INDUSTRIAL AND ENGINEERING
November, 1934
(2) Falkenhagen, H., Physik. Z., 32, 745 (1931).
(3) Hanks and Mcildams, IND. ENQ.CHEM.,21, 1034 (1929). (3A) Harned and Hecker, J. Am. Chem. Soc., 55, 4842 (1933). (4) Harte, Baker, and Puroell, IND.ENQ. CHEM.,25, 528, 1128 (1933). (6) Hatta, S., Tech. Repts. Tihoku I m p . Univ., 8, 1 (1928); 10, 613,631 (1932). (6) Hovorka, F.,J. Am. Chem. Soc., 55, 4899 (1933). (6A) . , International Critical Tables, Vol. V, p . 10,McGraw-Hill Book Co.. New York. 1926. (7) Ledig and Weaver, J. Am. Chem. SOC.,46, 650 (1924); Ledig, IND.ENQ.CHEM.,16, 1251 (1924). (8) Lewis and Whitman, Ibid., 16, 1215 (1924). (SA) Lewis and Williams, Ch.E. thesis, Univ. Va., June, 1934. (9)‘Markham and Benton, J . Am. Chem. SOC.,53,497 (1931). (10) Masaki, J . Biochem. (Japan), 13, 211 (1931); 15,29 (1932). (11) Mitsukuri, Sci. Repts. T h k u Imp. Univ., 18,246 (1929). (12) Mohanlal and Dhar, Z . anorg. allgem. Chem., 174, 1-10 (1928).
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(13) Payne and Dodge, IND. ENQ.CHEIM., 24, 630 (1932). (14) Shchukarev and Bondareva, Ukrain. Khem. Zhur., 7, Wiss. Teil. 1-11 (1932). (15) Taylor, H. J., “Treatise on Physical Chemistry,” Vol. 11, p. 1099, D.Van Nostrand Co., New York, 1931. (16) Weber and Nilsson, IND.ENQ.CHEM.,18, 1070 (1926). (17) Whitman and Davis, Ibid., 18, 264 (1926). (18) Williamson and Mathews, Ibid., 16, 1157 (1924). (19) Willihnganz, MoCluer, Fenske, and McGrew, Ibid., Anal. Ed., 6,231 (1934). (20) Wolf and Krause, Arch. Wtirmewirt, 10, 19 (1929). RECEIVED September 17, 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 a contribution from the Department of Engineering and the Cobb Chemical Laboratory, University of Virginia.
Rate of Mixing of Gases in Closed Containers ALLENS. SMITH,Cryogenic Laboratory, U. S. Bureau of Mines, Amarillo, Texas
The theory of Loschmidt for the measurement of the diffusion coeficient has been applied to determine the time required to approximate complete mixing of a range of binary gas mixtures.
A
MONG the many chemical engineering processes in which gas diffusion is a controlling factor, the mixing of gases is relatively unimportant in plant design, although it must be considered and equipment provided to accomplish it. I n experimental work on the properties or reactions of gas mixtures, however, the subject is of greater importance, as the preparation of samples containing two or more constituents is often required. It is desirable to make up such samples under pressure, using the required proportions of the compressed pure gases, to reduce the labor of frequent preparation and analysis; samples after preparation are usually allowed to stand a few days and are then analyzed. Towend and Mandlekar (7), for example, made up mixtures of butane and air a t 20 to 30 atmospheres pressure, allowed them to stand for 18 hours, and then analyzed them before and after experiments. Campbell (1) prepared samples of methane and oxygen at normal pressure, and “homogeneity in the mixture before analysis was insured by allowing the gases to remain for at least 24 hours after mixing and shaking.” Carpenter and Fox (@, on the other hand, found that the diffusion of carbon dioxide into air is rapid and complete even under extreme conditions. The following pertinent questions are raised: Are repeated analyses of a sample necessary, and if not, what length of time is required for essentially complete mixing? The first question must be considered for a specific mixture. A single checked determination of the composition of a mixture would be representative of the gas, if it were made after mixing was complete, only when liquefaction, polymerization, or reaction either with the container or in the mixture did not occur. I n large vessels the phenomenon of thermal diffusion, which may cause stratification in a mixture and even partial separation, must also be considered. It has been pointed out recently by Keffler (4) that the composition of a gaseous mixture may change because of the effusion of the components more or less in accordance with Graham’s law. The importance of this effect will depend upon the relative
densities of the gases in the mixtures and the size of the orifice through which the gas is discharged. Having decided upon the possibility of the occurrence of these factors which retard or prevent the attainment of a uniform mixture, the second question, that of the time which should elapse between the preparation and analysis of a sample, follows. It does not seem desirable to determine experimentally the conditions by which a uniform mixture of gases may be obtained since the kinetic theory affords a method of calculation which, for all usual purposes, should be sufficiently exact. The reill be maxima under the conditions selected to simplify sults w the calculations.
