Lewis Matheson

 

Studies in Distillation Design of Rectifying Columns for Natural and Refinery Gasolirw by. K .

LEITIS .4K D

G. L .

hfATHESON

Department of Chemical Engineering, Massachusetts Institute of Technology. Cambridge, Mas>.

T he Hausbrand equations equations fo r binary mixture s are applied applied to the solution of problems ir tinuous rectification of natural gasoline. S t ep s of the compu tation are outlined, the details of which are illustrated by a specijic problem

T

con-

HE design of rectifying equipment for natural and refinery gases is complicated by the presence in the ixtures of a large num ber of compon ents. Th e problem can be s olved olved by applying the ordinary H aus brand equations for binary m ixtures succes successive sively ly to all ooff the components whose propelties influence the separation. However, the multip licity ooff th e operations ooff com puta tion is suffici suff icient ent to confuse one unfamiliar with the techni technicc of handling the equations. Because of the growing imp ortan ce of rectification in the industry, it seems worth while to outline and illustrate the steps to be taken in solving a problem of this sort. The following nomenclature will be employed :

that the molal heat of vaporization of the componeiits i s reasonably constant under ordinary conditions of rectification by assuming average constant values for V n n d O n + above the feed plate and for the corresponding values of V , a n d 0 - below it, thus making it possible to use the graphical stepwise metho ds of of design which have so generally replaced the former algebraic technic. I n us using ing the above equation, Hausbrand calculated calculated the vapor composition, y from the liquid composition on the plate above, and then determined the liquid composition, xn, y the use of the equilibrium diagram, thus proceeding down the column. I n the ccase ase of natu ral gasolin gasolinee the process can be simplifi simplified ed because of the fact tha t the components

moles of vapor rising from any plate per unit time moles of overf overflow low descending from any plate per unit time mole fraction in liquid phase of any particular component under consideration mole fraction in v apor phaPe phaPe of any such component moles of feed t o the column per unit time moles of final product (distillate), whether vapor or liquid, leaving apparatus per unit time moles of reqidue leaving bottom of apparatus per unit time vapor pressure of component under consideration in pure state a t temperat temperature ure in question total pressure pressure on appar atus partial pressure of component under consideration

of th e mixture follo follow w Rao ult's law, at least within th e accuracy of desi design. gn. Thus, assuming 100 per cent plate efficiency, the partial pressure of any particular component above the nth plate is is equal to XZ nd this in tur n is ident identiical with its partial pres pressure sure in th e vap or above tJhe plate, yn7r. Hence,

V 0

= = =

y

D

= = =

W

=

P

=

z

T

p

= =

Count the plates up from the feed plate toward the top and dow n tow ard the bottom. bottom. Call any particul particular ar plat platee above the feed feed plate the nth plate and be belo low w , mth. Call the top plate the pth an d the bottom plat platee-i. i. e., the st stil illlthe wth plate. Designate the condit conditions ions referr referred ed to by means of a subscript indicating location locatthe ion material ooff the material in question or the point from the which came. Thus , y,, is the composition (mole/fraction of the componen t in questi question) on) of th e vapor risi rising ng from the n th plate, off th e feed to the colum n, etc . xf is the composition o Assuming contin uous ope ratio n of such a recti rectifying fying colu mn, H aus brand equated input to output of a given component in a section section ooff the a ppa ratus above the n th plate, as follo follows: ws: y,V,

= Tn+iOn+i f X d D

Th e left-hand side of of th e equa tion is the to tal am ou nt ooff component entering the top of the column from the nth plate per un it time, while the first term of the right-hand side is is the a mo unt of thi s com ponent flowing in the over overfl flow ow from the top of the column dow n on the nth plate, and the s econd econd tterm erm is the am ount in the dis til tillate. late. H aus brand employed weight units, but for reasons which will appear presently present ly it is more convenient in th is particular case to use moles. Th e expression X d D is determined by the conditions of the problem, and the amount of vapor and overflow flow can be calc calculated ulated a t an y temper ature level from a heat balance. bala nce. I n recent years it has become commo n practice in the case of bin ary mixtures to tak e adv antag e ooff th e fact

