INDUSTRIAL AND ENGINEERING CHEMISTRY
AUGUST, 1935
CORRESPONDENCE Distillation and Absorption in Packed Columns SIR: I n the article under the above title by Chilton and Colburn [IND.ENG.CHEM.,27, 255-60 (1935)], it ~v:as explained, with reference to their Figure 5, that the separation due to one “transfer unit” could be represented by a difference in ordinates (change in vapor composition) equal to the mean difference between the equilibrium and operating curves. A simple method for approximating this mean value and so determining graphically the number of transfer units on the customary McCabe and Thiele diagram is given below. On the graph OABCD represents the equilibrium curve, and W F and FP the two operating lines. Two other curves, L M and M N , are drawn in through a series of points located with the aid of a pair of dividers, so that every point lies midway (verti-
977
metic mean and the assumption that the sections of theequilibrium and reflux lines over the ranges considered are straight is generally negligible. I n cases where, owing to convergence or to curvature, this is not the case, in place of the half-way line a quarter-way line may be used in the same manner to give onehalf a transfer unit per step.
T.BAKER E. 1. DU
PONY DE h’5hlOURS
&
C O X P A N Y , INC.
WILMINGTOIV, DEL. Map 10, 1935
Viscosity of Petroleum Products SIR: In a recent article, Fenske and McCluer (3)point out that it is not possible to represent their results on the correlation of Saybolt Universal viscosity and kinematic viscosity by a single simple equation, but that exponents greater than two would be T necessary. We have used their results to plot ~ K / against l/Tz (where ?K = kinematic viscosity in centistokes, and T = time of outflow in Saybolt Universal seconds) ; the type of curve obtained is shown in Figure 1. Such a curve is obtained when the relationship between ?e and T is given by an equation of the form:
where k , a, n are constants.
x a l l y ) between the operating and equilibrium lines. The construction is then carried out as follows: Starting, for example, at point F , a line is drawn horizontally to the half-way line a t E, and extended an equal distance to G. From G a vertical line is drawn to intersect the operating line at H , whence the construction is continued in the same manner. Working up t,he column is only slightly more dificult. Starting on s vertical line through F , point J is obtained by trial through which EL horizontal to the operating line is drawn so that it will be bisected by the half-way line. From point K so obtained, the process is repeated. The proof of the construction is readily obtained on the assumption that the equilibrium curve is a straight line over the range of one transfer unit and that the arithmetic mean difference may be used in place of the true logarithmic mean. If a vertical line is drawn through point E on the half-way curve to meet the equilibrium line a t Q and the operating line a t R, line QR, which is equidistant from Blf and 6°F in the trapezoid, BHFC, will be the arithmetic mean of the lengths BH and CF. I’urther, since G H F and ERF are similar triangles and E bisects GI“, then GH = 2ER, and QR = 2ER by construction. That is, the enrichment represented by GH is equal to the average difference between the equilibrium and actual vapor compositions over the range considered from F to H . The inaccuracy due to the use of the arith-
Vogel (6) has formulated such an equation for the Engler viscometer, and work (as yet unpublished) in our laboratory has shown that the Redwood No. 1 viscometer gives results which satisfy such an equation. This equation would thus appear to be general for short-tube efflux viscometers, as, in fact, Vogel believed. However, with the Redwood viscometer three distinct equations have been found necessary-one for each of the usual temperatures of test which are 70”, 140°, and 200” F. The results obtained by Fenske and McCluer indicate, within the limits of their experimental accuracy, that no such temperature effect is found w t h the Saybolt viscometer, although certain of the runs reported suggest pronounced cooling in the receiving flask. Calculation shows that Equation 1 becomes, for their experimental data :
T tlR
-
10
(1
X 2.16
- F)
Equation 2 has been used to construct the full-line curve in the figure, which adequately represents the data. An analysis of the runs where T was greater than 300 seconds indicates that the equation, VK =
0.216T
will fit these runs with an accuracy warranted by the results; to this simple form, Equation 2 reduces a t values of T above 300 seconds. It is interesting to note that this value of k rvas adopted in 1922 by the American Society for Testing Materials (1) but mas later discarded. The shaded area in the diagram contains thirty-six of Fenske and McCluer’s runs on oils, having times of flow greater than 300 seconds a t 100” F., and the height of this band corresponds to an accuracy of 0.7 per cent, approximately. A comparison of calculated kinematic viscosities from Saybolt Universal times is as follows, using some well-know equations in comparison with the smoothed data as evaluated by Fenske and McCluer and by ourselves, using Equation 2:
