December, 1944
INDUSTRIAL AND ENGINEERING CHEMISTRY
1161
p = number of theoretical plate counting from solute-rich end of apparatus 8 = exponent in Equation 4, also slope of Equation 4 on lop plot q = number of molecules in equilibrium Equation 2
An equation for the general case of Xa and YOnot negligible may be obtained, but it is very complicated. In such cases evaluation of the concentrations plate by plate may be readily performed by means of Equations 5 and 8.
x'/y' NOMENCLATURE
X Y
--
--
8
(pounds solute)/(pound solute-free solvent in phase 8 ) (pounds solute)/(pound solute-free solvent in phase C) a degree of dissociation y = activity coefficient
-
A = molecular formula of solute [A] concentration of solute B = subscript indicating solvent phase B C subscript indicating solvent phase C (7 (pounds/min.) of solute-free solvent h phase C K equilibrium constant of Equation 3 Ki = equilibrium constant of Equation 4 K# = equilibrium constant of Equation 1 L (pounds/min.) of solute-free solvent in phase B m = exponent in power series of 8, Equations 10,11,14, and 15 n = exponent in power series of 8, Equations lo, 11, 14, and 15
-
LITERATURE CITED ( I ) Fock, A., 2. Krist., 28,337 (1897). (2) Goodman, J. B.,and Krsae, N. W., IND.ENC). &EM.,
23, 401
(1931). (3) International Criticd Tables, Vol. 111,p. 418 (1928). (4) Kihter, F. W.,2.ph&k. Chem., 13, 446 (1894). (6) Perry, J. H., Chemioal Engineer's Handbook, 2nd ed., p. 1128 (1941). (6) Varterehan, K. A., and Fenske, M. R., IND.ENO.CHEY.,28. 928 (1936).
5
Liquid Densities of Volatile Hydrocarbon Mixtures GEORGE H. HANSON', BLAINE B. KUIST', GEORGE GRANGER BROWN
AND
Univeraity of Michigan, A n n Arbor, Mich.
ETHODS for estimating the density of grtses from the theorem of corresponding states and from the use of partial molal volumes have proved satisfactory. Sage, Hicks, and Lacey (8) suggested a method of using partial molal volumes for computing the density of hydrocarbon liquids. Within the range covered by the data, the results agree within about 3% of the experimental values. However, the composition mnge is limited to about 10% by weight of methane; COnfjeouentlv. this correlation does not cover the low-moleculapweight liquids kmilar to natural gasoline and liquefied petroleum gases. Standing and Kate (3)presented a method for computing liquid 'densities, assuming additive volumes for all compounds less volatile than ethane and using apparent densities for methane L 0 and ethane in the liquid a t 60' F. and one atmosphere pressure. These apparent densities were a W given in the form of a chart (Figure 1) as a P function of the weight per cent of ethane, or fci methane, in the mixture containing ethane, or ( V methane, plus less volatile components, respectively, and the density of the remainder (less az 0 volatile) of the liquid. This method is convenient LL and was demonstrated to be reliable within about 0 1.570 in predicting the- densities of saturated crude oils in equilibrium with natural gas. Watson (4) reported a method for estimating mlthe density of a pure compound from its z m w >. molecular weight, critical temperature and nv)
premure, and an expansion factor, Gamson and Weteon (6) developed the application of these expansion factors to solutions based on Equation 3 of Watson's originaI article ( d ) , expressed by the following Equation 1:
v =+ 1 [%gmA where
v
P
-+ 2 m g +
+ . . .] (1) volume of liquid solution of mass r n ~+ t r t ~+ mc.+ . . . a t temperature T and pressure P
W'
PAI
PBI
PCI
mc
3
1 Preaent addresa, Phillips Petroleum Company, Bartleaville, Okla. * Present address, Standard Oil Company of California, El Sagundo, Cafif.
APPARENT
DENSITY
AT
60%
A N D I ATM.
, G M . /CC:
Figure 1. Apparent Density of Ethane and Methane
INDUSTRIAL AND ENGINEERING CHEMISTRY
1162 >.
c
Vol. 36, No. 12
.25
The use of apparent densities for methane and ethane in t h e liquid phase, suggested by Standing and Katz for estimating t h e density of crude oil saturated with natural gas a t high pressures, has been extended to liquid mixtures of volatile hydrocarbons as found i n natural gasoline. The modified expansion factor method suggested by Gamson and Watson also appears satisfactory for estimating t h e density of a complex liquid mixture such as natural gasoline from t h e composition of t h e mixture.
u)
z
W
t ul
z
W
P
Figure 2.
w'
WA,
Effect of Pressure on Density of Liquids a t 60' F.
rsure,
= expansion factor for entire mixture a t temperature
and determined as function Of pseu o reduced temperature and pressure ( 4 ) = expansion factor of component A at reference condition of temperature T,il and pressure P r t where its density is P A , .
