2408
Ind. Eng. Chem. Res. 1993,32, 2408-2417
Gas Distribution in Shallow Packed Beds Kenneth E. Porter,’ Quasim H.Ali, Ahmed 0. Hassan, and Adam F. Aryan Department of Chemical Engineering, Aston University, Aston Triangle, Birmingham B4 7ET, United Kingdom
A shallow packed bed is defined as one where the bed diameter is greater than the packed height. Some shallow packed beds are more than 5-10 m in diameter. It is shown that gas distributors may be developed and evaluated in the laboratory by measurements of air flow through a geometrically similar model of the full-scale plant. A maldistribution factor is defined in terms of the velocity of the air emerging a t 200 equally spaced positions a t the top of the bed. Distributors are compared in terms of the packed height required for the maldistribution factor to reach ita minimum value. In other experiments, measurements of the air velocity below and above the bed and of the static pressure variation within the bed show how a rotating gas flow below a packed bed produces a maldistributed gas flow within the bed and how increasing the depth of the bed reduces the maldistribution.
Introduction Many operations require gas to flow through a packed bed. Examples are catalytic reactors, adsorber beds, and the packed columns used in distillation and absorption. In some applications the depth or length of the bed is several times greater than its diameter and for most of the bed the gas becomes uniformly distributed across the column cross section. However,when shallowpacked beds are used, their performance may suffer because of gas maldistribution. We define shallow beds as those where the packed height is less than the diameter. Shallow beds are used in practice, either because of a requirement to reduce gas pressure drop (in for example adsorption,where a small depth of bed is preferred), or because of a large gas flow which requires a large diameter packed bed. An example considered below is that of a vacuum crude oil distillation column 7 m in diameter with a packed bed depth of 2 m. Other examples may be found in the absorption columns used for flue gas desulfurization. These may be as much as 12 m in diameter with a 4-or 6-m depth of packed bed. In all of these applications it is most important to ensure that the gas is uniformly distributed across the cross section throughout the packed bed. A maldistributed gas flow will result in premature breakthrough in adsorption and inefficient use of the adsorbent, while in distillation and absorption where the gas is in countercurrent contact with a liquid, a variation in the ratio of gas to liquid flow can result in reduced driving forces for mass transfer and a reduced separation. Thus in practice some form of gas distributor is provided. Despite the practical importance of achievinga uniform gas distribution in shallow beds as defined above, the topic has received little or no attention in the literature, although there are several studies of the increased gas flow near the wall of long packed beds in small diameter tubes. In this paper we first describe a method which may be used to evaluate distributors from measurements in a laboratorysized model of the full-scale plant. This is followed by an experimental study of the fluid mechanics of maldistributed gas flow through a packed bed. A Method of Evaluating Gas Distributors It is well-known to study the flow patterns in large fullscale plant by experiments on a model. If both geometric and dynamic similarity are maintained between the model and the prototype, then it is to be expected that the flow
patterns will also be similar. The theoretical basis for this approach has been described in several textbooks, for example that by Kay.4 In evaluating distributors for randomly packed beds it is necessary to develop a technique which allows for the following complications peculiar to this situation: 1. It is impossible to construct an exactly geometrically similar model of a full-scale randomly packed bed. Each time a bed is repacked a different orientation of the individual packing pieces will occur. 2. The packed bed itself acts as a distributor, and it is desirable that the effect of the interaction between the packed bed and the distributor be allowed for in evaluating the distributor. 3. Superimposed on the mean gas velocity through any region of the bed, there is a random variation in velocity caused by the randomness of the packing. 4. It is difficult to interpret measurements of gas velocity at variouspoints within the packed bed, where the direction of flow will vary as well as the velocity. The approach used in this work was to define a maldistribution factor in terms of measurements, at many points, of the vertical velocity of the gas leaving the top of the bed. The maldistribution factor is large at short packed depths for a badly distributed flow, and reduces to a minimum value as the packed height is increased. Thus distributors may be compared in terms of the packed height required for the maldistribution factor to reach the minimum value. The better the distributor, the less packed height is required. In the experiments described below we first show that the principles of dynamic similarity apply to the maldistribution factor, that is, that it has the same value for two geometrically similar randomly packed beds of a different size. We then demonstrate the use of the approach described above for evaluating distributors on a laboratory-scalemodel of a 7-m-diametervacuum crude oil distillation column.
