Phase Equilibria in Hydrocarbon Systems T
Joule-Thomson Coefficients for Gaseous Mixtures of Methane and n-Butane'
is HE of utility Joule-Thomson in the evaluation coefficient of the thermodynamic behavior of gaseous mixtures. This coefficient is especially useful a t pressures below 1000 pounds per square inch. The R. A. BUDENHOLZER, B. H. SAGE, AND W. K. LACEY present investigation involves the measurement of the Joule-Thomson California Institute of Technology, Pasadena, Calif. coefficients of five mixtures of methane and n-butane a t five temperatures between 70" and 310" F. Results were obtained at pressures beJoule-Thomson coefficients for five mixtures of methane and tween 50 and 1500 pounds per square n-butane were determined experimentally for five temperatures inch. These data permit the estimabetween 70' and 310' F. at pressures between 50 and 1500 pounds tion of the Joule-Thomson coefficient per square inch absolute. From these data, together with the for the methane-n-butane system isobaric heat capacity at infinite attenuation, the heat capacities throughout the gaseous region in the range of pressures where this coeffiof several mixtures were calculated as functions of pressure and cienj is bf greatest utility in the temperature. The results are presented in graphical and tabular evaluat'ion of the thermodynamic form. behavior of the system. The Joule-Thomson coefficient for methane was measured recently ( 2 ) temperature resulting from a small change in pressure under and is in good agreement with existing presaure-volumesuch conditions that the enthalpy of the gas remained contemperature measurements ( 6 ) . Perry and Herrman (6) stant. A sufficiently small change in pressure (12 pounds calculated the coefficient for methane by the use of the per square inch) was employed throughout this investigaBeattie-Bridgeman equation of state ( I ) , and these values tion so that the Joule-Thomson coefficient may be evaluated are also in reasonable agreement with the experimental directly from the measured finite changes in temperature measurements (2). The isobaric heat capacity of methane and pressure as indicated in the following equation : at infinite attenuation as calculated by Vold (IO) from spectroscopic data is in good agreement with values determined P = = H directly (8). The Joule-Thomson coefficient for n-butane was measured experimentally (4),and the results are in satisThe apparatus employed in this investigation was recently defactory agreement with published volumetric data (8). The scribed (2). In principle the method consisted of measuring the heat capacity of gaseous n-butane at atmospheric pressure change in temperature resulting from the flow of the gaseous mixture through a porous thimble under carefully controlled condiwas determined at temperatures between 100" and 340" F. tions. The change in temperature was measured by means of a (9). multilead three-junction copper-constantan thermocouple which These data for methane and n-butane, taken together was mounted upon suitable supports on the inside and outside with the Joule-Thomson coefficients reported in this paper, of the thimble. The change in pressure was measured by means of a mercury-in-steel manometer connected to the inlet and outpermit the establishment of the Joule-Thomson coefficients let of the porous thimble chamber. The entire thimble chamber and the isobaric heat capacities for the methane-n-butane assembly was immersed in an oil bath whose average temperasystem in the gaseous region at pressures below 1500 pounds ture did not change by more than 0.002" F. per hour. A speper square inch in the temperature interval between TO," cially constructed plunger-type compressor was employed to circulate the gas through the apparatus. The tubing connecting the and 310" F. compressor and the apparatus was steam-jacketed at a temperature in excess of 250" F. From information as yet unpublished Method it was established that at this temperature no condensation would occur with any of the mixtures investigated. The methane used in this investigation was obtained from The temperature of the oil bath was ascertained by means of a the Buttonwillow Field in California. After the removal of multilead copper-constantan thermocouple used in conjunction water and carbon dioxide by contact with magnesium perwith a White potentiometer and an agitated ice bath. The chlorate and granular potassium hydroxide, respectively, thermocouple was calibrated in place by comparison with a strain-free platinum resistance thermometer which had recently the methane contained less than 0.08 mole per cent of imbeen standardized by the National Bureau of Standards. I t is purities. The n-butane was obtained from the Philgas believed that the temperature of the gas entering the porous Division of the Phillips Petroleum Company, and their thimble was knovm in any case with an uncertainty of not more special analysis indicated that this sample contained 99.8 than 0.1" F. relative t o the international temperature scale. The three-junction multilead thermocouple employed in the mole per cent isobutane. measurement of the change in temperature of the gas during its The Joule-Thomson coefficients reported in this paper flow through the porous thimble was calibrated by the use of the were obtained by the direct measurement of the change in same platinum resistance thermometer. I t is believed that the differential thermocouple was calibrated with sufficient precision Previous articles appeared 1 This is the twenty-eighth paper in this series. to establish the change in temperature of the gas with an uncerduring 1934 t o 1939, inclusive, and in January, 1940.
