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The plate efficiency of multistage fluidized-bed adsorbers
The Chemical Engineering Journal, 21 (1981) 1 - 9 0 Elsevier Sequoia S.A., Lausanne - Printed in the Netherlands
The
Plate Efficiency
1
of Multistage Fluidized-Bed
Adsorbers
J. VANDERSCHUREN Service de GEnie Chimique,
Faculte’ Polytechnique
de Mons, rue de I’Epargne, 7000 Mons (Belgium)
(Received 12 December 1976; in final form 18 October 1979)
Abstract The operation of a continuous five-stage fluidized-bed pilot adsorber, in the drying of air on activated alumina, gives Murphree plate efficiencies which increase with the ratio of solid to air flowrates and reach maximum values at twice the minimum fluidization velocity. The results are interpreted according to the Cholette and Cloutier model which considers dead zones and bypassing of particles on the plates. This solids flow pattern is confirmed by means of tracer studies.
Ijlates which are supplied with downcomers for the overflow of solids. The number of theoretical plates of multistage fluidized adsorbers can be determined by means of the classical graphical or numerical methods for continuous countercurrent plate columns.
2. PLATE EFFICIENCIES
The overall column efficiency the well-known relation [ 121 E
=
ln[l
+EMG(l/r-ll)l
0
1. INTRODUCTION
Multistage fluidized beds are used in continuous adsorption processes such as gas drying [l - 31, purification of effluent streams containing nitrogen oxides [4] , carbon disulphide [ 51, hydrogen sulphide [6] or sulphurous oxide [ 71, and solvent or vinyl chloride recovery [ 8 - 111. Multistage fluidization is particularly suitable for these processes when the gas concentrations are low and the flowrates very large [lo]. A gas velocity much higher than in classical fixedbed adsorbers can be used [ 1,2, lo] , resulting in a lower bed cross-section and a considerable reduction of the initial weight of adsorbent in the column. The stages used are very shallow, [ 2, lo] , about 5 - 10 cm in depth, in order to obtain greater adsorption rates with the same total weight of adsorbent [8] and to reduce the total pressure drop. A minimum particle height is, however, required to maintain good plate behaviour. Two kinds of plates are used: high-free-area sieve plates with large holes through which gas and particles flow sirnultaneously, and the common low-free-area
is given by
(1)
W/r)
where EMo is a Murphree plate efficiency analogous to that used in gas-liquid contacting: E MG=
G-1
-c*
(2)
&I--l --c*(aI)
and r is the ratio of the slopes of the operating and equilibrium lines: r=
Qs/bQc
(3)
The equilibrium line is here supposed straight and has for its equation c* = a + bq
to be (4)
The Murphree plate efficiency depends on the mechanism of the gas-solid contacting process and on the mass transfer rates. Estimations of Murphree efficiencies can be carried out in two steps in the same way as for gas-liquid tray efficiencies. By means of a model describing the particle path and the extent of solids mixing on the plate, EM, is related to a point or local efficiency EPG: E,=
cn-1 cn-1
-cQ
-c*(qQ)
2
which itself depends on the mass transfer resistances between the phases. In the case of perfect particle mixing on the plate, EMMGand E,, are obviously equal. For plug flow of particles, without or with longitudinal dispersion, the relations are reported in the Bubble Tray Design Manual [ 121. E,,/EpG uersus E&r graphs [ 121 show that EMGIEpG increases with E&r and with the Peclet number for longitudinal dispersion. As will be seen later, the Cholette and Cloutier model [ 131 is also convenient to describe the residence time distribution of the particles on the plates. In this model (Fig. l), a fraction x of the solid feed bypasses the plate, and a fraction y of the stage volume is perfectly mixed, the other part 1 - y being a dead zone. Resolving the equations of this system (see Appendix) allows us to calculate the expression for E,, : E MG
YU -x1
-=
EPG
1 -X
+XYEpG/r
(f-5)
Fig. 1. Cholette and Cloutier model of the flow of solids on a plate.
Figure 2 shows that the Cholette and Cloutier model predicts a decrease of EMG/EpG as EpG/r, x or 1 - y increases. The point efficiency EpG in a plate section is assumed to be the efficiency E of a bed of equal depth which is not fed with particles, because the solid concentration is then uniform owing to the intensive mixing induced by bubbles. For normal fluidizing conditions (d, < 1 mm and H > 20 - 30 cm), Kunii and Levenspiel [ 141 consider that the gas exiting from a batch fluidized adsorbent layer is at mass transfer equilibrium with the solid particles.
014,II 03
05
10
j
4
1.5
I
3,
E&/r
-
Fig. 2. Murphree efficiencies given by the Cholette and Cloutier model.
This proposition is confirmed by the experimental works of Angelino and his collaborators [ 15 - 171 on the drying of air with activated alumina and the adsorption of COz on a molecular sieve. Under these conditions the efficiency E is thus equal to unity. But that will not always be so, especially for the very shallow beds used in multistage adsorbers. Actually, Ermenc [ 21 found, in the drying of air with silica gel, efficiencies lower than unity which increase with the weight of gel on the plates. Mass transfer equilibrium between gas and particles is not necessarily reached at the top of the fluidized layer, because mass transfer resistances are encountered between the bubbles and the gas of the emulsion, in the laminar gaseous film outside the particles and in the pores of the adsorbent.
3. THE EXPERIMENTAL
MATERIAL
Our investigation of plate efficiencies was made during the drying of air on fluidized beds of activated alumina. We took a 125 630 pm fraction of this adsorbent with a mean particle size d, equal to 448 pm. The other properties of the adsorbent are grouped in Table 1. The internal structure was studied by means of a mercury porosimeter and a nitrogen BET-sorptometer; the exis-
TABLE 1 Characteristics
of the activated alumina (125 - 630 pm) %M
%n
PP
Pb
(Wm3)
(Wm3)
1240
775
0.474
0.118
6 18
x
36
2920
tence of a bidispersed pore size distribution was revealed. The vapour pressures of the water adsorbed on this activated alumina were carefully determined for several water contents at different decreasing temperatures by using a modified isoteniscope. Figure 3 shows these adsorption isosteres. All the measurements were correlated with a mean error of 6% by the following equation : 54.20
T,ln~*=384.2--
4
0.6030 +-q2
0.002219 q3
(7)
in the range 0.02 B q < 0.09 kg/kg, 40 < T < 150 “C. The reference state for the water contents was obtained by regenerating the material at 205 “C.
