Design of Cooler Condensers for Mixtures of Vapors with Noncondensing Gases A. P. COLBURN, E. I. du P o n t de Nemours & Company, Inc., Wilmington, Del., AND 0. A. HOUGEN, University of Wisconsin, Madison, Wis. I n conahsing vapors from mixtures of vapors with noncondensing gases, the gas film and over-all heat transmission coeficients vary widely from point to point in the apparatus, and also the change in heat content of the gaseous mixture is not proportional to the change in temperature. For these reasons no simple relationship expressing the mean temperature difference between the gas-vapor and cooling-water stream can be used. This paper outlines a method of computing the required condenser surface in which values of 1 / U At are determined at a suficient number of points along the path of gas flow to permit calculation of a correct average value of U A t by graphical integration. The value of UAt at any point in the
T
H E design of a surface condenser for the condensation of vapors from a mixture of vapors with noncondensing gases presents several very unusual conditions and complications in heat transmission not encountered in the condensation of pure vapors or in the cooling or heating of homogeneous fluid streams. In the condensation of vapors from their admixture with noncondensing gases, all the properties of the gas stream vary greatly as the water vapor is removed. For example, the heat transmission coefficient of the gas film, the rate of gas flow, and the heat capacity of the gas stream per pound mole of inert gas decrease enormously as condensation proceeds. The condensation of the vapors depends upon the diffusion of the vapor molecules through the gas mixture; hence, mass transmission as well as heat transmission coefficients must be considered ; the problem involves principles of diffusion as well as of heat transmission. Also the condensate loses heat as it flows over the condenser surface so that more heat passes through the film of cooling water than through the adjoining gas film. For these various reasons no method of calculating mean temperature differences based upon terminal conditions is applicable. Indeed, the true average temperature difference between the two fluid streams interchanging heat may be greater than the temperature difference at either end of the condenser. An accurate method of calculation for this type of design problem has long been sought. Nevertheless, attention has heretofore been given principally to methods of estimating for design purposes the mean temperature difference between the vapor-gas mixture and the cooling liquid which are interchanging heat, since it is realized that the usual logarithmic mean of the terminal temperature differences of the heat interchanger is entirely inapplicable for the reasons mentioned above. The method, for example, of Haug and Mason (6) allows for the rapidly changing heat capacity of the vapor-gas mixture and provides for the estimation of the average temperature difference by calculating the temperatures on the two sides of the condenser surface from heat balances, thus tacitly assuming a uniform rate of heating of the water stream.
condenser is obtained, through trial and error, by equating the heat transferred through the condensate, the tube wall, and the cooling-water film, to the sum of the heat transferred by the sensible cooling of the uncondensed gas and the latent heat equivalent of the vapor transferred by diflmion and condensed. The necessary surface area is obtained by multiplying the heat transferred per hour by the integrated average value of 1 / U A t . Coeficients for the transfer of the vapor are estimated on the basis of a correlation previously published. I n a n example presented, the over-all coeficient, U, varies from 294 to 60, whereas the effective heat transmission coeflcient of the condensing vapor-gas film varies from 5600 to 75. I t has been recently pointed out by Tymstra (8) that the Haug and Mason method errs in that the temperature differences should be averaged according to the length of the exchanger rather than according to the heat content of the water stream since the inference of a uniform rate of heating the cooling water is inadmissible. Tymstra has proposed an approximate method for estimating an average temperature difference which consists in adding to the logarithmic mean temperature difference one-half of the “arithmetic mean temperature difference between a straight line connecting the gas inlet and outlet temperatures and the gas heat-content curve.” This method is in error in that it presupposes a uniform over-all heat transmission coefficient over the entire length of condenser. Actually the over-all heat transfer coefficient varies from point to point in a cooler condenser, being high where the vapors are relatively concentrated and low where most of the vapor has been removed. It is, therefore, obvious that no simple mean temperature difference and no simple average heat transfer coefficient is applicable. A basic statement of the problem is given by the equation: dA
