1252
INDUSTRIAL AND ENGINEERING CHEMISTRY
VOL. 32, NO. 9
AT ECONOMIC PIPE DIAMETERS TABLEI. VELOCITIES(FEETPER SECOND)
Bnom. Inches 1 2 4 8 a
z
7 -
-
Z = 105
Viscous FlowZ = 100 Z = 1000
3.06
.. .. ..
= centipoises.
0.97 1.6 2.5 4.1
b p =
0.31 0.49
0.77 1.3
-
p
= 0.0075b p = 0.075 Feet per second
20.8 22.8 26.4 31.0
41.6 44.3
51.0 01.0
Turbulent Flow p = 0.75 p = 7.5 10.5 11.4 13.2
15.5
p
5.3 5.5 6.6 7.7
= 50 3.1 3.2 3.8 4.3
p
= 75
2.6 2.9 3.3 3.9
pounds per cubic foot.
as would give this velocity. To illustrate the limits of such a procedure, tables for turbulent and viscous flow have been calculated which give the velocity under economic conditions for various viscosities, densities, and pipe sizes. From evidence on the turbulent table we could say with some degree of assurance that for most liquids the economic pipe size could be based on a velocity of 3 feet per second for small diameter pipes and of 4 feet per second for large pipes. But for lighter fluids and gases the economic velocity is much higher and varies over a wider range. As an approximation the velocity in the turbulent region may be said to vary inversely as the cube root of the density. I n the viscous table i t is impossible to pick any sort of average economic velocity. With a viscosity of 100 centipoises, the velocity varies from 1 to 4 feet per second as the pipe size changes from 1 to 8 inches; with a viscosity of 1000 centipoises, the velocity varies from 0.3 to 1.3 feet per second over the same pipe-size range. I n the viscous region the economic velocity varies inversely as the square root of the viscosity. The difficulty in trying to use an average economic velocity in the calculation of pipe sizes for pumping viscous fluids is therefore evident. Nomenclature The following consistent set of units has been used: AP = pressure drop, lb./sq. ft. L = length, ft.
p
V
Q
D q
Re p
= = = = = = =
density, lb./cu. ft. velocity, ft./sec. acceleration of gravity, ft./(sec.) (see.) pipe diameter, f t . flow rate, cu. ft./sec. Reynolds number, DV p / p , dimensionless viscosity, lb./(sec.)(ft.)
Other convenient units used are: 0 4 Z
= =
pipe diameter, inches viscosity, centipoises
Terms used in evaluating economic pipe diameter are as follows : =
= = = = = =
= = =
= = =
annual cost in dollars of 1 ft. of 1 in. i. d. standard pipe, (a,+ b) ( F 1) z cost of delivered energy, dollars/kw.-hr. annual cost of 1-ft. diameter standard pipe, dollars per linear f t . annual cost of supplying 1 ft.-lb. of energy per sec., dollars annual cost of pressure drop, dollars annual cost of pipe, dollars slope of logarithmic plot of cost of pipe us. diameter hours of operation per year optimum inside diameter, in. amortization expressed as decimal maintenance expressed as decimal factor for fittings and erection cost of 1-in. diameter pipe per ft. length
+
P-V-T Relations of Propylene WILLIAM E. VAUGHAN AND NOEL R . GRAVES Shell Development Company, Emeryville, Calif.
The P-I./-T relations of propylene have been measured over the pressure range 2 to 80 atmospheres and at temperatures varying from 0' to 300" C. The critical constants are as follows: t,, 91.4' C.; P , , 45.4 atmospheres; V,, 180 cc. per mole; d,, 0.233 gram per cc.
I
N RECEKT years the needs of the petroleum industry have greatly stimulated the investigation of the P-V-T relations of pure hydrocarbons and of mixtures. Demands for data by both production and refinery engineers have been answered by the presentation of much reliable and valuable information. However, these studies have been confined almost exclusively to paraffin systems, and there is an almost complete lack of comprehensive data on such materials as the olefins. Indeed, except for a few scattered and often unreliable values on critical constants of some of its homologs, ethylene is the only olefin for which a reasonably complete set of P-V-T data exists (2, 5-8). The rapidly increasing use of unsaturates as basic starting materials for
many important products requires exact knowledge of the physical behavior of these compounds. A step in this direction has been made by the following study of propylene in the temperature range 0-300" C. and a t pressures varying from 2 to 80 atmospheres.
