Calculation Method for Complex Mixtures .I
method iibing 4tiiple c-alc*ulu.i b p,re.entrtl for the cdvulatioii of 5apor-liquid equilibria for complex mixtures. The computations are based on the true boiling point curbe of the mixture and are performed with a plot of rlll/dTB 2's. T B . The procedures and equations used are similar t o thohe for component mixtures. The results obtained can be made exact within the acwirac.) of the data. Four illuatrati\e examples are giber1 of calrulat ion. itibo1bitig ti *ingle equilihrinm.
['M'r
I
h- tiENERAILthe calculation of prt.ssure-tt,iiip(~rat,urt~-i.iiiiiposition relat,ions and distillation miiditions involvw t \ Y o types of mixtures. The first of thrsr is the coniponent niisturc,, for which the composition is commonly espressrd as thc p c r w n t ages of the compounds present. Thus a nat.ural gas is raid t o contain so much niet,hane, ethane, etc. The othrr type is t h t . coniples mixture, 1Yhic.h consists of a large number of compound* and for which the composition is commonly espi ilktillation curvr. Thus a kernsmc. is said to ImiI I w t w r n 330' and 550" F. For coniponc~nt~ niixt,ures t8he use (it' eithvr Raoult'r I:LU ( 1 1 ' vapor-liquid cquilibriuni const.ants, K valucd, is cvnimoii for tht. ralculation of such vaporization propertie? as thc drm-point temperature (.5, 6, 10, 13, 1 6 ) . Thwe is a complete syPtoni of (lquiitionr and procedures for thew computations, and the result,.: ('2111 he made as accurate as the data used. T h r hasic cquatioiis uml for thew singlr clquilibrium calculations ('an tw wi.ittr>nas folliiu..: V.~POR-LIQT-III ~QlTl,IBRI\-M y =
K.,.
rir
( ~ER-.u,I.
121
51 ~ T E R I A I 13ir..i~-c.~.: .
I.' ('lr\lPOSF:ST
=
I.
+ I,
181
\IATb:RI.II. H.41.iSi'E
Fz
=
I-//
+
14,
f,J
( '( 1\1 P O h I T I U N ? ~ V . . \ . I \ I A T I O>S
ZFZ = I.'
zvy = I .
"l'S
=
I'
l'Li
For coiiipoiic'nt inisturcs t he fundanwntal vaporizat i o i i tlat :i :ire comnionly givcfi i n terms of the componrbnts presrni. Thus i t is said that the R value of 71-ht~aneis 4.5 at 300" F. and 20 pnuntls p r r squarc inch ahS(Jlutt! (21, But for a conipl(.x niisturc, tht. numtwr of conipouridi i:, large, .:I) that soin(' basis for t hc vaporizntion data other than nioli~culiirspc1cic.s is nccwsary. ~i commori *nil well tl(~vrloprdlaboratory dt.trrminatior1 for cnmplt~smixturf's is t i i f , t m i , boiling point riirvi', or TRP, which is obtained 1 ) ~ t h i . hatiah tlistillaticiri of the misturc: i n a niultiplatc rolumn at a high r i 4 u s i.atio. This i ~ u r wis usually given as liquid volunit: pixr cac,iit di.qt illtd ovt'r plotted against column top temperature o r tioiling point (I, against 7 ' ~ ) . For the method of this article thr, v:iporizatioii data of a romplrs misturcs \rill hr based on the t)oiling points as givcvi tly a TRP. Thuc it will bch said that t h r h' vnlur of t h r coniponc~ntthat, \mils at, 156" F. (rr-hexane) is 4.5 at 300" E'. and 20 pouiitij prr nquart: iiicti ahsolute. Va1uc.s of K d i i t i 1)oilirip tenipc,i'aturch h a w hecsn publkhed hy \\-hitis alii1 l3rl)~vrl( 1 8 ) .