1000
‘_
PH20. ImmHgl:
Fig. 3. Vapour pressures of water on activated alumina.
0.592
4. STUDY
(m2/g)
;A,
242
39
0.428
0.155
OF POINT EFFICIENCIES
Prior to the investigation of Murphree plate efficiencies in a multistage continuous adsorber, we determined the efficiencies of some batch fluidized layers of activated alumina (125 - 630 pm). The fluidization column consists of a Plexiglas cylindrical tube of 0.12 m inside diameter, equipped at the bottom with a 3 mm thick sintered bronze gas distributor. The column was first loaded with a given volume of freshly regenerated adsorbent. An air stream at constant flowrate and humidity was then fed to the bed. Temperatures were recorded continuously in the feed, in the exit air and at the top of the fluidized layer. These two latter temperatures are always equal because heat transfer equilibrium is reached at the top of the bed. They pass through a maximum value during the first part of the run, and then decrease continuously. Inlet and outlet humidities were measured with a dew point hygrometer, the outlet measurements being corrected by taking into account the air sampling line response time. From time to time during the run, small samples of solid particles were withdrawn from the bed and their water content determined by weighing after regeneration at 205 “C. For each particle loading q, the recordings give the corresponding air temperature TH and partial pressure pn , and thus the relative humidity qn. The equilibrium relative humidity cp*(q) is obtained by means of eqn. (7). The bed efficiency can then be calculated by the expression E=
The diffusivity of water vapour in the alumina particles was measured by using an unsteady-state concentration step method which give a mean value of D, equal to 10-l’ m2/s.
GlIf
s,
VO-PH cpo
-v*(q)
If the experimental results (pn, q) are represented in a (9, q) diagram together with the isotherms, it can be seen (Fig. 4) that E = -AB/AC.
wtherms
I7
frcml eqvatlon
I
LO’C 2o’c
/
0
Fig. 4. (9,
0.05
q
1kg/kg1
I 0.1
-
q) diagram for the batch runs.
The experiments were performed for three bed heights (0.035, 0.07 and 0.10 m) and three fluidization velocities (Q/u,.,,~ = 1.5,2 and 2.5) with inlet relative humidities cpo of about 0.4. Figure 4 shows that most of the bed efficiencies are equal to unity. However, although the particles are rather small, bed efficiencies become significantly lower than unity for the two shallowest beds (0.035 and 0.07 m) and u~/u,,,~ = 2.5, the mean values of E being equal, respectively, to 0.82 and 0.93. These results are in good agreement with predicted values made by using the two-phase model [ 181 for fluidized-bed contactors (see Table 2). For the computations, the rate of adsorption in the emulsion phase was taken from the experimental internal diffusion coefficient, and the bubble diameter estimated at mid-bed height by means of the correlation of Kato and Wen [19].
Calculated efficiencies of fluidized beds of activated alumina (125 - 630 pm)
1.5 2 2.5
-dry
air
1. five plate column 2. hopper 3. rotary valve L. davncomer 3 collection
vessel
6. flow meter 7. cyclone 8 air
6
sompbg
tine
g thermocouple
.~
TABLE 2
uol%f
of a continuous multistage pilot air dryer. The column is made of brass with an easily removable glass front face. It contains five rectangular boxes (cross-section 140 mm X 95 mm, height 150 mm), spaced 240 mm apart (Fig. 5). The bottom plates of these boxes are perforated with a 7.5 mm pitch of 2.5 mm diameter holes and covered with a wire gauze which prevents flow of particles through the holes. Each plate is provided with a cylindrical downcomer of 25 mm inside diameter and 265 mm total length, leading the solids from the upper surface of a bed into the fluidized layer below. The downcomers are alternately located on the left and right-hand side of the cross-section (Figs. 5 and 6). They can slide through the distributors to enable the bed height to be varied.
%f
t tumid
air
Fig. 5. Sketch of the five-plate continuous pilot air dryer.
04
0.035
0.07
0.10
0.135
0.971 0.912 0.800
1.000 0.990 0.941
1.000 0.998 0.997
1.000 1.000 0.999
c
/I__, i ‘I
‘i.!_/ 5. EXPERIMENTAL DETERMINATION OF MURPHREE EFFICIENCIES 5.1. Pilot plant and procedure The Murphree efficiencies were measured for the same adsorbent during the operation
_ -I_”
Fig. 6. Location of the downcomers on the plates.
5
The fresh adsorbent is fed to the column at a constant flowrate through a small rotary valve driven with a variable-speed motor. The solids are collected at the outlet in a sealed vessel. The air is provided by a liquid-piston rotary blower, of which the sealing liquid is water maintained at constant temperature; constant air humidity is thus ensured. Temperatures are measured on the plates and in the feed streams by means of chromelalumel thermocouples. At the inlet, outlet and between the plates, air lines are installed which can be connected either to manometers or to the cells of the dew point hygrometer. Several hours of operation are generally required to obtain a stationary state, indicated by the constancy of the recorded plate temperatures. After the temperatures, pressures and air humidities have been measured the run is stopped, the glass front face of the column removed and solid samples are taken rapidly from the plates and from the feed to determine their water content. The air humidities are plotted against the solid loadings to obtain the operating line, and the equilibrium gas concentrations on the plates c*(q,, Ts,), computed by means of eqn. (7), give the equilibrium line. Figure 7 shows these lines for a typical run. By using eqn. (2), the Murphree efficiencies of the plates are easily calculated. c [kg/kg
)
iwtherms(
WlO
_
OKI
_
from equatwn
7
in our experiments 0.095. The theory
I
lying between 0.075 and of Q 2 is thus applicable.
