Vapor-Liquid Equilibrium of Hydrocarbon 'Mixtures HAROLD A. BEATTYAND GEORGECALINGAERT, Ethyl Gasoline Corporation, Detroit, Mich.
T
HE improvements con-
stantly introduced in the technic of handling petroleum products make it more and more necessary to have accurate information regarding the thermod~namicproperties of such mixtures. This is evidenced by
The ideality of a binary solution may be determined by a series measurements the total vapor pressure, for which purpose a simple and accurate isothermal method is described. Results obtained f o r eight hydrocarbon systems are compared with data taken from the literature. he eBectof a small Aviation f r o m ideality upon the number of theoretical plates required to effect a given fractionation is calculated .for three systems.
the number published onofvarious articlesproperties recently of hydrocarbon mixtures. such as vapor and liquid densities, critical temperatures, etc. One of the important problems in the refining industry is the fractionation of the various crude materials into commercial products of definite specifications. The accurate designing of fractionating equipment as well as the accurate testing of such equipment necessitates the knowledge of the so-called x-y diagram-that is, the composition of the liquid and the vapor phases which a r e in - equilibrium with each other under given conditions. However, but few investigations have been published giving data from which such diagrams can be constructed for hydrocarbon s y s t e m s , and a critical study of these data reveals a wide disa g r e e m e n t between some of the authors. V 0 LO Three factors which M O L [ FRACTIOX, X are of particular imFIGURE1. TOTALAND PARTIAL portance-in the case of PRESSURES, IDEAL SYSTEM hydrocarbon mixtures make it possible and sometimes necessary to treat them in a somewhat different manner from that which is most advantageous in the case of other systems: 1. It is seldom possible t o analyze hydrocarbon mixtures by chemical methods on account of their lack of reactivity. Methods based on the physical properties of such mixtures are not very sensitive at best, and as a result the accuracy of analysis is comparatively low, particularly for the component which is present in the smallest amount. 2. From the few data available in the literature regarding hydrocarbon mixtures, the indications are that many such systems follow closely the ideal solution laws. It is of particular importance t o possess a simple and reliable method to determine whether a given system is ideal, since in that case the whole equilibrium curve can be calculated with far greater accuracy than it can be determined experimentally. 3. The hydrocarbon mixtures which are of practical interest are for the most part so complex that their analysis in terms of the individual constituents is well-nigh impossible. Hence it would be of great advantage t o be able to redict the shape of the liquidvapor equilibrium curves without laving t o resort t o an analysis of the two phases. The present paper shows how accurate information regarding the ideality of binary systems can be obtained by a simple
method, and:experimental data for this purpose are presented for eight s u c h h y d r o c a r b o n systems.
TBEORETICAL DISCUSSIOX Throughout this paper, each system will be considered under
~~~~~;,,,:;q''
~~~~~~
ventional nomenclature used is as follows :
va or pressures-of the pure components, 1 and 2, at t i e temperature involved, 1 being the more volatile component R = relative volatility of the two components-i. e., the ratio of their vapor pressures, P1!P2 2, 1 - x = mole fractions of these components in the liquid phase y, 1 - y = corresponding mole fractions in the gas phase = corresponding partial pressures p l , pz A = total pressure of the system PI, PA
=
If the mixture is ideal throughout the range of concentra. tion: pl = p2
=
PlZ
Pdl
- 2)
from which it follows that: ?T
= PIX t P,(1 - 2) = P*
+ x(P1 -
P2)
In this case the diagram of total and partial pressures is that illustrated in Figure 1, where all three pressure lines are straight. If the system is not ideal, the pressure lines are curves (e. g., Figure 2), with the same intercepts in the ordinates, z = 0 and x = 1, as in Figure 1. I n all cases the two partial pressure curves are related by the Duhem-Margules equation (5.4) which may be written:
According to Lewis and Randall (5.4) this is strictly accurate only when a p p l i e d to the f u g a c i t y of the two constituents, b u t no perceptible error is introduced when partial pressures are substiFIGURE2. TOTALAND PARTIAL tuted for fugacities at PRESSURES, NONIDEAL SYSTEM temperatures near the n o r m a l boiling points. When working under pressures well above atmospheric, this restriction must be kept in mind; but, since the present work deals with pressures close to atmospheric, the
504
May, 1934
INDUSTR I A L AND ENGINEERING CHEMISTKY
505
D u h e m - h l a r g u l e s Adding Equations 4 and 6, equation may be considered as a p p l y i n g quite accurately. Another relation- Since Equatioris 7 and 2 are incompatible, it follows that ship which is of value pl > P l x cannot hold. In like manner it can be shown in this connection is that pl < Plz cannot hold. Hence pl = P l x and p2 = the experimentally Pz(l - .c) is the only solution of Equation 1, and each partial established Henry's pressure curve follows the ideal line. This test was applied to systems on which data are availlaw, a c c o r d i n g t o able in the literature, as well as to a series of systems for which which the vapor pressure of the solute be- the present authors determined the total pressure as a func',, S A comes proportional tion of composition at constant temperature. to its concentration o 0.2 w 46 ab 1.0 as the dilution is inEXPERIMENTAL PROCEDURE N O L E FRACTION, X creased towards inFIGURE 3. PARAFFIN-PARAFFIN SYSThe experimental method followed consisted in deterf i n i t y (6B). From TEMS nlining, a t a suitable constant temperature, the vapor presthe Duhem-Margules CURVE SYSTEM REFIDRENCE equation and Henry's sures of each of the two pure components and of three or more 1, 0 n-Heptane-2,2,4-trimethylpentane Authors law one can readily different mixtures thereof. The apparatus used was a 2A, 0 2,2,4-Trimethylpentane-n-octane Authors derive Raoult's law Cottrell boiling point tube of 300 ml. total volume, containing 2B 2,2,4-Trimethylpenaccording t o which a Beckman thermometer. The side-arm condenser was attane-n-octane (1) 3A, X n-Heptane-n-octane Authors the vapor pressure of tached by an ungreased ground-glass joint, above which was 3B n-Heptanen-octane (4) 4A, A n-Hexane-n-heptane Authors the solvent becomes a vertical side tube (closed by a stopper when not in use) 4B n-Hexane-n-heptane (4) proportional to its through which liquid could be delivered from a weight buret. 5A n-Hexane-n.octane (4) SB n-Hexane-n .octane (18) mole fraction as the The upper end of the condenser was connected with a 75-liter l a t t e r a p p r o a c h e s reservoir, a U-tube mercury manometer, and lines to a vacuum unity. The partial pressure curve of each of the two con- pump and to the compressed air supply. When a sufficient amount of material was a t hand, the stituents, therefore, must start a t zero as a straight line of unvarious mixtures were made up separately in a weighing specified slope and must a t its upper end become tangent to the ideal straight line, Two such curves are illustrated in Figure 2. bottle to a total of about 90 grams. If, however, the supply A useful corollary of the above may be stated as follows: of material was limited, then the boiling tube was charged If the total pressure of a binary mixture a t constant tempera- with a weighed amount (about 50 grams) of one component, ture is a straight-line function of x , then the system is ideal. to which successive additions of the second component were That is, the equation R = Pz x ( P 1 - P2) is incompatible made from a weight buret, by which procedure less of each with the Duhem-Margules equation unless pl = P I Xand p? = liquid was required. The composition P2(l - 2 ) . This can be demonstrated as follows. - --28 of the boiling mixGO 2Ature was calculated Since 7r = P z Z(PI - P2) = pl -I- p , (1) from the weight of then dp, + dp, ( P I - P,) dx (2) 0 0.1 0.4 a6 a8 IO MOLE FRACTION, X each comDonent inStarting at x = 0, since Raoult's law must apply to component troduced and was FIGURE4. PARAFFIN-OLEFIN, AND 2, dp2/& = -P2; hence dpl/& = PI. Likewise, a t x = 1 , c o r r e c t e d , when PARAFFIN-NAPHTHENE SYSTEMS dpl/dx = P I ; hence dp2/dx = -P2, which means that both necessary, for the SYRTEM REFERENCE partial pressure curves are tangent to the ideal lines a t both r e m o v a l from the 1, 0 3-Heptene-n-heptane Authors solution of a frac2 ~ , n-Heptane-methylcyoloends. If the curves do not deviate from the ideal, dp,/dx = hexane Authors p,/x and dp,/dx = - p z / ( l - x ) throughout. If the curves tion O f t h e m a t e 2B n-Heptane-methylcyclohexane (1) do deviate from the ideal, it follows that dpl/dx must be larger r i a l , i n t h e form (or smaller) than p l / x near one extremity of the pl curve and of vapor and consmaller (or larger) near the other; there is, therefore, an densate, during the run. By using a large amount of liquid intermediate point, xo, at which dpl/dx = p l / x . The same and keeping the amount of vapor and condensate low, this applies to pa, and the point where dpn/dx = - p 2 / ( 1 - x ) is fraction removed was determined to be only 2 * 1 per cent. also a t x., by the Duhem-Margules equation. ilt this point Assuming 2 per cent distilled out, the change in composition a,ssume of the original mixture was calculated from the relative volatility, R, of the two components, assuming ideality. (In this connection, a deviation from ideality would introduce p1 > PIX or X > PI (3) only a negligible, second-order correction in the calculation for the systems studied here.) For those four systems in Since dpl/dx = p l / x , then from Equation 3 , which R was 1.07 or less (corresponding to a difference between the boiling points of the two components of 2.4" C. or dpl/dx > PI or dpl > Pdx (4) less), the correction was negligible, being a t most a change of -4t the same point, since p l p2 = PIZ P2(1 - x ) from 0.0003 in x or 0.015 mm. in T . For the remaining four systems Equation 1, and since pl > Plz from Equation 3, then in which R was about 2.5 (there being a difference of some 30' C. between the boiling points of the two components), the correction was from 0.002 to 0.005 in x , equivalent to p 2 < ~ ~ - (x) 1 or - 2 > - PZ ( 5 ) 1- x about 1 * 0.5 to 3 * 1.5 mm. in T, the exact amount of correction depending on the values of both R and x . Since dp? 'dx = -p2/(1 - x ) , then from Equation 5 , For each run of a given series the pressure was adjusted to bring the boiling point of the liquid to the same fixed temd p 2 / d x > -P?or d p > - P2dx (6)
+
'
+
+
+
y
A
__
506
INDUSTRIAL AND ENGINEERING CHEMISTRY
perature on the Beckman thermometer. It was found that, after steady operation had been attained, the supply of air (or the vacuum) could be closed off and the pressure would remain substantially constant; it was necessary only to make occasional slight adjustments to compensate for variations in the temperature of the air reservoir. Variations of the rate of boiling gave no indication of superheating. The magnitude of the temperature selected was later estimated from the vapor pressure curves of one or both of the pure components; it was, of course, unnecessary to determine this value with accuracy, the important point being that it was fixed and constant. Since the room temperature was approximately constant, no stem correction was necessary. The temperature selected was usually a little below the boiling point of the more volatile component, in which case the apparatus was always under more or less vacuum. Any slight difference between the observed and fixed temperatures was corrected for, with negligible error, using values of the pressure-temperature coefficient which had been determined during the course of the run.
MATERIALS.The various hydrocarbons used were commercial c. P. products, with the exception of n-octane and 3heptene which were synthesized in this laboratory by Dona1 T. Flood. Water in the hydrocarbons was removed by calcium chloride contained in a long wire basket placed in the lower part of the condenser tube. RESULTS. A summary of the results obtained for eight binary hydrocarbon systems is given in Table I and (together with comparable results from the literature) in Figurea 3 to 6 (percentage deviation from calculated total pressures). The systems are listed in Table I in order of increasing values of the relative volatility, R, of the two components. For each of the first four systems the boiling points of the two components are within 3" C . of each other, and the observed and calculated pressures for these systems should be accurate to 0.2 mm. The remaining four systems show differences in the normal boiling points between the components of about 30" C. in each case; for these, the calculated pressures may be in error by an amount not exceeding 1.5 mm. TOTALPRESSURE DATAFROM
TABLBI. VAPORP~ESSUT~ES AT CONSTANT TEMPERATURES
SYUTEM Benzene Cyclohexane
TBMP., O
C.
