Hughmark, G. A,, AlChEJ., 21, 1031 (1975). Johnson, H. A., Hartnett, J. P., Clabaugh, W. T.. Trans. ASME, 75, 1197 (1953). Kays, W. M., Perkins, H. C., in “Handbook of Heat Transfer.” W. M. Rohsenow, J. P. Hartnett, Ed., Sect. 7, pp 7-1/7-193, McGraw-Hill, New York, N.Y., 1973. Kolar, V., Int. J. Heat Mass Transfer, 8, 639 (1965). Lyon, R . N. Chem. Eng. Prog., 47, 75 (1951). Malina, J. A,, Sparrow, E. M., Chem. Eng. Sci., 19, 953 (1964). McCarthy, J. R.. Hines, W. S., Seader, J. D., Trebes. D. M., Bull. 6th Liquid Propulsion Symposium, pp 73-100, Chemical Propulsion Information Agency, Pub. No. 56, Silver Spring, Md., Aug 1964. Meyerink, E. S.C., Friedlander, S. K., Chem. Eng. Sci., 17, 121 (1962). Mizushina, T., Ogino, F., Oka, Y., Fukuda, H., lnt. J. HeatMss Transfer, 14, 1705 (1971). Nijsing, R., Warme- Stoffubertragung, 2, 65 (1969). Notter, R. N., Sleicher, C. A,, AlChf J., 15, 936 (1969).
Notter, R . N., Sleicher. C. A.. Chem. Eng. Sci., 26, 161 (1971). Notter, C. A., Sleicher, C. A., Chem. fng. fng. Sci., 27, 2073 (1972). Patel, V. C., Head, M. R., J. NuidMech., 38, 181 (1969). Petersen, A. W., Christiansen, E. B., AlChEJ., 12, 221 (1966). Petukhov, B. S., Adv. Heat Transfer, 6, 503 (1970). Petukhov, B. S., Popov, V. N., Teplofiz. Vysok. Temperatur, 1, 69 (1963). English trans., High Temperature, 1, 69 (1963). Seider, E. N., Tate. G. E., lnd. Eng. Chem., 28, 1429 (1936). Sleicher, C. A., Awad, A. S., Notter, R. H., lnt. J. HeatMass Transfer, 16, 1565 (1973). Sleicher, C. A., Rouse, M. W., lnt. J. Heat Mass Transfer, 18, 677 (1975). Wilson, N. W., Azad, R. S., J. Appi. Mech., 42, 51 (1975).
Received for review September 3 , 1976 Accepted October 29,1976
Longitudinal Dispersion in Packed Gas-Absorption Columns William E. Dunn, Theodore Vermeulen,’ Charles R. Wilke,. and Tracy T. Word Chemical Engineering Department and Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720
Axial-mixing experiments were conducted in a 2 4 diameter gas-absorption column by using tracer-injection techniques. The carrier streams were air and water. Empirical Peclet number correlations are presented for both phases, with I-in. Berl saddles, I-in. Raschig rings, and 2-in. Raschig rings used as packing materials. The extent of mixing was much greater in the liquid phase than the gas phase. Gas-phase Peclet numbers decreased with both liquid and gas flow rates. On the other hand, liquid-state Peclet numbers were found to increase with liquid flow rates, and no quantitative effect of gas rate was observed. It is found that mixing can contribute significantly to absorption-column design requirements, especially if liquid-phase diffusion controls.