Apparatus, Material, and Method The principal item of equipment is a steel compressor unit, with mercury as the liquid, onto which glass capillary tubes containing the samples are mounted. This form was first used by Andrews (about 1869) and extensively developed by Young (11). Our apparatus is essentially the same as that of Kay (3); the only significant changes have been the addi-
INDUSTRIAL AND ENGINEERING CIII3MISl'RY
1253
Ken; otherwive tho contact with t.be frozen liydrocnrbon rosulted i n vaporization and loss of a portion of the latter. Great care had to be exercised on this score.) Atmospheric pressure wm restored in the line; and after removal of the special glass joint, the capillary was ready for transfer to the compressor. The first attem t s to perform this operation met with &lure beemso a small bubble of air would invariably become trapped in the open end of tlie tube as it WBS capped and inwried in the large cup of mercury temporarily monnted an the tube holder on the compressor. The difficulty wm overcome, however, by fitting a small glass cap over theopen end of the capilh r y t o one of the rubbor gaskets on the tube; this cap could be filled with merciiry through a small opening 80 that the end of the tube itself was well covered. Any bubble of air would now rise into the cap rather than into the capillary as the latter ycm being invcrted. The buret and the experimental capillaries were calibrated at olosely spaced points by addition of weighed quantities of mercury; the distance of the mercury meniscus froin a finely etched reference line was measured with a cathetometer. Vohimes in the capillaries could be measured within =!=0.0002cc., which corresponds to about *2 cc. in the molal volume for the amounts of gas used in this experiment. The smallest division on tho vernier of the cathetometer was 0.05 mm. The instrument was checked against a meter bar calibrated by the Nat,ional Bureau of Standards and found to be correct within 0.05 mm. when tho object was at a distance of 1 meter The two nitrogen rnanoineters used a t 25.00' * 0.05"C. lor measuriiig the pressures were calibrated against an open mercury irianometer up to 2 atmospheres. Above this pressure the c a l i b r a t i o n was against a deadweight gagc:. The prossures could be read to 0.1 per cent except at the highest prcssnres, where the readings were precise to 0.2 per cent. After all of the P-V-Z' nieasurements hiid been completed, the manometers A. Female standard tapor No. 24/40 ioint were recalibrated n. Mnlc standard taper No. 24/40 joint with Uewnr-sealed tube lor holding and no change the onpiliery from the original c. Apierun a e d i n g oompound covered with determination was Rl1011a0 found. u. Experimental oapiilaiy tubs e. Glaas rod to prevent onpill~ry from The experimeiibeing aiicked upward by v&ouum tal capillaries were 5. Trap in rneroury line to prevent Ontry maintained a t the 01 foreign BBSes required temc;. hIioiostoDoooks
s UETE~M~N TIE I NP-V-T G REIATIONS or PIloPYLENE F r c o a ~I. A u p ~ a m u 808