(g)H [g]
384
MARCH, 1940
INDUSTRIAL AND ENGINEERING CHEMISTRY
tainty in any measurement of not more than 0.3 per cent. The mercury-in-steel manometer n-as calibrated at low pressures by direct comparison with a mercury-in-glass manometer (0.4 inch inside diameter). The differencesof mercury height in the latter were established by means of a vertical-component cathetometer with an uncertainty in individual measurements of not more than 0.005 inch in a length greater than 24 inches. Adequate supplies of mixtures of methane and n-butane were made up in steel containers at approximately the compositions desired for investigation. These containers were heated to a temperature in excess of 270' F. and were agitated for an extended period at this temperature in order to ensure uniformity of the sample. All of the connecting t,ubing between these containers and the circulating system of the apparatus was steam-jacketed to avoid condensation of n-butane. In the course of a set of measurements at a particular temperature, at least two samples were withdrawn from the circulating system for analysis, in order to ascertain any changes in composition which might occur. The compositions of t,he samples were determined by gravimetric gas density measurements at 100' I?.; sufficient care was exercised to permit the estimation of the mole fraction of n-butane in any of the mixtures with an uncertainty of not more than 0.003. together The volumetric data for methane (4)and n-butane (8), with unpublished experimental information concerning the volumetric behavior of gaseous mixtures of methane and ,n-butane, were employed in the estimation of the composition of the samples from the density measured at atmospheric pressure. Analyses of the material in the apparatus were made during the courEe of a given set of measurements, the samples being taken at different operating pressures. The results indicated changes in the mole fraction of n-butane of more t,han 0.005 in two out of seventeen cases. This probably resulted from some absorption of n-butane by the castor oil used in the lubrication of the compressor. In the other measurements these changes were much smaller and were neglected. These variations in composition necessitated in the two cases detailed interpolation of the individual isotherms, and in certain instances of the individual experimental points, in order to present the results at even compositions. I n measurements of this nature it is difficult to ascertain with accuracy the absolute uncertainty involved in the final results. However, it is believed that the composition of the system, the pressure, the temperature of measurement, and the change in temperature resulting from the measured change in pressure were established with sufficient accuracy so that the resulting Joule-Thomson coefficients are known with an uncertainty which does not exceed 2.5 per cent for a n y of the conditions reported in this investigation.
z
385
0.05
d 004 Y
c
\9
0.03
Y 0 02
~
250
500
753
Dqcssu?~
~a
2 50
1000 PER
so
Y
FIGURE 2. JOULE-THOMSON COEFFICIENTS FOR GASEOUS MIXTURES O F METHANE A S D n-BrrTaNE
Results
d typical set of measurements for a mixture containing 34.2 weight per cent n-butane is presented in Figure 1. The curves do not differ greatly in appearance from those for mixtures of methane and ethane, except that the maximum in the isothermal relationship of the Joule-Thomson coefficient to pressure is somewhat more pronounced in this case.
0.05
2 0
0 04
a W
a
\I.
Oo3
002
z_
I 1
006
I, 30
PER
CENT
I
40
N-BUTANE
FIGURE3. EFFECTOF COMPOSITION UPON THE JOULE-THOMSON COEFFICIENTS OF GASEOUS MixTURES O F METHANE Ah'D n-BaAxE AT 1000 POUNDS PER SQU.4RE INCH
005
m,
b .