I l l
17y = (VKl1,l(lJJ
O F dWId1'H A G O I N S T
uwtl in thfl vapor-liquid ( q u i But H TB1' a s suc~licannot lihrium valculations; coiisiqut~ritlyit must, tie changcd into a fomr that r:in. For dirwt use in thr coniputations tiy the rnrthotl o! [,his art~ic.1~~. the T B P is put t ' o m of thr diffrrmtial purvi 1131 ( 1 7 ' ~I R . 7'8, where .lf re niolw and T B is t h r h i l i n g ri~ni1)cmturc~.This curve p he connrrtions htwvcvn t ota,I nioles, roniponent moles, an zatiori proprrties that arc' i v qnirrd for the calculations. The ximplr ralculus of obtainink thi> i ~ ~ from v e a TRP will bo givrri, and after this the propc~rtiwand of thtb curv(: will tw tlrscrihcd and illustratrd. The hasic. rc,htinn u s r d in ohtailling a value of d.lf l d 7 ' H is t h ( i rlcxii ti Iy
(51
.\ niathematiml h y h t c m for complcs mixture> c~~nipa~,ahlc. wit Ii the one for componrnt mixturrs would secni to tiil desirahlr, particularly for refinery pro . ivork. In genwal, this typr of misture is either ronsidcrtad t o ho dividrd into artificial compounds having a short boiling range (3, 6 , 8 , R, 1 7 , 181 or trratctl cmpirically hg methods based on largr amounts of laboratory data (4,I f , 12, 14). The use of difftwritial r u r w s for complex mixtures has been frequently propnsed (3,6 , 7 , I ; ) , but the actual dctails required to make these calculations prartical are not commonly known. Thc present paper givrs the simple calculus for one method b y whirh eomples mixtures may hi: handled by cquat,ions and proctdures similar to thosr used for componrnt mix. The rr'sults obtained \vith this mcthod i'an tw made c'xart 11 the acruracy of the data i i s ~ d .
l i t , villut'h of tlic. dtfirivati re for tht. irifiriitc~siriialh e rions o f thr n i i s t u ~ , clwilrtl ~ o w r at a ttbmprrature. in a TBP r~olunin. i'a1ui.s of d.\/ i t U ' ~ arc: plot t c d at thP vorrtqxinding values of 7" to give tIc.sirid c u r w . .Isan esaniplr a plot oi d.l/ (17" against 7" \vi11 tw otitaintd the pc.troltlum n:tphrhii of Figure 1. ('urve .i is thc. trui, t)oiling point curve for this mixturc anti given thi, hoilirlg ttmpt'raturw of the liquid fractions distillrd ovrr. ('urv(3s €3 and C give the molecular \\rights m t l thr rlrnsitics of these liquid fractions, resprctivrly. The steps in ohtaining a plot of d.lr,'dTR against 7 ' ~from t h i w data arc as t'ol-
\vtic,i,c. t
1 h i 5
Io\vP:
STEP 1. Obtain a plot of rfr,'dl'i, for the mixture. Thc. slopes of the TRP, c u r w A of Figure 1, are measured. arid tht, 1118
September 1947
INDUSTRIAL AND ENGINEERING CHEMISTRY
1119
reciprocals, d u / d l ' B , are plotted against T E . T h e resultant points are carefully averaged a n d smoothed. T h e final values are given by curve A of Figure 2. T h u s a t 200' F. the measured slope of the TBP is 3.66, t n d the reciprocal of this, dzriintiispendently of the already cisisting systeni for rornponcnt niisturvs. , thc calculations a w quite similar i n niany r(Tspi3ct is not depciiilcnt o n any of the ns?umptions made for the vaporization data. It is ouly ry that t h e K value? be kiim\-n :ii :i funrtion of the boiling temperature, and any source of thew d:tta iiic.lutling direct 1:tburatory determinations c:tn be uwd. -L3 with eomponciit mixturrs, t h e assumption of cnns1:int rehtive volatility is a milvt,iiieiit xay of oht:iining K values :it eliffi.rcnt conditions, but i t ritinl to the method. EXA\IPLE I .
EQUILIBRIUM DIVIS80Y INTO VAPOR AND LIQUID
Thc frat cslcultition is t o determinc the d i ~ i b i o nof the iitlphtha of Figure 1 11rtn.een vapor and liquid at equilibrium for rlw couditioiis of 295" F. arid 20 pounds per Squurr iiieti nbsolutc.. The prin(4p:~lq u a t i o n used is
0
20
,
, I , , , , __yI, 40 63 Percent
Figure 6 .
