Thermodynamic Properties of light Hydrocarbons University of Michigan, Ann Arbor, Mich. __
n-butane (48, 64),and n-pentane (61) over the temperature range from 70" to 220" and to 280" F. in some cases, and from atmospheric to 3000 pounds per square inch absolute pressure. Konz (SO) investigated the thermal properties of n-pentane over the range from 100" to 800" F. and from atmospheric pressure to 3000 pounds per square inch absolute. These data represent substantially all of the thermal data for pure paraffin hydrocarbons. For pure liquid paraffin hydrocarbons heavier than pentane, the specific heat correlation of Watson and Kelson (63) for atmospheric pressure (Figure 1) affords a reliable means of estimating the specific heats of the heavier hydrocarbons. The enthalpies of the pure liquid paraffin hydrocarbons as reported in the literature (SO, 42, 44, 60, 51, 65,64) were referred t o liquid a t 32" F. and zero pounds per square inch absolute by calculation. The data on pentane (SO) are referred to saturated liquid a t 32" F.; for all practical purposes this may be considered the same as 32" F. and zero pressure because the isothermal change in enthalpy for liquid pentane a t 32" F. between the vapor pressure of pentane a t 32" F., 3.4 pounds per square inch absolute, and zero pressure is not more than 0.07 B. t. u. per pound mole. The isothermal changes in enthalpy between atmospheric and zero pressure for liquid hydrocarbons less volatile than pentane are of the same order of magnitude as the isothermal change in enthalpy for pentane. The enthalpy of hexane and heavier hydrocarbons a t atmospheric pressure as determined by integrating the heat capacity curves in Figure 1 above 32" F. according to Equation 1 may also be considered the same as the enthalpy of these hydrocarbons a t zero pressure:
The thermal properties of hydrocarbon mixtures covering the pressure range from 0 to 10,000 pounds per square inch absolute and the temperature range from - 200' to +I 100"F. for vapors and from 0" to 320' F. for liquids are presented in graphical form. The reference state for all enthalpies was selected as liquid at zero absolute pressure and 32' F. In making heat balance, the enthalpies of liquid and vapor streams are simply added or subtracted after applying any necessary corrections for the effect of pressure on the enthalpy of the fluid. The application of these data to commercial high-pressure absorber and fractionator operations indicates that heat balances can b e made on such equipment within the accuracy of measuring temperatures, pressures, and flow quantities in commercial equipment.
T
H E use of high pressures in the petroleum and natural gas industries in recent years has made it advisable to present reliable and useful thermal properties of hydrocarbon mixtures a t high pressures. Numerous data covering the thermal properties of hydrocarbons have been presented in the literature. However, none of these data are referred to a common reference state. The thermal properties of light hydrocarbon liquid or vapor mixtures a t pressures ranging from 0 to 10,000 pounds per square inch absolute, and temperatures from 0" to 320" F. for liquid mixtures and -200" to 1100" F. for vapor mixtures are presented in this paper. The reference state for all thermal properties was arbitrarily selected as liquid a t 32" F. and zero pounds per square inch absolute. At zero pressure where the ideal solution law applies, the enthalpies of the individual components in a solution are additive. The enthalpy of a mixture a t zero pressure is obtained, therefore, simply by summing up the products of the mole fraction of each component and its molal enthalpy a t zero pressure. At higher pressures the solutions are not ideal and the isothermal effect of pressure on the enthalpy may be obtained for the entire mixture a ithout assuming the mixture to be an ideal solution.
where AH = increase in enthalpy at constant pressure fivm ti t o t z F., B. t. u./lb. The enthalpies of methane and ethane as referred t o liquid a t zero pressure and 32" F. mere obtained by plotting the enthalpies of propane and heavier hydrocarbons a t zero pressure and different temperatures against the atmospheric boiling point of the individual hydrocarbons and extrapolating the curves back to the atmospheric boiling points of methane and ethane. Such a relation gives a straight line when the logarithm of the enthalpy in B. t. u. per pound mole a t zero pressure is plotted against boiling point as shown in Figure 2. Figure 2 was cross-plotted to obtain the enthalpies as a function of temperature above 32" F. a t zero pressure as shown in Figure 3. The curves in Figure 3 were extrapolated from 32" t o 0" F. The enthalpies of liquid paraffin hydrocarbon solutions a t zero or atmospheric pressure may be obtained by summing
Thermodynamic Properties of Liquid Hydrocarbons
Sage, Lacey, and eo-workers investigated the thermal properties of ethane (65), propane (42,64), isobutane (&), 1
____ -~
Present address, Universal Oil Products Company, Riverside, Ill.
590
INDUSTRIAL AND ENGINEERING CHEMISTRY
May, 1942 I
I
I
I
I
I
I
I
I
I
1
591
where AHT = isothermal increase in enthalpy brought about by pressure increase from PI t o P1, B. t. u./lb.
Pressure-volume-temperature relations for liquid paraffins from ethane through decane may be found in the literature (5, IS, 87, 44, 40, 60, 51, 53, 54, 68). I n addition, Sage, Lacey et al. presented data for a Kettleman Hills crude (48) and a Santa Fe Springs crude oil (6.9). The isothermal changes in enthalpy for propane, butane, pentane, and the Kettleman Hills crude oil were calculated by Sage, Lacey et al. (48, BO, 51,54) over the temperature range 70" to 220" F., and the pressure range from saturation up to 3000 pounds per square inch absolute, The thermal properties of n-pentane were also determined experimentally by Konz (30) up to 3000 pounds per square inch absolute. I n addition, the isothermal changes in enthalpy were calculated up to the critical temperature or to 500" F. when possible and up to 3000 Figure 7 . Specific H e a t of Hydrocarbon Liquids at O n e Atmosphere pounds per square inch absolute for the parafPressure fins and the two crude oils; the available exnerimental data and densities obtained from r up the product of the mole fraction of each component in the a correlation by Kurata ($1) were used over the temperature and pressure ranges not covered by experimental data. solution and its molal enthalpy as read from Figure 3. For As a means of extending the values to higher pressures, the hydrocarbons heavier than those given in Figure 3, the enthalpy at zero or atmospheric pressure above liquid at 32' F. isothermal changes in enthalpy for pentane and decane have been calculated between 3000 and 10,000 pounds per square may be obtained b y integrating the heat capacity curves in Figure 1 according to Equation 1. inch absolute over the temperature range from 32" to 200" F., using the P-V-T data of Bridgman ( 5 ) . All isothermal changes in enthalpy were referred to liquid a t zero pressure by extrapolating the calculated values to zero pressure from the saturation pressure a t that tempera-
.
3 1,000
I-
m >.
0% 700 600
0.
SO0
Q. _1
400
r
I-
300
t, 200
ATMOSPHERIC BOILING POINT ( O F + 4 6 0 )
Figure 2. Relation between Enthalpy of Paraffin Hydrocarbons at Z e r o Pressure and Atmospheric Boiling Point
At high pressures a correction for the effect of pressure of the enthalpy can be applied to the enthalpy of a mixture calculated from Figure 3. The ISOTHERMAL EFFECTSOF PRESSURE ON ENTHALPY. isothermal effect of pressure on the enthalpy of any material in a single-phase region may be calculated from Equation 2, provided the pressure-volume-temperature relations of the material are available: Fi ure 3.
