MAY, 1940 H
INDUSTRIAL AND ENGINEERING CHEMISTRY
total moles of holdup of all components in the column proper (exclusive of holdup in the condenser) n = equivalent number of plates in column y. = mole fraction of more volatile compound at a point equivalent to s perfect plates removed from still pot B = distance up the column, the unit of which is H. E. T. P. a = vapor pressure ratio of two components, assumed to be constant over range involved in any given distillation 2 = mole fraction of more volatile component in still pot when L total moles remain in still pot L = total moles in pot at any time y = mole fraction of more volatile component in product being removed when there are L moles in pot K = integration constant =
675
= mole fraction of more volatile component in still a t instant
XI
first drop of product is removed mole fraction of more volatile component in charge moles charged to still = 100 Lo I = moles of intermediate fraction as per cent of charge = =
20
Notations introduced for convenience in writing:
bf='
b x a n - 1 z = log (1
-I =
b p kl,kn = constants
+ bx)
a'
General Equation for a Batch Fractionation Curve ARTHUR ROSE
dL
z ax -f L
I N C E experimental data are lacking on the variation of H. E. T. P. values along the length of a column and also on the distribution of holdup, and since i t may be confidently expected that the nature of these functions will vary in specific cases, the generalized expression,
t
S
h = fx
. . . .)
(2,
dL
L y-x
dL ax
The first two papers showed that equations could be derived for calculating the distillation curves for batch fractionation if certain simplifying assumptions were used. The use and limitation of the resulting equations were indicated. This paper indicates the method of derivation and the form of the equation obtained when no simplifying assumptions are involved in the derivation. The resulting equation may be used for the calculation of any specific distillation curve, but it is necessary to use a graphical method similar to that described in connection with a previous discussion of the Rayleigh equation (page 673).
-y
+ cf,v(x, . . .) = -&(x,. . .) -cf;y(x,.. .) +fk (2,.. .) t
. . . *)
(2,
(30)
Y --z ax
where
A=$=
The indicated integrations can always be performed graphically if necessary, and Equation 31 is thus essentially an expression of the form, L = Icfi(Y)
+MY)
(32)
which is the desired relation between product composition and product distilled. The functions f i (y) and f2(y) will involve the various quantities characteristic of the mixture, column, and other conditions of the distillation under consideration. By variation of one of these a t a time the importance of each in a real distillation may be more or less exactly I
I
I
I
I
I
I
I
I
I
I
F/GUR€ 10.
(25)
I
will be used to represent the holdup of the more volatile component in the column. The relation between product and still composition will also be used in the generalized form, Y = fN
(29)
(26)
so that the derivation will not be limited by the applicability of Raoult's law or the matter of the constancy of the vapor pressure ratio or other usual simplifying assumptions. Proceeding now to make a material balance just as before (page 673) but including terms to represent holdup in t h e condenser, me obtain a basic differential equation which may then be solved as before:
L
R
predicted, depending upon the number of simplifying a s s u m p tions used.
Consideration of Reflux Ratio When holdup is inappreciable, Equation 31 reduces to the ordinary Rayleigh equation, and in such cases the effect of reflux ratio in any specific case may be calculated by the graphical method indicated in the first paper. The curves of Figure 10 were obtained b y this method. I n cases where holdup is inappreciable and the Smoker equation (11) is valid, the latter may be used to eliminate z from the ordinary Rayleigh equation.
INDUSTRIAL AND ENGINEERING CHEMISTRY
616
When holdup is appreciable, Equation 31 may be solved by a graphical procedure after correctly establishing fN(z) and fH(z)by graphical means or otherwise. When the Smoker equation is valid, it is possible to obtain definite functions of the form of Equations 25 and 26, so that the second term of Equation 31 may be expressed and integrated in terms of Smoker’s quantities.
Generality of Equation 31 Equation 31 is general and in particular is independent of whether functions fx and fN are expressed by means of a Raoult law relation with reference to reflux ratio, by the diffusion concepts of Chdton and Colburn (a), or by some other theoretical or empirical relation. The integrations involved can always be performed graphically if mathematical methods fail, although the latter are usually preferable even if various approximations must be used because more general conclusions may be reached. The validity and usefulness of Equation 31 depend only upon the validity and nature of the basic functions fH and fN, and both experimental and mathematical work is under way with the objective of expressing this equation in a comparatively simple general form not involving any untested assumptions or approximations. Such an equation and those derived from i t would obviously be powerful tools in studying the design and operation of batch fractionation columns, as well as other apparatus for batch separation processes of all types.
