Shaking of High Pressure Vessels According to the Resonance Principle
development
ANDERS BJORKMAN~ Swedish Foresf Products Research laborafory, Stockholm 2 6 , Sweden
N THE chemical industry mixing and agitation operations have been subject to considerable interest for many years. Several good solutions have been found and the problems can, in addition, be treated mathematically. Agitation under high pressure conditions is a rather recent variation in this field and valuable developments may still be made. This paper discusses a n almost forgotten principle-Le., resonance oscillations-which can be used to effect lively shaking and is especially applicable to heavy vessels used at high pressures,
I
is wanted, a more convenient way is t o use the rocking vessel which is standard equipment in American laboratories. When thorough mixing is required i t can also be done by stirring. Leakage through packing glands was formerly checked by a counter pressure of compressed gas. I n modern apparatus this counter pressure is built up in a small oil reservoir by a gas phase connection from the high pressure vessel. The oil acts between two glands and prevents any leakage from the vessel while its own leakage t o the outside can be easily reduced to a minimum Magnetic stirring ( 4 ) is also suitable for small sized vessels. A stirring rod with attached plate or the like is moved up and down (as in churning) under the influence of a n alternating magnetic field which can act through rather thick walls of a cylinder set on the cover of the pressure vessel. The strong agitation in these stirred vessels can only be replaced by lively shaking. Hoffman el al. have studied and compared the agitation in rocking and shaking vessels (6, 6). Conclusions as t o the degree of agitation were based on hydrogenation rates of nitrobenzene in
A
Rgure 1.
Diagram of an Oscillating System
1. Oscillating body 2. Spring 3, Double unbalanced weights (for which horizontal tercer equilibrate) 4, Dash pot damplne
f.0 Figure 2.
A simple and obvious way to achieve mixing in heavy vessels under pressure is to shake them in the same way as any other vessel in the laboratory is shaken. It is, theoretically, a n easy solution which may, however, cause practical difficulties and require very heavy equipment. When a moderate degree of mixing 1
Z
Amplitude vs. Ratio z
glacial ace tic acid. The observations and recommendations by these investigators are valuable. Shaking gave, under optjmum conditions, a hydrogenation rate which was three and a half times as fast as the best rate with rocking-type agitation. The advantage of shaking over rocking should become still more evident with more complex reactions-e.g., rpactions in which
Present address, Billeruds AB, Siiffle, Sweden.
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there are several phases which require intimate contact, or in which competitive reactions occur. With unfavorable conditions the rocking-type agitation may be useless.
Vol. 44, No. 10
maxjmum depend on the degree of damping. Low damping values allow high amplitudes. At higher values of z. the amplitude approaches a low final value. I n general, there are practical difficulties involved in maintaining an oscillation a t a point near the resonance-Le., the maximum amplitude-for any length of time. I n practical operations, the damping is caused by several factors, such as internal energy losses in the spring, resistance of air and, which is essential in the actual case, energy losses in a liquid shaken by the oscillating body. Energy may also be consumed at points of connection, in bearings, etc. An exact calculation of these quantities is very difficult if not impossible. Vertical oscillations can be uved for mixing and shaking (9). For a certain frequency, however, the amplitude must be sufficiently high to give the vessel a velocity downward which considerably exceeds that of gravity. This requires long and/or quick movements which do not make for easy construction. On the other hand, the ultimate degree of shaking will probably be obtained by vertical rather than horizontal oscillations.
4 Figure
3. Diagram of a Horizontal Shaking Device
Ii l'
I . Oscillating body 9. Shaker wrings
3. Supporting springs 4. Unbalanced weight
When the author constructed shaking equipment for complex high pressure work the principle of resonance oscillations was applied with great success ( 1 ) . The underlying calculations and two examples of actual performance are presented and the general value of the invention is discussed.
Theory A knowledge of the theory of resonance oscillations is essential t o an understanding of the construction and use of the new shaking device. For a further study of the basic principles involved, reference is made to the handbook by Marks (8). Figure 1 is a diagram of an oscillating system. Figure 2 shows the relationship, for this system, between the amplitude, A , of damped oscillations and the ratio, z , of the frequency (rotational) of the double unbalanced weights and that of the oscillating system. When the
Figure 5.