Enthalpy of Hydrocarbon Liquids at Z e r o Pressure dbove L i q u i d at Z e r o Pressure and 32" F.
TRY
Vol. 34, No. 5
in the left-hand portion. The values in Figure 4 are extrapolated above a specific gravity of 0.85 gram per cc. and below a temperature of 60" F. In correlating .the valuas of the isothermal changes in enthalpy between zero and 3000 pounds pressure a t a specific gravity of about 0.85 g r a m per cc., t h e average of the values for the Kettleman Hills (47) and the Santa Fe Springs oils (61)were used because these crudes have approximately the same specific gravities, 0.838 and 0.85 gram per cc., respectively, a n d t h e c o m p u t e d isothermal changes differed by a maximum of 0.3 B. t. u. per pound along the same isotherm. The 1000 pound pressure line as shown in Figure 4 was located by plotting the i s o t h e r m a l c h a n g e in enthalpy a t 1000 pounds per square inch absolute along the abscissa (at the bottom of the graphs) against the isothermal change in enthalpy a t 3000 pounds per square inch absolute for the same temperature along the ordinate. T h e s e p l o t t e d points for the hydrocarbons of various specific gravities determine the 1000 pound pressure line. The other constant pressure lines in Figure 4 were determined in the same manner. Above 3000 pounds per square inch absolute the constant pressure lines are based only on pentane and decane. The constant pressure lines in Figure 4 are extrup o l a t e d b e l o w the zero ordinate. The values computed by I Equation 2 agree with the 24 23 26 27 28 29 36 values read from Figure 4 (HP - No>t with a maximum deviation of d0.3 E.t. u. per pound Figure 4. Isothermal Changes in Enthalp with Pressure above Z e r o Pressure for in all cases. I n that porLiquid HyJrocarbons tion of the chart above 6 B. t. u. per pound along the ordinate, the agreement between the calculated and the ture. The isothermal effect of pressure on the enthalpy of correlated values is within 1 0 . 1 5 E. t. u. except for the hydrocarbons based on the specific gravity of the fluid is given Kettleman Hills crude oil (48). in Figure 4. I n constructing Figure 4,the isothermal change in enthalpy Latent Heats of Vaporization of Pure Compounds in B. t. u. per pound between zero pressure and 3000 pounds The latent heats of vaporization of pure compounds can per square inch absolute was plotted as a function of the specific gravity, a t 60"/60° F., of the hydrocarbons for isobe determined experimentally or they can be calculated from therms ranging from 0" to 500" F., as indicated by the curves the densities of the saturated liquid and vapor and the vapor
,
INDUSTRIAL AND ENGINEERING CHEMISTRY
May, 1942
593
pressure curve according to the exact thermodynamic relation given by Equation 3 :
or
where AV = specific volume of saturated vapor minus specific volume of saturated liquid at same temperature, cu. ft./lb. AH = latent heat of vaporization, B. t. u./lb. The latent heats of vaporization of propane and pentane as determined by Sage, Evans, and Lacey (41) represent substantially all of the experimentally determined latent heats for pure para& hydrocarbons over a range of temperatures. The sources of vapor pressure data and saturated liquid and vapor densities for calculating latent heats of hydrocarbons are given in Table I.
TABLE I. SOURCES OF DATAON VAPORPRESSURE AND SATURATED DENSITIES FOR CALCULATINQ THE LATENTHEATSOF PURECOMPOUNDS Hydrocarbon Methane
Citation No.
Temp. Range, F. -271 to -127 -281 -250 to -252
63 to 88.6 32 to 86 12s 130
Ethane
--
Ethylene
-163 t o -94 -174 to -181 -203 t o 49.3
Propane
-75 to 125 -45 69 to 204
Propylene
32 to 176 08 to 191 154 to 197 -35 to 50 -55 t o -226
[sobutane
(18)
(44)
-20 to 140 63 to245
n-Butane
$3
0 to 140 68 to 240
Hydrocarbon Isopentsne
Citation No.
Temp. Range, F. 50 to 369
n-Pentane
86 to 387 78 to 225 32
n-Hexane
140 to 463 154.5 32
n-Heptane
188 to 612 208.5 209.3
n-Octane
248 to 564 258 257
n-Decane
320
Dodecane
70 to 724 32 to 735
Benzene Cyclohexane
(OB) (S6)
;;;1
158 to 551 176.4 176 to 536 176
The correlated latent heats of vaporization of the paraffin hydrocarbons from methane through dodecane are given in Figure 5. Ethylene, propylene, benzene, and cyclohexane are also included. The latent heats were correlated by plotting the temperature of the hydrocarbon for a given latent heat in B. t. u. per pound mole against the temperature of water a t which the molal latent heat of water was the same as for the hydrocarbon as shown in Figure 6. This relation gives a straight line, except neax the critical, which can be extrapolated back to low temperatures for the hydrocarbons. This method was used to extrapolate the latent heats of the hydrocarbons heavier than propane to a temperature of -50' F. For propane and lighter hydrocarbons, data were available such that the latent heats could be calculated over the temperature ratlges indicated in Figure 5. The latent heats of nonane, decane, and undecane were obtained by cross .plottilr@e I&& heats of the other compounds against molecular weight and interpolating between octane and dodecane because sufficient data were not available on these three hydrocarbons for computing the latent heats over a range of temperatures.
Figure
5.
Latent H e a t of Pure Compounds
The calculated latent heats of vaporization for pure compounds are compared with the correlated values of Figure 6 in Table 11. AH OF VAPORIZATION OF HYDROCARBON MIXTURES.The latent heats of vaporization of the pure hydrocarbons are not directly applicable to mixtures of hydrocarbons. It is possible to vaporize hydrocarbons from mixtures which are a t a temperature above the critical temperatures and a t a pressure below the critical pressures of the pure hydrocarbons being vaporized; it is also possible to vaporize hydrocarbons from mixtures which are a t a temperature below the critical temperatures and a t a pressure above the critical pressures of the pure hydrocarbons. These phenomena occur in natural gasoline fractionators and high-pressure absorbers. The difference in enthalpy between a unit mass of a component in a liquid mixture and in a vapor mixture under equilibrium conditions a t the same pressure and temperature may be obtained by the well-known thermodynamic relation applicable to two-phase equilibria as expressed by the v a d t Hoff equation (32): (4)
where (d logla K / d T ) = slope of curve of logla K us. temperature at constant pressure AH = enthalpy of hydrocarbon in vapor phase minus enthalpy in liquid phase at same temperature and pressure The values for AH a t 32' F. and zero pressure were determined for paraffin hydrocarbons up to and including nheptane by Equation 4 and equilibrium constants (6, 96). The values for AH were first calculated a t pressures of 14.7, 50, 100, 150, and 200 pounds per square inch absolute for temperatures from 40° to MOO F. Each of t h e G ~ W W was first smoothed, and then the values a t a constant temperature and pressure were plotted against boiling point a t atmospheric pressure for further smoothing. The smoothed
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
594
TABLE 11.
