568
Ind. Eng. Chem. Process Des. Dev., Vol. 17,No. 4, 1978
Gas and Liquid Holdups in Mobile Beds under the Countercurrent Flow of Air and Liquid Masao Kito,' Koichi Tabel, and Kolchi Murata Department of Chemical Engineering, Gunma University, Khyu, Gunma 376, Japan
Gas and liquid holdups in mobile beds and their dependence on process variables was studied. The gas holdup depended on the gas velocity and was independent of the liquid flow rate and other variables. The liquid holdup was affected by operating regimes. In the primary regime, the amount of liquid retained per unit cross-sectional area of the bed was not affected by the gas flow rate. It increased with liquid velocity, although it was also affected by other variables. In the second regime, it increased with the increasing gas flow rate. The liquid holdup was studied in the primary regime. Correlations are presented for the gas and liquid holdups in terms of independent process variables.
Introduction A few papers on experimental measurements of liquid and gas holdups of a mobile bed have been published. Results of investigation under different operating conditions show the strong dependence of the liquid holdup on liquid velocities, the characteristics of the supporting grid, and the properties of packing. Chen and Douglas (1968) and Barile and Meyer (1971) presented empirical correlations for the liquid holdup, but the former has not taken into account the effects of the packing density and the characteristics of the supporting grid on the liquid holdup, while the latter is applicable only a t the minimum fluidization velocity. The gas holdup was studied by Balabekov et al. (1969), Kit0 et al. (1976a), and Krainev et al. (1968). An empirical correlation for the gas holdup was presented by Kit0 et al. (1976a), which was obtained under the liquid stagnant flow system. The correlation, therefore, applied only t o the systems investigated, and may not be extended for the design of apparatus operating under different process conditions. The purpose of this investigation is to determine the liquid and gas holdups and dependence on physical properties of liquid and process variables such as liquid and gas velocities, the diameter and density of packing, the characteristics of the supporting grid, and the static height of packing. Experimental Section The experimental apparatus is outlined in Figure 1. The main body of the column is a 10-cm diameter cylinder made of transparent acrylic resin. Sieve plates were used as the supporting grid. Table I lists their characteristics. The fluidized packings were spheres made of light plastics materials. Table I1 lists the properties. The static bed height of packing was varied from 10 to 30 cm. The system investigated was a countercurrent flow of air and liquid. Liquids used were water, an aqueous glycerin solution, and ethanol, Table I11 lists their physical properties. The superficial gas and liquid velocities were varied from minimum fluidization velocity to 350 cm/s and from 0.3 to 3.5 cm/s, respectively. Measurements were made usually with a starting flow rate slightly under the minimum fluidization velocity. The air flow was then increased gradually while the succeeding measurements were taken. The gas holdup was determined by directly measuring the height of the aerated bed and that of bed without aeration. The average fractional gas holdup can be given as t G = H G / ( f f c + HL + HP) 0019-7882/78/1117-0568$01.00/0
Table I. Characteristics of Supporting Grid grid 1 grid 2 grid 3
0.22 0.39 1.2
0.712 0.705 0.84
0.0186 0.0327 0.109
Table 11. Properties of Packing Dp,cm 0.97 0.98 1.16 1.95 1.95 2.85 2.85 pp,g/cm3 1.25 1.25 0.76 0.17 0.54 0.29 0.59 Table 111. Properties of Liquid (at 20 "C)
material ethanol 25 wt % glycerol solution 65 wt % glycerol solution water
surface density, tension, viscosg/cm3 dyn/cm ity, CP
0.797 1.068 1.165 0.998
22.5 70.8 67.5 72.8
1.38 1.33 14.45 1.01