Introduction In the design of packed columns for gas-absorption or stripping operations, the tower height is often estimated by multiplying the total number of transfer units (NTU) by a correlational height of a transfer unit. Previous work has shown that axial mixing, a deviation from piston flow, may be a significant design factor for liquid-liquid extraction systems in packed columns. Axial mixing arises from the fact that “packets” of fluid do not all move through a packed bed at a constant and uniform velocity, either because of either velocity gradients in the fluid, or eddy motion in the packing voids. Axial mixing tends to reduce the concentration driving force for mass transfer that which would exist for piston flow, as illustrated in Figure 1; the concentration profiles for piston flow are dotted lines, and solid lines represent the axial-mixing case (Miyauchi et al., 1963). To achieve a given separation, more transfer units are required for the axial-mixing case owing to the reduced driving force. Likewise, for a given column under conditions of axial mixing, HTU’s (heights of a transfer unit) estimated with plug flow assumed are higher than the true HTU’s that would be calculated from the actual mass-transfer coefficients. The object of this study has been to determine whether axial mixing is an important factor in gas-absorption column design, and to provide correlations of dispersion coefficients in the form of Peclet numbers for both liquid and gas phases. Axial mixing was measured for each phase separately, in the absence of interphase transfer of any solute. It appears that gas holdup is not affected in a major way by mass transfer, but may be different for liquids with lower surface tension than that of water. The flow patterns for liquid are also expected to be independent of mass transfer unless surface-active solutes are involved, so that the liquid-phase results obtained here may 116
Ind. Eng. Chem., Fundam., Vol. 16,
No. 1,
1977
prove to be rather generally applicable. The calculation of axial-dispersion effects in actual column separations has been discussed by Miyauchi et al. (1963), and Vermeulen et al. (1966), among others. A numerical example of the effect in absorber performance, based on results obtained in the present study, is given by Sherwood et al. (1975). A general discussion of axial dispersion has been given by Mecklenburgh and Hartland (1975). Theoretical The extent of axial mixing may be evaluated quantitatively, independently of any mass transfer, by tracer-injection techniques. A tracer amount of a component is injected into one of the bulk phases in the form of a step, impulse, or sinewave input. A step input was used as a basis for this study. The buildup of tracer at a fixed distance downstream from the injection point is measured as a concentration-time relation which is called a breakthrough curve. The characteristics of the experimental breakthrough curve may then be compared with the forms predicted by a mathematical mixing model; the value of the mixing parameter in the mathematical model that gives the best fit to the experimental curve is designated as the mixing parameter characteristic of the experimental system. Two such models were found to be pertinent to the case at hand, and their results are briefly described. Random-Walk Model. The random-walk model is characterized by “packets” of fluid moving through the packing in a series of discrete jumps corresponding to a certain mean free path, 1 , and with a characteristic velocity, u . If the total bed length is h , and the time that a packet of fluid has been in the bed is t , then the number of mixing lengths N (or column Peclet number) is defined as h/l , and the dimensionless time scale. T , as ut/l. If a step input of tracer with magnitude
c, or m c y
4
i .o
I
0.8
0.6
0.4
0.2
00.6
0.7
0.0 0.9 ID
1.25
1.5
1.75 2.0
T I N (dimensionless time)
z:o z.1 Figure 1. Concentration profile in a typical extractor (after Mi-
Figure 2. Random-walk model breakthrough curves.
yauchi).
Co has taken place a t N = 0 and T
1
= 0, it develops that the
fractional approach to the final concentration is as shown graphically in Figure 2 as a semilog plot of dimensionless concentration vs. log dimensionless time for contours of N . Here the time scale has been normalized about the stoichiometric time (the time required to replace one column holdup of the phase of interest), a t which T = N . T o compare these results to experimental curves, it was expedient to compute the midpoint slopes s relative to a time scale of t ( x = o . 5 , , where x = C/Co
A numerical approximation to the random-walk model solved for N was found to be
N = 4irs2 - 0.80
(2)
Now the column Peclet number based on the random-walk model may be evaluated explicitly from an experimental breakthrough curve by evaluating the midpoint slope and substituting in eq 2. The packing Peclet number, P , is proportional to the column Peclet number, N , with a proportionality constant d,/h (or B ) . Hence, N is equivalent to PB. Diffusion Model. An analogy between open-pipe flow and flow through a packed bed is assumed in the diffusion-model approach. The general one-dimensional diffusion equation may be expressed (3) With specific boundary conditions applicable to flow through a packed column, Yagi and Miyauchi (1953) have obtained an analytical solution which yields breakthrough curves qualitatively similar to those of Figure 2. In this case the midpoint slope is given empirically by the relation
N' = 4as2 - 1.60
(4)
In interpreting the experimental data, eq 2 was preferred for the gas phase, and eq 4 for the liquid. Experimental Section Apparatus. The experimental system consisted of a cylindrical steel column, a positive-displacement blower, a liquid feed pump, liquid- and gas-tracer injection systems, and the necessary indicating, controlling, and recording devices. The interrelationship of these components is indicated in the schematic diagram of the system shown in Figure 3.
