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I N D U S T R I A L -4.1'0 ENGISEERI.VG CHE-MISTRY
1701.
22, No. 3
Motor -Fuel Volatility I-Equilibrium Volatilityljz George Granger Brown and Emory M. Skinner UNIVERSITY
OF
MICHIGAN, ANN ARBOR,MICH.
OLATILITY and knock rating are the two important and Stark (21) determined the condensation point by a vaporfuel characteristics that determine engine performance. change method and related this to be the dew point of the As the first step in determining the quantitative re- air-vapor mixture. Later Stevenson and Babor (20) made a lationship between fuel-volatility characteristics and engine dynamic modification of the dew-point determination deperformance, a thorough study has been made of fuel vola- scribed by Gruse. The completely vaporized fuel was passed tility under equilibrium conditions. over a platinum-black surface, cooled to a temperature just Although generally used as a relative term, "volatility" below the condensation point of the vapor. The dew point designates such an important characteristic as to demand a was determined by visual observation of the platinum-black quantitative definition. In order that the term may indicate surface. A correlation of the condensation Doint of the fuel vapor and the dew point a characteristic of fuel of various air-vapor mixindependent of the apparatus dimensions, in this tures was reported. Equilibrium volatility is defined as the per cent by Whatmough (22, 23) depaper the volatility of a fuel weight vaporized under equilibrium conditions at termined t h e equilibrium is the per cent by weight specified temperature, pressure, and air-fuel ratio. boiling point by preparing vaporized under equilibrium It has been found impossible to determine accurately equilibrium solutions of c o n d i t i o n s a t specified the partial equilibrium volatility of motor fuels in various fuels and tried to temperature, pressure, and the presence of air in any form of apparatus that has relate these boiling points air-fuel ratio. been described. to the A. S. T. M. distillaThe universal method for Methods which have been previously proposed for estimating fuel volatility is tion. His conclusion, in estimating the equilibrium volatility from the A. S. agreement with that of the A. S. T. M. distillation T. M . distillation are shown to be inaccurate, although Gruse, was that any such (1). I n such a batch procconvenient. relationship is only approxiess the vapors are removed It has been found that the equilibrium volatility mate and depends upon BS rapidly as they are can be computed accurately from the continuous equithe composition and boiling formed and condensed, so librium vaporization or "flash distillation" data by range of the sample. Simithat the quantity of each making proper allowance for the molecular weight of lar methods were used by component present in the the vaporized part of the fuel. This relationship is (Iti). Ormandy and Craven distillation flask is conincorporated in a chart which is applicable to all types James (13) was apparstantly changing. and sources of motor fuel. ently the first to recognize Quite a different process the importance of partial takes place in the carburevaDorization. and develtor and manifold of an automobile engine. Here the fuel is introduced into a oped a method of continuous vaporization of the fuel stream of air and the vapor remains in contact with in the absence of air, from which he calculated the the unvaporized fuel, so that all components of the origi- equilibrium air-distillation conditions in a rational mannal fuel are in contact throughout the entire vaporization ner by assuming an average molecular weight of the process. If this process were carried out under equilibrium vaporized portion based on its average vaporizing temperaconditions, it might be classified as an equilibrium air dis- ture. Sligh (19) described a continuous air-distillation apparatus tillation. Numerous attempts have been made to relate the in which these results could be obtained directly and retwo processes for both complete and partial vaporization. ported data on several fuels over a considerable range of Previous Work temperatures, and air-fuel ratios from 4 to 15. The dew Howard (12) was one of the first experimenters in this field. points of these mixtures were found by extrapolating the Wilson and Barnard (24, 26) studied the initial condensation air-distillation curves to 100 per cent vaporization. Cragoe point of a completely vaporized fuel and reported that the and Eisinger (10) continued the work initiated by Sligh boiling point of the equilibrium solution so formed was ap- above 0' C. The authors of this paper (8) equipped a similar nir-disproximately the same as that of the 85 per cent point on the A. S. T. M. distillation of the original sample. Gruse (11) tillation apparatus with an air-conditioning system and developed a method of direct determination of the dew point direct ammonia expansion coil for vaporization of fuels at of air-fuel mixtures. His results differed by as milch as temperatures as low as -50" C. (-58" F.). Preliminary 20' C. (46" F.) from the condensation point calculated by results on twenty-six fuels indicated that, for equal volumes the relationship given by Wilson and Barnard. Gruse con- of fuel vaporized, the equation 3 cluded that the whole A. s. T. M. distillation curve had to be TAD12 = (TAfjTM-200) considered in estimating the dew point of the fuel. Stevenson in which T A ~ , = , air-distillation temperature, ' F., feed ratio 12 1 Received March 15, 1929; revised paper received February 10.1930.
V
Presented before the Division of Petroleum Chemistry at the 77th Meeting of the American Chemical Society, Columbus, Ohio, April 29 to May 3, 1929. 2 Based on a thesis submitted by E. M. Skinner in partial fulfilment of the requirements for the degree of doctor of philosophy at the University of Michigan.
T,,,,,
= A. S. T. M. distillation temperature of same volume per cent vaporized
could be used with an error usually less than *lo" F. (5.5' C.) between the limits of 30 and 60 per cent vaporized
March, 1930
INDUSTRIAL AND ENGINEERING CHEMISTRY
for an air-fuel feed ratio of 12:l. The dew points were compared with the 85, 90, and 95 per cent points on the A. S. T. M. distillation, corrected for loss, and the 90 per cent point relationship found most satisfactory. The following equation was suggested as indicating the dew point of a mixture of 12 parts of air to one of fuel within the limits of -6" F. (*3" C.) except in extreme cases such as benzene blends containing more than 35 per cent of benzene:
Dew point, O F . = 5 / 7 (A. S. T. M. 90% O F. - 186) This empirical equation is that of a straight line passing through an origin a t approximately the absolute zero, indicating that the ratio of the absolute temperature of the dew point and of the 90 per cent A. S. T. M. point is a constant for all fuels. Bridgeman (d,S, 4 ) has made a thorough study of equilibrium air distillation with a view to relating this process to the A. S. T. M. distillation so that the latter may be used as a basis for constructing the air-distillation curve. None of these methods of determining equilibrium volatility is entirely satisfactory. For this reason a critical study has been made with the object of determining the most accurate and satisfactory means of determining equilibrium volatility.