5.2. Results and discussion The runs were performed with three air flowrates equal to 1.5, 2 and 2.35 times the minimum fluidization flow-rate, and, for each of them, three solid flowrates, namely, QS/ Qo = kO.09, 0.14 and 0.17. The inlet concentrations were kept approximately constant at 0.0075 and 0.002 kg/kg in the air and in the adsorbent, respectively. It was impossible to work at fluidization numbers greater than 2.5 because that rapidly gives rise to flooding of the upper downcomers and then of the whole column. For these experiments the downcomers’ height was fixed at 5 cm, which corresponds to settled layers of approximately 3.5 cm depth (owing to solid projections, the level of the fluidized layers actually lies somewhat below the weir of the downcomers). Mean efficiencies are presented in Figs. 8 and 9. The effect of the depth of the fluidized layers was also investigated (Fig. 10) for u. / U = 2 and 2.35 and a flowrate ratio Qs/ 9”,’ = kO.09, for which operating and equilibrium lines are almost parallel, giving E, = E MGFor all the runs we observe that EMG increases from plate to 1 to 5 (Fig. 11) and sometimes we find for plate 5 efficiencies greater than unity. We think that these abnormally high values may be caused by plate 5 receiving the cold solid feed and the fines
MO6
001
003
005
007 qlkg/kgj
09
Fig. 7. Operating and equilibrium lines for a typical continuous run: Qs/QG = 0.173, UOIU& = 1.5, Hd = 5 cm.
In Fig. 7, the broken curves represent isotherms; it can be seen that temperatures decrease regularly from the top to the bottom of the column, although the adsorbent is fed in at the top at the ambient temperature. One can, moreover, observe that the equilibrium lines are almost straight, the slopes b obtained
Fig. 8. Murphree efficiencies - effect of the ratio of solid to gas flowrates.
6
Fig. 9. Murphree efficiencies - effect of the fluidization velocity.
0.2 _ 3
c
5
'
H,,lcd
Fig. 10. Murphree efficiencies - effect of the height of the solids.
06
L
L
1
2
3
4
5
Plate "umber
Fig. 11. Variation of Murphree efficiency with the plate number.
from the cyclone. Therefore, in all the diagrams we present the results as the mean efficiencies of the four lower plates. First of all, we see (Fig. 8) that EMG increases with the ratio QS/QG of the solid to gas flowrates. Such a behaviour can be explained if one applies the Cholette and Cloutier model for the particle path on the plates. Equation (6) and Fig. 2 indeed show
that EMGIEPG increases as E,,lr decreases, whereas the dispersion model [ 121 predicts the inverse variation. Considering the location of the downcomers (Fig. 6) and the short distance between the inlet and the outlet of the solids, particles can easily bypass the plates or remain a long time in quasi-dead zones situated behind the downcomer tubes at the left and right extremities of the plates. Next, we note that Murphree efficiencies reach maximum values at about twice the minimum fluidization velocity (Fig. 9). This can also be interpreted according to the Cholette and Cloutier model by considering two opposite effects. As u~/u,,,~ rises, the fraction 1 - y of dead volume decreases and the percentage x of bypass increases because of the better mixing and the greater bubbling of the beds. Finally, from Fig. 10, we find that the height of the fluidized layers on the plates seems to have no effect on &o. As these layers become deeper, the small increase in the short-circuiting of solids due to larger bubbles probably compensates for the slight growth of Era. The point efficiency lying between 0.7 and 1, and r being almost equal to unity for the experiments reported in Fig. 10, very high values of 3c and 1 - y (respectively 0.5 and 0.4) are required according to eqn. (6) to obtain such a small value of EMG as 0.32. In fact, eqn. (6) does not account for thermal effects: the solids are heated to a maximum temperature at the top of the column and then are regularly cooled while flowing down. This lowering of the solids’ temperature on the plates leads to a subsequent decrease of the Murphree efficiency, and the fraction of solids bypassing or the dead zone volume need not be as high as predicted above. We think that these thermal effects also explain, the variation of EMG along the column because it varies in the same way as the temperature. We would also like to mention some trouble we encountered with the plate distributors in the operation of our multistage column. The wire gauzes used to support the particles become progressively clogged with fines, which increases the pressure drop and finally leads to flooding. We notice that this phenomenon occurs along with an increase in the Murphree efficiencies. This can be explained by the accumulation in the down-
7
comers in series with the plates of an increasing volume of solids, not negligible on this scale, in quasi-plug flow. All the experiments presented
here
were
performed
with
Fractions of solids bypassing and dead zone volume obtained from tracer studies with particles of CaC03
clean
grids, the total pressure drop of the five plates never exceeding 25 mmHg for uO/umf = 2.35.
6. TRACER
TABLE 3
STUDIES
To determine the flow pattern of solids, we performed some tracer experiments on the first, plate of the column. Pulse input signals of sodium chloride were used in beds of calcium carbonate spherules. The salt, concentrations in the output were measured by conductivity after leaching the samples with distilled water. The solids and the particles of tracer had the same fluidization velocity and the bed depth was fixed at 5 cm. Some experimental C curves are compared in Fig. 12 with the theoretical curve relative to ideal mixing. They clearly show the influence of uo/umf. Regressions performed according to the Cholette and Cloutier model equation [ 201, for 0 >0 (9) exp -lsX 8 ( Y give the parameters x and y reported in Table 3. C=(1--x)2 Y
ct
Fig. 12. Residence time distribution curves for calcium carbonate.
The values of Qs/Qo have been divided by the ratio of the particle densities of carbonate and alumina to make them directly comparable with those used in the adsorption experiments. The ratio of the flowrates seems to have no effect on the parameters x and y, but, on the other hand, the fluidization number
“”
QS
hIIf
G
1.5 1.5 1.5 2 2 2 2.5 2.5
0.10 0.21 0.31 0.079 0.15 0.24 0.064 0.23
514 270 188 426 228 158 416 156
x
l--Y
0 0 0 0.031 0.036 0.022 0.124 0.118
0.195 0.250 0.164 0.029 0.069 0.013 0 0
has a strong influence. We find no bypass and a mean dead zone fraction of 0.20 for uO/ umf = 1.5, very small bypass and dead zone for uo/umf = 2, and no more dead zone but a bypass of 0.12 for uO/umf = 2.5. Although they were performed with different, solids and give different parameter values, these tracer experiments confirm the previous assumptions used to interpret the variations of the Murphree efficiencies. The particles of activated alumina have a wider size distribution and are less spherical than those of the carbonate, and there is no doubt that they lead to more bypassing, especially for the fines.
