Physical and Thermal Properties of Petroleum Distillates W. H. BAHLKEm
D
\Y. B. K ~ YResearch , Laboratory, Standard Oil Company (Indiana), Whiting, Ind.
3 Latent heatsof vaporization CCURATE data on tlie The P-T--?'relationships of two light-petroleum 4 Total heats as a function of physical a n d t h e r m a l fractions-one a commercial gasoline and the pressure and temperature properties of pet'roleum other a rather narrow boiling-range naphthahydrocarbon mixtures, extendI I E T H O D O F DETERJIIKiTIOlL or hare been determined experimentally over a wide ing over a vide range of temI'HY~IC LL P R O P E ~ Z T I E ~ range of conditions, extending f r o m near atperatures and pressures, are deFor determining the pre:>suresirable as a n aid in the developmospheric pressure to well beyond the critical volume-temperature-state relam e n t o f p e t r o 1e u ni-refining region. operations. Data of this charactionships, a small sample of t h r The complete P-T'-T data on these two mixtures ter are especially useful in the air-free liquid was confined over are gicen. Comparison with the properties of mercury in a thick-n alled capildevelopment of cracking procpure hydrocurbons is made, and methods of lary tube nhich was heated to esses. Although such data are a constant temperature by thc extremely useful, the literature correlation are indicated. vapors of a series of pure organit contains only meager informaThis incesfigation has shown that the P-TI-T tion relative to the properties of compounds. The capillary tube relationships of petroleum hydrocarbon mixtures communicated with a niercurypetroleum mixtures a t high temare similar in all respects to those of binary filled compressor for regulating perature and p r e s s u r e . The m ixtures heretqfore inz!estigated. the pressure on the \ample and usual practice in petroleum refining has been, whenever such with a gaq rnanonieter for mea+ From these physical data the thermal properties data were needed, to a;:\wine ceruring the pressure The tube qf one of the mixtures uas calculated thermohad been carefully calibrated $0 tain values which \yere estimated dynamically, making use of a n equation of state from the properties of pure hythat it nab possible to nieasurt' deceloped.for ihe superheated vapor region. Comdrocarbons. Insufficient proof of the total 1 oliime occupied by the. bining the properties calculated and preriously sample as ne11 as the volunie of t'he justification and limitations of these assumptions exists. the s e p a r a t e p h a s e - pre*ent published data on the speci'c heat of the liquid Equilibrium between the liquid I n view of t h e p a u c i t y of and mpor at atmospheric pressure, a total heat data in this field, the present temperature chart is presented. by itirring TT i t h a n electroauthors initiated a program of magnet stirrer. Obiervationresearch i n t h i s l a b o r a t o r v wliicli, it )vas believed, would establish the general behavior of of the pressure and volume of liquid and vapor phases a t ii complex hydrocarbon iniytures and ultimately lead to the constant temperature were made for a number of temperature.< possibility of readily estimating the properties of petroleum and covering a range of total volumes, extending from t,lir> fractions. This program coiiteinplated the measurement of volume occupied by the compressed-liquid phase to that b!. physical properties of a number of fractioiis and the general the expanded-vapor phase. correlation of these propertie. n i t h one another #is well as APPARATUS. The apparatus for determination of the P-I--T with other inore easily determined properties of the fractions, relationships was a modification of that employed by Sydney such as A. S.T. hI. boiling range, specific gravity, and molecular Young and is shown in Figure 1. weight. Further. it was proposed to calculate thermal propertieq from physical properties and obtain a similar I t consisted of the long steel compressor block, A , securely correlation. The developnient of means of ready measure- fastened in a horizontal position with three vertical branches at angles to it. The block, A , was fitted with a section, B , ment of some of these properties, for cases where very precise right through which the plunger, D , passed, a pressure-tight joint, data in the high pressure-high temperature region are re- being insured by the stuffing box, C. One end of the plunger quired, was also included in the program. m s threaded and held in a correspondingly threaded section This paper presents some of the data obtaliied in this pro- of B. I t could be turned by means of the hand lvheel, F , and permitted the volume of the space, E , which was filled gram. It gives data on the physical properties of tTvo thus with mercury, to be changed at will. petroleum fractions-one a commercial gasoline and the Each of the vertical branches was fitted with a stuffing box other a rather narrm- boiling-range naphtha. These two through which passed a thick-walled capillary tube. The tube distillates were chosen because they have approxiniately tlie was held in position by an enlargement, G , which rested on rubber washers against the loose-fitting steel ring, H. The same A. 1'. I. gravity and niolecular weight, but markedly packing of the stuffing box consisted of a perforated cylindrical different boiling ranges with nearly the same average boiling rubber stopper I which was forced around the tube by the gland, point. The methods and results of determination of the J ,by screning down the cap, K . The compressor was immersed pressure-volume-temperature-state relationships over a wide in a water bath whose temperature near that of the room was const,ant to within 0.02" F. ( O . O l o (2.). range of conditions are given. The behavior around the held The liquid under investigation was confined over mercury in critical region were rather closely studied, and the results the experimental tube, L , which was constructed of Pyrex are given. Further, the methods and results of calculations capillary tubing of about 1.5 mm. bore with an intermediate section of 4 mm. bore. The tube was carefully calibrated, and of the folloniiig thrrmal properties of the naphtha are given, the volume from the sealed end was expressed in terms of the 1 Difference in specific heats at constant pressure and distance from a reference line etched around the tube near constant volume as a function of pressure and temperature. the sealed end. This distance was measured to 0.05 mm. by 2 . Joule-Thomson coefficients as a function of pressure and means of a cathetometer. temperature. To bring about equilibrium quickly between the liquid and
A
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I S G C H E \I I S T R Y
pressure manometer determined by taking ie:tdings simu1t:ineously on both manometers. The pressure as determined by the manometer was corrected: for the difference in level of the mercury (corrected t o standard temperature) in the experimental tube and manometer; for the pressure of the column of unvaporized liquid; for capillarity and the vapor pressure of mercury when necessary; and for the deviation of nitrogen (in the manometer) from Boyle's law.