tioii of a secoud experimental capillary om the compressor block and modification of the filling apparatus and technique. A general view of the equipment is shown in Figure 1. The experimental capillary was fixed in the filling apparatus with a special joint into which it was sealed with Apiezon wax (Figure 2). In addition, the charging unit possessed the folloniiig parts: a mercury diffusion pump and McLeorl gage, a calibrated buret accurately therniostaied at 25' C., a crude auxiliary manometer, mercury iereling bulbs, a reservoir containing tho snmple of propyleire, a.nd the nccessarj, vslvcs and st,opcocks. The outlet of the buret was fitted with a thermostated all-metal valve, free of grease and paakiirg in wliiclr hydrocarbon could dissolve. These valves, elptihli: of holding high vaonum on either side of the seat, used a half-incli c ~ p p c rbellows as a body; the seat of suft mlilcr pressed against, the eiid of a small stainless steel tribe incli o. d. and ' j l Biiicli i. (I.)> and a tapered rod in the etviter of the seat and prujectiiig into tire tube provided fur dose regulation of flow. The filling proccdllre is described in some detail, not beaim of its uniqueness but rather as a possible aid to n'orkers i n the field; t,he following steps were evolved after rniiclr troublesome experirneiitatioii:
~"
~~
iiiaintnined for 30 minutes after &e System n n s h u t off from tIie diffusion pump. 2. Tho buret, inis filled with imq&ne. TYi'iienever volirine nicanire,mtmts were being made, tlie pressure in t,he hwet was always adjusted to atmospheric by means of a mercury lcveling bulb m d an open side iirm of t!io same intenm! diaiiieter LLSthe hiiret. When in propor adjustment, no difforencr i n tile levels in the buret and in the open skit: itnn WLS detectthle by eathetometer obaewation. 3. Aiter the evactmteci capillary ivuj shut off from tlie p u m p ing system by t~ mercury cutoff and tlia Apieaon scaling con,pound yias covered with mercury, the desired amllilnt of propylPIW was adnritted from the buret through the all-metd valve. The vo!unie was determined by mom~rcmuntof t,he distmres of the mercury level in tile buret from i ~ netched rdermce line by means of tlie eathetometer. The IIydroenrbon was condensed by cooling with liquid nitrogen. As long a time us 15 or 20 minutes was necessary fur condensation, after which the pressures were 0.0002 and 0.0004 mm. of mercury for capillaries 1 and 2, respectively. 4. Mercury was then flowed into the capillary. (The mrrcury WM chilled by flow through a zone eoolod with liquid nitro-
INDUSTRIAL AND ENGINEERING CHEMISTRY
1254
VOL. 32, NO. 9
TABLE I. COMPRESSIBILITY FACTOR Z FOR PROPYLENE Reduced Pressure, PI
0.05 0.1 0.15 0.2 0.25 0.3 0.4 0.5 0.6
0.7 0.8
0.9 0.98 1 .o 1.02 1.1
1.14 1.16 1.18 1.2 1.3 1.4 1.5 1.6 1.7 1.8
0,749
T,: 1.229
91.4 0.982 0.966 0.948 0.930 0.912 0.889 0.848
Reduced Temperature, 1.023 1.092 1.160 Temperature, O C.: 100 125 150 0.984 0.987 0.990 0.969 0.975 0.981 0.953 0.963 0.971 0.936 0.949 0,960 0.918 0.935 0.948 0.899 0.919 0.936 0.861 0.890 0.911
175 0.992 0.985 0.977 0.968 0,958 0.948 0.929
0.966 0.958 0.942
0.800
0.818
0.864 0.840 0.814 0.789
0,910 0.891 0.872 0.852 0,833
0.818
0.886
0.955
1.000
0 0.954 0.907 0,022 0.028 0.035 0.042 0,055
25 0.966 0.930 0.893 0.851 0.798 0.043 0.057
50 0.974 0.948 0.920 0.890 0.858 0.823 0.744
75 0.980 0.960 0.939 0.917 0.894 0.869 0.816
0.069 0.083 0.097 0.109 0.124
0.071 0.085 0.099 0.113 0.127
0.075 0.090 0.104 0.119 0.133
0.757
c
o:iis o:i4i
0 : i47
0.748 0.692 0.625 0.144 0.536 0.422 o:i57 0.273 0.686
0,210
o:i5i o : i % o:iSi o:iii ... ... ... ... ... ... ... ... o:i& o:i69 o:ii5 o:i84
0.202
0,179
0.219 0.230 0.242 0.254
... ... ... ... ...
0.183
... ... ...
... ...
0.188
... ,.. ... ... ...
0.197 0.211
... ... ...
...
...