Y

= znP,/n,

and consequently one one ma y rewrite rewrite the Hausbran d eq uation as

Similarly, below the feed plate,

It should he clear that by means of these equations one can

compute the change in concentration from plate to plate in a n y p a r t of the column, once the conditions on any given plate are known. C H A R A C T E I ~ I S TRI CO B L E MN DESIGN It will be worth while t o consider a characteristic problem in design. One w wil illl know the Composition and a mo un t of the feed to the column; the temperature and pressure under which it exists; exists; the tem perature w hich it is pract practicable icable to maintain in the reflux reflux ccondens ondenser er a t the top ooff the column with the cooling means available; the point a t which which it iiss des desir ired ed to ef effec fectt the s eparation; eparation; and the all allow ow able able o v e r l a p i. e., the amount of high-boiling material which may be tolerated in the overhead distillate and of low-boiling materi terial al in the residue from from the still still at the bottom of the column. With these da ta a t hand, the following following steps steps of of co mpu tation are necessary: 1) Calculate the amount and exact composition o f the dietillate and residue. (2) Determine the pressure which must be maintained on the condenser in order to produce the reflux which is necessary for the functioning of the column. This is the operating pressure. 8 of the apparatus. apparatus.

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Assuming for the mom ent a suitable value ooff the reflux, o the top of the column from the reflux condenser, calculate the com position ooff th e reflux. Th is will, of cours e, depend on the type and method of operation of the condenser employed. (4) Calculate th e compositi composition on ooff th e vapor from th e top plate, and, from from this, tha t of the liquid on the top plate and its temperature. 5 ) Calculate the tem pera ture o off t he still and the composition of the vapors rising from it. ( 6 ) . From a heat balance on the column, determin determinee th e variation in the reflux through the column. One can immediately determine by such a balance the reflux from the bottom of the column to the still, and it is usually sufficiently accurate t o wsum e the change in reflux per degree ooff t emp eratu re rise up the column constant, except a t the feed plate where the reflux is increased by the amou nt ooff liquid in th e feed. (7) By use of the Hausbrand equation applied from plate t o plate calculate the concentrations and temperatures on the plates, plat es, working down down from the top and up from the bottom. of the preceding ope rations as (8) Tnspection of the results of the tempe ratures ooff t he plates approa ch eac eachh other towards the middle of of the column will enable one to judge with reasona ble precision precisi on whether th e am ount of reflux assumed for the operat operation ion satisfactory actory of the column is satisfactory. If not, read just it to a satisf value value and re peat steps 3 to 6, inclusive. (9) By study of the compositions determined by working up from the bottom, pick a suitable feed plate. Estimate the concent conc entrat ration ion on t h s plate of th at com ponent ooff highest boiling point which does not appear in the residu residuee in appreciable amou nt. If necessary, recalculate the composition on the plate below and correct for th e concentr ation ooff t,his com ponen t on it. Then proceed proc eed with the computa tion ooff the concentrati concentrations ons up the column until the concentration of th e lowest-b lowest-boiling oiling cons tituen t

0

(3)

o f the residuehas which doesnegligible. not appear Ifin the appreciable amountthus in the distillate become concentrations

determined correspond substantially with those calculated by starting down the column from the top, the problem is solved. If not, the concentration on the feed plate must be reeatimated, and this last operation repeated. The number ooff plates thus determined, corrected for the plate efficiency, gives the number of plates required in the column when operated under these conditions. IO) To determine t,he influence of reflux ratio in column size and heat consumption, these operations must be repeated for a number of different values values of reflux. The plotted results w wil illl make it easy to determine the best operating conditions. ILLUS'FRATIOX

