Condensation of Vapors from Noncondensing Gases A Modified Method of Design JULIAN C. SMITH1 Cornell University, Ithaca, N. Y ,
is equal to the temperature The method of Colburn and Hougen of deof the main body of the gas. condensers for handling signing condensers to handle mixtures of This is necessarily inexact owmixtures of vapors and vapors and nonconderising gases neglects ing t o the temperature drop noncondensing gases is conpart of the heat loss by the condensate layer through the gas film and part siderably more complicated in calculating point values along the conof the condensate film. Howthan that of designing similar ever, in cases where the latent equipment for the condensadenser. When the condensing vapor is that heat of vaporization is large, tion of pure vapors, since heat of an organic solvent having a low beat of so that quantity 1overbalances is transferred from the gaseous vaporization, the entire heal loss of the conthe other three, this approximixture to the condensed liquid densate from point to point should be conmation is amply justified. both by sensible heat transfer sidered. A typical problem is solved by two This was the case in the original and by mass transfer of the example used to illustrate the condensing vapor. Thus, in methods to show the effect of neglecting the method, in which steam was addition to the ordinary gas point loss of heat by the condensate. The condensed from a stream of film coefficient any estimation required surface area calculated in the more nitrogen. of the over-all conductance exact solution is 14.5 per cent less than that On the other hand, data must include a coefficient given by the original method of design. taken on actual installations, based on the diffusion of the designed by this method and condensing vapor from the A graphical method for determining the handling mixtures of organic main body of the gas to the intermediate condensate temperatures is solvents and inert gases, have condensate surface. outlined, which avoids the tedious second indicated rates of heat transfer I n 1934Colburn and Hougen trial-and-error solution used in the modiconsiderably greater than were (7) described a useful method fied procedure. expected. I n attempting to of design for problems of this explain the discrepancies, it kind, which is based on the was noted that the heats of estimation of the heat flux. UAt, and the heat transferred, q, a t various points along vaporization of the solvents are only about one tenth that of water, and that possibly the assumption just mentioned was the condenser, followed by the graphical integration of the no longer justified. The following problem was then solved basic equation: by two methods to determine the effect of considering the dA = dqlUAt true temperature of the condensate in estimating the point values of q. The first solution is a dircct application of the The point values of UAt are calculated by equating the heat method of Colburn and Hougen; in the second solution both transferred froni the gaseous mixture to the condensate surface the total heat load and the point values of the heat transferred to that transferred from this surface to the cooling water. are based on the actual temperature of the Condensate film. This is expressed more succinctly by the equation:
HE problem of designing
T
k ( t c - t u ) = UAt he(& - t c ) f KMA(p9 - P c ) (1) For a given vapor temperature the condensate surface temperature, t,, is found by trial and error, and the resulting CAt is the heat flux a t this point. The amount of heat transferred a t any point is made up of the following quantities: 1. Heat transferred in condensing the vapor 2. Heat transferred in cooling the noncondasing gas 3. Heat trsri.iferred in cooling the uncondensed vapor 4. Heat transferred in cooling the condensed liquid
I n the procedure outlined by Colburn and Hougen, quantity
4 is calculated by assuming that the condensate temperature 1
Present address, E. I. du Pont de Nemoura & Company, Inc., Wilming-
ton, Del.
The Problem The problem is the design of a vertical tubular condenser to handle 100 pound moles of nitrogen per hour a t 5 atmospheres pressure, saturated with ethyl acetate a t 100" C. The outlet temperature is 20' C.; a maximum of 120 gallons per minute of cooling water a t 5.5" C. and 20 pounds per square inch gage pressure are available. The gaseous mixture is to pass through the tubes, the cooling water through the shell. Steel tubes, S/s-inch outside diamter, Birmingham wire gage No. 16 are used. The number of tubes are selected to give a mass velocity of the incoming vapor of 20,000 pounds per hour per square foot; the shell-side baffles are arranged to give a mass water velocity of 650,000 pounds per hour per square foot. 1248
INDUSTRIAL
October, 1942
A N D ENGINEERING CHEMISTRY
PHYSICAL PROPER TIE^. The specific heat and viscosity of both the ethyl acetate and the nitrogen vary throughout the condenser, but in view of the other approximations i t is probably close enough to use an average value for these quantities. In the present example they were evaluated at the logarithmic mean temperature of the gaseous miJeture, which is 50" C.: Ethyl acetate (vapor pressures at various temperatures are given in International Critical Tables 10) * Latent heat of vnoorisatidn, P: c . u./lb. 102 Molecular weight88 Viscosity of liquid Ib /(hr )(ft.) 0.97 63.1 Density of liquid ib.jcu. ft. Jp. heat of liquid P c. u /(lb.)(' C.) 0.46 0.37 Sp. heat of vapor: P: e. u:/(lb.)(' C.) Nitro en Mo%cular wei ht Viwoaity lb /fhr f t ) Sp. heat,'P. 1.u.j(h:)('
28 0.0436 0.26
C.)