\vhich is obtained by combiiiing Equations 2 and 4. The procc-tlure used is to assume a value of L T- for the equilibrium, arid. \\-ith the Equation 8 and t,he known K values, to calculate a division of the naphtha into vapor and liquid. From this a ne\\- calculated value of L,'V is obtained. This step is repeated until the assumed and calculated values of LIT' check. Exactly the &me procedure is used for component mixtures. T h e composition curves required in the calculation are given in Figure 4, and curve A represents the original naphtha. The tlcltailed procedure is as follovc-s:
,
, ,
_il___l
eo
00
Vapor
True Boiling Point Curies
Q = TPB of liquid i n equilibrium with original naphtha a\upor; B = TPB of portion of naphtha that is liquid a t 293' F . and 20 pounds per square inch; C = TPB of original naphtha: D = TPB of portion of naphtha t h a t i s vapor a t 293' F. and 20 pounds per square inch; E = TPB of vapor i n equilibrium with original naphtha in liquid
This value of Lr is plotted a t K = 3.0 to give onc point of cuIve B, Figure.4. T h e other points a t the K values shown were obmined similarly. This curve gives the required division of the original naphtha into liquid and vapor for a n assumed L / 1- of 1.0. STEP2. Obtain a new, calculatcd L;T' From the curve of step 1. T h e moles of liquid present are represented by the area under curve B, Figure 4, a n d t h e value is given bg the planimeter as L = 9.07. T h e corresponding moles of total mixture is the 'STEP 1. Assume a reasonable value of L / V , and, with Equa-. area under curve -1,Figure 4, a n d has been f m n d to be 18.67. tion 8 and the K values, calculate a division of the naphtha into Then by Equation 3, J7 = F - L = 18.67 -- 9.07 = 9.60, arid vapor and liquid. the new calculated LIT- is 9.09/9.60 = 0.946: Evidently this is The value of LIV assumed for the first trial is 1.0. At 295" F. not sufficiently close t o the assunied value of LIT' = 1.0, and a the K value of reference comDonent K = 1.0 is found t o be 0.93 neiv trial must be made. (curve B, Figure 3), and the-K values of t h e other components STEP3. Repeat steps 1 and 2 until the assumed and calcuchange in this same ratio of 0.93 t o 1.0 (constant relative volalated values of LIT- check. T h e third a n d final assumption \vas tility). T h e n for component K = 3.0, the K value at 295" F. L / T' = 0.72, and the resultant division of the naphtha is givcn is 3.0 X 0.93 = 2.79. From curve A, Figure 4, the value of dlM by curve C, Figure 4. T h e moles of liquid present are repred T B at K = 3.0 is F z = 1.57, and Equation 8 becomes sented by the area under this curve, and the value is found to be L = 7.84. Then T' = F - L = 18.67 - 7.84 = 10.83, arid the ne\v calculated L I T ' is 7.84/10.83 = 0.724. This is taken as sufl.57 = 0,415 Lx = (81 ficientlv close to the assumed value of L/T' = 0.72, SO that no 1 (2.79'1.01 further trials are required. Then c u r w c', Figure 4, can be considered to represent the filial division of t h e original naphtha into vapor and liquid at 295" F. a n d 20 pounds per square. inch absolute. STEP4. Convert the niolc fractions obtainid in step 3 into liquid volume per cent. For this a plot of dcldT8 1's. ?'a is prepartd for the values of curve C, Figure 4, by niwiis of Equation 6. T h e area under this C U I represents liquid volume an$ is givcn a s / ' 15.15 h g the planimeter. r h e eorrc>spontlirig area under curve -4, Figure 2. for the total oi,iginal misturc is v = 32.79. Then thtx liquid naphtha of curvc~(', Figure 4,is 100 X (15.15 32.79) = 46.2 liquid volume pcr cc,iit of tho total. Then as a final answer thcx naphtha of Figure 1 is 100 - -16.2 = 53.8" vaporiztd at 295' F. and 20 pounds. Tlik is a point on the equilibrium flash curve for thc misturc (curvtx 13, Figure 9). T h e TBP valuc+i of the liquid and vapor of the equilibrium are Figure 5. Composition Curies for Example I1 and D of Figure 6, i ~ ~ s p c c t i v t ~ tained from curves .1 and A = composition curve for original naphtha; B = composition of liquid i n equilibintegrating plots of tliildT~ ( ' 8 , l ' ~as already rium with original naphtha a s vapor (dew p o i n t ) ; C = composition of vapor i n equilibrium with original naphtha a s liquid (bubble point) described.
