-1oii
LITERATURE CITED
QI
=
qn
= amount of ion A exchanged and eluted/cycle
(1)
(qs)d
= amount of ion A in column at break-through point = q A / & = ratio of ion A to total exchangeable ions in the solution when the per cent leakage is small = equivalent fraction, dimensionless = q ~ / ( q=~ fraction ) ~ of ion A eluted = fraction of capacity saturated in equilibrium with influent = degree of dissociation of weak acid = concentrations in equivalents/liter
RDCEIVED for review hlarch 29, 103.
TA
X XA
y a
( )
total theoretical capacity-titrated
Exchange-
ultimate capacity
Heister, N. K., and Vermeulen, T., C h a . Eng. Progr., 48, 505-16 (1952). ( 2 ) Kay, J. H., Bregman, J. I., Fradkin, A. ll.,and D'Amico, J. S., I N D . ENG.CHEX., 46, 862-6(1954). (3) Kortschak, H. P., Gill, R. F., Jr., and Payne, J. H., Zbid., 41, 14069 (1949). (4) LIichaels, A. S , Ibid., 44, 1922-30 (1952). ( 5 ) Thompson, R. B., and Roberts, E. J., Chem. Eng. Progr., 43, 97-102 (1947). (6) Vermeulen, T., and Heister, X . K., J. C h a . Phys., 22, 96-101 (1964).
.
,
ACCEPTED November 15, 1954.
END OF SYMPOSIUM
Humidity of Compressed Air E. 31. LANDSBAUICI, W. S . DODDS, AND L. F. STUTXMAN h'orthwestern University, Evanston, 111.
T
HE uses of high pressure air are many and varied, and often it is necessary to reduce the water content of such air before it can be used. For the design of dehumidification equipment, knowledge of the equilibrium water content of air as a function of temperature and pressure is desirable. A simple presentation in chart form is usually adequate for most calculations and such a chart has been prepared, Figure 1, based on information on the water content of air and on the water content of other gases. Articles relating to this subject were investigated and considered, and although not all are referred t o specifically in this discussion, they are listed in the references. To date, experimental evidence has shown the water content per volume of compressed gas to increase with pressure, a t parameters of constant temperature. There is still a decrease in the weight of water per weight of compressed gas with an increase of pressure, but this decrease is less than would be calculated with the assumption that the vapor pressure of water does not change with total pressure. Pollitser and Strebel (IS) measured water-gas equilibrium at 122" and 158" F., a t pressures t o 3000 pounds per square inch, and with air, hydrogen, and carbon dioxide as the gas phase. The water content of the compressed gas increased much more for carbon dioxide than for air; that of hydrogen was slightly less than that for air. Bartlett (1) measured the equilibrium water content of nitrogen, hydrogen, and a mixture of the two a t 25", 37.50", and 50" C. and a t pressures t o 1000 atm. Saddington and Krase (17) determined water-nitrogen equilibrium at 100, 200, and 300 atm. and a t temperatures between 50" and 230' C. They determined the composition of both the liquid and the gas phases. Laulhere and Briscoe (8) studied the water content of California natural gas a t pressures to 500 pounds per square inch and at temperatures between 60 O and 100 O F. Deatori and Frost ( 5 ) did the same for a Texas natural gas and for air at pressures to ti00 pounds per square inch and at temperatures between 40' and 100' F. Olds, Sage, and Lacey ( I d ) studied the water-methane system and Reamer, Olds, Sage, and Lacey (16) studied the water-ethane system both a t pressures to 10,000 pounds per square inch and a t 60' intervals from 100" to 460" F. Russell, Thompson, Vance, and Huntington (16) measured the water content of an Oklahoma natural gas a t 1000, 1500, and 2000 pounds per square inch in the temperature range 50 O to 95 F.