7. CONCLUSION
Murphree plate efficiencies obtained in the operation of a continuous five-stage fluidizedbed air dryer increase with the adsorbent flowrate at constant air flowrate, and are greatest for twice the minimum fluidization velocity. .The performance of the multistage smallscale column is strongly dependent on the flow pattern of solids on the plates and especially on the degree of bypassing and the existence of dead zones. The small-scale columns cannot be extrapolated to full-scale columns because the solids will certainly follow different paths in the latter. Improved location and design of the downcomers and larger distances between them are likely to suppress completely the short-circuiting and to reduce the fraction of stagnant particles, thus giving much better efficiencies.
8 NOMENCLATURE
m, M
b c
Ll
slope of equilibrium straight line concentration of adsorbate in carrying gas, kg/kg C reduced concentration of tracer mean surface/volume particle 4 diameter, m apparent diffusion coefficient in the DP particles, m2/s E efficiency of batch fluidized bed E MG Murphree efficiency, eqn. (2) E PG Murphree point efficiency, eqn. (5) overall column efficiency, eqn. (1) ECI H fluidized bed height, m height of downcomers, m’ Hd n plate number counted from bottom partial pressure of adsorbate in gaseous P phase, mmHg loading of adsorbate on the free adsor9 bent solid, kg/kg carrying gas flowrate, kg/s flowrate of free adsorbent particles, kg/s r = Qs/b QG, adsorption ratio r = 2V,/S,, mean pore ratio, A, m internal surface area of adsorbent, S, m2/g t time, s mean residence time of solids on ts plate, s “C, K T TK temperature, minimum fluidization velocity, m/s knf superficial gas velocity, m/s uo specific volume of pores in particles, v, m3/kg fraction of solids bypassing plate X fraction of plate volume which is Y active Greek symbols void fraction E internal void fraction Ei e = MS, dimensionless residence time of solids bulk density of solid particles, kg/m3 Pb particle density, kg/m3 PP relative saturation (or humidity) cp Subscripts G relative to gaseous phase H at top of fluidized bed !? in vertical section of plate mf at minimum fluidization
S 0
relative at exit at exit plate relative at bed
to micropores, macropores of plate n of perfectly mixed zone of to solid particles inlet
Superscripts mean value * equilibrium value
REFERENCES
8 9 10
11 12 13 14 15 16
17 18
19 20
M. Cox, Trans. Inst. Chem. Eng., 36 (1958) 29. E. D. Ermenc, Chem. Eng. (London), (May 29) (1961) 87. I. 0. Protod’yakonov and V. S. Atoyants, Chem. Abstr., 78 (1973) 113153 f. E. D. Ermenc, Chem. Eng. Prog., 52 (1956) 488. H. M. Rowson, Br. Chem. Eng., 8 (1963) 180. E. T. Larin and 0. B. Erofeeva, Chem. Abstr., 83 (1975) 207927 s. S. Ehmaleh, J. L. Soulie and R. Ben Aim, Proc. Znt. Symp.: Fluidization and its Applications, Cepadues Editions, Toulouse, 1973, p. 122. W. Flock, Chem. Technol., 16 (1964) 647. A. A. Molodov and I. P. Ishkin, Chem. Abstr., 66 (1967) 12524 Z. D. A. Avery and D. H. Tracey, Trip Chem. Eng. Conf., Montreal, 1968 -Preprints Symp. on Fluidization Z, Inst. Chemical Engineers, London, p. 21. T. Kamada, Kagaku Kogaku, 40 (1976) 426. Bubble Tray Design Manual, AIChE, New York, 1958. A. Cholette and L. Cloutier, Can. J. Chem. Eng., 37 (1959) 105. D. Kunii and 0. Levenspiel, Fluidization Engineering, Wiley, New York, 1968. H. Gibert and H. Angelino, Chim. Znd. Genie Chim., ZOO(1968) 1049. H. Angelino, H. Gibert and H. Gardy, Trip. Chem. Eng. Conf., Montreal, I968 -Preprints on Fluidization Z, Inst. Chemical Engineers, London, p. 60. P. Sagetong, H. Gibert and H. Angelino, Chim. Znd. Genie Chim., IO5 (1972) 1825. J. F. Davidson and D. Harrison, Fluidized ParticZes, University Press, Cambridge, Gt. Britain, 1963. S. Mori and C. Y. Wen, AZChE J., 21 (1975) 109. 0. Levenspiel and K. B. Bischoff, Advances in Chemical Engineering, Vol. 4, Academic Press, New York, 1963, p. 168.
APPENDIX
Demonstration of eqn. (6) The equations of the system represented Fig. 1 are:
in
perfectly cn-1
-
mixed zone
Thus (A2) can be written
= EPG[Cn-1
CPM
= EPG(C,
gas
-c*(qPM)l -1
-
a -
cn-1 hM,)
YCPM
(4
-y)&-1
g(%
-Qn+l)
-a,)
x(4;-1
QG(c,-I -c,) = Qdqn -qn+l)
-4n
(Qn -4n+l)(r+x~)
-qn+1)
+ -
qPM)
---%I)
-aa,
-Qn+l)
= (4;-1
~Qn)Y&o
From (2), (3), (4), (A4) and (A6): (AV
(Al) becomes,
cn-1 = cn-1
with (4), =
-CPM
-x(q,:-I
l-x
E MG
cn-1
X
(A6) =4&I-1 + t1 -x)(d-1
Equation
-Qn)
YEPG
(A4)
of the two sides of (A3) from
d-1
-an+l)l
-x(q,:-1
or r(a, - qn+l) =
gives
qPM)
l-x (A3)
overall plate balance
qiel
-
=
Yb&o[(q;-1 + t1 -x)qPM
Subtraction
-1
and with (A4), (A5) and (4): + (1
=xqn+l
-CPM)
= ybEpG(qr:
solid balance qn
= Y(C,-1
(AlI
balance
c, =
-c,
= bEpG(q;-1
-ad
r
-cn
-a-bq,
=r
YEPG
r + xyEp~/(I
Q”
-(In+1
q;-1-4n ~(1
-X)=
-X)EPG
1-X +XyEpG/r
The
Plate Efficiency
1
of Multistage Fluidized-Bed
Adsorbers
J. VANDERSCHUREN Service de GEnie Chimique,
Faculte’ Polytechnique
de Mons, rue de I’Epargne, 7000 Mons (Belgium)
(Received 12 December 1976; in final form 18 October 1979)
Abstract The operation of a continuous five-stage fluidized-bed pilot adsorber, in the drying of air on activated alumina, gives Murphree plate efficiencies which increase with the ratio of solid to air flowrates and reach maximum values at twice the minimum fluidization velocity. The results are interpreted according to the Cholette and Cloutier model which considers dead zones and bypassing of particles on the plates. This solids flow pattern is confirmed by means of tracer studies.