-
Air Dis tillation Method
Apparatus-The apparatus used for the air distillations is shown in Figure 1. It consists of a thermostat or constanttemperature bath of cylindrical construction, 35.6 cm. (14 inches) in diameter and 50.8 cm. (20 inches) in height. The container is insulated on the sides and bottom with a 2inch (5.1-cm.) thickness of hair felt. The liquid medium in the thermostat is a solution of 60 Der cent of ethylene glycol and 40 per cent of water, by volume. This solution is entirely satisfactory for the temperature range from -50" C. (-58" F.) to 95" C. (203" F.). For heating a t temperatures below 0" C. an exposed electric resistance coil is used and for higher temperatures, a steam coil. The elect,ric heating coil can be thrown directly on the line for continuous heating or through a relay for automatic control. The bath is cooled by the expansion of ammonia in the cooling coils. The vaporizing coil consists of 20 feet (6.1 meters) '/Anch (1.27-cm.) outside diameter copper tubing wound into a helix 5 inches (12.7 cm.) outside diameter, with ample slope for good drainage. The lower end of this coil terminates in a separator which is 2 inches (5.1 cm.) in diameter and 6 inches (15.2 cm.) high. From the conical bottom of the separator the . unvaporized portion of the gasoline drains to the residue buret. From the top of the separator a tube conducts the vapor-air mixture through a valve, for pressure control, into the Pyrex explosion tube or to a water jet. The absolute pressure a t the discharge of the apparatus is indicated by a closed-tube manometer, connected just ahead of the pressure-regulating valve, and indicating the pressure very near to the point where the vapors and liquid are last in contact. The liquid fuel feed is controlled by positive displacement plungers in the fuel buret. The displacement plungers are of uniform size throughout their entire length, their rate o€ fall being controlled by a clock mechanism. The plungers
279
are supported by small steel (banjo) wire passing over a series of l1/*-inch (3.18-cm.) pulleys. The pulleys are carefully constructed and provided with adjustable cone bearings. In order to feed mixtures of different air-fuel ratios to the apparatus, it is necessary to use displacement plungers of different diameters. As the weight of different plungers is not the same, and that of each too great to be supported entirely by the clock mechanism, a system of counterweights is provided. The mass of the counterweight used depends upon the size and weight of the plungers. The effective weight of the plungers varies with their depth in the fuel on account of the buoyant action of the displaced fluid. This changes the force applied to the clock mechanism sufficiently to overcome the governing action of the escapement, thus defeating the primary purpose of the clock. To correct this an automatic counterweight mechanism is constructed. Its weight as applied to the apparatus decreases as the effective weight of the displacement plungers decreases. This automatic counterweight arrangement consists of a metal track 1 inch (2.54 cm.) wide, '/*inch (0.32 cm.) thick, and 10 inches (25.4 em.) in length. One end is supported by a fixed fulcrum, vhile the other end is supported by the displacement plunger wire through a single traveling pulley to reduce the distance of travel. The track carries a fixed pulley a t the stationary end and two pulleys, one above and one below, a t the moving end. Through these three pulleys is run a cord which is fixed a t each end 20 inches (50.8 cm.) from the average position of track. To this cord is attached the small car which rests on the track. Any up or down motion of the free end of the track produces a corresponding movement of the car along the track. By attaching weights to the car, the effective pull of the beam is affected
1 1
AIR DISTILLATION APPARATUS
Figure 1-Air-Distillation
Apparatus
proportionally. By proper combination of the fixed and the automatic counterweights a practically constant force on the clock mechanism can be maintained throughout a determination. If this precaution is not taken, the fall of the plungers is not uniform through the period of a test and erratic results will frequently be obtained. The fuel or gasoline is introduced into the burets through a charging funnel and is displaced from the bottom of the buret in order to avoid any change in composition due to surface evaporation. The three-way stopcock in the displacement delivery tube enables the fuel to be fed either
INDUSTRIAL AND ENGINEERING CHEMISTRY
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VOl. 22, No. 3
directly to the vaporizing coil or through the dew-point apparatus. This dew-point apparatus (20)is incorporated with the airdistillation apparatus in such a way that equilibrium may be approached by allowing the liquid to vaporize in the coil or by completely vaporizing the fuel and allowing the vapor
40 50 60 70 80 90 100 Per Cent Vaporized Figure %Effect of R a t e on Results of Air Distillation and Method of Extrapolating t o Zero Rate
0
IO
20
30
to condense in the coil. I n the dew-point apparatus the air and liquid gasoline meet a t the top and pass downward together through a number of wire-gauze plates where the fuel is vaporized by heat from an air jacket. This mixture of air and fuel-vapor then passes over a glass tip coated with platinum black, to which is welded an iron-constantan thermocouple. By cooling the platinum tip internally and observing the formation of dew on the tip, the dew point of the fuel-air mixture may be determined directly. Since all determinations are made a t a constant pressure of 760 mm. of mercury, which is usually higher than the barometric pressure, there must be no leak around the wires supporting the displacement plungers. For uniform operation of the clock mechanism there should be very little friction along these wires and what friction there is must be constant. After considerable experimentation the most satisfactory packing was found to be dry cotton slightly compressed in a packing gland carrying a well of mercury. The cotton acts as a support for the mercury, which makes the apparatus absolutely gas-tight. The amount of mercury in the well may be adjusted a t will to accommodate any reasonable pressure range. The air supply is taken from the laboratory pressure lines. In order to have a uniform pressure applied to the orifice meter, the greater part of the air drawn from the supply line is by-passed through tanks of water in series, sufficient total depth of water being used t o supply the necessary pressure head. The air to be used passes through multiple-control yalves of different sizes in parallel for accurate adjustment, through a surge tank to eliminate the pulsation due to the by-pass through the water, and then to a drier. The drier consists of an annular passage carrying an ammonia expansion coil which freezes the moisture from the air. The humidity of the air depends upon the temperature to which it is cooled; which temperature is maintained constant. The
I u' Y
.t Y
a
AIR DISTILLATION
$15-
--
AIR wEL RATIO 12 I EXTRAPOLATED TO ZERO RATE EXPERIMENTAL.