MOLE
Densities calculated by this equation were reported by Gamson and Watson to deviate less than 5% from the data on binary liquid systems reported in the literature. I n the course of other work it was possible t o determine the liquid densities of a number of mixtures containing the volatile
WEWT
t
MOLE WEIGHT
I
CORRECTION
Figure 3. Effect of Temperature on Density of Liquid Normal Paraffins
December, 1944
INDUSTRIAL AND ENGINEERING CHEMISTRY
1163
cent of ethane in the "ethane plus". A similar procedure is followed for methane to compute the density of the entire liquid, A somewhat simpler but less accurate procedure is incorporated in the use of Figure 4 instead of Figure 1. The density of the liquid, exclusive of dissolved methane and ethane, is computed as before. Using this density as the density of the remainder of the system, Figure 4 is entered a t the top. Follow this abscissa down until it intersects the line corresponding to the weigh; per cent of ethane in the liquid, including ethane and less volatile components but excluding pethane. Read the density of this liauid as indicated along the lek-hand ordinate. Use- this density as the point of entry at TABLE I. PROPERTIES OF LIQUID SAMPLES the bottom of Figure 4. Follow Sample No. 1 2 3 4 5 6 7 8 9 the abscissa vertically to the indicated weight per cent of 0 5574 0 3868 0 4612 0 3472 0 4199 0 1479 0 2866 0 3838 0.6251 methane in the total liquid and 0'1222 0'1314 0'1308 0'1326 0'0762 0:0438 0'0718 0'0756 0 0727 0:1369 0:1755 011490 0:1893 0:068l 0.0814 0:0780 0:0706 0:0597 read the density of the total 0.1066 0.1522 0.1323 0.1129 0.0840 o:ossi o:iiis o:iiie o : i i i 3 0 . m 8 0.5747 0.4313 0.3672 0.258b liquid along the righehand 0.0984 0.1624 0.1434 0.1697 .... .... .... ordinate. 39.16 44.16 33.27 42.32 42.03 57.69 49.01 43.87 36.77 Molecular 7ei ht 610.0 The density of the total liquid 592.9 663.7 692.3 612.0 732.0 656.2 609.8 543.4 Pseudo Ta, 6. 602.4 612.0 696.8 630.7 596.9 643.6 574.2 691.0 613.7 Pseudo Ps, lb./aq. in. abs. a t 60' F. and one atmosphere 1.049 0.906 0.963 0.874 0.946 0.765 0.853 0.919 1,031 Pseudo TI 2.748 3.786 3.373 2.977 3.880 0.9bl 1.693 2.195 2.829 Pseudo Pr pressure is corrected for the 7.3 100 77 77 100 100 77 100 100 Temperature F. effect of pressure by Figure 2. 1822 1640 2447 2032 2260 617 972 1297 1736 Pressure, lb./sq. in. abs. The temperature correction is 0.456 0.469 0.454 0.386 0.480 0.563 0.500 0.470 0.406 Exptl. density, p a m / c c . 0.496 0.460 0.486 0.446 0.566 0.378 0.508 then made with Figure 3 or by 0.466 0.369 Computed density (3) -1.8 1.2 -2.4 b.5 1.3 0.5 1.2 -0.9 -9.1 Per cent error the N.G.A.A.standardfactors for 0.094 0.102 0.088 0.100 0.097 0.109 0.101 0.096 0.086 Wataon expansion factor volume correction (1). The re0.470 0.434 0.487 0.377 0.455 0.543 0.489 0.453 0.384 Computed density (6) -2.1 -2.1 -4.8 3.8 0.2 -1.8 -2.2 -3.6 -6.4 Per cent error sults obtained with the N.G.A.A. standard factors on all mixtures whose densities at 60" F. and the indicated pressures were between 0.500 and 0.700 (the range covered by the N.G.A.A. facThe liquid density at the temperature and pressure in the tors) were nearly identical with the results obtained with Figure pycnometer was calculated from the volume and weight of the 3. Consequently, these values are not reported in Table I. In sample. The sample volume was computed from the total volume using Figure 3, the chart is entered using the density of the liquid of the pycnometer and the volume of the undisplaced mercury. at the left. The intersection of this ordinate with the indicated The weight of the sample was computed (a) from the results of temperature curve (in this case 60' F.) determines the equivathe fractional analysis made on the