The Maldistribution Factor The maldistribution factor is calculated from measurementa of the velocity of the gas emerging from the top of the packed beds at several hundred different positions. In this work, a hot-wire anemometer was used to measure the velocity of air (which was used in all of the experimenta), emerging from beds packed with polypropylene Pall rings. The velocity was measured at a distance
0 1993 American Chemical Society 0888-5885/93/2632-240~~~4.~/0
r
-
Ind. Eng. Chem. Res., Vol. 32, No. 10, 1993 2409 Table I. Dimensions of Geometrically Similar Beds model Drototwe bed diameter (mm) 381 610 16 (5/8 in.) 25.4 (1 in.) packing size (Pall rings) (mm) no. of point velocities 200 200 sampling mesh size (pitch) 25 40 (mm) sampling mesh height above 35 55 bed (mm)
Flange
above the bed equal to just over twice the size of the packing (2.17 d). This distance had been found to be optimum by some preliminary experiments. Further details of the experimental procedure are given in ref 1. The maldistribution factor is
Packed bed
-
Support ring
Support beam Perforated plate
Dlstributlon bed 63.5 mm Feed Inlet
The maldistribution factor may be compared with the coefficientof variation of the velocity measurements, which is
c=
[ $( 1
Cross baffle
9 q l i 2 Leg
However in this work there are advantages in using a fixed number of measurements of gas velocity at fixed positions; thus the value of n is constant. In all of the experiments described below a square wire mesh was placed on top of the packing and this was used to define the number and location of the measurements of gas velocity. The value of 4 is the average of three separate experiments with the bed repacked each time.
Tests with Two Geometrically Similar Packed Beds of a Different Size Two columns were constructed each to contain a packed bed of polypropylene Pall rings. One bed was 381-mm diameter and contained 16-mm (5/8-in.) Pall rings and the other was 610-mm diameter and contained 25.4-mm (1-in.) Pall rings. All the column dimensions were then made in proportion to the size of the packing, as were the sampling square mesh size and the distance above the packed bed at which the measurements of velocity were made. Air was supplied to the columns by a fan, and the air flow rate was measured by a Dall tube. The dimensions of the geometrically similar columns are given in Table 1 (including sampling mesh size, etc.). For each column the maldistribution factor was determined a t several different packed heights and at three different air velocities. In many of the experiments the air velocity in the 610-mm diameter column was set at 5 / 8 the velocity of a similar experiment in the 381-mmdiameter column so that each column was working at the same Reynolds number. Two types of experiment were performed. In one (series I), great care was taken to ensure a very uniform air distribution across the bottom of each packed bed. The geometrically similar distributors used for this are illustrated in Figure 1. In the other experiments (series 111, no distributor was used. The air entered through a small diameter radial inlet pipe so that the air entering the packed beds was badly distributed. The results of the series I experiments are shown in Figure 2. The maldistribution factor had a constant value of 20 for all bed heights and, most important, the same value was found for both columns. This is the minimum value for the sampling meshes used in the experiments
Slot w 2 2 0 --I IC 30
4k 32
t
All dimendons In mm (not to suale)
0
35 -
D-6lOmm D-381mm
8
a
U
25
-
c 0 20 3
f!
-Eg
15
g
10 5
0 18000
22000
26000
30000
34000
Roynolds Number
Figure 2. Measured values of the maldistribution factor in two geometrically similar columns of a different size for the case of a uniform air distribution at the bottom of the column.
(200measurements on a square pitch), and corresponds to a uniformly distributed air flow. The results of the series I1 experiments (Figure 3) show the maldistribution factor was large for a short packed depth and reduced as the packed height was increased to reach the minimum value equal to that observed in the series I experiments, indicating that a uniform gas distribution had been achieved. This illustrates the way in which the packed bed causes an improvement in the gas distribution. The results also show that varying the gas flow (i.e., air flow) had a negligible effect on the
2410 Ind. Eng. Chem. Res., Vol. 32, No.10, 1993 100 I
100
8
so
Re for both beds
-
Z=381rnrn
70 60 -
Z = 127mm
50
0
Re = 18,000
80
-
60
-
L
0
0 L
40
-
Z=63.5mrn
3
-
8
0
-
40-
30
-
I 8 20
2o 01 6 0 0 0
20000
24000
28000
32000
l0 o0.0
Reynolds Number
0.2
0.4
0.6
0.8
1.0
Packed HolghtlDIameter, ZID
Figure4. Variation of the maldistribution factor with packed height for two geometrically similar columns of different diameters.