Shaking Device for H i g h Pressue Vessels
5. 6. 7.
A
Worm gear Electric motor Heating mantle
1 As a shaking device of wide applicability, the horizontal one offers greater advantages though it is not so easy t o design as the vertical one. Figure 3 is a diagram of an arrangement which has been found t o work very satisfactorily. The theoretical considerations below are based on practical observation on such an apparatus.
L
I
Figure
4. Amplitude vs. Ratio z in the Possible Types of Oscillations of the Device in Figure 3 (e)
Vertical
(b) Horizontal
(c)
Tilting
unbalanced weights have a slow motion there will be little or no movement of the oscillating body. When z approaches 1.0; the amplitude increases t o a maximum which is reached a t a z value eomewhat higher than 1.0, The position and height of this
The oscillating body, 1, is inserted between t-xo walls and connected to them by shaker springs, 2. Gravity is compensated for by two long supporting springs, 3. A simple unbalanced weight, 4, is placed away from the center of gravity of the oscillating body (leaving the middle part of the body free for attached vessels, etc.). T h e center of gravity, the axis of the unbalanced weight, and the center lines of the shaker springs lie in the same horizontal plane. I n the vertical plane through all springs, three separate oscillations are possible: (a) a movement up and down in the supporting springs, ( 6 ) the desired horizontal shaking, and (c) a tilting motion around the center of gravity. Since the supporting springs are weak compared to the shaker springs, the frequency of (a) will be very low compared t o ( b ) . The supporting springs must be designed to give (c) a frequency considerably higher than that of ( b ) . These matters are further discussed below. The unbalanced weight, 4, should be very light compared to 1, and rotated by a relatively small, regulated force-e.g., an electric motor in series with a rheostat. When the frequency of the unbalanced weight, 4, is raised steadily the three indicated types of oscillations will appear, one after the other. They desTelop slo~*lyand will not have time to
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October 1952
reach a maximum amplitude while z passes over the corresponding resonance regions (cf. Figure 4). This is especially true for (a) because it is very slow. The desired oscillation, ( b ) , will come t o a certain amplitude while (a) vanishes. When z exceeds 22 (a) will cease to grow. At this oint, the energy input in 4 becomes much higher and (c) soon reactes almost its maximum, which is moderate because it is strongly damped.
safet factor. (Modern handbooks, such as the American 8ociety of Mechanical Engineers Boiler Code, prefer to give allowable stress instead of safety factors.) r, b, and n are shown in Figure 7 A combination of Equations 1 , 2 , and 3 gives: y=-
7
1
Svb3 2xmfkB
(4)
The mounted springs are prestretched so as to avoid backlash and to promote silent operation and longer life. Thus, the lengLh off should be that of the maximum desired stroke (double amplitude) or somewhat more. The minimum length, L (Figure 7 ) , of the unstressed springs can be ( n 1) X 2b but L may conveniently be a little longer. For the calculation of a shaker spring, an arbitrary value of b is chosen; r is obtainec from Equdtion 4 and n from Equation 3. If the resulting values of n and L are inconvenient, another value of b is tried, and so on. A figure somewhat lower than S , is recommended for use in Equations 3 and 4 if the springs can still be given a convenient performance. Supporting Springs. The spring constant, k,, of the two (vertical) supporting springs depends on kh of the shaker springs according t o the equation:
+
Figure 6.
Shaking Device for H i g h Pressure Vessels See legend of Fieure 5
The effective range of z is between z1 and 22 and the difficulty is to keep z below or a t 22. It was formerly believed t h a t 4 had to be of the double type mentioned above and carry a frequency regulator. Fortunately, such complicated additions were found to be superfluous, The reason is that damping is very low and the required effect is accordingly low. Thus, the unbalanced weight can be light and driven by a small force. When ( b ) has once reached a reasonable amplitude, the oscillations will prevent the driving force from bringing z above the critical value ZZ. If the force is increased, the added effect will increase the amplitude to a limit which depends on the magnitude of the unbalanced weight.
