Pressure Drop Due to Vapor Flow through Moving Beds T h i s investigation was undertaken t o study t h e flow of vapors through moving beds of catalyst in which t h e ent i r e bed moves w i t h respect t o t h e walls of t h e container, b u t t h e moving particles remain i n a fixed position relative t o each other. T h e experimental data obtained include studies on both concurrent and countercurrent flow of air through such beds. T h e material employed included granular, spherical, and pellet types of catalyst ranging in size f r o m 4 t o 60 mesh and representing both u n i f o r m grades and mixtures of sizes. Various spherical shaped seeds as well as 0.25- and 0.375-inch a l u m i n a
spheres were employed also. F r o m previous investigations a n d a study of t h e data obtained in t h i s work, a correlating equation has been developed by applying t h e NavierStokes dynamic equations t o t h e viscous motion of fluid through a n assemblage of u n i f o r m spheres. T h e method is extended t o t h e t u r b u l e n t region by use of dimensionless groups similar t o those employed i n problems involving flow of fluids through pipes or around various objects. A new function of t h e fractional void volume takes i n t o account factors introduced by flow t h r o u g h a granular medi u m .
JOHN HAPPEL' POLYTECHNIC INSTITUTE OF B R O O K L Y N , B R O O K L Y N . N . Y .
T
HE present investigation represents a n extension of studies which have been carried out by the Socony-Vacuum Oil Company, Inc., for a number of yearswith the purpose of obtaining suitable data for the design of iiioving bed catalytic cr\acking units (TCC units) (42,49,is0) now widely used in the petroleum industry. There is a considerable amount of current interest in the subject of contacting vapors with various types of solids and in recent years processes have been employed involving beds of solids in fixed, moving, and fluidized forms. While the correlation developed in the course of this study is particularly applicable t o moving beds, it is apparent t h a t all three types of contacting possess many common characteristics. A moving bed type of contactor may be defined as one in which granular solids move downward under the influence of gravity remaining in contact with each other and thus in the same relative position t o each other. If vapors are flowing countercurrently, upward through such a bed, their rate must be controlled below t h e point where the lifting force due t o vapor flow is greater than the downward force exerted on the packing, or boiling of the bed will occur. I n the case of concurrent flow of vapors, downward through the bed, the only limitation on vapor flow rate is the capacity of the vapor w i t h d r a n d system. It has been found t h a t regardless of the direction or rate of flow of vapor through such a bed, the apparent density of the flowing mass of particles corresponds t o t h a t obtainable under conditions of loosest packing in a fixed bed. Recent applications of the moving bed technique include in addition t o t h e catalytic clacking of petroleum, the heating of air or steam to high temperatures (43) and the recovery of hydrocarbon streams from vapor including separation of the various hydrocarbons involved ( 2 ) . The variety of these applications is illustrative of the versatility of the moving bed technique and it is believed t h a t there n ill be many new applications as methods of design and operation are further developed. T h e present study is devoted for the most part t o investigation of the factors influencing pressure drop due to vapor flow through moving beds and a comparison of the results with work in closely related fields. It is recognized that there are other major design problems involved in the application of this technique among which may be mentioned the maintenance of smooth arid uniform flow of solids and vapors through a bed, provisions for entry and withdrawal of solids, and methods for sealing vapors so t h a t they do not escape from the system. The prediction of pressure drop 1
Present address, College of Engineering, S e w York University, University
Heights, New York.
is perhaps of greatest importance because i t is this factor which usually determines the unit size required for a given capacity. PREVIOUS INVESTIGATIONS
The only published correlation specifically referring t o pressure drop through moving beds is t h a t of Newton, Dunham, and Simpson (42). Pressure drop through a granular clay catalyst bed was correlated by the Chilton and Colburn (9) equation for fixed beds. Later applications of moving bed processes have employed a wider range of shapes and sizes of particles and subsequent study has indicated the importance of variations in the fractional void volume not considered in this correlation. Studies on closely related types of solid-fluid contacting systems indicate t h a t the following three variables are of primary importance in pressure drop correlations: fractional void volume, type of liquid flow (viscous or turbulent), and size and shape gradation of the solids. The term fractional void volume here includes only the proportion of voids which exists between granules through which t h e fluid moves. It should be distinguished from porosity which is often defined as the pores within granules of porous material. Investigations of flow through assemblages of particles have covered a wide range of fractional void volumes, limited a t one extreme by fluid passing around a single particle (34) and at t h e other by flow through irregular channels in a solid body (14, 20). Purely viscous flow does not usually exist in practical moving bed applications and this circumstance constitutes a n outstanding difficulty to a purely theoretical approach t o the problem of developing a suitable correlation. Mathematical analysis under conditions of turbulent flow is difficult even in t h e case of a single spherical particle (34) and further complications arise in the case of an assemblage of particles ( 2 7 ) . The effect of differences in shape may be evaluated by means of shape factors (15, 26, 53) which relate irregu!ar particles t o equivalent spheres. A difficulty in applying shape factors (5, I S , 35, 36) is t h a t they are valid only for smooth, regular shaped particles, because surface roughness also has a n important bearing on pressure drop and is difficult t o evaluate independently. Sonuniformity of particles may be regarded as a special case of shape variation. It is a n important variable in t h e case of moving bed correlations because, when employing fairly regular shaped materials, fractional void volume can be changed only by varying the size distribution of particles. It is usually taken into 1161
INDUSTRIAL AND ENGINEERING CHEMISTRY
1162
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June 1949
INDUSTRIAL AND ENGINEERING CHEMISTRY
account by use of an average diameter. Many methods have been proposed for obtaining the proper average diameter (6, IS, 35,39) ; the one most commonly used is the so-called reciprocal mean diameter, D, = 100/(2wl/DJ, where 2wt/Dlrefers to the weight percentages wl,wz, etc., of materials of sizes DI, Dz, etc. It is difficult t o obtain definitive data t o determine which method is best because usually changes in mixture components result in simultaneous changes in fractional void volume. Investigations on specific solid-fluid systems of most interest in the present investigation may be conveniently considered under three broad classifications-namely, fixed beds, suspensions, and fluidized beds-which will be reviewed in this order. Since the historical investigations of D’Arcy (10) a great number of studies have been made on pressure drop through various types of fixed beds. Most of this work has been correlated by means of dimensionless groups. Blake (3) and others (8, IS, SO), using this method of correlation, assumed that resistance to flow could be expressed by an analogy to Poiseuille’s law in which the average diameter of the passages flow of fluid was expressed in terms of a modified hydraulic radius. Fair and Hatch (13, 24, 25) presented a general modification of this type of correlation and applied i t to nonuniform packing, using the reciprocal mean diameter. Leva (36, 36) employed a similar fractional void volume function but used a different method for obtaining average diameter than Fair and Hatch. Chilton and Colburn (9) considered that since pressure drop through a bed consists to a major extent of expansion and contraction losses, i t should not be correlated on the basis of flow in capillaries. Bakhmeteff and Feodoroff (i),agreeing with this viewpoint, presented a correlation in the form of dimensionless groups which used an entirely different function of fractional void volume to express the effect of this variable on resistance. These investigators also included a review of other recent studies in this field (18, 58,$9). Other investigators have resorted to various empirical Correlations to allow for changes in shape and fractional void volume. Thus Brownell and Kate ( 5 ) used as a basis a general correlation of flow in rough pipes by Moody (40). Rose (48)presented a graphical function for evaluation of the effect of changes in fractional void volume, which appears t o give results not far different from the function proposed by Fair and Hatch. The difficulty in applying these correlations is that they disagree markedly on the extent to which resistance changes with fractional void volume. Thus for a change in fractional void volume from e = 0.4 to e = 0.3the Bakhmeteff and Feodoroff equation would predict a 47% increase in pressure drop whereas that of Fair and Hatch would predict a 325% increase. Much of this disagreement is probably due t o the fact that fractional void volume can be changed both by difference in degree of compacting and by changes in the shape and size distribution of the solid particles. Oman and Watson (44)recognized this effect and proposed a method of correlation which takes into account variations in fractional void volume due to differences both in coppacting and changes in shape (they worked only with uniform sized materials and hence did not consider the effect of changes of size distribution). The most interesting theoretical studies have been those on the hydrodynamics of suspensions of spherical particles of uniform size. Those of Burgers (6) and Kermack, M’Kendrick, and Ponder (28) are concerned with the sedimenting velocities of assemblages falling in a viscous liquid enclosed in a vessel. More recent studies include the application of generalizations of Einstein’s (12) theory for impermeable spheres to the prediction of intrinsic viscosity, diffusion, and sedimentation rate of polymers in solution (11, d9). Brinkman (4) also has applied a modification of this theory t o the calculation of pressure drop through fixed beds. Steinour (51, 5d) conducted a coniprehensive theoretical and experimental study of the physical factors involved in sedimentation of concentrated suspensions of fine powders, including a review of previous work in the field.