COMPARISON OF CALCULATED LATEXTHEATS WITH CORRELATED VALUESIN FIGURE 5
Hydrocarbon Ethane
Propane
Isobutane
n-Butane
Temp., 0 F. 32 50 68 86 67.6 78.5 85.3 -128
- 50
Latent H e a t of Vaporization, B. T. U./Lb. Correlated. ' Cdcuiatrd Figure 5 Differenre 140 -5.4 134.6 ( 6 8 ) 122 -7.7 114.3 91 92.0 fl.O 46.8 46.8 0 91 87.4 (63) -3.6 f0.8 65 65.8 36 +9.6 46.6 212 211.0 (66) -1.0
0 40 80 125 69.4 104.3 145.3 170.5 190.6 204.1 44
184.2 (I??) 179.0 170.3 159.0 146.0 126.5 141.5 (60) 126.6 104.7 84.8 60.8 37.4 183.2 (28)
184 180 171 158 143 122 147 132 111 92 70 37 183
20 80 140 63 107.3 154.2 198.3 244.9
165.5 (12) 156.0 140.7 120.5 144.8 (44) 133.5 117.1 97.3 62.6
165 l5G.5 141.0 122.5 145.5 133 117 97 64
4-0.5 -0.5 -0.3 -2.0 -0.7 f0.5 +O. 1 f0.8 -1.4
170.3 (1B) 161.5 152.0 137.3 159.7 (8.4) 151.4 136.5 113.7 92.6
176 164 152.5 138 150 150.5 136 113 92
-5.7 -2.5 -0.5 -0.7 +0.7 fO.9 f0.5 f0.7 +0.6
152.3 ( 6 5 ) 142.3 129.2 116.6 105.5 84.0 44.4 14.5
153 142 130 116.5 105 83 45 15
-0.7 1-0.3 -0.8 f0.1 t0.5 +1.0 -0.6 -0.5
- 30
- 20
0 50 90 140 67.6 98.0 145.5 202.0 240.2
f0.2 -1.0 -0.7
fl.O f3.0 f4.5 -5.5 -5.4 -6.3 -7.8 -9.2 f0.4 +0.2
Vol. 34, No. 5
Thermodynamic Properties of Gaseous Paraffins
The enthalpies of hydrocarbon vapors are most useful when the same reference state is used as for the corresponding liquids (32" F. and zero pressure). In making a heat balance from such enthalpy data involving liquid and vapor streams, enthalpies are added or subtracted just as they would be if steam tables were used. To present such enthalpy data for hydrocarbon vapors, it is necessary to have heat capacity data as a function of temperature a t zero pressure, the AH between vapor and liquid a t zero pressure and 32" F., and the isothermal effect of pressure on the enthalpy of hydrocarbon gases so that enthalpies a t pressures other than zero may be obtained. H E ~ CAPACITY. T The sources of available experimental heat capacity data a t atmospheric pressure for paraffin hydrocarbons and volatile hydrocarbon mixtures are given in Table IV. TABLE IV. SOURCES OF HEATCAPACITIES OF HYDROCARBOX GASES Component hlethane Ethane Propane Isobutane n-Butane n-Pentane Methane-ethane Methane-butane
Citation No.
(5j
In addition, several correlations (1, 11, 16, 18, 63) of thc heat capacities of heavier hydrocarbon fractions have been suggested. Watson and Kelson (63)gave the most general158 212 ized of these correlations. 248 302 The experimental data referred to in Table IV were used 356 for determining the specific heat curves of the volatile hydro369.3 carbons from methane through pentane as shown in Figure 7 . 157 -2.8 86 154.2 ( 6 9 ) n-Pentane -1.0 145 144 140 Particular emphasis was placed on the curves for methane 126 0 212 126 and ethane because of the voluminous amount of data 0x1 101 f1.0 102 284 63 0 356 63 these two compounds and the excellent agreement between 25 28.2 f3.2 383 151 -2.6 148.4 (51) 113.7 the experimental data from different sources. The curves 137 -0.5 136.5 172.1 for methane and ethane were used as a basis for determining 122.5 -1.3 121.2 225.1 the shape of the curves for other compounds in the temperature ranges below about 30" and above about 800" E'. For compounds heavier than n-pentane the values in Figure 7 values of AH for each hydrocarbon were then plotted against are based on the correlated figures of Watson and Nelson (69) temperature with lines of constant pressure and extrapolated and Cragoe (11). back t o 32" F. Cross plots of these charts were made for The intermediate curves between methane and ethane the 32" F. isotherms which were, in turn, extrapolated back to in the temperature range from 70" to 250' F. are based on the zero pressure to give the values listed in Table 111. data of Sage, Lacey et al. on the methane-ethane (8) and methane-butane (9)systems. Outside of this temperature range these intermedjote curves were obtained by interTABLE 111. 4H BETWEEN V.4POR AND LIQUID FOR PARAFFIX RYDROCARBOXS IN SOLUTION A T 32' F. AXD ZERO PRESSURE polation. The values of the heat capacities as read from Figure 7 Hvapor - Hliquid, H v ~ p o r- m i q u i d , B. t. u./Lb. B. t . u. /Lb. agree with a maximum deviation of about d0.02 B. t. u. per Hydrocarbon Mole Ilydrocnrbon Mole pound per O F. with the reliable experimental data for the 9030 Methane 2000 Isupentane hydrocarbons from methane through pentane. The values 9110 Ethane 5500 n-Pentane 9300 Propane 7300 n-Hexane for methane and ethane as read fiom Figure 7 agree in most 9430 Isobutane 8560 n-Heptane 9530" n-Butane 8780 1%-Octane cases within less than *0.01 B. t. u. per pound per 'F. with a Extrapolated the experimental data. For hydrocarbons heavier than pentane, the values obtained from Watson and Nelson's correlation (63) are, at most, 0.02 B. t. u. per pound per F. higher than the values in The enthalpy of mixtures of hydrocarbon gases a t 32" F. Figure 7, while the values obtained from Cragoe's correlaand zero pressure referred to liquid a t 32' F. and zero pressure tion (11) are a maximum of 0.015 B. t. u. per pound per " F. can be computed by summing up the mole fraction of eacli higher. These deviations occur at high and low temperatures component in the gas times its corresponding value of AH as where the curves for the heavier hydrocarbons in Figure 7 given in Table 111, since a t zero pressure where the ideal have been drawn symmetrical to the curves for methane and solution law applies the molal enthalpies of the hydrocarbons ethane. are additive. Isopentane
80 104
INDUSTRIAL AND ENGINEERING CHEMISTRY
May, 1942
LL 700
vi
8 600 a 4
U
0
[L 500
. a2.
r !A
O400
w
a
3
$ 300 W
a
5 200 + IO0
0
-
50
100
Figure
200
6.
300
400
TEMPERATURE
500
000
OF WATER, "F.
