literature Cited
Gier, R. G., “Application of the Pulse Column to the Purex Process,” Symposium on the Reprocessing of Irradiated Fuels, Brussels, Belgium, May 1957 (TID-7534, Book I). Hamming, R. W.,“Numerical Methods for Scientists and Engineers,’’ McGraw-Hill, New York, 1962. Perry, John H., “Chemical Engineer’s Handbook,” 3rd ed., p. 383, McGraw-Hill, New York, 1950.
Sege, G., LYoodfield, F. W., Chem. Eng. Progr. 50, No. 8, 396-402 (1954). Weech, M. E., P’Pool, R. S., McQueen, D. K., “Interim Report on the Development of an Air Pulstr for Pulse Column Application,” IDO-14559 (Sept. 22, 1961) ( U S . Dept. of Commerce, Office of Technical Services, Springfield, Va.). RECEIVED for review October 31, 1966 ACCEPTED March 27, 1967
COCURRENT GAS-LIQUID CONTACTING IN PACKED C O L U M N S L. P H I L I P REISS1 Shell Development Go., Emeryville, Calif.
New experimental data obtained for a variety of packing materials in small-scale and semicommercialscale equipment for cocurrent gas-liquid contacting in packed columns are presented, including pressure loss, liquid holdup, radial liquid distribution, ammonia absorption, and oxygen desorption mass-transfer coefficients. Existing correlations for single-phase and two-phase pressure loss and liquid holdup adequately describe the experimental data. New correlations for mass transfer capacity coefficient are based on the concept of energy dissipation per unit volume. Cocurrent gas-liquid contacting is advantageous over countercurrent contacting when only one equilibrium contacting stage is required: physical absorption a t large liquid-to-gas ratios, physical desorption a t low liquid-to-gas ratios, and transfer with a consuming chemical reaction in one phase.
HE vast majority of the commercial packed columns for Tgas-liquid contacting is operated countercurrently. The liquid phase falls downward because of gravity, while the gas phase moves upward through the column because of a n imposed pressure gradient. The gas throughput in this type of operation is limited. Above a critical gas velocity the gravity forces on the downfloiving liquid are exceeded by the drag forces imposed on the liquid by the upflowing gas. This unstable condition is known as flooding and is the characteristic of all countercurrent gas-liquid contacting operations. One means of overcoming this throughput limitation of countercurrent operation is to operate the packed column cocurrently. Both the gas and liquid are introduced a t the top of the column and flow cocurrently doivnward through the column because of a combination of gravity and applied pressure gradient. There is no flooding limit for this type of operation and the throughput of gas and liquid, up to choked flow, depends only on the available pressure to drive the fluids through the column. Cocurrent operation appears advantageous from the fluid mechanics standpoint, in that flooding can be eliminated. However, from a mass-transfer standpoint, cocurrent operation has a definite limitation relative to countercurrent operation. The over-all concentration driving force and the number of equilibrium stages in countercurrent operation are greater than in cocurrent operation. I n fact, cocurrent operation results in only one equilibrium stage. There are, however, a number of gas-liquid contacting
Present address, Research and Development Laboratory, Shell Pipe Line Corp., Houston, Tex. 486
l&EC PROCESS D E S I G N A N D DEVELOPMENT
operations where only one equilibrium stage is required. For example, as pointed out by Wen et al. (1963a), if the transferring component is transferred from one fluid phase and is consumed by chemical reaction in the other phase, only one equilibrium stag? is required. For a conventional absorption a t large liquid-to-gas ratios, the concentration of the transferring component in the liquid phase is low, because of the excess of liquid. Because this shifts the equilibrium, only one equilibrium stage may be required to reduce the concentration of the transferring component in the gas phase to the desired level. The same applies in reverse for stripping operations a t low liquid-to-gas ratios. With an excess of gas, the gas-phase concentration of the transferring component may be so low that the equilibrium is shifted. Hence, a stripping operation could conceivably also be carried out in one equilibrium stage. Operation a t high liquid-to-gas or low liquid-to-gas ratios in the cocurrent mode does not present the flooding problem that these extreme liquid-to-gas ratios might present in countercurrent operation. Therefore, cocurrent gas-liquid contacting is generally applicable for operations involving only one equilibrium stage. These include absorption with chemical reaction in one phase-Le., gas-liquid chemical reactors, absorption a t high liquid-to-gas ratios, and desorption or stripping a t low liquid-to-gas ratios. Cocurrent operation is not limited by flooding. Hence, greater throughputs of gas and liquid can be achieved than in conventional countercurrent packed columns of similar size, or smaller equipment may be able to do the same job. There is a large body of literature devoted to the design and operation of countercurrent packed columns. By contrast,