HEATLOADON ,CONDENSER.This factor is calculated as = =
2.000 3.000
= =
0.096 4.904
= 66.67 = 1.96
= 64.71
Condensed
Heat transferred, P. c. u./hr. To condense EtOAc: 64.71 X 88 X 102 = 580,500 To cool nitrogen: 100 X 28 X 0.25 X (100 - 20) = 56,000 To cool uncondensed EtOAc: 1.96 X 88 X 4 3 7 x (100 - 20) = 5,100 To mol condensed EtOAc: 64.71 X 88 X 0.46 X
-
(100 20) Total heat transferred
For this gas ( ~ p / U / k )is~taken /~ as 0.89. The equation (8) for calculating latent heat (mass transfer) is:
The quantity k d , calculated from the vapor diffusion equation given by Gilliland (9),is 0.0665. CONDENSATE FILM. This coefficient is calculated at each point from the Nusselt equation for filmwise condensation on vertical tubes (11):
In the present example all quantities except I? in the right-
'follows: Inlet ressure conditions, atm. EtBAc vapor pressure pe Inert gas pressure pI Outlet ressure conditions, atm. E t d c vapor pressure, p , Inert gas pressure p , Pound moles EtOAc per hr. Entering: 100 X 2.000/3.000 Leaving; 100 X 0.096/4.904
= 209,800 = 851,400
As in the example given by Colburn and Hougen, the temperature of the condensate at the outlet is assumed equal to the temperature 6f the gaseous mixture. . C a o r ~ r mWATEBRATE
hand side of the above equation are assumed to remain constant. DIRT FACTORS. A water-side dirt conductance of 500 P. e. u./(hour) (square foot) (" C.), >and a vapor-side dirt conductance of 1000 P. c. u./(hour) (square foot) (" C.) are assumed. METALWALL. h, = 5440 P. c. u./(hour) (square foot) ("
C.). WATERFTLM. This is also obtained from the equation: h, = j~G/(cp/k)~/3
I n this case (~p/ulk)~'~ is taken as 4.7, gii-ing a conductance of 1080 P. e. u./(hour) (square foot) (" C.). COMBINED WALL,DIRT.AND WATERFILM COEFFICIENTS. l/ht = 1/500 l / l O O O + 1/5440 1/1080 = 1/243 ht = 243 P. c. u./(hr.)(sq. ft.)(' (3.).
+
For the Reynolds number,
D = 0.0412 ft.
G = 20,000 lb./(hr.)(sq. ft.) p = 0.0436 lb./(hr.)(ft.) 0.0412 X 20,000 = 18,900 Re = 0.0436
-
NUMBEBOF TUBES.A mass velocity of 20;QOO pounds/ (hour) (square foot) with a flow of 8760 pounds per hour requires a cross-sectional area of 0.4335 square foot. Using 5/s-inch, B. W. G. No. 16 tubes,
- 0.130)a X
r/4 X 1/12
0.4335/0.00133
5
-
0.00133 sq. ft.
j
- 0.130) X
'K
= 0.0034
The average molecular weight is M , = 52.0 For density calculation,
326 tubes required
(A)"'"
The perimeter of the tubes will be: (0.625
+
Solution 1 for Required Surface Area At point 1 (entrance), t u = 100' C.; p, = 2.000 atm.; p , = 3.000 atm. t, = 23.0' C.; At = 77" C.
851,400 = 5845 gal./hr. (23.0 5.5) X 8.345
(0.625
X 326
Ti
42.1 ft,
12
h,
Heat Transfer Coefficients The over-all conductance is made up of the conductances of the gas film, the condensate layer, the metal pipe, dirt and scale on the pipe, and the water film. All of these, except the conductances of the gas film and the condensate layer, remain essentially constant and may be grouped together as a single conductance. The following coefficients are all based on the inside surface area of the tubes. GASFILM. The coefficient for sensible heat is obtained (4) as follows: h. jcC/(cp/k)afa
-
1249
52.0 359 X 1/5 X 373/273 = 0*530 0.0436 ais = = (0.0530 X O m)
5
0.0034 X 20,000 1.134 52.0 X pof X 1.152 = 0.0034 X-20,OOO X 0.28 = 19.05
From Equation 1, 19.05(100
X - to) + 1.134 X 88 X 102 P Of
(2.000
- pc)
~
243 (to - 23.0)
By trial and error t, is found to be 46.0" C., and p , = 0.316 atm.; p,' = 4.684 atm.; p,! = 3.768 atm.