700
Relation b e t w e e n Temperature
of H y d r o c a r b o n and Temperature of W a t e r at Equal
Molal
Latent Heats
of Vaporization
595
each component of the mixture separately, because a t elevated pressures the vapors are not ideal solutions and the isothermal effects of pressure on the enthalpy are not additive as are the enthalpies at zero or atmospheric pressure. ISOTHERMAL CHANGESIN ENTHALPY. The isothermal effect of pressure on the enthalpy of gaseous mixtures may be determined experimentally or computed from compressibility factors obtained from experimental P-P -T relations The only experimental data on the isothermal effect of pressure on the enthalpy of light hydrocarbon mixtures are those of Sage, Lacey, and co-workers for the methane-ethane (8) and methane-butane systems (9). COMPRESSIBILITY FACTORS FOR NATURALGASES. The law of corresponding states may be applied to hydrocarbon mixtures in much the same manner as for pure hydrocarbons, using a pseudocritical temperature and pressure as suggested by Kay (26). For volatile hydrocarbon mixtures the pseudocritical temperatures and pressures are equivalent to the molal average absolute critical temperature and pressure of the individual compounds in the mixture. The pseudoreduced temperature is the absolute temperature divided by the absolute pseudocritical temperature, and the pseudoreduoed pressure is the absolute pressure divided by the absolute pseudocritical pressure. The sources of experimental P-P-T data on volatile gaseous hydrocarbon mixtures which are predominately methane are given in Table V. These data were used in preparing Figure 9 which gives the compressibility factor, 2 = P V / R T , as a function of pseudoreduced temperatures and pressures. Figure 9 includes the correlation (7) based on the data of Table V for the pseudoreduced pressure range from 0 to 6 and the extension by Standing (69) to a pseudoreduced pressure of 15. The compressibility factors in Figure 9 are accurate within about * 1 per cent for most natural gases.
I n Figure 7 the heat capacities for the light hydrocarbon gases are presented for various densities as referred to air; the heat capacities of the heavier hydrocarbon gases are given for various A. P. I. gravities of the condensed vapors (liquids). Reliable enthalpy charts can be constructed for hydrocarbon vaDors at atmomherio or zero Dressure over the temperature Eange from -200" to 1100' F. by graphically integrating Equation 1 between the desired temperature limits using the heat capacities in Figure 7. From heat capacity data in Figure 7 and AH between vapor and liquid hydrocarbons a t 32" F. and zero pressure as given in Table 111, the enthalpies of hydrocarbon vapors in solution as referred to liquids in solution a t 32' F. and zero pressure were determined as a function of temperature up to 320" F. a t zero pressure (Figure 8). In constructing Figure 8, the heat capacities and enthalpies of the hydrocarbon gases were assumed to be the same a t zero as a t atmospheric pressure. This assumption introduces errors varying from about 20 B. t. u. per pound mole for methane to 100 for heptane, which amount to one per cent of the total enthalpies of these compounds a t 32" F. and zero or atmospheric pressure. Heat balances may be made a t zero or atmospheric pressure from the thermal properties in Figures 3 and 8 simply by adding or subtracting liquid and vapor enthalpies. At zero pressure gaseous mixtures of hydrocarbons are ideal solutions. The enthalpy of a gaseous mixture at zero or atmospheric pressure is obtained by summing the products of the mole fraction of each component and its molal enthalpy as read from Figure 8. For pressures other than zero or atmospheric, the effect of pressure on the enthalpy of hydrocarbon vapors must be considered. I n correcting for the TEMPERATURE k isothermal changes in enthalpy with pressure for hydrocarbon mixtures, it is necessary to determine Figure 7. Specific H e a t of Hydrocarbon Vdpors at O n e Atmosthis effect for the entire mixture and not for phere pressure
INDUSTRIAL AND ENGINEERING CHEMISTRY
596 TABLE
v.
S o 7 ~ R c E 5OF
P-v-T DATA
CARBON
MIXTURES
Range, Temp.
Pressure Range
F. 70-220 70-220 77 77-131
Lb./Sq. In. Ab;.
70-220 70-250 70-250 77-185 77-185 77-185 77-239
14.7-3000 14.74750 50-3000 1000-3000 1000-3000 1500-3500 1500
8
(4)
77-239 77-131 77-239
1500-4300 1500-5000 1500-5500
(59)
35-250
1000-8220
Citation
Hydrocarbon Mixture Natural gases
No.
O
123 (8)
(4) (47)
CHrCaHa CHrCzHa CHI-~-C~H~
(46) (40)
N~CH~-~-C,HM N r C Hcn-C*His NrCHm-C7His Nrn-C~Hls
(4) (4)
Natural gas-cyclohexane Natural gas-benzene Natural gas-toluene High preasure natural xium ge.s-crude vapor oil equilib-
FOR GASEOUS HYDRO-
(4)
(4)
300-3000 400-3000 14.7-5500 14.7-5500
Vol. 34, No. 5
I n Figure 11 an increase in pressure causes a decrease in enthalpy a t constant temperature, as indicated by the minus sign before A H . This chart is applicable only for increases or decreases in pressure a t constant temperature. I n order that the reference state for all gases will be the same when using Figure 11, the reference pressure was selected as zero. For pseudoreduced temperatures less than unit, the values of - A H / T in Figure 12 may be used for hydrocarbon knixtures with an accuracy of about 1 5 0 B. t. u. per mole for the isotherms up to reduced pressures corresponding to approximately 75 per cent of the reduced pressures at the upper end of the isotherms. I n this region the values as read from Figure 12 are accurate within about * 100 B. t. u. per mole. ISOTHERMAL CHANGES IN ENTROPY.The isothermal effect of pressure on the entropy of volatile hydrocarbon gases may also be determined from the values in Figures 10 and 11 by the following thermodynamic relation: -AsT
=
-AH
AF +r
(7)
CALCULATION OF THERMAL PROPERTIES FROM COMPRESSIBILITYFACTORS. The isothermal effect of pressure OR the enThe values of - A H / T may be determined directly from thalpy Or heat content Of gases may be computed Figure 11, and the values €or A F / T may be calculated from from the compressibilities as given in Figure 9 by the folEquation 8 (191, using the values of Inf/p in ~i~~~~10:
lowing thermodynamic equation (20) : -AH
=
R
in B. t. u./lb. mole/" R.
(-)pe
(5)
The values of In f / P in Equation 5 were calculated from the compressibilities in Figure 9 by means of Equation 6 (19): In j / P =
'' -
(y) dP,
T,
P, = 0
The computed values of In f / P are plotted against pseudoreduced pressure with lines of constant pseudoreduced temperatures as shown in Figure 10. The calculated values of - A H / T in B. t. u. per mole per R. are plotted in Figure 11.
I t is impossible to determine the isothermal effect of pressure on the entropy above zero pressure because Equation 8 cannot be evaluated a t zero pressure, For this reason a reference pressure of one atmosphere was selected for the entropy chart, and the reference reduced pressure is that corresponding to atmospheric pressure for methane, or 0.0218. The values of -AST plotted for lines of constant
O
Figure 8. Enthalpy of H y d r o c a r b o n Vapors at Atmospheric Pressure above Liquid at Z e r o Prassure and 32" F.