FUEL 48
o
io
20
30
40 50 eo 70 PER C E N T D I S T I L L E D
G
P
eo
90
100
Figure 3-Air-Distillation Data of Fuel 48 for a 12:l Feed Ratio Extrapolated t o Zero Rate
orifice meter reading. The air and liquid fuel are now entering together a t the upper end of the vaporizing coil. These conditions are maintained constant, and the distillation is allowed to proceed for about 15 minutes in order to reach a steady state. The residual liquid collected up to this time is discarded. Time and residual liquid measurements are
March, 1930
INDUSTRIAL AND Eh'GI-VEERING CHEMISTRY
then made a t 5-minute intervals until check results are obtained. The residual liquid collected during thij period is withdrawn and its specific gravity taken. COMPUTATION-From the amount and specific gravity of the feed and the amount and specific gravity of the residue, the per cent by weight vaporized may be calculated. The temperature of the thermostat is then made higher or lower m desired, and the same procedure repeated using the same conditions of fuel and air feed. By this procedure an air-distillation curve may be constructed by plotting per cent (by weight) vaporized as a function of temperature. This curve represents the per cent vaporized when a particular fuel is fed a t the specified air-fuel ratio and rate of feed. DETERMINATION O F 100 P E R CENT V.4PORIZATIOlu-The end point or point of 100 per cent vaporization cannot be determined directly by the preceding method, but i j found by extending the vaporization curve to 100 per cent vaporized. This value is then checked directly by the dew-point apparatus. For this determination the three-way stopcock in the feed line is turned to feed the liquid fuel to the dew-point apparatus. The air valves are also changed to supply air to this apparatus directly. The dew-point temperature is then determined in the manner described by Stevenson and Babor (20). With proper precautions the de\\ points as determined by each process are identical. .ALTERNATE METHODO F FEEDING-The mixture of fuel vapor and air leaving the dew-point apparatus may be passed into the coil of the air-distillation apparatus in order to approach equilibrium from the vapor side. This method frequently gave a greater residue and less consistent results than feeding liquid fuel to the coil. As the results of the two methods did not agree, determinations were made in the customary manner by feeding liquid to the coil of the airdistillatian apparatus EFFECT OF VARIATION IX RaTEs-Early in this work it was discovered that over certain ranges different rates through the apparatus (for the same air-fuel ratio) resulted in different percentages vaporized at the same temperature. Where this effect wm noticed, higher rates through the apparatus gave lower per cents vaporized for any given air-fuel ratio. This is most pronounced a t low temperatures with lean mixtures, but seems to disappear at higher temperatures or near the temperature of 100 per cent vaporization. Results of Air Distillation
Determiiiations of the effect of rate on the vaporization of fuels indicated a straight-line relationship as shown in Figure 2. The open circles indicate experimental data plotted as a function of the air-rate in lineal feet per second through the apparatus: as indicated along the left-hand ordinate. These points fall on a straight line for each temperature. By drawing such a line and extending it to zero rate through the apparatus, the experimental data may be reduced to supposedly equilibrium conditions as represented by zero rate through the apparatus. Similar deviations in the experimental results have been noted by others ( 2 ) ,but the slope of these lines was heretofore considered constant for all temperatures. It is the writers' experience that experimental data a t two different rates of feed should be used in making this extrapolation, as the slopes of the straight lines decrease numerically as the temperature is lowered. Furthermore, a t higher temperatures, corresponding to over 60 or 65 per cent vaporization, this apparatus appears to give equilibrium results. Although this method appears logical, it is not entirely reliable. In Figure 3 the dashed curve represents the experimental data taken a t two different rates on a natural gasoline aviation fuel (So. 48) in a 12:l air-fuel ratio. Plot-
28 1
ting the experimental points as a function of the air rate through the apparatus, the data are extrapolated to zero rate in the manner indicated in Figure 2. The resulting extrapolated curve representing the per cent vaporized a t zero rate through the apparatus is shown as a solid curved line in Figure 3. Similar treatment of data obtained with different air-fuel ratios gives the curves shown in Figure 4. The resultant air-vapor ratios in the vapor phase can be calculated readily from these curves. For example, when 60 per cent is vaporized from a 12:1 feed mixture, the vapor phase will contain an air-vapor ratio of 12:0.6 or 20 :l. Such curves have been calculated for air-vapor mixtures of 8 :1 and 12:1, as indicated by the dashed lines in Figure 4. These resultant curves should be continuous smooth lines, since they depend upon the vapor pressure of the fuel residue, which changes continuously with temperature and per cent vaporized. In no case would a higher temperature be required for
0
10
20
30
40 50 €0 70 PER CENT DISTILLED
80
90
100
Figure 4-Air-Distillation Data for Fuel 48 Extrapolated t o Zero Rate and Indicating Resultant Air-Vapor Mixtures of 8 a n d 12
a lower percentage vaporized, or lower feed ratio. The extreme case would be that of a pure compound, where the resultant mixture curve would be a horizontal line owing to the constancy of composition of both the vaporized portion and the residue. The resultant curve for a complex mixture such as gasoline requires a gradually increasing temperature as more of the fuel is vaporized, owing to the decreasing vapor pressure of the residue. In no case will the residual liquid become more volatile with greater percentage vaporized, as is indicated between 20 and 40 per cent vaporized in Figure 4. The 20:1 air-fuel ratio curve apparently shows less vaporization than the 12:l air-fuel ratio curve at -60" F. (-50" C.). This is also impossible under equilibriuin conditions. These results are somewhat similar to those obtained by estimating the resultant air-vapor mixtures from the A. S. T. hl. distillation by the relationship first given by Bridgeman (S), as indicated for this same gasoline in Figure 5 . Apparently little confidence can be placed in this method for obtaining equilibrium conditions by extrapolating airdistillation data to zero rate of feed, particularly a t temperatures below -15" C. or about 0 " F. To interpret such data is extremely difficult and cannot be done without knoming the deviations from true equilibrium. Computed Air Distillation by Raoult's Law
Raoult's law usually may be applied to solutions of similar substances, and it seemed reasonable that the vaporization
Vol. 22, No. 3
I N D U S T R I A L A N D ENGINEERING CHEMISTRY
282
process in the presence of air could be computed by the use of this relationship in a manner similar to that used by Podbielniak and Brown (18). The gasoline was fractionally distilled to determine its composition in a fractionating column similar to that described by Podbielniak (17), taking extreme care to obtain a close and as accurate a separation as possible between the various components, with the results as given in Table I. Table I-Results
of Fractional DistillaItion Analysis of Fuel 48
FORMULA
COMPOUND Isobutane n-Butane Isopentane n-Pentane Isohexanes n-Hexane 2,4-Dimethylpentane 3-Ethylpentane n-Heptane Isooctanes n-Octane
C~HID C4HlO CsHie CsHn C6H14 CeH14 CrHie ClHl6 ClHl6 &Hi8
CeHis Av.