t
2 = 381 mm
5
40
3
0
Z = 127mrn
0
Z=63.5mrn
-
2ot
16000
0
-
= 20000
24000
Paokad Bad
Bam 0
32000 Reynolds Numbsr
I
28000
Figure 3. Maldistribution factor at different air flow Fbynolds numbers and packed heighta for a column of (a, top) 380-mmdiameter and (b, bottom) 610-mm diameter with badly distributed air flow at the bottom of the column.
maldistribution factor. In Figure 4, the maldistribution factor for both columns is plotted against the ratio of packed height to column diameter for a series of experiments at the same gas Reynolds numbers. These results demonstrate that, for geometrically similar columns, the maldistribution factor is identical. These experiments confirmed the validity of the proposal to evaluate the performance of gas distributors for large-scale columns by measuring the maldistribution factor obtained from geometricallysimilarlaboratory-scale models.
Gas Distribution in a Vacuum Crude Oil PumpAround Bed The experimental procedure described above was then used to evaluate gas distributors for a commercial-scale plant. The example chosen was the bottom pump-around bed in a crude oil vacuum distillation column. The full scale column is 7 m in diameter and the bottom bed is 2 m deep packed with metal rings. The column and ita intern& are shown in Figure 5. The bed is supported on standard Norton gas injection support beams which are themselves supported by a 1-m-deep lattice beam. A
Figurs 6. Arrangement of packed bed and column internale for the crude oil vacuum distillation column which is 7-m diameter.
liquid-draw-off tray below (and supported by) the lattice beam, collects the liquid from the packed bed. The liquid rates are relatively low in this application. A vapor-liquid mixture enters the column through a tangental inlet, and swirls round the annulus between the column wall and an internal cylinder, as shown in Figure 5. The liquid is thus separated from the vapor and runs down the column wall. The vapor is distributed around the bottom of the internal cylinder and then comes up the cylinder to pass through the draw-off tray into the packed bed. The purpose of these experiments was to determine the quality of the vapor distribution in the packed bed above the tangential feed pipe, and how this was improved by the presence of (a) the internal cylinder and (b) the drawoff tray.
Ind. Eng. Chem. Res., Vol. 32, No. 10, 1993 2411 220
(a) Same as full scale plant. (b) No draw -off tray. (c) No distributor.
180 160 200
140
-
Cross Sactlon In the Draw Off Tray Showing Gaa R i m
rnin “
1
0
.
I
60
.
I
120
.
1
180
.
I
240
.
I
300
Packed Height, 2 (mm)
’
3
Figure 6. Variation of the maldietribution factor with packed height for a geometrically similar model of the full-scale crude oil vacuum distillation column.
A geometrically similar model of the full-scale tower was constructed. The model was 1.2 m in diameter. The packings used in the model were 16-mm-size Pall rings. Experiments were performed as follows: (a) with the model set up exactly similar to the fullscale column; (b) with the draw-off tray removed, internal cylinder remaining; (c) with both the internal cylinder and the draw-off tray removed. The method used was to determine the maldistribution factor at several different packed heights for each arrangement, with the air velocity set at 0.75 mls. This corresponded to approximatelythe same Reynolds number which would be used in the full-scale plant. The maldistribution factor was calculated from 200 measurements of the air velocity leaving the top of the packed bed. The position of the sampling points was identical in all of the experiments and set by a wire mesh (8 cm X 8 cm) placed on top of the packed bed. This also acted as a hold-down grid. The results in Figure 6 show that when both the internal cylinder and the draw-off tray are removed, i.e., no gas distributor (curve c), at least 300-mm packed depth was required for the maldistribution factor to approach its minimum value. This implies that in the full-scale plant, which is six times larger than the model, the gas would be maldistributed throughout most of the 2-m packed depth. The results also show that the internal cylinder on ita own (curve b) had a negligible effect on improving the gas distribution. Curve b is almost the same as curve c. The main cause of improvement of the gas distribution was the draw-off tray. With the model set up exactly similar to the full-scale plant (curve a), the gas distribution was much improved but 244 mm of packing was required to reach uniform gas distribution, which corresponds to 1.4 m in the full-scale plant. The important contribution of the draw-off tray in improving gas distribution is surprising. Draw-off trays are designed to collect all the liquid falling from the packed bed, and many variations in design are possible. The design of the draw-off tray used in this work is shown in Figure 7. The improvements in gas distribution obtained with this design of draw-off tray may not be obtained with all draw-off-tray designs.
