ISDCSTRIL4LA S D ESGIA%ERISG CHEXISTRY
294
It is probable, therefore, that the lag phase is due to the necessity for the deyelopment of a sufficient number of bacteria capable of gron-ing at this low temperature.
5’01. 18, s o . 3
Further work on this point and on the nature of the bacteria entering into the reaction will be carried out in this laboratory.
Fractionating Column Calculations’ Relations between Height of Theoretical Plate, Radius of Packing Rings, and Nature of Liquids under Distillation in Packed Fractionating Columns By T. S. Carswell BATSSCHEMICAL C o , LANSDOWNE, PA
X THE packed type of column there is no one definite plate upon which the vapor and liquid approach equilibrium before passing to the succeeding plate. Instead, the interchange between vapor and liquid takes plnce gradually as they flow past each other in opposite directions. A definite length of packing is therefore required t o produce the same effect as one perfect plate, and Peters2 has termed this length the “height of the equivalent theoretical plate” (H.E.T.P.). This length Peters has shown t o vary with the liquid to be fractionated and with the radius of the packing rings. The manner in which the variation takes place may be mathematically analyzed in the following manner: Complete equilibrium between liquid and vapor is secured only when actual physical contact is obtained between the two phases. Therefore, the efficiency with which equilibrium is reached in any one section of the column will vary directly as the surface into which the backflow is broken up and indirectly as the volume of the space through which the vapor ascends. Consequently, the H.E.T.P., which represents the length of column in which perfect equilibrium is reached, will vary indirectly as the surface of the packing and directly as the \yolume of the vapor space, or
I
H.E.T.P. =
v
C-
S
(1)
where c = constant of proportionality V = volume of vapor space S = surface of paclung
As is well known, the most efficient column packing is secured when the height of each packing ring is equal to its diameter, since in this case there is most chance for even distribution of the packing and least chance for channeling. I n these calculations it will be assumed that the packing rings fulfil this condition. The surface S for one H.E.T.P. is the sum of the surfaces of each ring plus the surface of the column wall in that section, or S = 8 nrzm s (2)
-+
where r = mean radius of packing ring m = number of rings in one H.E.T.P. s = surface of column wall in one H.E.T.P.
Ordinarily, s is negligible in coinparison with 8ar2m,and therefore (2) may be simplified to S
=
8+tn
(31
The volume of the vapor space in one H.E.T.P. is the total volume of that portion of the column included in the H.E.T.P. less the space occupied by the solid portion of the packing rings, or V =vR2 (H.E.T.P.) - w ( r l z - r z z ) m where R = inner radius of the column rl = outer radius of one ring r2 = inner radius of one ring 1
Received October 9, 1925.
3
THISJ O U R N A L , 14, 476 (1922).
(4)
In dropping into the column the rings assume an irregular position, so that the radius of any one ring projected upon a line perpendicular to the axis of the column will vary between r and
d%,with an average radius of r(l?-).
De-
note this average radius by @. Then the average number of rings in one H.E.T.P. is R Z(H.E.T.P.) m = Q3r3
Substituting this value of m in Equations 3 and 4,and then substituting the values for S and V thus obtained in Equation l, we have
L -J When the packing has thin walls, as is usual, the term rl2- ry2 in Equation 6 becomes negligible, and Equation 6 Q 37 simplifies to H.E.T.P. = Cr
(7)
where the constant C includes all the multiplying constants. This equation means that for the same liquids and the same pressure of distillation, the height of the equivalent theoretical plate varies directly as the radius of the packing rings. Peters has indicated this relationship graphically, and from his data the following values of the constant C have been calculated for acetic acid-water mixtures. Mean radius of packing
Table I H.E.T.P. found Cm.
0.64
10 14 25 63 132
Cm. 0.16 0.32
1.58
2.54
C 62
44
Av.
