1、GPA TP-1 71 3824677 001058b 522 Technical Publication TP-I Liquid Densities of Ethane, Propane, and Ethane-Propane Mixtures Dr. J. R. Tomiinson Gulf Research 81 Development Company Pittsburgh, Pennsylvania February, 1971 Reprinted 1991 6526 East 60th Street Tulsa, Oklahoma 74145 Phone: 918/493-3872
2、FAX: 918/493. .3875 GPA TP-1 71 3824699 0010587 469 E FOREWORD This publication is a complete report of a research investigation by Dr. J. R. Tomlinson, Gulf Research sincere appreciation is also extended to Gulf Research = the approximate critical density calculated by the equation, T, = saturation
3、 temperature in OR, T,. = critical temperature in OR, and D, = saturation density. Calculated values of D,.c, for many light compounds invariably show a trend with T,. To avoid any connection with critical density, D, is redefined as normalized density, D,. The normalized density is then, D, = D,/ (
4、1 + 1.75 t$l + 0.75 (j:3) (16) where, T, Te t$l = (1 - - )1/3 (17) For the purpose of exhibiting a correlation check or fit, the normalized density, D, is plotted against 6. The use of 8 in place of T, expands the temperature scale in the neigh- borhood of the critical temperature. It is in this plo
5、t that judgment must be used in the location of the curve to represent the data. The second type of plot used in the correlation is the slope plot in which the natural logarithm of the slope is plotted against density. This plot is used only to determine the slope coefficients A and B. Slopes determ
6、ined from experimental points which lie far from the saturation curve are given more weight than those which lie close to the saturation curve. This is self-evident from the rearrange- ment of the linear isochor equation to yield, P-P, s=- (18) The reiterative process can best be described by a flow
7、 T-T, diagram, Revised T, -Ps -+ S Density Plot Slope Plot t -T,-Revised Sd In the calculations, the experimental density is always used. The calculations of P, S, and normalized density are then direct. The calculations of T, involve a backward or reverse solution to the equations. From the normali
8、zed density curve, the appropriate normalized densities are read off for selected values of 6 corresponding to 1F inter- vals. The saturation densities are calculated and the revised saturation temperature, T, corresponding to the experi- mental density is interpolated. For the calculation of T, use
9、d as input to the normalized density plot, the linear isochor equation and t.he vapor pressure equation are solved simultaneously by first assuming a value for T, and calcu- lating P,. Using these values along with the slope and the experimental P and T, a new value of T, is calculated. This process
10、 is repeated until T, is determined to 0.01“F. Usually the process needs to be repeated only a few times. In order to initiate the reiterative process, either the slope constants or the normalized density curve must be approximated. Although the experimental apparent isochors appear quite linear, th
11、eir slopes are poor estimates of the slopes of the true isochors. On the other hand, a linear extra- polation of an apparent isochor to the saturation curve to de- termine T, and the subsequent estimation of the small den- sity increase in this extrapolation yield a good approxima- GPA TP-3 73 = 382
12、4677 0030572 826 tion of the saturation density. These extrapolated satura- tion densities are then used to prepare the first normalized density curve. Further calculations involve the individual data points of each isochor. The key to the correlation is the location and shape of the curve drawn thr
13、ough the points in the normalized den- sity plot. The best curve through the points is not neces- sarily the right approach. Three types of deviation must be considered. The first is the slope error which must be cor- rected and the slope coefficients revised in the subsequent slope plot. A slope er
14、ror is evidenced by a trend in the deviation of points from a single apparent isochor. In this case, more weight must be given to the highest density points which require a shorter extrapolation to the saturation curve. In fact it may be necessary to visually extrapolate the points from an apparent
15、isochor beyond the highest density point to the approximate location of zero tempera- ture extrapolation. This approximation requires the con- sideration of the values of (T-T,) for each point. A second type of deviation is that produced by a single point of the isochor which indicates a pressure or
16、 temperature error. The third type of deviation is when all points from a single ap- parent isochor deviate to the same extent from the curve. This indicates a density error and such errors invariably in- dicate low densities. The source of these errors may be a slow leak in the pycnometer between d
17、isconnnection and we i g h i n g . The final normalized density plot for propane is given in Figure 1. The deviations of the individual points from the smooth curve show directly the density check. Density errors as the result of pycnometer leaks are apparent in two isochors occurring to the extent
18、of 0.02% or less. The curve in Figure 1 is well represented by, (19) D, =I 0.21670 + 0.0356 0 - 0.027 62 O2275 t I O 50 o 55 O 60 0.65 0.70 B Figure 1 Plot of Normalized Density Against 6 for Liquid Propane The equations developed for liquid propane are given in Table IV along with other pertinent i
19、nformation. The equations in Table IV predict the experimental pro- pane data to 0.01% in density and to approximately 0.03“F in temperature. The pressure fit varies from about 1 psi at the low densities to 2 psi at the high densities. This variation is the result of the change in isochor slope of a
20、bout a factor of two over the density range. The experimental densities of the two low isochors mentioned above must be corrected to TABLE LV Liquid Propane Density Equations A. P = Ph + S(T-T,). B. 1nS = 7.343 D, + 0.1233. C. InP, = 12.495 - 4060/T, (OR). D. D, = (0.21670 + 0.0356 0 + 0.027 02) (1.
