T H E JOURNAL OF I N B USTRIAL A N D ENGINEERING CHEMISTRY
492 90 per 90 per Crude Criidr
Per cent of Light Oil Used cent crude benzene 70 0 cent crude toluene 13 5 light solvent 4 . 5 F. D. 130’ C. heavy solvent 4 . 5 F. D. 160’ C.
Distillation 90 per cent 100° C. 90 per cent 120° C. 90 per cent 160° C. 90 per cent 200‘ C.
with caustic soda, soda-ash or milk of lime, and is then fractionated in a column still if a C. P. product is desired. T h e cuts are:
2.5
5,O -
TOTAL............^^^
The crude heavy solvent may be used directly as a fuel oil or as a solvent in mixing pitch paints. By polymerization large yields of re& may be obtained from this fraction. Naphthalene is separated from the naphthalene-wash oil residue by crystallization, and the wash oil is returned t o t h e scrubbing system, The crude distillation fractions are separately washed with sulfuric acid in lead-lined agitators. The benzene fraction is rather difficult t o wash down t o a proper color test, on account of the nature of t h e acid sludge produced in t h e washing. A clean separation is obtained in the toluene fraction. The light solvent fraction heats up violently and produces a very viscous and easily emulsified product. After a water wash, the acid-washed product is neutralized
C. P. toluene Rerun toluene Refined light solvent
Finished fore runnings C. P. benzene Rerun benzene ’
RCVdIIIP
Naphthalene Wash oil
Vol. 14, No. 6
The residue in the still is a resinous material, somewhat similar t o t h e polymerized coumarone and indene compounds found in t h e crude heavy solvent. This material is disposed of as a fuel, preferably mixed with crude heavy solvent or t a r . T h e refined light solvent is essentially a mixture of t h e three xylenes. These are separated by sulfonation t o remove t h e meta compound, followed by fractional distillation of the p- and o-xylenes. T h e writer has recently observed t h e manufacture of C. P. benzene in which the crude motor benzene fraction, containing all the benzene, toluene, and light solvent present in the original light oil, was washed and distilled for C. P. benzene. T h e products gave better color tests than were obtained by washing and distilling t h e 90 per cent crude benzene fraction, less acid was required, a better separation was obtained in the agitator, and very good yields of C. P. benzene were obtained.
‘The Efficiency and Design of Rectifying Columns for Binary Mixtures’” By W. K. Lewis DEPARTMENT OF CHEMICAL ENGINEERING, MASSACHUSETTS INSTITUTE OF TECHNOLOGY, CAMBRIDGB, MASSACHUSETTS
Basic equations of general applicability have been derioed, by means of which it is possible to calculate the theoretical rate of rectification within any column f r o m the terminal conditions and the amount of ooerflow, and compare this rate with that actually realized. The results of these calculations have been found to agree satisfactorily with actual tests. A complete example has been computed showing the use of these equations i n the design of Q continuous column, the determination of minimum ooerflow, of the best practical overflow, of the number of plates required and of the point of introduction of the feed.
A
FRACTIONATING column is an apparatus designed
to enrich the volatile components in the vapors arising from a still by allowing these vapors to interact with condensate produced by the partial condensation of the vapors previously given off by the same still. The most familiar type of column employs a succession of plates covered with liquid through which the vapor bubbles. The mahhematical theory of such a column as applied to the distillation of binary mixtures was first developed by Ernest S0re1,~ who calculated the enrichment from plate to plate by equating the amount of energy and of matter entering and leaving each plate and by assuming that equilibrium was realized between the vapors and the liquid through which they bubbled. Sore1 applied his method successively from one plate to the next in a column. In consequence the computations become very involved and it is difficult to visualize what is taking place. The following is merely a modification of Sorel’s method, which simplifies computation and makes it possible to present results in graphical form . The derivation will assume a column in continuous operation, with the feed, i. e . , the binary mixture to be separated, entering the middle of the column. The results may, however, Received April 11, 1922. Published as Contribution No. 16 from the Department of Chemical Engineering. M. I. T. 3 “La Rectification de l’alcohol,” Paris, 1893.
be applied to a discontinuous column a t any particular instant during its operation, provided the amount of condensate in the column is small in proportion to the amount in the still. CONSTANr MOLALOVERFLOW Where a column is large so that its surface area is small compared with the amount of vapor rising through it or where a small column is properly lagged, heat loss from the sides by radiation and conduction is negligible in comparison with the heat quantities carried by the vapor up through the column. As the vapor rises through the column and part of it condenses upon a given plate, an equivalent amount of liquid must be TTaporized from that plate so that its heat of vaporization will equal that of the condensed vapor.