Gas
Figure 7. Plan view of the draw-off tray provided for the crude oil vacuum distillation column.
Development of New Improved Distributors The technique described above may also be used in developing improved gas distributors. With a tangential gas entry such as is used in the column described in the previous section, the main cause of maldistributed gas flow is the swirling motion of the gas below the packed bed. Two new distributors were developed, each of which was intended to reduce this rotation of the gas. These are shown in Figures 8 and 9. In distributor D1 (Figure 8), vertical, radial plates are inserted across the annulus between the column wall and the internal cylinder. These are placed at the bottom of the internal cylinder and are intended to remove the rotation from the gas before it leaves the annulus. In distributor D2 (Figure 91,a cross baffle formed of two plates at right angles is placed within in the internal cylinder. This is intended to remove the rotation from the gas before it leaves the internal cylinder. The new distributors were then evaluated by placing them in the model tower and measuring the maldistribution factor at several packed heights The resulta, shown in Figure 10, permit a comparison of the new distributors with the original setup of draw-off tray and internal cylinder. For both new designs,the packed height required to achieve a uniform gas distribution is significantly reduced; i.e., both achieved the desired improvement in gas distribution. The cross baffle design, D2,is shown to be marginally superior to that of the annulus baffles, D1. It should be noted that neither design is such as to produce a significant increase in pressure drop, nor will they interrupt the separation of liquid from the vapor by ita rotation in the upper part of the annulus. Experimental Investigation into the Fluid Mechanics of Maldistributed Gas Flow The apparatus was modified by removing all the column internals below the packed bed. The packed beds were supported only by a wire mesh, which was maintained level by means of thin wires, passing through the bed and attached to a support structure at the top of the column.
2412 Ind.
Eng.Chem. Res., Vol. 32, No. 10, 1993
1
L
203mm
I Figure 9. New distributor (D2)provided with a cross baffle at the top of the internal cylinder. Figure 8. New distributor (Dl) provided with vertical plates in the annulus between the internal cylinder and the column wall.
0
180
The tangential air inlet was retained and provision made to use an inlet pipe of 304 mm diameter as well as the 152-mm diameter pipe used in the previous work. Three sizes of Pall ring packing were used (16, 25, and 50 mm) and a range of air flow rates.la The objective of the work was to investigate how a rotating gas flow below the packed bed produced a maldistributed gas flow within the bed and how the packed bed improved the gas distribution. The following measurements were made: 1. The horizontal velocity of the rotating air below the bed at different radii across a diameter parallel to the inlet pipe was measured by a pitot tube inserted through the column wall level with the center of the inlet pipe. 2. The static pressure within the bed was measured by a 1.5-m-long, 5-mm-i.d. steel tube inserted at different levels above the bottom of the packed bed through holes in the column wall, and positioned to measure the pressure at different radii across a diameter parallel to the inlet pipe. The measuring end of the tube was blocked and tapered like a conventional pitot tube with small holes round the circumference a small distance away from the blocked end. 3. The velocity of the air emerging from the top of the packed bed was measured by a hot wire anemometer. Measurements made across a diameter gave the velocity profile at the top of the bed. In some experiments the
160
e
__
Distributor 02 cross baffle
El Internal cylinder A Original set up
1
\
I
0 1 0
.
, 60
.
, 120
.
, 180
.
, 240
.
, 300
,
Packed Helght, 2 (mm)
360
Figure 10. Variation of themaldiatribution factor with packed height for the original setup and the new distributors.
maldistribution factor was obtained from measurements all over the top of the bed as described at the beginning of this paper.