Flow
Flow
-Liquid -feed pump
Figure 3. Schematic diagram of the experimental apparatus. The heart of the apparatus was a 2-ft-diameter column, shown in Figure 4, divided into three flanged sections: (a) a 3-ft long top section which served the liquid-feed and deentrainment functions, (b) a 6-ft long packed section, and (c) a 4-ft bottom section used as a liquid reservoir and gas entry port. A 20-hp blower (Sutorbilt, Model 1436) was used to supply air to the tower. A once-through flow of air was found expedient, necessitated by tracer buildup which complicated the analysis of gas breakthrough curves, when air was recycled in a closed loop. Once-through flow eliminated the use of steam coils and water cooling originally provided. Flow rates were measured by an air-impact nozzle, located upstream of the blower and connected to draft-gauge manometers. Liquid was recycled from the water reservoir through a centrifugal pump (Ingersoll-Rand, Model 4RVL, with an 8-in. diameter impeller) to the water-feed distributor in the top section. Flow rates were measured either by a 2 5 s - i n . orifice located in a 4-in. line or by a 1.25-in. orifice in a 2-in. line. Orifice pressure drops were displayed on a manometer. The tracer injected into the bulk-water phase was an aqueous solution of 0.3 to 1M sodium nitrate. A portion of the sodium nitrate solution was recycled through a centrifugal pump to a 55-gal storage tank. A side stream was withdrawn from the pump discharge, through a filter and rotameter; the stream was either returned to the storage tank or fed into the column through an injection manifold, the choice being conInd. Eng. Chem., Fundam., Vol. 16, No. 1 , 1977
117
Inlet
?,-in.
i.d.
&-in. outlet holes Front view
12~LiqcandceIl ~
3 Liq cand cell
71n
51n
,
1
Figure 4. Schematic diagram of column. Top, liquid tracer injection and gas sampling. Center, gas and liquid sampling. Bottom, liquid sampling and gas-tracer injection.
,'---Top view showing radial iocotion of legs
trolled by the setting of a three-way solenoid valve. A pressure gauge was installed on the line leading to the manifold to indicate the injection behavior. Observation of the gauge indicated that the tracer flow rate did approximate a step function satisfactorily; the precise moment when flow began could be determined by noting the instant the gauge responded. It was important that liquid-tracer injection conform closely to a step input and be evenly distributed across the column cross section. To avoid formation of air pockets the takeoff legs were attached to the top of the reservoir, rather than to the sides. A diameter for each leg of 0.09375 in. caused the flow to distribute quite evenly among all 16 legs (see Figure 5). The tracer used for the air phase was a stream of helium. The helium-tracer injection system is shown schematically in Figure 6. Helium flow to the column was initiated by pressurizing the surge tank with helium and opening a three-way solenoid valve to the gas-tracer injection manifold. This manifold consisted of 26 injection tubes distributed over the column cross section. Flow to the manifold was stopped abruptly the opening the two-way solenoid to the atmosphere, then de-energizing the three-way solenoid. This latter action simultaneously shut off flow to the manifold and opened the manifold to the atmosphere. Discontinuance of gas tracer approximated a step function more closely than tracer startup, so all gas breakthrough curves taken were for the tracerpurging step. Sodium nitrate concentration was continuously monitored downstream by means of an electrical conductivity measurement. Three conductivity cells were located midway down the packed section, and three more a t the base of the packed section. A cross-sectional drawing is shown in Figure 7. Liquid entered the samplers through the funnel-shaped top and left through the port in the side. A high-frequency voltage (approximately 300 a t 1000 Hz) was impressed across two rhodium-plated nickel pin electrodes, which were kept submerged in fluid to give a continuous reading. The conductance of the solution between the pins was determined by amplifying and 118
Ind. Eng. Chem., Fundam., Vol. 16,No. 1, 1977
Figure 5. Liquid-tracer injection manifold.