OF

DETAILS F

PROBLEM

Th e detail ooff these step s wil willl be best understood from a specific illustra tion. Assume as a feed stock a material specific containing 26 mole per cent of methane and permanent gases, 9 per cent ethane, 25 per cent propane, 17 per cent butane, 11 per cent pentane, and 12 per cent of hexane and higher. Assume th at the am oun t of iso isomers mers of th e normal hydrocarbons hydrocarb ons ma y be nnegle eglected cted and th at th e hexa hexane ne and higher hydrocarbons average heptane. Assume that conditions are such that one can maintain an effective top temperature-i. e., a tempe rature of t he gas and reflux reflux,, within the condenser itself, of 70 F. (294 K. ). T he feed feed is pumped in at 100 F. (311 K. . It is desired to take all propane and lighter overhead, and all butane and heavier as resi residue, due, bu t it is allo allowable wable to have 1 per cent of butane in the overhead distillate and 0.1 per cent propane in the residue. Th e re reflu fluxx condenser iiss ooff a t ype in which the v a p o r s ~ravel ~ravel with the liquid through the condenser and are separated after having been brought to the final condenser temperature of 70 F. Consequently, the final gas is in equilibrium with the reflux liquid. STEP1. STEP 1. Were the separation complete, there would be 60 moles of distillate an d 40 o off residue for each 100 moles of feed. Consequent Consequently, ly, in the actual column the buta ne In the distillate will be approximately 0.6 m o l e a n d t h e propane in the residue 0.04. 0.04. On th e basis ooff this, the fo foll llowowing table, showing showing the distr ibution of the co mponents ooff 100 moles of feed between distillate and residue, should be selfexplanatory:

HYDROCARBOS CHI + CzHe C3H8 CIHK CSHIP

C HE

A I

I

TR Y

DISTILL~TE M o l e yo Moles 26.0 9.0 24.96 0.61

CEHl

~

To ta l

42.9 1 4 ..9 9 41 .2 1.0

...

... ...

~

60.57

...

195

Moles

... ...

0. 04 16.39

11.0

12 0

100.0

39,43

RESIDCE .Vole . . .

0: 1 41 41 . 6 27.9 30.4 __

100.0

S T E P 2. At the temperature of the condenser the pressure must Le such that the overhead ga.j or distillate is at its dew point, since it was separated from a liquid condensed from it by cooling at constant pres pressure sure.. T herefore herefore,, th e partial pressure of each component in the gas must of necessity equal the partial pressure of that same component in the liquid from which th e gas was last separated, an d with which it was in equilibr equilibrium. ium. Kow a t the effecti effective ve con condenser denser temperature, 294 K., the pressure of of pure eth ane is 38 atmospheres, of propane 8.8, an d of buta ne 2.2. Consequently, one can write the following equations: pz = 3822 = 0 . 1 4 9 ~ p , = 8 8 ~ 3= 0 . 4 1 2 ~ pa = 2.224 = 0.01 T

Furthermore, neglecting the solubility of methane and permanent gases in the liquid, the sum of the mole fractions m us t obvio usly be unit unity-i. y-i. e., x~ x z4 = 1. Solving these equations, one obtains s = 18.1 atmospheres, which is the necessary operating pressure on the condenser, and

+ +

which, neglecting pressure drop through the colunin, is the pressure pres sure throughout the apparatu s. From the above calc calcuulations, 100 x 2 = 7.1 mole per cent ethane in the liquid condensate, 100 z3 = 84.7 per cent propane, and 100 x 4 = 8.2 per cent butane. STEP3. Since, from the condenser on this equipment, the final overhead gas leaves in equilibrium with the total condensate, the figures just given also represent the composition sition ooff the reflu refluxx to the column. STEP 4. Assume a ref reflux lux equal to double the am ou nt of of overhead vapor. O n the basis of 100 moles of distillate, there will therefore be 200 moles of reflux reflux.. Co nseq uen tly, the vapor rising into the partial condenser from the top plate will have the composi composition tion show n by th e fol followi lowing ng table : Total m o l e s

CHI = 4 2 . 9 C?.Ho = 1 4 . 9 CSHO = 4 1 . 2 CiHio =

+ 14.2 = + 169.4 = 1.0 + 16.4 =

?&

42.9 29.1 210.6

14.3 9.7 70.2

17.4 00.0

100.0

5

8

Since this vapor must be in equilibrium with the liquid on the top plate, one can write the following equations: 1