The problem, then, is: Does 19.05(100
- 46) + 1.134 X
88 X 102 X (2.000 - 0.316) = 3.768 243(46 23)?
-
1250
INDUSTRIAL AND ENGINEERING CHEMISTRY
1028
+
Vol. 34, No. 10
670
$. 2730 = 3395 (npprox.) U A l = 3398 U = 3398/72.1 = 47.0
4550 = 5590 (ap pox.) U A l = 5584 P. C. u./(hr.f)(sq. ft.) U = 5584/77 = 72.6 P. c. u,/(lir.)(sq. ft.)(' C.).
At point 2, t, = 90" C.; p . = 1.490 atm.; p , = 3.510 atm.
Similar solutions are made for a number of points along the condenser, and the required surface area is found by the graphical integration of l / U A t US. p (Figure 1).
Ethyl acetate condensed: 66.71 - (100 X 1.490/3.510) = 24.2 moles
Solution 2 for Required Surface Area
Heat transferred (in P. c. u./hour) is calculated as follows: To condense EtOAc: 24.2 X 88 X 102 = 217,500 To cool nitrogen: 100 x 0.25 X 28 X (100 - 90) = 7,000 To cool uncondensed EtOAc: 42.5 X 88 X 0.37 X (100 - 90) = 13,800 To cool condcnsed EtOAc: 24.2 X 88 X 0.46 X (100 - 90) = 9,800 = 248,100 Total heat transferred The change in water temperature is:
The water temperature itself is: = 23.0 - 5.1 = 17.9" C. = 20,000 - (24.2 X 88 X 0.4335) = 19,079 0.0412 X 19.079 = 18,000 Re = 0.0436 j = 00034 h, = 0.28 X 0.0034 X 19,079 = 18.14 M, = 45.9; p = 0.481; (f-)*'8 = 1.23 0.0034 X 19,079 - 1.150 K = 45.9 X P g / X 1.23 PO! X 24.2 = r = 88 42.1 he (from Nusselt equation) = 160 l/hr l/h, = 1/243 91,460 a 1/96.6 l/h" ho = 96.6 1.15 X 88 X 102 X (1.490 - p c ) 18.14(90 - t,) Pdf 96.6(te - 17.9) t , is found by trial and error to be 53.0' C., and
k
+
+
In this solution a n attempt is made to calculate the actual temperature of the condensate a t each point which, as stated before, must be below that of the gaseous mixture. Consequently, more heat is transferred in progressing to each point than is considered in the first solution, and the total heat load on the condenser is likewise increased. More cooling water must therefore be supplied in order to maintain the same terminal conditions. The temperature of the condensate a t each point is taken as the arithmetical average of the vapor-condensate interface temperature (te) and the temperature of the inner surface of the metal tube (tm). The interface temperature is known to a first approximation from solution 1; the metal wall temperature may be calculated from the water temperature, the combined water film, dirt, and metal wall conductances (h), and the quantity UAt, all of which are known from the first solution. The use of the arithmetical average of the condensate film boundary temperatures is open to some question, although it is difficult to determine just what the true condensate temperature is for a given point. A more accurate relationship for this value may be calculated on the basis of certain assumptions; but as long as viscous flow is maintained, the arithmetical average temperature i s probably close enough for normal design \.;ark. In the present example 4l?/p for the film at the outlet end of the condenser is 1000, which is well down in the viscous region. The temperature of the condensate (tg) at this point is then computed as follows: 9.2' C. (from solution 1) 5.5' C.; U A t = 287 h, = 243 P. c. u./(hr.)(sq. ft.)(' C.) tn = 5.5 4- 287/243 = 8.7' C. t, = (6.7 4- 9.2)/2 = 7.9' 6. t, = t, =
= 53.0" C.; p , = 0.421 ntm. pot = 4.579 atm.; p,! = 4.040 atm. 1,
The problem, then, is: Does 1.15 a< 88 X 102 X (1.490 - 0.421) 18.14(90 - 53) 44.040 96.6 (53.0 17.9) 1
-
The total heat load (in P.c. u. per hour) is calculated as follows : = 580,500 To condense EtOAc (from solution 1) To cool nitrogen = 50,000 To cool uncondensed EtOAc = 5,100 To cool condensed EtOAc: 64.71 X = 241,000 88 X 0.46 X (100 - 7.9) Total heat transferred = 882,600
The cooling water rate is: 882,600
(23
- 5.5) X 8.345 = 6050 gal./hr.