+
INDUSTRIAL AND ENGINEERING CHEMISTRY
1122 EXAMPLE 11.
Vol. 39, No. 9
DEW AhD BUBBLE POIh'l
w x t ~ a l u ~to' i be calcu1att:d fcjt,
t i l t , t~apttt 11:~ 0 1 E'igurcx I ai'[' t h i ~i h v and tiuhhlr point trnipeixtui~~~.: iti 20 pounil; pt31. xquaiv inrli atisoliitc,. Thr dew poillt is t h i s t c * ~ i i p ~ r : t t uartc ~\vhic~li t h c s fii,,st ihu1)s of l i q i i i i l c.oritlt:nsc in the, cmliiig oi' t111. t o i a l 111ixture as v a p w , ant1 the b u t h l r point is thc t r n i ~ ~ c ~ iat~ awliirli tu~~~ the fiwt 1iul)l)Ii~~ of vapor form in the heating o f t h c x tot:il 111i~tur(: as liquid. In scilving for the dew point of a eoiiipoitc~ittn i i i t UJ'I,, the usuitl j ) i ' i i i ~ i d u r tis~ to find tlie teiiipvratulc th:tt giv1.s h' v:iiiIt+ w c h th:it 1: !/. /i = Y .r = 1.0, n-hi'rc. tltc valui,.: of !/ uq(-(l at'[' r l i r , iwniposition of t 1 1 ~ ' mixture. For cwnip1t.x iiiistur(:q, ho\vc 'rh18
Thc. teinpri'ai ui,i, of an rquilihrium at a prtihhut'(1i composition o f t l i i , vapor and i h intic~pciitic~niot' t h c ~n.I:ttivc ainouiits of liquiil anti vapoi'. Thc~li.i n c*ali~ulatirip a tloiv tho aiiiourit of liquid prcwnt ran tic coiisiclrt~cdt o t ) t , finit(., I though at ail actual de\\- point this amount is i i i f i n i t r ~ i ~ ~ i a l . proccdurc~u s o d i;. t i a d on this property. .in L;IT valuc. i. a:.sunied, arid, \r.ith Equation 2 and the K values at 300" F., a t i i i i t c aniouiit of liquid in equilihriuni with t,hc original mistui.r a* vapor is calculated. K i t h the assumption of constant K value, ratios, the composition of this liquid is independrnt ai tht. t i ~ i n p ~ r a ture chosrn. From the amount of this liquid, caleulatc~d1-ah-s of 1; and Lil' are obtained. The t,emperatut,e is thcri fouritl n-hich gives K values such t h a t the assumed an11calculatrd valui%< of L / T7 check, and this temperature is t,ht. drn- p u i n t . Thc: n t t i i i r prucedure could he used for component m i s t u w ~ . Thr rompoPitiori curves required for the calculation of thts iIt.tv point ai'('y i v w in Figur? 5, where r u r w .Ire~prf~sifiiit~ the origiitaI naphtha. Tlit, (hatailed proeedurc. is a.; follo\r.: S r r w I. Consider the original mistuw IO 1i1, all v a p i ~ r ,atid calculate a liquid composition in equilibrium \vith it tiy niiwis of Equation 2. It is first necessary that a value of L l l ' b e a 0.40 i s c-hosen a s t h i s gives a convenientl, curvp. For component K = 0.55 the value o read irom curve A , Figure 5, and Equation 2 kirconiw
LX = 1.29 (0.40/0.d5)
0.94
(21
This value of L.r arid others similarly obtained are p l i ~ t t e dIU givi. curve B, Figure 5 , which is the required composition of t hi, liquid in equilibrium xvith the original mixture as vapor. STEP 2 . Drterminr the new calculated valurs of' L and I, I*. T h r moles of the original mixture as vapor are rcprcwntcd hy the area under c u r v ~-1, Figure 5, and the valuc: has lircn fouiitl to be V = F = 18.67. The corrpsponditiy'nioles of liquid are shown by the. area under curve B, Figure 5 , and the val tiy thr planimeter as I, = 10.90. Thr,n this n t ~ i v calcul . of LIT' i s 10.90,'18.67 = 0.584, as c*rinip:irt~dw i t t i t h valur of 0.40 u w d in strp 1. S T E P 3. Find t h f ' trnipi~raturc~ (dI,\Y [ ) l J i l l I I I l l : 3 t KiVI',. k
Tg - Tern p e r o t u r e
Figure 7 .