=
dp/UAt
(1)
where At = difference in temperature between gas and cooling medium. As pointed out above, the usual formula, A = q/UAt,
(2)
does not apply to this case. For the present case, to integrate Equation 1 analytically it would be necessary to find expressions for both U and At as functions of q. Such expressions were not obtained since the difficulties involved a r e too great, as can be seen later by studying, for example, the variables affecting U and At. Some approximations can doubtless be made to effect this solution, a t least for specific cases, but the authors have preferred for the general case the exact integration of Equation 1 by a graphical method. While it is difficult to find expressions for U and At in terms of q, it is quite straightforward for any given problem to calculate the product, UAt,
1178
November, 1934
INDUSTRIAL AND ENGINEERING
a t various values of q , and by plotting 1/ C A t vs. q to obtain A by graphical integration. This method takes account of the variations from point to point not only of the temperature difference but also of the over-all coefficient and mass velocity and, therefore, should give a true value of the required surface area. The procedure proposed for calculating the value of UAt is to equate by trial and error the heat transferred through the condensate, the tube wall, and the cooling-water film to the sum of the sensible heat transferred by cooling the uncondensed gas and the latent heat corresponding to the amount of vapor transferred by diffusion. This requires a knowledge of the temperature a t the int,erface between the condensate and the gas phase, t,, and the corresponding vapor pressure of the condensate. Various values are chosen until the desired equality is obt,ained, thus giving instantaneous values of UAt a t the gas temperature selected. Coefficients for the transfer of the vapor are estimated on the basis of the mass transfer factors for which correlations have been previously proposed by one of the present authors (3). An example is given below by which the method is more clearly explained.
EXAMPLE The problem is to design a tubular cooler condenser to handle 100-pound moles of inert gas (molecular weight 28i. e., 2800 pounds) per hour a t one atmosphere pressure and saturated with water vapor a t 95" C. The gaseous mixture and the condensate are to be cooled to 40" C. with cooling water available a t 25' C. It is desirable for the gas to pass through the shell side of the baffled exchanger and for the water to flow through the tubes, because the water is expected to deposit scale and the inside of the tubes can be much more easily cleaned than the outside. The gas stream is baffled to pass back and forth across the tube bank. A water velocity of 4 feet per second is chosen, sufficiently high to minimize the deposition of silt. It is assumed that reasonably high gas velocities can be used and that the pressure drop is not limited by other than economic considerations. The exchanger will be constructed of 0.75 inch 0 . d. brass tubes, 16 B. W. G. (Birmingham wire gage), 0.62 inch i. d., since this is about the smallest size tube that can be conveniently cleaned. The cooling water will be assumed to leave the apparatus a t 60" C., as higher temperatures tend toward air-bubble formation and favor corrosion. TOTAL HEATTRANSFERRED. Inlet conditions: Water vapor pressure, p , = 0.835 atm. Inert gas pressure, p , = 0.165 Exit conditions: Water vapor pressure, p , = 0.073 atm. Inert gas pressure, p , = 0.927 0 835 Lb. moles steam entering/hr. = 100 X -= 506 0.165 0 073 Lb. moles steam leaving/hr. = 100 X 0.927 = 7'9 Lb. moles steam condensed/hr. = 506 - 7.9 = 498.1 Heat transferred in condensing and cooling 498.1 lb. moles steam = 498.1 X [9760 18(95 - 40)] = 5,350,000 P. c. u./hr. Heat transferred in cooling gas = 100 X 7.0 X (95 - 40) 38,500 Heat transferred in cooling uncondensed steam = 7.9 X 0.455 X 18 X (95 - 40) 3,500 Total heat transferred = 5,392,000 P. c. u./hr. COOLING-WATER RATE. 5,392,000 - 154,000lb./hr. (equivaLb./hr. of cooling water = 60 - 25 lent to 308 gal./min). NUMBER OF TUBES. For 0.75-inch, 16 B. W. G. tubes, 1 gal./min. gives a velocity of 1.069 ft./sec. - 83 For 4 ft./sec., no. of tubes = 308 X 1.069 -
+
4
CHEMISTRY
1179
HEAT TRANSFERCOEFFICIENTS.The over-all conductance is made up of the conductance of the gas film, condensate, metal pipe, scale, and dirt on the pipe, and the coolingwater a m . All except the gas conductance can be considered essentially constant, and i t is convenient to group them together as a single conductance. Condensate Film, he. Values of h, for the condensate 6lm can be estimated by the Nusselt equation for filmwise condensation (7). Since, however, the thermal resistance of the condensate film is relatively small, and since the baffles prevent the accumulation of thick condensate layers, it is simpier and safe to assume an average value of h, equal to 2000.