entire sample and (b) from lent molecular weight of the normal paraffin which is used to read the weights of the pycnometer filled with mercury, the mercury displaced, the pycnometer filled with sample and undisplaced the density at the desired tempeqture. The method is indicated in the following example: mercury, the undisplaced mercury, and the weight of the empty pycnometer. The weights based on the fractional analyses proved to be the more accurate, and the densities calculated from CALCULATION OF DENSITY OF SAMPLE 8 these values are reported. Table I gives the compositions of the various liquid samples in CumulaMole Weight tive Wt. terms of mole fraction, the temperaturea and pressures at which Fraotion Gram' (Upward) we#at' the densities were measured, and the experimental densities in CIiA 0.3838 6.16 43.87 14.04 grams per cc. It includes the densities computed by the method CrHl 0.0766 2.27 37.71 6.01 CIHB 0.0705 3.11 3b.44 ... of apparent densities suggested by Standing and Katz (S),using 0.1129 6.56 n-CaHie ... ... n-CrHir 0.3672 25.77 an extension of their pressure correction chart (Figure 2) and the ... Cumuiatemperature correction chart (Figure 8). The table also gives the tlve pseudocritical temperatures and pressures, the Watson expansion factors, and the densities calculated by the modified expansion CHI 0.220° 28.00 91.44 factor method of Gamson and Watson (6). CIH~ 0.4366 5.21 63.44 CIHI 0.610 6.10 58.23 According to Standing and Kats (S),the density of the liquid n-CtHu 0.684 11.23 ... is computed a t 60' F. and one atmosphere pressure, using the n-CiH11 0.6ai 40.90 ... densities of the pure components as listed below and the apparent Density of CI 0.696: Fig. 1 gives apparent density CI 0.220. densities for ethane and methane indicated in Figure 1: b Density of Cs+ - 0.609: Fis. 1gives apparent density CI 0,435. Dsnrity at 60. F ,
p a r a h hydrocarbons from methane through hexane. The liquid mixture was prepared synthetically in a bomb under pressure in a thermostat. A steel pycnometer, previously filled with mercury and weighed, was also maintained at constant temperature in the thermostat. The liquid mixture was transferred under pressure to the pycnometer by displacement with mercury, and the pycnometer was then detached and weighed. The hydrocarbon liquid was analyzed in a Podbielniak low-temperature fractionation column. The undisplaced mercury in the pycnometer was collected and weighed.
....
....
...
-E-
-
QramdCo. 0. aio 0.664 0.684
0.626
0.6al 0.664
The density of the liquid, exclusive of dissolved methane and ethane, is computed at 63' F. and one atmosphere pressure, using the densities of the individual compounds. The apparent density of ethane is then determined from Figure 1, using the density of the liquid exclusive of methane and ethane and the weight per
.
Denaity of CI+
-
= 0.480
-
at 60' F. and 1 atmosphere.
Density a t 1297 lb./sq. in. and 60' F.
-
Density at 1297 lb./sq. in. and 100' F. 0.602 X 0.9278
0.480
--
+ 0.022 (from Figure2)
0.502
0.466 (from Figure 3) 0.466 (by N.G.A.A.
factors)
INDUSTRIAL AND ENGINEERING CHEMISTRY
1164
Vol. 36, No. 12
v
2
V
W
c
a
w
0.
I
c w 2
L
0 >-
t VI Z
W
n
Figure 4.
Graphical Calculation of Liquid Densities at 60' F. and One Atmosphere Pressure
INDUSTRIAL A N D ENGINEERING CHEMISTRY
k m b e r , 1944
In the modified expansion factor method (6)of Gamson and Wsteon the following values of pL/wl calculated from the densities et the normal boiling points of the components are used: Component CH4 CaHo CaHi n-CdHu n-CnHlr n-CeHu
a.36 4.42 4.76 6.04 6.16 6.24
0.3838 0.0766 0.0706 0.1129 0.3672
-
1.0000
Pseudo
Pseudo PS Lb./Sq. Id.
6.16 2.27 3.11 6.66 25.77
132.0 41.6 47.0 86.5 302.2
268.3 63.8 48.6 62.2 173. a
43.07
609.3
-
-
-.