January 1955
Webster (19) measured the water content of air a t -35 ', -20 ', 0", and 15' C. a t pressures to 200 atm. The data of Bartlett for nitrogen and that of Pollitser and Strebel for air, both a t 50" C. agree well in the range they both cover. Their data and that of Webster, when plotted versus temperature with parameters of pressure, give consistent results. The data of Saddington and Krase do not agree with these studies, although they claim their experiments were performed with greater accuracy. Theoretical correlations were made by many investigators. As early as 1881 Poynting ( I C ) pointed out that the vapor pressure of a liquid a t constant temperature should increase as the pressure impressed on the liquid from an inert gas increases. He presented the equation
This principle has been confirmed by others, although most data presented to date show a greater change of vapor pressure with pressure than that predicted by Poynting's equation. In general, the deviation increases as the inert gas deviates from an ideal gas. Fischer (4) derived equations for the equilibrium composition of water-air mixture by means of Gibbs' potential. H e calculated volume and weight per cents at different pressures which agreed with Knoblauch's (6)data. McHaffie (9-21) calculated activity coefficients for water from the data of Pollitxer and Strebel and later conducted experimental work t o 100 atm. Van Laar derived thermodynamic equations by which he esplains the results of Bartlett. Kritschewsky and Hasanova (7) proposed equations t o account for data of Bartlett, Saddington and Krase, and Pollitzer and Strebel. They have concluded that Van Laar's correlation of 13artlett's data is not based on consistent facts but rather is strictly a coincidence. According t o their theory, the vapor content will pass through a minimum and then increase as the prepsure of the impressed gas is increased. This minimum apparently is approached at about 1000 atm. which is the upper limit of Figure 1. Hammerschmid correlates experimental data on the water content of ethane, methane, air, and natural gas in one chart. The water content of hydrocarbon gases gives good correlations a t pressures below 2000 pounds per square inch, the data on the water content of air deviating slightly. The data of Olds, Sage,
INDUSTRIAL AND ENGINEERING CHEMISTRY
101
102
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 47, No. P
and Lacey on the water content of methane gas apparently was used for preparing the high pressure regions of the chart. At preseures above 2000 pounds per square inch and temperatures below 200 F the water-carrying capacity of the various gases is so different that it becomes difficult to correlate all data in one chart. At 9000 pounds per square inch and about 100" F. the mole fractions of n a t e r in ethane, methane, nitrogen, arid hydrogen are in the ratio of 6 : 4 : 3 : 2 Thus, for accurate work a t these highei pressures, experimental data on the particular gaj in question are required. CONSTRUCTION OF CHART
T h e experimental dat,a on water-air equilibrium are available in the literature a t constant temperature from - 3 1 " to 158" F., covering most of the temperature range of interest, but a t pressures to 200 atm. only. Therefore, an extrapolat,ion of the available data to highel. pressures was necessary. The experimental data from the literature on the equilibrium betneen n-ater and methane, ethane, nitrogen, and hydrogen, all a t constant temperature and a t preasures to 10,000 pounds per square inch, were plotted as the function, I." = .\-P/pO, against pressure, with parameters of temperature, and apparently yield straight lines. In this equation, F is a is inole fracfunction of the nonidealit,y, tion, P is total pressure of the syst>em,and p , is the vapor pressure of the rvater under its own vapor pressure. All data gave consistently straight lines except, that of wateret,hane at 100" F. ( 1 5 ) ; this exception may be due t o the nearness of ethane to its critical temperature, 90" F. The other gases are a t temperatures further removed from their crit,ical temperatures, and therefore estrapolation of the low pressure data on the water content of air to higher pressures is somewhat, justified. The available experimental data on xat,erair were plotted as F versus pressure, with parameters of constant temperature, where F = ArP/p0. Straight line extrapolations to 1000 atm. were made. Interpolation between lines was also made. Values of F were then t,aken from these plots, the equation was solved for N, then converted into the more usable units of pounds of water per pound of air. The function, F , has no sbrict t'heoretical basis but serves mainly to express the deviation of the actual vapor from the pure liquid under its own vapor pressure as a dimensionless quantity. Other dimensionless quantities that have been used in the literature for plotting the experimental data are p / p o and X / X ~ . These quantities did not give st,raight lines when plotted against pressure. Also, knowing F allows the calculation of water content from N , whereas if p / p ~or x / x O is known, the gas densitmy is also required. The relation between these three quantities is
F l z = p/po
= 2/28
INDUSTRIAL AND ENGINEERING CHEMISTRY
January 1955
where z is the compressibility factor of the impressed gas a t the stated conditions. F is 1 a t P = PO,increasing as P increases. T h e equation of line F versus P can then be written
F
=
NP/p, = 1
+ C(P - Po)
where C is a function of temperature, increasing with decreasing temperature. It follows from this equation that N / p 0 is linear in 1 / P and that, when the equation holds, the minimum water content is a t the maximum pressure. Attempts to find a generalized correlation for all gases were unsuccessful. These consisted mainly of trying to correlate F , C, and p / p o as functions of the reduced temperature and pressure of the impressed gas. D a t a were not available a t a sufficient number of temperatures to allow anything more complex. Data at other temperatures, particularly lower temperatures where the effect of pressure is more pronounced, are necessary. Usually any general correlation is based, in part, on theory. The theory of the phenomena discussed in this article is a t present not clear. It is to be expected, therefore, t h a t when a theory is advanced that will satisfactorily explain the data thus far encountered, a general correlation will be possible. CONCLUSION
T h e chart can be used directly t o determine the JTater content of saturated high pressure air, t h e dew point of such air when the pressure is reduced, and other applications. Copies of the chart may be obtained from the Library of Congress; see notice a t end of article. ACKNOWLEDGMENT
The authors wish t o thank G. M. Brown, B. J. Sollami, and W. F. Stevens for their aid in assembling the data and Lowell Koppel, who made many of the calculations. T h e chart and data presented here were prepared for use in a research project sponsored by the Wright Air Development Center. We wish to express our appreciation t o them for permission to publish this information.
