INDUSTRIAL AND ENGINEERING CHEMISTRY Goranson, R. SV., “Thermodynamic Relations in 1Iuiticoniponent Systems,” Carnegie Institute of Washington, Wmhington, D. C., 1930. Hatcher, J. B., and Sage, B. H., IXD.ENG.CHCM.33, 443 (1941). Hill, E. S., and Lacey, W.Pi., Ibid., 26, 1324 (1934). I bid., 1327. Ingersoll, L. R., Zobel, 0. J., and Ingersoll, A . C . , “Heat Con. duction,” McGraw-Hill, Sew York, 1945. Kirkwood, J. G., and Crawford, B., Jr., J . P h y s . Chem. 56, 1045 (1952). Lewis, G. N., J . Am. Chern. SOC.30, 668 (1905). Neyers, C. H., Bur. Standards J . Research 9, 807 (1932). Onsager, L., Phys. Rea. 37, 405 (1931). Ibid., 38,2265 (1931). Pomeroy, R. D., Lacey, ST‘. K.,Scuddcr, N . F., and Stapp. F. P., IND. ENG.CHEX.25, 1014 (1933). Reamer, H. H., Olds, R. H., Sage, B. H., and Lacey, W.N., I b i d . , 34, 1526 (1942). Reamer, H. H., and Sage, B. H., Reu. Sci. I n s t r . 24,362 (1953). Robb, W.L., and Drickamer, H. G., J . Chenz. Phys. 19, 1604 (1951), Rossini, F. D., “Selected Values of Properties of Hydrocar-
Vol. 48, No. 2
bons,” 2nd suppl., National Bureau of Standards, December 31, 1952, Washington, D. C. (22) Rzasa, 111.J., private communication, June 6, 1952. ( 2 3 ) Sage, B. H., and Lacey, W. Y., “Thermodynamic Properties of the Lighter Paraffin Hydrocarbons and Piitrogen,” American Petroleum Institute. Xew York. 1950. (24) Sage, B. K., and Lacey, 1%’S., . Trans’. Am. Inst. M i n i n g Melet. Enyrs. 174, 102 (1945). ( 2 5 ) Schlinger. W. G., and Sage, B. H.. IND. Exc. CHEX 42, 2155 (1950). :26) Schrage, R.TV., “Theoretical Study of Interphase ;\lass Transfer,” Columbia Univ. Press, Kew York, 1953. ( 2 7 ) Scott, E. J., Tung, L. H., and Drickamer, H. G., J . Chern., Phvs. 19,1076 (1951). (28) Selleck, F. T., Opfell, J. B . , and Sage, B. I$., ISD. ENG.CHEM. 45. 1350 (1953). (29) Shepard, A: F., Henne, A . L., and Ilidgely, T. J . A m . Chem. SOC. 53,1945 (1931). (30) Yherwood, T. K., and Pigford, It. L., “Absorption and Extraction,” hIcGraw-Hill, New York, 1952. (31) Trevoy, D. J., and Drickamer, H. G., J . Chern. Piius. 17, 1117 (1949) ( 3 2 ) Tung, L. H., and Drickamer, H. G., Ibid., 20, 6 (1952). (33) Ibid., 10.
(Difliesion Coeficieats in Hydrocarbon Systems)
ethane-n-Pentane-
ase
H. €I. REAAIEW, C. H. DUFFY, -4549B. M. SAGE California I n s t i t u t e of Technology, Pasadena, Calif.
K F O H l I A T I O S concerning the molecular transport characteristics of the lighter hydrocarbons is limited. A short review of the literature n-as piesented in the first article of this eeriea, page 275. This article relates t o measurements of the Ficlc diffusion coefiicients for methane in the liquid phase of the methane-n-pentane system. The investigation was made a t pressures up t o 1700 pounds per squaie inch in the temperature interval between 40” and 280” F. At temperatures above 100” F. it was not possible t o obtain data a t the indicated maximum pressure because of approach t o the critical pressure (3) of the methane-n-pentane system. In the present study the same equipment, methods of measurement, and analysis of results were employed as were used in the investigation of the methane-decane system. The magnitude of the correction factor for the quantity of methane introduced to the isochoric vessel in order t o obtain the quantity transported across the gas-liquid interface is given in Figure 1. Figure 2 presents the volumetric factor which takes into account the influence of hydrodynamic velocity upon the Fick diffusion coefficient. The data of Figures 1 and 2 were based upon available equilibrium measurements (3). Volumetric corrections shown in Figures 1 and 2 involve a probable error of 0.005. Experimental data involving the weight of methane added t o the diffusion chamber as a function of time were similar t o those found in the investigation of the methane-decane system. AXATERIALS
The methane employed for this work was obtained from a field in the San Joaquin Valley in California and is the same as that used in the study of the methane-decane system. Spectroscopic analysis indicated that samples of methane obtained from this well, after being subjected t o the sequence of operations described in the preceding article, contained less than 0.0005 mole fraction of material other than methane.
