SIMULTANEOUS CONDENSATION OF METHANOL AND WATER FROM A NONCONDENSING GAS ON VERTICAL TUBES IN A BANK J A M E S
T. S C H R O D T ' A N D E A R L R . G E R H A R D
Chemical Engineering Dejartment, University of Louisbille, Louisuille, Ky.
40208
Experimental dlota were obtained on the condensation of water and methanol from a n air stream in turbulent flow across vertical cylinders. The composition of the condensed phase and heat flux were measured. A mathematical model, requiring d a t a on the pure components plus vapor-liquid equilibrium data, was used to predict the measured results.
HE presence of noncondensable gases in vapors has for many T y e a r s been troublesome to engineers in their efforts to design cooler-condensers. Evaluation of thermal properties at the gas-liquid interface and heat and mass fluxes along the condenser's surface are the principal difficulties encountered in design procedures. I n a previous study by the authors (Schrodt and Gerhard, 1965), rate data \cere obtained on the transfer of sensible heat from air and \cater vapor condensing from saturated air streams flolcing across five short tubes vertically aligned in a staggered manner in a duct. Thej-factors calculated from these data were successfully correlated tvith the gas-phase Reynolds number, and it \vas concluded that Chilton's and Colburn's j-factor analogy is valid for the cross-flow geometry. At the start of this project, no studies had been reported on the condensation of more than one vapor from a noncondensable gas, and it was felt that such a study was needed to verify suggested design calculational procedures. '11vo papers have appeared subsequently on multivapor condensation from noncondensable gases. Porter and Jeffreys (1363) studied the condensation of ethanol and \cater from air and nitrogen on a horizontal, single-tube bafRed cross-flolc condenser. For this system the vapor composition in equilibrium with a given liquid composition is practically independent of the pressure. This allo\ved the liquid-gas interface temperature to be directly related to the pressure over a limited composition range. T h e design procedure of Hulden (1953), modified for binary condensation, \cas used to predict the average temperature and composition of the condensate in finite increments along the condensing surface. Unfortunately, in modifying the original equation the value of E', the logarithmic mean partial pressure of the inert gas, \cas improperly defined. I t incorrectly included the pressure of the other condensing vapor. T h e design procedure also requires a graphical solution. Mizushina and his co\corkers (1 964) undoubtedly recognized the shortcomings of Porter and Jeffreys' method and proposed instead a simplified three-point method based upon the inlet, outlet, and center point conditions in their single, vertical tube condenser. Although their method predicted over-all transfer areas Lcithin +2O7, accuracy for a number of three-
Present address, University of Kentucky, Lexington, Ky. 40506
R O W 12 '
ROW 9
Figure 1 .
ROW 8
ROW 7
'
ROW I
Layout of tubes in condenser
and four-component systems, no experimental results were obtained on conditions existing at specific points in their condenser. The main objective in the present \cork \cas to study the condensation of methanol and icater from air streams flolving across vertical cylinders in a compact arrangement closely resembling a differential section of a much larger condenser. Of greatest interest \vas the effect of various vapor concentrations in the mixture on the condensate's composition, the individual heat and mash transfer rates, and the validity of assuming no interaction of mass fluxes and the existence of interfacial equilibrium. Experimental
Apparatus. T h e condenser was constructed with five 10.0 X 0.73 inch 0.d. brass tubes aligned upright on 1.625-inch triangular pitches behind 7 ro\cs of false tubes in a 3.25 X 10.0 X 120.0 inch insulated duct. Three roLvs of false tubes \vere positioned doivnstream from the condensing tubes. Inside the condensing tubes. \vhich ivere sealed at their lower ends, smaller tubes of 0.50-inch 0.d. \\'ere used to increase the coolant velocity and the water-side heat transfer coefficient. All tubes had 0,0358-inch wall thicknesses. T h e total heat transfer area of the condenser was 0.82 sq. foot, and the minimum flo~varea for the gas mixture \vas 0.12 sq. foot. The arrangement of the tubes is shown in Figure 1 , T h e false tubes in front of the condensing tubes generated a uniform turbulence in the condenser. Vertical arrangement of the tubes permitted condensate to be collected from each tube, Tveighed, and analyzed. T h e run-off temperatures bvere measured continuously and a large portion of the tube's surVOL. 7
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so as tu minimize changes in stream properties. Less than 10% of the two vapors in the mixture was condensed in all cases, and nearly equal rates, run-off temperatures, and compositions from each condenser tube were noted. All properties and rates were arithmetically averaged over the section.
