October 1955
INDUSTRIAL AND ENGINEERING CHEMISTRY
these rates are considerably less than the corresponding absorption-per-mass rates obtained in the present investigation. The agreement is better at the lower temperature, as expected from diffusion theory. SUMMARY
Oxygen uptake measurements on polyethylene resin a t approximately 1-atm. pressure of oxygen have revealed the following facts. The oxidation reaction has a pronounced induction period, followed by a constant-rate stage and eventually by a gradual decrease in rate. The energy of activation for the constant-rate stage of the reaction is 35 kcal. per mole in the range from 110’ t o 160’ C. The energy of activation for the reaction occurring during the induction period is 25 kcal. per mole in the same range. The induction period can be greatly increased by the addition of antioxidants, the amounts of the increase being proportional t o the concentration of the antioxidant. The reaction is severely diffusion-limited, and care must be taken to obtain rates proportional to sample mass rather than surface area. ACKNOWLEDGMENT
For permission to publish this work the author is grateful to the Bakelite Company, a Division of the Union Carbide and Carbon Corp. The author also wishes to mention the contribution of June Stershic, who carried out most of the oxygen uptake measurements.
2205
LITERATURE CITED
Barrer, R. M., “Diffusion in and Through Solids,” p. 419, Cambridge University Press, Cambridge, 1941. Bateman, L., and Gee, G., Proc. Roy. Soc., A195, 376 (1949). Biggs, B. S., Natl. Bur. Standards, Circ. 525, 137 (1953). Biggs, B. S., and Hawkins, W. L., Modern Plastics, 31, No. 1, 121 (1953). Blum. G. W.. Shelton. J. R.. and Winn, H.. IND. ENG.CHEM., 4 3 , 4 6 4 (1951). Bolland, 5. L., Proc. Roy. Soe., 186, 230 (1946). Bolland, J. L., Trans. Faraday Soc., 46, 358 (1950). Bolland, J. L., and Gee, G., Ibzd., 4 2 , 2 4 4 (1946). Bolland, J. L..and Ten Have, P., Dascussions Faraday Soe., No. 2 , 2 5 2 (1947).
Bolland, J. L., and Ten Have, P., Trans. Faradag
Soc., 45,
93 (1949).
Booser, E. R., and Fenske, M. R., IND. ENG.CHEM.,44, 1860 (1952).
Brook, J. H. T., and Matthews, J. B., Discussions Faraday Soc., No. 10, 302 (1951).
Dufraisse, in Davis and Blake’s “Chemistry and Technology of Rubber,” Reinhold, New York, 1937. Hinshelwood, C. N ., “Kinetics of Chemical Change in Gaseous Systems,” 3rd ed., p. 227, Clarendon Press, Oxford, 1933. Mulcahy, M. F. R., Trans. Faraday Soc., 45, 576 (1949). Myers, C. S., IND. ENG.CHEM., 44, 1095 (1952). Robertson and Waters, Trans. Faraday Soc., 42, 201 (1946). Shelton, J. R., Am. SOC.Testing hIaterials, Spec. Tech. Pub., 8 9 , 1 2 (1949).
Shelton, J. R., and Cox, W. L., Rubber Chem. and Technol., 26, 632 (1953).
Shelton, J. R., Wherley, F. J., and Cox, W. L., IND.ENO. CHEM.,45,2080 (1353). Shelton, J. R., and Winn, H., Ibid.,38, 71 (1946). Wilson, J. E., J . Chem. Phyco., 22, 334 (1954). RECEIVED for review February 9, 1955.
ACCEPTED April 25, 1955.