THE DIFFUSIONCOEFFICIENT I n a cylinder of constant cross section in which diffusion occurs only along the axis of the cylinder, it is assumed that, if a concentration, c, exists a t a point, x, the concentration c dc will be present a t a distance x d x . A concentration gradient prevails between the two points which is equal to dc/dx and causes diffusion as long as i t exists. Fick’s law states that
+
+
de d n = - D A - dt
dx
where dn
amount of substance diffusing through area A in time 02 D = a proportionality constant depending upon the gases in question =
The application of integrated forms of Equation 1 requires a knowledge of the diffusion coefficient, D. Diffusivities may be obtained from the International Critical Tables or estimated by the empirical equation of Gilliland (S). Values of the diffusion coefficient have been reported, and calculation is facilitated for conditions a t 0” C. and 760 mm. pressure. I n changing the values of D12to different conditions of temperature and pressure, the following approximate equation has been used:
a d0
Vol. 26, No. 11
INDUSTRIAL AND ENGINEERING CHEMISTRY
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I
.2
I .4
6- Fu
I
I
,6
.8
I 10
FIGURE1. EFFECTOF PRESSURE ON MOLE-FRACTION DIFFERENCE
- Helium-methane (Do = 0.564) - - - Butane-air (Do = 0 . 8 1 )
in which m h a s a value from 1.75 to 2.0. The binary gas mixtures that were chosen for calculation were of particular interest in connection with work in progress, b u t t h e y represent about the extreme range in D found for the common gas mixtures. I n T a b l e I values for D a t 25' C. and f r o m 1 to 100 atmospheres pressure are assembled, calculated by means of Equation 2, using a value of 1.75 for m.
TABLEI. DIFFUSIOK COEFFICIEXTS AT 25" C. PRESSCREH e N z Atm. 1 0.665 5 0.133 50 0.013 100 0.007
DIFFUSIONCOEFFICIENT Nz-02 H2-CO2 C H r C 0 2 C4Hlo-Air He-CHI 0.216 0.043 0.004 0.002
0.591 0.118 0.012 0.006
0.187 0.037 0.004 0.002
0.094 0.019 0.002 0.001
0.657 0,131 0,013 0.007
RATE OF MIXING The theory of the Loschmidt method for the measurement of diffusion is convenient to apply as a means of determining the rate of mixing. This has been presented by Loeb (6) from which the following derivation is taken. I n Loschmidt's diffusion experiment (6) two cylindrical tubes were placed in a vertical position, separated by a sliding metal plate. A similar arrangement is assumed, the complete cylinder having a length, a,extending from x = 0 to x = a,with only A molecules in the lower half and B molecules in the upper half. When time t = 0, the mole fraction, F , of A molecules = 1 from z = 0 to x = 4 2 ; from x = 4 2 to x = a,no A molecules are present. Since no diffusion takes place through the ends of the cylinder, 6F/6x = 0 a t 2 = 0 and x = a a t all times. The variation of F with time a t each place in the cylinder is given by the Fourier series:
n = l
In the Loschmidt experiments the partition was withdrawn and the gases were allowed to mix for a definite time, after which it was replaced and the contents of each half were analyzed. The average value of F of A molecules in the lower and upper halves of the cylinder, FL and respectively, can be computed in terms of D and t from the series. The difference in the mole fractions then is given as
Pu,
- It is -obvious that when the concentration gradient is zero, FL - F u = 0. The time, t, to reach this condition may be evaluated from Equation 4 by a series of approximations.