REMOVALOF
PREPARATION OF SAMPLE MATERIALREACTIYEWITH MERCURT.
Petroleum distillates, even though rather highly refined, contain compounds rrhich react n i t h mercury and cause a finely divided precipitate to settle out. These compounds were removed by first shaking the sample with mercury a t room temperature and finally by vaporizing in contact with mercury vapor a t 675" F. (357.2" (2.). REMOVAL OF WATER. The sample was dried by standing over metallic sodium for several days or in contact with P,Os for about half a n hour. REMOVAL OF AIR. The general plan of deaerating the sample without changing its composition appreciably was to reflux i t for some time under high vacuum with the temperature of the condenser such as t o condense the more volatile hydrocarbon vapors but permit the exit of the air and other noncondensable gases. The apparatus for removing the air and filling the experimental tube with an air-free sample is shown in Figure 2.
vapor phases of the sample, the experimental tube was provided with a stirrer, consisting of a small rod of soft iron about 0.75 inch (1.9 cm.) long and of dumb-bell shape. The stirrer was moved hy means-of an electromagnet outside the apparatus.
In calculating the volume of the liquid and vapor phases of the sample from the experimental data, the following factors were taken into account: the volume of the mercury and liquid menisci; the thermal expansion of the tube; and the volume of the iron stirrer. The experimental tube, surrounded by the jacket, 0, was heated to a constant temperature by the vapors of a series of pure organic liquids whose boiling points lay within the temperature range desired. B boiling the liquid under reduced range of temperatures, constant pressure, a 70' F. (38.9' to within 0.02" F. (0.01' C.), was obtained with a single liquid. The liquids recommended by Young ( 7 ) were used. The temperature of the vapor bath (that is, the temperature to which the experimental tube was heated) was measured by a copperconstantan thermocouple, !/', inside a thin-walled glass tube, projecting into the vapor hath (as shown) to a point just ahove the experimental tube. To prevent the cold liquid condensate from running back on the couple, which would thereby give too low temperature readings, and also to shield the couple from radiation from the electric heater (not shown) surrounding the jacket, a bell-shaped metal guard, U , with several holes drilled through the side near the top, was placed over the end of the couple. The couple was calibrated using the standard temperatures of the boiling points of water, aniline, naphthalene, benzophenone, and sulfur. Melting ice served to maintain a constant cold junction temperature, and a Leeds and Northrup type K potentiometer measuring to 0.001 mv. was used for the e. m. f. measurements. The pressure was measured by means of the two gas manometers, M and N . The internal diameter of M (1 mm. bore), which served for the measurement of moderate pressures, was the same throughout. N , which served to measure high pressures, was provided with a reservoir of relatively large capacity a t the open end. Both tubes were carefully calibrated and filled with pure nitrogen. The gas constant for the low-pressure manometer was determined by comparing i t with a direct column of mercury in a tube of about 1.5 meters in height, which temporarily replaced the experimental tube. This tube was later replaced by a glass rod, and the constant for the high-
8.)
A high-vacuum mercury diffusion pump, A , was backed by a Cenco-Hy-Vac oil pump. The pressure in the apparatus was measured by the MacLeod gage, B , ca able of measuring less than 10-6 mm. mercury pressure. $he sample (about 175 to 200 cc.) in C was introduced through the mercury-sealed stopcock, D ,and stood over the mercury in the boiler, E. This stopcock contained no lubricant and was prevented from sticking by filling the lower compartment of the sheath with mercury The height of the mercury in the boiler, E , was regulated by the pressure over the mercury in the vessel, F. The by-pass tube, G , a small section of which was wrapped with electrical heating wire, served as a thermocirculator for the liquid sample as well as to cause gentle boiling. The hydrocarbon vapors, together with the air, passed to the condensers, H and I,.where the vapors were condensed and returned to boiler E while the air and noncondensable gas were removed from the system through the vacuum pump. Condenser H was cooled with a mixture of carbon dioxide snow and acetone; I was cooled with the same mixture or with liquid air, as the volatility of the sampIe demanded. The sample was refluxed a t a pressure of 0.001 to 0.0001 mm. for about 6 hours which, experience showed, was sufficient to remove all dissolved air. FILLISQ TUBE WITH AIR-FREE SAMPLE.When the sample had been sufficiently degassed, stopcocks J , K , and L were closed; and, as soon as the condensers w-armed up to near room temperature, the sample was forced up through the condensers several times by controlling the pressure in vessel F ,
INDUSTRIAL AND ENGINEERING CHEMISTRY
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SRAM LD
in order t,o flush out the more volatile constituents which had
adhered to the walls. Likewise, the line from the condenser through t,he U-tube, .If, to the compartment, 0, surrounding the experimental tube, was flushed out several times by small quantit,ies of the degassed liquid which was discarded to t'he vessel, Q , through the stopcock, P. Stopcock P was then closed and the liquid allowed to cover the end of the experimental tube, R , which was held in an inverted position in compartment 0 by a tight-fitting rubber stopper. The stopper was covered with a layer of mercury and made vacuum-tight hy a mercury seal. I n order to introduce the desired quantity of liquid into the experimental tube, a very narrow hair-like capillary, S, was drawn and inserted in the tube to the point T , about 3.5 cni. from the end. This capillary tube was held in a fixed position by an offset, V , near the top. The top projected into the compartment, W , which was connected to 0 through a mercury-sealed ground joint. When the liquid sample covered the end of the experimental tube, the liquid flowed in and completely filled tdhetube. Mercury was then introduced from X until the end of the tube was covered, when, by gently tapping the tube, the mercury entered a,nd displaced all of the liquid sample except that below the end of the small capillary. The appsratus was then brought to atmospheric pressure, section W removed, and the capillary viithdrawn while the end of the tube was still covered with mercury. The experimental tube was then removed from the apparatus, the end firmly closed n-ith the finger, and the tube turned up in the compressor a t an angle of about 45" with the open end under mercury. Any air that might have been trapped in the open end IT-asforced out by carefully warming the sample until it suddenly expanded. The tube was then fixed in place in the compressor. The weight of liquid in the tube was determined from the volume as measured with the cathetometer and the dengity as dctrrmined on a portion of the air-free sample in a pycnometer
phenomena occurring in the critical region. Thus the properties in this region were determined to be as given in Table IV. T - ~ B LI.E PHYSICAL MEASUREMENTS OF DISTILLATES -A. M O L . A . P. I. Ini-
5. T.31.DISTILLATION.--
WT. G R A Y . tial 10 20 30 40 50 60 70 80 90 Max.