Diffusion Coefficients in Hvdrocarbon Systems J
n-Heptane in Gas Phase of Methane-n-Heptane System L. T. CARMICHAEL, H. H. REAMER, B. H, SAGE, AND W. N. LACEY California Institute of Technology, Pasadena, Calij,
M
ATERIAL transport in the gas phase by molecular diffusion has been the subject of many investigations. Maxwell ( 1 2 ) and Stefan (21-24) carried out much of the early work and laid a surprisingly satisfactory basis for describing the behavior where the simple kinetic theory is applicable. Chnpman and Cowling (8) extended the treatment and included the effects of composition on the diffusion characteristics of the components of gaseous mixtures. Sutherland ( 2 5 ) proposed a rather satisfactory empirical expression describing the effect of temperature and molecular weight on the transport characteristics of the components of a gas phase a t low pressure. Sherwood and Pigford (20) reviewed some concepts of molecular diffusion and outlined the application of such processes to the prediction of absorption and extraction operations. Babbitt discussed the work of Maxwell and Stefan and presented a treatment of diffusion from their standpoint (1, 2 ) . Jost reviewed the status of diffusion in solids, liquids, and gases (10). Kirkvood and Crawford (11)presented the basic transport characteristics of homogeneous systems. Schlinger (17‘) considered the transport of one component through an essentially stagnant gas with fugacity and with partial pressure as the potential and reviewed the literature concerning
the experimental measurements of molecular diffusion of gases. The present discussion is concerned with the measurements of the Maxwell diffusion coefficients for n-heptane in the gas phase of the methane-n-heptane system a t temperatures from 100’ to 220” F. and a t pressures from 14 to 60 pounds per square inch absolute. Throughout this discussion and in the figures all pressures are presented in pounds per square inch or pounds per square foot absolute. METHODS AND APPARATUS
The methods used in this study involved an adaptation of the classical diffusion cell of Stefan (21). A schematic drawing of t h e apparatus constitutes Figure 1. The gas phase filled diffusion cell A and the n-heptane was introduced as a liquid in chamber B. It entered the lower part of cell A through fritted glass disk C. Thermocouples at D and D’were provided in order to determine the temperature of the upper surface of the fritted-glass disk. An electric heater a t E was provided t o maintain the temperature of the disk substantially the same as that of the gas in the d 8 u sion path. Steady-state condition was determined by the constancy of the capillary depression of the a-heptane liquid in t h e glass disk.
2206
r
ie,
INDUSTRIAL AND ENGINEERING CHEMISTRY
VOl. 47, No. 10
Equation 1 takes into account end corrections to the gross length of the diffusion path resulting from the introduction and withdrawal of the diffusing component. These corrections amount t o less than 1% of the average transfer distance. It also considers interfacial resistance t o transport (18, 19). Such interfacial resistance was assumed to be described by the following linear expression:
A
1
If it is desired to treat the phase as a perfect gas as well as an ideal solution, Equation 1 reduces t o (3)
If Equation 3 is applied to situations where there are no length corrections and no interfacial resistances, it assumes the conventional form ( 1 7 ) .
Figure 1.
Schematic arrangement of diffusion cell A
B
C
=
= =
D,D' = E =
Diffusion cell Chamber Fritted-glass disk Thermocouples Electricheater
It was desirable to solve for the coefficients Daw., and ri of Equations 1 and 3 a t a particular temperature of iterative methods such as have been applied t o the evaluation of coefficients for equations of state (6). Such iterative methods were applied in the present instance with the appropriate simplifications permitted by Equations 1 and 3. In order to use the data a t different pressures it was assumed that the change in the Maxwell diffusion coefficient with pressure was linear a t each temperature. After determining that the resistance coefficient was negligibly small and establishing the corrections to the gross transport length, it was possible to solve Equations 1 and 3 directly for the Maxwell diffusion coefficient. The solutions permitted the apparent effect of pressure on this quantity to be evaluated. Independent measurements of the secondary effect of the circulation rate a t the upper end of the transfer path on the net transfer distance were made and the effective transfer length