21、0 + 1.75 0 $- 0.75 6:s) TS T, 0 = (1 - -)I T,. I 665.68“R Valid Range Pressure Saturation 2000 psia Temperature 30“ + 120F Density 0.45 4 0.53 gm/cc yield pressure and temperature checks of the above magni- tude. In addition, the saturation density equation predicts a critical density (0 = O) which
22、agrees quite well with a recent selected value4 of 0.217 gm/cc. The experimental ethane density data were exceedingly more difficult to correlate into equation form. In the case of propane, the experimental densities ranged from 2 to 2.5 times the critical density. For ethane, the density range was
23、from 0.5 to 2.0 times the critical density. As the density approaches critical, the accuracy of the extrapolation to the saturation curve is considerably reduced. A further compli- cation is introduced by the evidence of positive curvature of the apparent isochors at high temperatures. In the comput
24、er approach these high temperature points were ignored and linear isochors assumed. For the new correlation) the high temperature points were accounted for by the addition of a quadratic term in the isochor equation. This addition re- quired the assumption of two additional slope constants. In view
25、of the complications associated with the devel- opment of correlation equations for ethane, it was neces- sary to apply an additional restraint to facilitate the calcu- lations. The normalized density curve was assumed to be linear. This assumption is not unreasonable in that the normalized density
26、curve for propane deviated only several hundredths of a percent from linearity, Figure 1. Eleven ethane isochors were used to develop the liquid ethane equations tabulated in Table V. Three isochors had to be eliminated from the correlation even though their data are considered to be quite good. The
27、 densities of these three isochors were either very close to, or well below, critical density. As in the case of propane, two of the eleven ethane iso- chors showed evidence of pycnometer leaks which resulted in low densities to the extent of 0.05 and 0.08%. The other densities are considered to be
28、precise to .03%. The pressure and temperature fits are about 1-2 psia and 0.05“F, respect- ively, The normalized density equation predicts a critical density of 0.2035 which agrees quite well with the recently selected value4 of 0.203. It should be pointed out that a comparison of the slope equation
29、s of this investigation and those tabulated by Francis is not justified. In the metering range, the data available to Francis were quite meager. In the case of the saturation densities of propane, the agreement is quite good. His - GPA TP-1 71 3824699 0030593 7b2 .- _ 8 ADDENDUM -PROCEEDINGS OF 49th
30、 ANNUAL CONVENTION _ .- -_ .- saturation densities for ethane are about 5% too high as is the case for several data tabulations. This point will be discussed in the following section. TABLE V Liquid Ethane Density Equations A, B. C. D. E. P = P, + SI (T-T,) + S2 (T-T,)? InSI = 8.00 D, + 0.321 lnP, =
31、 12.410 - 3227/T, (OR) a positive pressure correction must be added - see Table 1x1 D, = (0.20353 + 0.014188 8) (1.0 + 1.75 8 -t 0.75 8“) Sz = 0.05107 - 0.1044 D, (above about 70F T* T,. 8 = (1 - - )I/: K 83t 82 c 81 t 1 I I I I I I I I I I O .I .2 .3 4 .S .6 .7 .8 .9 1.0 MOLE FRACTION ETHANE Figure
32、 4 Volume Shrinkage for Ethone-Propane Mixture at 80F, 1000 psia 90 F 82 83 1 .I .2 .3 .4 .S .6 .7 .8 .9 1.0 MOLE FRACTION ETHANE Figure 5 Volume Shrinkage for Ethane-Propane Mixtures at 80“F, 750 psia ACKNOWLEDGMENT The author of this paper wishes to acknowledge the con- tribution of Warren Petrole
33、um Corporation for suggesting these studies and for their release of the data for publication. The author also wishes to acknowledge the assistance of Arthur V. Fareri and Ralph L. Pivirotto in making the ex- perimental measurements, and the guidance of John K. Rodgers who constructed and tested the
34、 experimental density equipment. REFERENCES 1. Kell, G. S., and E. Whalley, National Research Council (Canada), No. 7607 (1965). 2. Francis, A. W., Ind. Eng. Chem. 49, No. 10, 1779 (1957). 3. Guggenheim, E. A., J. Chem. Phys. 13, 253 (1945). 4. Kudchadker, A. V., G. H. Alani, and B. J. Zwolinski, Ch
35、em. Reviews 68, 659 (1968). 5. Cragoe, E, S., National Bureau of Standards, LC-736 (1943). 6. Technical Committee, Natural Gasoline Association of America, Ind. Eng. Chem. 34, No. 10, 1240 (1942). 7. “Physical Constants of Hydrocarbons C, to C,O, ASTM Special Technical Publication No. 109A (1963). 8