F i i u r e 9. Compressibility of Natural Gases
INDUSTRIAL AN
May, 1942
pseudoreduced temperature as a function of pseudoreduced pressure in Figure 13 were obtained by substituting the values from Figures 10 and 11 as indicated in Equation 9: SP,
-
0.021s
-
(H,, -H;) T (2 F,r 0.0218
SPr
=
+
(9)
0.0218)
T
The decrease in entropy from atmospheric pressure will vary slightly with the pseudocritical pressure of the natural gas, because the values in Figure 13 are based on a reference pseudocritical pressure of 673 pounds per square inch absolute. If the pseudocritical pressure of the natural gas differs from 673 pounds per square inch absolute, the value for -AS should be corrected according to the small diagram in the lower righthand corner of Figure 13. Since an increase in pressure causes a decrease in entropy, the numerical values indicated for -AS on the main chart of Figure 13 are to be decreased by the quantity indicated in the small diagram if the pseudocritical pressure is less than 673 pounds per square inch absolute. For example, if the decrease in entropy accompanying an increase in pressure from atmospheric pressure to pP, = 5 a t a reduced temperature of 1.3 is 13.73 as read from the main chart for a gas with a pseudocritical pressure of 673 pounds, the decrease in entropy for a gas with a pseudocritical pressure of 615 pounds per square inch absolute would be 13.73 - 0.2 or 13.53 B. t. u. per mole per O R. The effect of temperature on the entropy of a gas a t constant pressure is determined directly from the heat capacity as shown bv Equation 10:
OVER-ALLHEATBALANCE, FOR HIGH-PRESSURE ABSORBER. The operating conditions for a commercial high-pressure absorber are given in Table VI. Detailed calculations for the over-all heat balance are as follows: A.
a.
HEAT I N
Rich Gas at 85' F .
Component
-
Molal Enthalpy at 85' F. & P 0
T%%.
Mo!e Fraction
2,440 6,150 8,230 9,780 9,980 10,440 10,620 1 1,380 Total
where AS, = increase in entropy at constant pressure brought about by an increase in temperature from TI to TI,B.t. U./lb./' F. The heat capacities of gases at atmospheric pressure are given in Figure 7, and Equation 10 is solved by graphically integrating these data between the desired temperature limits. Application of Thermal Properties The application of the thermal data presented here can best be illustrated by heat and material balances for highpressure absorbers, natural gasoline fractionators, and the construction of enthalpy-entropy (Mollier) charts for natural gases.
PTI PPI -m/T
- AH
= (460
+
E. T.U./ Mole
f
85)/370 = 1.473 = = 1280/669 1 . 3 8 (Fi =11)1.92 = 1 . 3 8 X 7460 85) = 752 B. t.
.
+
2260 221 99 40 47 21 28 150 2886
U./mOk
Total enthalpy a t 1280 Ib. and 85" F. = 2866 - 752 = 2114 B. t. u./mole Total heat in with rich gas = 3380 X 2114 = 7,150,000 B. t. u./ hr.
b. Lean Oil at 96" F. Molecular weight = 208, specific gravity = 0.85 gram per cc., K = 11.85 (Universal Oil Products Company's value). From Figure 1, C, av. between 32" and 961 F. = 0.453 B. t. u. per pound F. for K = TABLEVI. OPERATING CONDITIONS FOR 1280-POUND COMMERCIAL ABSORBER 11.85. Then, e n t h a g of lean oil at (Rich gas 3379.9 moles/hour, lean gas 3110, lean oil = 143.2,rich oil = 413.1) zero pressure = (208) (96 - 32) (0.453) Component -Rich Ga-Lean Oil-Lean Gas-----Rich Oil= 6040 B. t. u./mole. From F i p r e Mole % Moles Mole % Moles Mole % Moles Mole % Moles 4 the correction for pressure at 96 F. 37.63 155.52 and 1280 pounds per square inch ab95.57 2972.23 3127.75 .. ... CH4 92.54 3.32 103.25 4.37 18.09 solute for oil of specific gravity 0.85 121.34 .. ... CsHa 3.59 0.80 24.88 C;Ha 1.20 40.56 . ... 3.79 15.68 is 3.3 B. t. u. per pound; then, isoIsO-C4Hlo 0.41 13.86 .. 0.18 :$: : :1 ! ;: thermal increase in enthalpy between n-CdHlo 0.47 15.89 . ... 0.12 Iso-CrHi~ 0.20 6.76 .. ... 0.01 0 31 1.66 6.45 0 and 1280 Ib. = 3.3 X 208 = 686 n-CrHa 0.27 9.13 .. .. ... 2.21 9.13 B. t. u./mole C iHt 1.32 44.61 ... lji:zA Total enthalpy at 96' F. and 1280 .. ... Absorber oil .. .. . lO0:OO 2& __ lb. = 6040 686 = 6726 B. t. u./ 100.00 3379.9 100.00 143.2 100.00 3110.00 100.00 413 10 Total mole Temp., ' F . 85 96 103 90 Total heat in with lean oil = 143.2 X 370 .. 355 .. PTC 6726 = 963,000 B. t. u./hr. Total heat 669 674 PPC d, gram/cc ... 0: 8s ... 0:74 into absorber = 7,150,000 963,000 = 8,113,000 B. t. u./hr.
-
-
:i
..
i!:!!
+
+
INDUSTRIAL AND ENGINEERING CHEMISTRY
598 TART E
m.
OPERATING CONDITIONS FOR A CO?LMERCIAL FRACTIONATOR OPERATING AT Feed
Liquid P a i t hIole/mole of feed XP
Componeut
Vapor P a r t l\lole/mole of feed fJP
0.0188 0.1340 0.0422 0,1820 0.0892 0.1537 0.1456 0,2376 1.0000
CzH6 CaHs
rso-cnrrlo n-CdHla Iso-CaHi? n-CsH,?
CaH14 CiHia Total hlole yo vapor Temp., F. P Tc PPC r l , iiram/cc.
64.94 238
~. . .
0,6494
1.0000
0,4093
0
CaHs
Iso-CaHia n-C~Hlo
Iso-CbHiz
PT P
=
(460
X
X
....
....
.... __
-
0
0.5907
....
3
.... __
3.5220
1.0000 0 273
1,0000
0 103
...
O.Gi3
=
6,720,000
+ 1,353,000 = 8,073,000
The difference between the total heat out of and the total heat into the absorber amounts to 40,000 B. t. u. per hour, which is equivalent to about 1' on the temperature of any stream entering or leaving the absorber. A similar heat and material balance on another commercial absorber operating a t 835 pounds per square inch absolute pressure, using these same thermal properties, indicates a difference of 9000 B. t. u. per hour between the total heat entering and the total heat leaving the absorber. This quantity of heat is equivalent to less than 1" on the temperature of any stream entering or leaving the absorber. OVER-.4LL HEATBALANCE FOR A COMMERCIAL NATURAL GASOLINE FRACTIONATOR. The thermal properties in Figures 3, 4, 8, and 12 were applied to a commercial natural gasoline fractionator. The operating conditions are given in Table VII. Detailed calculations for the over-all heat balance follow (basis one mole of feed) :
2478 212 69 18 13 1 2791
__
-
INCH ABSOLUTE
....
-0
1.0000
Total heat out of absorber B. t. u./hr.
2,590 6,400 8,660 10,200 10,400 10,950 Total
X X X
....
....
...
HEATOUT
X
0.9577 0.0332 0.0080 0.0018 0.0012 0.001
C2H6
....
100 103 651 627
u . L e a n Gas at 105" F .
CHI
. . .
...
594
....
0.1968 0.6804 0.1164 0.0074
....
100 238 728 572
...
...
..I
B.
0.0326
0 238
...