... o:iog
0.266
0.278
0.888
0.608
0.859 0.828 0.795 0.761 0.724
0.547 0.529
0 685
0 : 762
0:8i4
0:4i8
0.774 0.727 0.673
0.597 0.131
:
1.298
1.366
1.435
1.503
1.572
200 0.994 0.988 0.982 0.974
225 0.995 0.990 0.985 0,979 0.973 0.966 0.953
250 0.996 0.992 0.988 0.983 0.978 0.972 0.961
275 0.966 0.993 0.989 0.985 0.981 0.976 0.967
300 0.997 0.994 0,990 0,986 0.982 0.978 0.972
0,928 0.940 0.912 0.927 0.896 0.915 0.882 0.904 0.868 0.892
0.949 0.939 0.930 0.912
0.958 0.949 0.941 0.933 0.926
0.965 0.957 0.949 0.942 0,936
o:ss1
0 : 903
o:Sig
0:sio
o:Sio
0:8S3
o:iii ...
0:9i4
...
... ...
o:SS5
o:go4
0:iis
0:644
o:% ... ...
o:ii5
0,346 0.305 0.280 0.268
...
...
0:8is ... ...
0:6oo
0:7o7
o:ii5
0:8i3
0.255 0.256 0.262 0.270 0.280 0.288
0.549 0.499 0,456 0.421 0.397 0.381
0.680 0.652
0.757 0.809 0.737 0,795 0.719 0.781 0,699 0.765 0,679 0.751 0.661 0.736
... ...
0.625 0.598 0.571 0.543
0.920
... ...
... ... 0:860
. Liquid Satd.
Satd.
0.015 0.022
Vapor 0.943 0.896 0.857
0.060
0.798 0.773 0.724
0.007 0.029 0.036 0.044
0.826
0.137 0.167 0.214 0.273
0.678 0.630 0.578 0.514 0.433 0.352 0.273
... , . . ... ... ...
... .. .. .. ... ...
...
... ..
0.076 0,096 0.116
0.848 0.875 0.897 0,914 0.837 0.867 0.890 0.908 0.826 0.859 0.884 0.903 0.814 0.851 0.879 0.898 0.803 0.844 0.875 0 . 8 9 4 0.793 0.838 0.871 0 . 8 9 0
... ... ... ...
... ...
...
... ... 1
... ...
peratures by vapor baths manostatically controlled to within 2 mm., or approximately 0.1' C. The boiling liquids used were as follows: diethyl ether, acetone, isopropyl alcohol, tert-amyl alcohol, chlorobenzene, bromobensene, aniline, methyl salicylate, quinoline, l-bromonaphthalene, and benzophenone. I n order to increase the ease of maintenance of constant temperature, each vapor jacket was either Dewar-jacketed or sheathed with an electrically heated copper tube provided with two viewing slits. (The Dewar jackets, even when provided with expansion bellows, were very
susceptible to rupture because of thermal strain.) The temperatures were measured by single-junction copperconstantan thermels and a Leeds & Northrup Type K-1 potentiometer. Calibrations were made against a platinum resistance thermometer certified by the National Bureau of Standards. Readings precise to 1 microvolt could be obtained on the potentiometer, which corresponds to about 0.025' C. a t the lower temperatures. Thus the absolute values should be certain to at least 0.1' C. The propylene used in this experiment was prepared from isopropyl alcohol by dehydration in a furnace over a l u m i n a c a t a l y s t . The sample was distilled once in a pressure column a t a mean pressure of 180 pounds per square inch gage. As the sample still contained traces of impurities, i t was subjected to two carefully performed distillations a t atmospheric pressure in a Podbielniak column. The last minute traces of air were removed from the hyVS. REDUCED PRESSURE (Pr= drocarbon by evacuation with the mercury diffusion pc'45.4 Atm. pump while the sample was condensed in liquid nitrogen; the sample was frequently shut off from the 0.2 0.4 0.6 0.8 10 . 1.2 1.4 1.6 1.8 REDUCED PRESSURE pump, vaporized, recondensed, and repumped. FIGURE 3. PROPYLENE ISOTHERMS TABLE11. PROPERTIES 7 -
T:rnp.,
C.