At point 1 t, = 100" C. Conditions are the same as in solution 1, since no ethyl acetate h a c been condensed. At#point 2 f
1, f,
= 90" C.; t, = 53.0" @. = 17.9' C.; U A t = 3398 = 17.9 3308/243 = 32..5' C.
+
t , = (32.5 4- 53.0)/2 = 42.8" 6. 0
10
20
30
40
50
60
FIGURE1. HEATTRAVSFERRED q US. 106/UAT
70
90
80
4 i i D 1)s. -&REA
A
Heat transferred (in P. c. u. per hour) is calculated a s followe:
INDUSTRIAL AND ENGINEERING CHEMISTRY
October, 1942
To condense EtOAc (from solution 1) To conl nitrogm To cool uncondcnsed EtOAc To conl condensed EtOAc: 24.2 X 88 X 0.46 X (100 42.8) Total heat transferred
-
= 217,500
=
7,000
= 13,800
= 56,100 = 5%Gi
The change in water temperature is: 294,400/(6050 X 8.345) = 5.8' C. The corrected water temperature is: 23.0 - 5.8
17.2' C.
This is substituted in Equation 1 to give: 18.14(90
-
t,)
+ 1.150 X 88 X
102 X (1.490 - p c ) = POf
96.6
(tc
- 17.2)
Solving by trial and error as before, tr = 52.6" C.and UAt = 3428 U = 3428/(90
- 17.2) = 47.1
The temperature of the condensate must be recalculated, using this value of UAt, to get the true amount of heat transferred : tm = 17.2 f 3428/243 = 31.3" C. la = (52.6 3- 31.3)/2 = 42.0' C. The heat transferred in cooling the condensed ethyl acetate then becomes: 24.2 X 88 X 0.46 X (100 - 42.0) = 56,900 P. c. u./hr. The total heat transferred is then 295,200 P. c. u. per hour. This small correction does not affect the change in the water temperature, which equals 295,200/(6050 X 8.345) or 5.8" C., as before Similar solutions are again made for a number of points dong the condenser, and the required surface area is calculated by graphical integration. The results of both solutions are summarized in Table I.
Application of the Modification in Design
1251
At the hot end t, equals to since no condensation has taken place, and t. may therefore be calculated using the unmodified procedure, as illustrated by point 1 of the first solution. A plot of temperature against heat transferred, such as Figure 2, may then be made, since the condensate and water temperatures at both ends, as well as the total heat transferred, are known. The graph for the water temperature is a straight line; that for the condensate temperature, both in the present example and in that given by Colburn and Hougen, is slightly concave downward. Thus a reasonable estimate of the intermediate condensate temperatures may be made. For a selected intermediate vapor temperature, then, the corresponding water temperature is first calculated, as in the first solution, considering that t, equals t,. The estimated true t. corresponding to this water temperature is then read from the graph; and both the heat transferred and the water temperature corrected are calculated using this value. The corrected t, is substituted in Equation 1, and the trial-anderror solution for tois carried out as before. For design purposes this graphical method of estimating t, is probably sufficiently accurate because of the inaccuracies inherent in the procedure itself. Some of these errors and approximations are given below.