1163
A number of studies have been conducted also in the closely related field of fluidization, where the particles no longer move uniformly as in the case of moving beds and sedimentation. Earlier references include fluidization in solid-liquid systems (dS, 26,a?). Several recent publications deal with the fluidization of solid-gas systems (37, 4 5 , 5 5 ) ,but it appears that an exact approach to the general problem is difficult. Summing up, previous studies on solid-fluid systems indicaic that much is still to be desired even in the specific fields of investigation aside from their possible application to moving bed correlations. Fixed bed studies are greatest in number and have the closest applicability t o moving beds. The theoretical studies on sedimentation of spheres furnish some basis for resolving inconsistencies in factors proposed in fixed bed correlations for taking variations of fractional void volume into consideration. EXPERl M ENTA L PROCEDURE
Important process variables were studied over a range which it was thought include conditions of practical interest in the dciigii of moving bed installations. Concurrent and countercurrent flows of air through moving beds were studied employing a wide range of vapor and solid rates. Vapors other than air were not used because previous studies on static beds using steam, propAne, and hydrocarbon vapors indicated that the usual paramctcrs employed in friction factor correlations are adequate to allow For variations in fluid characteristics. Experimental conditions u w c maintained so as to obtain substantially isothermal operation, a t small over-all pressure drop and with uniform distribution of vapoi and solids. Materials and Their Properties. The materials employed i n this investigation and their properties are given in Table I. Tlirbl comprise forty-one different samples including fresh and used granular, pellet, and bead catalysts, as well as various spherical shaped seeds and tabular alumina spheres. In some experiment, the compositions of bead and pellet catalysts were altered by addition or removal of fines to provide a wider range of average particle size. Experiments on laboratory models indicated that the flowing bulk density of catalyst in a moving bed agreed to within less thaii 1% with the loose apparent density for a static bed of the samt‘ material. The loose apparent densities referred t o in Table I art‘ determined by placing a weighed representative sample in a container which is slowly inverted several times until the volume remains constant. The loose apparent density is computed froni the observed weight and volume of the catalyst. This density is not far from the random loose arrangement described by Oman and Watson (44), though these investigators follow the procedure of rapidly inverting the chamber to obtain loose arrangement. Fractional void volume which is used as the correlating parameter in this study, was computed from the “loose apparent density” and particle density, the latter being determined by mercury displacement for catalysts and by kerosene displacement for seeds. Countercurrent Flow Experiments. Most of the experiments on countercurrent flow of air and catalyst were carried out in apparatus of the type shown in Figure 1. I n this apparatus pressure drop was measured over a &foot section of 4-inch standard pipe through which catalyst and air flowed countercurrently a t measured rates. To test for possible wall effects, some experiments were conducted in a 6-foot section of 10-inch standard pipe. Referring to Figure 1, catalyst flowed from the feed hopper, A, into the disengaging drum, B, down through the test section t o the pressure drum, C, through a section of smaller pipe t o the pressure equalizing drum, D, and was discharged through a gate valve for regulation of the rate of flow. Catalyst was circulated continuously; a representative sample was taken for each set of runs by periodically diverting the entire discharge stream to a sample container. The composite sample so obtained was divided by a riffle sampler t o obtain representative samples for individunl tests.
1164
Vol. 41, No. 6
INDUSTRIAL AND ENGINEERING CHEMISTRY
THERMOMETER
OUTLET
-1111
DISENOAOING DRUM
45'CONe 4 - 4 " S T D . PIP6
EREHTIAL PRESSURE AIR INLET FROM METERS-
S T A T E PRESSURE
DIFFERENTtAL YAHOMETER
G
-
c
EATALYST O U T L E T
Figure 1.