Using the data of Table I, this has been done in Table I1 for two gas pairs representing the extremes in their values of the diffusion coefficient, assuming a temperature of 25' C. and a standard 1.528-cubic-foot (0.0432-cubic-meter) compressedgas cylinder in which a = 125 cm. Calculations of the effect of cylinder height a are given in Table 111. TARLE11. MOLE-FRACTION DIFFERENCE AT 25" 125 CN. FL
a =
-Bo.
277.8 hr.
CaHio-Air (Do = 0.081) 0.28 2.78 27.8 277.8 hr. hr. hr. hr.
0.354 0,0002 2 0 0.0002 0 . 7 9 3 0.354 0.012 0.851 0,537
0 . 9 0 4 0 . 7 5 2 0 . 2 4 6 >O 0.930 0 . 9 0 4 0.752 0.246 0 , 9 3 2 0.919 0.824 0.450
H e C H 4 (Do = 0.564)
PRES- 0 . 2 8 SURE hr. Aim. 5 0.793 50 0 . 9 1 4 100 0 . 9 2 3
c. AXD
2.78 hr.
27.8 hr.
OF CONTAINER HEIGHT ON MOLE-FRACTION TABLE111. EFFECT DIFFERENCE
---
(Helium-methane mixture at 250_C., DL = 0.564 CONTAINER PRESFL Fo HEIQHT SURE 0 . 2 8 hr. 2 . 7 8 hr. 2 7 . 8 hr. Cm. Atm. 125 5 0.793 0.354 0.0002 0.029 >0 62.5 0.585 >O >O 31.25 0.215 125 62.5 31.25 125 62.5 31.25
50 50 50 100 100 100
0.914 0.866 0.738 0.923 0.896 0,814
-
0.793 0.585 0.215 0.851 0.707 0.417
0.354 0.029 >O 0.537 0.154 0.001
7
2 7 7 . 8 hr.
>O
>O >O
0.0002
>O
10 0,012 >O >O
The data of Tables I1 and I11 are plotted in Figures 1 and 2 , respectively; the time of mixing is shown to be directly proportional to the pressure and container height, indirectly proportional to the diffusion coefficient, and asymptotic to a zero mole-fraction difference. In applyi n g t h e r e s u l t s of the foregoing calculations, it m u s t b e remembered t h a t , b e c a u s e i n practice there are always some convection currents, the calculations represent the theoretical maximum time inv o l v e d ; while not exact, the results should indicate t h e order of magnitude of t h e time required to approximate complete mixing of different gas pairs under different conditions. It is apparent that, if gases a r e t o b e FIGURE2. EFFECTOF CONTAIXER HEIGHT ON &$OLE-FRACTIONDIFFER- mixed in a container of r e l a t i v e l y great ENCE height and under conHelium-methane (Do = 0.564): - 5 atm. - - - 50 a t m . ; -. - 1 0 0 a t m . siderable pressure it would be d e s i r a b l e to accelerate the diffusion process in some manner. An approximate application of the curves may be made for multigas mixtures by considering the effect of the altered mean free path on the diffusion coefficient. LITERATURE CITED (1) Campbell, J. R.. J. SOC.Chem. Ind.,48, 93T (1929) (2) Carpenter and Fox, J. Biol. Chern., 73, 379 (1927).
November. 1934
I N D U S T R I A L .4ND E N G I N E E R I N G C H E M I S T R Y
(3) Gilliland, E. R., IND. ESG.CHEM.,26, 681 (1934). (4) KefRer, L. J . P., J. Am. Chem. SOC.,56, 1262 (1934). (5) Loeb, “Kinetic Theory of Gases,’’ McGraw-Hill Book Co., New York, 1927. (6) Los&midt, wien. Akad. Bw.,61, 367 (1870) ; c j . Melior, J. W., “Higher Mathematics for students of Chemistry and physics,” p. 491, Longmans, Green 19: Co., London, 1929.
