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Ind. Eng. Chem. Fundam. 1902, 21, 184-186
Axial Dispersion in Trickle Bed Reactors. Influence of the Gas Flow Rate A number of models are available to account for liquid backmixing in trickle bed reactors. The most practical one is still the “dispersed plug flow” model with a singleparameter Peclet number (Pe = d / D ) . Although the relationship between f e and liquid flow rate has been studied extensivdy in the literature, there is no published information on the effect of gas flow on this parameter. Gas flow has been shown, in the libratwe, to affect important operating characteristics such as catalyst wetting, mass transfer, liquid distribution, and heat transfer. The effect of varying the gas flow on the backmixing, therefore, is a question of concern in design and operation of these reactors. I n this publication results of recent work using a NaCI-tracer technique with a 5.1 cm i.d. glass column and air and distilled water as model fluids will be presented. These results show a peculiar relationship between gas flow and the Peclet number. A possible explanation is offered.
Several papers in the recent literature have dealt with axial dispersion in trickle bed reactors. A number of models have been proposed to account for liquid backmixing, but the simplest and most practical one is still the dispersed plug flow model put forth by Levenspiel and Smith (1957). A review of the models is given by Gianetto et al. (1978). In an earlier review Schwartz and Roberts (1973) concluded that the one-parameter, dispersed plug flow model is adequate to account for the effect of liquid backmixing on conversion in these reactors. The dispersion parameter D/uL or the particle Peclet number Ped = (uL/D) (dp/L) have been experimentally determined and reported by a number of workers (Farid and Gunn, 1979; Schwartz and Dudukovic, 1976; Schwartz and Roberts, 1973; Michell and Funer, 1972a,b;Furzer and Michell, 1970; Van Swaaij et al., 1969; Hochman and Effron, 1969; Sater and Levenspiel, 1966; Otake and Kunugita, 1958). In all of these studies D/uL or Ped was reported as a function of liquid flow rate. There appear to be no data in the literature on the effect of gas flow rate on backmixing in these reactors. The purpose of this note is to present our results on this subject. Experimental Section A 5.1 cm diameter glass column packed to a 90-cm height with 8-12 mesh glass beads (average diameter 1.9 mm) was used for the experiments. Distilled water and air were used as the model fluids. A pulse injection of 0.2% NaCl solution was used as a physical approximation of a Dirac &function. The concentration of the NaCl tracer was continuously measured and recorded by means of flow-type conductivity cells connected to Beckman Solumeters and a two-pen recorder. One of the cells was located immediately downstream of the injection point, which was upstream of the liquid distributor. The design of the distributor was similar to that described by Colombo et al. (1976). This design isolates liquid and gas prior to entry into the packed section. The second Uflow-cellnwas located downstream of the packed section on the exit line. In the design of the system, care was taken to minimize the volume of the unpacked sections between the inlet and the outlet cells. To separate “dead-space” response from reactor response, duplicate runs were made with and without the reactor. For the simple case of a measuring section in En infinite tube, Levenspiel and Smith (1957) found
where E(0) = cV/Q, 0 = u t / L , u is the mean real fluid velocity, c is the concentration, V is the vessel volume, Q is the amount of tracer injected, Pe is the Peclet number = (uL/D),D is the dispersion coefficient, t is the time, and L is the length of the measuring section. 0 196-4313/82/102 1-0184$01.25/0
Table I. Effect of Liquid Flow a on Hydrodynamic Properties kg/mz G1, s
ut,s
-t , s
DluL
ReL
Ped
5.0 7.0 9.0 11.0 13.0 15.0
4.6 3.5 2.8 2.1 1.1 0.9
37.2 31.1 25.4 22.5 17.6 15.5
0.0076 0.0063 0.0061 0.0044 0.0020 0.0017
95 133 171 209 247 285
0.29 0.35 0.36 0.50 1.10 1.30
a
G, = 0.004 kg/m2 s (constant).
The Peclet number for the overall system and the dead volume were calculated by matching the location and height of the peak of the experimental curves with the theoretical values derived from eq 1. The Peclet number for the reactor alone was then calculated by making use of the approximate relationship
and the additivity relationships
(3) toverall
-
=
beactor
+ fddead-space
(4)
where u t is the variance of the output tracer concentration curve, f is the average residence time = (V/u, u = flow rate). The approximation in eq 2 is good within 0.5% when D/uL is less than or equal to 0.010 (Levenspiel, 1962). A comparison of the curve-fit technique with the ”moments” method is given by Michell and Furzer (1973). It is felt, in submitting this note, that the effect of gas flow on Peclet number is significant because gas flow has been found to affect important operating characteristics such as catalyst wetting (Sicardi et al., 1981),mass transfer (Charpentier, 1976; Satterfield et al., 1978), liquid distribution, and heat transfer (Weekman, 1963). The effect of varying the gas flow on backmixing in trickle bed reactors, therefore, is a question of concern in design and operation of these reactors.