Apparatus for Countercurrent Flow
Air from a constant pressure source was admitted t o drum C, -passed upviard through the 4-inch pipe into drum B, and discharged to the atmosphere. -4ir discharge rates were measured with orifice and dry gas meters n-liich TTere calibrated against gas holders periodically. The temperatures of t,he air entering and leaving the system were observed. Losses of measured air from drum C to the catalyst outlet Tvere prevented by admitting air from a n independent source into drum D at a rate sufficient t o equalize pressures in drums C and D. A differential manometer .indicated equalization of pressure in the two drums. The pressure drop over the test section was measured by a water manometer. The accuracy of the readings vtas +O.OS inch of water. The stat#icpressure a t the bot,tom of this sect,ion mas nieasured by a mercury manometer, the readings being accurate i o *0.1 inch of mercury. The pressure taps for the manometers consisted of t,hree 0.25-inch holes which were evenly spaced around the pipe and manifolded. Barometer readings were taken daily. -4series of runs was made on ea,ch catalyst employed, varying -the flow rates of air and catalyst. In making each run, constant flon- rates of air arid catalyst \\-ere established, then meter read.ings, pressures, temperatures, and catalyst rates were recorded at .3-minute intervals for 9 minutes. In runs on used pellets t o which large amounts of fines had been added, the pressure differential usually fluctuated. Such runs \yere extended t o 20 t o 30 minutes to obtain more reliable data. Some experiments were made with no flow of catalyst. Catalyst n-as circulated prior t o making these runs in order to establish a loose-packed condition of the 'catalyst bed. I n r a m 189 t o 220 where i t was desired to test a wide variety of catalyst rates, the procedure was varied slightly; t h e pressure drop was held constant for each series while the catalyst rate was changed. The data obtained on the countercurrent flow experiments are given in Table 11, along with com-
puted results as described in the folloxing sections. Some 220 separat,e runs are reported x i t h catalyst rat,es varying from 1 t o 2 feet per minute to 30 feet per minute and with air rates up t o 100 feet per minute superficial velocity. Concurrent Flow Experiments. Most r,f the experiments on concurrent f l o of ~ sir and catalyst Twre carried out in apparatus of the type shown in Figure 2. In this apparatus pressure drop was measured over a 6-foot section of 4-inch standard pipe. I n some of the experiments with finc granular material a 26-inch bed of 2-inch st,andard pipe n-as employed. Also some experiments ix-it'h larger particles employed a 4-foot bed of 8-inch standard pipe. Referring t o Figure 2, catalyst f l o ~ e dfrom the hopper, down through the test section, into the bottom funnel and discharged through a gate valve for regulating catalyst flow. Catalyst was recharged t o the hopper between runs. Air was admitted to the ca.talyst hopper and flowed downm-ard through the 4-inch pipe, discharging to the atmosphere from the funnel a t the bottom. The pressure drop over the catalyst' bed and t,he &tic pressure a t the bottom of the bed were measured with water or mercury nianomet'ers or calibrated gages, depending on the magnitude of the pressures. The general program and experiniental procedure were similar to those used for countercurrent flow; the results are given in Table 111. -4total of 215 separate runs is reported with solids rates up t,o 80 feet per minute and air rates up t o 200 feet, per minute. Calculation Procedure. Reynolds numbers and friction factors, both unmodified and modified, mere calculated for each experiment using the relations developed in the following section. Dimensionally consistent units must be used in evaluating these functions, and in this study English engineering units are employed throughout. The English engineering system expresses both mass and force in pounds (64). Physical properties of air were obtained from Landolt-Bornstein (38). Where pressure drop across the bed was substantial, density and flow rate were taken a t the arithmetic mean of inlet and outlet pressures, thus using the integrated form of the flow equations for isothermal expansion (8, 48). I n calculating air rate through the catalyst bed on the concurrent apparatus allomance was made for the volume of catalyst flowing out of the drum. REYOVA0LE CAP (REPLACED BY FUNNEL WHEN LOADING HOPPER)
I"STD PIPE
m
I
-" CATALYST FEED
HOPPER
3 OUTLET PRESSURE TA
4"STD PIPE
m
4
OATALYST O U T L E T
Figure 2.
Apparatus for Concurrent Flow
June 1949 Average particle diameters mere computed f r o m t h e Tyler (46) screen analyses using the reciprocal mean method. The material retained on the coarsest screen used a n d t h a t passing through the finest screen were each assumed t o have average diameters between the opening of the screen used and t h a t of the next screen of the same series. For intermediate sizes, the average diameter of a screen fraction was assumed equal to the arithmetic average of the two s c r e e n s b e t w e e n which it was retained. METHOD OF CORRELATION
In view of the wide differences in methods proposed by various investigators, i t was thought d e s i r a b l e t o attempt to establish the fractional void volume function from more fundamental considerations. The derivation outlined in the following p a r a g r a p h s s u m m a r i z e s t h e method used. It is of interest t h a t the new function developed, though different in mathematical form from the Bakhmeteff and Feodoroff equation, results in close to the same quantitative evaluation of the effect of changes in fractional void volume for the range encountered in moving beds (Table V). The same dimensionless groups may be employed for correlation regardless of whether flow through granul a r s o l i d s is c o n s i d e r e d analogous to flow through tubes or around s p h e r e s . Thus, based on dimensional analysis, t h e following formula may be derived:
where D,is some characteristic quantity or group having a linear dimension, V , is a characteristic v e l o c i t y o r group having a velocity dimension, and x(t) is a dimensionless function of the fractional void volume. Since t h e dimensionless function X ( E ) cannot