Gasoline Naphtha
109 110
57.3 57.1
o F . ° F . o F . OF. OF. O F . O F . OF. OF. ' F . ' F . 98 149 191 230 260 282 302 325 348 371 414 211 230 238 245 252 258 264 272 282 295 326
The isotherms are shown in Figures 3 and 4, and the data are presented in somewhat different form in Figure 5 . Referring to Figure 5 , i t is notable that the boiling line increases regularly with pressure and temperature, whereas the dew line passes through both a maximum of temperature (termed
RESULTS OF PHYSICAL K~EAXREMEX~~ The -4.P. I. gravity, A. S.T. AI. distillation, aiid averago Iiiolecular weight (determined by freezing-point lowering of Iieiizene) of the two distillates as determined on the deaerated samples are given in Table I. A number of isotherms were determined experimentally, covering a range from near atmospheric conditions t o above the critical region. These data are pix-en in Tables I1 and 111. I n the determinations, particular attention was paid to the
"point of iiiaxiniuin temperature") and a inaxiniuni of pressure in the region of the critical point. This is particularly evident from a n examination of the data for the gasoline. The dew line and boiling line meet a t the critical point. .it
INDUSTRIAL AND EYGISEERING CHEMISTRY
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TABLE11. ISOTHERMS OF NAPHTHA
the critical point the properties of the saturated liquid and saturated vapor are identical. At any P-T intersection, within the area bounded by the dew line and boiling line, two phases-liquid and vapor-exist (Figure 5 ) ; outside this area one phase exists, the theoretical dividing line between liquid and vapor rising vertically from the critical point where the dew line and boiling line meet. The phenomenon of retrograde condensation of the first kind takes place between the critical temperature and the point of maximum temperature. Thus, when raising the pressure from a point of low pressure a t any temperature between these two, a liquid phase appears I I
I
o
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i
I
I
i
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I
DENSITY
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Vol. 24, No. 3
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Atm. Cc./gram
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a t the lower intersection of the dew line; and, on further compression, the volume of this phase first increases, then decreaces, and finally disappears a t the upper intersection of the dew line. At the critical temperature, condensation proceeds in a normal fashion as the pressure is increased until, when the system is just completely condensed, it suddenly vaporizes. ,4t the critical point and in the region of retrograde condensation, opalescence occurs on change of qtate. On changing conditions of the system a t pressures below the maximum pressure of the dew line, the phases are readily identified according t o the known starting point and the changes which occur in the system. At pressures higher than the maximum of the dew line, howerer, the identification of the phases must be made from knowledge of what occurs a t lower pressures. Thus on heating from a lon- to a high temperature a t pressures higher than the maxiniuni of the de\T line, no evidence of transition from one state to another ib ohserved JThen passing through the critical temperature. 1-isually the system behaves as if no change in itate occurs a t any point when heating under these high-pressure conditions, and naming the phase is really a matter of definition. The behavior of these complex hydrocarbon system- I
4:
t2
Hrn
$>
st
Atm. Cc./sram 3.63 59.257 3.97 51.344 4 . 4 0 42.332 4.89 33.933 5.39 27.280 6.23 19.158 7.15 13.157 9.89 3.578 10.19 3.009 11.00 1.702 12.95 1.702 4.99 60.890 216.9 (422.5' F.) 6.343 41.909 7.28 31.805 9.13 19.037 11.08 11.391 15.22 3.397 15.82 2.749 16.83 1.840 19.49 1.836 29.59 1.825 5.52 61.674 227.7' 5.68 59.831 1441.8' F.) 5 . 8 5 57.775 6.03 55.240 6 . 1 8 52.991 6 . 2 5 52.344 6 . 4 3 49.884 6.86 44.292 7.53 37.936 8.10 31.649 8 . 6 1 27.763 9.25 23.740 10.33 18.202 12.29 12.025 16.95 3.559 17.60 2.818 18.78 1.899 20.26 1.895 22.06 1.890 5.64 61.604 235 . I (45s , 2 O F.) 5.85 59.190 6.04 57.079 6.32 54.227 6 . 5 0 52.566 6.73 50.447 6.93 48.521 0
1.p ;i
24
111.