2ku =
1
-
C
4kh
where C is estimated from the requirement that the oscillations (a) and (c) must not interfere with ( 6 ) . It is not expedient t o have a low value of ku-i.e., too weak springs-because they will become too long when loaded. C = 25 - 30 has been used with
Construction The calculation of suitable springs is carried out on a n example
(W), shown in Figures 5 and 6. Performance is in accordance with Figure 3 but four shaker springs are used. Figure 6 reveals that the symmetry is complete, The use of formulas and symbols is in agreement with the handbook by Marks ( 7 , 8 ) . Shaker Springs. The frequency of the oscillation follows the equation:
k&A
where fh
=
frequency (horizontal)
Figure 7. Diagram of Spring
kh = spring constant of each of the four Rhaker springs-i.e.,
force necessary to produce a deflection of a spring equal to unity m = mass of oscillating body
I n case of high pressure vessels the weight of the charge and of the springs can be neglected and m is the mass of the frame and everything attached to it. For a desired frequency, kh can be calculated with reasonable accuracy with the help of the following equations:
k = : -4~ - 1 0.615 4 c - 4 + 7
c=_T
good results. The calculation of the supporting springs is made from Equations 2 and 3 by the iteration method used with the shaker springs. The length should be t h a t of the compressed spring. Moreover, these springs can well have a certain prestress since their loaded length may otherwise be unnecessarily large. If the required frequency of ( b ) is of ordinary size-e.g., 150 t o 200 oscillations per minute-and the oscillating body has the concentrated performance indicated by Figure 5 , there is only a slight risk that the frequency of (c) will be low enough t o interfere with ( b ) . The tilting frequency is calculated from the equation :
b 2Tfi =
where
G = modulus of elasticity in shear = maximum extension of the spring from a state without load or stress S , = highest allowable shearing stress in the sprin material. This means, of course, that S , must not exceej the “ultimate shearing stress” divided by some conventional
f
where
ft
I re
= = =
4F
frequency of (c) mrf = moment of inertia radius of gyration
General Remarks. The unbalanced weight is driven by a n electric motor (commutator type). The speed of the motor is
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Vol. 44, No. 10
Such an arrangement is fairly simple and in many cases preferable, but may be less reliable.
Conclusions The selection of the kind of mixing or agitation which will be most advantageous in a given high pressure application is determined mainly by three factors: the efficiency required by the reaction conditions, the expense, and the need for easy operation. A comparison of the efficiency of stirring and shaking is difficult. There is little or no theoretical and experimental evidence to
Figure 9. Oscillator V i e w e d from A b o v e
Figure 8.
High Pressure Vessel at Cellulosabolaget, Skonsmon, Sweden
varied by a rheostat (or transformer). The n!mnal speed of the mc?tw should be substantiallr greater than that required to give the unbalanced weight the frequency of ( b ) . The effect of the motor and the moment of the unbalanced u-eight depend, among other things, on the damping. Consequently, they cannot be calculated. The example referred t o has the iollowing data: Weight of the high pressure vessel Weight of the shaking body Nominal effect of the motor Moment of the unbalanced weight Frequency
35 kg. 90 kg. 185 watts 1 kg.-cm. 200 owillations per minute Maximum stroke 20 em. The high pressure vessel has a capacity of 1 liter and is made Cor a noininal pressure of 500 atmospheres at 400" C .