Errors and Approximations The latent heat of vaporization of the ethyl acetate varies through the condenser, and strictly should be evaluated a t t, for each of the point values. I n addition the viscosity and specific heat of both the liquid and gas vary with the temperature, as mentioned previously, but in view of the other approximations it was considered accurate enough to use average values for these quantities throughout the calculations. The equation for the water film coefficient was derived by Colburn by correlating data from tests on flow across a single bundle of tubes. I n baffled exchangers there may be some leakage through the baffles, and the coefficient may be less than that based on the assumed rate of flow. Data reported by Bowman (9)from tests on one line of exchangers indicate that a safe value for this conductance is 0.6 times the normal coefficient. As stated before, the use of the arithmetical average of the condensate film boundary temperatures is a possible source of error. A mathematical solution for this value, based on the assumptions of stream-line flow (neglecting variations in
The modification illustrated by the second solution scarcely affects the point values of UAt but changes the corresponding values of p so that the required surface area is 14.5 per cent less than that given by the first solution. The TABLEI. SUMMARY OF POINT VALUES refinement is probably great enough, Solutherefore, to be justified in industrial tion Point No. Quantity No. 1 2 3 4 5 6 design. The second trial-and-error 90 80 70 60 l., c. 1,2 100 50 solution, however, is unnecessarily tu, c. 1 23.0 17.9 14.6 12.2 10.2 8.8 tedious, since the following procedure 2 23.0 17.2 13.5 10.9 9.0 7.8 At 1 77.0 72.1 65.4 57.8 49.8 41.2 gives sufficiently accurate results and 2 77.0 72.8 66.5 59.1 51.0 42.2 tc. c. 1 46.0 53.0 44.3 36.1 28.9 22.9 necessitates only one trial-and-error 2 46.0 52.6 43.0 35.5 28.0 22.2 solution. 46.0 42.0 33.9 27.4 21.9 17.4 h. c. 2 I n order to estimate the total heat PO atm. 1,2 3.000 3.510 3.904 4.215 4 454 4 628 Q, h. e. u./hr. X 10-4 1 85.14 60.33 44.19 32.27 22.82 15.73 load on the condenser, the condensate 2 88.26 58.74 40 13 27.09 17.50 11.13 temperature a t the cold end may be G 1,2 20000 10079 185.70 18170 17920 17760 Re 1 2 18900 18000 17500 17200 16900 16750 obtained from the relation: 1.134 1.150 1 180 1219 1250 1 320 K 1:2
-
8 30 6.5 6.1 23.5 23.9 13.0 12.7 10.5
9 20 5.5 5.5 14.5 14.6 9.2 9.2 7.9
4.755 9.55 6.07 17655 16690 1.338 17.30 17.10 16.90 16.80
4.844 5.03 3 05 17585 16600 1.375 16.72
4.905 0 0 17535 16570 1.420 16.70
O
ha
(:-)odd
end
o*2
This equation is approximately exact both for the present example and for the example given by Colburn and Hougen, in which the conditions were widely different.
1,2
U U At
72.6 72.6 5584 5584 1.76 1.76
l / U A t X IO'
A , 8q. ft.
L,ft.
19.05
1 2
0
1
0 0
2
0
18.14 17.62 47.0 47.1 3398 3428 2.94 2.92
39.7 89.6 2590 2027 3.86 3.80
7
7 40 7.5 6.7 32.5 33.3 17.5 16.0 13.5
34.2 34.0 1978 201 1 5.06 4.97
30.0 29.8 1404 1520 6.70 6.58
26.9 23.9 21.5 19.7 26.8 23.9 21.4 19.7 1109 779 506 287 1132 514 287 796 9.02 12.84 10.58 34.80 8.84 12.55 19.48 34.80
58.3 113.2 166.0 221.2 276.8 342.3 414.5 546.7 68.6 111.8 187.9 242.9 291.0 343.7 300.9 4GS.7 1.38 2.68 3.04 5.25 6.57 8.14 9.84 13.00 1.63 3.13 4.46 5.76 6.91 8.15 9.29 11.12
INDUSTRIAL AND ENGINEERING CHEMISTRY
1252
viscosity) and a straight-line temperature gradient, results in the following equation ( 3 ): t.
tc
- 3/8&
This relation gives values of ta not widely different from those used n the second solution and since the assumptions may not be entire!y just fieti, the arithmetical average temperature is probably close enough for ordinary design calculations.
Vol. 34, No. 10
hand, the use of the true condensate temperature does make a significant difference in the required surface area, and the graphical procedure outlined above makes the additional labor involved in using i t relatively small.
Acknowledgment Grateful acknowledgment is made of the assistance of P. RT.Blaylock, of Shawinigan Chemicals, Ltd., whose suggestions led to this investigation; and of the invaluable criticisms and advice of C. C. Winding, of Cornel1 University, and A. P. Colburn, of the University of Delaware.
