Calculation o f
RELATIVE VOLATILITY FROM BOILING POINTS F. W. M e l p o l d e r
and
C. E.
Headington
THE ATLANTIC REFINING COMPANY, PHILADELPHIA, PA,
sure over a range of 300" C. and at pressures down to 10 mrn. of mercury. In order to facilitate the solution of distillation problems, a graphical solution of Fenske's total reflux equation for binary mixtures i s given.
A n improved method i s described for calculating the ideal relative volatility of nonpolar binary mixtures from the boiling pnints of the components. Based on recent precise vapor pressure data, the value of alpha was correlated with temperature and pres.
P R I KG rcAcmt xrars t h r petroleum indust,ry has i i d e rapid
wab devc~lop!~lfr1111i p t & e
hydrocarbon vapor pressure data rert.ntl? matic. availahltr by the National Bureau of Standards ( 1 ) and h w t h r s n c ~ w a c yncw-sary for plate and rnflus ratio [*Rlr.llla-
D
progress in t h e utilization of f r a c h n a l distillation t.echnique, both in product separation and in product evaluation. Xew and better equipmmt is becoming available t o meet thy increasing demand io? the isolation of pure, or relativclly pure, hydrocarbons, and acwunulating literature on the subject of fracrional distillation is gradually rendering it more susceptiblc~ rigorous mat heniat icnl int erpret a t ion. The interpretation of niany fract,ional tiist illation prohlenis, however, is dependent tin a knowledge of the relative volatility,of the components involved. Il-here reliable vapor prcwure curves are available the ideal relative volatility cy of a binary mixture i> the i,atio of the vapor p r c w u r t ~of t h e coinponenh. I n s u l x e q u m t discussion t,he terms ',alpha" and '.rt*laLive volatility" will be defined as tmheratio of tht. vapor prcsauri+ of the compounds as difftbrentiated from the t r u e relative volatility. which may be drterniined by liquid-vapor equilibrium studies. I n indirect but simple method for evaluating cy is clesirable) however, for systrni;: where vapor pressurr curves are not available, and particularly where no reliable vapor pressure d a t a arc at hand. .1 new correlation utilizing only the boiling points of thi. components has t ht.r(,fore bet>rideveloped for this purpose. Although a number of inveotigators have proposed methods for calculating the value of a from boiling points (2, 3, 6, 7 , 8)tlic. authors have found none t h a t have the clwired degree for spplication to prwisr. ili~tillati~in.T h r p r c ~ m T
s;
tions. THEORETICAL BASIS
.IIIwpl)i~osiniatt~ rrslatioii tiet\vc~~n relative volatility and t)oiiiIg point:. n-as tierived by Edgeworth-Johnstone (3)from the U a u $ius-Clapeyron equation and Trouton's rule by assuming vanstlalit ninlal heat of vapirizat ion:
Sincc. Troutoii's rule ia orily an approximat ion, the coct€i(it~ntK iiiight t i r espected t o be a variable. This wa:: substantiated by tht, 111,servation that Trodton's constant does vary apprcxiably with both tcmpcraturcx and prrssure. I t !vas ilso obsclrvcd that ilit, v:triat.ioris of R approsiniate the deviation:; of Trouton's constant a t corresponding tpnipcratures and prr'ssur t-orrel;ttion t,herefore yivlds a corrccted value for tc.niperatures and pressures. It is \wll known t h a t idritl values of u h:tvt, little significaiicr for niisturm trhirh sho\t- appreciable deviat.ion froni Raoult's Ian.. For inixturibs which (lo milform to Raoult's laiv, the polarrypv i ~ i i i i ~ ~ ~ ~r(,tjuii,(* i i n ~ l iniuc,h highw values of h ' than tlo mistiii'i'> of nonpolar conipnund-, and t h i s niagnitutli, of K v:ri.icv n-it h the ptilarity, as rviclc~iictd b y I tit, relativt.ly high values gix-txn liy Trout on's rule for polar ronipouiitls. A i ~ ~ i i ~ c ~ l a rion of t h t w variitions of li with t c~mpt.raturcand ~ ) r i w u r e tias not ytbt I1t.t.n ohtaincd. The ne^ c.iiri~c~laticin i- thrarcJforeapplicahlr only t o tliiiary niixturm, such a: paraffin hytlroiwlions, wherc~it ia lii10\\.11 ihat 1 1 0 significant tloviatic~n~froni Raoiilt 's
500
4--400
$a a
300
-z
J
6 200 m w L3 a a w 3
Iatv
o('l'ur.