8
E N G I N E E K I ?u' G C H E hl I S T R Y ISOTHERMS O F 3'0; -.
z ZZi
:2 ;A $5
.. .. ..
..
.0. h b
0.16 0.24 0.29 0.37 0.48 0.62 0.91 0.95 1.00
.. ..
V. L. = volume of liquid. Liquid too small in amount to measure. Mercury meniscus was in an irregular section of the tube, and total volume of tube had not been calibrated a t this point. d Trace of liquid present. With increase in pressure, quantity.of liquid a t first increased. reached a maximum, and then decreased until a t aucceeding reading no liquid was present. Temperature was l.00 unsteady to measure volume of liquids. a b e
Moreover, the critical temperature of any mixture is fixed by its composition; that is, in any normal mixture the greater the concentration of the constituent of higher critical temperature the higher the critical temperature of the mixture, and vice versa. Now in any condensation of a normal mixture below the critical temperature the liquid formed is less rich in the more volatile component than is the vapor from which it is condensed; but, as condensation proceeds, the liquid becomes richer in the more volatile compon&t until, when the system is totally condensed, the composition of the liquid is equal to that of the original vapor from which it was produced.
Gasoline Naphtha
GASOLINE
* I
183.2 (361 .So F.)
TABLE
295
IV. PROPERTIES O F GASOLIVE AYD N A P H T H ~ IN CRITICAL REGION
PROPERTIES A T POINT O F >fax. TEMP. PROPERTIES AT CRITICAL POINT Density Pressure Temp. Density Pressure Temp. (vapor) Lb./in 2 Lb./in.l abs. ' F . Gram/cc. abs. F. Gram/cc. 642 686 0.325 492 603 0.204 434 591 0.258 436 593 0.239
I t follows from what has just been said that, as condensation progresses, a t constant temperature below the critical from a lower to a higher pressure, the liquid produced has a progressively lower critical temperature. Xow if condensa-
il
*a
u"
TEMP.
&
c. Atm. 269.2 26.79 (516.5" F.) 28.31 29.71 33.65 280.8 6.59 (537 5OF.) 7.16 8.19 9.79 12.27 13.91 15.14 16.05 16.59 17.36 18.39 19.92 28.70 29.66 31.33 32.60 33,30 290.1 7.40 (554.1' F ) 8.55 9.82 11.58 13.84 15.34 16.69 18.21 18.81 19.05 20.77 21.67 22.28 31.68 33.49 36.52 299.7 7.58 (571.5' F ) 8 . 9 0 10.59 13.04 16.06 18.20 19.89 22.17 22.57 24.54 34.43 35.85 307.6 8.98 12.13 (585.6'F.) 16.50 23.89 36.90
.
Cc /ora m
2.944 0 . 9 1 2.205 1.00 2.186 ,. 2.149 ,. 57,874 53.126 45.854 .. 37.351 .. 28.416 .. 24.390 .. 21.683 .. 19.930 .. 18.812 0 17.000 b 14.834 0 . 1 5 12.069 0 . 2 5 3.549 0.81 2.969 0 . 9 0 2.355 1 . 0 0 2.328 .. 2.279 .. 52.621 44.825 , 38.358 31.539 .. 25.531 ,. 22.203 .. 19.697 .. 17.224 .. 16.362 0 15.989 b 13.103 0.11 11.698 0.16 10.874 0 20 3 . 3 5 1 0 83 2.518 1.00 2.424 .. 52.188 . 44.003 .. 36.200 .. 28.329 .. 21.754 .. 18.203 . 15.908 .. 13.220 .. 12.837 0 10.423 0.10 3.344 0.80 2.811 1.00 43.787 31.456 ,. 21.667 12 279 3: 312 Critical point
..
...
.
..
..
C. 311.8 (593.2OF.j
Aim 6.95 8.50 10.13 13.44 17.72 23.32 28.17 37.13 316.9 8.67 (602.5°F.:i 10.74 13.61 17.31 24.44 33.46
Cc./aram 58.558 47.567 39.156 28.529 19.905 13.081 8.987 3.685 46.984 37.415 28.674 21.119 12.f48
,.
..
.. .. .. ,.
P0i;lt
of ma\ teiiip
326. 5 (619.7'F.:
7.00 8.59 14.35 17.50 25.40 327.8 40.23 (622.0° 17.;' 37.35 35.17 32.88 30.85 28.59 7.15 8.26 9.59 10.97 12.57 14.82 18.83 26.87 40.17 340.5 (645.OOF.) 37.94 35.33 33.39 31.48 30.14 355.6 7.24 (672.2'F.) 8.40 9.93 12.00 14.43 16.81 21.46 28.30 356.3 40.62 (673.3'F.) 38.08 35.95 33.95 32.00
58.238 47.563 27.492 21.369 12.401 4.092 5.067 5.999 7.028 8.259 9.514 58.708 51.314 44.366 38.595 33.155 27.558 20.401 12.293 5.310 6.082 7.120 7.989 8.871 9.525 59.486 51.913 44.336 36.366 29.716 24.707 18.158 12.450 6.279 7.119 7.919 8.762 9.529
.. ,
.
.. ..
.. .. .. ,.
..
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..