The equipment employed for this investigation is rather complicated and has been described in detail ( 7 ) . Many principles of operation are similar to those employed in an earlier investigation of gaseous diffusion a t atmospheric pressure ( 1 7 ) . In principle, the equipment consisted of the transport cell of Figure 1 and an injector which permitted the rate of transport of the n-heptane t o be determined with accuracy ( 1 4 ) . The mixture of methane and n-heptane circulated from the upper part of t h e transfer cell was passed through an agitated condenser maintained a t 32" F. The temperatures were measured with strain-free platinum resistance thermometers (IS) with an uncertainty of 0.01" F. relaTable I. Primary Variables tive t o t h e international Estimated Value Probable platinum scale. Symbol Unit Minimum Maximum Error Quantity A g a s e o u s m i x t u r e of Transport rate X 108 5 1 Ib./(sec.) (sq. ft.) 4 X 10-8 175 X 10-8 0.05 X 10-8 methane and n-heptane in Temperature t F. 100 220 0.03 Transport path equilibrium with the liquid f F. 100 220 0.05 Interfacial lb./sq. ft. 2048 8634 5.0 P phase of this binary system Pressure Length a t 32" F. was circulated past ft. 0.20 0.37 2 x 10-4 Gross ft. 0.20 0.37 1 x 10-8 Net the upper part of the cell in Compressibility of gas phase Methane . . . 0,99370 0,99871 0.001 order to maintain a known, n-Heptane z o ... 0.00000 0,92610 0,020 z ... 0.99370 0.99808 0.002 Mixture small concentration of the Volume d i f f u s i n g component a t F . n-Heptane in liquid phase a t 1 1 5 O F. vo cu. ft./lb. 0.024176 0.024176 0.0005 Provision was made for adFugacity lb./sq. f t . 1859 6992 50.0 n-Heptane justing the gross length of the $,, Ib./sq. f t . Vapor pressure 1000 227.5 227,5 0.5 transfer path from 0.5 to 4.5 160' 880.0 880.0 2.0 inches. 2200 2517.8 2517.8 5.0 Composition a t exit ?TI. mole fraction 0.97602 0.99971 0.001 For equipment of this kind Diffusion coefficientn DM Ib./seo. 0.16 0.29 0.004 Ideal solution the Maxwell diffusion coeffiPerfect gas 0.16 0.29 0.002 cient (17) in a n ideal solution Probable error in diffusion Coefficient was obtained from uncertainties in primary variables by summing estiwith Eugacity as the potential mated variances. A large part of uncertainty lies in estimating equilibrium properties of system. may be established from
E.
2-0
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
October 1955
could be related to the gross transfer length by an expression of the following form:
I = la
- a'Re
=
IC -
a
172 11
x
et
(5)
Table 11. E x p e r i m e n t a l M e a s u r e m e n t s of Transport Processes Transport Temperature, F. 100.05 99.91 100.00 99.01 99.97 100,44 100.26 160.01 160.01 160.00 l59,99 160.01 160,30 220.13 220.16 220,31
Pressure, Lb./Sq. Ft. Absolute 2628 2049 2235 5669 8634 2279 4349 8608 2295 5718 7337 7349 2392 4237 6595 8630
Equation 5 is based on the assumption that the effective transfer length is solely a function of the gross transfer length and the Reynolds number of the flow in the circulating system. The experimental data employed to establish the coefficients of Equation 5 are I t was assumed that available (7'). there was no change in viscosity of the gas phase as a result of the presence of small quantities of n-heptane in the circulating system provided a t the upper end of the transfer path, thus permitting a simplification in the evaluation of the coefficient for the second equality. The pertinent variables and the probable error with which each was determined are set forth in Table I. This table lists the quantities measured or calculated from experimental information along with the range of each variable and the associated probable error of measurement. It is estimated that the Maxwell diffusion coefficient was determined a t each state with a probable error of 1% except for uncertainties in establishing the fugacity of the n-heptane. This estimate of statistical error was based on the indicated undivided uncertainties in the experimentally measured quantities reported in Table I. The accuracy with which the Maxwell hypothesis describes the molecular transport processes in this system must be established from the agreement of the experimental data with the original hypothesis On which Equations 1 and 3 are based. MATERIALS