78.8
3-Heptene n-Heptane
97.2
n-Heptane 2,2.4-Trimethylpentane
97.2
*-Heptane Methyloyclohexane
2,2,4-Trimethylentane n-8otane
97.2
98.1
n-Heptane n-Octane
97.2
Benaene Toluene
79.6
n-Hexane n-Heptane
67.5
VAPOR
R
P R B ~ ~ U R EDIFFBRENCE
t
Obsvd. Ideal Mm. M m
1.021 0.0000 0.2036 0.5261 0.7620 1.0000
711.3 755.4 7 i 4 : 4 783.0 719.3 771.9 722.9 . . . 726.5
1.023 0.0000 0.2828 0.5559 0.7848 1.0000
731.5 746.6 743:5 758.85 755.1 767.5 764.85 774.0 ...
1.052 0.0000 0.1888 0.4078 0.6195 0.8583 1.0000
718.3 721.1 724.6 728.0 732.4 734.6
1.070 0.0000 0.2590 0.4731 0.7372 1.0000
684~6 697.25 s9i:i 707.4 707.4 719.95 720.1 .... 732.8
Mm.
%
....
....
....
....
.... 3.1
....
....
....
41.0 63.7 49.0
3.75 2.65
5.43 8.13 6.35
0.42 0.50 0.35
.... .... -0.04 -0.3
72i:4 724.95 -0.35 728.4- - 0 . 4 0.1 732 3
....
-0.05 -0.05 0.01
....
....
....
....
....
0.02 0.15 0.00 0.0 -0.15 -0.02
.... 2.214 0.0000 332.J 0.2750 440.1 442:95 - 2 . 8 5 0.5189 538.7 541.25 -2.55 0.7520 634.1 635.25 -1.15 .... .... 1.0000 735.2
....
....
-0.64 -0.47 -0.18
....
....
2.265 0.0000 0.3280 0.5104 0.6516 1.0000
322.9 453.8 456:7 527.7 531.0 583.05 588.6 .... 730.7
-2.9 -3.3 -5.55
-0.66
2.610 0.0000 0.1329 0.2836 0.3307 0.3796 0.5675 0.7251 0.8562 1.0000
290.4 349.4 417.0 442.65 460.5 546.85 619.0 679.0 743.95
-1.25 -2.0 2.25 -2.05 -0.9 -0.3 0.15
-0.33 -0.48 0.51 -0.44 -0.16 -0.05 0.02
2.658 0 0000 0:3172 0.5606 0.8095 1.0000
280 1 423:7 4 2 i : 4 530.8 535.8 653.6 656.0 .... 744.5
350:(\5 419.0 440.4 462.55 547.75 619.3 678.85
.... ....
.... . . . . ....
-3.7 -5.0 -2.4
....
-0.62 -0.94
.... ....
.... ....
-0.87 -0.93 -0.37
Equilibrium having been attained, the manometer and barometer were read, with the usual precautions, to 0.1 and 0.05 mm., respectively, the proper temperature corrections being applied to each reading. The pressure and temperature readings were then repeated a t intervals, both to insure that equilibrium had been attained and to increase the net accuracy; the final probable error in the observed pressure was estimated to be no more than 0.2 mm. in most cases, equivalent to about 0.01O C.
Vol. 26, No. 5
THE
LITERATUR~
Vapor pressure and boiling point data for binary hydrocarbon systems available in the literature have been examined; in those cases related to the present work, total pressure deviations from the ideal have been calculated and are shown in Figures 3 to 6. Bromiley and Quiggle (1)give boiling point data a t 760 mm. pressure for the systems n-heptane-methylcyclohexane, n-heptanetoluene, 2,2,4-trimethylpentane-noctane, and toluene-n-octane. Using the best available vapor pressures for each component, the present authors have calculated from the data of B r o m i l e y __------_ a n d Quiggle t h e ideal total pressures , and t h e o b s-e r v.e d percentage d e v i a I i a 0.2 a4 a6 0.a I,O tion therefrom. M O L E FRACTION 9 X Similar calculatio~ls FIGURE5 . AROMATIC-AROMATIC SYSwere made for nTEMS hexane - benzene SY0TEM REFERENCE CURVB using t h e data of Benzene-toluene Authors lA, 0 Tongberg and 1B Benzene-toluene (8) 1C Benzene-toluene (1 0) Johnston (11) and 1D Benzene-toluene (19) 2 Toluene-eth ylbenzene (fa Jackson and Young @), a n d f o r ben: zene-toluene, n-hexane-n-octane, and toluene-ethylbenzene from the results of Young and Fortey (12). [While these data are isobaric and not isothermal, it is known that percentage deviations from ideality do not vary greatly with temperature (6, 9). The above procedure seems, therefore, justified.] Direct determinations of the vapor pressure of benzene toluene mixtures a t constant temperature have been made by Schmidt (IO) and Rosanoff, Bacon, and Schulze (8), with the results shown in Figure 5. Based on the Diihring lines of Leslie and Carr (4),the present writers have constructed isothermal pressure-composition diagrams for n-hexanewheptane, n-hexane-noctane, and n-heptane-n-octane, from which the deviations of the total pressure from the ideal may be directly obtained. Two of the eight systems investigated, n-he~tane-2~2~4trimethylpentane and n-heptane-methylcyclohexane, appear to be practically ideal. Five other systems, 3-heptene-n-heptane1 2,2,4-trimethylpentane-n-octane, n-heptane-n-octane, n-hexane-n-heptane, and benzene-toluene, show deviations greater than the calculated experimental error, but less than 1 per cent of the
5
I
INDUSTRIAL AND ENGINEERING CHEMISTRY
May, 1934