Metal Pipe. h, = 2-6 0.065 = 12,000 Dirt and Scale Film. As cooling water is generally river or similar water and not clean, the resistance of the dirt and scale deposited should be considered. A value of h d = io0 is chosen for this film. Water Film Coeficient, h,. This is obtained from A h Adams (6). For V = 4 feet/second, D' = 0.62 inch, t u = 60" C., h, = 1210 P. c. u./(hour)(square foot)("C.). The conductance of the combined films above, when calculated on the outside surface area, is ho = 310. This will be considered as constant throughout the exchanger, though h, will change somewhat with the water temperature. Gas Film. (a) Sensible heat. This coefficient is obtained from the equation: (3)
h, = jcG/(cp/k)ala
For this gas it is assumed that ( c ~ / k ) ~=/ 0.83. ~ The factor j is obtained from Figure 19 of reference 3 or Figure 2 of reference 1 where i t is a function of Reynolds number, D G / p , based on the outside diameter of the tubes. (b) Latent heat. T o calculate the rate of diffusion of the vapor molecules through the gas film, the same Figure 19 (3) is used in conjunction with the mass transfer equation:' (4)
For this case (p/pkd)P'3 will be taken as 0.71. GASVELOCITY. Although the quantity of gas-vapor mixture is much decreased in passing through the condenser, and although there is more justification economically for a higher velocity on the cold end than the hot, for the sake of standard apparatus all baffles are to be evenly spaced.
+ +
Entrance rate = 2800 9100 = 11,900 ib./hr. Exit rate = 2800 140 = 2940 lb./hr.
If a minimum free cross-sectional area of about 1.1 square feet is chosen, the mass velocity G will cover the range from 10,800 to 2700 pounds/(hour) (square foot) and the optimum velocity is assumed to lie between these limits. REQUIRED SURFACEAREA. This requires knowing values of the product of the heat transfer coefficient and temperature difference a t various points in the gas stream, say a t 5' or 10" C. intervals.
Point I (Entrance).
Gas temp., t, = 95" C. Water temp., t, = 60" Temp. difference, At = 95 - 60 = 35" C. Partial pressure of steam, pv = 0.835 atm. Partial pressure of inert gas, p , = (1 - 0.835)
=
0.165 atm.
1 For saturated mixtures the mass transfer coefficient could be converted to a corresponding heat transfer coefficient by the us of a heat balance and the Clausius-Clapeyron equation relating A p and At. As it would still be necessary to cut and try for the condensate surface temperature, there appears to be no advantage in making this transformation.
1180 (.
INDUSTRIAL AND ENGINEERING CHEMISTRY
To calculate the mass transfer coefficient, it is first necessary to compute the Reynolds number, D G / p :
Then t,
=
60 - 10.3
= p =
Now the rate of heat transfer through the gas film must equal that through the tube and the water film-that is:
- t o ) + KM,X(pr
h,(t,
- p c ) = ha(t,
- tu)
= UAt
The condensate as it flows over the tube also gives up heat to the cooling water. This can be neglected in calculating U and At but not in calculating the final value of A. For the first point: 34.5(95 - t,)
+(4'88) (9760)(0.835 - p , ) = 310(t, - 60) POI = 0.695;
Try t, = 90' C.; p , p,' = (1 - 0.695) = 0.305; p o l is the logarithmic mean of p , and p,'-i. e., of 0.165 and 0.305 = 0.228. Does 34.5(95 - 90) 0.228 (4'88) (9760)(0.835 - 0.695) = 310(90 - 60)? 173 29,200 = 9300. N o . Try t, = 93" C.; p , = 0.775; p,' = 0.225; p,! = 0.193
+
+
Does 34.5(95 - 93) 69 Try t,
=
+
49.7" C., and At
=
93 - 49.7
=
43.3"
The gas film coefficients are:
D
0.75/12 = 0.0625 ft. 0.0142 X 2.42 = 0.0344 lb./(hr.)(ft.) = 19,600 Therefore at entrance, Re = ,(0.0625)(10,800) 0.0344 From Figure 19 (3) or Figure 2 (f), j = 0.0063 Av. mol. weight = 19.7; c = 0.42 (0.0063)(0.42)(10,800) = 34.5 By Equation 3, h, = 0.83 (0.0063)(10,800/19.7) = 4.88 By Equation 4, K = P01(0.71) Po!