INDUSTRIAL AND ENGINEERING CHEMISTRY Table 11. Catalyst Rate, Lb./Min./ Sq. Ft.
Run No.
Experimental Data for Countercurrent Flow
4 i r Rate a t Av. Bed Av. Bed Conditions Reynolds Pressure, Bed Cu.,Ft./ ’ Pressure Lb./Sq. Temp., Min./ Gradient, Number, I n . Abs. F. Sq. Ft. In. H$O/Ft. KRs
Fresh Pellet Catalyst No. 0.0 15.16 0.0 15.35 15.58 0.0 15.17 31.6 15.35 34.5 15.55 33.9 15.17 112.0 15.35 113.0 15.60 114.0
1169
Friction Factor,
f
Modified Modified Reynolds Friction Number, Factor. N R ~ ~ fm
7 (Av. Diam. 0.054 In., Fraction Voids 0.475) 3.03 18.2 87 39.5 4.57 24.9 54.1 87 27.0 5.87 66.0 88 19.4 3.03 42.2 81 26.7 4.59 81 58.0 33.7 5.92 83 73.1 19.8 3.04 A5 43.1 26.2 4.53 57.0 86 36.2 5.92 78.6 86
4-111. Pipe, 35.2 28.4 24.5 30.8 24.8 20.1 29.6 25.4 17.4
6-Ft. Bed Depth 243 19.5 13.1 196 169 14 2 213 10.2 171 14.0 139 17.7 204 10.4 175 13.7 19.0 120
Fresh Pellet Catalyst No, 8 (Av. Diam. 0.097 In., Fraction Voida 0.475) 10 0.0 3.08 58.1 15.06 94 69.1 4.53 74.0 15.25 0.0 11 94 90.4 5.92 89.3 15.45 12 109.2 0.0 55.8 15.12 13 3.03 69.8 22.5 74.1 4.53 15.30 90.4 22.4 14 90.3 5.90 18.45 22.3 15 110.2 00.6 2.79 15.15 34.5 16 61.7 4.50 15.30 34.6 17 74.4 91.6 5.91 18 90.9 111.0 15.45 32.2 5.91 15.50 19 34.3 91.0 111.0 20 08.0 3.05 15.01 56.8 70.7 4.50 21 74.9 15.25 56.5 90 91.3 j.96 92.1 15.45 57.6 22 90 112.1 15.02 55.1 113.0 3.05 23 91 69.2 75.7 4.53 16.20 24 91 113.0 92.3 5.92 15.45 25 90.9 113.0 110.9 90
4-In. Pipe, 21.3 18.0 15.9 20.4 17.9 15.6 24.0 17.3 15.4 15.4 20.0 17.5 15.2 21.0 17.3 15.5
6-Ft. Bed Depth 147 124 111 141 123 10s 166 120’ 106 106 138 121 106 48.4 143 28.9 119 39.8 107 47.6
~~
Fresh Pellet Catalyst No. 12 ( A r . Diam. 0.162 In., Fraction Voids 0.475) 4-111. Pipe, 6-Ft. Bed Depth 101 76.7 14.6 0.0 15.30 85 3.04 91.8 100 13.3 15.50 4.66 0.0 78 73.3. 1 0 . 6 128 15.70 5.95 0.0 86 89.2 12.9 81.9 3.07 80 53.2 15.11 69.8, 1.i xn A1 112 4.52 10.1 54.2 92.2 13.2 98.8 4.48 58.1 15.50 67.6. 129 9 . 8 1 5 . 6 7 6.00 53.0 60.7 141 8.8 6.00 53.7 15.60 87.@ 12.6 82.5 15.11 3.05 113.0 92.5 13.4 82.9 3.24 111.5 15.33 82.2 107 1 1 . 9 4.69 112.6 15.51 78.1 11.3 106 4.52 113.0 15.30 60.7 139 8 . 8 5 . 8 7 112.0 15.50 60.7 142 6.04 8.8 112.0 15.70 40 41 42 43 44 45 46 47 48
Rape Seed No. 15 (Av. 15.28 0.0 0 ..o 15.45 15.70 0.0 15.26 33.8 34.8 15.50 34.8 15.65 113.0 1p.25 113.0 10.45 112.4 15.65
49 50 51 52 53 54 55 56 57
Vetch Seed No. 16 (Av. Diam. 15.17 0.0 88 0.0 88 15.36 15.55 0.0 78 15.21 78 32.4 15.35 78 34.2 15.60 78 35.0 15.16 81 112.8 15.40 81 113.0 112.0 15.60 80
0.139 In., Fraction Voids 0.430) 4-In. Pipe, 6-Ft. Bed Depth 112 16.0 63.9 3.00 93.7 82.6 14.3 145 121.2 98.0 172 13.3 141.0 67.2 118 14.7 98.3 85.5 13.1 150 125.0 100 12.3 176 147.0 14.2 67.2 118 99.2 13.0 85.5 150 125.6 12.2 102 147.1 180
86.6 77.2 71.8 79.8 70.7 66.4 76.6 70.2 65.g
58 59 60 61 62 63 64 65 66
Okra Seed No. 18 (Av. Diam. 0.170 In., Fraction Voids 0.450) 4-In. Pipe, 6-Ft. Bed Depth 15.17 3.02 163 12.9 89.7 0.0 115.6 11.4 4.52 216 119 149.5 0.0 15.40 9.5 147 185.2 15.55 5.86 268 0.0 12.3 92.4 3.05 168 119.1 43.2 15.16 122 4.66 121 11.1 154.0 39.5 15.40 148 5.97 269 9.6 15.50 186.5 41.4 91.8 12.9 3.03 167 115.6 15.21 110.3 11.9 11G 4.53 210 146.0 15.40 113.0 147 5.98 ’ 267 9.8 184.0 15.60 110.0
77.8 68.8 57.2 74.0 66.8 57.7 77,7 71.8 58.B
67 68 69 70 71 72 73 74 75 76 77 78 79 80 81
Diam. 0.067 In., Fraction Voids 0.430) 4-In. Pipe, 6-Ft. Bed Depth 16.1 28.3 81 3.14 21.7 38.0 4.50 81 26.6 81 46.6 5.90 16.3 28.6 3.02 81 21.9 74 38.4 4.61 .. 26.4 46.4 5.86 81 16.2 3.15 28.4 81 21.8 38.2 4.49 81 27.2 47.7 5.93 81
Used Pellet Catalyst No. 20 ( A r , Diam. 0.112 In., Fraction T’oids 0.425) 1.75 40.0 0.0 80 42.4 58.3 3.02 78 0.0 61.0 80.4 4.60 78 83.4 0.0 79.9 4.63 79 82.9 0.0 93.5 6.92 79 95.9 0.0 61.3 3.05 73 36.2 63.8 79.6 4.57 74 81.9 36.2 4.40 76.5 74 78.5 36.2 5.30 84.6 79 86.9 37.2 55.2 2.40 59.7 84 47.5 4.40 80.2 53.0 86.6 82 97.2 5.98 84 105.1 41.8 3 . 0 0 57.0 79 6 0 . 0 115.2 72.5 4.40 76 113.0 74.9 8 7.1 5 . 4 5 79 115.2 89.9
4-In. Pipe, 36.4 30.0 24.3 24.7 23.4 27.9 25.0 26.1 25.6 24.8 21.2 19.4 30.8 28.6 24.4
6-Ft. Brd Depth 192 23.0 158 33.5 128 46.2 130 45.9 123 53.8 147 35.3 132 45.8 137 44.0 13.5 48.6 131 31.7 112 46.2 55.9 102 32.8 162 41.7 151 129 50.2
(Continued on p a g e 1166)
1166
be independently analveed further by dimensional analysis i t is desirable t o asiociate it by other means I? ith the dimensional parameters of the system such as V, and D,. Fair and Hatch, hasing their reasoning on analogies t o Poiseuille’s law, accomplished this by using in effect, Equation 1 whew L), = DE/(^ - E ) and Vo = V / E , D being particle diameter and V superficial fluid velocity through the bed. l - h g these values for D, :cnd V,results in a modified friction factor and Reynolds number and the function X ( E ) i. eliminated. Bakhmeteff and Feodoroff employed diffeient reasoning so that D,= De’/$ and V , = V / E ~which /~, are applied to Equation 1 i u the same fashion. Many investigators ( I , 3, 5, 8, I S , 30, 36, 44, 48) have used irindamentally this approach, \ 200
(")
0.1 94 In., Fraction Voids 0.426) 8-111. Pirii:
80.8 135,B 212.0 80.5 131.0 204.0 327.0 002,o 637, 0
27.5 1Y.5 16.6 27.4 20.8 17.3 13.6 12.45 11.25
46.4 77.7 122.0 46.2 75.0 117.0 187,s 288.0 366.0
146.5 103.2 87.7 145.0 110.0 Ql.5 71.9 66.8 59.5
(Concluded on p a g e 1171)
The correlation given in Figure 4 is valid for concurrent flow a t any pressure gradient and for countercurrent flow a t a pressure gradient below t h a t which will cause boiling of the catalyst bed, due t o the lifting force of the vapor exceeding the downward forrr exerted on the bed. To test the applicability of the curve shown in Figure 3 , groups of data were plotted separately a8 follows to determine
June 1949
INDUSTRIAL AND ENGINEERING CHEMISTRY Table I 11.
Run NO.
Fresh Beads 137 138 139 140 141 142
f 10% of 19.7 19.7 19.7 19.7 19.7 19.7
Fresh Bead Catalyst 143 144 145 146 147 148 149
19.7 19.7 19.7 19.7 19.7 19.7 19.7
whether any trend could be noted:
Experimental Data for Concurrent Flow (Concluded)
.
Air Rate a t Av. Bed Av. Bed Conditions, Pressure Cu. Ft./ Pressure Lb./Sq.' Temp., Min./ Gradient, In. Abs. F. Sq. Ft. In. HsO/Ft.
Catalyst Rate, Lb./Min./ Sq. Ft.