=

320

1 . 7 5 5 = zzPz P3 = 0 . 7 0 2 ( 1 8 . 1 ) = 1 2 . 7 = Zap3 PI = 0 . 0 5 8 ( 1 8 . 1 ) = 1 . 0 5 = z ip Pz = 0.097 (18.1) =

K

P

64 17 4.65

0. 027 0.747

0 226 1 ,000

These equations cannot be solved directly because they contain six unknowns for three equations, although there relationshi ionship, p, x = 1. How ever, the va lues ooff is the fourth relat Pz a , a n d P are determined by the unknown temperature of the top pl plate. ate. T his ttemperature emperature mu st be such th at it will will satisfy th e above relati relation. on. It can easily be determined by successive approximation. As a ma tte r of fact, in thi s case the top-plate temperature is 320 K., a t whi which ch temperatur e th e pressure pressure of of each pure com ponent an d the corre corre-sponding mole fraction in the liquid phase on the top plate are shown in the two columns following the equation. It will be found that at no other temperature will the equations be satisfied. satisfied. While solution by successive approximation is always in a certain sense unsatisfactory, in the

 

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case of equ atio ns of this typ e a little experience soon m akes it easy. ST E P 5 . The composition ooff the boil boiling ing liqui liquidd in t he still is known. Further more , it is boil boiling ing under a pressu pressure re ooff 18.1 atmospheres. Consequently, the temperature of the

C HEM I

S

I

T

VOI.

24,

NO

5

When one endeavors t o make a hea t balance o n this column to determine the reflux reflux a t the bottom, one fi finds nds tha t the data available on hea t ooff vapo rizatio n a t these hi high gh pressures 1) ar e unsatisfactory, particularly in the case of th e highhigh-boiling boiling constituents (i. e., the liquid boiling in the still). Csing the highest values which the available data would indicate as possible, the overflow decreases somewhat as one goes down the column. Using lower values gives an opposite result. I n order to eliminate con confusi fusing ng complications, complications, it wil willl change ther therefore efore ed th and at, in th e case ooff in thisthecolumn, the in be theassum overflow consequently vapor rising up the column is negligible from plate to plate except a t the feed plate. Hen ce, on the basis ooff 100 pa rts ooff feed, the overflow in the upper part of the column is 2 (60.57) = 121.1, and the vapor, 3 (60.57) = 181.7. Th e corresponding values below the feed plate are 176.3 and 136.9. STEP 7. The Hausbrand equation of the operating line above the feed plate is

However, in this equation th e term P , is unknown because However, one does not know th e tempe rature of th e plate below. This mu st be assume d, the value of P read off for each component, the corresponding values of z c o m p u t e d , a n d t h e process repeated until a value of t is found which makes = 1.

1

= 331

+ 0.899 = + 2.485 = 12,06xn+i+ 0 0603 =

Pmz = 12.OGzn+i Pax3 = 12.06xn+i =

Pmr

FIGURE

CONCENTRATIONRA D IEN THROUGH

CaHs C4HlO CaHiz CBHl4'

0.1 41.6 27.9 30.4

= 413.5

P 80 32.2 13.3

K.

P

0.08 13,39 3.71 0.90 18.08

2 95

0.014 0.536 0.450 ,000

(as ) 0.44 74.06 20,52 4.98 100.00

Th e composition ooff th e liquid on the second pla te down is given in the last column. B y repetition of this process, using the same equations but with the proper values of a n d x n + 1 one can go down the column from plate to plate T he Hausbrand equation bel below ow the feed plate is

Y

The composition of the vapor from the still is given in the fifth column. STEP . It is first necessary to determine the condition in which which the feed enters the column . This calculation calculation is most easily made by reference to the following equation, derived from Raoult's law and a mater ial balance. Call N the total moles of feed which enter in the liquid state per 100 moles of to tal feed, th e to tal moles of a given compon ent per 100 moles of of feed, an d n the moles of the component entering in the liq liquid uid in the feed feed.. E quality of input and output giv gives es

no= +;(+)

P 90 21.5 6.2

1.23 11.52 2.79

CoLu>rN

still must be determined by successive approximation as i n the preceding case, and Zy must. equal unity. Th e technic is shown shown in th e following table: t

K.