A shutter located under the supporting grid was used to determine the amount of liquid held up in the bed. The height of clear liquid, HL,represents the corresponding volume of liquid retained per unit cross sectional area of the bed. Results and Discussion Gas Holdup. Figures 2 and 3 show effects of the packing density, physical properties of liquid, and the static bed heights on the gas holdup. The value of EG is nearly independent of packing density, the liquid viscosity and the static bed height. Figure 4 shows that the effect of the liquid velocity on the gas holdup, tG for different liquid velocities coincides with that for the liquid stagnant flow system. t G is seen to be unaffected by the liquid velocity. Figure 5 shows the effect of the free opening of the supporting grid on tG. In Figure 5, the present work was also compared with that of Balabekov et al. (1968) and Krainev e t al. (1968). Even though measurements are conducted under different conditions, t G is in agreement with that of Balabekov e t al. (1969) and Krainev et al. (1968). The result shows that t G is independent of the free opening area and the hole diameter of the supporting grid. No effect of the packing diameter on t G was observed over the range of gas flow rates studied. The plot of experimental data, EG, against on log-log paper gave a straight line with the slope of -0.22. Many variables come to mind as factors that influence t G , As is shown by the results of Figures 2-5, this study assumed the factors responsible for their effect on t~ as 0 1978 American Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 4, 1978
-,
569
05
I
w" 0 17
02 80 100
300
200 UG
400
[cmlsecl
Figure 5. Effect of the free opening area of the supporting grid on @Tank
@Packing
Q Pump
@Gas
@ Rotameter @ Solenoldvrivc
@ Shutter I
-
Dp = 0.97 2.85 ~ c m l
@Gas Disperser
@ Llquid
Disperser
@Cas
@Mobile
Bed
@Manometer
C Cock,
CG*
Distributor
V Valve
Manormter
Pressure
for Drop
Figure 1. Schematic diagram of experimental apparatus, IO Pp
-A
Igicm31
05
Y
[crnisecl
Ut
Figure 2. Effect of
pp
on
t ~ .
1
25wt'I.
glycerol
soln.
EGCd1.r- 1
I+]
65wtn/. g l y c e r o l s o l n .
Figure 6. Comparison between
and
CG tal.
10
130
150
uc
200
250
LClllSeC1
Figure 7. Relation between HL and UL.
1
I , , / , I
0.1 10
30
50
100
I
,
300 500
6
DP=I 95Um3 PP=O17t9lcm33 Hs=lOCcml grid 2 Key Material A O 25wt*/. W a t e r glycerol soin
UG[crn/ s e c ]
Figure 3. Effect of physical properties of liquid on
1 /-
..
tG.
0
65wly. glycerol soin Ethanol
0
1
CG obs
05 U ~ = O c r n l s e c3 ~
/o 013
OS2
130 UG
Figure 4. Effect of UL on
200 300 400 [crnlsecl
' " I
06
10
20
35
Figure 8. Relation between H L and UL.
tG.
= C(We)a(Fr)b
From the results obtained, eG for the fully fluidized mobile bed could be expected as follows tG
'
UL t c r n / s e c ~
being UG, g , g, and pL to obtain the following empirical equation. tG
'
= 0.19(We)E11(Fr)E22
(1)
In Figure 6, all the data are plotted in accordance with eq 1. Liquid Holdup. The amount of liquid retained per unit cross-sectional area of the bed, HL, is shown in Figure 7. From Figure 7 , it is evident that in the range from the minimum fluidization Velocity to the flooding velocity (about 120 and 300 cm/s under the given operating condition, respectively) HL is not affected by the gas in Figure velocity. The value of H L is proportional to ULo,GQ
570
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 4, 1978 Dptcml
Hs=,O[cml grid 2
pp[g/cm31 Ut=l5[cmiuo ~ ~ - ? ~ t c m / s e c ~
195
017
2.85
029
0
A A
10-
~
1
3 4 PL IC P I
2
5
10
7
20
Figure 9. Relation between HL and WL.
0
mi
QOZ
a03
004
005
(fa) (G) 8
Figure 11. Generalized correlarion of
30
20
40
50
70
100
Figure 10. Relation between HL/pL*.'' and u.
8, although it is also affected by physical properties of liquid. Figures 9 and 10 illustrate that HL is proportional to pLo.I6and u0.34.Plots of experimental data, HL, against Hs, pp, Dp, and fd/D on log-log paper gave straight lines with slopes of 0.6, 0.18, -0.84, and -0.58, respectively. Thus, the value of H L can be represented as follows HL =
(
uL)o.64(~L)o.16(.)o.34
(2)
Barile and Meyer (1971), Chen and Douglas (1968), and Gelperin et al. (1968) reported relations between the liquid holdup and the experimental dimensioned variables such as UL,Dp, and Hs. In their results, the exponents of Hs and U , range between 0.5 and 1.0, and that of Dp ranges between -0.5 and -1.0, respectively. The liquid holdup defined as HL/(HG HL + H p ) will be a complex function of process variables such as the gas and liquid velocities, the properties of packing, and the characteristics of the supporting grid. As shown in Figure 7 the value of HL is independent of the gas velocity. Thus, the liquid holdup is simply defined as HL J H s , instead of H L / ( H G+ H L + Hp). Since the liquid holdup is a balance of viscous, gravity, and surface tension forces, the Froude number, the Galileo number and the Weber number are expected to appear in the correlation. From the results obtained, an experimental correlation for the liquid holdup could be represented by dimensional analysis as follows HL CSL = - = HS
+
(
c -$)-0'4(
007 03'
IlL
C~L.