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tion is carried out a t progressively higher temperatures (starting a t a temperature below the critical), a temperature is finally reached which is identical with the critical temperature of a liquid having the composition of the system in question, and a t this point the liquid produced will pass into the vapor state when the system is just completely condensed. A temperature slightly higher than this corresponds to the critical temperature of a liquid slightly less rich in the more volatile component, and consequently if condensation occurred in the normal manner a t this temperature, the liquid formed would suddenly vaporize before the system \vas completely condensed. Instead of the condensation-vaporization process occurring in this manner (which would lead t o anomalous relationships between the composition of the saturated liquid and vapor a t and near the critical point), the liquid first formed soon begins to dissolve in the relatively large amount of highly compressed vapor remaining and is eventually revaporized by this means. While the hydrocarbon systems studied here are much more complex than any studied by Caubet, the explanation of retrograde condensation as given above is still tenable. The relationships between density and temperature for the saturated liquid and vapor are shown in Figure 6, which includes also the data of Young on normal octane. It will be noted that the density-temperature relationships for these hydrocarbon mixtures are, in general, similar to the behavior
INDUSTRIAL AND ENGINEERING CHEMISTRY
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Vol. 24, No. 3
IA
I3
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?'F ASSXio3
of pure compounds except that in the case of mixtures the mean density line passes through the point of maximum temperature rather than the critical point. However, in this respect also these complex systems are similar in behavior to the simpler binary systems. The relationships between pressure, temperature, and percentage of liquid evaporated are shown in Figures 7 and 8 where log pressure is plotted against the reciprocal of the absolute temperature for various percentages evaporated. As might be expected, a straight line relationship between
possible, so that a number of determinations required can be reduced to a minimum. For the purpose of correlation the theorem of corresponding states offers perhaps the best possibility. This theorem has been rather generally tested by Young (8) who found that it holds with quite good accuracy for certain closely related substances whose critical pressures are very nearly equal, and with fair accuracy for closely related substances having quite different critical pressures. If the theorem of corresponding states were strictly true, all pressure-temperature-volume relationships for pure compounds could be represented by a single relationship such as is shown in Figure 9 where the reduced isochors - = v c constant, for isopentane (9) are shown as related to reduced
v
T
0.b
bo
105
b
REDUCED TEMPERATURES
1 P and holds a t constant percentage evaporated, except in the region of retrograde condensation.
CORRELATION OF PHYSICAL PROPERTIES Data such as are given in the preceding paragraphs are extremely useful in the development of high-pressure hightemperature processes in the petroleum industry. However, the determinations of the isotherms over a useful range of Dressures is a laborious and time-consuming operation, and it is therefore desirable to have some method of correlation if
1
temperature - and reduced pressure TO E; As shown by Figure 10, however, where similar relationships for five hydrocarbons are giyen, the theorem of corresponding states is only approximately correct. There appears, however, a systematic shift with molecular weight which could no doubt be evaluated if necessary. The theorem of corresponding states was applied to the two hydrocarbon systems studied here, and the reduced isochors are shown in Figure 11 in comparison with the data of isopentane. The agreement between the two hydrocarbon systems in the superheated vapor region is as good as might be expected. Moreover, the data are in fair agreement with those of isopentane except in the critical region. It appears, therefore, that the data for some other hydrocarbon system in the superheated region could be estimated over a fair range of pressures and temperatures from Figure 11, together with a determination of the critical temperature, pressure, and volume.' The relationships, as in Figure 11, along the saturation lines are a function of the boiling range of the fraction under consideration, and further data are necessary before general correlation can be made. ,
CALCULATION OF THERMAL PROPERITES The P-T-V data are not only valuable in themselves but serve for the calculation of various thermal properties which are difficult to measure with accuracy. From the data in the foregoing sections it is possible to calculate, using the exact 1 Since this paper pa8 compiled, Cope, L e a k , a n d Weber [ I N D . ENQ. C H r M . , 33, 887 (1931)]have presented a method of calculating t h e P-V-T d a t a of a hydrocarbon In the superheated region, based on a modlfication of t h e theorem of correspondmg states Values of t h e specific volume of the vapor of gasoline a n d naphtha calculated b y this method agree with t h e experimental to within about 4 per cent. However, within t h e range of t h e experimental d a t a , for pressures a n d temperatures near t h e critical region, t h e deviations are s o m e n h a t greater and are of t h e order of 5 to IO per cent.
XZarch, 1932
INDUSTRIAL AND
ENGINEERING CHEMISTRY
laws of thermodynamics, the following thermal properties: change of *pecific heat with pressure; difference in specific heat a t ronstant pressure and constant volume; JouleThoni+i~ncoefficients; latent heats of vaporization; and ratio. of -peelfie heat..
291
I n selecting an equation of state, one may be guided by the forms which have been shown t o express the relationships for similar substances ( 2 ) However, simplicity of mathematical form must be considered if the equation is to be of greatest use in the calculation of the various properties. For the present purpose various equations were examined by the authors, and the one finally chosen was that proposed by Linde ( 6 ) for superheated steam, I n its expanded form it is as follows:
‘“Tfa
+
PV = AT P(D where A , C, D ,E , and F = constants
+ FP)
As applied to naphtha, the constants in the above equation were evaluated as follows: A C
n
E F When P 2‘ V
REDUCED TEMPERATURE
From the values of the above thermal properties and a temperature-total heat relationship under one condition, a complete temperature-pressuretotal heat diagram can be constructed. This has been done for the naphtha studied here, and the method and results of the calculations are given in the following paragraphs. The first and second laws of thermodynamics provide the basis of the equations necessary for the calculation of thermal properties. The derivation of the equations are in all cases perfectly general; hence they apply to mixtures as well as to pure substances. The derivation of the equations used below for calculation of thermal properties are given in most textbooks of thermodynamics and have therefore been omitted here. For calculation of the various thermal properties the following equations were used: 1.
Change of specific heat with pressure,
2.
