Pressure Aeration in a 55-Ft Bubble Column lnaky J. Urza and Melbourne L. Jackson* Department of Chemical fngineering, University of Idaho, Moscow. Idaho 83843
Steady and unsteady transfer of oxygen from air to liquid was observed using a 3-in. diameter column. Oxygen transfer efficiencies obtained were roughly 1% per foot from 14 to 53 ft for sulfite solutions. Air input through single orifices of l/4- and lie-in. diameters showed similar column performance with the larger diameter favored. Average values of the transfer factor, ( K L a ) , were 14 h r - ’ for steady-state transfer to sulfite and 13 h r - ’ for unsteady-state transfer to water at the same air rate. This provides validity for the experimental and interpretative methods employed. Possible advantages from use of tall tanks are lower energy requirements for air compression by at least a factor of 4, smaller land area needs, and simplified construction and piping requirements. A disadvantage is increased liquid pumping costs. Design implications for biological reactors are reduced tank volumes, less tendency for upset resulting from high oxygen availability, and a sludge mass which is more reactive and easily suspended.
The phenomenon of oxygen transfer from air bubbles to liquid has been studied and reported by many investigators, but the effects of elevated pressures on gas-liquid transfer for pressures corresponding to liquid depths above 15 ft ( 5 m) have been neglected. The efficiency of oxygen transfer in conventional aeration basins may be as low as 3-5%. The reasons for low absorption efficiencies are short bubble residence times, poor interfacial contact, and the existence of unreactive zones. The use of tall columns increases the bubble detention time and increases the limiting solubility of the oxygen in the liquid. Other advantages are reduced net compression energy requirements from lower air volumes, reduced tank volumes through more effective oxygen transfer and reduced land area needs. A disadvantage arises in increased liquid pumping energy, but a net decrease in overall energy input is indicated. The present study considered oxygen transfer characteristics for increments of liquid depths up to 55 f t (17 m) for both steady-state transfer to sulfite solutions and unsteady-state transfer to tap water.
Transfer Model for Tall Bubble Columns-Steady State Several different investigators, Westerterp, et al. (1963), and Yoshida and Akita (1965), report that KL, the transfer coefficient, is essentially independent of operating conditions of column height, gas flow rate, bubble diameter, and mixing intensity. Likewise, Calderbank (1967) found that gas flow rates had no effect on the value of the liquid phase mass transfer coefficient and did not change with bubble size within the separate ranges of “small” and “large” bubbles. In a review of mass transfer in gas-liquid contacting systems, Sideman, et al. (1966), concluded, from the mass of data available, that KL was independent of column height up to 10 ft, gas flow rate, bubble diameter, and mixing. Thus, the design term (KLu) is dependent primarily on the interfacial area per unit volume, a =A/V. The variation of a over a tall column is subject to a change in bubble population if coalescence or break-up occurs, and to an expansion in bubble size because of decreasing pressure and a volume reduction from oxygen depletion. The complexity of these changes and the lack of detailed information for bubble swarms in very tall columns precludes the use of an expression for interfacial area from bubble characteristics. However, as is shown 106
Ind. Eng.Chem., Process Des. Dev., Vol. 14, No. 2, 1975
experimentally later for unsteady-state transfer in a narrow column, the changes which occur appear to be compensating under the conditions of a tall, small diameter column. The result is that (KLu)is surprisingly constant over the column except for a section above the air inlet where the large bubbles emerging from a pipe outlet break up into an established pattern. The fact that an average &a) may be usefully determined over a tall column permits direct integration of the rate equations. A model for the steady-state transfer of oxygen from air to a liquid having either a zero back pressure of oxygen, as for catalyzed sulfite solutions, or a low constant value of the oxygen concentration in the bulk liquid as may be approximated by a system of growing microorganisms in a waste treatment plant, has been derived (Leber, 1974). The model is based on oxygen and nitrogen balances over the column with the assumption that the liquid side ~ K L ) ,valid for gases of low transfer processes control ( k = solubility, and that the transfer factor (KLu)changes little over the column and may be taken as an average. An oxygen rate balance on the gas phase, mass entering = mass leaving + mass transferred, can be expressed as
For a sulfite solution, C = 0, and expressing the interfacial concentration in terms of the Henry’s law constant for dilute solutions
and eq 1in differential form becomes -d(n?y)/dz = (KLa)3. 4 6 P y / H
(3)
Because rn and y are each functions of 2, a second relationship is required which is obtained from a nitrogen balance on the gas phase for steady-state operation
m o ( l - yo) =
?H(1 -
y)
(4)
Upon differentiating, this becomes (5)
Expanding the differential in eq 3, combining with eq 4 and 5, rearranging, and placing limits
02 INALYZER
DRY TEST
ROT4METER'
The total absolute pressure a t any point in the tall column is given by
P = Pa + h, - (h,/h)z
55 F T P
I
40 FT I n 1
( 7) 2 7 FT
Substituting for P from eq 7 and integrating, the final transfer model is obtained
(nl
14 F T 11)
REGUL4TOR
Figure 1. Schematic of experimental apparatus.