=
Vol. 26, No. 11
II
Reynolds No.
= 0.0351 =
j =
Av. mol. wt. h,
= =
(8180)(0.0625) = 14,540 (0.0351) 0.0071 20.3; c = 0.39 (0.0071)(0.39)(8180) = 27.3 0.83
Just as above, it is now necessary to determine by trial and error the condensate surface temperature which will give an equality in the heat transferred. This is finally obtained as follows: Try t, = 89.8; p e = 0.69; p,' = 0.31; po, = 0.265 (4'04) (9781)(0.775 - 0.69) = Does 27.3(93.0 - 89.8) -.--310(89.8 - 49.7)? 89 12,660 = 12,400. 0 . K. Then U A t = 12,600; U = 291; ht = 4500.
+
+
By the same methods, calculations are made for a number of intermediate points and the results are given in Table I. I n calculating values of UAt a t successive points in the condenser, the heat given up by the condensate in flowing over the surface was neglected. More heat actually flows through the water film than through the condensing gas film because of the cooling of the condensate as it flows over the
+ 0.22~ (4'88) (9760)(0.835 - 0.775) =
14,700
93.4' C.; p ,
310(93 - 60)? 10,200. NO. 0.788; p,' = 0.212; p g f = 0.188
= =
Does 34.5(95 - 93.4)
+ 0(4'88)(9760)(0.835 .18~ - 0.788) =
310(93.4 - 60)? 55 11,900 = 10,360. NO. Try t, = 93.6; p c = 0.795, p,' = 0.205; pol = 0.185
+
Does 34.5(95 - 93.6) f +(9760)(0.835 (4 88) 48
+ 10,100 = 10,400.
0. K.
- 0.795)
=
310(93.6 - 60)?
The mean value 10,300 = UAt; since At = 35, U = 294. As a matter of interest, a hypothetical coefficient, ht, is defined as dq/dA(t, - to). For this point, b = 5600. Now consider a point in the exchanger where the gas temperature is lower, say 93" C.; the corresponding coolingwater temperature is determined by a heat balance, as follows : 0
Point 2. to = 93" C.; p , = 0.775; p , = 0.225 (0 775) = 344 lb. moles/hr Moles steam remaining = (100)0.225 Gas rate = 2800 6200 = 9000 lb./hr. Mass velocity for 1.1 sq. ft. cross section = 8180 lb./(hr.)(sq. ft.)