Composition C u r i e s for E\amplta I I I
4 = composition curve for orginal naphtha; broken lines gire divisions b e t w e r n vapor and liquid and are laheled w i t h ,slue of 1. I assumed in ralculalion
This value is plottcd on t,he K = 3.0 line 1 0 givL onc point of curve I,, I ? = 0.5. Tho other point> wf thc curvi: and the other C U ~ V E SL J ~this figurt wrre ohtainc~tisimilarly. TIit..v rui'vc's givc (,quilihriuni division- 01' the total mixturf, i n t o vapo' and liquid.
INDUSTRIAL AND ENGINEERING CHEMISTRY
September 1947
1123
S w i ~2. Detcarniiiic. t tic, tc*iiipcmturerequired Tor the equilihrium of st ('p 1. If the K values at 300" E'. usrid iri step I w c r ~ ~ niultiplied ti? the ratio (I, 1.1,(I, and the cslcxlutioii rc,pratrd, th(3n tht. assumcd and calcuIatcd va1ur.s of L;17 \voulcl cht>,.li,a n d the K value? \voultl i ~ t .at the tc~nipet'st ure of the equilibrium (c*oiistaiitK value ratiosi. The planimet('r g i w s thc, iii'ea under c ~ v eL i T- = 0.5 as P I, = 6.32, arid the corresponding area under cur\ s!9 I .I of Fipurt, 7 for the total original naphtha D I.' = 18.67. By Equation 3. l7 = F - I, = 18.67 - 6.32 = 12.35, and the new calculated L/T7 is 6.32 32.35 = 0.51 as compared with thv assumed value ~ i L' / l v = 0.50. T h r n f o i , rciei.erice component K = 1 .O, the K valucx at t h trmperaturt of the equilibrium is K x (I, l-),.'(I,!J7)a = 0 1.0 X ( 0 3 1 ~ 0 . 5 0=~ 1.02. Fruni curve c', FipTg-Tcmperot,ra ure 3, the teiiipc,t,ature corw~pondingto this valui, of h-is 301 O F.,and this is tho tc~iiipt~rnturc~ of this Figure 8 . C:o~npositioiiCurie* f o r E x t t i i p l e I \ rquilihiiuni. STEP 3. Deteriiiiiie the liquid volunicb pc'r for original naphtha: I,ruhrn lines give liquids remaining in i = runtpusition c u r ~ e vaporized in the equilibriuni of step 1. the still and arc labeled w-ith v a l u e nf H , H ? awurned in calculation For this a curve of d w d 7 ' ~rs, T B is prrpawd for the liauid of curve Li17 = 0.5 tiv means of Equation 6. The area under this curve representsliquidvolume and is found t o be 1' = 12.41. The c*orl,cqiurltl'I'lit. tlrtailed t~xl(ulatiiiiit i i t , : t i t : t - ~ i i i i i t ~ ( ivnliit~( ~ B f , H , of 2.U is ingarea under curve A of Figure 2 for the total mixture is 2) = 32.7!1. a s fOllO\V. : Then the mixture is 100 x (12.41/32.79) = 37.9 liquid volumt3 2 liquid and 62.1Ci vapor for t,he conditions of the equilibriun?. STI.:P1. .issume ti value* of H v H , aiiil, \vitli Ecluatioii !I, Then the final values obtained for a n assumed LiV of 0.5 I* valculate a liquid remaining i n rhr still. 62.tyO vaporized at 301" F., and this point is plotted o n tht, T h e reference componmt, H. is 1akt.n a s conipviieiil = 1.0, equilibrium flash curve of the mixture (curve B, Figure 91. and for the present calculation H , I?:! is considcred to h r . 2.0The other points of this curve lvere obtained similarly and are t h a t is, half of component K = 1.0 has betln d i s t i l l d ow'r. I f :1 given in Table I. T h e end temperatures. the bubble and dt,w is taken as component K = 1.4, thtm .11 = b'z = I ..I4is givt.11 by points, are from example 11. These points are nearly a straight iwrvv A , Figure 8, and P:quaticiri ! I iit,cwniw l i w . T h e original naphtha of Figure 1 is a comparatively sharp (,ut, so that the tails frequently present on flash curvcs (lo not o ( w r t o a11 apprcciahle p x t e i i t . [ Y S ~ I
-1s an example of a mort' coniplirattd calculation the, diff m w t i d ilistillatioii curve for the naphtku of Figure 1 will he ohtainecl. In a differential distillation the mixture is boiled, and the vapors, which arc: in equilihrium w i t h thta rtmaining liquid, are removed as fast as formed. The final curvt, is plotted as boiling tcmperature against liquid volumc p t cent ~ clistilled ovcr (1' is. I ). The, hasic tquatioti uwd is thti iirtegrattd foim of thc Raylf4gki i'quat ion if.? : (Al'A2)
=
rN, H?)k.'
