2298
INDUSTRIAL AND ENG INEERING CHEMISTRY LITERATURE CITED
(1)Bacon, R. F., and Fanelli, R., IND.ENG.CHEhi., 34.1043 (1942). (2) Bacon, R.F., and Fanelli, R., J . Am. Chem. SOC.,65,639 (1943). (3) Bradley, R. S.,Evans, N. G., and n’hytlaw-Gray, R. W., Ptoc. Roy. Soc. (London),186,368 (1946). (4) Conroy, E. H.,Jr., and Johnstone, H.F . , IND.ENG.CHEM., 41, 2741 (1949). (5) Fanelli, R., Ibid.,38,39 (1946). (6) Frossling, E.,Gerlands Beitr. Geophys., Bd. 52, 1-2, 170 (1938). (7) Gilliland, E. R.,IND.ENG.CHEM.,36,681 (1934). (8)Houghton, H.G . , Physics, 4,419 (1933). (9) Hickman, K. C. D., IND. ENG. CHEM.,ANAL. ED., 9, 264 (1937).
Vol. 42, No. 11
(10) Johnstone, H. F.,Pigford, R. L., and Chitpin, J. H., Trans. A m . Inst. Chem. Engrs., 37, 95 (1941). (11) Kellas, A. M.,J . Chem. Soc., 113, 903 (1918). (12) Kelley, K.K.. U. S. Bur. Mines, Bull. 406 (1937). (13) Langmuir, I., Phys. Rev., 12,368 (1918). (14) Le Bas, O.,“The Molecular Volumes of Chemical Compounds,” London, Longnians Green and Co., 1915. (15) Powell, R. E., and Eyring, H., J . A m . Chem. Soc., 65, 648 (1943). (16) Preuner, G.and Schupp, W., 2.Physik. Chem., 68, 129 (1910). (17) West, W.A. and Menzies, A. W. C.,J . Phys. Chem.. 33, 1880 (1929). RECEIVEDJune 14, 19.50.
FOG FORMATION IN COOLER-CONDENSERS H.F. JOHNSTONE,MAX D. KELLEY’,
AND
D. L.
MCKINLEY
University of Illinois, Urbana, Ill.
Fog formation in cooler-condensers often results in the loss of valuable or obnoxious materials. The conditions under which fog may form are considered from a thermodynamic viewpoint. A theoretical equation is presented for the limiting conditions for the temperature of the
interface and the gas composition and temperature. Verification of this equation was obtained by observing the conditions under which fog formation takes place in mixtures of nitrogen and the vapors of sulfur, n-butyl alcohol, and water.
I
mixture crosses the dew point curve a t any point. Because of variation in the heat transfer coefficients, a step-by-step integration is usually necessary, such as that proposed by Colburn and Hougen (6). Recently, Mickley has discussed the enthalpy potential method, proposed by Merkel, for calculations on forced draft air-conditioning equipment (8). He points out that the formation of fog in a dehumidification tower becomes possible at the point where the “condition line” (bulk air enthalpy-temperature curve) crosses the equilibrium line for saturated air on the enthalpy-temperature plot. The condition line for dehumidification is usually curved but its locationmay be found by agraphical procedure based on simplifying assumptions which are specifically applicable to mixtures of air and water vapor.