I 20
*EIGHT
0 & I
a w a
1 IO
'04
a
I
I
I
250
500 PRESSUGE
750 LE.
1
I
1000
I250
PER
50
IN
FIGURE 1. JOULE-THOMSON COEFFICIENTS FOR A GASEOUS MIXTURE O F METHANEAND %-BUTANE CONTAIXING 34.2 WEIGHTP E R CEST n-BuTAh-E
I n this instance the changes in composition with temperature and pressure that mere encountered in the experimental study were sufficiently small (0.003 weight fraction) so that they have been neglected in the presentation of the data. V a n y of the experimental points shown were obtained from different sets of measurements made a t the same temperature. Figure 2 presents similar information for a number of mixtures containing smaller concentrations of n-butane. I n these cases the change in composition from one temperature to another was significant, as the curves indicate. The experimental points were taken both upon increase and decrease of pressure in the system, and the analyses taken at each temperature indicated that for these mixtures the
INDUSTRIAL AND ENGINEERIKG CHEJIISTRY
386
COEFFICIENTS AND ISOB.4RIC HEATCAPACITIES TABLE I. JOULE-THOMSOS TURES O F METHANE AND ?&BUTANE
Absolute Pressure
Temp.
F. 70
130
190
250
310
a p
b C,
-
-
-lO.O--
--2O.O-
FOR
Weight Per Cent n-Butane as Follons: 7-30 0 d 0 0C? P C? P cv
GASEOCSM I X - 4 0
0--.
-
Lb./sp. in. II CP P P CP 0.0519a O.5160b 0.0566 0.5018 0.0634 0.4875 0.0752 0.4733 . . . . 0.4691 0 0,5003 0.0546 0,5398 0.0594 0.5266 0.0668 0.5154 0 . 0 7 7 8 0.5064 . . . . 250 ........................ 0.0549 0.5684 0.0599 0.5580 500 0.0535 0,5995 0.0574 0.5909 . . . . . . . . . . . . . . . . . . . . . . . . 750 0,0505 . . . . 0.0524 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1000 0,0464 . . . . 0.0452 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1250 1500 0.0414 . . . . 0.0360 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.0411 0.5367 0.0450 0.5229 0.0506 0.5091 0.0589 0.4953 0.0705 0.4815 0 0.0429 0,5550 0,0469 0.5429 0.0527 0.5319 0.0612 0,5222 0,0746 0.5150 250 0.0433 0,5755 0.0473 0.5669 0.0531 0.5587 0.0615 0,5536 0,0732 . . . . 500 0.0422 0.5980 0,0460 0.5907 0.0520 0.5861 0.0585 0.5854 . . . . . . . . 750 0.0403 0.6220 0.0440 0,6149 0.0494 0.6100 0.0530 0.6061 . . . . . . . . 1000 1250 0.0377 0.6471 0,0413 0.6350 0.0454 . . . . 0.0446 . . . . . . . . . . . . 0.0346 .... 0.0382 . . . . 0,0400 . . . . 0.0340 . . . . . . . . . . . . 1500 0 0.0328 0.5610 0.0356 0.5472 0.0399 0.5334 0.0455 0.5196 0.0520 0 . 5 0 5 8 0.0342 0,5761 0,0369 0.5633 0.0414 0.5519 0,0466 0,5406 0,0534 0.5318 250 0.0345 0.5924 0.0373 0.5812 0.0417 0.5726 0.0470 0,5647 0.0536 0,5599 500 .... 0.0336 0.6095 0.0365 0.6004 0.0408 0.5940 0.0461 0.5911 0 . 0 5 2 5 750 0.0320 0,6273 0.0348 0.6195 0.0383 0.6169 0.0439 0.6176 0.0506 . . . . 1000 0.0296 0,6454 0.0324 0.6403 0.0358 .... 0,0420 . . . . 0,0478 . . . . 1250 0.0271 0.6628 0.0296 0.6580 0.0327 . . . . 0.0396 . . . . 0.0442 . . . . 1500 0 0.0256 0.5873 0.0282 0.5734 0.0315 0.5594 0.0357 0.5454 0.0404 0.5315 250 0 . 0 2 6 9 0.5998 0.0292 0.5863 0.0326 0.5730 0.0366 0.5609 0.0416 0.5520 0.0271 0.6127 0.0296 0.6001 0.0328 0.5881 0.0370 0.5781 0,0418 0,5717 500 0.0263 0.6260 0.0289 0.6147 0.0320 0.6044 0.0362 0.5969 0.0412 0.5936 750 1000 0.0250 0.6400 0.0276 0.6298 0.0309 0.6220 0.0350 0,6170 0,0398 . . . . 12.50 0.0233 0.6530 0.0259 0.6460 0.0290 0.6411 0.0333 0,6382 0,0378 . . , . 0.0214 0.6670 0.0239 0.6613 0 . 0 2 7 1 0.6594 0.0309 0 . 6 6 0 6 0,0353 . . . . 1500 0 0.0198 0.6151 0.0226 0,6008 0.0256 0,5865 0.0290 0.5722 0.0328 0.5579 250 0.0208 0.6252 0.0234 0.6112 0,0266 0.5965 0.0300 0.5832 0.0340 0,5724 500 0.0210 0.6360 0.0236 0.6221 0.0268 0,6085 0.0303 0.5951 0.0343 0 , 5 8 2 5 0.0203 0.6470 0.0230 0.6336 0.0261 0.6203 0.0294 0.6081 0.0334 0.5990 750 1000 0.0193 0.6581 0.0218 0.6456 0.0249 0.6328 0.0284 0,6224 0.0324 0.6142 1250 0.0182 0.6692 0.0206 0,6580 0.0234 0.6471 0,0266 0.6378 0.0305 0.6294 1500 0.0170 0.6813 0.0192 0.6702 0.0218 0.6616 0,0245 0.6544 0,0282 0.6495