The n-pentane was obtained flom lhe Phillips Petroleum Co. and was reported to contain less than 0.005 mole fraction of material other than 12-pentane. This hydrocarbon was subjected to t n o fractionations in a glass column containing 16 glass plates a t reflux ratios greater than 40, and the central 80% of the overhead was retained. This portion of the overhead from the second fractionation n-as passed over activated alumina, and the remaining hydi ocarbon xTas deaerated by prolonged refluxing a t reduced pressure. The purified, deaerated sample had a specific weight of 38.T042 pounds pei cubic foot, as comparcd to a value of 38 792 pounds per cubic foot a t 77“ F. reported by Rossini ( 3 ) . The index of refraction relative t o the I)-lines of sodium a t 7 7 ” F. vias 1.3549, .ilhich compaied favorahly with a value for the air-saturated sample of 1.35475 submitted bg Rossini as a critically chosen value. The agreement of the specific weight and index of refraction with accepted values leads the authors t o believe that the sample of n-pentane used in this study contained less than 0.001 inole fraction of impurities. EXPEWI\IEUTAL R E S U L T S
Following the experimental methods described in the preceding paper, measurements of the rate of solution of methane in the liquid phase of the methane-n-pentane system were carried out a t five temperatures between 40” and 280” F. The detailed experimental measurements are available (1). Table I records the quantities Am?/@which were obtained from the slopes of straight lines associated with such measurements (see the first article in this series). The deviation of the weights of methane added from the straight line corresponding t o the recorded slope was included as a standard error of estimate. I n the evaluation of this standard error of estimate it was assumed that all the error was found in the weight of methane and none in the time. The Fick diffusion coefficient was evaluated first neglecting the hydrodynamic velocity (pee preceding paper) and secondly by
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
February 1956
283 ~
Table I. Pressure. Lb./Sq. Inch Absolute Initial Final
~~~
Experimental Fick Diffusion Coefficients for Methane in Liquid Phase of Methane-n-Pentane Methane Compn., W t Fraction Initial Final
Methane Concn., Lb./Cu. Ft. Initial Final
(Amr\p
Std. Fick Diffusion Error of Coefficient, Estimate, Sq. Ft./Seo. X 10-8 c~~~~~~~~~ Lb. Factor x 10-5 Uncorrected Corrected
e
Volumetric
Lb,'/sec. X lo-"
41.1 342 2 0.0064 0 039" 1159.2 1484.8 0.134 0.176
0 136O 1.219' 4.142 5.408
40' F. 77.97b 101.20
0 9744 0.8852
4.3 8.0
11.23 13.19
1 0 .94 11.67
108.9 409.3 0.008 763.4 1053.5 0.066 1402.6 1702.7 0.135
0.034 0.177
0.280 2.264 4.330
1.187 3.218 5.340
100' F. 69.06 77.79 74.65
0,9748 0,9328 0.8890
4.9 4.1 13.1
14.45 16.56 17.77
14,09 15.45 15.80
7 7 . 1 377.2 0.002 549.9 849.8 0.038 1037.8 1338.8 0.080 1482.8 1784.1 0.128
0.024 0.064 0.111 0.168
0.069 0.830 1.280 2.074 2.518 3.361 3.756 3.627
160' F. 65.94 68.06 66.10 60.06
0,9819 0.9579 0.9326 0.9091
1.2 1.9 4.0 6.1
19.83 20.70 20.39 22.62
19.48 19.83 19.02 20.57
151 6 452.7 0 . 0 0 3 518.5 823.5 0.030 1228.7 1529.7 0.090
0.025 0.050 0.125
0.114 0.925 2.651
0.782 1.636 3.270
220' F. 67.73 65.29 49.28
0,9842 0.9700 0.9430
3.1 2.3 3.8
27.61 26,02 26.15
27 17 25.24 24.66
617.1 918.1 0.030 822.1 1123.2 0.046
0.054 0.075
0.843 1.260
1.449 1.881
280' F. 67.73 53.14
0.9811 0.9793
8.3 9.1
45.37 41.63
44.51 40.77
b
~
0.096
Values of Concentration and compositiun a t 10° F. are extrapolated. The cross-sectional area of the interface was 0.021850 sq. ir.
taking this influence into account. The results are presented in Figure 3 for the Fick diffusion coefficient taking the hydrodynamic velocity into account. I n this figure the curves have been drawn t o yield the minimum standard error of estimate for all the data based upon a simple variation in the diffusion coefficient with temperature and pressure. I n this figure the diffusion coefficient is shown as a function of the average pressure of measurement. I n addition, lines of constant weight fraction methane for the liquid are included. I n Figure 3 the experimental points have been located at the linear average of the pressure or of the composition covered by the experimental measurements. This figure includes lines of constant composition which were established from available equilibrium measurements ( 5 ) .