r? flat I
I
Results
A complete set of the experimental results is available (Schrodt, 1966). Data from the methanol-air studies were used to calculate j-factors. These, along with the previously reported results on air and water-air (Schrodt and Gerhard, 1965), are presented in Figure 3. The line of minimum deviation through the points is represented by the equation
1
TC
n
jH= jD= 0.79 Re-0.415
Figure 2. 1. 2.
3. 4. 5.
6.
7.
Schematic diagram of apparatus
Blower Flow control Orifice meter Manometer Preheaters Feed tanks Pumps
8.
9. 10. 11. 12. 13.
Rotameters Vaporizer Demisters Duct Condenser Coolant bath
faces could be seen through a plastic window in the side of the duct. This window was covered with insulation during the test runs. T h e condenser was equipped with all the necessary instruments for the experiments, as shown in Figure 2. Operation. Before the two vapor- as system was investigated, six runs were made using mettanol and air. These were made in identical fashion to the water-air studies of Schrodt and Gerhard (1965), except that the air was never saturated with the methanol. Twelve runs were made with methanol-water-air. For each, the mixture’s temperature was recorded at the inlet and outlet of the condenser. The inlet partial pressure was calculated from the liquid vaporized, the air rate, and total pressure; and the outlet partial pressure was calculated from these values adjusted for the condensation of vapors. Temperatures of the condensates were determined from thermocouples, and the liquid samples collected over timed intervals were weighed and analyzed by a chromatograph. T h e coolant’s inlet and outlet temperatures and flow rate were recorded, so that the total heat transferred to the coolant could be calculated. T h e condenser was successfully operated as a differential section of a much larger condenser by adjusting flow conditions
(1)
Heat transfer data obtained by Snyder (1953) from tubes in rows 8, 9, and 10 of a 10-row bank of equilateral staggered tubes, and mean data collected by Bergelin et al. (1952) over a 10-row bank of tubes, are also presented for comparison with the data of the authors in Figure 3. For the methanol-water-air experiments, individual heat and mass transfer rates were calculated from the measured d a t a which are presented in Table 1. Latent heat rates of methanol and water were calculated from the condensation rates, with the A’s taken at the gas stream temperature, To. With this approach the subcooling of the condensate had to be evaluated over a temperature change of T , to T,, the condensate run-off temperature. Heat transfer resulting from liquid mixing was negligible (Benjamin and Benson, 1963). Gas-phase sensible heat was calculated from a weight average heat capacity of the gas mixture with adjustment for loss of vapor from condensation. These heat transfer rates are presented in Table 11, and their summation is compared with the enthalpy gained by the cooling water in Figure 4. T h e condenser tubes were polished with emery paper and rinsed with a caustic solution in an effort to promote film condensation. I n the water-air and methanol-air experiments this treatment successfully promoted uniform film condensation ; however, irregular or “roping” films developed in the methanol-water-air tests, predominantly on the tube surfaces facing upstream. Along vertical lines estimated to be
0.03
0.0 2
-7
0.0 1
0.005 2000
10,000
5000
20,000
Re Figure 3.
X 0 0
A ’
282
IO00
Heat transfer Water condensation Methanol condensation Snyder (1 9 5 3 ) Bergelin ef of. ( 1 9 5 2 )
I&EC FUNDAMENTALS
3000
1500
Heat and mass transfer correlation
Q,
Figure 4. Comparison of transfer to coolant
QE
5000
(01 u/hrl
and
0 QE 0 QP
QP
with rate of heat
Run
GI,
Gz,
Gas Mixture GI,
No.
lb./hr.
lb./hr.
lb./hr.