Reynolds Number, NR*
Friction Factor,
f
Modified Reynolds Number, NRem
Modified Friction Factor, fm
Bead Fines No. 35 (Av. Diam. 0.142 In., Fraction Voids 0.428) 8-In. Pipe, 4-Ft. Bed I>epth 14.55 74 38.1 1.o 45.4 33.0 25.9 176.0 14.69 72 61.5 2.0 74.1 25.2 42.3 134.5 14.91 74 92.7 4.2 113.0 22.9 64.6 122.0 15.35 71 142.5 8.0 180.0 11 7 16 06 3 .. 0 0 94 4 .. 5 8 16.27 70 216.5 15.3 290.0 3 .. 98 5 1 7 16.87 75 258.5 20.7 354.0 12.9 203.0 68.8
+ 20 Wt.% Bead Fines No. 36Bed(Av.Depth Diam. 0.1.38 In., Fraction Voids 0.418) 8-In. Pipe, 4-IN. 14.62 14.74 14.98 15.42 15.42 16.39 17.19
78 77 74 76 75 74 82
28.7 855.7 9.3 132.5 139.0 206.5 241.5
1.0 41..08 8.1 7.9 16.1 23.0
32.8 64.1 106.0 161.0 169.0 269.0 321.0
56.8 27.0 22.7 20.4 18.1 15.5 15.9
19.1 3 7.3 61.6 93.5 98.4 156.5 187.0
288.0 137.0 115.0 103.5 91.5 78.8 80.6
Used Granular Catalyst No. 40 (Av. Diam. 0.0395 In., Fraction Voids 0.492) 2-In. Pipe, 26-In. Bed Dnpt,h 150 151 152 153 154
0
0
0 0 97 I55 695 166 708 157 1040 158 1040 150-168(Av.), . 159 0 160 161 0 162 0 163 0 164 0 165 97 166 118 167 118 168 236 169 236 170 292 171 292 172 306 173 320 174 417 175 570 176 576 177 625 178 625 179 708 180 848 181 875 182 1040 183 1180 184 1540 185 1560 186 1600 187 1600 188 1610 189 1900 190 1970 191 2400 192 2400
. .
.
19.0 19.0 19.0 19.0 19.0 19.0 19.0 19.0 19.0 19.0 17.4 17.4 17.4 17.4 17.4 17.4 17.4 17.4 17.4 17.4 17.4 17.4 17.4 17.4 17.4 17.4 17.4 17.4 17.4 17.4 17.4 17.4 17.4 17.4 17.4 17.4 17.4 17.4 17.4 17.4 17.4 17.4 17.4 17.4
(Approx.) 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 60 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80
215 216 218 222 219 217 218 218 224 220 157 161 162 164 167 169 161 159 161 169 170 166 169 163 162 166 161 167 157 159 169 168 164 160 172 166 161 163 166 163 170 166 172 174
62.7 62.7 62.7 62.7 62.7 62.7 62.7 62.7 62.7 62.7 37.7 37.7 37.7 37.7 37.7 37.7 37.7 37.7 37.7 37.7 37.7 37.7 37.7 37.7 37.7 37.7 37.7 37.7 37.7 37.7 37.7 37.7 37.7 37.7 37.7 37.7 37.7 37.7 37.7 37.7 37.7 37.7 37.7 37.7 37.7 25.1 25.1 25.1 25.1 25.1 25.1 25.1 25.1 25.1 25.1 212.9 5.1 12.9 12.9 12.9 12.9 12.9 12.9 12.9 6.27 6.27 6.27 6.27 6.27 6.27
159-192(A~.).. . 193 0.0 194 0.0 195 0.0 196 0.0 197 70 196 278 199 292 200 403 201 515 2 02 1100
17.4 16.4 16.4 16.4 16.4 16.4 16.4 16.4 16.4 16.4 16.4
80 80 80
80 80
166 131 132 130 136 137 138 138 141 134 131
193-202(Av.). . . . 203 0.0 204 0.0 205 97 206 139 207 362 208 543 209 655 203-209(Av.). . . 210 0.0 211 42 212 70 213 97 214 181 216 320
16.4 15.4 15.4 15.4 15.4 15.4 15.4 15.4 15.4 15.0 15.0 15.0 15.0 15.0 16.0
80 80 80 80 80 80 80 80 80 80 80 80 80 80 80
136 85 86 83 84 85 91 67 86 48 46 47 46 48 51
.
. .
80 80 80 80 80
80
....
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....
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....
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ii:i
92.5
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64.1
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1.i.5
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47.0
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3. 2. .. 6.
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49.5 ... ....
16.4
25.2
, . . .
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29.2 ....
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210-215(Av.), . 15.0 80 48 0.27 16.0 Contained small amount of dust (1%) elytriated o u t before run 5. b Outlet from catal s t bed was 1.5 inches ~n diameter. Air r a t e correctel for catalyst displacement.
...
...
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.
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128
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22.5
14.8
171.5
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35.7
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1171
...
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Concurrent runs Countercurrent runs Fresh catalysts with high fractional void volumes Used catalysts with low fractional void volumes Spherical materials alone Catalyst in different sized pipes I n no case was there any substantial deviation of the separate groups of data from t h e average curve given on Figure 4. I n the case of fixed beds, wall effects on pressure drop due t o vapor flow are negligible if the vessel diamet,er is over eight t o ten times the particle diameter ( 7 , 9 ,i 7 , 4 4 ) . I n this study ratios of pipe diameter t o part,icle diameter of at least 28 t o 1 were employed and no effect of diameter was detectable. The correlations presented imply t h a t there will be no effect of changes in catalyst rate on the pressure drop through a moving bed. Runs t o check this assumption were made both for concurrent and countercurrent flow. For catalyst rates up to 1000 pounds per minute per square foot with countercurrent flow and 2400 pounds per minute per square foot with concurrent flow, there is little change in air flow rat,e for a given pressure drop, the rate of flow of air being measured relative to the bed. Rates of air flow relative to pipe walls may be obt'ained by adding corrections for concurrent flow or subtracting for countercurrent flow. For engineering purposes, ti plot of modified Reynolds numher against the product of modified friction factor and the square of the modified Regnolds number will facilitate direct computation of the vapor velocity corresponding to a given pressure drop. Such a plot is close t o being a straight line when plotted with logarithmic coordinates and thus can be converted readily t o a convenient nomographic form. It may be of interest also t h a t f m N k , , is by coincidence the same dimensionless group as used by Wilhelm and Kwauk (56)in their correlation of fluidization data.