Ijlates which are supplied with downcomers for the overflow of solids. The number of theoretical plates of multistage fluidized adsorbers can be determined by means of the classical graphical or numerical methods for continuous countercurrent plate columns.
2. PLATE EFFICIENCIES
The overall column efficiency the well-known relation [ 121 E
=
ln[l
+EMG(l/r-ll)l
0
1. INTRODUCTION
Multistage fluidized beds are used in continuous adsorption processes such as gas drying [l - 31, purification of effluent streams containing nitrogen oxides [4] , carbon disulphide [ 51, hydrogen sulphide [6] or sulphurous oxide [ 71, and solvent or vinyl chloride recovery [ 8 - 111. Multistage fluidization is particularly suitable for these processes when the gas concentrations are low and the flowrates very large [lo]. A gas velocity much higher than in classical fixedbed adsorbers can be used [ 1,2, lo] , resulting in a lower bed cross-section and a considerable reduction of the initial weight of adsorbent in the column. The stages used are very shallow, [ 2, lo] , about 5 - 10 cm in depth, in order to obtain greater adsorption rates with the same total weight of adsorbent [8] and to reduce the total pressure drop. A minimum particle height is, however, required to maintain good plate behaviour. Two kinds of plates are used: high-free-area sieve plates with large holes through which gas and particles flow sirnultaneously, and the common low-free-area
is given by
(1)
W/r)
where EMo is a Murphree plate efficiency analogous to that used in gas-liquid contacting: E MG=
G-1
-c*
(2)
&I--l --c*(aI)
and r is the ratio of the slopes of the operating and equilibrium lines: r=
Qs/bQc
(3)
The equilibrium line is here supposed straight and has for its equation c* = a + bq
to be (4)
The Murphree plate efficiency depends on the mechanism of the gas-solid contacting process and on the mass transfer rates. Estimations of Murphree efficiencies can be carried out in two steps in the same way as for gas-liquid tray efficiencies. By means of a model describing the particle path and the extent of solids mixing on the plate, EM, is related to a point or local efficiency EPG: E,=
cn-1 cn-1
-cQ
-c*(qQ)
2
which itself depends on the mass transfer resistances between the phases. In the case of perfect particle mixing on the plate, EMMGand E,, are obviously equal. For plug flow of particles, without or with longitudinal dispersion, the relations are reported in the Bubble Tray Design Manual [ 121. E,,/EpG uersus E&r graphs [ 121 show that EMGIEpG increases with E&r and with the Peclet number for longitudinal dispersion. As will be seen later, the Cholette and Cloutier model [ 131 is also convenient to describe the residence time distribution of the particles on the plates. In this model (Fig. l), a fraction x of the solid feed bypasses the plate, and a fraction y of the stage volume is perfectly mixed, the other part 1 - y being a dead zone. Resolving the equations of this system (see Appendix) allows us to calculate the expression for E,, : E MG
YU -x1
-=
EPG
1 -X
+XYEpG/r
(f-5)
Fig. 1. Cholette and Cloutier model of the flow of solids on a plate.
Figure 2 shows that the Cholette and Cloutier model predicts a decrease of EMG/EpG as EpG/r, x or 1 - y increases. The point efficiency EpG in a plate section is assumed to be the efficiency E of a bed of equal depth which is not fed with particles, because the solid concentration is then uniform owing to the intensive mixing induced by bubbles. For normal fluidizing conditions (d, < 1 mm and H > 20 - 30 cm), Kunii and Levenspiel [ 141 consider that the gas exiting from a batch fluidized adsorbent layer is at mass transfer equilibrium with the solid particles.
014,II 03
05
10
j
4
1.5
I
3,
E&/r
-
Fig. 2. Murphree efficiencies given by the Cholette and Cloutier model.
This proposition is confirmed by the experimental works of Angelino and his collaborators [ 15 - 171 on the drying of air with activated alumina and the adsorption of COz on a molecular sieve. Under these conditions the efficiency E is thus equal to unity. But that will not always be so, especially for the very shallow beds used in multistage adsorbers. Actually, Ermenc [ 21 found, in the drying of air with silica gel, efficiencies lower than unity which increase with the weight of gel on the plates. Mass transfer equilibrium between gas and particles is not necessarily reached at the top of the fluidized layer, because mass transfer resistances are encountered between the bubbles and the gas of the emulsion, in the laminar gaseous film outside the particles and in the pores of the adsorbent.
3. THE EXPERIMENTAL
MATERIAL
Our investigation of plate efficiencies was made during the drying of air on fluidized beds of activated alumina. We took a 125 630 pm fraction of this adsorbent with a mean particle size d, equal to 448 pm. The other properties of the adsorbent are grouped in Table 1. The internal structure was studied by means of a mercury porosimeter and a nitrogen BET-sorptometer; the exis-
TABLE 1 Characteristics
of the activated alumina (125 - 630 pm) %M
%n
PP
Pb
(Wm3)
(Wm3)
1240
775
0.474
0.118
6 18
x
36
2920
tence of a bidispersed pore size distribution was revealed. The vapour pressures of the water adsorbed on this activated alumina were carefully determined for several water contents at different decreasing temperatures by using a modified isoteniscope. Figure 3 shows these adsorption isosteres. All the measurements were correlated with a mean error of 6% by the following equation : 54.20
T,ln~*=384.2--
4
0.6030 +-q2
0.002219 q3
(7)
in the range 0.02 B q < 0.09 kg/kg, 40 < T < 150 “C. The reference state for the water contents was obtained by regenerating the material at 205 “C.