Results The Velocity Profile below the Bed. Below the bed the horizontal or swirl velocity is much higher near the column wall than in the center of the column (see Figures
;;k 24
O)
2
22 20
1
0
GI 0
-
Ind. Eng. Chem. Res., Vol. 32, No. 10, 1993 2413
Air flow rate = 0.814 m3h (Vav feed Pipe =46 m h ) Air flow rate = 0.407 m3h (Vav b e d pipe = 23 m/s) Air flow rate = 0.208 m3/s (Vav feed pipe = 1 1.5 m/s)
A'
j'h 0
11
Feed pipe diameter = 6' Feed pipe diameter 12"
-
(Air flow rate = 0.407 m3/s) (Air flow rate 0.814 m3/s)
510
3
12
.0
. .-1-
3
>
5
10
21w i
8
4 3
1
-60
-48
-36
-24
-12
0
12
24
36 48 r, (em)
"
60
-60
Figure 11. Radial variation of the horizontal swirl velocity below the bed of packing when the diameter of the feed pipe is 150 mm.
-48
-36
-24
-12
0
12
24
36
48 60 r, (cm)
7 I
0 0
z' 6
-
Air flow rate = 0.814 m3/s (Vav feed pipe = 11.5 m h ) Air flow rate = 0.407 m3/s (Yav feed pipe 5.75 m/s)
3
-i L
-g 5 f 4
! !
3 2
1
- W-FQJ
I
I
o " l ' t . l . l " ' l ' l " ' t " -60 - 4 8
-60
-48
-36
-24
-12
0
12
24
36
48
60
r, (cm)
Figure 12. Radial variation of the horizontal swirl velocity below the bed of packing when the diameter of the feed pipe is 300 mm. (Note the reduction of velocity near the column wall shown on the right-handaideofthediagramisprobablyduetoaslightmisalignment of the feed pipe.)
11and 12). The velocity decreases as the air flows round the circumference of the column from the feed pipe, presumably because air entering the packed bed reduces the circulation flow. The swirl velocities below the bed are directly proportional to the air flow rate in the feed pipe but less than the feed pipe velocity (Figures 11and 12 ). For the same air flow note that the swirlvelocity is inversely proportional to the inlet pipe diameter, so that if the pipe diameter is doubled and the flow rate is also doubled, the same velocity profile is produced below the bed. This is illustrated in Figure 13a, where almost identical velocity profiles are produced for the 150-mm pipe diameter at 0.407 m3/s and the 305-mm pipe diameter at 0.814 m3/s. A similar result is shown in Figure 13b. That is, u, is proportional to Qld,. As shown in the Appendix, starting with the assumption that the loss of momentum from the air to an adjacent surface is proportional to the flow of momentum at that point (pu2),the following equation may be derived which agrees with the experimental observations:
-36
-24
-12
0
12
24
36
48
60
r, (em)
Figure 13. (a, Top; b, bottom) Radial variation of the horizontal swirl velocity below the bed of packing for two experiments at the same value of gas flow rate to inlet pipe diameter ratio but with different pipe diameters and flow rates.
u,d$/Q = constant (3) In these experiments the swirl velocity profiles were found to be approximately parabolic, i.e., UR(r/R)2 (4) But note that URchanges with circumferential distance from the inlet pipe. In Figure 14 a parabola is fitted separately to each half of the curves. The Static Pressure Distribution within the Packed Bed. A nonuniform static pressure was observed a t the bottom of but just inside the packed bed. The pressure was much greater near the wall of the column than in the center. The pressure profile becomes flatter as distance increases above the bottom of the bed, and at a sufficient height the profile is approximately flat (see Figure 15). The static pressure inside the bed, and the variation in static pressure across a diameter both increase as the air flow rate increases. This may be seen by comparison of Figure 15a and Figure 15b. For the same packing size, the static pressure profile at the bottom of the bed depends on the swirl velocity distribution and on the air flow rate but the velocity generated pressure distribution depends only on the swirl velocity distribution (seeFigure 16).These results show that, at the same value of the (Qld,) ratio, U, =
2414 Ind. Eng. Chem. Res., Vol. 32, No. 10, 1993 24 n
22
E
20
0
Experimental
0
Vr=k(r/RP
A
"
-48
-60
.