1 2 3 4 5 6 7 8 9 10 11 12
11.6 17.9 22.0 19.2 23.7 19.9 15.6 23.6 35.8 35.0 29.2 40.5
31.5 47.3 13.6 25.2 23.7 13.6 13.6 13.6 24.4 16.6 14.0 13.6
338 312 325 334 315 343 433 433 315 336 235 336
F. 178.0 182.6 172.1 170.2 176.0 152.2 148.9 148.0 179.7 167.0 168.9 154.4
Table 1.
Measured Data
( T )out, BF. 166.4 172.3 159.1 158.7 165.0 141.0 139.3 138.4 167.0 154.4 158.2 143.4
PT,mm. HE 748.0 748.0 748.5 748.1 748.0 747.2 750.1 750.1 748.3 751.0 755.2 747.2
Cooling Water W, (tw)in, (t,)out, F. F. !b./hr. 253 79.1 61.3 258 65.6 86.2 258 60.2 71.6 254 59.9 74.5 261 62.7 77.7 256 60.0 67.0 256 63.2 70.2 256 62.4 69.6 250 62.4 72.9 256 62.0 72.9 256 67.0 76.5 256 61.0 68.7
Condensate
N, 16 ./hr . 2.866 3.815 1.462 2.109 2.532 0.540 0.612 0.844 1.415 1.415 1.154 0.840
Tc, 21
OF.
0.059
87.5 84.1 78.8 81.9 86.5 80.1 84.6 86.5 87.5 87.5 79.0 80.7
0.081
0,084 0.120 0.131 0.133 0,134 0.151 0.216 0.216 0.230 0.285
Table II. Calculated Data
Run No. Re 1 4243 2 4421 3 4070 4 4327 5 41 67 6 431 2 7 5156 8 5304 9 4362 10 4477 11 3260 12 4588 B.t.u./hr. sq. f t . OF. Lb. molelhr. sq. f t . atm.
u O a
54.6 63.9 36.1 46.4 47.6 26.3 28.2 29.1 35.7 36.5 32.3 28.6
hoa 15.9 15.1 14.1 14.6 14.4 14.2 15.7 16.0 14.8 14.7 12.2 14.6
k,ib 2.00 2.05 1.76 1.87 1.85 1.77 1.93 1.98 1.95 1.90 1.60 1 .90
k2,b
2.64 2.73 2.35 2.49 2.47 2.37 2.59 2.66 2.60 2.54 2.14 2.55
where the gaseous boundary layers separated from the tube surfaces, rivulets of liquid were observed to flow down the tubes. I n runs 1 through 5, where the condensation rates were highest and the condensates were principally water, the films were more stable than in the other runs. Always the tubes appeared to be thoroughly wetted. Formulated Model. T h e proposed model is one that predicts an interfacial temperature, T,, mole fractions of methanol and water in the condensate, x 1 and (1 - X I ) , interfacial partial pressures of methanol and water, P,1 and P,z, and heat and mass transfer rates in the condenser. Colburn and Hougen’s (1934) design equation for a pure vapor condensing from gases was modified for a two vapor-gas system as follows:
+ cLI(Tg - Td1 + ~ , z M z ( P O- P,)Z[X,Z+ C L Z ( T~ Tc)]
k,lM1(Pg
QW
- P,)l[Xgl
(2)
This equation neglects any heat transfer resulting from liquid mixing in the condensed phase and interaction of the mass fluxes. Sensible heat transfer f:rom the diffusing species is coupled to the mass fluxes in Equation 2; and the coefficients h,, kol, and koZ were related by Chilton’s and Colburn’s j-factor analogy and calculated from the author’s empirical correlation in Figure 2. T h e logarithmic mean partial pressure of the nondiffusing air applied to k o l and k,z was taken as
4503 5321 2949 3696 3918 1792 1791 1845 3080 2789 2429 1971
Heat Rates, B.t.u./Hr. Qxl QX2 Qd 132 2566 1156 237 3273 1078 101 1244 1222 199 1762 1151 247 1990 1068 55 430 1087 64 494 1124 96 650 1140 270 1654 1212 218 951 1290 176 777 789 165 496 1131
QC
234 337 122 163 201 33 34 44 186 91 85 48
I n this equation the summations apply over the condensing components only. T h e mixture’s flow rate, G, temperature, T o , and partial pressures, Pol and P,z, and the coolant’s flow rate, W , and its temperature, t,, were taken as the average values from each experimehtal run. I n Equation 2 the value of T , was taken equal to T,, because T , is generally unknown in most coolercondenser design problems. T h e value of h,’ was taken as a combination of the condensed liquid, tube wall, and coolant coefficients. T h e theoretical equation of Nusselt (1916) for predicting heat transfer through a laminar falling film on a vertical surface was used to predict a mean condensed liquid film coefficient. This coefficient varied from 1250 to 2500 B.t.u./hr. sq. ft. OF. for all runs. The coolant