The n-heptane used in this investigation was obtained from the Phillips Petroleum Co. and the air-free sample had a suecific weight of 42.4100 a t 77" F. This compares with a value of 42.417 reported by Rossini (15) for air saturated material. An index of refraction a t 77" F. and atmospheric pressure of 1.3854 relative to the D-lines of sodium was obtained, as compared to a value of 1.38517 recorded by Rossini. The methane was obtained from a well in the San Joaquin Valley and as received a t the laboratory contained less than 0,001 mole fraction of hydrocarbons other than methane. After passage over calcium chloride, potassium hydroxide, Ascarite, and anhydrous calcium sulfate, a t a pressure in excess of 500 pounds per square inch, a mass spectrographic analysis, confirmed by partial condensation analysis, indicated that the methane contained less than 0.0005 mole fraction of impurities. EXPERIMENTAL RESULTS
M ~ ~ ~ ~ ~ e were m e made n t s at pressures from 14 to 60 pounds per square inch. At the higher temperatures information was not obtained for the lower pressures because they were exceeded by the vapor pressure of n-heptane. Experimental measurements were made a t temperatures of loo", 160", and 220" F. At each temperature data were obtained a t three transfer lengths varying
2207
Transport Rate X 108, Lb./(Sec.) (Sq.Ft.) 14.43 19.12 16.46 5.81 4.18 9 28
4.72 20.72 87.02 30.09 24.52 25.56 46.74 174.21 95.37 73.25
Lenp:th, Ft. Net Gross 0.2061 0.2002 0.2065 0.1977 0,2065 0.2021 0.2064 0.2038 0.2063 0,2009 0.3743 0,3722 0.3725 0.3744 0.2017 0.2063 0.2032 0.2063 0.2033 0.2063 0.2013 0.2063 0.2065 0.1986 0,3744 0.3724 0,2062 0.2038 0.2062 0.2038 0.2062 0.2012
Composition a t Exit Mole Fraction Methane 0.9990 0.9992 0.9986 0.9991 0.9997 0.9983 0.9990 0.9987 0 9898 0.9964 0.9983 0,9989 0.9916 0.9760 0.9870 0.9951
Temperature, Interfacial
F. 100.10 99.75 99.90 98.98 100.02 100.48 100.29 160.01 160,Ol 159.94 160.10 160.07 160.25 219.76 219.95 220.15
between 0.12 and 0.45 foot. Results obtained a t the two greater transfer lengths are presented in Table 11. The data obtained with the shortest transport path were used only to establish the effect of the rate of circulation of methane a t the upper end of the transport path on the effective length. These data are available (7') together with a discussion of the experimental details. From supplemental measurements a t different circulation rates, the following coefficient for Equation 5 was established t o evaluate the effect of circulation rate on the effective transport length: I = lo - 4 90 x 10-4 177 x r'nt
v
(6)
-
In order to establish the viscosity of the gas phase, available information concerning the behavior of methane was employed ( 1 6 ) , no regard being taken of the effect of the small quantities of n-heptane on the viscosity of the gas circulating at the upper end of the transport path, The reference viwcosity correspondfl to that of methane at-100' F. and atmospheric pressure. The fugacity and compressibility factor of n-heptane and those of methane for each of the states investigated, as recorded in Table 111, were obtained by application of the Benedict equation of state ( 3 , 4,9 ) . The vapor pressure of n-heptane was taken from a critical review by Rossini (15), supplemented by the experimental measurements of Young (@), and was recorded i n Table I11 for the temperature of the interface near D of Figure 1. This temperature differs slightly from that of the transport path. Composition of the gas phase for equilibrium a t the interface and in the condenser was estimated from the measurements of Roomer ( 5 ) . On analysis of the experimental data in accordance with procedures described, the resistance a t the interface was less than the probable error associated with its evaluation. In all case8 the maximum resistance was less than 2% of the total resistance