Packed section Packing ruppo l o g manifolds
2- way
Surge
1
Tracer- ga cylinders
Figure 6. Schematic diagram of the gas-tracer injection system.
recording the output signal. A two-channel amplifier provided simultaneous measurement of liquid conductivity a t two points in the column. The recorder response vs. sodium nitrate concentration was determined to be truly linear for both channels, although it had a positive intercept. To determine the lower limit of liquid flow rate to which the samplers would respond, flow through a sampler was observed outside the column. An experiment was assembled in which
{
Sample
1‘1 wire
/Screw
cap
Tef Ion-disc
I 2)
tube
- in.
Figure 8. Detail of gas sampler: A, gas sample; B, 0.125-in. 0.d. tube; tube; C, screw cap; D, seal formed with waterproof tape; E, porous Teflon; F, 0.5-in. drilled holes; G, protective cage.
0.0935 diamrhodium- plated nickel Dins
Table I. Packing Characteristics
Section A-A
A i l dimensions in inches
d,, in.
Packing
t
1-in. Raschig rings 2-in. Raschig rings 1-in. Berl saddles
0.682
60.8
0.376
0.690 0.740
29.8 79
0.749 0.237
f;,k
Figure 7. Cross-sectional drawing of a liquid-conductivity cell. as a packing particle. From the properties of a sphere column conditions were simulated, and satisfactory operation of the samplers could be observed if the liquid flow rate was maintained above 1000 lbh-ft2.Consequently, no runs were made for L values less than 2000 lbh-ft2. Helium tracer was monitored a t the top of the packed section by either of two steel gas samplers (Figure 8). A vacuum system provided suction for flow through either gas sampler to a thermal conductivity cell used to measure helium concentration. A dc voltage was impressed across an extremely fine (0.45-mil diameter) tungsten wire which thus became heated to a certain temperature. The heat transfer, hence the temperature of the wire, depends in part upon the thermal conductivity of the gas stream flowing past the wire, This wire was incorporated in a Wheatstone bridge circuit. The wire resistance, which is dependent on temperature, was measured indirectly by amplifying and recording the out-of-balance voltage of the bridge circuit relative to a null position. The low sensitivity of the bridge circuit made it necessary to install a preamplifier (ahead of the Brush amplifier) which could be used to boost the signal by a factor of 10. The recorder response was linear with respect to the helium concentration flowing through the cell. As in the case of the liquid recorder, an external switch was provided to mark the start or end of injection on the recorder chart. Packing. The void fraction, t, was measured for all packings used: the 1-in. Raschig rings, the 1-in. Berl saddles, and the 2-in. Raschig rings. The surface area per unit volume, ap,was measured for the 1-in. and 2-in. Raschig rings. For the 1-in. and 2-in. Raschig rings, which were a standard geometric shape, these packing characteristics were determined by measuring the dimensions of representative samples of the packing with calipers, by counting the number of particles per unit volume and by calculating t and a,,. The void fraction of the 1-in. Berl saddles was obtained by packing a large container of known volume with the saddles and measuring the amount of water necessary to fill the voids. Equivalent diameter of the packing was reported as the diameter of a sphere with the same surface-to-volume ratio
d, =
6(1 - t) ~
UP
For these experiments as well as for the runs, the packing was “dry-packed, unshaken.” Results are shown in Table I. Procedure. Runs were made a t liquid flow rates of 2000, 5000,8000,and 11 000 lbh-ft2, and the gas rate was increased until either flooding or excessive entrainment of water overhead was encountered. The following method was used to measure breakthrough. First the liquid and gas rates were adjusted to the desired values, and the column brought to steady-state operation. The liquid-conductivity amplifier gains were adjusted so that approximately full-scale deflections would be obtained. The liquid-conductivity recorder chart was started, and the sodium nitrate tracer flow (about 1%to 4% of the total flow) was begun by activating the solenoid valve to the liquid-tracer manifold, which in turn produced a mark on the chart. After the two traces were obtained, the tracer concentration in the liquid recycling through the column was reduced by opening a drain valve and a water-makeup line simultaneously, adjusting the latter manually to maintain a constant liquid level in the water reservoir. By this method, traces were obtained for all six liquid samplers. For gas-phase measurements, the suction head was adjusted to give the prescribed sampling rate. The bridge circuit was balanced by adjusting the variable resistance position recorder reading. Amplifier gain was then adjusted to give approximately the desired full-scale deflection. Helium flow to the column, about 3 mol % of the air flow, was started, and the recorder was turned on. Then the chart was marked to denote the beginning of a purging run as the helium flow was stopped. After six liquid traces and two gas traces had been obtained a t the same L and G values, the liquid holdup in the column was measured. T o do this, the pneumatic valve in the liquidfeed line was closed, and the liquid-level rise in the bottom reservoir was observed as the water in the packing drained into it. Ind. Eng. Chem., Fundam., Vol. 16, No. 1, 1977
119
Table 11. Summary of Gas-Phase Peclet Numbers, I-in. Saddles G
0 0 0 0 0 2 000 2 000 2 000 2 000 2 000 5 000 5 000 5 000 5 000 8 000 8 000 8 000 11 000 11 000
300 500 700 900 1100 300 500 700 900 1100 300
500 700 900 300 500 700 300 500
160 145 120 120 91 140 130 92 73 65 160 88 77 66 66 63 66 65 51
A
% Dev
P
171 115 125 121 80 141 124 102 69 60 127 102 83 70 86 71 73 52 61
6 17 15 12 8 1 10 8 10 7 14 12 7 10 19 7 16 13 10
0.68 0.45 0.49 0.48 0.32 0.56 0.49 0.40 0.27 0.24 0.50 0.40 0.33 0.28 0.34 0.28 0.29 0.21 0.24
Sampler 1-B
Sampler 1-A
L
190 94 135 120 77 140 100 115 63 62 125 99 78 78 89 66 89 47 66
(260)" 122 150 94 72 145 125 96 79 52 130 94 96 61 115 78 81 52 61
160 97 94 150 81 140 140 105 60 60 92 125 82 76 75 77 56 65 64
175
Numbers in parentheses have not been included in the final average. Table 111. Summary of Gas-Phase Peclet Numbers, I-in. rings
0
L
G
0 0 0 0 0 2 000 2 000 2 000 2 000 5 000 5 000 5 000 8 000 8 000 11 000
300 500 700 900 1100 300 500 700 900 300 500 700 300 500 300
Sampler 1-A 82 59 40 (7710 35 82 49 50 42 44 36 31 25 32 39
Sampler 1-B
99 59 71 55 40 68 52 60 42 54 54 38 47 40 33
94 55 52 55 28 72 60 63 55 47 35 32 33 41 42
78 60 57 58 37 69 57 48 39 51 33 54 22 32 54
68
58
59
47 44
46 43
41
25 49
52 34
65
39
29
37
A
% Dev
P
88 60 55 56 35 73 55 52 45 48 41 39 34 38 40
10 5 16 2 10 7 7 15 12 6 13 20 26 14 9
0.55 0.38 0.34 0.35 0.22 0.46 0.35 0.33 0.28 0.30 0.26 0.24 0.21 0.24 0.25
Numbers in parentheses have not been included in the final average.
Table IV. Summary of Gas-Phase Peclet Numbers, 2-in. Rings ~~
G
-
N
1151 I
m
G i=
0
ai
/ / I / / l I
h
r-
/ / / I / / I l dNl J ri
f .c
'I-0
r i w
-B
v - 0
3
m
N
c"
0
N N
1 0
0
000000 00000
mmt-mri
3
0 0
m
000000000000 0000 00000
mr-mh
ri
mmr-m+
ri
Z
0
% v,
c;i
ai
n
0 0
0 N
0 0 0 N
0 0 0 N
0 0 0 N
000 000 000 N N m
0 0 0
000000000000 000000000000 000000000000
m
mmmmwwmwwmriri -ri
0 0 0
0
0 g
8 8 z
ri ri
Ind. Eng. Chem., Fundam., Vol. 16, No. 1,
1977
123
1 P 0 10-
eG.0
AGs3oc IG : 500 0 G i 700 (Gz900
0011
0
4000
8000
12000
4000
L (Ib/hr f t 2 )
Figure 14. Liquid-phase Peclet numbers, 2-in. Raschig rings.