N A cooler-condenser fog is often formed by condensation of the vapor at some point in the gas stream rather than on the
cooling surface. The small droplets are difficult to remove from the gas and frequently result in a loss of valuable or obnoxious material unless a fog removal device is used. Fog formation is most noticeable in the condensation of certain organic vapors in the presence of an inert gas and it is also pronounced in the condensation of sulfur vapor. Thus it is an important problem in the recently developed processes for converting hydrogen sulfide and sulfur dioxide to elemental sulfur (1, 7, IO). A theoretical and experimental study of the conditions under which fog will form in a cooler-condenser is reported here. An equation is presented from which it is possible to predict whether fog can be formed if the gas temperature and composition are known as well as the temperature of the condensing surface. Experimental results on mixtures of nitrogen and the vapors of sulfur, n-butyl alcohol, and water confirm the predicted critical conditions. Colburn and Edison point out that the formation of fog in a cooler-condenser depends upon the relative rates of decrease of temperature and concentration ( 4 ) . If these are such as to cause the mixture to become supersaturated, a fog will form, provided nucleation occurs. From the rates of heat and mass transfer across a film, Colburn and Drew (3) show that the rate of change of partial pressure of the vapor with temperature is given by the following equation:
The term (e” - l ) / a corrects for the amount of heat conducted to the interface by the diffusion of the solute vapor. This term is important mThen the rate of condensation is high-i.e., when the relative amount of inert gas present is very low. In order to use the Colburn and Drew equation to predict fog formation, it must be integrated to determine whether the cooling path of the gas
* Present addresa, Standard Oil Company of California, Richmond, Calif.
CRITICAL CONDITIONS FOR FOG FORMATION From a thermodynamic point of view, fog may form if a condition of supersaturation exists a t any point in the gas. This will occur whenever heat is removed from the gas at a rate compared to the rate of mass transfer sufficient to cause the temperature to fall below the dew point. If condensation takes place on a surface, such as a metal wall or a liquid, there will be finite partial pressure and temperature gradients extending from the surface across the gas film. The conditions a t any point in the condenser may be represented by profiles of temperature and partial pressure. Corresponding to the partial pressure profile there is also a dew point profile. Figure 1 shows the various relations which may exist in a condenser. The curve t. - t, is the actual temperature profile; p v p , is the partial pressure profile; while t d f, is the dew point profile. For film-type condensation, t, is the temperature of the liquid-gas interface and for dropwise Condensation it is the temperature of the metal-gas interface. Either can be calculated approximately from rate balance equations provided the transfer coefficients are known or can be estimated (6). In case I condensation takes place only a t the surface. The
-
-
E;r
INDUSTRIAL AND ENGINEERING CHEMISTRY
November 1950
dew point curve and the actual temperature curve must meet at t,. Case 111 represents supersaturation in the gas stream. Here the dew point curve and the temperature curve meet a t a point in the gas, either in the film or in the main body of the gas. Case I1 represents the intermediate condition between condensation at the surface and supersaturation in the gas-i.e., the point where the gas temp6rature &nd dew point curves are tangent a t the condensing surface. This may be termed the critical case. If a transition from case I to case TI1 takes place owing to a decrease of t, or tv, or to an increase in pv, case I1 will be intermediate in time sequence. If condensation is taking place at the surface, and t, is lowered, the two temperature curves will meet a t an angle which decreases until the curves are tangent at the surface. If t. is lowered still more, the curves will meet somewhere in the gas film, giving case 111. When the two temperature curves are tangent a t the surface, their slopes are equal-that is,
t,
t
0 -
2299
/ pv~
pv ps
4 X D I S T A N C C FROM INTERFACE CASE I SURFACE CONDENSATION NO fOC
Figure 1.
x-
n
CASE C R I T I C A L CONDITION
1
4
m
CASE FOG F O R M A T I O N
Concentration and Temperature Profilea in a Cooler-Condenser
.
(2)
In general, the temperature profile across the film will be a curved line for which the slope a t the condensing surface is a
(3)
The right side of Equation 2 may be written as (4)
From the diffusion equation (5)
From the Clausius equation
ture of the surfaces. Equations 9 and 12 give the limiting conditions under which fog may form. Fog may or may not form with a slight degree of supersaturation-Le., a departure from case I1 toward case III-depending upon the kinetics of nucleation, but it is theoretically impossible for fog to form unless the limiting conditions predicted by the equations are exceeded. Equation 9 is useful in graphical form for representing the limiting conditions for fog formation since, for a constant latent heat and SchmidbPrandtl ratio, a plot of pv versus tu gives essentially straight lines for various values of ts. Hence, for any value of p, and t. on an equilibrium vapor pressure curve, there is a line for which the slope is given by Equation 9 that establishes the limiting conditions of vapor composition and temperature for the formation of fog. Figures 2, 3, and 4 show the limits of fog formation for the three systems studied. For any condition of the vapor mixture represented by a point lying above the line for a given surface temperature, fog formation is possible. If the point for the given conditions lies below the respective line, fog formation is impossible. Equation 12 is
(6)
If the analogy between heat and m a s transfer proposed by Chilton and Colburn is now introduced (a), h,
kgpEM
=
(C~c(/k)*/~
(7)
CM, ( p / p D . ) s / *
and if the gas obeys the ideal law -1 = - RT P p p m
(8)
By combining Equations 2 to 8 one has
Now if Equation 6 is integrated between the limits T., corresponding to po and p.