0 25
50 75 90 91 91.4
Tr=
T/364.56 0.7493 0.8179 0.8864 0.9550 0.9962 0,9989 1.0000
P. Atrn. 5.76 11.38 20.28 33.50 44.18 45.08 45.4
P, 0,1267 0.2507 0.4467 0.738 0.973 0.993 1,000
Molal vol.,
cc.
71
78
OF
SATCRATED PROPYLENE LIQUIDAND Density,
T'r
0.394
88 106 143
0.433 0,489 0.589 0.794
152
0.844
180
. -Molal
Saturated Liquid
1.000
P17/RT 0.0182
0.0363 0.0673 0.124 0.212 0.229
0.273
g/cc.
0.590
0.537 0.478 0.397 0.294 0,277 0.233
vol
cc.
VAPOR
Sa-curated Vapor
,
3410 1715 919 473 242 223 180
T -7
18.94 9.53 5.106 2.628 1.344 1.239 1.000
PV/RT
Density, g./cc.
0.875 0.798 0 0 . 5703 55
0.0246 0.0458 0.0890
0.3.59 0.336 0.273
0.174 0 189
0.0123
0.233
\lean Density. g./cc.
0.301 0.281
0,262 0.243 0.234 0.233 0.233
SEPTEMBER, 1940
INDUSTRIAL AND ENGINEERING CHEMISTRY
The gas density, which was a necessary datum for the calculation of the amount of hydrocarbon in the tubes, was measured by standard methods and with proper precautions. The values of the density a t 760 mm. of mercury and 25" C., in grams per liter, were 1.7459, 1.7448, and 1.7455 (average, 1.7454 * 0.0004). Our values compare well with that found recently by Powell and Giauque (9),who give 1.7461 grams per liter a t 1 atmosphere and 25" C. The density a t 0" C.
1255
the elevated temperatures. Although corrections were made on the assumption that the partial pressure of mercury was the same as the vapor pressure of pure mercury, i t is possible that the propylene was not completely saturated or that Dalton's law does not hold for this mixture. No stirring was deemed necessary for this study of a one-component system; in future work involving two-component systems, a soft iron stirrer magnetically actuated will be used. In calculating all volumes and pressures, corrections were made for the volume of the meniscus, capillary depression, and differences in mercury levels. All mercury heights were corrected to 0" C.
The Data No comparison of the present data, other than the critical constants, with previous work is made, since little pertinent information exists on the physical behavior of propylene. We believe, however, that the values given are accurate to approximately one per cent. D EXPERIMENTAL TUBE NO.
I
%EXPERIMENTAL TUBE NO 2
TEMPERATURE, C '
FIGURE 4. ORTHOBARIC DENSITIES OF PROPYLENE and 1 atmosphere was measured by Batuecas ( I ) , who found 1.9149 grams per liter as the average of a series of seemingly careful measurements; however, calculation on the basis of this value and the present compressibility factors gives 1.734 grams per liter at 25' C. and 1 atmosphere. We can offer no explanation of the discrepancy. The purity of the sample is also indicated by the difference between the bubble- and dew-point pressures. Kay (4) sets 2 pounds per square inch as a limit and considers any sample which has this difference or less to be of sufficient purity. We have adopted the same criterion, and a series of measurements from 0" to 91" C. showed that the contents of capillaries 1 and 2 fulfilled the restriction. However, as KO. 2 showed the larger difference in almost every case, only half as much weight was given to the points obtained therefrom. Although the bubble points were always sharply detectable, there was some uncertainty in the visual determination of the dew point. The compressibility factor ( P V / R T ) was always greater for the gas in capillary 1 than for that in 2. The differences in the compressibility factor were determined for each isotherm at three different pressures and the average values were: 60-65 atmospheres, 1.1 per cent; 40 atmospheres, 0.9 per cent; 10 atmospheres, 0.2 per cent. The experiment was carried out by making a series of volume and pressure measurements a t a constant temperature. The pressure ranged from 2 to 80 atmospheres; and points were obtained a t intervals of from 2 to 4 atmospheres. After all of the isotherms (except that a t 300" C.) had been completed, a few points were again obtained for the isotherm first determined, that a t 50" C. These new points checked with the original values, showing conclusively that there had been no changes in the propylene, the capillaries or the manometers. At the highest temperatures (above 200" C.) the experimental low-pressure points were found to be unreliable and were discarded. Values given in the tables are obtained by interpolation between higher pressure points and zero pressure where P V / R T is 1. The poor results in this region are thought to be due to the high partial pressure of mercury a t