INDUSTRIAL AND ENGINEERING CHEMISTRY
1172
Table I V . Comparison of Methods for Moving Bed Pressure Drop Estimation-Uniform Spheres
-
*
Values for Friction Faator f = 2LGZ At N R =~ 10 At I V R ~ 100 A t N R R = ~ 1000 6.01 4.08 Levaa (36) 6 . 6 4 Wilhelm and Kwauk ( 6 6 ) 22.'8 (2.38) 6.76 3.68 Carman (8) Fair and Hatch ( I S ) 2 7 . 1 3.44 8.20 Brownell a i d Kataa 15) 35.9 8.68 4.75 8.12 10.5 15.0 7.67 19.0 13.5 7.0 9.0 a Based on correlations for smooth particles such as glass o r celite. b Based on correlation for dense beds divided by 2.2 t o allow for loose packing of spheres. c Chilton and Colburn values X 0.52; method assumes that = 0.40 correfor their data and A p is proportional a p roximately 40 e 3 / ( l sponding t o n = 1.7 in Fair and Hatcg type equation. Reference
COMMENT
Limiting Solids Flow Conditions. In moving beds, the correlations developed above apply as long as the bed moves uniformly downward n ithout relative movement of particles t o each other. The effect of conduit diameter and particle size gradation may be of importance in some cases in limiting the conditions for such smooth solids flon. In addition t o the forces exerted on the bed due to vapor flow and gravitational force on the particles, there will be mechanical friction of the solids against the conduit walls. I n the case of large diametei beds, such as normally used in reactors and kilns in which movement of the granular solids is slow, the effect of Tvall friction on solids flow may be neglected. I n smaller pipes, such as feed and exit lines, it will be appreciated that even with no vapor flow there will be a limit to the solids carrying capacity of a vertical conduit. Countercurrent flow of vapors will decrease this carrying capacity and concurrent flow, on the other hand, will increase it substantially above free flow capacity. Within the limits that smooth catalyst flow is obtained, the correlations developed above are applicable. If much fine material is present in a circulating bed, countercurrent vapor flow may result in uneven flow or bridging of the bed. This condition is avoided in commercial operations by elutriation of the very fine material which accumulates due to attrition of catalyst. Comparison with Other Methods. To facilitate ready comparison of friction factors predicted by the present correlation as compared with those reported in the literature, values of un-
( '$:@)
modified friction factor f =
were computed for several
values of unmodified Reynolds number (fjrRs= DaG/p) for each correlation. In older to make the results comparable, a bed of spheres of uniform diameter was choscn as the basis (E = 0.47). The results of these calculations are summarized in Table Is'. Most of the predicted pressure drops are lower than those found experimentally for moving beds, probably because the investigators for the most part recommend excessively large correction factors to allow for the change in fractional void volume from fixed to loose packed beds. Differing degrees of surface roughness of materials investigated are also partially the cause of variations in predicted resistance. Table IV is a comparison of predicted pressure drops from correlations exactly a9 reported by the various authors, not plots of the present data by their method of correlation. The method of Bakhmeteff and Feodoroff gives results in closest agreement with Equation 12-that is, using Figuie 4 to evaluate f. It will be recalled that this method also agrees substantially with the method adopted in this investigation for the prediction of the effect of changes in fractional void volume. The latest discussion by Bakhmeteff and Feodoroff ( 1 ) of thrir work indicates that in the viscous region the friction factors may be 90% of the value shown in Table IV-that is, a t N R =~ 10, f = 44.6.
Vol. 41, No. 6
The Chilton and Colburn correlation gives friction factors somewhat higher than predicted using Figure 4. This correlation is based 0n.a somewhat denser packing (probably E = 0.36 t o 0.42) than that approached in moving beds of uniform diameter spheres (t,hough not far from that obtained in the usual nonuniform beds). Making allowance for t,hisdifference in fractional void volume by means of the Carman, Fair, and Hatch type of equation (assuming that the change is entirely due t'o compaction since Chilton and Colburn employed uniform spheres) results in fairly good agreement with the present study. These lines are plotted on Figure 3 for comparison. Thus, the equation of Bakhmeteff and Feodoroff and the corrected correlation of Chilton and Colburn agree closely with the proposed correlation, except t,hat in the transition zone, corresponding in Table IV to the values report,ed a t = 100, the values predicted by Figure 4 are about joy0higher. I t is possible that the movement of thc bed induces turbulent flow at lower Reynolds numbers than in the case of static beds. -4s Rose (48) has pointed out, even with st,aticbeds the values of pressure drop in the transition zone are subject to considerable variation. Effect of Changes in Fractional Void Volume. The major point of disagreement among the various methods advanced for correlation of pressure drop dat8athrough granular beds is the proper evaluation of the effect of changes in fractional void volume. An attempt,, therefore, was made to st,udy this effect apart from the other variables involved and to compare various proposed methods for taking it into account. The fact that it is possible t o obtain a much wider variation in fractional void volume in a suspension than in a bed has resulted in the application of functions derived in this manner t o packed beds (13, 48). I t is felt that t,his procedure should be used with caution. In the case of sedimentation data, as a suspension becomes more concentrated by settling, the ratmeof settling is reduced not only by effect,s of fluid friction but by contacts between the particles themselves. Thus Steinour's (51) empirical correlation applies from E = 0.3 t o 0.7, and since even for perfect spheres B < 0.47 is impossible without contact between particles, it is apparent that, a t the lower E values some mechanical contact must occur, complicating the calculation of pressure drop from settling rates. With fluidization data, on the other hand, there appears to be considerable nonuniformity of solids distribution in concentrated suspensions result,ing in fluid by-passing with friction factors far below those predictable by correlations of the type used here ( 5 5 ) . Fractional void volume functions based on fixed bed studies involve less extrapolation to reach the range of moving bed data. They may, however, involve effects of change in packing arrangement due to a more complicated structure than is found in moving
Table V.
Comparison of Fractional Void Volume Functions Of Relativc Pressure Drop Fractional to E~=_0.40) Void Volume _ _ (Referred _ _ _ _ _ _ (Proportional At n = 1 htn = 2 To ' P ) e = 0 3 E = 0 5 e = 0.3 e = 0 . 5
- e)n+l
Equation 12
(1
Balchmeteff and feodoroff ( f )
G +
Brownell and Kata (6)
Graphical
Oman and Watsona (44)
1.30
0 695
1.59
0 578
1.47
0.746
1.82
O.li8R
1.40
0.557
2.66
0.386
2.20
0.475
1.90
0.574
e3
Roae (48) Graphical 2.28 0.440 2.28 0.440 Carman (8); Fair and (1 0.35s 2.77 0.42ii 3.25 Hatch (IS) €3 a Applies t o changes in fractional void volume due to differences i n shape; for compacting of regular shaped particles, the Fair-Hatch equation applies approximately.