Equation 6 provides the oxygen transfer efficiency = 100(yo - y)/yo for known values of the transfer factor ( K L u ) ,air flow rate, liquid depth, and the hold-up height. Conversely, it may be solved for (&a) in terms of a known outlet gas composition. Local M a s s Transfer Factors
For comparison with ( K L u )values obtained using sulfite solution, and for observations of the variation of (KLu) over the height of the column, the unsteady-state transfer of oxygen to water was employed, The defining equation is (dC/dt) = (KLa)(C* - C)
(9)
A profile of the oxygen concentration over the column was taken a t time zero and after air input for several time periods. Values of the rate of transfer, bulk liquid composition, and interfacial liquid composition (obtained from gas compositions) change continuously with time and the evaluation of eq 9 for a particular position in the column is accomplished by determining the mean values of the three variables over each time period. The procedure employed was as follows. C us. time is plotted for constant position lines, and cross-plotted as C us. height for constant times. A mean value of (dC/dt) is obtained from the latter plot by graphical integration. However, the plot of C us. time was found to be a smooth line of low curvature and the slope at the midpoint of the time interval gave the mean value with sufficient accuracy. The mean value of the liquid composition was obtained from the same plot by the graphical integration
Values of C* were obtained from a determination of the mean gas-phase composition over the time interval with a calculation of the interfacial liquid composition from equilibrium relationships. The mean gas composition was obtained by a determination of the amount of oxygen absorbed by the liquid during the interval and an oxygen balance on the gas phase
Equation 11 was evaluated graphically by determining the area between two time lines in the first plot for the region of the column from the bottom to the position, z, in question. The mean amount of oxygen remaining unabsorbed over the time interval was that entering the bottom less that transferred to the liquid. This amount divided by the sum of the nitrogen entering and the oxygen unabsorbed gives approximately the mean mole fraction of the oxygen,
y . This neglects the amount of nitrogen absorbed during the interval. The magnitude of this error introduced was estimated to be small for the time intervals following an initial period. The rate of nitrogen absorption is about twice that for oxygen. This indicates that more nitrogen will be absorbed near time zero and that the error will diminish with time because nitrogen will approach equilibrium faster than the oxygen. For example, a t the lower 13-ft position for the first time interval, the mean oxygen gas concentration should be corrected by increasing it 5% and reducing ( K L u )by 7.6%. Thus, ( K L u )values during later time intervals would be more nearly correct and ( K L u )values during a second period should be lower than for the first interval.
Apparatus and Procedures The 5 5 f t column (17 m ) was constructed of 3-in. (7.6 cm) diameter Corning glass sections. It spanned four floors in a pipe chase of the Buchanan Engineering Laboratory. The equipment arrangement is shown in Figure 1. Sample ports were placed a t each of five positions. The air flow out from the top of the column was measured with a Rockwell dry test meter having an accuracy of f$%. The column was operated a t four heights with the upper sections removed for a particular liquid level; measurements were made of gas rate and composition just above the top of the liquid a t each height. Oxygen concentrations of the outlet air were measured with a Beckman Model F3 paramagnetic oxygen analyzer. This instrument determines the 0 2 content of the air continuously with a stated accuracy of kl% of full scale over two ranges, 0-25% 0 2 and 16-21% 0 2 by volume. The 0 2 analyzer was standardized before each run by setting the zero with nitrogen gas and adjusting the span to 20.9% O2 for dry ambient air. The span was checked periodically for consistency. The oxygen concentration in the liquid was determined for unsteady-state transfer (water only, no sulfite) with a 50-ft (15 m ) dissolved oxygen membrane probe and meter (YSI Model 54). Pressurized laboratory air was used for the air source controlled by a pressure regulator and a rotameter. The air was introduced into the column through single orifices of either %-in. (0.64 cm) or lh-in. (0.32 cm) inside diameter copper tubing. Bubble size and distribution characteristics were observed by flash photography (up to 1/50,000-sec exposure) a t each level for various air flow rates and each orifice. Landberg, e t al. (1969), discuss experimental procedures in the testing of surface aeration equipment by the unsteady-state transfer method. Another method used to estimate the effectiveness of aeration is the sulfite oxidaInd. Eng. Chem., Process Des. Dev., Vol. 14, No. 2 , 1975
107
_...."_ .. __. .."_._
__""
-.._
. . . . _ . _ . . _ I __._^
- ......
intervals of aeration. Original data, including some not reported herein, are on file (Urza, 1972).