100 -

n

The equation is applied successively to each component and the condition imposed that Z n = N . At the feed temperature, 311 K., the pressure of ethane is 53 atmospheres,' of propane 13. 13.7, 7, buta ne 3.7, pentane 1.05, an d heptane 0. 0.11 11.. Solving these equations, N equals 55. 55.2. 2. In other words, the feed rest gas. enters this column as 55.2 per cent liquid and the This temperature IS above the crltical point of of etha ne. However, for the purpose of romputing t he small amount of ethane which wlll wlll dlssolve dlssolve in the liquid under theae conditions, in the absence o off exact d at a as to th e solubility, it is allowable to extrapolate the vapor pressure curve to the t emper at ur e i n question. The figure is rough but undoubtedly sufficiently accurate for the purpose In hand

-

= zm

PT

zul

TO

= 0.0429xmP,

+

0.2237~,

Since the temperature of the still is known, the corresponding values of P are determined, and one can calculate the composition of of the overflow from the plat e a bove directly as shown by the equations in the ffoll ollowing owing table. Th e arithmetical accuracy of the operation is checked by the summ ation of the concentrations to unity . How ever, bbeefore one can proceed further up the column, it is necessary to know the temperature ooff the plate abov above. e. T his must be such that the pressure will be 18.1 atmospheres. It is determined by successive approximation as before, as shown in the last two colum ns ooff t he table: = 395 23

24 25

2 7

= =

0.0429zmPm 0.0429zmPm 0.0429zmPm 0.0429zmPm

+ + +

+

0,000224 0,093 0,0624 0,068

K. = =

p Z 0.00365 62 0,6680 23.5 9.25 0.2214 0.1066 1.9

Pa

0.23 15.63 2.04 0.20

~

.99965

18.1

One can proceed from plate to plate up the column by repeating this step. S T E P 8. Working down the column from the top and uthe p t propane h e c o lu lu mand n f rbutane o m t h e concentrations b o t t o m i n t h i s come w a yy,, otogether n e f i nndd squite that rapidly. In other words, the refl reflux ux assumed is adequate. If a reflux ratio of one be assumed in this case, it is found that the concentration and temperature changes from plate to plate through the column are far less and are too small for satisfactor y operation operation.. In other words, a refl reflux ux ratio

 

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of 1: 1 is too smal small. l. E xac tly what ratio to use must be decided by th e engineer on the basis ooff this typ e of of computation , interpreted in th e light ooff th e operating conditions in question. S T E P . Th e conditions ooff t he various plates in the column thus com puted are given in Figure 1. It will be noted that four plates below the top plate the propane has fallen to 13.9 mole per cent, n-hile five plates above the still it has ris risen en to substantially substantially the same valu value. e. In other words, this ab ove it th eisstill ma y well be chosenthe as feed the feed plate.fifthIf,plate however, desired to introduce on plates above or below this point, this may be tried out by the methods now to be discus discussed. sed. ALLOWAKCES

OR

HIGH-

AKD

L O W - B O I L I N GIATERTALS

The difficulty with the computations so far conducted lies in the fact that they take no cognizance of pentane or heavier above the feed plate, or ethane below the feed plate. There is a certain amount of high-boiling constituents in the overhead overhead product. Ha d this bbeen een exact exactly ly known, it could have been allowed for in the computations, and the amo unt ooff these constit constituents uents in the upper pa rt of of t he column computed. Simil Similarl arly, y, had the exact da ta on the trace of of ethane in th e resid residue ue from th e sti still ll been been known, its am oun t up the column coul couldd have been calcul calculated. ated. Furthermore, the composition of of t he liquid on the feed plate as determine d by these two comp utation opera operati tions ons-i. -i. e., from the top down and from the bottom uupp-wo woul uldd be th e same. However, the analytical methods are incapable of determiiiing with precision these traces of the lowest-boiling, materials in the still still product and th e hig highest hest-boi -boilin lingg in t he overhead even in the case ooff a n operating unit. Still les lesss is the designer in a positi position on to predict these in advanc e. How ever. t o design the unit with assurance, allowance must be made for these factors. T heoreticall heoretically, y, one could could m ake th is allowance by assuming the am ount ooff these contaminating traces and check checking ing up by trial and error on the column calculations until the compositions on th e fee feedd plate come together. Th e followfollowing is a practical method of making suitable allowance for these corrections. Th e percentage ooff ethan e o n the feed plate m us t necessaril necessarilyy be les lesss tha n t he percentage of thiq thiq component on th e plate immediately above the feed. feed. However, assume, for the moment, th at these concentrations differ by a neg negli ligi gibl blee am ount and apply the Hau sbran d equation for ethane over the feed, .cqL