0.0800 0.2787 0,0476 0.0030
0.1130 0.3565 0,0655 0.2328 0.0659 0.0919 0.0415
POUNDS PER SQUARE
Cold Pumped-Back Bottoms External Reflux hIole/mole of Moles/mole of feed XB feed XR .... 0.2720 0.0771 2,2014 0,6254 0.0099 0.0166 0.984; 0.2793 0.3586 0.2118 0.0182 0.0641 0.0741 0.1254 .... .... 0.1124 0.1899 .... .... 0.1325 .... 0.0781 ....
Overhead Dist. RIole/mole of feed YlJ
0.0734 0.2317 0.0427 0.1510 0.0428 0 . 0596 0,0270
0.0212
215
Vol. 34, No. 5
+ 103)/355 = 1.585
PPr = 1280/'674 = 1.90 - A H / T = 1.12 (Fig. 11) -AH = 1 . 1 2 X 563 = 630 B. t. u./mole
Total enthalpy at 1280 lb. and 103' F. = 2791 - 630 = 2161 B. t. u./mole Total heat out with lean gas = 3110 X 2161 = 6,720,000 B. t. u./ hr.
Bich Oil at 90' F .
b.
Component
A.
Molal E n t h a l p y a t 90° F. & P = 0 (Fig. 3), B. T. U.
Mole Fraction
208 (00-32) (0.453) Total
=
B.T.U / Mole 336 60 61 36 56 34 50 324 IO00 285i
a.
per cc. :
Component
The molecular weight of the rich oil is 97.6 and the specific gravity is 0.74 gram per cc. From Figure 4 the isothermal correction for pressure at 90' F. and 1280 pounds is 4.28 B. t. u. per pound. Then, isothermal increase in enthalpy 0 and 1280 lb. = 4.28 X 97.6 = 418 B. t. u./mole Total enthalpy of rich oil = 2857 418 = 3275 B. t. u./mole Total heat out with rich oil = 413.1 X 3273 = 1,353,000B.t. u. ' mole
Mole Fraction
238" F. The specific gravity is 0.594 gram
FEED AT
Liquid Portion of Feed.
blolal Enthalpy a t 2 3 S ° F . & P I0 (Fia. 3).
B. T. c'
B. T. U / Mole
5,300 6,430 7,280 7.620 8.600 8,850 10,200 11,530 Total
100 842 306 1390 766 1332 1490 2735 8ZKl
Correction for pressure (Fig. 4) = -0.6 R. t. u.,/lb. = -44 B.t. u./lh. mole Total enthalpy of liquid feed = 8961 - 44 = 8917 R. t. u./mole Total heat in with liquid feed = 0.3506 X 8917 = 3125 B.t. u .
+
TABLE 1'111. CONRTRUCTION O F ENTH4LPY-ENTROPY CHART FOR A NATURLL GAS HAVING A PSEUD~CR 11, IT TEMPERATURE IC OF 383' R , A PSEUDOCRITICAL PRESSURE o r 664 POUXDS PER SQUARE h c i I ABSOLUTE,AR'D -1 G R ~ V I T OF Y0 7 1
T:mp.,
F.
82 100 200 300 400
a
3
2
Temp., O
R.
pTr =
T/383
492 1.275 560 1.45 660 1.71 760 1.97 860 2.23 P P r = 14.7/684 = 0,0221, P P r = 1000/664 = 1 . 6 0 5
4
H, B.T.U./ hlole 0 675 1740 2895 4150
6
3
s,
-
7
8
- A H / T from F i E . 1 1 , B . T . U . /
B. T. U./ h l 0 1 c / ~F.
P = 14.70
0 1.285 3.03 4.67 6.21
0.021 0.014 0.009 0.005 0.004
Mole/o R.
P =
IOOOb
1.92 1.125 0.681 0.461 0.318
Diderenee (7 - 6)
+1.90 +1.111 +0.672 +0.486
+0.314
9
+ a~
n.r.n.) Mole (8 X 2) -937 -622 - 444 -346 -270
11
10
+AS, B. T . C.1 3loie/' F. -9.73 -9.12 -8.85 -8.70 -8.62
12
I
B.T.u./ Mole
(4
+
9)
-937 +53 1246 2549 3880
S,
B.T.C/
3101e/o F. ( 5 4- 10)
-9.73 -7.83 -5.82 -4.03 -2.41
INDUSTRIAL AND ENGINEERING CHEMISTRY
May, 1942
m
--
8
---
/a-
599
-- .
PSEUDO REDUCED PRESSURE, ~ P R
Figure
11. Isothermal Changes i n Enthalpy above Z e r o Pressure f o r
Figure 12. Isothermal Changes in Enthalpy for Hydrocarbons below Critical Conditions
Natural Gases
b,
Vapor Portion of Feed
Component
Molal Enthalp at 238' Fa.& = 0 (Fig 8)
PT,
c.
5
Mole Fraction 0.1133 0.3565 0.0658 0.2326 0.0659 0.0918 0.0415 0.0326
B.T.u./
B. T'.U:
Mole 1,000 4,025 895 3,220 995 1,393 685 580 12,793
8,280 11,270 13 620 13:830 16.120 15,180 16,600 17,750 Total
= (238
+ 460)/728
= 0.958
Total enthalpy of vapor feed at 215 lb. and 238' F. = 12,793 746 = 12,047 B. t. u./mole Total heat in with vapor feed = 0.6494 X 12,047 = 7830 B. t. u. Total heat added t o reboiler = 23,650 B. t. u. Total heat into fractionator = 3125 7830 23,650 = 34,605 B. t. u.
+
+
HEATOUT
a. Overhead Distillate at 103' F.
Component C9Hs CaH8 Iso-C4Hio n-C~Hia
PTP PPT - AH/T - AH
= = = =
Molal Enthalpy at 103"F.&P=O (Fi 8
B. %.
X
X X X
Molal Enthalpy at 273OF.&P=O 3&
gi&,
Mol? Fraction
B. T.U./
fi
6,400 8,560 10,200 10,400 Total
.. P P
=
Mole 1253 5830 1190 77 8350
-
+
(103 460)/651 = 0.865 215/627 = 0.343 1.33 (Fig. 12) 1.33 X 563 = 749 B. t. u./mole
-
Total enthalpy of overhead distillate = 8350 749 = 7601 B. t. u./mole Total heat out in overhead distillate = 0.4093 X 7601 = 3110 B. t. u. b. Condenser. Total heat removed in condenser by cooling water = 24,200 B. t. u.
R. T. us/ hfole 143 3,265 1,292 2,010 1,618 2,455 10,783
-
X
X
I
X
=
X X
3
E
-
=
X Total
-
Mole Fraction 0.1958 0.6804 0.1164 0.0074
Component
-
= 215/572. = 0.375 t p i H / T = 1 . 0 7 (Fig. 12) = 1.07 X 698 = 746 B. t. u./mole AH
R.
Bottoms Product at 273" F. The specific gravity is 0,633 gram per cc.:
Correction for pressure (Fig. 4) = -0.25 B. t. u./lh. = -18 B. t. u./mole Total enthalpy of bottoms = 10,783 - 18 = 10,765 B. t. u./mole Total heat out in bottoms = 0.5907 X 10,765 = 6370 B. t. u. Total heat out of fractionator = 3110 24,200 6370 = 33,680 B. t. u.