et al. (1975), and Chen and Douglas (1968) are also correlated well by eq 3. The value of C in eq 3 determined from Figure 11 is 12.8. The liquid holdup, CL, is correlative with C S L as follows (4) C L = (Hr,,"s)(Hs/H) = es~/(H/Hs)
P Ldynicml
C(Hs)0.6(Dp)-o.84(pp)o.18 f;)-0,58(
a06
08'm-m4 (7 (%)L ) ( 1 ( DPULZPL T ) L
d -0% Hs-O1gDdPd Oo9
f%)-O'Is(Ga)O.Os(Fr)~66(Re)-0.34(We)t0.34
(3) where H s / D p is a measure of the number of expansion contraction cycles which the gas must undergo in passing through the bed giving rise to substantial form drag on both liquid and packing. In Figure 11,all the data are plotted in accordance with eq 3. Results obtained by Tichy et al. (1972), Blyakher
The term H / H s in the denominator means the expanded bed height. Kit0 et al. (1976b) proposed the following correlation for the expanded bed height. H / H s = (1 + ~ S L- csp)/(1 - C G ) (5) From eq 4 and 5 , cL can be respresented as q = CSL(1 - € G ) / ( 1 + CSL - CSP)
(6)
Equation 6 will be useful for the prediction of the liquid holdup. Conclusion The gas and liquid holdups have been measured in a mobile bed. The following conclusion can be drawn from this study. 1. The gas holdup depends on the gas velocity and the surface tension force of liquid and is independent of the liquid velocity, the properties of packing, and characteristics of the supporting grid. The gas holdup can be represented by eq 1. 2. The value of the liquid holdup tSL defined as the ratio HL/Hs in the fully fluidized mobile bed is essentially independent of the gas velocity up to the flooding point and can be represented by eq 4. Acknowledgment The author wishes to thank Professor C. Y. Wen, West Virginia University, and Professor S. Sugiyama, Nagoya University, for their discussion. Nomenclature A = cross-sectional area of tower, cm2 D = equivalent diameter for free sectional area, cm Dp = packing diameter, cm d = equivalent diameter of slot or orifice, cm Fr = Froude number, WG/(gDp)'/', UL/(gDp)1/2 f = free opening of supportin grid Ga = Galileo number, gDp3p, 8/ P L ~ g = acceleration due to gravity, cm/sz H = expanded bed height, cm HG = V G / A ,cm HL = height of clear liquid; liquid volume retained per unit cross sectional area of bed, cm HP = net static packing height HSCSP, cm H s = static packing height, cm Re = Reynolds number, D p u ~ p ~ / w ~
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 4, 1978 571
UG= superficial gas velocity, cm/s UL = superficial liquid velocity, cm/s VG= gas volume in aerated bed, cm3 We = Weber number, DpUG2PL/U, DpUL’pLla Greek Letters t~ = gas holdup, HG/H tL = liquid holdup, HL/H tSL = liquid holdup defined by eq 3 tsp = void fraction in a dry packed bed pL = viscosity of liquid, g/cm s PI, = density of liquid, g/cm3 pp = density of packing, g/cm3 a = surface tension, dyn/cm Subscripts cal = calculated G = gas
L = liquid obs = observed Literature Cited Bahbekov, 0. S..Romankov, P. G., Tarat, E. Ya., Mikhlev, M. F.,J. &pi. Chem. U.S.S.R., 42, 1454 (1969). Blyakher, L. G., Zhivaikin, Ya., Yurovskaya, N. A., Int. Chem. fng., 7 , 485 (1975). Barile, R. G., Meyer, D. W., Chem. f n g . Progr. Symp. Ser., 87, No. 119, 134 (1971). Chen, 8. H.. Douglas, W. J. M., Can. J . Chem. f n g . , 48. 245 (1968). Gelperin, N. L., latyshev, Yu. M., Blyakham, L. I., Int. Chem. E-., 8, 691 (1968). Kto, M., Sawada, M. Shimada, M., Takata, T., Sakai, T., Sugiyama, S., Kagaku Kogaku Ronbunshu, 2 , 12 (1976a). Kito, M., Kayama, Y., Sakai, T., Sugiyama, S., Kagaku Kogaku Ronbunshu, 2 ,
..- \.’.-“,.