j2
n
- -
(Feed pipe diameter 6") (Air flowrate 0.814 mYs)
0
1 0
-36
-24
-12
0
12
24
36 48 r, (em)
60
-
E
/I
-60
-48
-36
-24
-12
0
12
24
36
-48
-36
-24
-12
0
12
24
36
48
60
r (cm)
(Feed pipe diameter 6") (Air flow rate = 0.407 rnYs)
Experimen I vr=urmP
-60
48 60 r, (cm)
Figure 14. (a, Top; b, bottom) Parabolic shape of the swirl velocity profile below the bed shown by fitting a parabola to each half of the curve of experimental results.
the velocity generated static pressure profile is approximately the same. The velocity generated static pressure is reduced as packing size increases. This is shown by comparing the static pressure profile obtained with 50-mm Pall rings Figure 17with that produced with 16mm Pall rings (Figure 15a), noting that the air flow rate and inlet pipe diameter and thus the swirl velocity profile were the same for both experiments. The Static Pressure under the Packed Bed. This was measured at the same time as the measurements of velocity below the bed by disconnecting the dynamic side of the pitot static tube and using only the static side. It was observed that the static pressure below the bed is constant over most of the column cross section, but increases near the wall of the column in an annular region approximately equal in width to the diameter of the feed pipe. This is shown in Figure 18. The Velocity Profile above the Bed. The velocity of the air emerging from the top of the packed bed was measured across a diameter parallel to the inlet pipe. In general, the shape of the velocity profile was similar to that of the static pressure profile near the top of the bd. A t packed depths sufficient for this to have become approximately flat, then the velocity profile was also flat (see Figure 19a). However, for shallow packed beds, the
6
i
Distance above .bottom of bed. 0 Ocm L1
-60
-48
I
!
15cm
-36
Air flow rate = 0.407 m3/s Feed pipediameter-6'
.
0
!
-24
-12
0
12
24
36
48 60 r (cm)
'
Figure 15. Static pressure profiles within the packed bed measured at different distances above the bottom of the bed. Air flow rate (a, top) 0.814 ms/s and (b, bottom) 0.407 ms s. Packing 16-mm Pall rings.
vertical velocity of the air leaving the top of the bed was much greater near the wall than in the center of the column. In an experiment with a packed bed of 16-mm Pall rings only 6 cm deep it was observed that the air flow in the center of the bed was in the downward direction, while that round the column wall flowed in the upward direction. This is shown in Figure 19b.
Effect of Packing Size and Inlet Pipe Diameter on the Maldistribution Factor versus Packed Height Relationship In Figure 20 the maldistribution factor for three sizes of Pall rings (16,25, and 50 mm) is plotted against packed height. The diameter of the air inlet pipe in these experiments was 152 mm. As noted previously, the value of the maldistribution factor decreases with an increase of packed height as a result of the improving gas distribution. The larger size packings require a larger packed height to achieve the same quality of gas distribution (i.e., the same value of the maldistribution factor). In these experiments there is no longer geometric similarity. Each combination of packing size and inlet pipe diameter in the 1.2-m-diameter tower may be considered to represent one size of a different family of
I
Ind. Eng. Chem. Res., Vol. 32,No. 10,1993 2415 Dirtanco
- -
i
~ ~ O V O
bottom of bod.
Air fbw rate 0.814 m3/s Feed pipe diameter 6'
!
n f 4
t
t 0
3
2
-60
-48
-36
-24
-12
12
0
24
48
36
60
r (cm) Figure 17. Static pressure distribution within a packed bed packed with 60-mm Pall rings. Compare with Figure 16a for 16-mm Pall rings at the same air flow rate.