Difference in specific heats,
(g), =
-T
3. Joule-Thomson coefficient, i.c = ( $ ) H
=
T
Latent heat of vaporization, dII = TdS
157 7234 X 10’ 20 102 X 10‘ 0.52 lb. per sq. in. abs. ‘Rankine cu. in. per lb.
The degree to which the equation fits the experimental data is shown in Figure 12. The solid lines represent the experimental data while the broken lines were calculated using the equation of state. The agreement is excellent except near the saturation line. At 200 pounds per square inch the deviation is insignificant, 6ut a t 6igher- pressures it becomes a p preciable. For this reason all thermal properties calculated, using the equation, are certain to be in error to some extent in FlG.1 I REDUCED FISOCHORS GASOLIN~~NAPHTHA
1.20
ISOPENTANE a GASOLINE
+ w
0
NAPHTHA
-ISOPENTANE
LOO
($)p
1
($)
- &5
am
09s
lclo
ID5
uo
REDUCED TEMPERATURE
-v
CP
4.
= = = = = = = =
+ VdP
The evaluation of the above equations can be accomplished either graphically or through use of an equation of state by differentiation. Since, for most refinery operations, the evaluation of the thermal properties in the vapor state are most useful, an equation of state applying to the vapor state serves to the most probable range of utility. The heat of vaporization, however, is best evaluated graphically as will be shown.
this region. The regions where this occurs have been indicated by broken lines in the various plots of these properties. OF SPECIFIC HEATC, AT HIGHPRESSURE. 1. CALCULATIOK The thermodynamic formula is:
(%)
=
-T(g)p
From the equation of state by differentiation,
and
p P
(g)p + T4 + T’ (g)p - 3CP 3EP2 A = -12CP 12EPZ
=
T6
‘
I N D U S T R I A L A N D E N G I N E E R I N G C H E ILI I S T R I'
298
-12C
or
VOl. 24, No. 3
12EP
T5 Substituting in Equation 1, 12C
=
($)T
I
I
T4
I
12EP
From the equation of state by differentiation,
+ -qT-
($)T
=
-
[g8 + +V
($)p
=
p A
+ 3C + 3EP TI
I
I
and
2E
Substituting in (4) the values of
-
($)p
D
- 2F
and
1
($)T
Substituting for 1' its value,
v = -AT P
OF
NAPHTHA VAPOR
('
+ (D + F P )
+ T3
the following formula is obtained: I
I
50
100
I
I 200
150
I
I
2%
PRESSURE Las. PER sa IN. A B S
300
350
c p
Integrating the above equation (T = constant) between the limits of a pressure, P , and atmospheric pressure,
-
where C,
+
=
(5
E AT T3 - F + F
'
Equation 5 may be simplified by rearrangement to give
+
+ +
[AT4 P(3C 3EP)]2 (6) T4 [PZ(E - FT3) A T ' ] 9331.7 where C p -CV = B. t.u. per lb. A , C, E , and F = constants in equation of state when P , 1.' and T are expressed as Ib. per sq. in. abs., cu. in. per lb. and O F. abs., respectively. c p
6 E ( P 2- 14.79 (P 14.7) T4 - (2) T4 = sp. heat at const. pressure at atrn. pressure.
- cv
- cv
=
Kow for the vapor state ( I ) , CP, =
6450 4'0 - (t + 670)
where S = sp. gr. of liquid at 60" F./60° F. t
= O F .
Substituting the abo\-e value for CPO,the final equation is obtained :
CP
=
40
-8
(t
12c + 670) + [m ( P - 14.7) + 6E (P2 $4'72)]
where C p
=
k7
(3)
B. t. u. per lb.
NAPHTHA VAPOR
t
= OF. C and E = constants in equation of state when P, V , and T
are expressed as lb. per sq. in. abs., cu. Ib., and O F. abs., respectively.
In.
per
Substituting the appropriate values of the constants in Equation 3, the following equation for the specific heat a t constant pressure of naphtha as a function of temperature and pressure is obtained: c p =
4.0 - 0.7500 (t 6450
- 151)lO' + 670) 4-(9.316P +(t 0.065P2 + 459.6)4
This equation has been used to calculate the specific heat a t constant pressure from atmospheric pressure to 350 pounds per square inch abs. The results of the calculation have been plotted and are shown in Figure 13. 2. CALCULATIOX OF C p - C V . The thermodynamic formula is:
Substituting the appropriate values of the constants in Equation 6, the following formula for the difference in the specific heats of the naphtha is obtained: c p
- cv
=
+
+
[157T4 P(21730 305P)107]' T4[P2(948,970X lo7 48052'6) 1,465,000T41
-
+
The results calculated from the above formula for pressures from atmospheric to 350 pounds per square inch absolute are given in Figure 14. 3. CALCULATIONOF JOULE-TROMSONEFFECT. The thermodynamic equation is:
I h D U S T R I A L A N 1) E N G I N E E R I N G C H-E-M I S T R Y
3laich. 1932
299
Heat Content from 0' F. (-17.8" C.) to Boiling Point. The change in heat content of a system is given by the exact thermodynamic equation: dH = C p d T
(d63p 1
- T -
-V
dP
(10)
For the liquid state, however, c a l c u l a t i o n reveals that for the pressure range considered here the second member of the equation is i n s i g n if i c a n t (ex c e p t near the critical state) and may be disregarded. I
L 300
T
($)*
Y
-
($)p
=
400
500
'EMPERAXRE
(7)
dH = C p d T
For the liquid state
(4)
cp =
CP
where t
From the equation of state by differentiation
=
Then
700
600
'F
' F. and S
-
2'10 2030 ~
=
(t
+ 670)
sp. gr. at 60" F /80" F.