total pressure. These deviations are all negative, with the exception of that of 3-heptene-n-heptane, in which case the deviation is positive. Only one system, benzene-cyclohexane, shows a larger (positive) deviation, the maximum being some 8 per cent of the total pressure. On the basis of these d a t a , t h e figures reported in t h e literature f o r n-heptane-met hylcyclohexane ( I ) , 2,2,4trimethylpentane-n-octane ( I ) , n- hexane-n-heptane ( 4 ), n-heptane-noctane (4),and some of the data on benzene-toluene (IO) are in error (cf., for example, Figure 3, curves 2A and 2B; also 3A a n d 3 B ) . UOlE FRACTION, X Some of them (4) FIGURE6. AROMA~C-PARAFFIN, AND are erratic in that AROMATIC-NAPHTR&NE SYSTEMS CURVl SYSTEM REFERENCE they show large deviations, both posi1. 0 Benzene-cyclohexane Authors 2 n-Heptane-toluene (1 ) t i v e a n d negative, 3 n-Hexane-benzene (8 2 2 ) for systems which, 4 Toluene-n-octane i2) judging from other indications, should be either ideal or nearly so. These discrep ancies alone constitute sufficient evidence for the unreliability of the corresponding data. Moreover, isobaric methods are not, in general, as satisfactory for the determination of total pressure deviations as isothermal methods, for two reasons: (1) Accurate boiling points a t a fixed pressure are difficult to determine, whereas a fixed temperature can readily be maintained to a few thousandths of a degree. (2) The calculation of pressure deviations from boiling points requires a knowledge of the vapor pressures of each of the pure components over the temperature range in question. These data are seldom available in the literature with the required accuracy. On the whole it appears that, when R is not greater than 2.5, the simple isothermal method used in the present work (requiring no elaborate apparatus and no analyses), permits one to determine whether or not a system is ideal with greater accuracy than can be obtained either by an isobaric boiling point method or by actual analysis of the two phases. Although the data presented here are insufficient to support any broad generalizations, there is a strong indication that hydrocarbon systems differ substantially from ideality only in cases where an aromatic hydrocarbon is mixed with a hydrocarbon of another family. It would seem worth while to test other hydrocarbon systems similar to those mentioned above to determine the validity of this assumption.
DETERMINATION OF THE z-y DIAGRAM AND OF TBE NUMBER OF THEORETICAL PLATESREQUIRED FOR FRACTIONATION From the foregoing, it is evident that but few systems will be found to be strictly ideal, within the limits of experimental error. For the remaining cases it is of importance to determine the effect of a small deviation from ideality upon the z-y diagram and upon the number of theoretical plates required to obtain a given fractionation of the mixture. For strictly ideal systems, the z-y relationship is give? by:
507
If, as is usually the case, the fractionation is conducted a t constant pressure rather than constant temperature, then R is not strictly constant. However, for the purpose of comparison of ideal and nonideal solutions, it is sufficient to assume for each case a constant value of R, a procedure which greatly simplifies the subsequent computations. The x-y diagram for an ideal soIution is then a symmetrical (hyperbolic) curve. In determining the number of theoretical plates required to effect a given separation of the constituents, it is convenient to assume infinite reflux in each case and to use the graphical method of computation of McCabe and Thiele (Y),as modified by Keyes, Soukup, and Nichols (S), the “safety factor” being, of course, omitted.’ In the case of nonF ~ ideal solutions, it is z; necessary to know $2 the partial pressures $8 0 in order to draw the 1.0 a c t u a l x-y c u r v e MOLE fRACTfON, X and d e t e r m i n e the FIQURE7. TYPICAL P n E s s m DErequired number of VIATIONS plates g r a p h i c a l l y In the absence of accurate partial-pressure data, we may, in the case of a small deviation from ideality, construct synthetic partial-pressure curves based on the observed total pressure curve. Examination of total and partial-pressure data in the literature indicates that the deviations of these pressures from the ideal lines vary with z in a more or less uniform manner which is well represented by synthetic curves of the particular shape shown in Figure 7, whose ordinate scale
.