(!,
KH
Tlieii \vheri conipont~titK = I .0 is half distilled ovei', 11ic ainmilT i ) f cwmporient 6 = 1.4 remaining i n the still liquid is L X = 0.56. cind this value is plotttd on the K = 1.1lint, for curve' HI H, =
2.0, Thv othrr points of this cur figure \vew ohtained siniilarl>-. staiit relative volatility thi. ratio K.1, K B is *till temperature. STEP 2. Detrrmiiir t h t , Imilitig tcinperatui~c!\)ul)hlt~1 ) o i t i i t IIP liquid compimitiori ohtaiiitd i n , t ( L p 1,
,
\vhc~wA i i aiiy c-onipoiivtit aiid H i- t h r r v f t ~ i ~ ~ ~~ i~iowi i i ~ ~ o i i t ~ t i ~ T h e ratios A l , ' A , and R,,'B, arcs the rtviprocaals of tiits tractioii. of t h t w cwmponcnts that wniain in the still. 111 o1~1c.rto oliiairi one point o n tho tiiffercritial distillatiori curve, a valuc is a-sumcd for R I ,H?, anti the rtwdtant composition of the liquid remaining i n thc, still is found with Equation 9. The boiling tcmprratui't~ and tli(a liquid volume pttr cent of this still liquid a r t~h r n deterniincd. These two values give the coordinates of one point, 011 t hc. differential distillation curve. Thta same prorcdurt. would h i t used for component mixtures. The composition curves for t h i b ealrulation at'e givt~rii t i Figurt. 8. \vh(lrr curve h represcnts the oi,ipinal naphtha of Figuw I
t
0
I
l
20
40 PQrCGn'
6C
,~
80
I cc
Vapor
F i g u r e 9. Distillation C l i n e s for Petroleurn Uaphlha 100 0
338
i = TPB of naphtha; B = rquilibrium Hash curve f r o m e\.implea I1 and 111: C = differential distillation curve from examplea 11 and 1V
I o
TTRTE FIGUHE 9)
DIFFEREXTIAL
(CURYE
c',
T , Still Tenip ,
r , Liquid Tol.
S O I I E N C L iTtiiKE = \ : i l u c ~ of
/j
=
// 1,'
=
Fz
= =
/i
=
/.