Table 111. Maxwell Diffusion Coefficients for n-Heptane a n d Properties of G a s Phase of M e t h a n e - n - H e p t a n e S y s t e m Pressure, Transport Lb./Sq, Ft. Temperature, Absolute O F. 2628 2049 2235 5669 8634 2279 4349 8608 2295 5718 7337 7349 2392 4237 6595 8630
100.05 99.91 100,00 99.01 99.97 100.44 100.26 160.01 160.01 160.00 159.99 160.01 160.30 220,13 220.16 220.31
Compressibility Factor Methane n-Heptane 0,9980 0.9984 0,9982 0.9958 0.9937 0.9982 0.9968 0.9958 0,9988 0.9971 0.9964 0.9964 0.9987 0.9986 0.9978 0.9972
0,8677 0,9002 0.8900 0.5441 0.0000 0.8875 0.7311 0.574.5 0.9261 0.7858 0.6861 0.6850 0.9227 0.8995 0.8335 0.7654
n-Hentane
Vapor pressure, Lb./Sq. Ft. 228.10 226.22 227 09 221.90 227.52 230,OO 227.52 879.98 879.98 878.40 881.28 881.28 878.40 2505.60 2508.50 2508.50
%-Heptane Fugacity
Diffusion Coefficient, Lb./Sec, Ideal solution
Lb./Sq. Ft. Perfect gas 2317 1859 2009 4219 5280 2044 3495 6282 2130 4689 5642 5650 2212 3841 5639 6992
0.1659 0.1678 0.1622 0.1563 0.1641 0.1702 0.1524 0.2240 0.2133 0.2140 0.2235 0.2288 0.2189 0.2553 0.2598 0,2707
0.1679 0 1700 0.1641 0.1585 0.1686 0.1739 0.1541 0.2333 0.2198 0 2208 0.2309 0 2373 0.2260 0.2717 0.2775 0.2876
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
2208
I
L
I
I
i
i
I
I
Vol. 47, No. 10
I
Figure 3.
Effect of temperature on Maxwell diffusion coefficient
0.2(
9w
0.1:
01 w n
cr;
-
J
-.
0.1c
n
X L a
0.0:
VERTICAL POSITION IN CELL FL 10
Figure 4.
Distribution of composition in diRusion cell
to transport and the average resistance was somewhat less than 1% of this total. Utilizing the correction to the length of the gross diffusion path as set forth in Equation 6 and neglecting the small interfacial resistance, Maxwell diffusion coefficients were calculated from Equations 1 and 3 and the results are recorded in a part of Table 111. Experinientd results are presented in Figure 2. The Maswell hypothesis is a reasonable description of the transport phenomena in this biliary hydrocarbon system a t low pressure since the diffusion coefficient is not a marked function of pressure. Figure 3 shows the effect of temperature on the A'laxwell diffusion coefficient. The curves in this figure were based on fugacity as a potential but under these conditions of pressure and temperature the results are not greatly different from those obtained Kith partial pressure as the potential. The trends with pressure shown in Figures 2 and 3 result from the inability of the Maxwell hypothesis to describe in detail the effect of composition and pressure on the transport properties of the components of the methane-a-heptane system in the gas phase (6). Probably the pfedictions of Chapman and Cowling (8) more properly take into account the effect of composition and pressure on the transport characteristics of gases than do the aimple concepts employed by Maxwell. Table IV records smoothed values of the Maxwell diffusion coefficients based on fugacity as a potential with the gas phaae treated as an ideal solotion. Throughout the present measurements no marked variation was made in the composition of the gas at the exit of the diffusion section. Investigations in
Figure 5 .
20 PRESSURE
1 50
22 . 40 LB. PER SQ IN
1
Fick diffusion coefficients for n-heptane
which the composition of the phase in the diffusion section was varied systematically under isobaric-isothermal conditions appear necessary in order to establish with certainty the range of applicability of the Maxwell hypothesis to transport in gases.
Table IV. Smoothed Values of NIaxwell Diffusion Coefficientsafor n-Heptane in Gas Phase of .Methane-+Heptane System Temperature F. 100 160 0.1662 0.2230 0.1630 0.2210 0.1590 0.2190 0.1588 0.2203 0.1618 0.2265 0.1688 0.2360 fugacity as potential and assuming
Pressure Lb./Sq. In'ch Absolute 14.696 20.0 30.0
40.0 50.0 60.0 a Computed with a n ideal solution.