+
+
The radiation and unaccounted-for losses from the fractionator amount to the difference between the total heat in and the total heat out, or 34,605 - 33,680 = 925 B. t. u. per mole of feed. The radiation losses amount to approximately 200 B. t. u. per mole of feed. The unaccounted-for losses are 725 B. t. u. per mole of feed. This quantity of heat is equivalent to about 2" F. on the temperature of each stream leaving and entering the fractionator. This 2" F. is within the accuracy of temperature measurements on commercial equipment of this type.
Enthalpy-Entropy (Mollier) Charts for Natural Gases Enthalpy-entropy charts for natural gases are most useful in computing horsepower requirements for compressors operating a t high pressures as encountered in the natural gas industry. If a natural gas is compressed isothermally, the indicated energy required to compress and deliver one mole of the gas may be computed directly from the data in Figure 10 by Equation 11,which was derived from the flow equation: -w, =
s
V d P = AFT = RT In fi/fl
%
(11)
.
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 34, No. 5
Column 6 gives - A H / T obtained from Figure 11 for atmospheric pressure. This value is subtracted from this function listed in column 7 for a reduced pressure of 1.505 corresponding to a pressure of 1000 pounds per square inch absolute. This difference (column 8) is multiplied by the corresponding absolute temperature (column 2) to obtain AH (column 9). The value in column 9 is added to column 4 to obtain H or enthalpy in column 11. The increase in entropy due to the increase in pressure from atmospheric to 1000 pounds per square inch absolute as read from Figure 13 is listed in column 10. The values in column 10 are added to entropy in column 5 t o obtain the entropy listed in column 12. The values for H in column 11 and for S in column 12 are used to plot the 1000pound pressure line in Figure 14. By making similar calculations for different pressures the complete enthalpy-entropy diagram of Figure 14 was obtained for this gas. Figure 14 is directly applicable only to natural gas which has a pseudocritical pressure of 664 pounds per square inch absolute and a pseudocritical temperature of 383' R.; but the effects of pressure and temperature on the enthalpy and entropy of other gases closely approximating the gravity of this gas, 0.7 (air = l ~ O ) ,are relatively similar, and the data computed by Figure 14 for other gases of about this gravity will not be in serious error. From similar charts for natural g a s e s of d i f f e r e n t g r a v i t i e s t h e Ps1 energy required for compressing the gases can be closely estimated. The Figure 13. Isothermal Changes in Entropy above Atmospheric Pressure following examples explain the use of for N a t u r a l Gases Figure 14: EXAMPLE 1. If the gas of Figure 14 is expanded freely and adiabatically as through a choke or throttle, from an initial pressure of 5000 In commercial operation the compression usually occurs pounds per square inch absolute and temperature of 160" F. over a path which is not isothermal but very close to an adiat o a pressure of 1000 pounds, what would be the final tembatic or an isentropic path. For this type of compression the indicated energy required to compress and deliver the perature at the end of the expansion? gas may be determined from the following relation: For free adiabatic expansion in flow enthalpy H is constant. Initial conditions are: PI = 5000 pounds, tl = 160' F., -tu. = AE A ( P V ) = AH (12) H I = -360 B. t. u./mole. Final conditions are: Pt = Equations 11 and 12 can be easily solved by an enthalpy1000 pounds, H 2 = -360 B. t. u./mole. By following the entropy chart for the particular gas being compressed. The constant enthalpy line of -360 B. t. u./mole horizontally method of constructing such a chart for a natural gas from the across Figure 14 to the intersection of the 1000-pound presthermal properties in Figures 7, 11, and 13 is indicated in sure line, the final temperature is read as 70" P. Table VIII. The enthalpy and entropy as given in columns EXAMPLE 2. ~f 1,000,000 standard cubic feet (measured 4 and 5 are taken as zero a t 32" F.and atmospheric Presat 60' F. and 14.4 pounds per square inch absolute) of the sure. The corresponding values for the enthalpy in Column gas of Figure 14 are compressed isothermally per day of 24 4 at atmospheric pressure and. a t the higher temperatures hours a t looo F.from 1200 to 3000 pounds pressure, what is were obtained by graphically integrating the heat capacity the horsepower required for compression? from Figure 7 over the indicated temperature range acFrom Equation 11 the work of compression is RT In f2/f1. cording to Equation 1. Similarly, the values for entropy in The initial conditions are: column 5 were obtained by integrating Equation 10, using the heat capacity data of Figure 7 . pT, = (100 460)/383 = 1.462 The corresponding values for enthalpy in column 4 and p P , = 1200/664 = 1 81 entropy in dolumn 5 were plotted on Figure 14 to determine j / P 1 0.52 (Fig. 10) = 0.82 X 1200 = 985 the atmospheric pressure line. fl
+
+
INDUSTRIAL AND ENGINEERING CHEMISTRY
May, 1942
601 are: L1 = 100" F., Pi = 1200 p o u n d s , H I = -100 B . t. u . / p o u n d mole, Si = -8.4 B. t. u./ pound mole/ " F. ; the final conditions are: Pz = 3000 pounds, Sz= -8.4 B. t. u./ pound mole/" F. By following the constant entropy h e of -8.4 vertically upward from the initial conditions until it intersects the 3000-pound pressure line, the final temperature is read as 221 " F. and the enthalpy as 870 B. t. u. per pound mole: Work of compression = AH a H z - HI = 870 (- 100) = 970 B. t. u./lb. mole Indicated horsepower = . 970 X 107.5 = 40.9 2545
Figure
14. Enthalpy-Entropy Diagram for a 0.7-Gravity Natural G a s ( A i r
=
Using a n efficiency of 85 per cent for the compressor,
1)
Brake horseuower =
R.
9Pe-884 pounds per square inch absolute; $Tc-383'
40.9 0.85
The final conditions are:
5
48.1
Nomenclature
p T , = 1.462 pP, = 3000/664 = 4.52 f / P = 0.664 (Fig. 10) = 0.664 X 3000 = 1992 fg
C,
E F f*
1992
Work of compression = 1.987 X 560 In - = 785 B. f. u./lb. 985 mole. Vol. of 1 mole gas at 60" F. and 14.4 lb. pressure = 387 cu. ft.
.
=
heat capacity at constant pressure, B. t. u./lb./" F.
= internal energy, B. t. u./lb. mole
= =
E - TS + PV
fugacity, Ib./sq. in. abs.
= fugacity at a low pressure where a gas may be sssumed
ideal f;lP = activity coefficient H = enthalpy, B. t. u./lb. mole K = equilibrium constant = y/x P = total pressure, Ib./sq. in. abs. PO = vapor pressure, Ib./sq. in. abs. pP. = pseudocritical pressure, Ib./sq. in. abs. pP, = pseudoreduced pressure R = gas constant, 1.987 B. t. u./lb. mole/' R. S = entropy, B. t. u./lb. mzle/" F. T = absolute tempzrature, R. (" F. 460) t = temperature, F.
+
The heat t o be removed during the comp
in order by 8 etermined above\fro
to maintain isothermal compression can be o tracting the work of compression the increase in enthalpy as read fr
HI = -100 B. t. u./lb. mole AH =
Ha
- Hi
Hz = -1000 B. t. u./lb. mole = -1000
- (-100)
= -900B. t. u./mole
+
Heat removed during compression = - AH work of compression = 900 785 = 1685 B. t. u./lb. mole Heat removed per hr. during: compression 181,200 B. t. u.