100
NEW CORRELATION
0 3.6
4.0
4.4
4.8
Figure 1.
52
5.6
K
6.0
6.4
6.E
Effect of Temperature on Value of
K
763
7.2
7.6
8.0
111 order to detrsrinirie a iiwv v:tlue of K for hydrocarbons, a s:criw of K values 1vei-e calculated fi.iini Equation 1 for a numbttr
764
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 39, No. 6
I
5
6
7
K
Figure 2.
*I
Effect of Pressure on Value
I
100
0
of K a t 0 " Kelvin
Component 1
an8-2-Butene n-Hexane 2-liethylheptane Isopentane 5-IIethylhexane 1-Butene Isopropylhenzene Toluene Propene
-76.31 -25.0 12.3 -57.0 -9.1 -81.60 38.33 6.37 -112.11
cis-2-Butene 3-lletliylpentane n-0 c t ane ?a-Pentane n-Heptane cis-2-Butene 1,2,3-Trimeth~lhenzelie Ethylbenzene 1-Butene
Isobutene .\I ethylryclohexane Isopropylhenzene 2-llethylheptane Isopentane Isohutane C t ha ne
-67.90 16.3 5Q,8l 32.16 -41.15 -72.52 -132.74
1-Butene Ethylcycloi,erit ane ti-Propylhenzene n-Octane n-Pentane n-13utane Propane
1-3IethyI-3-ethylhenzene 5-blethylheptane hiethylcyclopentane Isopentane 1-Butene Isopropylhenzene Toluene Benzene Propene Ethane
95.9 58.30 17.86 -20.16 -48.87 88.14 51.94 26.09 -84.12 -119.33
Isohutene n-Heptane n-Heptane l-l\lethyl-3-ethylhenzene rn-Xylene Isopropylbenzene Nethylcyclopentane Isopentane 1-Butene Ieohutane Benzene Propene Ethane n-Pentane
-6.90 98.43 98.43 161.30 139.10 152.40 71.81 27.85 -6.35 -11 73 80 10 -47 70 -88 63 36 07
1-Methyl-3-ethylbenzene 2-Methylheptane Isopentane Toluene Benzene
180 134 41 127
0 77 80 52
95 71
500
I!oiling p o i n t , C.
I're-bure, 311~1.H
C.
g
a? froin
Deviation of a?
P?/PI 1.27 1.41 1.51 I 68 1,57 1 98 2 . 5! 9 1 16.4
Equation 4
froni ai
1.28 1 4.3 1 5:3 1.71 1 59 2.01 2.73 .I. 34 17.2
70.8 11.4 +1.3 +I 8 7-1,:
wlittion tvt \ w t ~ nIi v:ilucs :it zcro tc~nipwtturc and thc 1og:trithm of t hc Iircwutx~. For t h r prwsurc’ ranpi’ in\-csrigat c d , t h e Iiwt straight line T W ? (Ir:twi through the, poin:s anti c~ztix1)ol:itcd t o log P = 0. .\t this point tlic ~-:ducof I< :it 7’ = 0 a r i d liig P = 0 i- s w n t o iie 7.30. In nrtlor ti) l~v:rluntc~the, ( . f f l , C t [ I f t t ’ l l l ~ ~ ~ ~ r : t t l l l ’ l ’ , ttw .-lopc~-: of t l w iwti:it,ic, l i n w i n I’iguic. ‘1 \vcw t h i b i i c~:tli~ul:ttc-ti:lii(i plot t c d :xg:iin>t 1og:~rith i l i of t I I ( ~ prcwurc~ t o givi t l i c x qt i,:iigllt I i i i c skion-ii i n Figiirc~3. I~~\-alii:it iiln of Ii \v:i. t 11(,ti ni:irlr~ f r o m T I N W ~ gi,apli.~f t ~ ) mt h i s rt8l:it i r i n
40
30 20 W 0
w z
a
w IO
LL
;e + 6
2-5
0
a
765
h cross plot
50
4
; 3
t l i ( 8
2 om2
I
1.02 1.031.04 1.06
1.01
1.4
1.6 1.820
VOLATILITY
(ALPHA,)
1.2
1.1
RELATIVE
1.3
3
4
5 6
810
Ii
=
Ii,r
~
0.