In all runs the bubbles were formed a t a single orifice oriented with the opening upward. Typical bubble cbaracteristics, observed by a photographic technique, a t several air flow rates and column heights, are shown in Figure 2. The circular column distorts the view of the bubbles by elongation in the horizontal direction. Bubbles emerge as single, large volumes with occasional clusters. At the lower air flow ranges (1.6-4.0 ftS/hr) bubble clusters were more evident. The bubbles formed initially ranged in size from 0.4 to 0.6 in (1-1.5 cm) in diameter (major axis) with a length to height ratio of about 2 to 1. The bubble population was very low just above the inlet, hut a t the first level the bubble population increased substantially and the average bubble size became smaller, ranging from 0.4 in (0.9 cm) to minute size with an average of about 0.3 in (0.7 cm). At the second level the bubble population increased further with an average diameter of about 0.2 in (0.5 cm). At the third level, as in Figure 2, the bubble population was greater, but the average bubble diameter was about the same and was similar a t the fourth level. In general, the bubbles form singly a t the orifice and break up as they rise; also, some coalescence may occur. The bubbles formed by the %in. orifice were slightly larger than those formed by the ],kin. orifice, but a t the first level they attained similar sizes. As the bubbles rose some reduction in size and increase in number occurred. A range of bubble sizes was apparent a t all liquid levels. Dreier (1956), using a large, shallow basin, indicated that bubble patterns are not established until about 2 4 ft above the inlet and that large bubbles break up and smaller ones coalesce. The volumetric bold-up ratio was determined for each run, is related to the velocity of rise of the bubbles (hence bubble size), and is given by 108
Ind. Eng. Chem., ProcessDes. Dev., Vol. 14, No. 2, 1975
Figure 2. Photographs of bubbles from the Y-in. orifice: top, just
Higher bold-up ratios were reported (Bartholomew, et al., 1950), a t the same conditions, for porous plates as compared to orifices a t the same air flow rates. The effect of the different types of gas distributors (hence bubble size) on bold-up disappears only a t high mixing rates where bubble size becomes independent of the type of distributor (Sideman, et al., 1966). Figure 3 shows percentage hold-up ratios, over a range of air flow rates for the Y4-h and Ih-in. orifices a t four liquid levels, to he linear with air flow rate. These relations hold for constant bubble size distributions and corresponding terminal bubble rise velocities. The hold-up ratios are observed to decrease with increasing column height which results from the reduction of gas volume by the increased pressure and by the mass loss a t the higher efficiencies. The hold-up ratios for the two orifice sizes are seen to be similar, indicating the similarity of the bubble populations produced. Figure 4 is a plot of overall oxygen transfer efficiencies us. column height for all air rates employed for the %in. and ys-in. orifices a t liquid depths ranging from 14 to 53 ft. The overall efficiency for transfer to sulfite solutions in the 55-ft column is observed to be a t least 1%per foot of liquid depth and does not become less than this until a depth of 60 ft. The high oxygen transfer efficiencies observed for the tall 3-in. column result from high driving
O P E N POINTS
- 1/4-#n
CLOSED P O I N T S -
FOR
LINES
ORIFICE
114-in
ORIFICE
118-h O R I F I C E
LINE F O R
2 5
30
-I
FOR 5 3 F T
/#LINE
i i
:-
a w
0 > IO
O
2
3
INPUT
RATE
I
AIR
4
5
6
.-
0
14 F E E T
A
27
0
40
’’
53
’,
”
4
-
- SDCFI HR
Figure 3. Hold-up for various liquid depths and orifices (transfer to sulfite solution).
0
1
2
AIR
INPUT
3
4
5
6
RATE - SOCF/HR
Figure 5. Transfer factors for a range of air input rates I
,=
$ 0 1
%
8 X
0
O 0L-0
-
Y
I
I
I
I
I
,’’L IO
20
LIOUID
30
40
DEPTH,
50
60
70
FEET
Figure 4. Range of oxygen transfer efficiencies.
forces a t elevated pressures from the hydrostatic head, increased residence times of the bubbles from the height of rise, and large interfacial areas from small bubble sizes. The time of contact increases linearly with liquid depth, and uniformly distributed bubble populations minimize the “chimney effect.” The latter refers to high air input from a single row of spargers or tubes, positioned adjacent to the side of a tank, which creates a pumping effect from effective density differences. The chimney effect increases the rate of rise of the bubble masses and reduces transfer time. Von der Emde (1968) indicates that the use of a set of diffusers along the side of a tank gives liquid circulation rates above 2 ft/sec (0.6 m/sec) a t the tank perimeter but as low as 0.7 ft/sec (0.2 m/sec) in the central region. The average bubble rise rate observed in the tall column was about 1ft/sec (0.3 m/sec). Oxygen Transfer Factors For the steady-state sulfite observations, overall ( K L u ) values were calculated for each orifice for each of the four liquid levels using eq 8. Factors for the range of air flow rates employed are given in Figure 5 for the yd-in. orifice; results for the l/s-in. orifice were the same for the 53-ft liquid depth where (K1.a) increases nearly linearly with air rate. At the lowest two levels, values for the smaller orifice were less than for the 14-in. orifice. Considering (KL) as independent of air flow rate and column height, the increase in (K1.u) results from the increased interfacial transfer area ( a ) . As the air input rate increases, the
0
IO
20
LIQUID
30
40
50
DEPTH, FEET
Figure 6. Variation of the transfer factors with liquid depth.
