of molecules, the mixture is considered as a solution of groups. The activity coefficients are then determined by the properties of the groups rather than by those of the molecules. The activity coefficients are calculated from two terms: a combinatorial part essentially due to differences in size and shape of the molecules and a residual part due to energetic interactions between the groups. The UNIFAC method was developed by Fredenslund et al. (1975). The method was revised and detailed descriptions of the method have been presented (Fredenslund et al. 1977a,b). The parameters needed for the use of W A C are group volumes (RK),group surface areas (Qd, and group interaction parameters (a, and urn). Extensive tables with parameters are given by Skjold-Jerrgensen et al. (1979) and by Gmehling et al. (1982). The method now comprises 40 groups and it allows for the calculation of activity coefficients for most of the binary and multicomponent mixtures of interest in chemical technology. For
0M e t h a n o l 11)Methylacetate( 2 ) 0
,
0
-
-10
0
0
0'
1)from Raoult’s law, while the chloroform-containing mixtures in Figure 4 have negative deviations (-yi < 1). It may be noted from Figure 3 that the flash points are much less influenced by the water content at low water concentrations than at high concentrations. This phenomenon is more pronounced for 2-propanol than for methanol. UNIFAC describes this behavior very well. The values of Li(t)from eq 3 are strongly dependent of the value for Li(25). This means that a small error in the
value for the pure component flash point, which gives Li(25),will influence the calculation of the flash points for the mixture. This phenomenon can be seen from the chloroform (1)-methylethyl-ketone (2) mixture in Figure 4. A somewhat higher experimental flash point for methyl ethyl ketone would have raised the UNIFAC predicted curve giving rise to a better agreement between experimental and predicted values. Table I shows that the UNIFAC method may be used for the prediction of flash points for multicomponent mixtures. It is seen from Table I that an assumption of ideality of the liquid mixture leads to flash points which deviate much more from the experimental values than the UNIFAC predicted ones. Supplement. A computer program for the calculation of flash points by means of UNIFAC is available from the authors. Acknowledgment The authors thank Professors U. Onken and Aa. Fredenslund for criticism and helpful comments to this work. The authors further thank “Bundesministerium fur Forschung und Technoiogie” and “Statens Teknisk-Videnskabelige ForskningsrAd” for economic support. There have not been published very many experimental flash points for mixtures. We are most grateful that De Micheli and Delogu (1980) and Choe and Schecker (1981) have made their data available for us. Literature Cited Choe, M.; Schecker, H. G., University of Dortmund, private communication, 1981. Coward, H. F.; Jones, G. W. U . S . Bur. Mines Bull. 503, 1952. DeMichell, S.; Delogu, P. Report from Reaction Technique Department, Montedlson D I E Research Center, Bolbte, Italy, 1980. Ellis, W. H. J. Coat. Technol. 1976, 48, 44. Fredensiund. Aa.; Jones, R. L.; Prausnitz, J. M. AIChEJ. 1975, 2 1 , 1086. Fredenslund, Aa.; Gmehling, J.; Micheisen, M. L.; Rasmussen, P.; Prausnitz, J. M. Ind. Eng. Chern. ProcessDes. D e v . 1977av 16, 450. Fredensiund, Aa.; Gmehiing, J.; Rasmussen, P. “Vapor-Liquid Equilibria Using UNIFAC”, Elsevier: 1977b. Gmehling, J.; Rasmussen, P.; Fredensiund, Aa. Ind. fng Ch8m Process Des. D e v . 1982, 27, 118. Gmehling, J.; Onken, U.; Ark, W. “Vapor-Liquid Equilibrium Data Collection”, DECHEMA Chemistry Data Series, Vol. I (12 Parts); 1977. Jensen, T.; Fredenslund, Aa.; Rasmussen, P. Ind. Eng Ch8rn. Fundarn. 1981, 20, 239. Lance, R. C.; Barnard. A. J.; Hooyman, J. E. J. Hazard. Mater. 1979, 3 , 107. Le Chatelier, H. Ann. Mines 1891, 8 , 388. SkJoldJsrgensen, S.; Kolbe, E.; Gmehling, J.; Rasmussen, P. Ind. Eng . Chem. Process Des. D e v . 1979, 18, 714. Wu, D. T.; Finkelman, R. Presented at the 175th National Meeting of the American Chemical Society, Anaheim, CA, March 1978, Division of Organic Coatings and Plastics Chemistry. Zabetakis, M. G. U S . Bur. Mines Bull. 627, 1965.
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I
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Lehrstuhl Technische Chemie B University of Dortmund 46 Dortmund-Hombruch, West Germany Instituttet for Kemiteknik The Technical University of Denmark DK-2800 Lyngby, Denmark
Jurgen Gmehling
P e t e r Rasmussen*
Received for review June 23, 1981 Accepted F e b r u a r y 10, 1982