Nomenclature fH
= generalized function relating still composition to holdup
of more volatile component
VOL. 32, NO. 5
j~ = generalized function relating product composition to s t i composition in terms of a,n,R, or any other characteristics of the mixture, column, or conditions used in a dis-
tillation
j ~jz, = notations introduced for convenience
jh,fi c e
=
derivatives off^ andfnr, respectively, with respect to z
= holdup in condenser = base of natural system of logarithms
R = reflux ratio (ratio of overflow to product) (Other symbols have the same meaning as in the second paper of the series.)
Literature Cited Bogart, M. J. P., Tram. Am. Inst. Chem. Engrs., 33, 139 (1937). and Colburn, A. P., IND.ENQ.CHEM.,27, 255, Chilton, T.H., 904 (1935). Cryder, D . S., private communication. 24,482 (1932). Fenske, M. R., IND.ENQ.CHEM., Fenske, M. R.,“Science of Petroleum”, pp. 1630-2, Oxford Univ. Press, 1938. Ibid., pp. 1659-60. Lewis, W. K.,J. IND.ENO.CHEM.,1,522 (1909). Lewis, W.K.,and Robinson, C. S., Ibid., 14, 481 (1922). Peters, W. A,, Ibid., 15,402 (1923). Rosanoff, M. A., Bacon, C. W., and Schulze, J. F. W., J. Am. C h a . Soc., 36,2000 (1914). Smoker, E. H., Tram. Am. Inst. C h m . Engrs., 34, 166 (1938). Smoker, E.H.,and Rose, Arthur, unpublished work. Walker, W. H., Lewis, W. K.. McAdams, W. H., and Gilliland, E. R., “Principles of Chemical Engineering”, p. 532, New York, McGraw-Hill Book Co., 1937; Badger, W. L.,and McCabe, W. L., “Elements of Chemical Engineering”, p. 336, McGraw-Hill Book Co., 1936. Young, S.. “Distillation Principles and Processed’, p. 117, London, Macrnillan Co., 1922. (15) Ibid., p. 120. PR~SENTED before the Division of Physiod and Inorganic Chemietry at the 97th Meeting of the American Chemical Society, Bsltimore, Md.
Partly Aromatic Constitution of Artificial Carbohvdrate Coals J
E. BERL AND W. KOERBER Carnegie Institute of Technology, Pittsburgh, Penna.
ISCHER and co-workers (8) as well as Bone (2) have defended the viewpoint that natural bituminous coal could not have been formed from cellulose and other carbohydrates, because when these materials are oxidized with air under pressure in the presence of alkali or are oxidized with permanganate and alkali, only aliphatic oxidation products are obtained. Katural bituminous coals give oxidation products of partly aromatic nature just as lignin and its derivatives do. Therefore i t was concluded that the aromatic lignin, and not the aliphatic carbohydrates, is the parent material of bituminous coals. The error of such a conclusion comes from the fact that those authors investigated the oxidation products of cellulose and other carbohydrates and not the oxidation products of cellulose coals. The chief object of this study was to determine whether cellulose coals would also give aromatic products through oxidation. If this could be confirmed, the objections of Fischer and of Bone would be void. The preparation, oxidation, and isolation of those products are described here.
F
Experiments on Cellulose Coal PREP-~RATIOK. Two hundred grams of cotton linters were heated in a rotating bomb with one liter of 0.05 N sodium hydroxide solution a t 325” C. A black solid coal and small amounts of black tar which solidified at room temperature were separated by filtration from the dark-colored acid solution. The analysis of these reaction products gave: carbon 79.93 per cent, hydrogen 4.89, ash 4.5 (calculated on an ashand water-free basis). OXIDATION. A 118.3-gram portion of this wet cellulose coal, corresponding to 74 grams of dry material, was ground to 150 mesh and oxidized with about 400 grams of hydrogen peroxide (1333 grams of 30 per cent hydrogen peroxide), diluted to about 5 per cent hydrogen peroxide content a t room temperature. Every day for 12 days 33 grams of hydrogen peroxide (110 grams of 30 per cent hydrogen peroxide) were added. In order to stabilize the peroxide, 20 CC. of a 40 per cent sodium silicate solution were added. The solution was kept slightly alkaline by the addition of the