'
O'
-hO
-40
-20
d
20
TEMPERATURE,
40
60
80
'C
FIGURE 5 . \-ARI24TIOX WITH TEMPERATURE OF HEATOF VAPORIZATIOX OF PROPYLEXE
The figures in the tables are smoothed data, rather than the experimental values, and were taken from curves drawn to give approximately twice as much weight to the points obtained from capillary 1. Cross plots were also made as a n aid in smoothing and in order to be certain that the data would be consistent among themselves with a precision of 0.2 per cent. P-V-T VALUES. Table I gives the compressibility factor, Z = P V / R T , as a function of the temperature and the reduced pressure, p,. These data are presented graphically b y Figure 3. Various properties of the saturated liquid and vapor are given in Table 11, and Figure 4 is a plot of the rectilinear diameter embodying such data:
R
+
= 82.06 cc. atmospheres; T o K. = t o C. 273.16 V , = V/V,; P, = PIPc; T, = T I T ,
HEATOF VAPORIZATION.The heat of vaporization has. been calculated for several temperatures by use of the Clapeyron equation, dP/dT = A H / T A V
The dope OS tlie v a p r pressure curve was obtained a t several temperatures from a large-scale plot of log 'I against 1/T. The calculated values are as follo~~s:
Althougli it is (lifficult to estimate tlic accuracy of these, i t seems t.hat they are valid to about one per cent. Consideration of Figure 5, a plot of our AfI (vaporiaatioii) values against temperature, bears out tliis contention, since extrapolation to -47.75" C. (boiling point of propylene) gives 4390 calories per mole, to be compared with Powell and Giauque's recent and accurate direct calorinietric value of 4402 calories per mole (9). CHITICAL C o ~ s ' r a ~ ~The s . critical temperature was taken as the highest temperaturc a t which a permanent meniscus could be observed. At 0.05" C. above the cliosen critical temperature a meniscus could be foimed liy sudden expansion from shove the critical pressure (cooling by expansion), but it disappeared upon standing. At 0.05' C. below the critical tcrnperature the amount of liquid could be increased by slow compression, but rapid compression caused the meniscus to disappear because of adiabatic heating. The experimental
THE APOTHECARY Artist Unknown
No.
117 in the Berolzheimer Series of Alchemical and Historical Reproductions is a real puzzle. It has been impossible to ascertain the locatioii of the original painting, the name of the artist, or the date when the original was painted. The photograph from which our halftone was made was obtained from a commercial photographer w h o "copied it from somewhere" because h e liked i t . T h e "menagerie" hanging from the ceiling, the "yarbs" on the bench and shelf, and the meager supply of laboratory equipment clearly exclude alchemy. But w e think that this picture fits appropriately into our series merely because we like it. D. D. BBROLZHEIMEH 50 East 41s' Street New York, N. Y.
values are: capillary 1, 91.36' C.; capillary 2, 91.43' C. The critical pressure and volmrie were obtained from the appropriate plots. Additional isotherms were obtained at 90°, 91", 91.4', and 92" C. in order to obtain a better definition of the critical region: Critical temperature, 91.4O C. (364.56O K.); critical pressure, 45.4 atmosplieres; critical volume, 180 ce. per mole; critical density, 0.233 gram per cc.; molecular weight, 42.08. These data and the "beat" values critically choseii by Soiiders (10) are in excellent agreement. Souders' values are: t,, 91.9' C.; P,, 44.6 atmospheres; IFc, 179.7 ec. per mole; do0.234 gram per cc.
Aeknowled,"rntmt We are indebted to F. I). Tueminler and F.F.F ~ i sS