transfer area increases because of the proportionally larger bubble population, and for the deepest liquid is linear over the range observed. Bubble break-up influences the lowest liquid level most as shown by the upward curvature of the line for the 14-ft depth. A cross-plot of Figure 5 is given in Figure 6 for the 1i4-in. orifice which serves to show the variation of ( K L u ) with liquid depth. For a given constant air input rate (standard dry cubic feet per hour) the overall transfer factors are linear with column height. This implies some constancy of bubble inlet and formation characteristics, and once formed, indicates a small variation of transfer characteristics over a column of given depth. The increased pressures from greater hydrostatic heads reduce the ( K L u ) values but the further implication is that bubble populations remain nearly constant with little coalescence during rise. This is particularly true of the taller columns where inlet conditions and initial bubble formation have less effect on performance. Table I gives mean values of the transfer rate, driving ) a total liquid depth of 53 ft. The force, and ( K L ~for Ind. Eng. Chem., Process Des. Dev., Vol. 14, No. 2, 1975
109
Table I. Unsteadv-State Local Mass Transfer Coefficientsa
o2transfer rate (c*- C) Column position, ft 48 43 38 33 28 23 18 13 8 3 0 (bottom)
(lb-mollhr-
(lb-mol,/ft3
f t 3 x 105)
x 105)
A
B
A
B
10.9 13.4 17.0 21.4 25.0 27.7 29.6 30.4 29.6 27.5
7.0 8.1 9.5 10.5 11.7 12.5 14.8 16.0 16.4 16.8
0.72 0.87 1.08 1.25 1.48 1.74 2.00 2.20 2.69 3.21
0.56 0.66 0.78 0.85 0.97 1.02 1.16 1.39 1.71 2.20
is that resulting from formation a t the orifice. The results reported herein, for very tall columns, indicate that while the effect may be true for the short columns in which K, n many bubble studies have been made, it is not correct for (1 ’ h r ) the present work. Rather, the opposite results; the initial ~-~ section of the column is less effective, in proportion to the A B driving force, than are the levels where bubble popula15.2 12.5 tions have become stabilized.
15.4 12.4 15.7 12.2 17.1 12.4 16.8 12.1 15.9 12.2 12.8 14.8 13.8 11.5 11.0 9.4 _8.6_ _ 7.6 _ 14.4 11.5 Average 13.0 a Liquid depth = 53 ft, A = 0-3 min; B = 3-6 min; air input rate = 2.6 sdcf/hr.
transfer rates for the “A” period are much higher than that for “B” because the driving force (C* - C) is greater. The rates a t the bottom of the column are 2.5 times those a t the top, and the driving forces are 5 to 6 times greater a t the bottom. ( K L u ) is smaller near the bottom of the column where the large bubbles are breaking up and the interfacial area is smaller. The average ( K L u )values are larger for the period “A” compared to those for the second period, resulting, in part a t least, from the lack of a correction for nitrogen absorption. Also, changes occur more rapidly during the initial period compared to the second time interval. The average value of (KLu) for the periods for unsteady-state transfer was 13 and the value for sulfite absorption was 14 hr-1. The two values compare well considering the different methods of determination and evaluation. Assuming the difference to be significant, the higher values for the sulfite as compared to water could be attributed to a chemical reaction in the layer of liquid adjacent to the interface. The effect of nitrogen absorption also results in calculated unsteady-state ( K L u ) values higher than actual. The most interesting result from the unsteady-state determinations is the near uniformity of the ( K L u ) values with column position. Those for the “B” determination are especially constant except for the section near the bottom where the interfacial area is obviously increasing. The procedure of calculating an overall ( K L u )value based on the air concentration change in the model described by eq 8, which assumes ( K L u )as an average for the column with minimum variation, is thus justified. Jackson and Collins (1964) compared transfer in a 4-in. venturi aerator to both sulfite solution and to water after depletion of the sulfite and found the transfer characteristics to be very similar. Venturi aeration represents a situation of high turbulence between the bubble and liquid phases and is a contrasting example to bubble column aeration for the transfer of oxygen to sulfite solution as compared to water. Nevertheless, transfer processes in either case indicate that the chemical reaction between oxygen and sulfite is sufficiently slow that little reaction occurs in the interfacial layer. It has been reported by several investigators that transfer processes occurring upon initial bubble formation, I e . , a t the orifice, may result in oxygen transfer rates which are substantially higher than those occurring later. The inference is that a substantial fraction of the total transfer 110
Ind. Eng. Chem. Process Des. Dev., Vol. 14, No. 2, 1975