+
EXAMPLE 3. If 1,000,000 standard c 60' F. and 14.4 pounds pressure) of th compressed adiabatically (at con 24 hours from 1200 pounds per squ to 3000 pounds, what is the horsep pression? For an adiabatic compression the work is equal to AH for the compression. From Figure 14 the initial conditions
2
s
= compressibility factor = PV/RT
ts
, F, R
= bottoms product, overhead distillate, feed, and
respectively, applied to a fractionator 1, 2 = initial and final states, respectively
Literature Cited ay, IND. ENO.CHSM..21,942 (1929). cksey, J. Imt. Petroleum Tech., 21,867 (1935). Docksey, in "Science of Petroleum", Vol. 11, p. 1245, Oxford Univ. Press, 1938. (3) Boomer, Johnson, and Piercey, Can. J. Research, 16B, 319 (1938). (4) Ibid., 16B,396 (1938).
602
INDUSTRIAL AND ENGINEERING CHEMISTRY
(5) Bridgman, “Physics of High Pressure”, London, G. Bsll and Sons, Ltd., 1931. (6) Brown, Petroleum Eng., 11, No. 9, 55 (1940). (7) Brown and Holcomb, Ibid., 11, N o . 6 , 23 (1940). (8) Budenholzer, Sage, and Lacey, IND.ENG. CHEM., n, 1288 (1939) (9) Ibid., 32,384 (1940). (10) Burrell and Robertson, J . Am. Chem. Sac., 37,2188 (1915). (11) Cragoe, U. S. Bur. Standards, Misc. Pub. 97 (1929). (12) Dana, Jenkins, Burdick, and Timm, Refrig. Eng., 12,387 (1926). (13) Deschner and Brown, IND. ENQ.CHEM.,32,836 (1940). (14)Euoken and Lude, Z . physik. Chem., B5,413 (1929). (15) Eucken and Parts, Ibid., B20,184 (1933). (16) Fortsch and Whitman, IND.ENG.CHEM.,18,795 (1926). (17) Frank and Clusius, 2. physik. Chem., B42,395 (1939). (18) Gary, Rubin, and War, IND.ENG.CHEM.,25, 178 (1933). (19) Hougen and Watson, “Industrial Chemical Calculations”, 2nd ed., p. 425, New York, John Wiley & Sons, 1936. Ibid., p. 429. International Critical Tables, Vol. 111,p. 230 (1928). Ibid., Vol. V, p. 137 (1929). Ibid., Vol. V, p. 138 (1929). John, 2.physik Chem., 11, 787 (1893). Katz and Hackmuth. IND.ENG.CHEM..29. 1072 (1937). t27j Keiso and’Felsing, J : Am.’ Chem. Sac., 62,3132 (1940). (28) Kemp and Egan, Ibid., 60, 1521 (1938). (29) Kistiakowsky and Rice, J . Chem. Phys., 7,281 (1939). (30) Konz, IND. ENG.CHEM.,33, 617 (1941). (31) Kurata, Univ. of Mich., M.S.E. thesis, 1938. (32) Lewis and Randall, “Thermodynamics”, p. 223 (1923). (33) Maass and MoIntoch, J . Am. Chem. Sac., 36, 737 (1914). (34) Maass and Wright, Ibid., 43,1098 (1921). (35) Mabery and Goldstein, Am. Chem. J., 28,66 (1902). (36) Matthews, J . Am. Chem. Sac., 48,562 (1926).
Ormandy and Craven, J . I m t . P e t , d c z m Tech., 9, 368 (1932). Pall and Maass, Can. J. Research, 14B,96 (1.036). Pitzer, Petroleum Div., A. C. S., Cincinnati, 1910. Sage, Budenholzcr, and Lacey, IND.E N G . C H E U . , 32, 1262 (1940). (41) Sage, Evans, and Lacey, Ibid., 31,763 (1933). (42) Sage and Lacey, I b i d . , 27, 1484 (1935). (43) Ibid., 28,249 (1936). (44) Ibid., 30, 673 (1938). (45) Ibid., 31, 1497 (1939). (46) Sage and Lacey, Refiner iVatumZ Gasoline M f r . , 18, 47% (1939). (47) Sage, Lacey, and Schaafsma, IND.ENG.C H ~ M26, . , 214 (1W4). (48) Ibid., 27,162 (1935). (49) Sage, Lavender, and Lacey, Ibid., 32, 743 (1940). (50) Sage, Schaafsma, and Lacey, I b i d . , 26, 1218 (1934). (51) Sage, Webster, and Lacey, Ibid., 27, 148 (1935). (52) Ibid., 28,984 (1936). (53) Ibid., 29,658 (1937). (54) Ibid., 29, 1188 (1937). (56) Ibid., 29, 1309 (1937). (56) Satterly and Patterson, T r a n s . R o y . Soc. Can., 13,Sect. i i i , 123 (1919). (57) Sheele and Heuse, Ann. P h y s i k , 40, 473 (1913). (58) Smith, Beattie, and Kay, J . Am. Chem. Soc., 59,1587 (1937, (59) Standing, Univ. of Mich. Ph.D. thesis, 1941. (60) Thayer and Stegeman, J . P h y s . Chem., 35,1505 (1931). (61) Vaughan and Graves, IND. EXG.CHEW.,32,1252 (1940). (6%) Vold, J . Am. Chem. Soc., 57, 1192 (1935). (63) Watson and Nelson, IND.ENG.CHEX.,25,880 (1933). (64) Weibe and Rrevoort, J . Am. Chem. Soc., 52, 622 (1930). (65) Wilson and Balke, IND.ENG.CHEM.,16, 120 (1924). (66) Witt and Kemp, J . Am. Chem. SOC.,59, 273 (1937). (67) Wrinkler and Maass, C a n . J . Research, 9, 610 (1933). (68) Yee, Univ. of Mich. Ph.D. thesis, 1936. (69) Young, Sci. Prac. Ray. Dublin Sac., 12,374 (1910). (37) (38) (39) (40)
END OF SYMPOSIUM
THE ALCHEMIST . .
.
Vol. 34, No. 5
By Robert Fawcett
THROUGH the courtesy of The Barrett
Division of Allied Chemical & Dye Corporation we are enabled to add another modern artist to the Berolzheimer Alchemical and Historical Rcproductions. This, No. 137 in the series, is by Robert Fawcett, born in London, England, in 1903. He obtained his art education at the Slade School in London, in Paris, and a t the Art Students’ League, New York. Mr. Fawcett has excellently grasped the medieval spirit, including the usual cluttered appearance of the laboratory. We particularly like the illumination of the alchemist’s face. The apparatus is simple, although adequate for the elementary metallurgical operation being undertaken. The original is a combination wash-drawing done in India ink, aniline dye, and crayon, and was reproduced in the Saturday Evening Post this year. D. D. BEROLZHEIMER 50 E. 41st Street New York, N. Y. The lists of reproductions and directions for obtaining copies appear as follows: 1 to 96, January, 1939, page 124; 97 to 120, January, 1941, page 114; 121 to 132, January, 1942, page 119. An additional reproduction appears each month.