characterized by mean deviation of 30%. Part of the scatter was undoubtedly caused by the difficulty of determining the slope of the breakthrough curves which sometimes fluctuated erratically in the region of interest, reflecting the actual fluctuations of flow in the column. Semilogarithmic plots of Peclet number vs. liquid flow rate are shown in Figures 12, 13, and 14. In contrast to the gasphase results, axial mixing decreases a t increasing liquid rates. The quantitative effect of gas-phase flow rate is negligible compared with the scatter of the present data. For the 1-in. Berl saddles, a trend does seem to be established in which the Peclet number increases with gas rate, but this trend tends to be lost or reversed elsewhere. For all types of packing studied the dependence of liquidphase Peclet number on liquid flow rate was found to be approximately the same. The following empirical representation of the data was developed: for 1-in. Berl saddles P = (0.033) x 104.93X1@-,iL (9) for 1-in. Raschig rings (10)
and for 2-in. Raschig rings
p = (0.051) x 104.93XIO-'L
(11)
These hold for the range 2000 5 L 5 11 000 lb/h-ft2, and 0 5 G 5 1100 lb/h-ft2. The straight-linerelations drawn in Figures 12-14 represent only one of the possible curves for fitting the data. In all three packings, the slope of log Peclet number against L tends to diminish with increasing L . A log-log plot of Peclet number against L indicated that it would not be unreasonable to represent the relation as a square-root dependence of Peclet number on L . This was the form of correlation developed by Otake and Kunugita (1958). Another important conclusion is that the extent of mixing in the liquid phase is much greater than in the gas phase. The Peclet number difference is roughly one order of magnitude in the low flow rate ranges used in these experiments. In both phases, the Peclet number values obtained correspond to axial-dispersion coefficients in the range of 100 to 200 cm2/s; the difference in magnitude of Peclet number between the two phases is offset by a corresponding difference
124
Ind. Eng. Chem., Fundam., Vol. 16, No. 1 , 1977
1200
L (Ib/hr f t ' )
Figure 13. Liquid-phase Peclet numbers, 1-in. Raschig rings.
p = (0.038) X 104.93X10-5L
8000
in superficial velocity. Because molecular diffusivity is in the range of 0.7 cm2/s and 10-5 cm2/s for the gas and liquid phases respectively, its contribution to the observed Peclet numbers is negligible. A liquid mixing length ( E / u )of approximately 7 nominal packing diameters was computed for a typical column run. This was slightly lower than the 10-30 range computed for the same run from the data of Stemerding (1961), who used a lower flow rate range. Nomenclature u p = packing surface area per unit volume, ft2/ft3 C = dimensionless concentration in a flowing phase CO = magnitude of step concentration change d, = equivalent-sphere diameter of packing, in. E = eddy-dispersion coefficient of a flowing phase, cmz/s G = gas flow rate, lb/h-ft2 h = column height 1 = mean free path L = liquid flow rate, lb/h-ft2 N,N'= column Peclet number P = packing Peclet number of a flowing phase, Nxd,/h s = dimensionless midpoint slope of breakthrough curve t = time T = dimensionless time u = characteristic velocity of a flowing phase x = dimensionless concentration, C/C, 2 = dimensionless length of column along direction of flow t = void fraction Literature Cited Mecklenburgh, J. C., Hartland, S., "The Theory of Backmixing", Wiley-lnterscience, New York. N.Y.. 1975. Miyauchi, T., Vermeulen, T., Ind. Eng. Chem., Fundarn., 2, 113 (1963). Otake, T., Kunugita. E., Chem. Eng. (Jpn), 22, 144 (1958). Sherwood, T. K., Pigford, R. L.. Wilke, C. R., "Mass Transfer", pp. 609-614, McGraw-Hill Book Co., New York, N.Y., 1975. Stemerding, S., R o c . 2nd Eur. Symp. Chem. Reaction Eng., Chem. Eng. Sci., 14, 209 (1961). Vermeulen. T., Moon, J. S., Hennico, A,, Miyauchi, T.. Chern. Eng. Prog., 62 (9). 95 (1966). Yagi, S., Miyauchi, T., Chern. Eng. (Jpn), 17, 382 (1953); 19, 507 (1955).
Receiued for reuiew September 8, 1976 Accepted October 21, 1976