(g)p= A p 3C + F 3EP +F AT
3EP
3C
T + F + Ry - T Then
/1=-
S O K
v = -14P-T
H - H u = L
[g + 67Ot] -
where H o
CP
= 0
at i
= 0"
-
F.
This equation for the total heat content of the liquid from 0" F. to a temperature t, when applied t'o naphtha becomes
and from Equation 3
H
=
6.6502
x
10-4
(g + mot)
t = "F. H = B. t. u. per !b.
Substituting these values in Equation 8 and simplifying
+ U P ) - T 4 ( D+ F P ) ]9331.7 (t + 670) + 12C ( P - 14.7) + 6E (P* - 14.72)
[T(4C
[s1
T4
where
= O F. per lb. per sq. = t o F. 459.6 = lb. per sq. in. abs.
p
+
T P S
(9)
in.
= sp. gr. a t 60" F./60° F. of liquid C, D, E, and F = constants in equation of state
When the appropriate constants are substituted into Equation 9, the following equation for the Joule-Thomson coefficient for naphtha results: i(
==
T(3.10 ~
+ 0.044P)lO' - T'(O.0022 + 0.00006P) (t + 670)] + P(9.31 + 0.065P)10r
T4[4.0 ;i5t750-
The coefficient for various pressures from atmospheric to 350 pounds per square inch have been calculated and are bhown in Figure 15. 4. CALCUL.4TION O F TOTALHEATCONTEXT FROM 0" F. The heat required to change a liquid'distillate at 0" F. (-17.8" C.) to a superheated vapor may conveniently be divided into three parts: (1) the heat required t o heat the liquid from 0" F. to the boiling point; (2) the heat required to vaporize the liquid; and (3) the heat required to lieat the vapor.
Calculation of Heat of I.upon'zation. The process of vaporization of a pure compound takes place a t constant temperature and constant pressure. I n the case of a mixture, however, when vaporization takes place at constant pressure, the temperature increases; and, when vaporizatioii takes place a t constant temperature, the pressure decreases (retrograde condensation region excluded) and the heat required for vaporization from saturated liquid to the same final saturated vapor state will vary, depending upon whether the process is carried out a t constant temperature or a t constant pressure. The heat content of the vapor will, of course, be the same in t'he two cases. It does not appear that the heat of vaporization a t constant pressure is readily calculable from the physical properties directly. On the other hand, the heat required for raporixation a t constant temperature can be so calculated according to the method given below.' t3y combining these values with the heat of the liquid, bhe total heat of the saturated vapor at any temperature and its corresponding pressure may be obtained. The heat of vaporization a t constant pressure can then be computed by substraction of the heat of the liquid u p to the temperature of tlie boiling point at that pressure. 2 The amount of heat t h a t would be absorbed if the vaporization of a mixture were conducted reversibly a t constant temperature is greater than the difference in heat content of saturated vapor and boiling liquid a t the same temperature. I n actual refinery operation this type of vaporization does not occur; however, the change in heat content is more important. There appears to be no generally accepted definition of the heat of vaporization of a mixture. As used in this paper, it means change in heat content of unit weight of the system when the temperature is constant and the pressure decreases from t h a t of the boiling point to t h a t of the dew point.
INDUSTRIAL AND ENGINEERING CHEMISTRY
300
The method of calculation of the heat of vaporization at constant temperature is as follows: By a combination of the first and second laws of thermodynamics, it can be shown (,?) that
+
where
H S
T V P
dH TdS VdP heat content entropy = abs. temp. = volume of system = pressure = =
TEMPEPATURE 'C.
sb
io0
I
I
254
j
SP 0.4343 T 2
v
(g)
Using this equation, the values of are calculated for a number of different volumes (at constant temperature), and these values plotted against the corresponding values of the volume of the system and a smooth curve drawn through the
($)"
This equation is perfectly general and may be applied t o the calculation of the change of heat content when any system undergoes a change. 140
Vol. 24, No. 3
360
1
I
points. The average value of between the saturated volumes of liquid and vapor is then determined graphically. The value of VdP in Equation 14 is obtained graphically by determining the area under the isotherm between the saturation pressures of the liquid and vapor. The above-described method for the calculation of the latent heat of a mixture has been applied to the data on naphtha. The calculated latent heats in B. t. u. per pound have been plotted against temperature, and are shown in Figure 16. Calculation of Total Heat of Vapor State. The thermodynamic equation is: dH
=
- V]
CpdT - [ T R P
dP
(17)
SOW C P = CPO
1
360
,; II
12CP 6EP2 + T3 + -p-
and
i
V
la
C EP AT - - - -7 D P T3 T
+ + FP
I n its application t o the vaporization of a liquid mixture at constant temperature T, Since
Equation 13 becomes
Putting dH = L , the latent heat, and ( ~ V ) = T (Vv - 1 7 ~ ) ~ , the difference between the volumes of unit weight of saturated vapor and liquid, respectively, a t temperature T , Equation 14 is obtained:
Since the equilibrium pressure varies continuously through-
($)v
changes continuously, and it is out, the vaporization necessary to determine the average value during the course of the vaporization. This may be done graphically as follows: From a plot of the isotherms similar to Figure 4, the values of the pressure and temperature a t constant volume are read off for a number of constant volumes. The pressure-temperature data for each volume are then plotted as loglo p against l/T(abs.), and the slope of the lines measured. These slopes are plotted against the corresponding values of the volume to give a curve from which the slope of the line can be obtained for any volume of the system during vaporization. If s = slope of line, then