Results Table I shows the results of the experiments performed at fixed gas flow (Gg= 0.004 kg/m2 s, the minimum necessary to prevent flooding) and varying liquid flow. All ut and E values are averages for four or five injections at a given set of conditions. When plotted in Figure 6 of Hochman and Effron (1969) (Pedvs. ReL), the results of the present work lie within the limits of scatter of their points. Also, when placed in Figure 1of Gunn (1980),these points are within the spread of results from six sources and show the same increasing trend of Ped with ReL. These comparisons show that the present measurements and 0 1982 American Chemical Society
Ind. Eng. Chem. Fundam., Vol. 21, No. 2, 1982
185
Table 11. Effect of Gas Flow on Hydrodynamic Properties G1,
kg/mz s 5.0
7.0
9.0
11.0
13.0
15.0
G g, kg/mz s 0.004 0.040 0.070 0.225 0.740 0.004 0.040 0.070 0.225 0.740 0.930 P a 0.004 0.050 0.110 0.150 0.320 P 0.540 0.004 0.045 0.070 P 0.250 0.450 0.004 0.025 0.045 P 0.070 0.250 0.004 0.022 0.040 0.050 P 0.110
at, s
4.2 3.8 3.6 3.1 3.2 3.2 3.0 3.0 2.6 2.3 1.9 2.6 2.1 1.9 1.8 1.5 1.3 1.5 1.4 1.3 1.1 0.9 1.05 0.89 0.76 0.69 0.59 0.91 0.70 0.60 0.55 0.22
-
t,s
DluL
ht, cm3/ cm3 void
36.5 33.0 32.1 26.6 22.2 30.2 25.8 24.2 20.8 16.7 15.0 24.4 20.4 18.4 17.5 15.0 13.2 20.4 18.3 17.4 14.6 12.0 17.0 15.9 15.0 14.3 11.9 14.9 14.2 13.5 13.0 11.0
0.0066 0.0066 0.0063 0.0068 0.0104 0.0056 0.0068 0.0077 0.007 8 0.0095 0.0080
0.62 0.59 0.55 0.47 0.38 0.72 0.61 0.58 0.49 0.40 0.36
0.33 0.33 0.35 0.32 0.21 0.39 0.32 0.29 0.28 0.23 0.28
1.31 1.44 1.42 1.85 3.38 1.34 1.90 2.30 2.7 1 4.11 3.85
0.0057 0.0053 0.0053 0.0053 0.0050 0.0048 0.0027 0.0029 0.0028 0.0028 0.0028 0.0019 0.0016 0.001 3 0.0012 0.001 2 0.0019 0.001 2 0.0010 0.0009 0.0002
0.75 0.63 0.57 0.54 0.46 0.40 0.76 0.69 0.65 0.55 0.45 0.73 0.73 0.69 0.66 0.55 0.79 0.7 5 0.7 2 0169 0.62
0.39 0.42 0.42 0.42 0.44 0.46 0.82 0.76 0.79 0.79 0.79 1.16 1.38 1.70 1.84 1.84 1.16 1.86 2.20 2.45 11.02
1.69 1.88 2.08 2.19 2.41 2.63 0.96 1.14 1.16 1.39 1.69 0.81 0.73 0.63 0.61 0.73 0.92 0.61 0.54 0.50 0.12
Ped
D , cmZ/s
P: Beginning of pulsing.
calculations are consistent with other workers’ results; that is, increasing the liquid flow causes the Ped to rise. Table I1 shows the results of the next series of experiments in which the liquid flow rate was fixed and the gas flow was gradually increased. The onset of pulsing in the column is indicated by P. I t is clear that, for each liquid flow, ut and f decrease with increasing gas mass velocity (G,, kg/m2 8). Because ut is proportional to the spread of the residence time distribution function (Eq l),the above observation means that with increased G, fluid elements have shorter residence times and a narrower spread around the mean. If f (average residence time) remained constant at fixed GI, then from eq 2 as ut decreases ( D / u L ) should decrease or, conversely, Pe should increase. But T is not constant as G, is increased because ht (liquid holdup) decreases with increasing G, as shown in Table I1 and
Thus, from eq 2 and 5
and
Therefore, as G, increases, both the numerator and the denominator decrease, which implies that the relationship between gas flow rate and Ped may not be a simple one and that it probably depends on the liquid flow rate as well.
Indeed the results shown in Table I1 indicate that the derivative of Ped with respect to G, at constant GI changes as GI varies; that is, it is negative at G1 of 5.0 and 7.0 kg/m2 8, is approximately zero at GI of 9.0 and 11.0 kg/m2 s, and is positive at GI 13.0 and 15.0 kg/m2 s. Table I1 also shows values of D calculated from ( D / u L )in eq 2. These indicate that D rises with G at GI = 5.0, 7.0,9.0, and 11.0 kg/m2 s but decreases wit% G, at GI of 13.0 and 15.0 kg/m2 s. There appears to be no correlation between the onset of pulsing and any hydrodynamic parameter. It is possible, however, that the results observed relate to the flow regime in the column. It could be argued that, at liquid rates of 13.0 and 15.0 kg/m2 s where the regime is “bubble flow” or “dispersed bubble flow” up to fully developed pulsing, the gas is confiied in bubbles and exerts no effect on liquid backmixing by way of interfacial turbulence. Thus, improved radial distribution of liquid due to higher gas flow reduces backmixing and increases Ped, but below 13 kg/m2 s liquid rate, where bubble flow is not observed and both phases are continuous, increased gas flow causes increased interfacial turbulence, which possibly increases backmixing and hence the dispersion coefficient D. The results presented in this note are not conclusive, but they seem to indicate a trend which should be investigated further in order to attain a better understanding of this hitherto neglected aspect of trickle bed reactor hydrodynamics. Literature Cited Charpentier. J. The Chem. Eng. J . 1976, 7 7 , 161. Colombo, A.; G. Baldl, J.; Slcardi. S. Chem. Eng. Sci. 1976, 37, 1101. Farld, M. M.; Gunn, D. J. Chem. Eng. Scl. 1979. 3 4 , 579. Furzer, I. A,; Mitchell, R. W. A I C E J . 1970, 76, 380. Glanetto, A,; BaMI, G.; Specchla, V.; Sicardi. S. AIChE J. 1978. 24, 1087. Gunn, D. J. C h m . Eng. Sci. 1980, 35, 2405. Hochman, J. M.; Effron, E. I n d . Eng. Chem. fundam. 1969, 8 , 63.
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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, D e l m a r e 19898
Guray 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