Td
and
Figure 2. Limits of Fog Formation for Mixtures of Water Vapor and Nitrogen
Substitution in Equation 9 gives
(3(-) which may be written
where PI,"is the log mean of the partial pressures of the vapor in the main gas stream and the saturation pressure a t the tempera-
riguro3.
Limits of Formation for Mixturao of n-Butyl Alcohol and Nitrogen
INDUSTRIAL A N D E N G I N E E R I N G C H E M I S T R Y
2300
Vol. 42, No. 11
face is known. Similarly, if any three of the variables are known, the fourth may be evaluated. The equilibrium compositions of sulfur vapor, taken from the data given by Preuner and Schupp (9),were used for the calculation of the partial vapor pressure, p,. Since the composition of the molecular species depends on the gas temperature, the weight ratio of sulfur vapor to nitrogen is used in Figure 4 instead of partial pressure.
Figure 4. Limits of Fog Formation for Mixtures of Sulfur Vapor and Nitrogen
useful in evaluating the fog possibilities without directly considering the latent heat of condensation, or where the latent heat varies with temperature. For example, using the dew point curve and the concentration of the vapor, the lawest permissible gas temperature for operation without fog formation may be found, provided the temperature of the condensing sur-
Figure 5.
Apparatus for Study of Sulfur Fog Formation
Table I. Fog Formation from Mixtures of Water Vanor and Nitrogen Partial Pressure of Water Vapor.
Atm.
0.101 0.101 0,098 0.097 0.142 0.142 0.142 0.140 0.141 0.143 0.113 0.124 0.125 0.123 0.123 0.123 0.095 0.100 0.102 0.096 0.098 0.098 0.151 0.178 0.169 0.169 0.172 0.172 0.174 0.176 0.176 0.222 0.144 0.143 0.143 0.143 0.139 0.141 0.142 0.152 0.154 0.138 0.138 0.137 0.140 0.140 0.140 0.140 Critical
Gas Temp. 0
c.
111 110 107 105 98 98
101
106 112 131 90 93 110 111 112.5 117.5 123.5 134 136.5 135 132 130.5 122 126 131 129 135 137 139 140 142 128 90 101
116 116 116 122 128 130 130 125 127 128 131 132 138 142 condition.
Inside Condenser Surface Tpn.,
Estd. Surface Critiz%n$tions for Fog Formation, O
c.
Dropwise Condensation 12.0 8.0 10.7 8.3 9.6 8.5 8.3 8.3 14.0 17.6 16.2 17.6 16.7 17.3 12.4 15.6 10.0 14.5 9.5 11.7 13.7 15.0 14.0 16.0 13.7 12.6 12.4 12.4 12.0 12.0 11.1 11.2 11.1 5.0 6.0 4.5 4.7 4.5 4.5 3.7 3.5 4.3 3.2 4.7 11.1 14.0 14.0 16.7 14.0 14.7 16.5 15.0 15.0 14.5 16.0 14.2 16.0 14.0 15.0 14.0 16.5 13.8 14.3 20.3 Filmwise Condensation 14.5 20.0 14.7 17.3 8.5 14.0 8.7 14.0 10.0 13.5 6.3 12.7 10.2 12.2 7.5 12.7 6.5 12.9 Q.1 12.2 8.2 12.0 7.0 11.7 6.3 11.5 10.0 11.3 6.4 10.3 7.5 9.7
Prediction of Fog
Observation of Fog
No fog No fog Nopg
No fag No fog Nofog No fog Fog Fog No fog No fog Fog Fog
Fog Fog Fog Fog Fog Fog Fog Fog Nofig a
$i%g
kofog No fog No fog Fog Fog Fog Fog Fog No fog No fog Nofog No fog No fog No fog Fog Fog Fog Fog Fog Fog Fog Fog Fog Fog Fog Fog Fog
2 Fog Fog
Fog Fog Nofog Fog Fog Fog No fog Nofog No fog Fog Fog Fog Fog Fog Fog No fog NFkg No fog Fog No fog Fog No fog No fog Fog Fog Fog Fog No fog Fog N?kg No fog No fog N35g
Fog No fog
Table 11. Fog Formation from Mixtures of n-Butyl Alcohol Vapor and Nitrogen
Partial Pressure of Butyl Alcohol Vapor, Atm. 0.181 0.178 0.178 0.180 0.186 0.180 0.201 0.180 0.180 0.182 0.181 0.182 0 173 0.180 0.182 0.182 0.185 0.182 0.178 0.182 0.136 0.140 0.136 0.136 0.137 0.139 0.139 0.139 0.138 0.139 0.147 0.149 0.149 0.149 0.153 0.152 0.147 0.107 0.107 0.110 0.106 0.108 0.109 0.110 0.108 a Critioal
(Filmwise Condensation) Gas T q p
Inside Condenser Surface Temp., 0
218 229 257 265 285 287 234 138 152 167 212 230 295 292.5 302.5 315 324 331 342 303 95.6 162.3 174.0 180.0 206.5 209.0 210.0 210.4 207.5 207.5 229.0 250 261.5 256.2 260.0 252.0 220.8 122.0 122.0 128.0 129 169 180.5 190 195 oondition.
c.
33.7 35.0 30.3 31.0 26.0 26.7 32.5 56.6 43.9 45.9 38.7 32.0 25.4 28.2 25.7 26.4 23.5 21.7 23.7 24.1 54.8 37.0 34.7 32.4 34.0 31.7 30.3 33.1 32.2 32.8 32.6 29.1 27.3 26.3 28.8 27.7 31.4 38.7 38.5 42.1 38.7 31.2 34.4 32.9 33.7
Estd. Surface Tem a t Critical CPdnditions for Fog Formation,
c.
33.7 32.7 30.7 30.2 29.3 28.5 34.3 44.0 41.5 39.3 34.3 32.7 28.2 27.7 27.7 27.5 27.3 26.7 25.7 27.7 49.0 35.3 33.3 32.7 30.2 30.3 30.3 30.2 30.5 30.6 29.5 28.0 27.7 27.6 28.3 28.0 30.2 37.0 37.0 36.3 35.3 30.2 29.0 28.0 27.5
Prediction of Fog No fog Fog No fog Fog
Observation of Fog Fog No fog Fog No fog Fog
2;fog
NO fog
N O
N o fog
Nofog No fog Fog "."g Fog Fog Fog Fog Fog Fog No fog No fog No fog Fog pi0 fog No fog ?io fog
KO fog Nofog No fog No fog
$;g
Nokg Fog No fog No fog No fog No fog No fog No fog Nofog No fog No fog
%
N2kg
KO fog Fog
NFp;og Fog N o fog
Fog Fog No fog Fog No fog Fog Fog Fog
No fog Fog Fog No fog
N?kg No fog No fog Fog Fog Nofog Fog Fog No fog Fog No fog Fog N?kg No fog No fog
INDUSTRIAL A N D E N G I NEERING CHEMISTRY
November 1950
Table 111. Fog Formation from Mixtures of Sulfur Vapor and Nitrogen (Dropwise Condensation)
Weight Ratio of Sulfur to Nitrogen
Gas TtmZ.,
0.2M) 0.195 0.193 0.195 0.193 0.197 0.200 0.193 0.193 0,200 0.195 0.198 0.195 0.196 0.197 0.193 0.196 0.196 0.192 0.191 0.187 0.191 0.190 0.191 0.191 0,191 0.190 0,191 0.190 0.190 0.191 0.191 0.191 0.195 0.191 0.190 0.193 0,360 0.352 0.352 0.328 0.336 0.345 0.340 0.365 0.355
438 443 445 445 453 439 359 388 392 381 369 374 388 375 383 374 363 360 356 362 421 371 397 376 378 372 375 378 379 379 376 382 383 381 373 379 359 360 352 352 414 376 462 466 463 376
a
Inaide Condenser Surface T.""$.'