1000
‘_
PH20. ImmHgl:
Fig. 3. Vapour pressures of water on activated alumina.
0.592
4. STUDY
(m2/g)
;A,
242
39
0.428
0.155
OF POINT EFFICIENCIES
Prior to the investigation of Murphree plate efficiencies in a multistage continuous adsorber, we determined the efficiencies of some batch fluidized layers of activated alumina (125 - 630 pm). The fluidization column consists of a Plexiglas cylindrical tube of 0.12 m inside diameter, equipped at the bottom with a 3 mm thick sintered bronze gas distributor. The column was first loaded with a given volume of freshly regenerated adsorbent. An air stream at constant flowrate and humidity was then fed to the bed. Temperatures were recorded continuously in the feed, in the exit air and at the top of the fluidized layer. These two latter temperatures are always equal because heat transfer equilibrium is reached at the top of the bed. They pass through a maximum value during the first part of the run, and then decrease continuously. Inlet and outlet humidities were measured with a dew point hygrometer, the outlet measurements being corrected by taking into account the air sampling line response time. From time to time during the run, small samples of solid particles were withdrawn from the bed and their water content determined by weighing after regeneration at 205 “C. For each particle loading q, the recordings give the corresponding air temperature TH and partial pressure pn , and thus the relative humidity qn. The equilibrium relative humidity cp*(q) is obtained by means of eqn. (7). The bed efficiency can then be calculated by the expression E=
The diffusivity of water vapour in the alumina particles was measured by using an unsteady-state concentration step method which give a mean value of D, equal to 10-l’ m2/s.
GlIf
s,
VO-PH cpo
-v*(q)
If the experimental results (pn, q) are represented in a (9, q) diagram together with the isotherms, it can be seen (Fig. 4) that E = -AB/AC.
wtherms
I7
frcml eqvatlon
I
LO’C 2o’c
/
0
Fig. 4. (9,
0.05
q
1kg/kg1
I 0.1
-
q) diagram for the batch runs.
The experiments were performed for three bed heights (0.035, 0.07 and 0.10 m) and three fluidization velocities (Q/u,.,,~ = 1.5,2 and 2.5) with inlet relative humidities cpo of about 0.4. Figure 4 shows that most of the bed efficiencies are equal to unity. However, although the particles are rather small, bed efficiencies become significantly lower than unity for the two shallowest beds (0.035 and 0.07 m) and u~/u,,,~ = 2.5, the mean values of E being equal, respectively, to 0.82 and 0.93. These results are in good agreement with predicted values made by using the two-phase model [ 181 for fluidized-bed contactors (see Table 2). For the computations, the rate of adsorption in the emulsion phase was taken from the experimental internal diffusion coefficient, and the bubble diameter estimated at mid-bed height by means of the correlation of Kato and Wen [19].
Calculated efficiencies of fluidized beds of activated alumina (125 - 630 pm)
1.5 2 2.5
-dry
air
1. five plate column 2. hopper 3. rotary valve L. davncomer 3 collection
vessel
6. flow meter 7. cyclone 8 air
6
sompbg
tine
g thermocouple
.~
TABLE 2
uol%f
of a continuous multistage pilot air dryer. The column is made of brass with an easily removable glass front face. It contains five rectangular boxes (cross-section 140 mm X 95 mm, height 150 mm), spaced 240 mm apart (Fig. 5). The bottom plates of these boxes are perforated with a 7.5 mm pitch of 2.5 mm diameter holes and covered with a wire gauze which prevents flow of particles through the holes. Each plate is provided with a cylindrical downcomer of 25 mm inside diameter and 265 mm total length, leading the solids from the upper surface of a bed into the fluidized layer below. The downcomers are alternately located on the left and right-hand side of the cross-section (Figs. 5 and 6). They can slide through the distributors to enable the bed height to be varied.
%f
t tumid
air
Fig. 5. Sketch of the five-plate continuous pilot air dryer.
04
0.035
0.07
0.10
0.135
0.971 0.912 0.800
1.000 0.990 0.941
1.000 0.998 0.997
1.000 1.000 0.999
c
/I__, i ‘I
‘i.!_/ 5. EXPERIMENTAL DETERMINATION OF MURPHREE EFFICIENCIES 5.1. Pilot plant and procedure The Murphree efficiencies were measured for the same adsorbent during the operation
_ -I_”
Fig. 6. Location of the downcomers on the plates.
5
The fresh adsorbent is fed to the column at a constant flowrate through a small rotary valve driven with a variable-speed motor. The solids are collected at the outlet in a sealed vessel. The air is provided by a liquid-piston rotary blower, of which the sealing liquid is water maintained at constant temperature; constant air humidity is thus ensured. Temperatures are measured on the plates and in the feed streams by means of chromelalumel thermocouples. At the inlet, outlet and between the plates, air lines are installed which can be connected either to manometers or to the cells of the dew point hygrometer. Several hours of operation are generally required to obtain a stationary state, indicated by the constancy of the recorded plate temperatures. After the temperatures, pressures and air humidities have been measured the run is stopped, the glass front face of the column removed and solid samples are taken rapidly from the plates and from the feed to determine their water content. The air humidities are plotted against the solid loadings to obtain the operating line, and the equilibrium gas concentrations on the plates c*(q,, Ts,), computed by means of eqn. (7), give the equilibrium line. Figure 7 shows these lines for a typical run. By using eqn. (2), the Murphree efficiencies of the plates are easily calculated. c [kg/kg
)
iwtherms(
WlO
_
OKI
_
from equatwn
7
in our experiments 0.095. The theory
I
lying between 0.075 and of Q 2 is thus applicable.