film coefficient, which was practically constant at 205 B.t.u./hr. sq. ft. O F . for all runs, was evaluated from sensible heat transfer data taken at the end of the methanol-waterair studies. T h e remaining unknowns in Equation 2 were T,, PSI, and PS2. Interfacial equilibrium, which is frequently applied to pure vapor-gas systems (Colburn and Hougen, 1934; Ivanov, 1962; Renker, 1954) and binary vapor systems (Kent and Pigford, 1956), was assumed to apply to this binary vapor-gas system. Since the weights and compositions of the condensate samples collected from the five tubes were nearly equal and the thermal resistances of the condensate films were very small, it was assumed that there was negligible variation in the compositions along the tube surfaces, and a state of equilibrium existed a t the interface. Consequently, the terms PSI and P,z were related to the condensate mole fraction, x , and the vapor pressures of the condensables at T , by the expressions
P,1 = YIXIP1°
VOL. 7
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Table 111.
Interface
Run No. 1 2 3 4 5 6 7
p.1,
ho'a
188.75 190.65 188.35 186.23 189.76 187.04 192.17 8 188.79 9 180.42 10 181.94 11 181.81 12 176.91 B.t.u./hr. sq. f t . OF.
T d ,"F. 95.46 108.95 80.49 88.86 90.94 77.20 77.50 77.73 92.63 84.99 88.70 81.12
M m . Hg 15.81 23.88 32.26 25.87 32.78 27178 19.66 28.85 47.46 47.78 54.01 53.46
Paz, 40.57 60.57 22.30 31.34 32.73 20120 21.55 20.47 32.64 24.20 27.11 19.68
T h e activity coefficients, 71 and 72, in these equations are functional with T,, XI, and the total pressure, P. Logarithms of the activity coefficients a t infinite dilution were evaluated a t T , from the following equation (Van Ness, 1964)
Predicted Data Condensate N, lb./hr. x1 0.054 3.099 4.520 0.044 1.477 0.178 2.624 0.091 2.596 0.126 1.468 oli63 0.896 0.099 1.085 0.170 3.031 0.180 2.050 0.225 2.156 0.230 2.031 0.310
Heat Rates, B . t . u . / H r . QP
QXI
QA2
Qa
Qc
4144 5448 2351 3502 3431 21% 1743 1865 3759 2730 2642 2492
134 157 191 184 245 179 70 138 393 325 349 427
2790 4144 1066 2227 2060 1102 759 806 2165 1357 1408 1141
991 847 983 905 939 805 859 857 985 915 749 813
229 299 111 185
5.0
10.0
189 ~~
91 56 63 216 133 137 111
20 0
10 0
Coefficients at infinite dilution and To = 25.0 O C . were available from the methanol-water equilibrium data of Butler e t al. (1933). These data were thermodynamically consistent and fitted the Van Laar equation exactly. Heat of solution d a t a a t infinite dilution for methanol in water and water in methanol were available in the desired temperature range (Benjamin, 1963). Coefficients obtained from Equation 6 were then used to calculate activity coefficients a t the required x's from the V a n Laar equation. Apparently, one additional equation was needed to relate mole fraction x to the mass fluxes, and this was provided by the equation
5.0
3 0
2 0
I .o 1.0
2.0
30
20.0
Pae-Pse Pal -Psi
Figure 5. Correlation of liquid-phase concentrations according to Equation 7
With the given conditions the composition of the condensates, and Ps2,and all the heat and mass the interfacial values T,, Psi, transfer fluxes were computed from Equations 1 through 7 . These equations are nonlinear and could not be solved explicitly; therefore, a double iterative procedure was used with a digital computer. This iterative procedure converged rapidly to the solution. T h e fluxes computed in this procedure were then multiplied by the total surface area of the tubes to provide the transfer rates. These results are presented in Table 111. Discussion