June 1949
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
beds. As Graton and Fraser (80) have discussed, compacting of fixed beds tends to result in more or less systematic arrangements to accommodate the larger number of contacts between particles. It is also possible that different systematic arrangements may exist to some extent in moving beds involving alignment of particles to the condition corresponding t o minimum pressure drop. T o eliminate variables other than fractional void volume, it is convenient t o compare the relative pressure drops caused by the same change in fractional void volume from E = 0.40 as an arbitrary reference. Pressure drop is a function of V* where the exponent n = 1 in the viscous zone and n = 2 in the turbulent zone. Most investigators find t h a t the fractional void volume function will also vary with n. For Reynolds numbers even over 1000, n does not exceed 1.8 either for beds or individual spheres, so it must be presumed that completely turbulent flow is not attained. Comparisons on this basis are shown in Table V. Lapple has also used this method for comparing several proposed functions of this type (38). The effect predicted by Equation 12 agrees fairly well with the Bakhmeteff and Feodoroff relation but is far from agreement with the Carman, Fair, and Hatch equation. It is believed that a fairly simple explanation can be advanced to explain these discrepancies: the various investigators were measuring combinations of at least two different effects. Asmaller effect due to change in fractional void volume results when the change in fractional void volume is due to differences in shape and size gradation as compared with differences caused by varying degrees of compaction. Utility of Method. This method of correlation has been applied t o a number of tests on commercial TCC’units. I n general, the results check within the reliability of obtaining accurate Iarge scale data, usually t o better than =!=25%. I n many cases it is necessary t o make allowance for variations in the temperature and pressure gradients throughout the bed. This is especially true in cracking heavier stocks of higher molecular weight. Problems are involved also in the securing of representative samples of catalyst from which t o determine average catalyst diameter. Therefore, plant tests can never approach the accuracy possible in laboratory experiments. It is believed that Equation 12 as evaluated by the data given in Figure 4 constitutes a n improved method for the estimation of pressure drop through moving beds, taking into account the simultaneous effects of changes in uniformity and in fractional void volume caused thereby, as well as the usual variables. It should be useful not only in design problems for typical conditions but also to explore the effects of changes which influence pressure drop. ACKNOWLEDGMENT
Appreciation is expressed to D. F. Othmer of the Polytechnic Institute of Brooklyn, under whose direction this work was conducted, and to R. s.Aries of the same organization for encouragement throughout its course. The investigation was conducted while the author was in the employ of the Socony Vacuum Oil Company, Inc. G. S. Dunham and W. M. Holaday of this organization approved the program and generously placed facilities and assistance of the company’s laboratories at the author’s disposal. Acknowledgment is due t o many members of the Socony-Vacuum Research and Development Laboratories and especially to R. D. Drew who Conducted most of the experimental work. J. B. Rather approved the manuscript for publication, The author is also indebted to Manson Benedict, A. P. Colburn, C. C. Monrad, and R. L. Pigford for valuable suggestions. NOMENCLATURE
-4
= any arbitrary particle in a n assemblage
no
= = =
B D
any arbitrary particle in an assemblage diameter of particle; diameter of tube, feet average diameter of particles in a bed by reciprocal mean method, feet; D, = 100/2 (wul/D1)
1173
characteristic linear dimension of particle or duct, feet friction factor, gcApD,p/2LG2 modified friction factor, f x ( e ) ; in Equation 12, x ( e ) = 1/(1 e ) 3 frictional resistance of a particle to flow of fluid past it, Ib. force acceleration of gravity, 32.2, (ft./sec. )/( see.) conversion factor in Newton law of motion, 32.2, (lb.) (ft.)/(sec.)a (Ib. force) mass velocity, (lb.)/(sec.)(sq. ft.) proportionality constant length of a tube or bed, feet exponent of velocity in flow equations characterizing type of flow; for viscous flow n = 1, for completely turbulent flow n = 2 Reynolds number, D a G / ~ modified Reynolds number, N . R ~ x ( Ethe ) , function, x, being different than for modified friction factor; in Equation 21, X ( E ) = (1 - E) pressure drop, Ib. forcejsq. f t . distance from reference point origin in spherical coordinates, feet; r = 4 x 2 y2 f za velocity of fluid induced in a field b y presence of a particle or particles, ft./sec.; u = v - V induced velocity of fluid at center of a particle, B, f t ./sec. (hypothetical) mean induced velocity of fluid over surface of a particle, B, ft./sec. velocitv of fluid at anv Doint in field surrounding - a -particlei ft./sec. approach velocity of fluid, ft./sec.; for a single particle taken at a distance from the partic!e; for sedimenting particles, V i s the total velocity of solids relative t o the walls of the container; for a bed, V is the superficial fluid velocity over the entire bed cross section effective velocity of fluid which must be used to apply Stokes’ law t o a n assemblage of particles, ft./sec. characteristic velocity around particles or through channels in a bed of particles, ft./sec. total volume in a system of particles through which fluid is passing, cu. ft. Divided into 21,ZZ,and 28, 2 1is a volume of thickness, D / 2 , along the walls of the vessel. Zzis the region between the surface of particles, A , and a spherical surface with a radius, D. 2 3 is the remaining s ace weight percentages o f screened fractions of material 201, w2,etc., having average diameters of D I , Dz, etc. rectangular coordinates; 2 = T cos 8, y = r sin 0 cos 4, andz =rsinBsin4 finite difference a2 a2 a2 Laplacian operator, .tr 2 = 32 2 + @ + 52
-
+
I
_
fractional void volume in a suspension or granular bed; for a moving bed as in Equation 12, e is at loose apparent density viscosity, absolute, lb./(sec.)(ft.) density, usually refers t o fluid, lb./(cu. ft.); where dlstinction is necessary subscripts s and f used to refer t o solids and fluids, respectively function; used as x ( e ) , the fractional void volume function in friction factor relationships function; used as $ ( N R # ) ,the function of Reynolds number in friction factor relationships BIBLIOGRAPHY
(1) Bakhmeteff, B. A. and Feodoroff, N. V., J . Applied Mechanics, 4, A97 (1937) ; Ibid., 5, A86 (1938) ; Proc. 6th Intern. Congr. Applied Mechanics, p. 555 (1938); Trans. Am. Geophys. Union, 2 4 , 5 4 5 (1943). (2) Berg, C., Trans. Am. Inst. Chem. Engrs., 42, 665 (1946). (3) Blake, F. C., Ibid., 14, 415 (1921-2). (4) Brinkman, H . C., Applied Sci. Research A l , 27 (1947); Proc. Koninbl. Abad. Wetenschap. Amsterdam, 50, 618, 860 (1947). (5) Brownell, L. E. and Katz, D. L . , Trans. Am. Inst. Chem. Engrs., 43,537 (1947). (6) Burgers, J. M., Proc. Koninkl. Abad. Wetenschap. Amsterdam, 43, 315, 425, 645 (1940); 44, 1045, 1177 (1941); 45, 9, 126 (1942). (7) Burke, S. P., and Plummer, W. B., IND.EXG.CHEM.,20, 1196 (1928). ( 8 ) Carman, P. C., Trans. Inst. Chem. Engrs. (London), 15, 150 (1937); J . SOC.Chem. I n d . (London), 57, 225 (1938); 58, 1 (1939).