691.0
-
Pseudo T, 560/609 0.919; pseudo P, 1297/591 2.195. Using Figure 1 of Watson's original article ( d ) , the expansion factor for the entire mixture a t 1297 pounds per square inch and 100' F. equals 0.096: I,
1 [56 0.096 3.35
-
96.92 cc. 43.87
= 0.453 gram/cc. CONCLUSION
Ts,* R.
Weight, Oram
Mol? Fraotion
-
Density
-
PIIWI
Calculation of liquid densities by this method is illustrated below for sample 8:
CEI CaE; CaHa n-CtHu n-CtEn
v.=-0.096
1165
2:27 4 42
6.56
311
4-
~
4-
25.77
m+ml
The use of apparent densities (3)and the modified expansion factor method (6)appear reliable for calculating the liquid densities of volatile hydrocarbon mixtures from the compositions of the mixtures. The average error in the use of apparent densities in the calculation of the liquid densities of the volatile hydrocarbon mixtures reported here is -0.50j0, and the average error in the use of the modified expansion factor method is -2.0%. LITERATURE CITED
(1) Natural Gasoline Assoc. of Am., Standard Factors for Volume Correction and Specific Gravity Conversion of Liquefied Petroleum Gases and Volatile Gasolines (adopted May, 1942): tables expanded Dec.. 1942. (2) Sage, B. H., Hicks, B. L., Lacey. W. N., A.P.I. Drilling and Production Practice, p. 402 (1938). (3) Standing, M. B.,and Kats, I). L.,Trans. Am. Inst. Minino Met. Engra., 146,169 (1942). (4) Watson, I(.M.,Im. ENQ.CaEm., 35,398 (1943). (6) Watson, K.M., private oommunication. PBIIINTED
before the Division of Petroleum Chemistry at the 106th Meet-
ing of the AMBRIOAN CEBMICAL SOCIBTT. Pitteburrh, Pa.
Plastic Characteristics of Coal CORRELATION WITH CHEMICAL AND PHYSICAL PROPERTIES AND PETROGRAPHIC COMPOSITION t l l HE chemical and physical proper-
R. E. BREWER
by the type or types of coal present. Earlier investigations (3,81, dd, $4) Central Experiment Station, showed that, with increasing temperaOf U. S. Bureau of Mines, Pittsburgh, Pa. ture in an inert atmosphere, the order of coal. The rank of a coal is a measure fusion of the banded ingredients of coal of the degree of metamorphism, or prois vitrain, clarain, and durain; that of the petrographic compogressive alteration, produced in the original coal-peat deposita nents is anthraxylon and translucent attritus. Opaque attritus by geological processes acting over very long periods of time. is much more stable toward heat. Coals containing high conThe type of a coal is determined by the kind of plant material centrations of opaque attritus either do not fuse or show only and the extent of the biochemical changes in the peat stage of poor fusion a t temperatures up to the formation of semicoke. coal formation; it is, therefore, an inherent characteristic of the Fusain, whether it occurs in bands or is dispersed among the coal. Correlation of various technologically important properother components, is practically unaffected by heat. Potoni6 ties of bituminous coals with r a d alone have been signifioant and Bosenick (29) found that fusain from Bismarck gas-flame for relatively homogeneous or bright coals. With less homogene(high-volatile) coal did not fuse up to 700' C., a t which temperao m coals more satisfactory correlations can usually be obtained by considering also the type variation or petrographic compositure the test was discontinued. Observations were made by a tion of the particular coal. heating microscope on particles about 1 mm. in size a t a heating An attempt was made in this paper to discover what correlation rate of 5' C. per minute. Under the same test conditions with exists between rank and type factora and the data obtained in the same coal, vitrain fused a t about 410° C., clarain a t 430°, measurements of plastic properties of bituminous coking coals. and durein at 480". The relations found are suggestive and may assist in planning Pieters and Koopmans (Sf)heated coal, 0.5 to 1 mm. in size, future rasearch designed to provide more specific information. a t selected constant temperatures. Particles, consisting chiefly of vitrain in a good coking coal containing 26.8% of volatile ma+ RELATION OF RANK AND TYPE TO FUSION TEMPERATURE ter, divided into smaller rounded particles, and some changed into hollow spheres a t 410' C. Additional hollow spheres from vitrain In general, the fusion temperature of bituminous coking coals particles and spheres with partition walls from structured parinareseee with increase in rank of the coals, but it is influenced also
1 vary ties of bitumino&-coking coals both with rank and