Although the coolant and gas-phase sensible heat transfer coefficients did not vary appreciably throughout these studies, the over-all heat transfer coefficients varied from 26.3 to 63.9 B.t.u./hr. sq. ft. O F . The presence of air in the methanol and water vapors lowered the rate of condensation and heat transfer from that which is normally experienced in pure vapor condensation. Formation of a flowing semipermeable layer of air around the tubes owing to the condensation of vapors a t the interface lowered the partial pressures, PS1and Psz,and the temperature, T,, and these conditions were maintained by the steady diffusion of vapors from the main stream under the potentials (P,- P,)l and ( P , T h e irregular characteristics of the condensing films was attributed to surface tension effects resulting from the high rate 284
l&EC
FUNDAMENTALS
of heat transfer through the films and not to any surface characteristics of the tubes. This conclusion is supported by the findings of Molstad and Parsly (1950), Pratt (1951), and Norman (1954). They found that when heat is transferred from a flowing gas to thin moving liquid films, instability and uneven flow resulted with breakdown of the films into rivulet flow. T h e experimental results may be used to assess the reliability of the formulated model. T h e authors assumed that a condition of thermal equilibrium existed at the interface and interaction of the mass fluxes was negligible. If these assumptions were valid, according to Equation 7 a plot of log (1 - x ) / x us. log (Po- P,)z/(P,- P,)l a t a constantvalue ofkpz/kol should be a line of slope 1. T h e ratio kos/kol, which varied slightly with (D1/Dz)2'3,-hasa mean value of 1.34 with a standard deviation of 0.0025. In Figure 5 the line has a slope of 1 and an intercept of 1.34; the data points fall along this line, indicating that the average condensate compositions were predicted by the equilibrium data at T , and the methanolwater-air system displayed negligible interaction of the mass fluxes. Summations of the predicted heat transfer rates compare favorably with both the sum of the experimental rates and the enthalpy gained by the coolant as indicated in Figure 4 ; however, a less favorable comparison exists between the predicted and experimental rates of condensation.
?‘he ratio of the experimental rate of condensation to the predicted rate varied from 0.37 to 0.99 with a mean of 0.71. At first it was suspected that the initial assumption of negligible mass flux interaction was invalid; however, it was discovered that methods which purport to account for interaction predicted rates of mass transfer slightly greater than when the interaction effect was disregarded, and this increased the discrepancies. I t was finally conclluded that the mathematical model had not properly accounied for the heat transfer through the unstable and asymmetric condensate films and had, in some cases. actually predicted an interface temperature 1’ or 2’F. lower than the true average temperature. Because partial pressures P,Iand Ps2 are directly functional with temperature T,, their computed values were too low, and consequently, the predicted mass transfer rates were too high. However, in runs 1 through 5 , where the condensate films were more stable, the predicted rates were in better agreement with the experimental rates. For ihese runs the ratio was 0.91.
PT
Conclusions
o s
The rate of condensation and composition of the condensate in a multivapor-gas condensation process are functions of the main stream composition, mass transfer coefficients, and interface temperature. For systems where mass, flux interaction is negligible, binary mass transfer coefficients calculated from a suitable correlation of j us. R e can be used to predict the mass fluxes. T h e concept of interfacial equilibrium can be applied to multivapor condensation from gases, provided heat transfer through the condensate film can be predicted with moderate accuracy.