1
When R is constant and the mixture is ideal-i.
e., z
=
R
1
+ (R - 1)z
1)
+ 1’
it is not necessary to draw the actual steps on the 2-y graph: instead one can. more readily, calculate the theoretical number of plates, n. between any two values 21 and zn by the formula:
2d1 -2n) n =
log zn(l- 2 0 )
log R
%herezn < 20. (If zn > 20, they are to be interchanged in the formula.) The derivation of this formula follows from the fact that, when 20, a,met, . znare the valuea of 2 corresponding t o n 0 , 1, 2, n, and zn < 20, then:
-
..
zo = y, =
. ..
1
(;o-
1)
+1
until Zn
- (: R”
whence the above formula follows. z n > zo. then
1
- 1) +
1
In like manner it can he shown that, if 1
zn =
RZ ___
=
(i -
1
and
I,
and
2)
must be interchanged in the above formuls.
q
508
INDUSTRIAL AND ENGINEERING CHEMISTRY
is determined by the magnitudes of the deviations. The representative relationship between the total and partial pressure deviations is given by
Vol. 26, No. 5
increase the above value of n to about 110 plates. However, as shown in Figure 8, their partial pressure data do not follow the typical deviation curves of Figure 7; as a result, graphical computation from a large-scale plot of their x-y curve gives A pi = AT ( I - Z) a value for n of only 65 plates. It may be concluded that in this case the 2-y curve obas shown in Figure 7. Taking the maximum value of AT equal to * 1 per cent of tained by analysis of the two phases is entirely too inaccurate the total pressure, and using the curves of Figure 7 , the to permit the calculation of n and the testing of equipment for corresponding x-y diagrams for three different mixtures fractionation. I n general it appears that systems having a have been constructed; the theoretical number of plates low value of R are unsuitable for this purpose unless the required in each case to pass from a concentration of x = experimental technic is improved so as to determine x, y, PI, 0.50 to one of x = 0.95, and also from x = 0.50 to 0.05, and PI?with the necessary precision (which appears to be have been computed graphically. The results are com- difficult), or unless it can be shown with certainty that the pared in Table I1 with those calculated for the same solutions, s y s t e m s a r e s o 2 assuming no deviation from ideality. It must be emphasized nearly ideal that the z6 that, while two simplifying assumptions have been made in x-y c u r v e c a n b e Q the foregoing calculations, the order of magnitude of the calculated with the deviations involved is so small that the results of the calcula- requisite a c c u r a c y 6 tions will not be appreciably affected by replacing the actual from known values of R. The proceti deviations by those assumed. dure illustrated in -2 3 -9t TABLE 11. NUMBER OF THEORETICAL PLATESREQUIRED the present p a p e r FOR FRACTIONATION permits the -latter $ 0 0.2 04 06 0.8 1.0 to be done in the NUMBER OF THEORETICAL M O L E FRACTION, X PLATES case Of a number Of R CE4NQE IN Z Ideal .Maximum deviation FIGURE 8. PRESSURE DEVIATIONS FOR +1% -1% h y d r o c~. a r b o n Vs- n - HEPTANE - METHYLCYCLOHEXANE 1 ,5 0.5 to0.05 3.3 ... 3.4 tems. There is also FROM DATAOF BROMILEY AND QUIG0 . 5 to0.95 3.3 .,. 3.1 suggested the possiGLE ( 1 ) 6.5 0 . 0 5 to 0 . 9 5 6.6 bility of obtaining l.L 0 . 5 to 0.05 8.8 8.4 9.3 0.5 to0.95 8.8 9.7 8.1 generalizations which can be applied to complex unanalyzed 0.05 t o 0 . 9 5 1s. 1 17.4 17.6 mixtures. 1.07 0.5 to0.05 43.5 32.9 0 . 5 to 0.95 43.5 83.6 A subsequent paper will illustrate a method of analyzing 0 . 