40 39 52 47
It will be noted that the agreement between the values of C is quite satisfactory, with the exception of the first case, where T = 0.16. Here the radius is so small that the term
”*, neglected
112Q37
in Equation 7, has an appreciable magni-
tude, and its neglect introduces an error. The fact that the term R, the radius of the column, drops out during the derivation of Equation 6 indicates that under ideal conditions the G.E.T.P. is independent of the radius of the column. That this must actually be the case follows from the consideration that the number of rings in the column, and consequently the total surface exposed, varies directly as the volume of the column. Consequently, the ratio V:S must be constant and independent of the radius of the column. Peters also points out that the H.E.T.P. varies with the nature of the liquids that are under separation, and states
I.VDCSTRIAL A S D ESGINEERISG CHEMISTRY
March, 1926
that the H.E.T.P. is greater for liquids of high molecular weight. This fact may be explained on the basis of the assumption ma,de in Equation 1, that the H.E.T.P. varies indirectly as the surface of the backflow and directly as the volume of the vapor. At the boiling point the vapor volume of a unit weight of a substance is indirectly proportional to the molecular weight and directly proportional to the absolute temperature a t which boiling takes place. Consequently, in the case of a substance of high molecular weight, an equal volume of vapor comes into contact with a smaller quantity of backilow than in the case of a substance of low molecular weight. The surface of the backflow will evidently vary indirectly as its density at the distillation temperature. Then for different materials in the same column and with the same type of packing, the H.E.T.P. will vary directly as the molecular weight and density of the backflow, and indirectly as the absolute boiling temperature, or Md (8) T constant cif proportionality average molecular weight of substances under distillation
H.E.T.P. = k
where k
M
= =
T d
= =
295
temperature of distillation density of hackflow a t distillation temperature
Peters gives some data for the H.E.T.P. of various substances, using a 0.64-em. filling. From his data the writer has calculated the value of k in Equation 8. The data and the results of the calcuIation are given in Table 11. I t will be noted that k is, within the experimental error in this type of work, quite constant for the substances given. Calculations of the value of k from the data which Peters gives for nitric acid-water and acetic acid-water mixtures result in values of 200 and 316, respectively. These abnormal values may be due to the fact that the vapors of these substances are associated. Table I1
H.E.T.P. Av. SUBSTANCE Cm. mol. wt. Ethyl alcohol-water, 88 per cent 9.2 31.4 10.7 39.9 Ethyl alcohol-water, 88 per cent Methanol-water (taken as 50 per cent mixture) Acetoneethyl alcohol (taken as 50 per cent mixture) Benzene-toluene (taken as 50 per cent mixture)
Boiling point OA. 366 351
d 0.86
k
0.83
92 78
7.6
24.5
353
0.87
96
15.2
51.3
34 1
0.86
86
25.4
84.4
368
0.80
88
Av.
88
The Enclosed Continuous Filter' By Justin F. Wait WOOLWORTH
BUILDIIVG, NEW
Continuous filtration has effected large operating savings in many industries, but its use has heretofore been limited to comparatively free filtering materials because of the necessity of subjecting the filtered liquor to vacuum. Industrial development has demanded a continuous filter in which valuable volatile liquids may be handled economically even at elevated temperatures, and in which the pressure differential is not limited to that attainable between atmospheric and some lower pressure. To meet these requirements a continuous filter has been devised which is enclosed in a case, allowing the application of pressures as great as 14 kg. per sq. cm. (200
YURK,
N. T.
lbs. per sq. in.) and making possible a pressure differential up to 14 atmospheres as compared with the limiting value of a single atmosphere in vacuum filters. In addition to the greater pressure difference which it renders practicable, the new filter prevents exposure of either the cake or solution to the air where this may be deleterious and at the same time materially reduces evaporation losses. Highly flammable liquids may be successfully handled and the possibility of working at elevated temperatures greatly increases the efficiency of the filter as compared with others where viscous liquids must be clarified.
.... . . .. ,. .. ..
T
H E fundamental requirement of a continuous filter is that it shall provide means for creating a pressure differential across a suitable filtering medium so supported that a continuous discharge of clear filtrate and uniform cake of satisfactory quality may be maintained. This is best accomplished by a revolving drum carrying a filter cloth supported over chambers connected with the discharge. Pressure differential may be established by applying vacuum to the discharge or pressure to the feed or both. An enclosed continuous filter embodying these principles and designed €or use with either vacuum or pressure or both is shown in Figure 1. It difiers from the ordinary vacuum type in being enclosed and in having external controls and sight glasses to observe operation. These auxiliaries permit the enclosed filter to be operated quite as easily as the open type. Its workings may be mderstood by reference to the schematic diagram in Figure 2 . The perforated drum, 1, supporting the filter cloth revolves in the shell, 2, in which the liquid to be filtered is held a t the level 5 under superatmospheric pressure. Several hollow sections, 6, are constructed within the drum and these are connected to the fill
Received
October l , 1925.
trate outlet, 9, through drains 7 controlled by valves 8. At the opposite ends of these chambers valves 8-A and pipes 7-A connect to a supply of vapor under pressure for blowing back to lift the cake from the drum or for cleaning the cloth. For low pressure or vacuum operation the several valves 8-A may be replaced by a special filter valve located preferably outside the shell. As soon as operation starts the pressure differential across the cloth, produced by air, steam, or other vapors under pressure in the shell, starts a flow of liquid through it while the solids form in a cake. As the sections carrying cake reach the scraper, 3, the solids are removed and drop into the conveyor, RR, which dumps them into vertical chute 4 and thence to the receiving hopper. The vertical chute, 4, may be provided with an agitator, A , if necessary. The receiving hopper may also be provided with an agitator to insure uniformity and positive discharge through the valve F. If the product is powdery, the vertical chute and hopper may be eliminated and a mechanical discharge device similar to the Star feeder used. Where products can be sluiced away, water or other liquid for this purpose may be introduced directly into the conveyor trough and discharged through a throttle valve or nozzle.
