r
INDUSTRIAL AND ENGINEERING CHEMISTRY
April, 1941 k =
D/E
(22)
Using the average diffusivity of salt in water a t 18' C. as 1.3 x 10-6 sq, per second and a value of k of 0.50, the film thickness is about 0.016 111111.
Nomenclature
weight of solid salt at time e, grams or lb. weight of salt dissolved in initial volume of water a t time 8, grams or lb. w s = weight of salt dissolved in initial volume of water a t saturation between 10' and 40° C., grams or lb. w, = initial weight of salt used, grams or lb. k = diffusion rate constant, weight dissolved/(unit time) (unit area) (c, - c ) , in grams/(min.) (sq. cm.) (grams/ cc.) or lb./(min.) (sq. ft.) (lb./cu. ft.) n = number of uniform particles in initial wei ht of salt, wi = a constant relating area and volume of sa% particles = a 6 for a cube, = 4.83for a sphere w
=
wd
=
".
457
= density solid salt, grams/ct.. or lb./cu. f t . Vr = initialvolume of wLter, cc. or cu. ft. V = volume of solution a t time 8, cc. or cu. ft. V, = volume of saturated salt solution formed from initial volume of water, Vi, at temperature of operation, cc. or cu. ft. 0 = time, min. A = total area of solid salt at time e, sq. cm. or sq. ft. c = salt concentration in solution a t time e, = wd/V, grams/ cc. or Ib./cu. ft. cs = salt concentration in solution at saturation a t temperature of operation = wa/Vs, rams/cc. or lb./cu. f t . LY = a constant relating X and V , b i 2 = film thickness, om. or ft. D = diffusivity of salt in water, sq. cm./sec. d = equivalent particle diameter, calculated from sphere of equal weight, mm. p
Literature Cited (1) Brunner and St. Tolloozko, I . physik. Chem., 35, 253 (1900). (2) Hixson and Crowell, IND. ENQ.CHDM.,23, 923,1002, 1160 (1931). (3) Hixson and Wilkens, Ibid., 25, 1196 (1933). (4) Murphree, Ibid., 15, 145 (1923). (5) Noyes and Whitney, I.physik. Chem., 23, 689 (1597).
Prevention of Fog in Cooler-Condensers A. P. COLBURN' AND A. G. EDISON2 E. I. du Pont de Nemours & Company, Inc., Wilmington, Del.
HEN condensation of a vapor takes place in the presW ence of a n inert gas, some fog is generally formed. The fog then passes out of the condenser with the inert gas. This is undesirable if the fog is composed of valuable or noxious materials; as a result a fog removal apparatus is required. Such equipment is usually large and involves considerable pressure drop of the gas, so that a means of condensation without fog formation would be preferable. The purpose of this study was to evaluate the theoretical mechanism of fog formation and then to develop a practical means for its preventi on.
Mechanism of Fog Formation When a mixture of vapor and inert gas passes over a surface which is sufficiently colder than the mixture so that the equilibrium partial pressure of the vapor at the surface is less than the partial pressure in the mixture, there is a simultrtneous flow of heat and mass to the surface. This means a decrease in temperature and vapor content of the mixture. Whether or not fog will be formed depends upon the relative degree of the decreases in temperature and concentration; if these are such as to cause the mixture to become supersaturated, a fog will form. The information needed to study the cooling history of the mixture includes the vapor pressure-temperature relation and heat and mass transfer rates. The rate of change of partial pressure of vapor, pv, with respect to temperature, tv, was shown (2) to be:
where pi, 1
3
ti
= vapor pressure and temperature at interface b e
tween gas mixture and condensed liquid
Present address, University of Delaware, Newark, Del. Present address, E. I. du P o n t de Nemours & Company, Inc., Seaford.
Del.
A theory is developed to explain the occurrence of fog when vapors are condensed in the presence of inert gases. The path of the concentrationtemperature curve is most apt to cross the saturation curve with vapors of high molecular weight, which are usually valuable or toxic and therefore important not to be lost in the waste gases as a fog. Based on the apparent mechanism of fog formation, a theoretical method of eliminating this undesirable condition is to supply a small amount of heat to the vapor-gas mixture during the condensing process. The method was tested experimentally and found to work on mixtures of air with steam, butyl alcohol, and trichloroethylene.
- p ) ,P
= log mean of ( P = total pressure
- pv) and ( P - pi)
C,p,lc,p,D~= heat ca acity a t constant pressure, viscosity,
therma? conductivity, density, and diffusivity, respectively, of vapor-gas mixture
The term (e" - l ) / a , based on a theoretical study of Ackermann ( I ) , corrects for the condition that some of the heat conducted across the interface is supplied by the removal ef sensible heat from the diffusing vapor and thus decreases the temperature decrease in the remaining gas. This term is important when the rate of condensation is high-i. e., when the relative amount of inert gas present is very low.