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(7) Towend and Mandlekar, Proc. Roy. Soc. (London), -4141, 484 (1933). RECEIVED October 3, 1934. Presented as part of the Symposium on Diffusional Processes before the Division of Industrial and Engineering Chemistry at the 88th Meeting of the American Chemical Society, Cleveland, Ohio, September 10 to 14, 1934. Published by permission of the Dirertor, U. 5. Bureau of Mines. (Not subject t o copyright )
Packing Materials for Fractionating Columns M. R. FENSKE, C. 0. TONGBERG, AND D. QUIGGLE, Pennsylvania State College, State College, Pa. The many mriables in distillation and in the determination of H. E. T . P. render the drawing of definife conclusions hazardous unless a large number of experiments hare been made. Based only on the results presented here, the following conclusions have been drawn: ( 1 ) New type packing materials give double or triple the eficiency of former packings. (2) The best packings are oneturn and two-turn wire helices, one-turn and twoturn glass helices, carding teeth, and No. 19 jack chain. (3) A n increase in height reduces the eficiency of a packing, the effect being much more
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DESIGKING columns for the fractionation of Pennsylvania gasoline it was found necessary to develop a new type of packing material of a much higher efficiency than any previously used in either laboratory or commercial work. A large number of packing materials have been in use or have been tried (3, 5 , 8, 11, 14, 15, 21). Data on the efficiency of the packings are incomplete, are not always comparable, and fail to take into consideration the effect of the height and diameter of the column in which the test was made. Accordingly, a study was made of various types of packing material. The purpose of the packing in a fractionating column is to bring about as intimate contact as possible between the ascending vapor and the descending liquid without too great a reduction in the throughput or capacity of the column. The vapor-liquid contact or the scrubbing efficiency may be expresqed in terms of H. E. T. P. (height equivalent to a theoretical plate) (10) and is the most important feature of a packing. It has been repeatedly shown (1-5, 17, 18) that to separate close-boiling substances a large number of theoretical plates is necessary. Regardless of any other advantages a packing may have, unless it has a low H. E. T. P. it will not make a good separation. Two other important points are throughput and holdup. A packing, unless it will allow a wperficial vapor velocity under operating conditions of a t least 0.6 foot per second, is of little practical use except in special cases where the time factor is unimportant. The question of holdup has been very well discussed by Podbielniak (11). For a sharp qeparation between two substances the operating holdup should be low. Packed ccilumns occupy an intermediate position between the low holdup of indented and spiral packed columns and the high holdup of bubble cap columns. The operating holdup of various packings is not greatly different. Since very efficient packings have been developed having a large number of plates in a given height, it is possible in making a given separation to reduce considerably the height of packed section necessary and therefore ?;
pronounced with 3/4-in~h(small) diameter columns than wilh 2-inch (large) diameter columns. ( 4 ) An increase in the diameter of a column reduces the eBciency of a packing. (5) Different hydrocarbon mixtures give approximately the same H. E. T. P. value. (6) The effect of the rate of distillation varies with different packings and with the diameter of the column. (7) Laboratory columns made and operated by different persons have given similar results, showing that ejicient ones can be made easily and so that they give reproducible results. the holdup. If, in addition, proper consideration is given to the volume of the charge in relation to the size of the column, the problem of holdup will have been overcome. The study of packing materials was based, therefore, mainly on their H. E. T. P. value under total reflux and their throughput. It is realized that the H. E. T. P. under operating conditions may be different from that under total reflux. However H. E. T. P. values under total reflux can be obtained easily, and, although they do not show the complete picture of fractionation, they are an important guide in studying and designing fractionating columns. It is appreciated that in the final analysis the test of a fractionating column is the actual separation it will make in a reasonable amount of time. The packings found in this work to have low H. E. T. P. values have been in considerable actual use in the chemical laboratories of the Pennsylvania State College and have given sharp as well as complete separation. Figure l is a photograph of the control room for fractionating equipment charging 40 gallons and packed with jack chain.
COMMERCIAL APPLICATIONS The packings studied are of commercial as well as laboratory importance. Several of the packings are already in industrial use. In addition to its plant use, jack chain is used in many semiworks installations. The results obtained here should furnish useful information to the operators of plant and semiworks packed columns and should emphasize the importance of periodic tests of the efficiency of the columns by means of two liquids whose vapor-liquid equilibria are known. Many of the packings used in this work were relatively inexpenqive. The iron carding teeth cost approximately $40 per cubic foot. The cost of the nickel wire necessary to make up one cubic foot of this type packing is about $80. The metal helices were readily made by machine in this laboratory.
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