A7R IIQ7Rhl
Krainev, N. I., Niyazov, M. I., Levsh, I. P., Umarov, S. U., J . Appl. Chem. U.S.S.R., 41, 1961 (1988). Tichy, J., Wong, A., Douglas, J. M., Can. J . Chem. Eng., 5 0 , 215 (1972).
Received for review January 16, 1978 Accepted June 13, 1978
A Comparison of Correlations for Saltation Velocity in Horizontal Pneumatic Conveying Peter J. Jones” and L. S. Leung University of Queensland, St. Lucia, Queensland 4067, Australia
Eight well-known published correlations for horizontal saltation velocity are compared using the accumulated solids-air data of many workers in the field. The correlation of Thomas (1962) is recommended a s being the most accurate available for a priori prediction of saltation velocity. Other correlations tested were due to Zenz (1964), Matsumoto et al. (1974, 1975), Rizk (1973, 1976), Mewing (1976), Rose and Duckworth (1969), and Doig and Roper (1963).
Figure 1 is a schematic diagram of the variation of pressure drop along a horizontal pipe with gas velocity at various solids mass fluxes. Line AB is for gas only in the pipe. As solids mass flux increases, the pressure drop per unit length of pipe increases. For any particular solids rate (i.e., a line of constant solids mass flux CDEF) the pressure gradient in the pipe decreases as superficial gas velocity is decreased until a minimum is reached (D). This point is defined as the “saltation point” and the corresponding gas velocity is the “saltation velocity”. If the gas velocity is further reduced, the pressure gradient increases dramatically and the pipe operates in the dense phase regime with or without slugging. The “saltation point” coincides approximately with the point a t which particles are observed to drop out of suspension and remain in a stationary layer on the bottom of the pipe, or a t which particles stop rolling or sliding along the bottom of the pipe. For economic operation of pneumatic conveyors it is not desirable to have particles on the bottom of the pipe. By the same token, the gas velocity should be as low as possible t o minimize pipe erosion and power consumption in the blower. To quote Scott (1977): “... the greatest difficulty facing the designer is the choice of an acceptable gas velocity. If the minimum transport saltation velocity for a given material in a particular system is known a reasonable prediction can be made for that material in other systems. However, the choice of an acceptable minimum velocity for a new material must a t present be based on experiments or on the designer’s experience.” 0019-7882/78/1117-0571$01.00/0
We shall therefore evaluate each of the well-used correlations for saltation velocity to give the designer a “best buy” expression for a priori estimation of a minimum acceptable air rate in horizontal conveying.
Correlations for Saltation Velocity Several workers have published correlations for saltation velocity as defined above. Each expression presented below has been converted to S.I. units for consistency and clarity. The first and simplest of these is due to Dallavalle (1942). He proposed the relation (for both vertical and horizontal pneumatic transport lines)
Us = k p s d p “ ’ / ( p s+ 1000)
(1)
(dp in mm, p s in kg m-3, and Us in m s-l) where the parameters k and n’and their respective vertical and horizontal values are: h, 8.96, 8.35; n’, 0.60, 0.40. Clearly, his correlation takes no account of the solids loading in the pipe, which has been shown to be an important variable by every other worker in the field. For this reason, the Dallavalle equation will not be considered further here. Barth (1954, 1958) and Welschof (1962) recognized that a dimensionless expression might be more fruitful. It was observed that the Froude number a t saltation (defined as Us/(gD)’I2)varied in a power law relationship with the solid t o gas flow ratio. Barth proposed that
W s /W ,
M* = KFr:
0 1978 American Chemical Society
(2)