Throughout the evaluation of these data microscopic equilibrium was assumed. An estimate of the critical locus for the system was included, and the behavior in this region has been indicated by dashed lines as a result of the uncertainty associated with the extrapolations. The influence of temperature upon the Fick diffusion coefficient is presented in Figure 4. A4tthe low temperatures there is a n increase in the diffusion coefficient with pressure, whereas at the high temperatures there is a rapid decrease in the coefficient with the increase in pressure. Table I1 presents smoothed values of the Fick diffusion coefficient as a function of pressure and temperature. The corresponding values of average weight fraction and concentration of methane in the liquid phase have been included for each state. Smoothed data of this table show a standard deviation from the
I PRESSURE
LB. PER
sa.
500
IN.
Figure 1. Effect of changes in volume of liquid phase 0 13 weight of methane crossing interface
PRESSURE
Figure 2.
1000
LE. PER
I500
so.
IN.
Volumetric correction factor
INDUSTRIAL AND ENGINEERING CHEMISTRY
284
low
500
PRESSURE
Figure 3.
Table I f . Methane Concn., Lb./Cu. Ft.
4.44 250 500 750 1000 1250
0.00 0.88b 1.80 2.70 3.60 4.47 5.48 6.56
TEMPERATURE
Methane Compn., Wt. Fraction
8.81
0.000
15.7a 250 500 750 1000 1250 1500 1750 2000 2250
b
Effect of temperature on Ficlc diffusion coefficient
Methane Concn., Lb./Sq. Ft.
94.9a
0.042 0.065 0,091 0.118 0.147 0.185 0,236
16.6C
0.319
17.20
Vapor pressure of n-pentane is expressed ,i? lb./sq. inch absolute. All values of concentratmn and composition for 40' F. are estimated. Extrapolated.
experimental measurements portrayed in Figure 3 of 0.54 X 10-8 square foot per second, assuming that all the uncertainty exists in the diffusion coefficient and none in the evaluation of the temperature and pressure or concentration. The present experimental data follow the same trends as were reported in the preceding paper for the diffusion coefficients of methane in the liquid phase of t,he methane-decane system. It was not possible to extend the measurements t o as high a pressure in this case, because of approach t o the critical state (3') of this binary system a t a lower pressure. LITERATURE CITED
. and Sage, B. H., American Docu-
Methane Compn , W t . Fraction 160' F.
Fick Diffusion Coefficient, Sq. Ft./Sec. X 1 0 F
0.000 0,015 0.034 0.054 0.077 0.101 0.129 0.163 0.213 0.307
9.9c
10.4 10.8 11.3 11.8 12.3 12.9 13.6 1 4 , 3c 15,ZC
14.2C 14.4 14.7 15.0 15.3 15.6 15.S o 16.20
0,020
(1) Reamer, H. H.. Duffy, C. H
Pressure Lb./Sq. Inch Absolute
F. 0.000 0.029b 0.057 0,085 0.115 0,146 0.179 0.214 0.269 0.333
7.68
Fick Diffusion Coefficient, Sq. Ft./Sec. X 10-
100' F.
a
Figure 4.
300
'F
Ficli Diffusion Coefficients for Methane in Liquid Phase of Methane-rz-Pentane
40'
1500 1750 2000 2250
200
IO0
PER 5 9 IN
Effect of pressure and composition on Fick diffusion coefficient
Pressure, Lb./Sq. Inch Absolute
I
2000
1500 LB
Vol. 48, No. 2
250 500 750 1000 1250 1500 1750 2000
0.00 0.23 0.89 1.47 2.03 2.61 3.20 3.82
4.48
2206 F. 0.000 0.010 0.029 0.048 0.070 0.093 0.121 0.157 0.211
26.80 26.5 26.0 26.6
25.2 24.9 24.5 24.lC 28.7C
!SOo F.
185. 6Q 250 500 750 1000 1250 1500
0.00 0.13 0.51 1.11 1,62 2.16 2.71
0.000 0.005 0.021 0.040 0.062 0.089 0.134
54.5c
53.5c 48.QC 44.5 40.3 36.4C 3 3 . Oc
mentation Institute Auxiliary Publications, Washington, D. C., Doc. 4684, 1955. ( 2 ) Rossini, F. D., "Selected Values of Properties of Hydrocarbons," National Bureau of Standards, Washington, D. C., 1947. (3) Sage, B. H., Reamer, H. H., Olds, R. H., and Lacey, W. N., ISD.ENG.CHEM.34,1108 (1942). A more detailed form of this paper (or extended version. or material supplementary to this article) has been deposited as Document No. 4684 with the AD1 Auxiliary Publications Project, Photoduplication Service, Library of Congress, Washington 25, D. C. A copy may be secured by citing the document number and b y remitting 81.25 for photoprints or $1.25 for35-mm. microfilm. Advance payment is required. Make checks or money orders payable to Chief, Photoduplication Service, Library of Congress.