MOLECULAR MOL WEIGHT PERCENT 58.077 0.54 58.077 4.14 72.092 11.06 72.092 31.51 86.108 14.03 86.108 12.30 7.54 100,12 5.53 100.12 100.12 3.32 7.16 114.14 2.87 114.14 83,923
Temperatures were calculated by this method (18) using the vapor-pressure data of Coats and Brown (9) for 5, 10, 30, 70, and 90 mol per cent vaporized, under different pressures to yield the short dashed lines shown in Figure 6. In order to compute the equilibrium air-distillation curve, the partial pressure of the gasoline vapor in the air-vapor mixture for a particular air-fuel ratio and per cent vaporized was determined. The temperature corresponding to this pressure and per cent vaporized was then found from Figure 6 (dashed lines), because the partial pressure of the gasoline vapor is the effective pressure in the air distillation. From the analysis of fuel 48 its average molecular weight is 83.923. That of air was taken as 28.9. I n a feed ratio of 12 pounds of air to 1 pound of gasoline, the ratio would be 12/28.9 = 0.415 mol of air to 1/g3.9s = 0.01194 mol of gasoline. This ratio is equal to 3475.0 mols of air per 100 mols of gasoline. When 90 mol per cent of gasoline is vaporized, the total number of mols in the air-vapor mixture is 3475 (air) plus 90 (gasoline) or 3565 mols. The resulting mol fraction of gasoline vapor is 9°/3665.0 = 0.0252. This value multiplied by the total pressure of 760 mm. gives a partial pressure of gasoline vapor of 19.2 mm. From the calculated data for total fuel vaporized and per cent vapor as given in Table 11, it is seen that 90 mol per cent vaporized a t 19.2 mm. pressure corresponds to 88 per
cent by weight. According to Figure 6 these conditions exist a t -8.9" C. (+l6" F.). By a similar process other values were found, from which a plot of per cent vaporized as a function of temperature was prepared, as shown in Figure 7, dotted line, for a 12:l airfuel ratio. In this figure the dashed lines represent experimental data determined with two different rates of feed. It is seen that this computed curve, based on the assumed validity of Raoult's law, does not agree in any way with the experimental results. At the higher temperatures, where rate does not affect the experimental results, the calculated temperatures are below the experimental, or the calculations show a greater percentage vaporized than is found by experiment a t the same temperature. But a t lower temperatures the computations show a smaller percentage vaporized than do the experimental results. Other investigators (8) have shown that an application of Raoult's law to binary mixtures of paraffin hydrocarbons gives results indicating too high a vapor pressure for the less volatile component and too low a vapor pressure for the more volatile component. This same tendency is shown here, but the exact deviation is not obvious. Apparent Deviation from Raoult's Law I n order to determine the apparent deviation from Raoult's law in the case of fuel 48, so that the equilibrium vaporization of this fuel a t low temperatures could be correctly computed, equilibrium vaporization of this fuel was conducted a t atmospheric pressure in the continuous-vaporization apparatus described by Podbielniak and Brown (18) for equilibrium vaporization of natural gasoline. This vaporizer had been found to give results independent of rate and therefore a p proximating true equilibrium vaporization ( 1 4 ) over a feed range of 6 to 15 cc. per minute. I n order t o be sure of the initial point of these equilibriumvaporization curves, and to serve as a guide in estimating the true equilibrium-vaporization curves a t reduced pressures, the gas-free vapor pressure of the sample was determined by the method described by Bridgeman ( 4 ) and checked by another method which will be described in a later paper. The temperatures corresponding to the gas-free vapor pressure are shown as the points for zero per cent vaporized i4 Figure 6. The results of a series of continuous vaporizations on fuel
Table 11-Calculated Vaporization Data of Fuel 48 (Basis, 100 mols feed) AMOUNT VAPORIZED (v) VAPORPRES- T (V) SUR&
-
Mols 100 5 5 5 10 10 10
Mm.
C.
...
. . ..
10 20 100 10 100 740
-46 -35.5 5.5 -45 4 -47
-
~
~
~
TEMP.
RBQUIRRD
.