i. .~ o
+
h’ip
Figure
4.
Relative Volatility of Binary Hydrocarbon Mixtures at Atmospheric Pressure
of tvo-component hydrocarbon . tenis a t several arbitrary pres5iires (Tahle I I. These values of I< were then plotted against the alcrage boiling point on the absolute scale, and straight isobaric lines were drawn t.hrough the point? and cstrapolattd t o z t r o tvmperature (Figure 1).
MOL PER CENT
LIGHTER
I
K P\VW found f r o m Figure 2 t o be -1.15 log,~Z-’:mcl t h a t of KT from Figure 3 t o tie 3‘1179 IogIoP. The value of K at, any temperature and pres8ul.e is thcrrforc:
IO
Figure
+
Graphicdl Solution of Fenske’s Equation for Total Reflux
(3)
766
INDUSTRIAL A N D E N G I N E E R I N G C H E M I S T R Y
Vol. 39, No. 6
NOMENCLATURE
/
=
/.
= 7' = /'., = = P = (I =
lioiliug p i i i i i t t i t lo\ver boiliiig compoiiriit, . ('. tmiling point of higher boiling conipoiirnt, ' C:. ;ti)acilute boiling point of the mistiir~c~. ' I i i i d , nim. Hg i ~ l n t i v rw h t i l i t y
COMPARISON of RECTIFICATION and DESORPTION in PACKED COLUMNS Donald
W. Deed', P. W . Schutz',
and Thomas
C O L U M B I A U N I V E R S I T Y , N E W Y O R K , N. Y .
HE unit opelutioii \I-hich coirsictc ~ i bi,iugi~ig i :I strearii t ~ liilf uid and a stream of gas countercurreiitlg into direct contact to allow spontaneous interphase transfer of their constituents :inti of enthalpy is called "rectification" if the in(-oiriing liquid i y .U}Iplied by condensing part of the gas leaving, or if the iiicoriiing ga? is produced by reboiling part of the liquid leaviiig. 111most c i t l i c ~ r circumstances the term '~at~sorptioii," in it> grneralizeti seiiw, iaccepted. The character of the effect- inilurrd anti t h e typec ( i t equipment found useful ai'e indepentieiit i i f the soui'ce- u i t lit. fluid stream>. So also, presumably, x h o i i l ~ tt)e the rehtiiriih :iinciiig the parameters u i performance i'iJrniula~,tlitx I)riipei'tie.> oi tlic streams, and t h e operating varialiles. Ho\vevc>r,e*tiniate+ F ~ . i i i i i published data o r rectification ( 2 , 4,16) uI'tlir height.. i i f iiidiyidual and ovrr-:iIl liquid-film trail-frr unit> liavc led to v:iItic~sermiiigly a t variance with the re-ulta fi.cini atjrorptioii trst-, liirt 11 az,to magnitude and manner of v:~riatioii \\-it11 tlir licluiii, rate,. Sii illogical a situation aeemed t o require iiivrstigatioii. To avoid poahihle rnisi~~ter~ii~rtatiori iJwau-1' (if i l [ i i , r s r t : > i i i t >
T
1
I'reaent addresb, > t ~ i i ~ d x nOI! I l l c ~ v t ~ l o p i i t c ~I 'io~t1i i p
. nereased.
,x
I
B. Drew