judge from. With regard t o expense, the resonance shaker is probably moderately priced compared t o a stirred vessel. Its parts are not expensive and do not require much precision machining contrary t o the sealing assembly of a stirrer for high pressures. Moreover, leakage is more easily checked in a shaken vessel with its simple closure. A complete evaluation of operational characteristics of stirring and shaking, however, requires more experience than is available to the author. Further discussion is, therefore, limited t o horizontal shaking. Because the general device for this purpose makes use of a crankshaft, a smoothly running and silent a.pparatus will necessarily be very heavy. This, in turn, implies: much space, high energy consumption. and high expense. The resonance apparatus is cheap, light, and requires a minimum of space. It can be designed for any frequency and length of stroke, but t h e oscillations will cause no disturbance to the surroundings. The advantage of resonance oscillations becomes more pr+ nounced for larger oscillating bodies. Because of its cheapness and other favorable features the resonance apparatus offers an alternative in operations requiring very heavy vessels in which stirring and rotation have previously been the only methods ( 3 ) . Figure 8 shows a 2-liter vessel (nominal pressure 500 atmospheres a t 400" C.), weighing 150 kg. together with its heating mantle. The total weight of the oscillating body is 250 kg.; the stroke is 20 cm.; but the motor. driving the unbalanced weight,, is only '/4
The frequency is inversely proportional to the square root of m in Equation 1. The same device used for a 0.2-liter vessel has a total weight of 75 kg. but the frequency is increased only to 220 oscillations per minute. The shaking is, in both cases, smooth and silent and the device works very reliably. The life of the shaker springs is limited but they are inexpensive. ]Then a spring breaks the shaking stops and no inconvenience is experienced. Heavy bodies must oscillate between very rigid supports (like walls). If these supports yield more or less, the value oi kh in Equation 1 will be different; in addition, the damping may be considerable and may restrict the movements. The iiiibalanced weight can be replaced by an electromagnetic device which has some connection to the support. The direction of the force (the electromagnetic field) is regulated by the oscillation itself, using a reciprocating contact. The shaking has t o be started by hand either by pulling the whole body or the electric contact back and forth in harmony with the oscillations.
hp.!
Figure I O .
Oscillator
Viewed
from Side
The frequency is fixed by weight for a given sct of shaker springs. A variable frequency can he obtained ab shonn in Figure 9 by variation of the angles d It is also po&blr to increase t h e efficiency of the shaking if the vessel is given an inclination at the ends of the stroke as indicated by Figure 10. This movement is realized by a suitable arrangement of springs. Though the use of resonance oscillations is particularly suited t o heavy vessels, it is evident that any application is possible if t h p vieight of the body relative to the weight of the material t o be shaken is increased by the addition of an appropriate piece of heavy metal.
October 1952
INDUSTRIAL A N D ENGINEERING CHEMISTRY Acknowledgment
T h e author wishes to thank Erik Hagglund, in whose laboratories the first apparatus was built, and Folke K. G. Odqvist with whom the author has had many fruitful discussions. Acknowledgmentis also due to Andrew Forbes for reviewing the English text. literature Cited (1) Bjorkman, Anders, Swed. Patent 133,476 (1945). (2) Bjorkman, Anders, Tek. Tid., 76,250 (1946).
(3) Egloff, E. C., Chimia (Switzerland), 1,71-4 (1947). (4) Gilson, A. R.,and Baskerville, T. W., Chemistry & Industry,
1943,450-2. (5) Hoffman, A. N., Montgomery, J. B., and Moore, J. K., IND. ENQ.CHEM., 40,1708-11 (1948). (6) Ibid,, 41, 1683-5 (1949),
(7) Marks, L. s,, ''Mechanioal ~ ~Handbook," ~ 5th ed., i p. 456, New York, MoGraw-Hill Book Co., 1951. (8) Ibid., p. 486. (9) Perks, T.E., Brit. Patent 315,860 (1929). RECEIVED for review December 31, 1951.
tion of Hydrogen and Carbon Monoxide and Their Mixtures by Cobalt Fischer-Tropsch Catalysts J.
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C. GHOSHI, M. v. c. SASTRII,
AND
ACCEPTED May 19, 1952.