FOR
V MOLS VAPOR Mol 0.54 0.25 0.23 0.18 0.35 0.29 0.23 0.50 0.49 0.48 0.47 0.45 0.43 0.41 0.54 0.53 0.53 0.52 0.52 0.54 0.54 0.54 0.53
Mols 4.14 1.31 1.20 1.02 2.09 1.75 1.42 3.65 3.49 3.41 3.32 3.21 2.98 2.89 4.09 4.07 4.00 3.97 3.90 4.13 4.12 4.11 4.08
Mols 11.06 1.15 1.11 1.05 2.25 2.09 1.91 6.92 6.48 6.31 6.03 5.88 5.49 5.39 10.55 10.39 10.06 9.94 9.69 10.94 10.89 10.85 10.73
Mols 31.51 2.02 2.08 2.09 4.24 4.45 4.33 15.64 14.74 14.54 14.24 13.94 13.50 13.35 29.17 28.71 27.66 27.36 26.68 31.02 30.83 30.68 30.32
Mols 14.03 0.23 0.25 0.32 0.53 0.72 0.86 2.48 2.64 2.68 2.82 2.98 3.15 3.29 10.62 10.34 9.99 9.96 9.86 13.31 13.16 13.03 12.87
Mols 12.3 0.13 0.15 0.21 0.29 0.47 0.63 1.26 1.56 1.70 1.85 2.06 2.33 2.50 8.18 8.11 8.11 8.18 8.22 11.42 11.31 11.22 11.13
Mols 7.54 0.03 0.04 0.07 0.08 0.16 0.24 0.35 0.48 0.57 0.66 0.76 0.92 1.02 3.48 3.73 3.98 4.06 4.23 6.59 6.54 6.48 6.47
Mols 5.53 0.01 0.01 0.03 0.03 0.07 0.12 0.12 0.17 0.21 0.27 0.33 0.45 0.52 1.59 1.82 2.23 2.34 2.54 4.37 4.35 4.37 4.47
Mols 3.32 0.005 0.007 0.01 0.01 0.03 0.06 0.05 0.07 0.09 0.12 0.16 0.23 0.27 0.77 0.86 1.19 1.27 1.43 2.44 2.48 2.52 2.61
Mols 7.16 0.005 0.008 0.02 0.01 0.04 0.09 0.05 0.08 0.11 0.15 0.22 0.34 0.42 0.92 1.22 1.86 2.08 2.45 4.38 4.60 4.76 5.18
Mols 2.87 0.0006
0.001 0.003 0.001 0.006 0.02 0.005 0.01 0.01 0.02 0.04 0.07 0.09 0.11 0.18 0.37 0.45 0.62 1.01 1.20 1.36 1.69
Mols 100 5.1406 5.0851 5.003 9.881 10.08 9.91 31.025 30.21 30.11 29.95 30.03 29.89 30.15 70.02 69.96 69.98 70.13 70.14 90.15 90.02 89.92 90.08
O
c.
..... -46.25 -35.7
- 5.5 -44.8 - 4.25
-47.3 -55.8 -39.7 -29.1 - 17 + 1 4-34.08 4-52.42 -43 -27.5 4-12.5 +27.8 $63.25 -19.3 2.5 +19.7 +70
+
VAPOR
Grams % b y ut. 8393.77 100 355.25 4.23 354.19 4.22 355.32 4.23 693.46 8.26 723.68 8.62 728.59 8.68 2203.36 26.25 2204.97 26.27 2207.00 26.29 2208.06 26.31 2230.23 26.67 2245.93 26.76 2280.65 27.17 5453.48 64.97 5476.22 65.24 5536.38 65.96 5568.49 66.34 5606.90 66.8 7382.46 87.95 7385.99 87.99 7389.30 88.03 7434.48 88.57
48, a t 740 mm. pressure, appear in Figure 6 as the heavy dashed line a t 740 mm. pressure. It can be seen that this experimental curve crosses the calculated (dotted) curve for 740 mm. pressure. This experimental curve closely approximates the true equilibrium vaporization conditions for this fuel a t the pressure of the investigation. Comparison of these experimental results with those calculated by Raoult's law gives a quantitative measure of the apparent deviations from Raoult's law as applied t o this fuel. The calculated curve shows about 8 per cent less vaporized than does the experimental curve a t the 10 per
I
Ch
\+/ -40
0
10
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I N D U S T R I A L A N D ENGINEERING CHEMISTRY
March, 1930
20
Jo
A I
I I
40 50 BO 70 80 PER CENT VAPORIZED BY WEIGHT
90
Im
Figure 5-Resultant
Air-Vapor Mixture Ratios as Computed f r o m A. S. T. M. Distillation Data
The almost perfect agreement between computed results and all experimental data obtained under equilibrium conditions is direct evidence that the computed results closely approximate equilibrium conditions. Plots of these computed equilibrium-volatility curves of fuel 48 (Figure 10) yield resultant curves (dashed lines) drawn in the same manner as those of Figure 4 that are continuous, and indicate always a higher temperature for the same partial vapor pressure as the residue becomes less volatile. These results are entirely rational, as contrasted with the ridiculous results of Figures 4 and 5. Fuel 68, representing a different type of fuel, was submitted t o the same tests, with similar results, as indicated in Figures 7, 8, 9, and 10. The computations are not given in detail, as they would be largely a repetition of those reported for fuel 48. Similar results obtained from a number of fuels indicated a systematic deviation of the experimental results from equilibrium conditions depending upon temperature, per cent vaporized, and rate through the apparatus. Although it is possible to use these deviations in constructing equilibrium volatility curves from the experimental airdistillation curves of this particular equipment, as has been done for fuel 52 in Figures 7, 8, and 9, the relations are of no value t o other investigators. Not only are the resultant curves from these volatility data as shown in Figure 10 consistent with known physical characteristics of complex mixtures, but their 100 per cent points have been checked by the continuous vaporization apparatus and the dynamic dew-point determination. The initial points have been independently checked by determinations of the gas-free vapor pressure of the various fuels. Furthermore, the curves as finally adopted check the air-distillation curves a t all points where the results of the
cent point, The opposite is true a t the 90 per cent point, for here the calculated results show about 12 per cent more vaporized than the experimental. Calingaert and Hitchcock (8) report deviations in the partial pressures of binary mixtures of paraffin hydrocarbons varying from zero to *16 per cent. Brown and Caine ( 7 ) have found deviations for niidcontinent, Pennsylvania, and California naphthas of 14, 12, and 10 per cent, respectively, as compared with about 10 to 12 per cent indicated for 80 per cent vaporization of natural gasoline as represented by fuel 48.