103
NOMENCLATURE
C F
N P p
PO
= constant, function of temperature only = function of water content of air = N P / p , =
mole fraction
= total pressure of system = vapor pressure of water = vapor pressure of water under its own vapor pressure
V L = molal volume of liquid water a t P Vu = molal volume of water vapor a t p = weight of water vapor per unit volume a t P 2 20 = weight of water vapor per unit volume a t p o z = compressibility factor REFERENCES
(1) Bartlett, E. P., J . Am. Chem. Soc., 49, 65 (1927). (2) Deaton, W.Nl., and Frost, E. XI., Jr., Am. Gas. Assoc. P r o c . , 22, 187 (1940). (3) Deaton, W. N., and Frost, E. hl., Jr., Am. Gas. J . , 155,No. 4, 61 (1941). (4) Fischer, V., 2. tech. Phus., 6, 192 (1925). ( 5 ) Hammerschmid, E. G., Am. Gas J., 165, No.2, 21 (1946). (6) Nnoblauch, O., Raisch, E., and Hausen, H., “Tables and Diagrams for Water Vapor,” Oldenbourg, Berlin, 1923. (7) Kritschewsky, I. R., and Hasanova, N. E., A c t a Physicochens. (U.S.S.R.), 10, 199 (1939) (in English). (8) Laulhere, B. M., and Briscoe, C. R., Gas, 15, No. 9, 21 (1939). (9) McHaffie, I. R., Phil. Mag., 1 (7), 561 (1926). (10) Ibid., 3 ( 7 ) ,497 (1927). (11) Ibid., p. 505. (12) Olds, R. H., Sage, B. H., and Lacey, W. N., IND.ENG.CHEai., 34, 1223 (1942). (13) Pollitzer, F., and Strebel, E., 2. physik. Chem., 110,768 (1924). (14) Poynting. J. H., Phil. Maa.. 12 (4).32 (1881). (15) Re;mer,H. H., and associates, I N D . ENG. CHEM.,35,790 (1943). (16) Russell, G. F., Thompson, R., Vance, F. P., and Huntington, R. L., Am. Inst. Mining Met. Engrs., Tech. Publ. 1792, 1945. (17) Saddington, A. W., and Krase, N. W., J . Am. Chem. Soc.. 56,353 (1934). (18) Van Law, J. J., 2. physik. Chem., 145A, 207 (1929). (19) Webster, T. V., J . Soc. Chem. Ind. (London),69,343 (1950). RECEIVEDfor review M a y 19, 1954. ACCEPTED September 7, 1954, Figure 1 of this article has been deposited as Document number 4407 with the AD1 Auxiliary Publications Project, Photoduplication Service, Library of Congress, Washington 25, D. C. A copy may be secured b y citing t h e Document number and by remitting 51.25 for phot,oprints, or 81.25 for 35 mm. microfilm. Advance payment is required. Make checks or money orders payable to: Photoduplication Service, Library of Congress.
Vapor-Liquid Equilibria of Formaldehyde-Meihanol-Water STANLEY J. GREEN1 AND ILAYlMOND E. VENEK Drexel Institute of Technology, Philadelphia, Pa.
T
HE commercial importance of formaldehyde is indicated
by the tremendous expansion in the production of this vital low-cost chemical intermediate over the past two decades. The total manufacturing capacity of plants in the United States alone is already well over a billion pounds per year. Formaldehyde is still produced principally from methanol. I n plants producing formaldehyde by the catalytic oxidation of methanol, the gaseous mixture leaving the converters contains unreacted methanol, formaldehyde, water, and noncondensable gases (26,SO). This gaseous mixture is scrubbed with water t o recover the methanol and formaldehyde and the resulting aqueous solution is fractionated to separate methanol and t o produce a marketable grade of formaldehyde. Vapor-liquid equilibrium and boiling point data of the related binary and ternary systems 1
Present address, Westinghouse Electric Corp., Pittsburgh, P a .
are desirable for the design of absorption and distillation equipment. This study was limited to solutions of less than 50% formaldehyde, as solutions containing more than this are rarely encountered in commercial operations. The entire range of compositions for the methanol-water system was studied to define experimental techniques; the formaldehyde-water system was investigated because of the varied results presented in the literature. The ternary system was studied at all methanol-water ratios and a t formaldehyde-water ratios ranging from 0 t o 1. Throughout this paper the term “azeotrope” is used t o designate mixtures of two or more liquid compounds, also referred to as “constant boiling mixtures,” the boiling point of which does not change as vapor is generated and removed. I n the systems discussed, the compositions of the liquid and gas phases are not identical. Furthermore, relatively slow chemical reactions are