220 O.Zi20 0.2710 0,2742 0.2814 0.2912 t h a t gas phase warn
TRANSPORT CHARACTERISTICS
The relationship between the Fick and Maxwell diffusion coefficients for a perfect gas is
This relationship assumes the following somewhat more complicated form in the case of a n ideal solution:
INDUSTRIAL AND ENGINEERING CHEMISTRY
October 1955
Table V.
Fick Diffusion Coefficient for Methane and n-Heptane in Gas Phase
Diffusion Coefficient, (Sq. Ft./Sec.) x 10-4,io00 F. Methane n-Heptane
Pressure I,b./Sq. Inch Absolute
Composition Wt. Fraction n-Heptane
14.696
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0
4.923a 4.046 3.173 2,302 1.428 0.671
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0
2.381 1.878 1.375 0.887 0.426 0,056
20.0
40.0
2209
Composition Wt. Fraction n-Heptane
0.708 0.5818 0.4663 0.3311 0.2054 0,3821
0.0 0.2 0.4
0.6
0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0
0.0 0.2 0.4 0.6 0.8 1.0 60.0 0.0 0.2 0.4 0.6 0.8 . . 1.0 dctual value of quantity recorded is 0.0004923 square foot per second. 0.202 0.1593 0.1166 0.0782 0.0362 0.0048
I
Diffusion Coefficient, (Sq. Ft./Sec.)~X ' 10-4,1600 F. Methane n-Heptane ~
6 ,746 6.571 4.386 3.206 2.025 0.864 4.785 3.944 3.095 2.267 1,404 0.573
2.481 2.014 1.546
1.086
0,627 0.193 2.166 1.70'3 1.274 0.838 0.425 0.072
0.980 0.8092 0.6371 0.4667 0.2941
Composition Wt. Fraction n-Heptane
... ...
-
Diffirainn ..- -- f'n&i,.iant --___I__._", (SS. Ft./Sec.) X 10-4, 220° F.
Methane
... ..
...
.. .. ,.
...
0.1241
...
...
0.695 0.5729 0.44'35 0.3278 0.2039 0.0832
0.0 0.2 0 4 0.6 0 8 1.0
5,881 4,879 3.838 2.830 1,789 0.774
0.312 0.2533 0.1944 0.1366 0.0788 0.0243
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8
3.007 2.455 1.910 1.380 0.835 0.305
1.0
..
, . .
, . .
...
n-Heptane
0.414 0.338 0,263 0.190 0.115 0.042 0.271 0.220 0.168 0.117 0.0668 0 0200
Under the conditions associated with this investigation the hydrodynamic velocity in the diffusion cell may be established from
1.5
d b
a 6 10
I
10
20 PRESSURE
Figure 6 .
30 40 LB. PCA SQlN.
I
50
Ficlc diffusion coefficients for methane
If the concentration of the diffusing component is very small or if the molal volumcs of the two components are the same, the bracketed term reduces to unity. Equations 7 and 8 are general and are subject only t o the limitations of the equations of state assumed for the gas phase in the derivation of these expressions. The variation in concentration from point to point under steady transport through a gas phase on the basis of the Maxwell hypothesis follows the distribution shown in Figure 4 for atmospheric pressure. Utilizing Equations 7 and 8, i t was possible to establish the Fick diffusion coefficient as a function of position. The results of such calculations from the Maxwell diffusion coefficient based on an ideal solution are shown for 160' F. in Figure 5 and recorded in Table V. The corresponding values of the Fick diffusion coefficient for methane a t 160" F. are given in Figure 6. The Fick coefficient is a marked function of composition and of pressure. The coefficients for methane and n-heptane are related by (9)
The specific volumes of the methane and n-heptane in the pure state were obtained from the Benedict equation of state (3, 4,9).