;
E: ng
ri ng
Process development
K. A. K I N 2
General Chemistry Secfian, Indian Insfifufe of Science, Bangalore 3, India
HE various mechanisms proposed for the synthesis of liquid hydrocarbons by the Fischer-Tropsch process have, almost without exception, stressed the importance of the chemisorption of the reactant gases-namely, hydrogen and carbon monoxide-n the surface of the catalyst metal. While the earlier mechanisms proposed b y Fischer and his coworkers (6) and also by Craxford and Rideal (3, 4)and Matsumura ( 1 2 ) postulated t h e conversion of chemisorbed carbon monoxide to the metal carbide, M2C, investigations carried out at the United States Bureau of Mines ( 1 , 9,16) have established t h a t bulk phase cobalt carbide is not formed a t any stage of the synthesis and that it is neither a n intermediate nor a catalytically active substrate for the reduction of carbon monoxide t o higher hydrocarbons. Indeed, it has been shown t h a t the presence of extensive amounts of carbide in cobalt catalysts inhibits the Fischer-Tropsch synthesis. These results were confirmed by the experiments of Kummer, DeWitt, and Emmett (IO)using carbon14 as a tracer. I n their more recent studies, using radioactive ethyl alcohol in the synthesis gas, Kummer et al. ( 1 1 ) obtained evidence t o show that either ethyl alcohol or some adsorption complex of it functions as an intermediate in Fischer synthesis over iron catalysts. These interesting results support the view, originally held by Elvins and Nash ( 5 ) and by Hamai (8),t h a t enolic complexes of carbon, hydrogen, and oxygen are first formed by the interaction of carbon monoxide and hydrogen in the substrate. A study of the activated adsorptions of carbon monoxide and hydrogen a t various temperatures on Fischer-Tropsch catalysts may be expected to throw light on the nature of the reactants held on the catalyst surface under the conditions of the synthesis. Thorough and systematic research on such lines does not appear to have been carried out so far on Fischer-Tropsch catalysts. Matsumura and his coworkers (12) studied the adsorption of hydrogen, carbon monoxide, carbon dioxide, and water on cobalt and iron catalysts which were active in hydrocarbon synthesis. They reported that on cobalt catalysts the adsorption of either hydrogen or carbon monoxide was of the physical (van der Waals) type at temperatures below 60" C. and that the amount of hydro1 Present address, Indian Institute of Technology, Kharagpur, West Bengal, India. 2 Fuel Research Institute, Jealgora P.O.. Bihar, India.
gen adsorbed reached a maximum value at about 200" C. Van Itterbeek and Dingenen (16)claimed to have found a positive correlation between the adsorption of hydrogen and carbon monoxide on nickel and copper-thoria catalysts and their activity in hydrocarbon synthesis. From the standpoint of the reaction mechanism, the simultaneous adsorption of the reactants from suitable mixtures of the two will have a more direct bearing on the problem than the adsorption of either component studied singly. Though the importance of adsorption from mixed gases has long been recognized, such studies have so far been confined t o noncatalytic systems. In the present investigation, the adsorption of hydrogen and carbon monoxide, from the pure gases as well as from two mixtures of the initial compositions 1CO : lHz and 1CO :2Hz have been studied at a series of temperatures on two cobalt catalysts, which have been developed and tested in these laboratories for Fischer synthesis. T h e compositions of t h e two catalysts are as follows : Catalyst A. Cobalt: copper: thorium oxide: cerium oxide: kieselguhr = 100:12:7:0.7:173. Catalyst B. Cobalt: copper: thoriumoxide: cerium oxide: chromium 0xide:kieselguhr = 100:12:7:0.7:14: 159. Experimental
Materials. The catalysts used in this investigation were prepared in the usual manner by precipitation from a hot solution of the pure nitrates of the component metals with potassium carbonate solution. The kieselguhr used was previously digested with hot nitric acid and heated for a few hours a t 600' to 800" C. T h e catalyst was thoroughly reduced a t 250" C. by passing a rapid stream of hydrogen until no more moisture was found in the exit gas. This took approximately 20 hours. T h e initial and reduced weights of catalyst samples investigated were as follows: Catalyst A Catalyst B
Initial Weight, G r a m 9.41 10.10
Reduced Weight, Grams 8.35 7.55
I n each case, the same sample of reduced catalyst was used for determination of surface area as well as for carbon monoxide, hydrogen, and mixture adsorption studies. Carbon monoxide and h drogen were prepared and purified in the usual way and storeJover pure mercury. Argon of high
~