(T)V =
or
-s = -0.4343 T2 ( E ) P 6T v
I
,bo
200
460
300
600
500
Substituting in the above equation and simplifying: Cpo
+
-1
+ 6EP2 T4
dT
-
[E +
4EP T
Since
the above equation when integrated gives (15)
$0
TEMPERATURE 'F
-D
- FP],dP
IKDUSTRIAL AND E N G I X E E R I N G
&larch, 1932
where S = s,p. gr. of liquid 60’ F./60° F. t = F T = O F. abs. H O = constant H = total heat content, B. t. u. per lb. D, F , C, and E = constants in equation of state when P , T , and V are expressed as lb. per sq. in. a b s , O F. abs., and cu. in. per lb., respectively. The value of Ho is determined by substituting a known value of H a t some pressure and temperature (for example, a t the temperature of the saturated vapor at atmospheric pressure) and by solving the equation for Ho. Substituting the appropriate Tralues of the constants in the above equation’ the following equation is obtained for the lieat content of naphtha from 0” F. (-17.8” (2.) to any temperature ( t o F.) where the distillate exists only in the vapor state:
H =
4.0 - 0.7500 6450 -
[ZO 47P
[f t
1 + 6701] + 9331.7
P
+ 0 258P2 - ~3 (28,970 + 203.413) X
CHEMISTRY
301
critical region. This arises partly through the fact that the equations for specific heats of the liquid cannot be guaranteed as exact in this region. I n general, however, the total-heat curves along the dew-point and boiling-point curves should be rounded to meet at the critical point. ACKKOWLEDGMEST The authors are indebted to E. TV. Thiele for valuable suggestions with reference to the calculation of the latent heat, and to E. R. Kirn who aided in the experimental work on gasoline. LITERATURE CITED Bahlke and Kay, IND.ENO.CHEM.,21, 942 (1929). Bureau of Standards, Circ. 279, 77 (1926). Caubet, Z . physik. Chem., 40, 2 5 i (1902). Fortsch and Whitman. IKD. ESG. CHEM.,18, 795 (1926). (-5) Lewis and Randall, “Thermodynaniics,” p. 133, McGraw-Hill,
(1) (2) (3) (4)
1923.
(6) Linde, Xitt. iihcr Porsch-arbeiten w t u T - c
LO7]
7 167
The values of the total heat for various pressures and temperatures have been calculated for naphtha , and the results plotted against temperature in Figure 17. It will be noted t h a t Figure 17 is not complete in the
I-.
dcut.
Ino., 21, fi4
(1905).
( 7 ) Young, Sydney, J. Chem. Soc., 47, 640 (1885). (8) Young, Sydney, P h i l . Trans., 177, Part 1, 135 (1886). (9) Young, Sydney, Z. p h y s i k . Chem., 29, 193 (1899). RECEIVED November 9, 1931. Presented before the Division of Petroleum Chemistry a t the 82nd Meeting of the American Chemical Society, B u f f d o , N. Y . , August 31 t o September 4, 1931.
Tower-Absorption Coefficients-IV 1,. AI. BENKETCH AND C. W.SIMMONS, Department of Chemical Engineering, Lehigh Uni\rersity, Bethlehem, Pa.
LIfole-Jow ratio and free-volume concepts are introduced into the derimtion of a general absorption equation which is applicable equally to systems obeying either Henry’s or Raoult’s law
M
UCH has been written concerning the mechanism of gas absorption by countercurrent tower processes, and much emphasis has been placed on the graphical solution of tower-design problems. It is the purpose of this paper to give a mathematical analysis of countercurrent tower processes, to derive a n absorption equation, and to apply this equation to some experimental data. DOiiNAN-MASOB COXCEPT
The derivation of a satisfactory equation representing the continuous countercurrent absorption process, such as is used in gas scrubbing, depends chiefly upon the function representing the rate of solution of the solute gas in the extractor. This rate of solution Wac given by Donnan and Masson (3) to be
where m n
= =
gram concentration of solute in carrier gas gram concentration of solute in extractor
At equilibrium, when no absorption occurs, f ( m ) , sunif function of m, and n are equal. In addition, in a system obeying Henry’s law, f ( m ) equals k ( m ) where h: is Henry’s coefficient. Cantelo ( 1 ) utilized this fact t o transform the original equation of the rate of solution to
where K
=
Cantelo dissolution coefficient, which, for strictly specified conditions of gas and extractor flow, etc., will remain a constant
With the aid of a second equation based on the fact that a steady state prevails mithin a countercurrent absorption unit, Cantelo integrated Equation B obtaining a formula for investigating tower-absorption coefficients. LEKIS COSCEPT
It was proposed by Lewis (/t) and Whitiiian and Neats (6) that the rate of solution of soluble gas in extractor can be more accurately represented by
where P , - PJ = difference between partial pressure of solute in gas and vapor pressure of solute in extractor Here equilibrium conditions prevail when P , = PL. The Lewis form may be equated to the Donnan and Masson form by applying Henry’s or Raoult’s law and converting the partial pressures to gram concentrations. Thus in
Pr X H
= = =
PI = H X vapor pressure of solute in extractor its mole fraction either Henry’s or Raoult’s factor
However, the fundamental difference between these equations for the rate of solution is in the units expressing solute concentrations. The first form which uses gram concentrations introduces a n inaccuracy, owing to the fact that the concentrations in Henry’s and Raoult’s laws must be given in mole fractions. The Lewis rate-of-solution equation readily lends itself to evaluation in mole-fractional quantities, and i t is therefore used as the basis of the derivation in this article.