1
2
FIG. 1
THE JOURNAL OF INDUSTRIAL A N D ENGINEERING CHEMISTRY
June, 1922
Liquids can be divided into two groups, the associating and nonassociating liquids. Within each group the molal heat of vaporization divided by the absolute temperature
493
overflow. Designate the point of origin of the particular vapor or overflow referred to by the use of a subscript: thus, V, is the moles of vapor rising from the n t h plate, while On+l is the moles of overflow coming down to that plate from the plate above. Use the subscripts f and c to refer to the feed line and to the condenser, respectively. Thus Of is the amount of feed and V, is the amount of product. Call the mole fraction of the more volatile component in the liquid x and the mole fraction in the vapor y. Again indicate the liquid to which reference is made by subscripts, thus xw is the mole fraction of volatile component in the waste or slop leaving the still a t the bottom of the column, while ym is the mole fraction of the same component in the vapor arising from the m t h plate. The quantities required in discussion are assembled in the following table: x = Mole fraction of more volatile component in liquid. y = Mole fraction of more volatile component in vapor.
V, = Moles of distillate produced per unit time. ye = Mole fraction of more volatile component in the distillate produced O n+ Moles of overflow from plate n+ 1 to plate n xn = Mole fraction of more volatile component in overflow 0, tl. Vn = Moles of vapor passing from plate n to plate n + l per unit time (both components included). yn = Mole fraction of more volatile component in vapor Vn. Of= Moles of the mixture fed t o the column per unit time (both components included), xf = Mole fraction of more volatile component in feed,Of. ow = Moles of waste per unit time. x w = Mole fraction of more volatile component in waste 0,. Ofn + I = Theoretically minimum overflow from plate n+l, per unit time,
-
0.1
0.2 0.3 0.4 05
0.6
0.7 0.8 0.9 LO
Mo/e fiadion o f &/coho/ /n//quid xn
FIG.Z - ~ A P O R COMPOSITION CURVEFOR ALCOHOLAND WATT~R
dn
is substantially constant, provided the boiling temperatures are not far distant from each other (Trouton’s rule). Since distillation is a serious problem only where the boiling points of the components are nearly the same, this is equivalent to saying that the molal. heats of vaporization of components in the column will be practically equal if both components are associating (water, ammonia, alcohol, etc.) or if both are nonassociating (hydrocarbons and most organic liquids). Let us assume temporarily that the two liquids in the column belong to the same group; hence their molal heats of vaporization are nearly the same. On the basis of this assumption, for each mole of high boiling constituent candensed out of the vapor a mole of low boiling constituent must be volatilized from the liquid, or in other words, above or below the feed plate, both the molal overflow from plate to plate and the moles of vapor passing up the column must be constant or nearly so throughout the column. The moles of vapor will, however, obviously be greater below the feed plate than above if the feed enters below its boiling point, since some vapor must condense to heat it up. In all cases the overflow is greater below the feed plate than above it, as a result of the amount of mixture fed into the column.
= Rate of increase in concentration of liquid per plate.
k = Fractionation efficiency of the tower and plates, i. e., ratio 01 theoretically required to actual requirement.
n = The number of the plate under consideration, counting from the feed plate up. The number of the plate under consideration, counting from the feed plate down. Qn = Heat of vaporization of Vn (molal). r, = Heat of vaporization of more volatile component (molal). 7% = Heat of vaporization of less volatile component (molal).