Nomenclature A = area, sq. ft. c = sp. heat at constant pressure, P. c. u./(Ib.)(O C.) D = diamrter of tube, ft. dA = elemrnt of surface area dq = incremrnt of total heat transferrrd per unit time g L = arccleration duc to gravity, 4.18 X lOUft./(hr.)’ G = mass velocity, Ib./(hr.)(sq. ft.) h = film coefficient of heat transfer, P. c. u./(hr.) X (sq. f t . ) ( O C.) h, = condensate h, = metal wall h, = combined conductances other than gas film 0 10 20 30 40 50 60 70 80 90 h, = gas film ht = combined water, metal wall, and dirt PIGURE 2. TEMPERATURES FROM SOLUTION 2 us. HEAT TRANSBEERED q conductances h, = water film = heat transfer or mass tranvfer factor j = thermal conducJivity, P. c. u./(hr.)(sq. ft.)(’ C./ft.) A slight error arises from neglecting the heat transferred in = diff uaion coefficient, sq. f t. /hr. cooling the condensate when calculating the point values of = molar mass transfer coefficient, Ib. moIes/(hr.)(sq. ft.) UAt. Equation 1 was derived by equat’ng the heat trans(atm.) ferred from the gaseous mixture to the condensate surface to = length, ft. = molecular weight that transferred from this surface to the cooling water; = av. gas molecular weight actually, more heat is transferred to the water than reaches = partial pressure, atm. the condensate surface from the gas. This additional heat is p c = vapor pressure a t to that transferred in cooling the condensate itself. To estimate p g = noncondensable gas partial pressure in main hnrlv this accurately would require that the condensate temperapp’ = that Ldjacent to condensate surface ture be known a t each point; furthermore, a:l of this heat p g f = logarithmic mean of p , and p j does not flow through the entire condensate layer. In the p , = vapor pressure present example, where this amount of heat is a considerable q = heat transferrrd, P. c. u./hr. Re = Reynolds number, DG/M part of the total heat transferred, this error may be fairly t = temperature, ’ C. serious. It is difficult to allow for it, however, and in general = av. temperature of condensate t, it is safe and considerably simpler to neglect this quantity = temperature of condensate surface t, = temperature of inner face of tubes (8) t, tu = gas temperature I n regions of high vapor concentration, the vapor molecules t, = water temperature diffusing through the gas film to tlie liquid interface absorb At = over-all temperature drop much of the sensible cooling effect and reduce the tendency Atc = tempernture drop through condensate film of the main body of the gas to cool. Consequently the usual U = over-all coefficient of heat transfer, P. c. u./(hr.)(sq. ft.) ( 0 C.) equation for sensible heat transfer is no longer exact. -4 r = mass rnte of flow, lb./(hr.)(ft. of wettcd prriphery measquantitative treatment of this effect was given by Ackermann urrd on plane normal to direction of fluid flow) ( I ) , and d scussed by Colburn and Drew in 1937 (6). 1 = latent heat of vaporization, P. c. u./lb. Finally, i t is unlikely that a saturated mixture entering a fi = viscosity, lb./(hr.)(ft.) p = density, lb./cu. ft. condenser will cool and condense a t just the right relative rates to remain saturated. With large organic molecules the Literature Cited rate of mass transfer is slow, and the heat transfer may outAokermann, G., Forschungsheft, No. 382, 1-16 (1937). strip the diffusion and bring about supersaturation. Colburn Bowman, R. A., “Heat Transfer”, pp. 75-81, Am. Soo. Mech. and Edison ( 6 ) believe that with organic vapors this will alEngrs., 1936. most invariably take place, even though the Ackermann Colburn, A. P., private communication. effect tends in the opposite direction. I n the present example . m . Past. Chem. Engrs., 29, 174 (1933) Colburn, A. P., T r a r ~ s A Colburn, A. P., and Drew, T.B., Ibid.,33, 197 (1937). this error may be quite large, perhaps great enough to make Colburn, A. P., and Edison, A. G., IND.ENQ. CHEM.,33, 457 the proposed correction unjustifiable in this case. However, (1941). in problems dealing with small organic molecules, or in all Colburn, A. P., and Hougen, 0. A,, Ibid., 26, 1178 (1934). cases in which the heat transferred in cooling the condensate Colburn, A. P., and Hougen, 0. A., Univ. of Wis., Bull. 70, 35-7, 81 (1930). is an appreciable part of the total heat load on the condenser, Gilliland, E. R., IND. ENG.C H ~ M26, . , 681 (1934). the present modification should be considered. International Critical Tables, Vol. 111, p. 219 (1928). All the above errors except the last are usually small and Perry, J. H., Chemical Engineers’ Handbook, 2nd ed., p. 985. for design purposes are not worth evaluating. On the other S e w York, iMcGraw-Hill Book Go., 1941. 0