5.2. Results and discussion The runs were performed with three air flowrates equal to 1.5, 2 and 2.35 times the minimum fluidization flow-rate, and, for each of them, three solid flowrates, namely, QS/ Qo = kO.09, 0.14 and 0.17. The inlet concentrations were kept approximately constant at 0.0075 and 0.002 kg/kg in the air and in the adsorbent, respectively. It was impossible to work at fluidization numbers greater than 2.5 because that rapidly gives rise to flooding of the upper downcomers and then of the whole column. For these experiments the downcomers’ height was fixed at 5 cm, which corresponds to settled layers of approximately 3.5 cm depth (owing to solid projections, the level of the fluidized layers actually lies somewhat below the weir of the downcomers). Mean efficiencies are presented in Figs. 8 and 9. The effect of the depth of the fluidized layers was also investigated (Fig. 10) for u. / U = 2 and 2.35 and a flowrate ratio Qs/ 9”,’ = kO.09, for which operating and equilibrium lines are almost parallel, giving E, = E MGFor all the runs we observe that EMG increases from plate to 1 to 5 (Fig. 11) and sometimes we find for plate 5 efficiencies greater than unity. We think that these abnormally high values may be caused by plate 5 receiving the cold solid feed and the fines
MO6
001
003
005
007 qlkg/kgj
09
Fig. 7. Operating and equilibrium lines for a typical continuous run: Qs/QG = 0.173, UOIU& = 1.5, Hd = 5 cm.
In Fig. 7, the broken curves represent isotherms; it can be seen that temperatures decrease regularly from the top to the bottom of the column, although the adsorbent is fed in at the top at the ambient temperature. One can, moreover, observe that the equilibrium lines are almost straight, the slopes b obtained
Fig. 8. Murphree efficiencies - effect of the ratio of solid to gas flowrates.
6
Fig. 9. Murphree efficiencies - effect of the fluidization velocity.
0.2 _ 3
c
5
'
H,,lcd
Fig. 10. Murphree efficiencies - effect of the height of the solids.
06
L
L
1
2
3
4
5
Plate "umber
Fig. 11. Variation of Murphree efficiency with the plate number.
from the cyclone. Therefore, in all the diagrams we present the results as the mean efficiencies of the four lower plates. First of all, we see (Fig. 8) that EMG increases with the ratio QS/QG of the solid to gas flowrates. Such a behaviour can be explained if one applies the Cholette and Cloutier model for the particle path on the plates. Equation (6) and Fig. 2 indeed show
that EMGIEPG increases as E,,lr decreases, whereas the dispersion model [ 121 predicts the inverse variation. Considering the location of the downcomers (Fig. 6) and the short distance between the inlet and the outlet of the solids, particles can easily bypass the plates or remain a long time in quasi-dead zones situated behind the downcomer tubes at the left and right extremities of the plates. Next, we note that Murphree efficiencies reach maximum values at about twice the minimum fluidization velocity (Fig. 9). This can also be interpreted according to the Cholette and Cloutier model by considering two opposite effects. As u~/u,,,~ rises, the fraction 1 - y of dead volume decreases and the percentage x of bypass increases because of the better mixing and the greater bubbling of the beds. Finally, from Fig. 10, we find that the height of the fluidized layers on the plates seems to have no effect on &o. As these layers become deeper, the small increase in the short-circuiting of solids due to larger bubbles probably compensates for the slight growth of Era. The point efficiency lying between 0.7 and 1, and r being almost equal to unity for the experiments reported in Fig. 10, very high values of 3c and 1 - y (respectively 0.5 and 0.4) are required according to eqn. (6) to obtain such a small value of EMG as 0.32. In fact, eqn. (6) does not account for thermal effects: the solids are heated to a maximum temperature at the top of the column and then are regularly cooled while flowing down. This lowering of the solids’ temperature on the plates leads to a subsequent decrease of the Murphree efficiency, and the fraction of solids bypassing or the dead zone volume need not be as high as predicted above. We think that these thermal effects also explain, the variation of EMG along the column because it varies in the same way as the temperature. We would also like to mention some trouble we encountered with the plate distributors in the operation of our multistage column. The wire gauzes used to support the particles become progressively clogged with fines, which increases the pressure drop and finally leads to flooding. We notice that this phenomenon occurs along with an increase in the Murphree efficiencies. This can be explained by the accumulation in the down-
7
comers in series with the plates of an increasing volume of solids, not negligible on this scale, in quasi-plug flow. All the experiments presented
here
were
performed
with
Fractions of solids bypassing and dead zone volume obtained from tracer studies with particles of CaC03
clean
grids, the total pressure drop of the five plates never exceeding 25 mmHg for uO/umf = 2.35.
6. TRACER
TABLE 3
STUDIES
To determine the flow pattern of solids, we performed some tracer experiments on the first, plate of the column. Pulse input signals of sodium chloride were used in beds of calcium carbonate spherules. The salt, concentrations in the output were measured by conductivity after leaching the samples with distilled water. The solids and the particles of tracer had the same fluidization velocity and the bed depth was fixed at 5 cm. Some experimental C curves are compared in Fig. 12 with the theoretical curve relative to ideal mixing. They clearly show the influence of uo/umf. Regressions performed according to the Cholette and Cloutier model equation [ 201, for 0 >0 (9) exp -lsX 8 ( Y give the parameters x and y reported in Table 3. C=(1--x)2 Y
ct
Fig. 12. Residence time distribution curves for calcium carbonate.
The values of Qs/Qo have been divided by the ratio of the particle densities of carbonate and alumina to make them directly comparable with those used in the adsorption experiments. The ratio of the flowrates seems to have no effect on the parameters x and y, but, on the other hand, the fluidization number
“”
QS
hIIf
G
1.5 1.5 1.5 2 2 2 2.5 2.5
0.10 0.21 0.31 0.079 0.15 0.24 0.064 0.23
514 270 188 426 228 158 416 156
x
l--Y
0 0 0 0.031 0.036 0.022 0.124 0.118
0.195 0.250 0.164 0.029 0.069 0.013 0 0
has a strong influence. We find no bypass and a mean dead zone fraction of 0.20 for uO/ umf = 1.5, very small bypass and dead zone for uo/umf = 2, and no more dead zone but a bypass of 0.12 for uO/umf = 2.5. Although they were performed with different, solids and give different parameter values, these tracer experiments confirm the previous assumptions used to interpret the variations of the Murphree efficiencies. The particles of activated alumina have a wider size distribution and are less spherical than those of the carbonate, and there is no doubt that they lead to more bypassing, especially for the fines.