0 5 t o 0.95 87.1 116. and correcting data for systems which show significant deviations from ideality. Owing to the uncertainty of the efficiency of actual plates, the theoretical number of plates, n, required to effect a given LITERATURE CITED fractionation need not be known with great accuracy (3). Table I1 shows that for values of R = 1.4 or 2.5, a deviation in (1) Bromiley, E. C., and Quiggle, D., IND.ENG.CHEY.,25, 1136 (1933). T of 1 per cent from ideality has no significant effect on n. (2) Jackson, D.H., and Young, S., J . Chem. SOC.,73,922 (1898). For a value of R as low as 1.07, such a deviation may affect n (3) Keyes, D.B.,Soukup, R., and Nichols, W. A , Jr., IND. ENO. by as much as 35 per cent. CHEW,20,464(1928). In the case of the isobaric distillation of an ideal system, and Carr, A.R., Ibid., 17,810 (1925). (4) Leslie, E.H., (5Ai Lewis, G.N., and Randall, M., “Thermodynamicsand the Free the use of a mean value of R in the determination of n inEnergy of Chemical Substances,” 1st ed., pp. 207-10, troduces no significant error, for when R is sufficiently small McGraw-Hill. New York. 1923. so that its variations have a profound effect on the value of (5B) Ibid., p. 234. n, then the boiling range is also small. As a result the actual (6) Marshall, A., J. Chem. SOC., 89,1350(1906). (7) McCabe, W.L., and Thiele. E. W.. IND.ENG.CHEY., 17, 605 values of R change very little over this range, and the x-y (1925). curve obtained from these actual values differs from that ob(8) Rosanoff,M. A., Bacon, C. W., and Schulze, J. F. W., J . Am. tained using a mean value of R by an amount too small to be Chem. SOC., 36,1993(1914). significant. As an illustration, for the system n-heptane(9) Rosanoff, M. A.,and Easley, C. W., Ibid., 31,953(1909). methylcyclohexane used in the example given below, R (10) Schmidt, G.C., Z. physik. Chem., 99,71(1921): 121,221 (1926). C. E., and Johnston, F., IND. ENQ.CHEY.,25, 733 varies from 1.0710 to 1.0728 over the normal boiling point (11) Tongberg, (1933). range (98.38’ to 100.8’ C.). Taking these two extreme values (12) Young, S.,and Fortey, E. C., J . Chem. SOC.,83,45 (1903). of R, the number of theoretical plates calculated from z = RECEIVED January 2 , 1934. 0.05 to x = 0.95 varies only from 85.86 to 83.80. A practical example of the considerable variation in n due to a slight departure from ideality a t low values of R is furnished by the system n-heptanemethylcyclohexane. The PETROLEUM RESEARCH IN FRENCHMOROCCOPROMISES writers’ results (Table I) indicate that this system, at 97’ C., DEVELOPMENTS. That Morocco may prove t o possess valuable is ideal within an experimental error of 0.2 mm. in the total petroleum resources is revealed in a report made public by the pressure, and the same may be safely assumed to be true over Commerce Department,. A French syndicate has been conducting exploration work in the whole boiling point range. Taking the mean value, over Protectorate and recently brought in what is re orted t o this range, of R equal to 1.0719, we find for the number of the be a gusher a t Tselfat Mountain. The actual possigilities of plates required, at infinite reflux, to effect a change in x of this well cannot be determined but the best information available from 0.05 to 0.95 is 85; the uncertainty in this value, corre- would indicate that the well has a producing capacity of about sponding to an error of 0.2 mm. in T , is not more than 2 plates. 600 tons a day. Moroccan authorities and interested oil companies are very Nevertheless, the results of Bromiley and Quiggle (I) for much encouraged as the result of their activities and believe this system (Figure 8) show a positive deviation of 0.7 per that the considerable sums which have been expended in research tent in x which, according t o Table 11, would be expected to have been justified.
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