36、. Sliwinski, P., Z. Phyik. Chem. N. F. 63, 263 (1969). 9. Seeman, F. W., and M. Urban, Erdol und Kohle-Erdgas Petrochemie 16, No. 2, 117 (1963). 10. Sage, B. H., J. G. Schaafsma, and W. N. Lacey, Ind. Eng. Chem. 26, No. 11, 1218 (1934). 11. Deschner, W. W., and G. G. Brown, Ind. Eng. Chem. 32, No. 4
37、, 836 (1941). 12. Reamer, H. H., B. H. Sage, and W. N. Lacey, Ind. Eng. Chem. 41, No. 3, 482 (1949). 13. Dittmar, P., F. Schulz, and G. Strese, Chemie. Ing. Tech. 34,437 (1962). 14. Van der Vet, A. P., Congress Modid du Petrole, Vol. II, p. 515, Paris, 1937. GPA TP-1 71 I 3824699 0030596 471 I 15. N
38、GPSA Engineering Data Book, 8th Edition, Natural 20. Sage, B. H., D. C. Webster, and W. N. Lacey, Ind. Eng. Gas Processors Suppliers Association, Tulsa, Okla., 1966. Chem. 29, No. 6, 658 (1937). 16. Tester, H. E., “Ethane” in Thermodynamic Functions of worth, London, 1961. A.1.Ch.E. 43, 25 (1947). G
39、, vol, 111, pp, 162-193, edited by F. i, tt- 21. Reamer, H. H., R. H. Old% B. H. Sage, and W. N. Lacey, Ind. Eng. Cliem. 35, No. 10, 956 (1944). 17. . H., J. L. and c. O. Hurdy Trans. 22. Beattie, J. A., G. Su, and G. L. Sirnard, J. Am, Chem. Soc. 61, 926 (1939). 18. International Critical Tables, V
40、ol. III, p. 231, 1928. 19. Kuenen, J. P., Phil Mag. 151, 40, 173 (18951, 5j, 44, 23. Michels, A., W. Van Straaten, and J. Dawson, Physika 174 (1897) and 6, 3, 628 (1902). 20, 17 (1954). APPENDIX A EXPERIMENTAL APPARATUS AND CALIBRATION Density and Bubble Point Apparatus The density and bubble point
41、apparatus are shown sche- matically in Figure 6. The density apparatus (top of Figure 6) is described as two distinct sections, the sample storage section and the density measurement section. DENSITY APPARATUS DEAD WEIGH TESTER PRESSURE NUL I N D I CATOR 9 - RESERVO1 R DISPLACEMENT PUMP BUBBLE POINT
42、 CELL Figure 6 Density and Bubble Point Apparatus The storage section consists of two sample storage reser- voirs where components may be confined over mercury and two mercury displacement pumps. Dual storage was neces- sary for the preparation of the multi-component samples. The density measurement
43、 section consists of the pycnom- eter, the pressure null indicator, and the connecting line to the storage section. The volume of this section, which is ex- ternal to the pycnometer, is termed “dead space” and is less than 1% of the pycnometer volume. The sample under measurement is confined in two
44、interconnecting volumes: the pyconometer which is thermostated at the selected tempera- ture for the measurement, and the “dead space” which is maintained at 77F (25C). Omitted from Figure 6 for clarity are the constant tem- perature bath, the dead weight tester, and the pressure gauges on the displ
45、acement pumps. The pycnometer was constructed of stainless steel and includes valves 5, 6, and 7. Valves 5 and 7 are three-way valves which close only the lines leading to the main pycnometer volume. The other two connections of each of these valves form a common line in which the closed needle is c
46、entered. This arrangement allows an efficient purge of the line. Valve 6 is a vent valve used in this purge. The pycnometer had a nominal volume of 308 cc and weighed approximately 1235 grams. Valve 3 was used for evacuation or venting. Valve 4 was used to isolate the storage system and null detecto
47、r for subsequent disconnection of the pycnometer. It was also used for purging by venting liquid sample contained be- tween it and valve 6. The constant temperature bath contained naphtha E as a fluid and was fitted with cooling coils, a bare nichrome ribbon heater, a stirrer, a platinum resistance
48、thermometer. and a Wheatstone bridge thermoregulator sensor. The bath was thermostated to -c 0.03”F. The temperature of the bath was continuously monitored by the platinum resistance thermometer and a Rubicon-Mueller bridge set to the se- lected temperature according to the resistance thermometers c
49、alibration. During the course of a measurement, the un- balance of the Mueller bridge was periodically corrected by minor adjustments to the automatic regulation system. This system included a thyratron-controlled heater and manually- controlled cooling supplied by a refrigeration unit. For tem- peratures above 90F no cooling was needed. In the auto- matic regulation system, bath temperature was sensed by one arm of a Wheatstone bridge. A variable adjacent arm outside the bath furnished coarse and fine temperature con- trol. The unbalance of this Wheat