The hydrodynamic velocity is shown in Figure 7 as a function of composition for several different initial weight fractions of methane. I n this figure the product of the distance along the transport path and the hydrodynamic velocity has been employed in order to simplify the presentation. Figure 7 indicates that the hydrodynamic velocity is a marked function of the ratio of the initial weight fraction o€ the stagnant component t o that at the point in question in the diffusion path. I n computing the hydrodynamic velocity from Equation 10 no regard was taken of the distrib u t i o n of s h e a r within the diffusion cell. It is probable that the transport O0 WOEPI G H T O FRACTION 4 O B METHANE lo phenomena are Figure 7. Effect of material transsomewhat more port and pressure on hydrodynamic complicated t h a n velocity those assumed by Equation 10 as a result of the shear gradients in the gas phase. Such gradients will cause small radial velocities which were not considered in the analysis of the experimental results recorded in Table 11. ACKNOWLEDGMENT
This work is a contribution from Project 37 of the American Petroleum Institute a t the California Institute of Technology. Jacques Bodes assisted with the experimental work, Betty Kendall with the calculations, and Evelyn Anderson with the preparation of the manuscript.
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
2210
NOMENCLATURE
Benedict, M., Webb, G. B., Rubin, L. C., and Friend, L., Chem. Eng. Progr., 47, 419, 449, 571, 609 (1951). Boomer, E. H., Johnson, C. A , and Piercey, A. G. A., Can. J. Res., B16, 396 (1938). Brough, H. W., Schlinger, W.G., and Sage, B. H., IND. ENG. CHEM.,4 3 , 2 4 4 2 (1951). Carmichael, L. T., Reamer, H. H., and Sage, B. H., Washington, D. C., Amer. Doc. Inst., Doc. No. 4611. Chapman, S., and Cowling, T. G., ”Mathematical Theory of Non-Uniform Gases,” Cambridge Univ. Press, Cambridge, Eng., 1939. Connolly, T. J., Frankel, S. P., and Sage, B. H., “Application of Automatic Digital Computing Methods to Prediction of Phase Behavior,” AIEE Mise. Paper, 50-259 (1950). Jost, W., “Diffusion in Solids, Liquids, Gases,” Academic Press, New York, 1952. Kirkwood, J. G., and Crawford, Bryce, Jr., J . Phys. Chem.,
= specific gas constant, ft./”R.
b
DPJ = Fick diffusion coefficient of component 1, sq. ft./sec. D M , I= Maxwell diffuqion coefficient of component 1, lb./sec.
f
= fugacity, lb./sq. f t .
k,
=
ratio of concentrations of component a t interface f c equilibrium I = effective transport length, ft. I, = effective correction t o gross transport length, It. lo = gross transport length, i t . 1.n _= natural logarithm T - weight rate of transport, lb./(sq. ft.) (sec.) m = total weight rate of transport, lb./sec. Mi = molecular weight of component 1 121 = weight fraction of component 1 mole fraction of component 1 n, = - partial pressure of component I, ( P v L )lb./sq. * ft. $ l = pressure, lb./sq. ft. absolute R e = Reynolds number ri = interfacial resistance, sec. /ft. T = thermodynamic temperature, OR. u = hydrodynamic velocity, ft./sec. specific volume, cu. ft./lb. z = distance along transport path, ft. z = compressibility factor of gas phase dimensional constant in Equation 5 f f = = dimensional constant in Equation 5 v = absolute viscosit ,(lb.) (sec.)/sq. ft. u = specific weight orphase, lb./cu. f t . u1 = concentration of component I,lb./cu. ft. a = oartial differential oDerator
-
v
56, 1048 (1952).
Maxwell, J. C., “Scientific Papers,” Cambridge Univ. Press, Cambridge, Eng., 2 , 623 (1890). Meyers, C. H., J. Research Natl. Bur. Standards, 9, 807 (1932). Reamer, H. H., and Sage, B. €I., Rev.Sci. Instr., 24, 362 (1953). Rossini, F. D., “Selected Values of Properties of Hydrocarbons,” Natl. Bur. of Standards, Washington 25, D. C.,
=
1947.