Critical condition.
Estd. Surface Tern . a t Critioal dnditions for Fog Formation, 0
199 200 202 203 205 207 226 214 203 218 221 215 212 209 245 239 236 232 226 221 219 212 200 194 186 197 198 202 206 212 23 1 219 215 203 202 194
187 193 222 212 250 240 215 198 170 240
c.
207 218 212 211 213.5 215 216 212 214.5 213 214.5 217 217.5 217.5 216
207
214 210 213.5 213 214 213 213 212.5 212.5 213-5 2ia.s 212.5 213 214 212.5 217 240 242 242 227 234.5 223 222.5 224 237
Predia- Observation of tion of Fog Fog
No fog No fog No fog N%g N o fog
Fog Fog NFoofBOp
No fog No fog No fog No fog No fog No fog No fog
FOE
Fog Fog Fog Fog Fog NFooplog No fog No fog No fog Fog Fog Fog Fog N%g N!%g No fog Fog Fog N?kg
2301
formation. The water and butyl ulcoliol were pumped directly into the uartz va rizer by means of a stainless steel metering ump. '?he liquid%fur was pumped by displacement with oil &he meterin pump had a capacity of 1.17 ml. per revolution and was operate8 at a speed of 1 to 10 r.p.m. by a variable drive. The condenaer assembly is shown in Figure 6. In order to approximate r i n t conditions, the stainless steel condenser was made only 1. 6 inches Ion . The inside diameter was inch. The condenser was j a c k e d with a 2.5-inch tube through which a coolant was circulated. Two Chromel-Alumel thermocouples were silver soldered in the wall of the condenser, I/@ inch from the .inside surface and on opposite sides of the tube. The temperatures indicated by these couples were taken as the temperature of the condensing surface. The temperature of the gas stream a t the inlet of the condenmr \vas measured b a Chromel-Alumel thermocouple in a thin wall stainless steel tiermowell. Radiation errors in measuring the gas temperature were eliminated by keeping the outside wall at this int a t the same temperature as the gas. The thermowere calibrated by comparison with a Bureau of Standards thermometer. In order to prevent conduction of heat from the heated section of pipe on either side of the condenser, a/Anch Transite gaskets were used in the Ban ed connections leading to the 1-inch standard pipe crosses. 'fhe glass windows were fitted into the opposite horizontal a r m of these crosses so that the inside of the condenser could be illuminated with a parallel beam of light. These windows were easily removable to allow cleanin of the condenser surface and swabbing with oils to promote fropwise condensation. Oleic acid was y e d as a promoter for the dropwise condensation of water, and silicone oil was used in the condensation of sulfur. The sulfur condensed on the surface of the tube above 160' C . tended to build up on the surface in large dro due to the high viscosity of the liquid. In order to decrease viscosity, a trace of hydrogen sulfide was added to the inlet gas stream. No promoter was found that would produce dropwise condensation of butyl alcohol. In the runs with water and butyl alcohol vapors, the temperature of the condenser wall was maintained constant by circulating water a t high velocity from a controlled temperature reservoir. For the condensation of sulfur vapor, Dowtherm was used as a coolant. The gas velocity was kept constant a t about 2 feet er second through the condenser. This corresponded to a !&ynolds number of about 700 At higher gas velocities, observation of fog formation was di'fficult and not reproducible.