Implications for Wide, Tall T a n k Design Although the energy required for air compression increases with column height, it is less than linear with pressure. For a given air input rate the power requirement does not increase linearly with increasing water depth because the gas volume decreases with compression. This is illustrated in Table I1 by a comparison of compression requirements as a ratio to a reference pressure of 5.9 psig (0.41 bar) which corresponds to the usual shallow basin depths of 13.5 f t (4 m ) . The energy needed for adiabatic compression was calculated from Perry, et al. (1963). In doubling the liquid depth of the usual aeration basin the compression energy to overcome a liquid head of 27 ft (8 m) increases only 1.8 times. Increasing the relative depth to four requires only three times the energy. and for a relative depth of eight only five times. A measure of equipment performance, in addition to that of oxygen transfer efficiency, is the amount of oxygen transferred per unit of energy input. Nogaj (1972) estimated the energy “efficiencies” for a commercial air diffuser installation to be 1.23 lb of Oz/hp-hr (0.75 kg of Oz/kwh) for 4% oxygen transfer efficiency. The value included line and compressor losses for the usual shallow aeration basin. Also, Weber (1972) gives a value of 1.8 lb of O Z / hp-hr for compressed-air type aeration systems with oxygen transfer efficiencies “as high as 1270,”but that “more frequently” values of 0.5-0.8 lb of Oz/hp-hr are obtained. It is further indicated that for basins of 15-ft depth an air rate of about 3 cfm per lineal foot of basin is necessary to provide a surface roll velocity of 1.5 ft/sec and prevent sludge deposition. Bayley (1963) found, for conventional fine-bubble diffused air systems, that the oxygen transfer per unit energy input to deoxygenated water showed a maximum value when the depth of the water was approximately 3 ft. The compression efficiency dropped for liquid depths above 4 ft and leveled off a t about 15 f t . Because Bayley used fine-bubble diffusers the oxygen transfer at initial depths was relatively more significant compared to the total. Aeration efficiencies varied from 3.3 to 5.7 lb of OZ/hp-hr (2 to 3.5 kg of Oz/kwh) for air input requirements only. For a 53-ft liquid depth and 55% oxygen transfer efficiency in the 3-in. column, the energy efficiency for compression only is 14.3 lb of Oz/hp-hr (8.7 kg of Oz/kwh). This gain over that for a shallow basin would be reduced by liquid pumping requirements which increase with tank height. An optimized plant design for 4 million gal/day of sulfite liquor indicates that energy and cost savings can be substantial (Edwards, et al., 1974). Jackson. et al (1974), confirm and extend present results in a ’ij-ft, narrow column for a larger range of air rates. Tall tanks for waste water treatment require large diameters in order to process the high flow volumes inherent in such applications. The scale-up of the data obtained from a small, 3-in. diameter column for large tank design represents an extreme situation, but some indications are possible. It is stated that wall effects increase hold-up for columns up t o 3 in. in diameter (Hughmark, 1965; Sideman, et d . , 1966). The hold-up is related to the interfacial
14
Table 11. Energy Requirements for Compression Pressure, lb/in.2 abs.
Pressure, lb/in.2 gauge
Liquid depth, ft
13.5 19.4 25.2 30.9 36.6 50.1 60.8
0 5.9 11.7 17.4 23.1 35.4 47.3
0 13.5 27 .O 40.0 53 .o 8 1 .O 108 .O
Ratio Ratio of of energy liquid head required 0 1.o 2 .o 3 .O 3.9 6 .O 8 .O
1
1
,
1
I
l
l
1
I
ONE 114-in N O Z Z L E IN THE 3” X 55’ COLUMN
0
1.o 1.8 2.4 3 .O 4.1 4.9
N a n d K DATA
area per volume of tank through bubble number, size, and 0 rise velocity, and (K1.a) should be less a function of diam0 0 5 10 eter above 3 in. The data reported for the 3-in. column inAIR RATE / TANK VOLUMES C F H / FT3 dicates that the bubbles acted essentially independently, Figure 7. Comparison of transfer factors for a narrow and a wide which was confirmed by cine camera (few bubble interaccolumn. tions) and from the constancy of ( K L Q )over the column except for end effects. Tank design can be undertaken with some assurance, a t least, that multiple air inlets in a wide diameter tank would give a performance approxibe reduced substantially for use of the correct interfacial mating that for the 3-in. column for each inlet. liquid concentration. Japan is interested in deep tanks for waste treatment The (KLu) values reported do permit an assessment of because of the shortage of land space for treatment purlarge tank design by a comparison with transfer factors for poses. The data from the 3-in. column can be compared to the narrow column. Figure 7 gives the data for the square work of Nagashio and Kurosawa (1969), who report ( K L Q ) tank as reported by Nagashio and Kurosawa. One intervalues for two sizes of deep, wide tanks: 4.2-ft diameter X esting result is that the method of introducing the air 85 f t liquid depth, and 11.5 f t 2 X 60 ft effective liquid through orifices results in only a small change in (KLQ), depth. Although the method of analysis employed raises and use of a single nozzle is better than several of the questions as to the accuracy of‘ the results reported, the same size for the same total air input rate. Approximating main purpose of the paper was to demonstrate perfora more correct result for the single 3b-in. nozzle in the mance and effect of deep tanks on microorganisms in the large tank by doubling the reported (KLQ)values, to acactivated sludge process. count for air depletion in the bubbles a t the midpoint and Determinations were made by following the change of for the much lower equilibrium interfacial saturation conoxygen concentration in water, which was deoxygenated centration, the line is near to that for the 3-in. column. by sulfite, with a dissolved oxygen probe. The distribution This “agreement” can be considered as only approximate of dissolved oxygen over the tower was stated to be linear but does indicate that the results of the narrow column and the value a t the mid-point of the tank was considered provide a measure of behavior for nozzles in large tanks. equivalent to the average over the tank. (KLQ)values were Further, the general trends of performance, oxygen transdetermined by taking readings of the probe, located a t the fer efficiencies, transfer factors, and hold-up values midpoint, with time, and using an integrated form of eq 9 should, to a degree, be useable for the design of large diameter tanks. Nagashio and Kurosawa also provide data for the performance of the square tank operating as an activated sludge unit, for the treatment of alcohol distillation waste. As employed, this procedure gives the value of the transThe BOD reduction varied from 80 to 9670, mixed liquor fer factor a t a point which is assumed to be the average suspended solids from 3200 to 6600 ppm, and the sludge for the entire tank. volume index from 107 to 243. For operation of the tall, The values for (KLa) reported by Nagashio and Kurosaround tank on “amino acid sewage” the BOD reduction wa involve incorrect values for C*. The tank was operated was from 80 to 98%, the MLSS values varied from 3000 to with air until the composition of the liquid a t the mid3900 ppm, and the SVI values were 77-100. Operations point reached a constant value which was taken as the were reported as having “no weak points for waste treatvalue for C*. In the 60-ft tank this was observed to be 30 ment or the multiplication of microorganisms.” Residence ppm compared to a calculated value of 17 ppm which cortimes were not given. responds ‘to a bubble of 21% oxygen content under a 30-ft Concerning oxygen transfer efficiency in the larger tank, liquid head and a 1 atm barometer. The limiting value Nagashio and Kurosawa indicate that the value for a 60 ft was observed to vary with the rate of air input. The atliquid depth is 4.2 times that a t 16 ft. This conclusion tainment of a liquid composition above the equilibrium confirms that for the 3-in. column where the transfer effivalue apparently results from circulation and upwelling of ciency approximates 1% per foot of height. The limiting liquid from the lower levels induced by the rising bubbles. height to which this “rule of thumb” can be applied was The correct value of C* is fixed by gas composition and not established by the range of data obtained in the narpressure only, and not by a liquid composition resulting row column. from a dynamic limiting situation where no oxygen is The implications for improved biological treatment and transferring. The true value of C* would be something less control are several. Downing (1968) and Downing, e t al. than 17 ppm for the situation cited because of oxygen dep1.etion. Thus, the correct values for (KLQ)are higher than (1962), indicate that present activated sludge plant designs give little consideration to oxygen demand and that those reported because the ratios of (C* - C) in eq 9 will Ind. Eng. Chem., Process Des. Dev., Vol. 14, No. 2. 1975
111
the constant aeration rates commonly employed are highly inefficient. Matching feed with oxygen supply and demand should be a primary design consideration resulting in improved capacity for treatment. Tapleshay (1956) states that of the air input to a horizontal basin more may be required to induce liquid circulation and prevent sludge settling than to provide the oxygen for biological metabolism. The use of vertical tanks with uniform air bubble distributors would permit convenient use of step feeding to match oxygen supply with no extra air required to effect sludge suspension. The effect of higher oxygen partial pressures on the biological reaction rate for individual cells is usually considered to be negligible above an oxygen concentration in the liquid of 0.5 to 1.5 ppm. However, Wells, et al. (1937), reported the "remarkable effect of increased air pressure" on gluconic acid fermentation; for the same reaction time, operation at 45 psig gave a yield of 85% as against 32% at 5 psig. The flocs of the sludge mass may .contain anoxic cores which are not penetrated by the diffusion of molecular oxygen because of depletion by the other layers. Increasing the oxygen partial pressure would increase the diffusion rate markedly and could make the cell mass more reactive as a whole, again increasing the capacity. Oldshue (1970) discusses favorably the case for deep aeration tanks on a relative performance basis for impeller-sparger systems, and indicates that only economic considerations dictate liquid depth and usage.
for the large change in gas phase compositions over the column and the increasing liquid compositions for the water runs, these values are considered quite comparable. They indicate that the sulfite reaction is relativelv slow and occurs mostly in the bulk phase rather than in the diffusion film, and that transfer factors for sulfite solutions should be comparable to those for water. As is well established, the presence of surfactants and other dissolved materials in waste water may reduce ( K L ~values. ) The results of the study have implications for the design of tall tanks for waste water treatment and for possible savings in operating costs and capital investment. Reduced land requirements are also possible where this may be necessary. No appreciable reduction in the oxygen transfer efficiency was observed up to the 55-ft level and useable heights appear to be in excess of this level. Comparison of (&a) data for larger diameter tanks with the performance of the 3-in. column indicates the latter to provide useful performance characteristics. Possible advantages for biological control are design for local oxygen demand, increased capacity from a more reactive sludge mass, and ready suspension of the sludge mass. Acknowledgment Financial assistance from the University of Idaho research resource program, Graduate School, for capital equipment is gratefully acknowledged. A preliminary version of this paper was presented at the 74th national A.1.Ch.E. meeting, New Orleans, La., March 1973.