l

0 . 0 8 3 ~ J ' ~ - 0.0745

C H E RI I S T R Y

497

away rapidly and conditions then approximate those coniputed by figuri figuring ng down from the top . If one assumes a wrong value value of ethane on t he feed plate, dif diffic ficult ulties ies are encountered. Thu s, if th e value is too small, the equations will indicate a negative incrpment in ethane concentratio concent rations ns going going up the column a t some plate, usually the feed plate or the one above it. L arger as assumed sumed valu values es will will avoid this diffic difficulty, ulty, but, unless they are. correct, will indicate on the upper plates where the concentrations of pentane and higher have fallen to a negligible point-ratios of eth ane :pr opa ne: but ane whi which ch are out ooff line with those computed by working down the column and which, therefore, are incompatible with the column set-up. Thus, by successive approuimation, one can determine the proper ethane concentration on the feed plate. P L A T E NUMBER

FROM T

P OF

COLUMN

42

40

L

36

34

32 PLATE

FIGIJRE .

NUMBER

FROM

BOTTOM

OF

COLUMN

TEVPER HROUGH TURE G R ~ D I E U T

COLUMU

This process may sound involved, but aboye the feed plate the penta ne an d heavier usually fade out ooff th e picture quicklyy tha t the es estimation timation is reasona reasonably bly rapid. At any so quickl rate, it is far shorter and more satisfactory than the more obvious me tho d ooff estimating overhead an d botto m concentrations of of th e materials present in traces only and checking them by refig refiguri uring ng the whol wholee column. I n computing the ethane, it is desirable to express the amo unt on the feed plate to a pr preci ecisi sion on far beyon beyondd t ha t with which it can possibly be known, a precision unjustified, for example, by the uncertainty in the extrapolated value of P z which is is us3 us3dd in determining it. Th e reason for this is the extreme sensitiveness of of t he larger a nd im portant concentratio concentrations ns on t he plates above to very m inor chang changes es in this value of the Concentrati Concentration on on the feed plate.

The temperature of the feed is 3 6 3 IC., a t which 1 (extrapolated) is 125 atmospheres. Using this value and the assumpt i o n t h a t z,,+~ = xn, it is seen that the concentration of ethane on the feed plate mu st be a t least 0.00 0.00795 795.. As will appear later, it must actually be higher than this by a small amount. Below the feed plate the operating equation for ethane isz,-, = 0 . 0 4 2 9 ~ 2 , . B y m e a n s of t hhii s , o n e c a n r e ad ad iill y determine the ethane ethane concentrat concentration. ion. T hus, on the pl plate ate below the feed, the concentration is about 0.0015. O n t h e next plate below it would be 0.0003. It is obvious that quantities as small as this may be neglected. Now using

T he concentrations and temperatures thus computed are plotted in Figures 1 and 2. T he absci abscissas ssas are pl plate ate numbers indicated by subscripts 1, 2, etc. Where the point was computed from the bottom of the column, t he absci abscissas ssas are given given a t the bottom of th e fi figure gures; s; wher wheree computed f r om om t h e t o p t h e p l at at e n u m b eerr s a r e s h o m a t t h e t o p ooff t h e diagram. It wil willl be not ed t ha t these abscissas do not correspond exactly. exactly. T h e conce concentrat ntrations ions work working ing up meet the curve workin workingg down in between plates plates.. T his means that the column balance is not such that an integral number of