1
Nomenclature
logarithm of activity coefficient a t infinite dilution, dimensionless surface area. sq. Ft. heat capacity of liquid, B.t.u./lb. O F . diffusivity, sq. ft./hr. gas flow rate, lb./hr, hrat of solution at infinite dilution, B.t.u./lb. mole gas-phase heat transfer coefficient, B.t.u./hr. sq. ft. OF. combined heat transfer coefficient of condensate, tube and coolant, B t.u./hr. sq. ft. OF. diffusion factor heat transfer factor mass transfer coefficient, lb. mole/hr. sq. ft. mm. H g molecular weight, lb./lb. mole condensation ratr, lb./hr. partial pressure, mm. Hg logarithmic mean partial pressure of inert, mm. Hg
Po QE
QE Qp Q8
= = = =
= =
Qtu =
Qx q
R
Re
T, T, T, t,
U, W x
X y
= =
= = = = = = = = = = =
total pressure, mm. H g pure vapor pressure, mm. H g heat transfer rate of condensate, B.t.u./hr. sum of experimental heat transfer rates, B.t.u./hr. sum of predicted heat transfer rates, B.t.u./hr. heat transfer rate of gas mixture, B.t.u./hr. rate of heat transfer to coolant, B.t.u./hr. latent heat transfer rate, B.t.u./hr. heat flux, B.t.u./hr. sq. ft. universal gas constant, 1.987 B.t.u./lb. mole OR. Reynolds number, dimensionless condensate temperature, OF. mixture temperature, OF. interface temperature, OF. coolant temperature, OF. over-all heat transfer coefficient, B.t.u./hr. sq. ft. OF. coolant flow rate, lb./hr. mole fraction latent heat of Condensation, B.t.u./lb. activity coefficient
SUBSCRIPTS i = vapor species
2 3
= datum state = interface = methanol = water
= air
literature Cited
Benjamin, C. Y . , Can. J . Chem. Eng. 37, 193 (1963). Benjamin, H., Benson, G. C., J . Phys. Chem. 67, 858 (1963). Bergelin, 0. P., Brown, G. A , , Doberstein, S. C., T r a m . A m . Sod. Mech. Eners. 74. 953 (1952). Butler, J. A. V., Thomson, D. W., Maeleman, W. H., J . Chem. Sod. 55, 674 (1933). Colburn, A. P., Hougen, 0. A., Ind. Eng. Chem. 26, 1178 (1934). Hulden, B., Chem. Eng. Sci. 7, 60 (1959). Ivanov, M. E., Intern. Chem. Eng. 2, 282 (1962). Kent, E. R., Pigford, R. L., A.I.Ch.E.J. 2, 363 (1956). Mizushina, T., Ishii, K., Ueda, H., Intern. J . Heat Mass Transfer 1, 95 (1964). Molstad, M. C., Parsly, L. F., Chem. Eng. Progr. 46, 20 (1950). Norman, W. S., Trans. Inst. Chem. Engrs. (London) 32, S1, S14, S15 (1954). Nusselt, W., Z. V u . deut. Ing. 60, 541 (1916). Porter, K. E., Jeffreys, G. V., Trans. Inst. Chem. Engrs. (London) 41, 126 (1963). Pratt, H. R. C., Trans. Inst. Chem. Engrs. (London) 29, 195 (1951). Renker, W., Ph.D. dissertation, Dresden Institute of Technology, Dresden, Germany, 1954. Schrodt, J. T., Ph.D. dissertation, University of Louisville, Louisville, Ky., 1966. Schrodt, J. T., Gerhard, E. R., IND.ENG.CHEM.FUNDAMENTALS 4, 46 (1965). Snyder, N. W., Chem. Eng. Progr. Symp. Ser., No. 5, 49, 11 (1953). Van Ness, H. C., “Classical Thermodynamics of Nonelectrolyte Solutions,” p. 134, Macmillan, New York, 1964. RECEIVED for review March 29, 1967 ACCEPTED January 11, 1968
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