Sage, B. H., and Lacey, W’. N., Trans. Am. Inst. Mining Met. Engrs., 127,118 (1938).
Schlinger, W. G., Reamer, H. H., Sage, B. H., and Lacey, W. N., “Diffusion Coefficients in Hydrocarbon Systems. n-Hexane and n-Heptane in Air,” to be published in Fun: damental Research on Occurrence and Recovery of Petroleum. American Petroleum Institute. New York. Schrage, R. W., “Theoretical Study of Interphase Mass Transfer,” Columbia Univ. Press, New York, 1953. Scott, E. J., Tung, L. H., and Drickamer, H. G.. J . Chem.
ff’
SUBSCRIPTS 1 = stagnant component 1
= diffusing component 7 e = conditions a t equilibrium g = gas phase i = conditions a t interface I = liquid phase o = initial state r = reference state t = conditions a t exit of transfer section SUPERSCRIPTS o = pure state ” = two phase
Vol. 47, No. 10
7
Phys., 1 9 , 1 0 7 5 (1951).
Sherwood, T. K., and Pigford, R. L., “Absorption and Extraction,” McGraw-Hill, New York, 1952 (21) Stefan. J.. Ann. Phus.. 41. 725 (1890). (22) Stefan, J., Sitz. Akad. Wiss. Wien, 63, Abt. 11, 63 (1871). (20)
(23) (24) (25) (26)
LITERATURE CITED
Babbitt, J. D., Can. J . Phys., 29, 427 (1951). (2) Babbitt, J. D., Can. J. Res., A28, 449 (1950). (3) Benedict, M., Webb, G . B., and Rubin, L. C., J. Chem. €’hue., (1)
8 , 3 3 4 (1940).
Ibid., 65, 323 (1872). Ibid., 83, 943 (1881). Sutherland, W., Phil.Mag., 38, (ser. 5) 1 (1894). Young, S., Sci.Proc. Roy. Dublin Sac., 12, 374 (1910).
RECEIVED for review December 27, 1954. ACCEPTED June 9 , 1955. A more detailed form of this paper (or extended version, or material supplementary to this article) has been deposited as Document No. 4611 with the AD1 Auxiliary Publications Project, Photoduglication Service, Library of Congress, Washington 25, D. C. A copy may be secured by citing the document number and by remitting $3.75 for photoprints or $2.00 for 35-mm. microfilm. Advance payment is required. Make checks or money orders payable to Chief, Photoduplication Service, Library of Congress.
Ethane-Ethvlene-Acetvlene Svstem J
J
J
VAPOR-LIQUID EQUILIBRIUM DATA AT -35O, O o , AND 40° F. R. J. HOGAN, W. T. NELSON, G . H. HANSON,
AND M.
R. CINES
Research Division, Phillips Petroleum Co., Bartlesville, Okla.
HE current literature contains innumerable references to
T
the recovery and utilization of high-purity ethylene and acetylene from various cracked gases. One method of separating CZ mixtures is low-temperature fractionation. For detailed evaluation of that process, reliable equilibrium data are needed. While some data are available ( 3 , 5, 6, 9 ) , in general they cover the region above 0’ F. The data on the binarv svstem, ethaneat o ~ -, 4 0 ~ , and -1000 F., have already appeared (4). As the apparatus used in those measurements contained brass components, a rocking-bomb type unit wag built for study of mixtures containing acetylene. I
”
EXPERIMENTAL WORK
Materials. The ethane and ethylene used were Phillips “research grade’’ materials (purity 100.0%). Linde Prest-0-Lite acetylene was used; it contained nitrogen, oxygen, and carbon monoxide in addition t o acetone. Small quantities of this acetylene were purified as needed according to the procedure discussed later. Analysis of purified material by mass spectrometer showed a minimum purity of 99.5%. As a precautionary measure, bkfore the-hydrocarbons were introduced into the system, the ethane and ethylene were passed through Ascarite and Drierite, and the acetylene was dried with calcium chloride. Apparatus. The vapor-liquid equilibrium apparatus was a