-----0
EXPERIMENTAL 140 M M CALCULATED FROM RAOULTS LAW CORRECTED CALCULATED CAS FREE VAPOR PRESSURE
T
I 150
PRESSURE ABSOLU IN MILLIMETERS
100
Equilibrium Volatility from Continuous Equilibrium Vaporization
Using the vapor-pressure data to determine the initial point on the vaporization curves a t reduced pressures, and assuming that the deviations from Raoult's law expressed in percentages vaporized are approximately the same a t lower partial pressures as has been indicated by Piroomov and Beiswenger ( I O ) , the solid lines were drawn in Figure 6 as representing the corrected calculated vaporization curves a t reduced pressures. From these equilibrium vaporization curves the correct equilibrium vaporization in the presence of air may be computed in the manner already described. Such values for several different air-fuel ratios are given in Table 111, and when interpolated by plotting log of pressure versus temperature yield data plotted as solid lines in Figures 7, 8, and 9 for fuel 48. These equilibrium volatilities computed from the experimental equilibrium vaporization curve agree almost perfectly with the experimental airdistillation curves (dashed lines) a t the higher temperatures and nearly complete vaporization where the air distillation is not affected by rate. The dew points calculated by this method are also in agreement with the dew points as determined by the air distillation method and by the dynamic dew-point apparatus.
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Figure 6-Continuous
1
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50 60 70 PER CENT DISTILLED
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I 80
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Equilibrium Vaporization of Fuel 48
air distillation were fmnd t o be independent of rate. No unproved assumption has been made in drawing these equilibrium air-distillation curves. Even possible errors in the fractional distillation analysis and application of Raoult's law have been eliminated. Inspection of Figures 7, e, and 9 shows that under many conditions the air-distillation apparatus actually gives more material vaporized than would be the case under equilibrium conditions. I t is difficult to visualize just what process would permit such results, unless they were due t o entrainment. The fact that the discrepancy is most evident a t low temperatures might suggest that the warm air entering the ther-
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that in most cases the more volatile, low-boiling components seem to possess a molecular weight as would be indicated by the normal paraffins as plotted in Figure 11. This is particularly true in the case of natural gasolines, which contain almost exclusively low-boiling compounds and are known to be composed very largely of paraffin hydrocarbons. I n most commercial gasolines the higher boiling components appear to have a lower molecular weight for the corresponding boiling points than would be indicated by the norms1 paraffin curve. Investigation of highly cracked or aromatic gasolines indicates that curve A in Figure 11 represents approximately the other extreme relationship between molecuTable 111-Calculated Equilibrium Air Distillation, by Raoult's lar weight and normal boiling point. For most average Law a s Corrected, for Fuel 48 gasolines, as produced from midcontinent or mixed-base (Basis. 100 mols nasoline) crudes, curve B may be used. Such a smooth curve is, of AIR-FUSL RATIO PARTIAL PREssVRe LOCIO TEMPERArnnE course, applicable only to unfractionated samples such as (FEED) VAPOR Mols yob y ut. Mm. Hg F. c. obtained from a continuous equilibrium vaporization. 20: 1 90 87.95 11.63 1.0656 +13 -10.6 Assuming that the molecular weight of the vapor formed 70 65.25 9.07 0.9576 -16 -26.7 50 45.0 6.51 0.8136 -40 -40.0 when a specified weight per cent of the fuel is vaporized under 30 26.25 3.91 0.5922 a low partial pressure, as in the air distillation, is the same 12: 1 90 87.97 19.19 1.2831 +27 70 65.40 15.01 1.1764 - 3 - 1 9 . 4 as when the same weight per cent is vaporized in the absence 50 45.20 10.78 1.0326 1272:; of air, as in the continuous. equilibrium vaporization, the 30 26.30 6.51 0.8136 1:; 8:1 90 87.99 28.42 1.4536 +38 $. 3 . 3 pressure of fuel vapor in any resultant air-vapor mix70 65.m 22.29 1.3481 +-179 +- 2172..28 partial 50 45.30 16.06 1.2057 ture may be estimated as a function of the average boiling 30 26.30 9.71 0.9872 -44 -62 -- 54 22,. 22 point of the vaporized portion from the relationships indi20 17.20 6.51 0.8136 4.1 90 88.10 54.8 1,7388 +js +14.4 cated in Figure 11. This has been done as indicated in 70 65.75 41.62 1.6193 +3: Figure 12, for paraffins, average commercial, and highly aro50 45,40 31,45 1,4976 30 26.35 19.19 1.2831 -25 -31.' matic gasolines corresponding to curves P , B, and A in 20 17.30 12.9 1.1106 -44 -42.2 10 8.30 6.51 0.8136 -6s -55 6 Figure 11. 1:l A second assumption, that. the v a p x pressure-temperature 20 30 21 67 ., 54 7 09 . 81 9 4 1.6911 1.8506 10 8.40 25.37 1,4043 -31 -35.: relationship of the residue from the continuous equilibrium 5 4.23 12.9 1.1106 -52 -46.8 +20 - 6 . 7 vaporization process is similar to that of a pure hydrocarbon %:l 20 17.50 ~ ~ . 2 3 1,9649 10 8.50 49.1 1.6911 - 9 -22.8 having the same normal boiling point, allows the temperature
mostat a t the lower end of the vaporizing coil and near the separabor where the final separation of liquid and vapor takes place serves to heat the separator and lower end of the vaporizing coil to a temperature above that supposed to exist in the vaporizing coil and indicated by the thermometer in the bath. However, if this were the major factor, the departure from equilibrium would be less a t low rates through the apparatus rather than more, as was actually found. The bath was violently agitated by means of the propeller just above the separator. This would also tend to minimize the effect of such heating by the entering air.