+
The loss in heat content is as follows: Steam condensed = 506 - 344 = 162 lb. moles/hr. Heat of condensation = 16219760 18 (95 - 93)l = 1,586,000 P. c. u./hr. , . Heat removed from uncondensed steam = 344 X 0.455 X 18(95 - 93) = 5.640 P. c. u./hr. Heat removed from gas = 1,400 P. c. u./hr. 100 X 7 X (95 - 93) = Heat transferred in interval 95" - 93" C. = 1,593,040 P. c. u./hr 1 593 400 Change in water temp. = = 10.3" C. 1-..-,""I .KA nnn
+
,
2
+
4
q (MILLIONSOF P.c.u. FIGURE 1. HEATTRANSFERRED, PER HOUR)US. 1OS/UAt AND US. AREA, A (SQUARE FEET)
condenser surface. This difference averages 4.5 per cent in the present problem and the neglect of it introduces a slight error in the calculated point values of UAt. However, in finally calculating the total area of the condenser, the heat lost by the condensate is included so that this effect in calculating values of UAt introduces only an insignificant error in the calculation of A . The required surface area is now readily determined hy graphical integration of the area under the curve of 1/UAt vs. q (Figure l ) ,by any convenient method. Curve A represents the integral of the curve of l / U A t , and the final value is 696 square feet. The corresponding mean value of U A t is 7750 P. c. u./(square foot) (hour). The length required to
November, 1934
I N D U S T R I A L .AND E N G I N E E R I N G C H E M I S T R Y
furnish 695 square feet of outside tube surface, using eightythree tubes of 0.75 inch 0 . d. is: 695 l2 = 42.6 ft. 83 X 0 . 7 5 X a
Figure 2 shows the gas and water temperatures plotted against the quantity of heat transferred, q, and Figure 3 shows these temperatures against the length of the exchanger. The curves of Figure 3 are of the same general shape as those found for an experimental cooler condenser by Colburn and Hougen (4). Figure 4 shows plots of q and LT vs. length.
1181
shell. The large empty area on each side of the tube bank appears desirable to keep down the pressure drop around the baffles. As the widest row of tubes is approximately 22 inches, the 1-inch space a t each end is to be filled by a longitudinal baffle. This layout gives an average clearance of 0.526 inch between tubes. To provide a cross section of 1.1 square feet, based on the free area between tubes in a row, a baffle spacing of 17 inches is indicated. Each of the two condensers of 25.0-foot tube length requires fourteen baffles. The free area between the baffles and the shell, allowing for passage of gas from one interval of tube length to the next, is made 1.1 square feet also. The pressure drop across the tube banks, taking account of the variation in velocity and density of the gas mixture through the exchangers, is estimated as 13.3 inches of water by means of the friction curves on Figure 19 of the paper cited ( S ) , which are based on the correlations of Chilton and Genereaux ( 2 ) . The preswre drop around the baffles is estimated a t 8.3 inches. The total losses due to expansion and contraction and to friction in the connecting pipe are estimated at 1.0 inch; the total pressure drop is therefore about 22.6 inches. This is considered a reasonable value, not indicatin g excessive power costs. 100,
9
FIGURE 2. G.4s TEMPERATURE, to, .LXD WATER TEMPERATURE, t,, vs. HEATTRANSFERRED, q (MILLIOKS OF P. c. u. PER HOUR)
This length of 42.6 feet requires two units in series, each with tubes, say, 25 feet long, to provide some margin of safety on the surface area, and to take care of the inactive regions a t the gas entrance and exit connections. While the use of more tubes in parallel would call for a shorter unit, it would mean either a lower water velocity, with lower transfer coefficients and more rapid fouling of the inside tube surface, or a higher water rate in gallons per minute with higher cooling-water costs. Multipass construction on the water side is not feasible since, for the conditions stated, the temperature of the cooling water would be required to rise above the desired gas outlet temperature halfway through the exchanger; to avoid this, a greater quantity of water with lower outlet temperature and %her costs would be required in this case also. TABLEI. Point
1
c
95 60 c. ' C. 35 C. 93.6 atm. 0.165 q , (P. hr.)/lOn c. u./ 5.39 m,lb./hr. 11,900 He 19,600 0.185 atm. tu, tu., At, tc,
pj, h, hi U
i:;:
5,600 294 10,300 UAt loa/(uAf) 97.1 -4, s q f t . 695 42.6 L,ft.
SUMMARY OF
2
3
4
93 49.7 43.3 89.8 0.225 3.79 0.265
90 42.3 47.7 84.3 0.305 2.66 6,280 10,070 0.371
85 35.8 49.2 73.0 0.430 1.66 5,200 7,600 0.537
l:,Z: 4,500 291 12,600 79.4 555.7 34.1
ii3; 2,300 274 13,070 76.6 468.6 28.7
&1: 950 234 11,500
9,000
14,540
87.0 387.6 23.8
POIKT VALCES
5 75 30.5 44.5 54.4 0.622 0.848 3,890 5,370 0.734
:41:
360 166 7,370 136 302.2 18.5
L
to, A N D WATER FIGURE 3. G.4s TEMPERATURE, TEMPERATURE, 1,, VS. LENGTH OF EXCHANGER, L (FEET)
The friction through the tubes on the water side is about 2.1 pounds per square inch, and the enlargement losses, etc., add UP to about 0.6 pound per square inch, making a total of 2.4 p o u n d s per square inch, which is also a reasonable value.