4
-
1*4
E
10
0
Q-0.814m3/s;dp-6'
i
Q-0.407m3/s:do-6'
I
i
k
a 3
t m al
g2
1
n "
-60
-48
-36
-24
-12
0
12
24
36
48
60
r (cm) Figure 16. (a, top) Static pressure variation inside the packing at the bottom of the bed for two different air flow rates and two feed pipe sizes,at the same ratio of flow rate to pipe diameter. (b, bottom) Velocitygenerated pressure variation inside the packing at the bottom of the bed for two different flow r a t a and two feed pipe eizea at the same ratio of flow rate to feed pipe diameter (packing size 16 mm).
geometrically similar towers. The results for all combinations of packing size and pipe diameter are plotted in Figure 21 as functions of the dimensionless ratios (Dld), (zld),and (Dld,). That is, the tower diameter and packed height are measured in length units of packing size. The results show that the larger the reduced diameter (Dld),the greater the reduced packed height (zld) required to achieve a uniform gas distribution. On average between one-thud and one-half of the diameter is required for the gas flow to become uniformly distributed, depending on the inlet pipe diameter.
Discussion It is well-known that it is difficult to achieve a uniform gas distribution in a shallow packed bed. This is especially so when the bed is of a large diameter and the gas must be fed to it from a gas duct which must be kept of small diameter to reduce its cost. There is little or no previous work which gives guidance for when a distributor is necessary or on how to evaluate any proposed distributor design. This work has confirmed that the packed bed itself causes an improvement in gas distribution.
0.0 -60
! ! *
I
-48 - 3 6
'
I
-24
.
I
-12
.
'
'
0
I
12
.
I
24
*
I
36
'
I
48
.
60
r (cm) Figure 18. Radial variation of static pressure measured below the packed bed.
In all of these experiments a uniform gas distribution was achieved if the depth of packing was at least half that of the diameter of the column. This confirms our definition of a shallow packed bed as one in which the depth of packing is less than the column diameter. For this situation it is necessary to use a gas distributor. In practice it is desirable that the distributor occupy as small a volume as possible and cause the smallest possible pressure drop. It is often difficult if not impossible to evaluate the quality of gas distribution achieved in an industrial packed bed of large diameter. It is believed that the method of evaluating gas distributors which has been described above provides a practically useful means of developing and evaluating improved distributors within the laboratory. As far as we know, no other method has been proposed. However it may be that before too long advances in fluid dynamics willbe such that gas distributors for packed beds may be designed by computer (computational fluid dynamics, CFD). At present the predictions of CFD require testing by experiments, and it is hoped that the experimental results presented here will be of some assistance in these developments. This work has shown how the improvements in gas distribution with packed
2416 Ind. Eng. Chem. Res., Vol. 32, No. 10, 1993
-
*
=-8
--
Tower diameter, D 1220 mm Inlet pipe diameter, dp 305 mm 0 Dld 24; d = 50.8 mm 0 Dld = 48: d I 25.4 mm
*
1.2
0
Dld = 76.25; d = 16 mm
300
z
L
1.0
250
U
5
0.8
200
L
0
-I2a!
0.6
g
0.4
0.2
1
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.
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i
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-48
-36
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12
’
100
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150
36
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8
6oo
-c 0
e
300
-sln
2
6
4
8 10 12 14 16 18 20 Packed heightlpacklng size, Zld Tower diameter, D = 1220 mm Inlet pipe diameter, dp = 152 mm 0 Dld = 24: d = 50.8 mm 0 Dld = 48; d = 25 4 mm D/d = 76.25; d = 16 mm
I \ -
L L
-
2
100
0
2
4
6
8
10 1 2 1 4 1 6 1 8 20 2 2 Packed heightlpacking size, Zld
FigureZl. Variationofthemaldietributionfactorwithpackedheight for a ratio of tower diameter to feed pipe diameter (a, top) Dld, = 4 and (b, bottom) Dld, = 8. Packing Size, d 350
”
r
0
0
10
20
30
25.4mm
40
50
Packed Height, 2 (crn)
Figure 20. Variation of the maldistribution factor with packed height for three eizee of Pall ring packing 16, 25, and 50 mm in the 1.2m-diameter tower.