COUPE
tg
OBSERVATION OF FOG FORMATION
It was possible to obkerve clearly the condensation and fogging in the condenser. By adjusting the temperature and concentration of the gases, the fog could be made so intense that a 60watt light was entirely obscured. When the fog was very light, it appeared to stream out from the wall. The conditions could be adjusted so that the condenser was perfectly clear, and conwithout fogging took The results shown in Tables I, 11,and 111are representative uf the observations for the three systems studied. In the con-
EXPERIMENTAL The apparatus shown in Figure 5 was used to obtain experimental verification of Equation 9. In the presence of nuclei generated by the sublimation of sodium chloride, fog could be produced or dis elled in a condenser as desired by varying the temperature of the gas and the temperature of the condensing surface. The mixtures of inert gas and condensable vapor were produced by pumping the liquids a t a controlled rate into a heated vertical quartz tube through which preheated nitrogen was passed. The as mixture was superheated to the fesired temperature, n u c l e a t e d with s o d i u m chloride, and passed into a short honli zontal condenser equip ed a t each end with a glass wincfow throu h which the condensation could %e observed. The vaporizer-superheater assembly was heated with two 600watt Hoskins electric furnaces. The liquid inlet was located between the two furnaces. The section of tube below the inlet which sefved as. the vaporizer was packed with 6/einch Berl saddles. The empty section above the li uid inlet served as a superheater Tor the as-vapor mixture. At the top of &e superheater a Chrome1 wire spiral coated with Figure 6. Condenser Assembly sodium chloride was kept a t a dull A. Removalla obnervation windown C. Sodium chloride nualnimer red heat and provided nuclei for fog E . a u stream thenmowell T. Thermocoupln looationn
2302
INDUSTRIAL AND ENGINEERING CHEMISTRY
densation of water and butyl alcohol, no fog could be produced within the range of conditions of the gas or temperature of the condensing surfase studied, unless salt nuclei were added to the gas stream. In the case of sulfur, fog could be formed in the absence of salt nuclei when the temperature of the surface was 50" C. or more below the estimated critical temperature. In the presence of nuclei, the observations on the presence or absence of fog agreed in most cases with those predicted by Equation 9. The difference between the temperature of the inside condenser surface and the estimated surface temperature a t the critical condition for fog formation is a measure of the validity of the theory. In a few cases, fog was not observed when the condenser surface was slightly below the critical temperature. The discrepancy was more apparent when the condensation occurred as a film, either with butyl alcohol, or when the dropwke promoter was intentionally omitted in the case of water. Here it was obvious that the true temperature of the interface was actually higher than the condenser wall temperature. In a few cases, failure of the salt vaporizer to supply sufficient nuclei could have been responsible for the absence of fog. In other cases, the presence of fog was recorded when the wall temperature was slightly above the critical temperature. This discrepancy can only be accounted for by slight fluctuations in the vapor composition caused by variations in the pumping rates. This explanation of course could account in part for the discrepancies observed in the opposite direction. In Table 111, the partial pressures of sulfur vapor were calculated on the assumption that the molecular species were in equilibrium at the temperature of main gas stream. At weight ratios of sulfur to nitrogen greater than 0.35, fog was usually not observed until the surface was brought considerably below the estimated critical condition. For such rich vapors, the rate of condensation is very fast, and equilibrium may not exist between the molecular forms. Furthermore, deviations from the simplifying assumptions made in the derivations and in the calculations of the Schmidt and Prandtl groups are likely to exist when the mole fraction of the condensable vapor is high. PRACTICAL CONSIDERATIONS In an actual cooler-condenser the composition of the gases varies widely from the inlet to the outlet end. In general, fog formation occurs when the concentration of the vapor is high. This is not necessarily true, however, if the interface temperature is maintained high when the partial pressure of the vapor is high. For many li uids it is possible to calculate the thickness of the condensate. zlm from. the Nusselt equation. From the thermal conductivity of the liquid, the temperature drop across the liquid film can then be estimated. In order to prevent fog formation, it is necessary to keep the interface temperature a t every point sufficiently high so that the gases cannot become saturated. I n general, filmwise condensation is less likely to produre fog than dropwise condensation since the temperature of the interface is higher than that a t the wall. Low rates of condensation do not necessarily prevent fog formation since the dew point of the gas may be only a few degrees higher than the wall temperature and the conditions may be such that fog will still form. The dependence of fog formation on the presence of condensation nuclei is impressive. It is known that, in practice, some condensers suddenly will begin to produce fog without any noticeable change in operating conditions. This may continue for several days after which the fog gradually disappears. Evidently this behavior is related to the presence or absence of fog nuclei which may be formed from im urities present in the gases. Mixtures of condensable vapors a n 8 inert gases produced from contact catalysts that tend to dust are especially prone to produce fogs in a condenser. This suggests that high purity is desirable as a means of preventing troublesome fog formation.