Joule-Thomson coefficient, F./lb. per sq. in. = isobaric heat capacity, B. t. u. per Ib./" F.
\ 01,. 32,
NO.3
(10) and n-butane (9) by the concept of ideal solutions which applies with accuracy t o gaseous solutions a t infinite attenuation. The results of this calculation are recorded iri Table I. The isobaric heat capacity is presented in Figure 4 as a function of composition for several pressures at a temperature of 250' F. These results indicate a progressive increase in the isothermal coefficient relating isobaric heat capacity to precsure with an increase in the concentration of n-butane. The linear relation for states corresponding to infinite attenuation results from the assumption of ideal solutions under these circumstances. The change in the compressibility factor ( Z = PV/bT) with temperature may be ascertained from the Joule-Thomson coefficient and the isobaric heat capacity by means of the following general thermodynamic relation:
changes in composition of the system v i t h pressure Tvere inIntegration of Equation 2 permits the establishment of the volumetric behakior from a knowledge of the volume as a significant. The variation in the Joule-Thomson coefficient with comfunction of pressure a t a single temperature. Table I1 preposition for a series of temperatures a t a pressure of 1000 sents a comparison of experimentally determined compressibility factors for several mixtures of methane and n-butane pounds per square inch is depicted in Figure 3. These data with those determined from the information in Table I. I n indicate a progressive increase in the coefficient with an increase in the concentration of n-butane a t the lower prescalculating the values from the Joule-Thomson coefficient, the compressibility factors a t 250' F. were taken equal to sures. However, a t the higher pressures the coefficient reaches a maximum and decreases with a further increase in those determined experimentally. The agreement between the concentration of n-butane. These curves for the higher the two sets of values is not so good as was found in the case of the methane-ethane system (7). I n the present instance pressures cannot be extended t o states in the vicinity of pure discrepancies as large as 2 per cent were encountered a t the n-butane because of the separation of a liquid phase. The boundary between the single- and two-phase regions for this lower temperatures for the mixtures containing a large system has been established from unpublished dew point measurements. Because of the number of different compositions investigated, i t was not feasible to tabulate the experimental results directly. They were intemolated araDhicallv to even values of I pressure a i d comcoskon ahd are recorded in m 0.65 1250 ! -1 J a part of Table I. It is believed that no uncertainties greater than 0.3 per cent result from i n w these interpolations. From a consideration of a the precision of measurement attained in estab3 lishing the pertinent quantities involved in tascertaining these Joule-Thomson coefficients, m it is probable that no uncertainties greater 0.55 than 3 per cent are involved in the recorded values. By methods which have been outlined in detail (3) it is possible to compute the isobaric heat capacity as a function of state from the 20 30 40 50 heat capacity a t infinite attenuation and the WEIGHT PER CENT N-BUTANE recorded values of the Joule-Thomson coefficient, The heat capacity a t infinite attenuation FIGKRE4. ISOB.U~IC HEAT CAPACITIESO F G.ksEOUS MIXTURESO F METHaNE AND n-BrT.4SE AT 250' F. was established from published data for methane