m
=
hTO1fENCLATT;RE
The nomenclature is indicated by Fig. 1. In this figure there is shown for sake of simplicity a Gngle condenser, so that the overflow back into the column is of the same composition as the product. However, this has nothing to do with the derivation and does not affect the validity of the formulas. Let each plate be designated by a number. Start numbering the plates from the feed plate upward and downward, the plate on which the feed enters being the zero plate. Call any particular (variable) plate above the feed plate the n t h plate and below it the mth. Call the top plate the p plate and the still, or, if none, the bottom plate, thew plate. Call the amount of vapor, measured in moles per unit time, passing any particular section, V, and the amount of liquid for overflow passing the section 0. These quantities are to include the moles of both components in the vapor and
FIG.3-vAPOR
ALCOHOLA N D Low CONCENTRATIONS
C O M P O S I T I O N C U R V E FOR
WATER AT
494
THE JOURNAL OF INDUSTRIAL A N D ENGINEERING CHEMISTRY
While the reasoning employed and the equations developed are general, it is easier to visualize each step and appreciate its significance by discussion of a special case. Consequently the following will refer to the case treated by Sorel, the
For conditions of perfect rectification below the feed plate, one can derive similarly Am =
l,"
dx
- (o;-v,)
Ym-xm
Mole fracf/on of a/coho//n /iqu/d x, FIG 4-v.4~0~ C o M P o s i T I o s CURVEF O R A I . ~ O H OALN D
+ Vc
Furthermore the total alcohol entering this section must equal that leaving it, i. e., xz
+I
+ YCVC.
On + I
Whence. and Xn
+i
-
En =
y n - Xn
vc
-
BETWEEN CALCULATED AND
ACTUAL REFULTS
IN
DISTILLATION
BASICEQUATIONS Consider the whole apparatus above a section drawn between the nth and the ( n + l ) t h plate just below the latter. The only thing entering this section is the vapor from the nth plate,~V,, Leaving it is the product Vc, and the overflow from the (n 1 ) t h plate, 0, + 1. Therefore
yn V n =
(4)
Plate number F I G . &-AGREEMENT
separation of alcohol and water, alcohol being the more volatile component.
V n = Onti
(ym-xw),(Of+On+,)
W A T E R A T HIGH
COXCENTRATIONS
+
Vol. 14, No. 6
(yc-yn)
(2)
This quantity, x, + 1 - Zn, is the enrichment per plate, i. e., frow one plate to the plate above it. Since this enrichment is usually small, it .is substantially identical with the slope of the curve obtained by plotting composition, x, against number of plates, n, i. e . , it equals d x l d n . Hence
In using these equations, it must be kept in mind that, even in an indefinitely tall column the rate of rectification, dz/dn, must be positive and cannot possibly be less than zero; whence inspection of Equation 3 shows that the ratio of reflux to distillate cannot fall below the theoretically minimum value O'n
+i/Vt
L (yc-yn)/(yn-xn)
(5)
Similarly below the feed plate, 0 'm +i/(Of- Vc)
2 (ym - X W ) /(ym - x m )
(6)
Indeed the overflow at each point in the equipment must be kept distinctly larger than these limiting minimum values in order to have rectification go on in the column at a reasonable rate. Inspection of Equation 3a shows that the integral may easily be evaluated in the case already referred to, where the molal overflow O m + i is constant from plate to plate. This is substantially the case for alcohol-water mixtures and for all mixtures of hydrocarbons whose boiling points are close together (e. g., benzenertoluene, etc.). This simplification makes it much easier to visualize what is happening
I,
dx/dn = y n - x n
VC -(yc-yn) On +i
(3)
Since these equations represent nothing but equality of input and output, their validity cannot be questioned. Their utili&, however, is limited by the uncertainty as to the relation between zn and y, actually existing in a column. If we assume perfect rectification, i. e., that equilibrium is realized between the liquid on a plate and the vapor rising through it, these equations are valid and can be used to calculate the theoretically minimum number of plates required for a given rectification, by combining them with the experimentally determined relation between R: and y for the mixture under consideration. Calling An the number of plates necessary with perfect rectification to enrich from x1 to xz,integration gives dx A= = L r Y w
- xn - vc(yc - y n ) / o n + I
Q
0.3 --.
.Q
*
$ o.2 .Q
0
0.1
-*
$
1
1
I l l
Plofe number
(3a) F I G . 6-AGREEMENT
which may be evaluated graphically.