height are associated with a flattening of the static pressure profiles within the packed bed. This is accompanied by gas flow in the horizontal (i.e., radial) direction as well as
in the vertical direction within the bed. The rate at which the horizontal gas flow corrects the nonuniform vertical flow will depend in part on how far the gas must flow in the horizontal direction, i.e., on the column diameter. This explains why larger diameter towers are expected to need agreater packed height to obtain a uniform gas distribution than smaller diameter towers (Figure 21). It is to be expected that these changing flows within the packed bed may be predicted by a three dimensional vectorial Ergun equation. In our paper “Gasflow patterns in packed beds: A computational fluid dynamics model for wholly packed domainsn’,6we have shown that such an equation succeeds in predicting gas flows through nonuniform beds in which different regions are packed with different sizes of packing. There is greater uncertainty in describing the process whereby the horizontal velocity of the swirling gas below the bed generates a static pressure within the packed bed. It is significant that the pressure generated is smaller with a larger packing; thus the packing resistance to gas flow (which is smaller for larger packings) appears to be important. A mathematical description of the bottom of the bed boundary condition needs to take into account both the possibility of a boundary layer in the moving air below the bed and a velocity profile inside the bed. Such a boundary condition has been evaluated by parson^.^
Ind. Eng. Chem. Res., Vol. 32, No. 10, 1993 2417 A small part of the pressure generated near the walls of the column is produced below the packed bed by the continuous change in direction of the gas circulating in an annular region similar in size to the feed pipe diameter. In general we might expect that any method of delivering the gas which causes it to flow horizontally and change direction while in contact with the bottom of the bed is likely to produce regions of increased pressure and a resulting maldistribution. Thus the improved performance of the new distributors is a result of removing the rotation of the gas beneath the packed bed.
Nomenclature A = area of bottom of the packed bed C = coefficient of variation defined by eq 2 D = tower diameter d = packing size d, = gas inlet pipe diameter LB,L, = defined in the Appendix, see eqs A1 and A4 m = exponent in velocity equation (eq A21 n = number of measurements of velocity used in calculating the maldistribution factor Q = total flow of air entering the column r p = gas inlet pipe radius s = constant in momentum loss equation (eq A l ) u = velocity of swirling air below the packed bed u,, UR= value of u at any radius r, and at the column wall u = average value of all the point velocities, ui ui = measured gas velocity of air leaving the top of the bed at any point up = average velocity of air in the inlet feed pipe z = packed height p = density of gas (air) 4 = maldistribution factor defined by eq 1 Appendix. A Momentum Balance Model for Correlating the Swirl Velocity It is assumed that the momentum of the air leaving the feed pipe is lost to the bottom of the packed bed, and that the momentum lost, dL,to an incremental area of the bottom of the bed, dA,a t radius r, given by
dL = spu," dA
(AI) Thus the momentum lost to the bottom of the bed is
L, = spLR(2ar)u," dr Assuming the variation of the swirl velocity, U r , is given by Ur
Then
UR(r/R)m
(A2)
3
spaU;R2 m+l
(A31
The momentum of the air leaving the feed pipe is
L , = Q ~ U , rP= ~ ( ~ ) ~ Assuming Lg = L,. Then from eqs A3 and A4
and
( Urd$ 7 = --( 4 7) m ) + 1 "'(;)* = constant
(A6)
It is seen that eq A6 is the same as eq 3. It is likely that some of the momentum entering is lost to the walls of the column below the packed bed which cause the air to change direction. It may be that this effect could be taken into account, approximately, by using a value of m greater than the value of 2 which was observed in the experimental work. The experimental observations confirm the validity of eqs A6 and 3.
Literature Cited (1) Ali, Q.H. Gas distribution in shallow large diameter packed beds. Ph.D. Thesis, Aston University, Birmingham, 1984. (2) Aryan, A. F. The fluid mechanics of maldistributed gas flow in shallow packed beds. Final Year Practical Project Chemical Engineering, Aston University, 1986. (3) Haasan, A. 0. The effect of inlet pipe to tower diameter ratio and packing size on gas distribution devices. M.Sc. Thesis, Aston University, Birmingham, 1985. (4) Kay, J. M. An Introduction to Fluid Mechanics and Heat Transfe;Cambridge University Press: Cambridge, UK, 1957. (5) Parsons, I. M. Gas distribution in shallow packed beds. Ph.D. Thesis, Aston University, Birmingham, 1991. (6) Parsons, I. M.; Porter, K. E. Gas flow patterns in packed beds: A computational fluid dynamics model for wholly packed domains. Gas Sep. Purif. 1992, 6 (4), 221.
Received for review February 22, 1993 Revised manuscript received July 15, 1993 Accepted July 30, 1993. e Abstract published in Advance ACS Abstracts, September 15, 1993.