=
/J
=
1
1
.I1 ))I
DISCUSSION
T o a person familiar with t,he details ttic methods giveti hctx, are both direct and quick. They require less time than the corresponding discont,inuous methods, in which the complex mixture is divlded into artificial components having short boiling ranges. T h u s a point on a composition curve can be found as easily as a mole fraction and averaged temperature can be obtained for artificial component. I n determining total moles, a planimeter can obtain a n area almost rn quickly as a column of figuros can be added. Values of Lr and V u can be as easily set down by it point on a curve as b y a number in a table. The dew point c d culation of example I1 can be completed in less than ten minutes of comparatively slow work, with seventeen points used to dotermine the liquid composition in equilibrium with the original misture as vapor. Another advantage of the method is that Ihe differential plots of the compositions give a much clearer pict,ureof an equilibrium o r distillation than do the corresponding columns of figurt~sof t h t , discontinuous methods. Thus a coniparision of Figuws 7 and 8 3 h o w that a differential distillation gives a bettcr sepxration 01' the naphtha into its high and low boiling component. thrii tlita corresponding equilibrium flash. T h e greater slopes IJC the liric+ dividing vapor and liquid in Figure 8, as compared n-ith Figure 7, mean t h a t less heavy constituents are removed in the vapor, arid less light constituents remain in the liquid for a differrmtial distillation. ;in additional advantage of the met,hodb giveti here is that the use of poitit values and the exact calculus is more desirablv theoretically than is the corresponding use of A arithmetic in the discontinuous methods. If riiore ailti stii:illc~r finite divisions are used in the discotitiiiuous calculations, the errors are reduced, but, also, the time required is iiicrea.sed. Pure compounds can easily be conibined tvith complex mixturea in these calculations. A convenient \vay of doing this is to plot t hr compound as a vertical line at the corrert boiling temperature
/,.r for gc~irralctiiiipoii(~iitiii still liquid for, ez:iniple I\' :in11 Equatirlii 9 v:iluts of 1,s for refereric~componc~iit(coiii~iiiiictit ti = 1.0; iti a t i l l liquid for examplc I\- :tiid Equation !I liquid density, pourids per gallon t o t i i l moles of original mixturc. total original amount of :t c o i i i p i i i i t b i i t prcw~tit (//.If,' 1 1 2 ' ~for complex mixtures v:tpor-liquid equilibrium coriataiit, defined by equutioti (I7!/) = (I-/< ,I, (Lc) for c.implcx misturczs total moles of liquid in thc equilibrium aniouiit of a coiiiponent 111 t i t as liquid (d.11 d7'8 for complex mixturcs 1 tiumber of moles iriolccular \wight temperature of equilibrium. 1.'. boiling point temperature,, F.,ol)t aiiiecl F i , o n i T U P io,. coniplex mixtures total moles of vapor in the cquilibriuiii amount of a component present. as vapoi' 1d.11 d 7 ' ~ for complex mixtures) liquid volume per cent of total niistur,r. inole fraction of component in liquid mole fraction of component in vapor mole fraction of component i i i total original mixture
.I
=
rl'
= =
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= =
= = = =
/
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z
a = assutiicd valur, oil L;l7 c = calculated value, on L,/V I = coiiditioris a t begiririing of distllatiori i n I.:quation 0 2 = c~onditionsat any time during distillation in Equation 9 LITER.4TURE CITED
S o c . for T e h n g hlaterials, Standards on Petroleum Products and Lubricants, Method D-86-35 (1937). B w x n , Petroleum E n g r . , 1 1 , S o . 9 , 55 (1940). Docksey, .J. Inst. P e t r o l e u m Tech., 23, 316 (1937). Gcddes. ISD. ESG. CHEM..33, 795 (1941). Huntington, Refiner S u t u r a l G n s d i n e M j r . , 19, 1 6 1 8 , SW4. 125-6, 164-6, 219-21, 256-9. 287-90, 33-1-8, 389-92 (1940); 20, 26-9.47-50,97-102 (1941). 1i;itz and Brown, ISD. ESG. C H E l r . , 25, 1:37:3 (1933). I i r c ~ n s c r ,S n t l . Petroleum .Yeus, 22, S o . 21. 4:3-9 (1930). L e v i s and Bnioley, A m . Pttroletrm I i i s t . Btr/l., 11, 7 3 11980). Lewi2 :ind Kilde. Trritis. d m . I m t . C'henr. Eri(/rs.. 21, 99-126, 1928). S c l s o n . "Petroleum Refinery Engineering," 2nd cd.. 1). 220, lIcGrarv-Hill Hook Co., Inc., 1941. Selaon and Hanshurg, Oil G u s J . , 38, S o . 12. 45 (1939). Tralis. 1 v r . I n s t . Ciiern. E I I ~ L37, ~ . ,S o . 1 . 56 (1941). ('hemica1 Engineers' Handbook. 2nd cd., yp. 1355-9, -1401. llcGraw-HiIl I3ook Co.. Inc., 1941. o v and Beiswengcr, A m . P o t d r i i i n I n s t . B u l l . , 10, To. 2 ,
i 11 . \ i n .
(2) (3)
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i
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3 r d e d . , lIcGraw-HiIl Book ('o.. Inr.. 1939. 1.17) 'Thiele nnd Geddes. I N D E . s o . T H E Y .25, . 289 (,1933). ( 1 % K h i c' a r i d Brown, I h i d . . 34, 1162 (19-121).