1174
INDUSTRIAL A N D ENGINEERING CHEMISTRY
(9) Chilton, T. H., and Colburn, A. P., Trans. Am. Inst. Chem. Engm., 26, 178 (1931). (10) D’ilrcy, H. P. G., “Les Fontaines Publiques de la Ville de Dijon,” Victor Delmont, Paris, 1856. (11) D:bye, P., and Bueche, A. M.,J . Chem. Phys., 16, 573 (1948). (12) Einstein, A., Ann. Physik, 19, 289 (1906); 34, 591 (1911). (13) Fair, G. M., and Hat,ch, L. P., J . z4m. Water Works Assoc., 25, 1551 (1933). (14) Fraser, H. J . , J . Geol., 43, 785 (1935). (15) Furnas, C. C., U . 8.Bur. Mines Bull. 307 (1929) (16) Furnas, C. C., IWD. EXG.CHEM., 23, 1052 (1931). (17) Gamson, B. W., Thodos, O . , and Hougen, C. A , , Trans. Am. J 7 ~ s t .Chem. Engrs., 39, 1 (1943). (18) Givan, C. V., Trans. Am. G q p h y s . Union, 15, 572 (1934). (19) Goldstein, G., Proc. Roy. SOC.(London),A123,225 (1929) (20) Graton, L. C., and Fraser, H. J., J . Geol., 43, 785 (1935). (21) Cuth, E., KolloidZ., 74, 147 (1936). (22) Guth, R., and Simha, R., Ibid., p. 266. (23) Hancock, R. T., Mining N a g . , 55, 90 (1936); 67, 179 (1943). (24) Hatch, L. P., J . Applied Mechanics, 62, A109 (1940). (25) Hatch, L. P., Trans. Am. Geophys. Union,24, 537 (1943). 126) IIevwood. €1.. 3. Soc. Chem. Ind.. 56. 149 11937). (27) Hi&, A. A., Tr.ans. Inst. Xn\ng Engrs. (London), 85, 236 (1932-33) ; 9 4 , 9 3 (1937-38). (28) Kerniack, W. D., LI’Kendrick, A . G., and Ponder, E., Proc. Rog. Soc. Edinburgh, 49, 170 (1929). (29) Kirkwood, J. G., and Riseman, J., 3. Chwn. Phys., 16, 565 (1948). (30) Koseiiy, J., Sitrbe?. Akad. m i s s . Wien, 136, IIa, 271 (1927). (31) Lamb, H., “Hydrodynamics,” 6th ed., p . 598, D o m r Publications, New York, N.Y., 1945. (32) Landolt-Bornstein, “Physikalisch-Cherriirche Tabellen,” Julius Springer, Berlin, 1935. (33) Lapple, C. E., Trans. Am. Inst. Chem. Engrs., 43, 544, ,546 (1947). (34) Lapple, C. E., and Shepherd, C. D., IND.I-KG. CHmf., 32, 605 (1940). (35) Leva, M,, Chem. Eng. Progress, 43, 549 i1947). I
~
ROPS
Vol. 41, No. 6
(36) Leva, M., and Grummer, M., I b i d . , pp. 633, 713. (37) Leva, M., Grummer, M., Weintraub, M., and Pollchik, M., Ibid., 44,511 (1948). (38) Lindquist, W., First Congress of Large Dams, Stockholm, Sweden, Rept. 81 (1933) (39) Meyer, W.G., and Work, L. T., Trans. Am. Inst. Chem. Engrs., 33, 13 (1937). (40) Moody, L. F., Trans. Am. SOC.Mech. Engrs., 66, 671 (1944). (41) Muskat, M . , “Flow of Homogeneous Fluids Through Porous Media,” McGraw-Hill Book Co., New York, 1937. (42) Newton, R. H., Dunham, G . S., and Simpson, T. P., Trans. Am. Inst. Chem. Engrs., 41, 215 (1946). (43) Norton, C. L., Jr., J . Am. Cerum. SOC., 29,187 (1946). (44) Oman, A. O., and Watson, K. M., Natl. Petroleum News, 36, R795 (1944). (45) Parent, J. D., Yagol, N., and Steiner, C. S., Trans. Am. Inst. Chem. Engrs., 43, 429 (1947). (46) Perry, J. H., editor, Chemical Engineers’ Handbook, 2nd ed., McGraw-HillBook Co., New York, 1941. (47) Pipes, L. A., “Applied Mathematics for Rngineers and Physicists,” p. 24, McGraw-Hill Book Co., New York, 1946. (48) Rose, R. E., Proc. Inst. Mech. Engrs. (London), 153, 141 (1945). (49) Simpson, T. P., Evans, L. P., Hornberg, C. V., and Payne, J. W., Proc. Am. Petroleum Inst., 23, 59 (1942). (50) Simpson, T. P.,Evans, L. P., Hornberg, C. V., and Payilr, ,J. W., I b i d . , 24, 23 (1943). (51) Steinour, H. H.. IXD. EKG.CHEM.,36, 618, 840, 901 (1944). 152’1 Steinour. €1. H.. Research Laboratoiv. Portland Cement , Assoc., Chicago, Assoc:, Chicago’, Ill., Bull. 4 (1946). ( 5 3 ) Wadell, H., J.Franklin Inst., 217, 459 (1934). (54) Walker, W.H., H , Lewis, W.K., McAdams, W. H., and Gilliland, E. R., “Principles “Piinciples of Chemical Engineering,” 3 3rd 1 d ed., New York, McGraw-HilI Book Co., 1937. (56) Wilhelm, R. H., and Kwauk, M., Chem. Eng. Progress, 44, 201 (1948). (56) Work, L. T., and Kohler, A. B.,IND.EKG.CHEM.,32, 3929 (1940) ; Trans. Am. Inst. Chern. Engrs., 36, 701 (1940). I
“
I
I t w E w m February 21, 1949.
e encountered in Conveying
Particles of Large Diameter in Vertical Transfer Lines D a t a on pressure drop are presented for t h e vertical transport of spherical catalyst approximately 0.04 and 0.08 inch i n diameter. A tentative correlation of these data is developed i n which total pressure drop is expressed as a static t e r m based on actual particle density in t h e transfer line, and a friction t e r m which involves t h e particle mass velocity, b u t is independent of particle diameter and density. T h e data are compared w i t h t h e data and correlation of Vogt and White, and i t is shown t h a t their correlation involves a n apparently incorrect dependence on ratio of tube diameter t o particle diameter. A modified correlation of their type m a y be satisfactory.
D.H.BELDEN A N D LOUIS S. KASSEL UNIVERSAL OIL P R O D U C T S C O M P A N Y , C H I C A G O , ILL.
P
KEUMATIC conveyers have long been used for transport of granular solids, particularly in handling grain. I n recent years pneumatic transport has come into extensive use for circulation of catalyst in catalytic cracking systems. In this application, and in a few others of less frequent occurrence, the solid being transported moves continuously around a closed circuit. The pressure balance around this circuit is of critical importance in plant design. The work here reported was done several gears ago t o obtain data for the design of a catalytic cracking pilot plant of movingbed type, Myith gas-lift catalyst transport. The work mas not planned for the purpose of developing a general correlation, but more or less accidentally a tentative correlation was produced which seemed suitable for publication. The work of Vogt and White (6appeared long after the authors’ apparatus had been
dismantled, and there has been no opportunity to reinvestigate some points of apparent disagreement. EXPERIMENTAL DATA
The apparatus used in obtaining data on pressure drop in vertical transfer lines is shown in”Figure 1. The orifice used to control catalyst flow mas equipped with a gas by-pass. Such a device delivers catalyst at a rate which depends upon catalyst characteristics and orifice dimensions, but is independent of conditions in other parts of the circuit. The actual discharge rate was determined for each orifice-catalyst combination by weighing the catalyst discharged in a measured time. This type of orifice can be used only with free-flowing particles. Catalyst particles discharging from the orifice were picked u p by a stream of metered 70” F. gas and transported vertically 13.5