Vol. 42, No. 11
Cooler-condensers are often operated by direct heat exchange with the cooled condensate that is circulated through an outside cooler or heat exchanger. In the case of the condensation of sulfur vapor, such a device is likely to give fog if the liquid sulfur returned to the condeming tower is cooled to too low a tempera; ture. Since the range between the melting point of sulfur, 119 C., and the viscous point, 160"C., is small, only a small temperature rise of the liquid is permissible. From Figure 5, at surfaee temperatures as low as 185" C. for mixtures of sulfur vapor and nitrogen, very low concentrations of sulfur vapor mny produce fog. If the surface tem erature of the liquid sulfur can be maintained a t 250' C. a t the got end, and at about 150" C. a t the cold end, fo formation should not take place when the weight ratio of suyfur to inert gas in the rich gases is &s high as 0.35 This suggests that in such condensers it is desirable to circul'ate the sulfur a t a somewhat higher temperature than can be done with unmodified sulfur because of the low viscous point. Fanelli has shown that the addition of a small amount of hydrogen sulfide, or of the halo ens, to sulfur greatly reduces the viscosity above 160' C. ( 6 ) . 8hus a higher tem erature can be maintained in the cooler-condenser, as a means o f preventing fog formation. Another means of avoiding the possibility of fog formation, as pointed out by Colburn and Edison ( d ) , is to add heat to the gas stream in order to raise its temperature. Equations 9 or 12 may be used to determine the temperature increase that is necessary a t any point. ACKNOWLEDGMENT This work was carribd out under a research assistantship grant supported by the Texas Gulf Sulphur Company. The suggestions of Thomas Baron are gratefully acknowledged. NOMENCLATURE (CP/kP'S In p - P* a = bllPpJ2'a p - P. c = specific heat capacity of gas D, = diffusivity of gas h, = heat transfer coefficient for gas film k = heat conductivity of gas k , = mass transfer coefficient for gas film M , = mean molecular weight of gases P = partial pressure of vapor E ' = barometric pressure R = gas constant t = temperature, C. x = distance from interface T = temperature, '-K. A = molar latent heat of evaporation I J = viscosity of gas P = density of gas
Subscripts BM = mean partial pressure of inert gas in the film d = dew point Zm = logarithmic mean across the film s = surface or interface 2) = body of gas (1) (2)
LITERATURE CITED Appleby, M. P., J . Soc. Chem. Id.,56,139 (1937). Chilton, T. H., and Colburn, A. P., IND.ENG.CHEM.,26,317
(1934). (3) Colburn, A. P., and Drew, T. B., Trans. Am. Inst. Chem. Engrs., 33,197 (1937). (4) Colburn, A. P.,and Edison, A. G., IND. ENQ.CHEM.,33, 457 (1941). (5) Colburn, A. P., and Hougen, 0. A., Ibid., 26,1178 (1934). (6) Fanelli, R., Ibid., 38,39 (1946). (7) Lepsoe, R.,Ibid., 30,92 (1938);32,910 (1940). (8) Mickley, H. S., C h a . Eng. Progress, 45,739 (1949). (9) Preuner, G.,and Schupp, W., 2. physik. C h m . , 68,129 (1909). (10) Weber, G.,Oil Gas J . , 45,58 (March 8,1947).
RECEIVED March 27. 1950.
END OF SYMPOSIUM Reprints of this symposium may be purchased for 15 cents from the Reprint Department, American Chemical Society, 1155 Sixteenth Street, N.W.,Washington 6, D. C.