o nany desired assumed value for ethane the feed plate, plate, re remembering membering thathe t this valueconcentration m ust be some somew h a t b u t n o t m u c h a b o v e 0.008, one can calculate concentrations up the column from the feed plate by using the Hausbrand operating equation for conditi conditions ons above th e feed already employed above. Doing tthis, his, one fi finds nds tha t th e concentration of pentane and heavier above the feed fades

in Howtheoretically way. ever, as in theperfect case ooffplates designwill ooff cfunction olumns for this binary mixtures, using the next largest number of integral plates will give a column which will give a somewhat hetter separation. I n this case, as in the ordinary one, it is unne unnecess cessary ary t o try to readjust top and bottom conditions so that the plate numbers come o ut exactly int integral. egral.

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It is w orthy of note that the temperature gradient of Figure 2 is nearly uniform above and below the feed plate. This is quite different from the corresponding plot of a binary mixture, where the temperature gradient is large near the feed plate and small toward both ends ooff th e column. This difference is due to the fact that, in complex hydrocarbon mixtures of several components, the components of intermediate boiling point accumulate in the middle of the column in a way th at effectivel effectivelyy flattens out th e tempera-

butane. Using Using Raoult’s law, the vapor in equilibrium with this liquid should contain 47 per cent propane and 49.3 per cent butane. A s ample of the vapor rising from this plate showed upon analysis 49.3 per cent propane and 53.8 per cent butane. In other words, words, the vapor ri rising sing from the plate w as richer in butane and poorer in propane than it would have been had it left the plate in equilibrium with the liquid liquid on it. This is anoth er way of of saying that th e liquid on the plate had not completely dissolved the butane

ture It curve. should be clear that the low-temperature portion of the curves is calculated down from the t op of th e column, and the high-temperature high-temperature part up from the bottom. These two portions blend in tangentially where they meet. However, if the upper portions are continued down, they give a too low value of temperature and a too high value of the low-boiling constituents, because in calculating downward from the top it is impossible to allow for the high-boiling constituents. This portion of the curve is shown dotted in Figure 1. The only point regarding the concentration curve which merits special special attentio n is the accumu lation ooff butan e in the middle par t of the co column. lumn. This iiss the component of boiling point intermediate between the bottom and top temperatures of the column, and, as already indicated, this accumulation in the middle of the column is characteristic. The slight rise rise in butane concentration on the firs firstt plate above

ou t ooff the vapor rising rising into the plate, down to the equilibequilibrium value. However, the dif differe ference nce in com position is small. Th e vapor approached closely closely to equilibrium equilibrium with the liquid, which means t ha t th e plate effici efficiency ency was reasonably high. It is very desirable that accurate determinations of ac tua l plate efficiency efficiency an d ooff th e heigh t ooff th e equivalent theoretical plate for the different types of tower-filling used in the indus try be mad e in order to s erve as a s uitable guide for designing and operating engineers.

the feed feed is more striking. While the general tren d of of buta ne concentration above the feed plate is downward, a rise of this sort may occur where the temperature is sufficiently high to give a value of P , sufficient to reverse the slope of the Hausbrand line. Dependable data as to plate efficiency in natural gasoli line ne columns are exceedingly exceedingly meager, meager, b ut all the indication s are tha t the effi efficie cienci ncies es are high high.. Th us, a sample ooff th e li liquid quid on the plate in the upp er pa rt ooff a colu column mn gave upon analysis 15.7 mole per cent propane and 70 mole per cent

SUhlM.4RY

The H aus brand equation for the calculation of plate-toplate concentration gradients in the rectification of binary mixtures can be applied directly to the calculation calculation of of gradients in the isopiestic rectification of mixtures however compIex, pIex, provided the composition of the feed feed and the point and sharpness of of cu t be known, an d the co mpo nents of of th e mixmixture follow Raoult’s llaw. aw. These equations are, therefore, therefore, direc tly applicable in the design design ooff rectificati rectification on equ ipm ent for natural or refinery gasolines and, in general, for any mixture of hydrocarbons in which the concentrations of the individual components are know n.

LITERATURE ITED 1)

M cAd ams, W . H., and Morrell. J. (1924).

C

IN

ENO

’HEX..

6. .