0
I1i:i zli:i
'
5 2
4.23 2.0
25.37 10.2
1.4043 1.0086
-33 -60
-36.1 -51.1
If equilibrium between liquid, vapor, and air is attained early in the passage through the vaporizing coil, there can be 110 further vaporization or condensation regardless of the relative motions of the liquid and vapor, since the temperature is uniform and the vapor in the air stream is always in equilibrium with the liquid with which it comes in contact. However, if equilibrium is not rapidly reached, as is evidently the case a t low temperatures where the fuel is more viscous and reactions are always slower, these conditions are not fulfilled and the apparatus may act as a combined partial vaporizer and absorber, or at least more like an actual engine manifold than an instrument of precision approaching equilibrium conditions. Satisfactory results were obtained in this investigation only when the equilibrium air-distillation curve was computed from, or interpreted by, data obtained by the continuous equilibrium vaporization of the fuel. If the molecular weight of the material vaporized in the continuous equilibrium vaporization process is known for the different temperatures and pressures corresponding to the partial pressures of the gasoline vapor in the equilibrium air distillation, the equilibrium volatility (air-distillation curve) can be accurately computed in the manner described above. However, this information is not available from the ordinary equilibrium vaporization, and the molecular weight of the vapor must be estimated from some known property of the vapor, such as its mean boiling point. If the molecular weight of pure hydrocarbons is plotted as a function of the normal boiling points, as in Figure 11, it is seen that the investigator may be allowed considerable freedom in the molecular weights chosen for a given boiling point when dealing with gasolines of unknown composition. In using this method, which is essentially an improvement of that originally suggested by James (13), it has been found
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COMPUTED EXPERIMENTAL rnu-llrrn A C C O R D I N G TO RAOULTS LAW 0 COMPUTED BY EQIJATIONS FROM A 5 T M '/ A 0 DISTILLATION GOYPUTED FROM EQULlBRlUM VAPORIZATION ,+/
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+_
,
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Figure 7-Air-Distillation Data as Determined by Different Methods. Air-Fuel Ratio, 12:l Solid lines indicate equilibrium air distillation as determined by best methods available
of the equilibrium air-distillation corresponding to any total pressure, resultant air-vapor mixture, and per cent vaporization to be computed readily from the continuous equilibrium vaporization curve, a vapor-pressure chart for the hydrocarbons, and proper use of the chart Figure 12. James (13) recommended this method for determining the dew points of air-vapor mixtures using the temperature-
INDUSTRIAL AXD ENGINEERING CHEMISTRY
March, 1930
r -COMPUTED
-
80
-
70-
RIZATION CUR
-CXPERIMENTAL 0 COMPUTED BY EQUATIONS FROM A I T M DISTILLATION COMPUTED FROM EQULlBRlUM VAPOR12ATION CURVL
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DISTILLED
Figure 8-Air-Distillation D a t a a s Determined by Different Methods. Air-Fuel Ratio, 4:l
40 SO 60 70 FCR CENT DISTILLED
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Figure 9-Air-Distillation Data as Determined by Different Methods. Air-Fuel Ratio, 1:l
-200
-300
9
ib
-200 80 P
33 40 50 E CENT ~ VAPOR ZED
60
0r
70
80
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WEIGHT
Figure 10-Equilibrium Air Distillation of Fuel 48 a n d Corresponding Air-Vapor Mixtures
molecular weight relationship for the olefin hydrocarbon.?, and the temperature a t which 50 per cent by weight was vaporized in the continuous equilibrium vaporization as the average boiling point, of the vaporized fuel. If the average boiling point is taken, not as the temperature :it which 50 per cent is vaporized, but as the arithmetical mean between the initial and final boiling points on the continuous equilibrium vaporization curve, and the boiling point-molecular weight relationship is corrected for compounds other than paraffins and olefins, as indicated in Figure 11, satisfactory results may be obtitined. In estimating the temperature corresponding to partial volatility, the average boiling point of the vaporized part of the fuel should be taken as the arithmetic mean of the initial boiling point of the entire fuel and the temperature a t which the corresponding weight per
SO
IW MOLECULAR
Figure 11-Molecular
150
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WEIGHT
Weight a s F u n c t i o n of Mean Boiling Point
cent is vaporized in the continuous equilibrium vaporization. The method can be made clear by an example. To compute the temperature a t which fuel 48 will show 50 per cent by weight vaporized a t atmospheric pressure for a 20: 1 air-fuel feed ratio; 50 per cent vaporized in a 20: 1air-fuel ratio gives a resultant air-vapor mixture ratio of 40:l. Aecording to Figure 6, or better, Figure 17, 50 per cent by weight is vaporized a t 60" C. (140" F.) and the initial point is a t 40" C. (104" F.). The average boiling point of the vapor is then the arithmetic mean of these two temperatures, or 50" C. Sample 48 is of natural gasoline, and may be assumed to be entirely paraffin. Use of the P curve in Figure 12 indicates a partial pressure of 0.0095 atmosphere for a resultant air-vapor mixture of 40:l. The vapor pressure of the residue is 740 mm. a t 60" C. By reference to a vapor-
INDUSTRIAL A N D ENGINEERING CHEMISTRY
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This method of computing or estimating the equilibrium volatility curve from the continuous equilibrium vaporization curve has proved entirely satisfactory for all practical purposes and gives results within the experimental error in testing motor fuels. Direct determination in the air-distillation apparatus may not be depended upon for accurate results. Considering the great practical importance of continuous equilibrium vaporization data to the petroleum refiner in controlling his operations, and to the user of the finished fuel in giving a true picture of the fuel volatility, it is believed that the use of the continuous distillation test of gasoline should be encouraged as giving more practical information regarding motor-fuel volatility than the present batch distillation. Comparison with Other Methods
Figure 12-Chart for Determining Partial Pressure of Vaporized Fuel a s a Function of Its Mean Boiling Point For natural gasolines take temperature of mean boiling point as in$cated along top of figure. For most commercial motor fuels follow 45 lines from temperature scale at top to curve B. For highly aromatic and cracked gasolines follow 45' lines from mean boiling point to curve A .
pressure chart (22) we find that a hydrocarbon having 740 mm. vapor pressure a t 50" C. exerts a vapor pressure of 0.0095 atmosphere, or 7.1 mm., a t -38" C. (-36" F,),which is within 1" C. (2" F.) of -37" C. (-34" F.), as indicated by the 50 per cent vaporization on the equilibrium air-distillation curve in Figure 10 for 20:l air-fuel feed ratio for fuel
Dew points estimated in the manner outlined are in good agreement with those calculated from the Depp6 end point as outlined by Stevenson and Stark ( $ I ) , or estimated from the 90 per cent point of the A. S. T. M. distillation by Brown (7), and with the dew points as estimated from the continuous equilibrium vaporization end point (normal dew point) or the 90 per cent A. S. T. M. distillation point by the relationship suggested by Bridgeman (3). This is to be expected, since the air-distillation apparatus has been found closely to approximate equilibrium conditions a t the higher temperatures, particularlywhen most or all of the fuel is vaporized. The dew points estimated by the method as outlined by James are almost invariably lower than those computed by the methods outlined above. On the other hand, the temperatures of partial volatility are more accurately estimated by the method proposed by James (13). Because the dew points could be estimated in a satisfactory manner from the A. S. T. M. distillation, it was hoped that the partial-volatility temperatures could be estimated in the same manner. Earlier work had indicated that corresponding percentages might be related through a temperature ratio or possibly some more complicated expression. Figure 15 indicates the ratio between the absolute temperatures on the A. S. T. M. and equilibrium air distillation for different per-
48.