7. CONCLUSION
Murphree plate efficiencies obtained in the operation of a continuous five-stage fluidizedbed air dryer increase with the adsorbent flowrate at constant air flowrate, and are greatest for twice the minimum fluidization velocity. .The performance of the multistage smallscale column is strongly dependent on the flow pattern of solids on the plates and especially on the degree of bypassing and the existence of dead zones. The small-scale columns cannot be extrapolated to full-scale columns because the solids will certainly follow different paths in the latter. Improved location and design of the downcomers and larger distances between them are likely to suppress completely the short-circuiting and to reduce the fraction of stagnant particles, thus giving much better efficiencies.
8 NOMENCLATURE
m, M
b c
Ll
slope of equilibrium straight line concentration of adsorbate in carrying gas, kg/kg C reduced concentration of tracer mean surface/volume particle 4 diameter, m apparent diffusion coefficient in the DP particles, m2/s E efficiency of batch fluidized bed E MG Murphree efficiency, eqn. (2) E PG Murphree point efficiency, eqn. (5) overall column efficiency, eqn. (1) ECI H fluidized bed height, m height of downcomers, m’ Hd n plate number counted from bottom partial pressure of adsorbate in gaseous P phase, mmHg loading of adsorbate on the free adsor9 bent solid, kg/kg carrying gas flowrate, kg/s flowrate of free adsorbent particles, kg/s r = Qs/b QG, adsorption ratio r = 2V,/S,, mean pore ratio, A, m internal surface area of adsorbent, S, m2/g t time, s mean residence time of solids on ts plate, s “C, K T TK temperature, minimum fluidization velocity, m/s knf superficial gas velocity, m/s uo specific volume of pores in particles, v, m3/kg fraction of solids bypassing plate X fraction of plate volume which is Y active Greek symbols void fraction E internal void fraction Ei e = MS, dimensionless residence time of solids bulk density of solid particles, kg/m3 Pb particle density, kg/m3 PP relative saturation (or humidity) cp Subscripts G relative to gaseous phase H at top of fluidized bed !? in vertical section of plate mf at minimum fluidization
S 0
relative at exit at exit plate relative at bed
to micropores, macropores of plate n of perfectly mixed zone of to solid particles inlet
Superscripts mean value * equilibrium value
REFERENCES
8 9 10
11 12 13 14 15 16
17 18
19 20
M. Cox, Trans. Inst. Chem. Eng., 36 (1958) 29. E. D. Ermenc, Chem. Eng. (London), (May 29) (1961) 87. I. 0. Protod’yakonov and V. S. Atoyants, Chem. Abstr., 78 (1973) 113153 f. E. D. Ermenc, Chem. Eng. Prog., 52 (1956) 488. H. M. Rowson, Br. Chem. Eng., 8 (1963) 180. E. T. Larin and 0. B. Erofeeva, Chem. Abstr., 83 (1975) 207927 s. S. Ehmaleh, J. L. Soulie and R. Ben Aim, Proc. Znt. Symp.: Fluidization and its Applications, Cepadues Editions, Toulouse, 1973, p. 122. W. Flock, Chem. Technol., 16 (1964) 647. A. A. Molodov and I. P. Ishkin, Chem. Abstr., 66 (1967) 12524 Z. D. A. Avery and D. H. Tracey, Trip Chem. Eng. Conf., Montreal, 1968 -Preprints Symp. on Fluidization Z, Inst. Chemical Engineers, London, p. 21. T. Kamada, Kagaku Kogaku, 40 (1976) 426. Bubble Tray Design Manual, AIChE, New York, 1958. A. Cholette and L. Cloutier, Can. J. Chem. Eng., 37 (1959) 105. D. Kunii and 0. Levenspiel, Fluidization Engineering, Wiley, New York, 1968. H. Gibert and H. Angelino, Chim. Znd. Genie Chim., ZOO(1968) 1049. H. Angelino, H. Gibert and H. Gardy, Trip. Chem. Eng. Conf., Montreal, I968 -Preprints on Fluidization Z, Inst. Chemical Engineers, London, p. 60. P. Sagetong, H. Gibert and H. Angelino, Chim. Znd. Genie Chim., IO5 (1972) 1825. J. F. Davidson and D. Harrison, Fluidized ParticZes, University Press, Cambridge, Gt. Britain, 1963. S. Mori and C. Y. Wen, AZChE J., 21 (1975) 109. 0. Levenspiel and K. B. Bischoff, Advances in Chemical Engineering, Vol. 4, Academic Press, New York, 1963, p. 168.
APPENDIX
Demonstration of eqn. (6) The equations of the system represented Fig. 1 are:
in
perfectly cn-1
-
mixed zone
Thus (A2) can be written
= EPG[Cn-1
CPM
= EPG(C,
gas
-c*(qPM)l -1
-
a -
cn-1 hM,)
YCPM
(4
-y)&-1
g(%
-Qn+l)
-a,)
x(4;-1
QG(c,-I -c,) = Qdqn -qn+l)
-4n
(Qn -4n+l)(r+x~)
-qn+1)
+ -
qPM)
---%I)
-aa,
-Qn+l)
= (4;-1
~Qn)Y&o
From (2), (3), (4), (A4) and (A6): (AV
(Al) becomes,
cn-1 = cn-1
with (4), =
-CPM
-x(q,:-I
l-x
E MG
cn-1
X
(A6) =4&I-1 + t1 -x)(d-1
Equation
-Qn)
YEPG
(A4)
of the two sides of (A3) from
d-1
-an+l)l
-x(q,:-1
or r(a, - qn+l) =
gives
qPM)
l-x (A3)
overall plate balance
qiel
-
=
Yb&o[(q;-1 + t1 -x)qPM
Subtraction
-1
and with (A4), (A5) and (4): + (1
=xqn+l
-CPM)
= ybEpG(qr:
solid balance qn
= Y(C,-1
(AlI
balance
c, =
-c,
= bEpG(q;-1
-ad
r
-cn
-a-bq,
=r
YEPG
r + xyEp~/(I
Q”
-(In+1
q;-1-4n ~(1
-X)=
-X)EPG
1-X +XyEpG/r