Summary and Conclusions Oxygen transfer efficiencies and transfer factors are presented for a very tall bubble column. Transfer efficiencies were observed to be roughly 1% per foot of height for liquid depths of 13 to 53 feet (4 to 17 m). For example, 55% of the oxygen entering in the air was transferred for 53 f t of liquid and a moderate air rate. Energy requirements for compression become relatively less for the higher compression ratios because of the progressively smaller air volumes required for increasing liquid depths, and a reduction by a factor of 4 for 53 f t is indicated. Only small differences were observed in the performance of single orifices of y8- and y,-in. diameters (0.32 and 0.64 cm) with the larger size being favored. This performance of tall columns results from independent bubble movement, from slower rise velocities and longer rise distances, and from elevated oxygen partial pressures as compared to shallow basins. Observations made in the 3-in. (7.6-cm) diameter column confirm literature reports that the liquid side transfer coefficient is relatively independent of bubble size and aeration rate. The controlling characteristic for transfer rate is the interfacial area and this was determined in combination with the transfer coefficient as the transfer factor (K1.a). Steady-state oxygen transfer (to catalyzed sulfite solutions) and unsteady-state oxygen transfer (to water) were observed. Compensating effects of pressure changes on the saturation oxygen content at the liquid interface and of interfacial area from bubble break-up and expansion minimize the variation of transfer rates with column height for a given air input rate. Unsteady-state ( K I , ~values ) were lowest at the air inlet but attained relatively constant values within 10 ft. The behavior observed permitted use of averages based on terminal gas compositions for the calculation of (K1,a) for transfer to sulfite solution; a model for steady-state transfer is presented. Average (K1,a) values at an air rate of 2.6 sdcf/hr were 14 hr-I for the sulfite solutions, and 13 hr-1 for water for the 53-ft depth. Because of approximations 112
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Nomenclature A = interfacial transfer area, f t 2 a = specific interfacial area, = A / V , ft2/ft3 C = oxygen concentration in the bulk liquid phase, lbmol/ft3 C* = oxygen concentration in the liquid phase at the interface a t saturation, lb-mol/fts h , h = total column height in feet for no air flow, and when expanded from air flow H = Henry's law constant, f t of water/mole fraction KL = overall mass transfer coefficient based on the liquid, ft/hr k L = liquid film coefficient ma m = lb-mol of air/hr-ftz entering the tank and at height z P, Pa = absolute pressure, lbf/in.2, and barometric pressure S = column cross section, f t 2 t = time, hr, at an initial time, 1, and a later time, 2 V = liquid volume, ft3 u b = ascending bubble velocity, ft/sec Us = superficial gas velocity, ft/sec y , yo = entering mole fraction of oxygen in gas phase and a t height z z = distance up the column, f t
,
Literature Cited Bartholomew, W. H.. Karow, E. O., Sfat, M. R . , Wilhelm, R. F1.. Ind Eng. Chem., 42, 1801 (1950). Bayley, R . W., J. Proc. Inst. Sewage Purification, Part 2, 174 (1563) Calderbank, P. H.. Chem. Eng. (London). CE 209 (Oct 19ti7). Also, Chapter 5 , in N. Blakebrough, Ed., "Biochemical and Biological Engineering Science," p 101, Academic Press, New York. N. Y.. and London, 1967. Cooper, C. M.. Fernstrom. G. A,, Miller, S A , . Ind. Eng. Chern.. 36, 6 (1944). Downing, A. L., in E. F. Gloyna and W. W. Eckenfelder. "Advances in Water Quality Improvement," p 190, University of Texas Press, 1968 Downing, A. L.. Boon, A. G.. Bayley, R. W.. J. Proc. Inst. Sewage Purification, 66 (1962). Dreier. D . E., in J. McCabe and W W. Eckenfelder, "Advances in Biological Waste Treatment," p 215. Reinhold, New York, N . Y., 1956. Edwards, L. L.. Leber, B. P., Jackson, M. L.,"An Economic Evaluation of Deep Tank Aeration for Waste Treatment," preprinted for the Jolnt International AIChE-VTG meeting, Munich, Sept 1974.