6
7
8
9
65 28.0 37.0 42.0 0.754 0.453 3,390 4,450 0.836
55 26.6 28.4 34.6 0.844 0.248 3,130 4,040 0.895
45 25.4 19.6 29.7 0.906 0.073 2,990 3,800 0.932
40 25 15 27.9 0.927
:i42 189 117 4,340 231 232.7 14.3
:i1:
:io$
123 88.5 2,510 399 168.1 10.3
&*;
87.3 68.2 1,335 750 67.7 4.2
2,940 3,680 0.945 74.8 60.3 905 1,lOi
COMPARISON WITH OTHERPROPOSED DESIGS METHODS The true mean temperature difference, obtained from Figure 3 by a graphical average, is 35.2' C., which is considerably greater than the logarithmic m e a n t e m p e r a t u r e difference of 23.6' C.-higher, i n d e e d , than either of the terminal differences. If this logarithmic mean value were used with the average of the over-all coefficients a t the two ends-namely, 177-the calculated area would be:
0
A =
PRESSURE DROP An estimate has been made of the pressure drop in the exchanger, which it' is assumed Rill be built in two separate units, as follows: A tentative layout of eight>y-three tubes, 0.75 inch 0 . d. and on 1.25-inch centers, on equilateral triangular spacing, indicates five rows of tubes in a 24-inch
5'390'000 = 1290 sq. ft. 177 X 23.6
This value is almost double the correct area, indicating that in this case such an approximation method would be inapplicable. It is of further interest to compare previously suggested methods of calculating the mean temperature difference. The Haug and Mason mean temperature difference is esti-.
1182
INDUSTRIAL AND ENGINEERING CHEMISTRY
mated to be 42.4" C., whereas the Tymstra value is about 32.3" C. It is apparent from a comparison of the space between the gas and water curves on Figures 2 and 3 that the Haug and Mason mean would be much greater than the true mean. Although the value predicted by Tymstra's method is close to the true mean, it is again emphasized that without knowing what mean value of the widelv varvinn coefficient to use &th such a mean temperature kfferckcej the latter
Vol. 26, NO. 11
as compared with 695 square feet in the design used in the example above. Because of the low rates of flow, a condenser nearly nine times as large is required. This emphasizes the faulty design used in some standard equipment and the desirability of providing for high velocities of both water and gas streams.
ACENOWLEDGMENT The authors acknowledge with thanks the assistance of T. H. Chilton, R. P. Genereaux, and S. J. Hill in the calculation of the above example.