-
Poinfs experimen fa/ by Soref. See Mariller V i s filla fion, f rac fionn &e, ef la Recfifieafton"
B E r W E E N CALCULATED AND
DESTILLATION
ACTUAL RESULTS
IN
495
T H E JOURNSL OF INDUSTRIAL W D EhrGINEERING CHEMISTRY
June, 1922
/50
/40
130 120
/lo /OD 90 80 70 60
50
40 30
20
/O 0.M
FIG. 7 - M I N I M U M
OVGKFLOW ABOVE
FGBD
i40
I30 120
//o 100 90
$0
70
60 50 40
30
Y F I Gg. - d n / d x
PIS. xYzAT
O =5 O M(i~.rs FEEDPLATE. PROBLEM
0.2 0.3 0.4 0.5 0.6 i
x,
X,
/50
%-x
0.1
0.10 0.30 0.40 0.50 0.60 0.70 0.80 0190
Mole fiacfion ukohoi in the liquid
FIG. B-dn/dx
us.
xn
ABOVE THE F E W PLATE.
PKonLLCM 0 = 5.0
MOLES
T H E JOURNAL OF INDUSTRIAL A N D ENGINEERING CHEMISTRY
496
in the column and is therefore adopted in the following paragraphs.
Vol. 14, No. 6
ing columns the influence upon IC of type of plate, rate of flow of vapor and of reflux, etc., in order to be able to use these equations in problems of column design with safety and assurance.
APPLICATION OF FOR~IIULAS-DESIGN OF CONTINUOUS RECTIFYING EQUIPMENT
xn FIG. 11--dn/dx
us. rn
BELOW THE
FEEDPLATE. PROBLEM 0 = 5.0 MOLES
Quantitative discussion will be limited to alcohol-water mixtures, and plots of vapor composition, y, as a function of liquid composition, 2 , are given in Figs. 2 , 3, and4. The two last give the data a t the two extremes of the curve.
TESTRESULTS
I n order to illustrate the value and method.of use of these equations the following typical example is worked through. It is desired to rectify continuously a 10 per cent alcohol solution to produce a 94.5 per cent product and leave only 0.l per cent alcohol in the waste, using the type of equipment shown in Fig. 1. m h a t overflow should be used? What will be the height of the column required and a t what point should the feed be introduced? The best amount of reflux depends upon an economic balance between overhead charges and operating cost. This can be determined only by a knowledge of the relation between the amount of overflow and the number of plates required. The value of /c has been assumed constant and equal to 0.8. Four different amounts of overflow have been assumed, i. e., 3.8, 6, 10, and 20 moles per mole of product, and for each the number of plates required determined. Complete methods are shown for the second case (6 moles overflow per mole of pyoduct) and all others have been calculated similarly. Fig. 7 shows the minimum overflow as calculated for various points in the column above the feed plate. Inspection shows that unless the feed is introduced at a point lower than TC = 0.028 the minimum overflow will be 3.00 moles, representing the minimum allowable at 5 = 0.835. The minimum overflow below the feed plate is not shown, as calculation later shows that any overflow sufficient above the feed plate, together with the feed itself, is more than the minimum overflow below the feed. Knowing k , and assuming a value of 5.0 for 0, Figs. 8, 9, 10, and 11 have been calculated from Equations 3a and 4, and graphic integration under these curves gives the required 2 vs. n curves of Fig. 12 which are enlarged in Fig. 13 in the neighborhood of the feed plate. Especial attention must be given to Fig. 9, which shows the reciprocal of the rate of enrichment as one goes up the column. Note that the enrichment curves for the bottom
No adequate data are available in the literature to test out properly these methods of computation. Mariller4 quotes results of tests on alcohol-water mixtures by Sore1 and himself, but does not give overflow. By estimating both overflows and plate efficiencies from the data he does give, and substituting these in Equation 3a the curves of Figs. 5 and 6 have been calculated. The points shown are the experimental data given by Mariller. Inspection of these figures shows that the equations correspond in type to the experimentally determined results. PLATEEFFICIEKCY
It is obvious that in practice equilibrium will not be reached between vapor and liquid. The number of plates actually needed for a given enrichment divided into the number theoretically necessary according to these formulas may be called the plate efficiency of the column. This will obviously vary with type of construction. If in a given column, with a given overflow and a given vapor rate, the plate efficiency, k , is otherwise constant from plate to plate, as is not improbably the case, this quantity k may be multiplied into An in Equation 3a or Am in Equation 4, and these equations then become applicable to actual columns. It is necessary only to determine from experimental operating data upon exist4
“Distillation FractionCe et la Rectification,” Paris.
P!afe number FIG. I2-CALCULATED
VAPOR A N D LIQUID ENRICHMENT IN COLUMN. PROBLGM0 = 5 . 0 MOLES
.