Fuller, E. C., Crist, R. H., J. Amer. Chem. SOC.,63,1644 (1941). Hughmark, G. A., Ind. Eng. Chem., Process Des. Develop., 6, 218 (1967). Jackson, M. L., James D. R., Leber, B. P., "Oxygen Transfer in a 23Meter Bubble Column," preprinted for the Joint International AIChEVTG meeting, Munich, Sept 1974. Jackson, M. L.. Collins, W. D.. lnd. Enq. Chem., Process Des. Develop., 3,386 (1964). Landberg. G. G.. Graulich, B. P.. Kipple. W. H.. Water Res., 3, 445 (1969) Leber, B. P., Jr.. M. S. Thesis. Chemical Engineering, University of Idaho. Moscow. Idaho. 1974. Nagashio, I . J., Kurosawa, K., Chem. Techno/., 33,927 (1969) (in Japanese). Nogaj, R. J., Chem. Eng. (N.Y . ) , 95 (Apr 17, 1972). Oldshue, J. Y . . Chem. Eng. Progr. 66,73 (Nov 1970). Perry, R. H., Chilton. C. H., Kirkpatrick, S. D., "Perry's Chemical Engineers' Handbook." 4th ed, pp. 6-16, McGraw-Hill, New York, N. Y.. 1963. Sideman, S., Hortacsu, O., Fulton, J. W., lnd. Eng. Chem., 58, 32 (1966)
Tapleshay. J. A., in J. McCabe, W. W. Eckenfelder. Jr., ed., "Advances in Biological Waste Treatment," p 225, Reinhold, New York, N. Y., 1956. Urza. I. J.. M . S. Chem. Engr. Thesis, University of Idaho, Moscow, Idaho, 1972. Von der Emde, W., "Advances in Water Quality Improvement." E. F. Gloyna and W. W. Eckenfelder. Ed., p 237, University of Texas Press, Austin, Texas, 1968. Weber, W. J.. Jr., "Physicochemical Processes for Water Ouality Control," p 518, Wiley-lnterscience, New York, N. y . . 1972. Wells, P. A., Moyer, A. J., Stubbs. J. J.. Herrick. H. T.. May, 0. E . , Ind. Eng. Chem., 29, 653 (1937). Westerterp, K. R., Van Dierendock, L. L., de Kraa, J. A , Chem Eng. Sci., 18, 157 (1963). Yoshida, F.,Akita. K..A.l.Ch.E. J., 11,9 (1965).
Received for reuieu: November 9, 1973 Accepted October 16,1974
Simulation of the Comminution of a Heterogeneous Mixture of Brittle and Nonbrittle Materials in a Swing Hammermill D. M. Obeng' and G. J. Trezek* Department of Mechanical Engineering, University of California, Berkeley, California 94720
Four matrix models were used to study and mathematically simulate the comminution process in the swing hammermill. The feed material was domestic packer truck refuse, a mixture of approximately 25% brittle and 75% nonbrittle constituents. The validity of the analytical models was substantiated through comparison with experimental data generated in a 10 ton/hr swing hammermill size reduction facility operating under controlled conditions. The *-Breakage Model and the Repeated Breakage Cycle model are both suitable for predicting the product size distributions for primary, secondary, and tertiary grinding processes. However, the x-Breakage Model is in closer agreement for the three grinding conditions
Introduction Packer truck refuse is a material of unique properties and characteristics. In general, this material is a heterogeneous mixture of approximately 75% nonbrittle materials: newsprint, mixed paper waste, cardboard, plastics, organic constituents, etc., and 25% brittle materials: ferrous metals, aluminum, glass, etc. Contingent upon proper constituent recovery, refuse can be a valuable resource in terms of its material and energy content. Modern solid waste management technology, predicated on the premise of resource and energy recovery as a means of dealing with critical disposal problems, nearly always requires some size reduction of the incoming refuse stream as an initial step in processing. This holds whether the process ranges from the simple magnetic removal of the ferrous materials, to advanced processes dealing with the recovery of the predominant cellulose fibre constituents, or to other complex processes dealing with sophisticated combustion or pyrolysis. In some instances, the latter process may require several comminution stages. Control of the size distribution of the ground product is critical to the proper performance of the subsequent stages of processing which are often carried out with standard equipment items. Thus, the present work is motivated by '
African Graduate Fellow (AFGRAD)
the need for developing an understanding of heterogeneous material comminution and for developing an analytical technique capable of predicting the size distribution of the product for a specified size distribution of the feed, i.e., the heterogeneous refuse mixture being comminuted in a swing hammermill. A semiempirical analysis of the breakage process was conducted as a means of achieving the above objectives. The influence of two Comminution parameters, the feed rate and moisture content. as well as the effects of secondary and tertiary grinding on the product size distribution are reflected in the experimental data base. Because of the nature of refuse, an extrapolation of brittle material comminution results to refuse has not been feasible (Patrick, 1967). Further, the product size distribution for brittle materials can usually be described by various relations such as the Gaudin-Schuhmann (Gaudin, 1926; Schuhmann, 1940) or the Rosin-Rammler (1933) equations. In addition, Gaudin and Meloy (1962) give a theoretical size-distribution equation for single fracture, and other size distribution equations (Bergstroni. 1966; Harris, 1968, 1969, 1970) have been proposed with additional parameters, ostensibly for greater curve-fitting flexibility, as further generalizations of the above relations. Due to the fact that refuse is a heterogeneous material it is unlikely that a single breakage law can describe I n d . Eng. C h e m . , P r o c e s s D e s . Dev., Vol. 14, No. 2 , 1 9 7 5
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