L
FIGURE4. OVER-ALLCOEFFICIENT OF HEAT TxmsmR, u (P. c. U./(HOUR)(SQUARE FOOT) (" C.), AND HEATTRANSFERRED, q (MILLIONSOF P. c. u. PER HOUR)vs. LENGTH OF EXCHANGER, L (FEET) value is of little use. The true mean can be calculated only when the surface area required has already been determined and hence is of academic interest only. I n the present problem 695 square feet of condenser surface is required to condense 9000 pounds of water vapor per hour from 100 pound moles of inert gas. I n order to condense 9000 pounds of water vapor per hour in the absence of inert gas and otherwise under similar conditions of temperature, water velocity, and design, 340 square feet of surface would be required. The presence of the inert gas requires for this case a condenser twice as large to condense the same amount of water vapor. If only the inert gas were to pass through the same heat interchanger, 152 square feet of surface area would be sufficient to cool the gas from 95" to 40" C. A common design of condenser used in the gas industry for removing water vapor and tar from coal gas consists of large vertical tubes, 3.5 inches 0.d., spaced on 7-inch centers. Water flows inside the tubes and the gas mixture flows downward outside the tubes, countercurrent to the water stream. With the terminal conditions of both gas and water streams as in the problem cited, both streams will be moving a t a slow rate and the water below its critical velocity. To condense 9000 pounds of water vapor from 100 pound moles of inert gas entering saturated at 95" C. and leaving a t 40" C., a condenser surface of 6120 square feet would be required
NOMENCLATURE A = area, sq. ft. c = sp. heat at constant pressure, P. e. u./(lb.)(" C.) D = diam. of tube, ft. dA = element of surface area dq = increment of total heat transferred per unit time G = mass velocity through min. cross section, lb./(hr.) (sq. ft.) h = film coefficientof heat transfer, P. c. u./(hr.) (sq. ft.)(" C.); h, refers to the condensate, hd to the dirt film, ho t o the combined conductances other than the gas film, h, to the sensible heat transfer coefficient, hr to dq/(t, - tJdA, h, to the water film j = heat transfer or mass transfer factor (1, 3) k = thermal conductivity, P. c. u,/(hr.) (sq. ft.) (" C./ft.). Izd = diffusion coefficient, sq. ft./hr. K = molar mass transfer coefficient, lb. moles/(hr.)(sq. ft.)(atm.) L = length, ft. M = mol. weight; M , refers to the av. gas compn., M , to the condensable vapor, M,x to the molar latent heat. m = weight flow, lb./hr. P = partial pressure, atm.; p , refers t o the vapor pressure at to p , to noncondensable gas partial pressure in the main body, p,' to that adjacent to the condensate surface, pgf to the log mean of p , and pg', pv to vapor pressure ' q = heat transferred, P. c. u./hr. Re = Reynol? number, D G / p t = temp., C.; t, refers t o gas temp., t , to temp. of condensate surface, t, t o water temp.; At = over-all temp. difference, At, = log. mean of terminal temp. differences u = over-all coefficient of heat transfer, P. c. u./(hr.)(sq. ft.)(" C.) x = latent heat, P. c. u./lb. viscosity, lb./(hr.) (ft.) P = P = density, lb./cu. ft.
LITERATURE CITED (1) Chilton, T. H., and Colburn, A. P., IND.ENQ.CXEM.,26, 1183 (1934). (2) Chilton, T. H., and Genereaux, R. P., Trans. Am. Inst. Chem. Engrs., 29, 161-73 (1933). (3) Colburn, A. P., Ibid., 29, 174-209 (1933). (4) Colburn, A. P., and Hougen, 0. A., Bull. Univ. Wis., Eng. Expt. Sta. Ser. No. 70,81 (1930). (5) Huff, W. J., Chairman, Am. Gas Assoc. Proc., 7, 1147-56 (1925). (6) MoAdams, W. H., "Heat Transmission," p. 185, Figure 72, McGraw-Hill Book Co., New York, 1933. (7) Ibid., p. 263. (8) Tymstra, S. R.,Bull. Univ. Wash. Eng. Expt. Ser. No. 72 (1933).
RIWSIVED September 15, 1934. Presented as part of the Symposium on Diffusional Processes before the Division of Industrial and Engineering Chemistry a t the 88th Meeting of the American Chemical Society, Cleveland, Ohio, September 10 to 14. 1934. This paper is Contribution 145 from the Experimental Station of E. I. du Pont de Nemours & Company; it is a revision of a paper presented by 0. A. Hougen under the title "Condensation of Vapors from Nonoondensing Gases in Surface Condensers" a t the Ithaca meeting of the Society for the Promotion of Engineering Education, June 20. 1934.
CORRECTKON. In the article by Ashraf, Cubbage, and Hunt- note refers to the 7-foot commercial column mentioned in Table ington on "Entrainment in Oil Absorbers" which appeared in the I1 instead of to the 12l/2-inch column. On page 1071, Table 111, CHEMISTRY,section D, the tray spacing should read 16 instead of 15 inches. October number of I N D u s T R u L AND ENGINEERING R. L. HUNTINGTON two minor errors have been found: On page 1069, Table I, foot-
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