Although the two assumptions on which this method is based are not strictly true, actual deviations do not generally exceed the experimental error in determining the continuous equilibrium vaporization curve (about * 2" C. or 3.5" F.). The molecular weight of the vaporized material is less a t lower pressures than would be indicated by the continuous equilibrium vaporization a t atmospheric pressure. This is partially compensated in the recommended procedure by using curves representing normal paraffin hydrocarbons in Figure 11, as the basis for calculations applied to natural gasoline which contains large amounts of isomeric paraffins, as the normal paraffins have a lower molecular weight than the isomeric paraffins for the same boiling point. A similar compensation is made by the use of curves A and B as incorporated in Figure 12, and also by the method of estimating "mean boiling points." For purposes of comparison the points as computed by this method are plotted in Figures 7, 8, 9, and 10 and in Figures 13 and 14 for other representative fuels whose equilibrium volatility curves were also determined in the same manner as those for 48, 68, and 52. I n most cases the agreement between the two methods is within about, +1.5" C. (*2.5' F.), or well within the experimental error in determining the equilibrium vaporization curve.
Figure 13-Equilibrium Volatility of Fuel 13 and Corresponding Points as Computed from A. S. T. M. Distillation and f r o m Eauilibrium Vaporization Indicated for Purposes of Compariion
INDUSTRIAL AND ENGINEERING CHEMISTRY
March, 1930
centages vaporized in the case of five fuels representing the different types within the present commercial limits. For purposes of comparison, the ratio of absolute temperatures as given by Bridgeman (3) as applicable to motor fuels is also plotted as a dotted line. An air-fuel ratio of 4:l was chosen because this was the only feed ratio which was completely covered by Bridgeman's relationship. Other similar plots were made for different air-fuel ratios and a comprehensive 5
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I n order to find corresponding temperatures for other air-vapor mixtures, Bridgeman ( 5 ) assumed that the temperature difference between equilibrium-air distillation curves of different air-fuel ratios was constant for all percentages vaporized and that the temperature for any air-vapor mixture might be estimated from the temperature of the 16:l air-vapor mixture ratio curve by a relationship represented by the equation: TEAD= T E A D ~ 51.7 ~ - 43 log R
+
-120
+
or TEAD= TEAD>#51.7
100 FR
- 43 log %
(4)
in which R = resultant air-vapor ratio by weight FR = feed ratio by weight
This last assumption is not accurate, as the temperature differences become larger a t higher temperatures. But the limits of accuracy of these equations do not justify any attempt t o correct for this relatively small error. Combining Equations 1, 2, and 4, we have for the absolute temperature ( O K.) on the equilibrium air-distillation curye, the expression:
100 FR - 43 log - ( 5 ) 5% ,I
Figure 1 P E q u i l i b r i u m Volatility of Fuel 60 and Corresponding Points as Computed f r o m A. S . T. M . Distillation and f r o m Equilibrium Vaporization Indicated for Purposes of Comparison
study was made of a number of fuels in an effort to find some systematic relationships between these temperature ratios and the A. S. T. 11. distillation characteristics of the fuel. After more than four years of work, agreement with Whatmough's statement that no such relationship exists has been reached. Recently Bridgeman (6) has derived a relationship between the equilibrium air-distillation temperature and the A. S. T. &I. temperature a t the same per cent vaporized, which appears to be as satisfactory as can be expected. The relationship is derived in an empirical manner to compute the temperature a t which a resultant air-vapor mixture ratio of 16:l will be formed. He found that the ratio between the absolute temperatures for the same volume per cent in the A. S. T. M. as for weight per cent in the equilibrium air distillation for a resultant mixture of 16:l might be represented by the equation: _C_
'AFT, - 1.5 TEAD,, TEAD,~
-
104/slope
---
AVIATION FUELS C
FUEL 48 FUEL 6 0
MOTOR FUELS -FUEL
OS I3 1 FUEL 52
Ic---c FUEL
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0
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t
Equation 2 applies between the limits of 10 and 90 per cent vaporized. The temperature a t which a 16:l air-vapor mixture would be formed from a very large volume of fuel and small volume of air may be related to the 10 per cent point on the A. S. T. ll. distillation if the following value for C is used: .= 39
Equation 5 is applicable between the limits of 10 and 90 per cent vaporized and as given above expresses the temperature on the equilibrium air-distillation curve for a given weight per cent vaporized, in terms of the absolute temperature of the corresponding volume per cent vaporized in the A. S. T. M. distillation, the slope of the A. S. T. M. distillation curve, and the air-fuel feed ratio.
I Y
(1)
in which C depends upon the slope of the A. S. T. hI. curve in degrees Centigrade per per cent vaporized, and the per cent by volume distilled on the A. S. T. hl. distillation, as indicated by the equation:
c
in which T = absolute temperature, a C. S = slope, in C. per per cent by volume vaporized on A . S. T. M. distillation yo = per cent by weight vaporized in equilibrium air distillation
(3)
The dew point may be estimated from the 90 per cent point on the A. S. T. hl. distillation in the same manner bv combining Equations 1 and 3.
a Y
9 1.3
1.2 0
10
20
Figure 1 5 - R a t i o of Absolute Temperatures 0n-A. S. T. M. t o That of Equilibrium Air Distillation
The corresDondinp eauation relatine: the initial vaDorization temperature