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
458
Vol. 33, No. 4
ing sensible heat to the vapor-gas mixture a t the same time it is being cooled and condensed. The path of the cooling curve will then be that shown in Figure 3. The addition of sensible heat t o the vapor-gas mixture will not affect the rate of condensation of vapor, since the latter is a diffusional process not affected by the temperature. One means of supplying sensible heat is t o put an electrically heated rod through the vapor tube of an ordinary Liebig ti t“ 4 t condenser as shown by Figure 4. On a large scale such “cores” could be heated by circu2. CONDENSA-FIGURE 3. CONDENSAFIGURE 1. CONDENSA-FIGURE lating some liquid of sufficiently high boiling TION OF STEAM IN THE TION OF AR- ORGANIC TION O F A VAPOR IN THE PRESENCE OF AIR WITHPRESENCE OF AIR WITH VAPORIN THE PRESENCE point, so as to have a temperature gradient OF AIR WITH FORMATION OUT FOGFORMATION FORMATION O F FOG parallel to the vapor-gas stream. Or if the OF FOG T h e dashed line represents T h e dashed line represents vapor-gas mixture flows across tube banks, a the approximate path the T h e dashed line represents the approximate path the number of the tubes can be heated instead of mixture tends t o follow when the approximate p a t h the mixture follows when cooled cooled, if care is taken that no condensate drips in the apparatus shown in mixture tends t o follow. the interfacial temperature Figure 4. throughout the condenser is on them. The amount of sensible heat necesheld a t f i . sary will usually be small compared to the latent heat removed in the condenser. The idea was tested experimentally on a small scale. An If the three ratios ( P - p w ) / ( P- p ) f , (e: - l ) / a , and electrically heated rod mas installed as a core in the condensing ( C P / ~/s/(Iu/pD0)2/~ )~ are essentially equal to unity, the rate of tube of a Liebig condenser (Figure 4). A mixture of air and change of partial pressure of vapor with temperature becomes vapor was passed through the condenser, first with no heat equal to the term (pg - pi)/(tp, - Si), which is the ratio of being supplied to the rod. Under these conditions most of driving forces, and the cooling path follows a straight line the vapor was condensed, but the exit air contained fog. Then between points p,, tp, and pi, ti on the vapor pressure diagram heat was supplied t o the rod, and fog no longer appeared in the shown by Figure 1. The occurrence of fog depends upon exit gas. The rate of condensation, as indicated by the rate of whether the line cuts across the saturation curve, and this may dripping of condensate from the condenser outlet, was not renot happen if the original mixture is considerably superduced by the sensible heat added to the vapor-gas stream. heated or the temperature drop is not great. The ratio = (Cp/k)2/3/(w/pDo)2’3 is nearly equal t o unity for the diffusion of water vapor in air. Owing to the low diffusivities of organic vapors having high molecular weights, these materials will result in low values of +, such as 0.4 for the system butyl alcohol-air. The other ratios are unimportant except where the air is very dilute. I n the cooler part of a cooler-condenser for butyl alcohol-air mixtures, therefore, the slope of the cooling curve will be approximately:
+
Figure 2 shows a dashed line as a plot of Equation 3. This line is an indication of the path the vapor-gas mixture tends to follow. However, when the mixture passes to the left of the saturation curve, it becomes supersaturated and will form enough fog t o drop to the saturation curve. During the rest of the cooling process, the path tended t o be followed is given by Equation 3, but sufficient fog will be formed so that the actual path will be near the saturation curve. I n case of very low concentrations of inert gas, the ratios ( P - p v ) / ( P - p ) j and (ea - l)/a may cause an increased slope of the dpu/dt, curve so that fog is not formed in this region. The presence of initial superheat will not prevent fog formation unless it is sufficiently high so that the cooling path does not cross the saturation curve. Prevention of Fog
According to the above analysis of fog formation, slow cooling will not be uniformly successful in the prevention of fog, indeed rapid cooling may even be preferable. For no matter how small the temperature difference, the mixture will eventually tend to become supersaturated, whence fog mill be formed. A solution of the problem is t o cause the path of cooling t o lie always under the vapor pressure curve so that the mixture never becomes supersaturated. This can be done by supply-
FIGURE 4. EXPERIMENTAL COOLERCONDENSER Fog formation was prevented by adding a slight amount of sensible heat t o t h e vapors during the cooling process.
Experiments were carried out on mixtures of air with water vapor, trichloroethylene, and butyl alcohol. Fog was formed and then caused to disappear with heat in case of all three vapors. This apparatus as used would not remove fog present in the vapor-gas mixtures fed to it but acted only in these experiments to condense vapor from an air mixture without forming a fog. I n conclusion it may be pointed out that this relatively simple method of preventing fog formation in a cooler-condenser is the result entirely of a theoretical analysis based on heat transfer and diffusion analogies. Literature Cited (1) A o k e r m a n n , G., Forschungsheft, No. 382, 1-16 (1937). (2) Colburn, A. P., and Drew, T.E., Trans. Am. Inst. Chem. Engrs., 33, 197-215 (1937).