only comparatively few references have appeared o n cocurrent contacting. Table I summarizes the experimental data available i n the literature which are applicable to the design of cocurrent gas-liquid packed column contactors. T h e gas and liquid rates range from those characteristic of “trickle phase” operation (V, x 0.5 foot per second, Vi x 0.01 foot per second) to higher rates which are more representative of absorption operation ( V g = 5 feet per second, V i= 0.1 foot per second). T h e more significant papers o n cocurrent contacting are by Larkins (1959, 1961), McIlvroid (1956), and Wen (1963, a, b). Larkins measured pressure drop and liquid holdup for cocurrent flow through beds of dumped packing and correlated these data using a n approach similar to that of Lockhart and Martinelli (1 949). These represent the only design correlations for two-phase pressure drop and holdup i n cocurrent flow i n packed beds. Pressure drop data obtained by Weekman and Myers (1964) were also correlated using the Larkins approach, and additional pressure loss data are presented by Dodds et al. (1960b). McIlvroid (1956) presents pressure drop and liquid phase controlling mass-transfer data for cocurrent contacting in beds of small dumped packing. Wen (1963) measured pressure loss and mass-transfer rates using the ab5orption of water vapor from air into calcium chloride solutions. Wen’s (1963) and McIIvroid’s (1956) papers represent the only data on mass transfer i n cocurrent flow which can be used for design purposes. Additional design information, relative to cocurrent contacting, is the radial distribution of liquid within the packing and the pressure loss for single-phase flow through packing. Very limited data on radial distribution of liquid have been reported (Hoftyzer, 1964; Porter and Jones, 1963 ; Weekman
and Myers, 1964), and i n only two cases (Hoftyzer, 1964; Weekman and Myers, 1964) the flow was actually cocurrent. Extensive pressure loss data are available for single-phase flow through random and stacked packing. A successful means of correlating these data has been suggested by Ergun (1952). There are many areas where design data are insufficient or completely lacking (Table I), particularly i n cocurrent contacting mass transfer, and no consistent design procedure has been established for cocurrent gas-liquid contacting in packed columns. This is somewhat surprising i n view of the potential attractiveness of this mode of packed column operation. This work presents new experimental data on single-phase and twophase pressure loss, liquid holdup, liquid radial distribution, and gas-phase and liquid-phase resistance controlling mass transfer for cocurrent gas-liquid contacting i n packed columns and correlates these data empirically into design equations to give a consistent design procedure. The accuracy of this procedure is adequate for preliminary design leading to initial cost estimates. Experimental Equipment
Columns. Design data for cocurrent gas-liquid contacting were obtained on two packed column scales. T h e smallscale equipment consisted of two columns, 3 and 4 inches in i.d., and the large-scale column was 16 inches in i.d. T h e schematic flow diagram for columns on both scales is shown in Figure 1. Figure 2 is a photograph of the 16-inch column. Air and water are introduced into the top of the column through a n inlet distributor, which was designed to give good initial distribution of gas and liquid over the packing. T h e gas and liquid flowed cocurrently downward and were separated in a sump tank. The air was vented to the atmosphere. The water could be operated as only a once-through flow, a
Experimental Data Available in the Literature for Cocurrent Gas-liquid Downflow in Packed Beds Experimental Data Reported V , Range, Ft./Sec. V , Range, Ft./Sec. AP -.kla Ref. h Liquid k l7a Packing 7 y p e dik. Min . Max. AZ 3in. Max. Table 1.
Dumped Raschig rings, inches
‘14 ’/4
”8 ’I2 ‘/2
1 1
1.8 0.35 0.50 0
0.35 0.35 0 1.8
18
3.5 26 0
3.5 3.5 2.6 12
Dumped Pall rings 1
0.25 0.051 0.87 0.0033 0.051 0,051 0.030 0.13
0
0
0,0033
0.0033
0
0
0.0033
0.0033 0.051 0.13 0.13
Berl saddles, inches ‘12
0.092 0.015 0.020 0.0033 0.015 0.015 0.0033 0.019
0.70 1.8 1.8
4.5 12 12
0.70 0.70
4.5 4.5 12 12
0,0074 0.0074
0.17
1.3 18 18 4.1
0.0027 0.031 0.031 0.0055
4.75
0.17
4.1
6.48
0.17
4.1
3 1 8 inch Pellets inch
0.50
‘/z
1 1
Intalox saddles, inches ‘12
1 1
1‘/2
Dumped spheres, mm. 3
1.8
1.8 0.089
1.8 1.8
26
0.0074
0.019 0.019
0.051 0.051 0.13 0.13
X
X X
X X
X X
X
X
X
a
X
Y
X
Porter and Jones (1963)
X
Porter and Jones (1963) TVen et al. (1963b) Dodds et al. (1960a, b ) Dodds et al. (1960a, b )
X X
TVen et al. (1963b) \Yen rt al. 11963b) Dodds et al. (1960a, b ) Dodds et al. (1960a, b )
X X X X
X X
0.081
X
X
0.42 0.42 0.11
X
x
X
x
X
0.0055
0.11
X
0.0055
0.11
X
0.020
0.87
X
0.019
0.019
McIlvroid 11956) iVen et al. (1963a, b ) Larkins (1959, 1961) Porter and Jones (1963) Tl‘en et al. (1963a, b ) TVen et al. (1963a, b ) Hoftyzer (1964) Dodds et al. (1960a, b )
X
X
26 0.50 0.020 0.87 X Statistical analyses of variables afecting GO? absorption into ‘VaaOH solutions; no design data cocurrentj7ow available f r o m Weekman and Myprs (1965). a
x
X X
a
X
Larkins (1959, 1961) McIlvroid (1956) McIlvroid (1956) Tl’eekman and Myers (1964, 1965) LVeekman and Myers (1964, 1965) Tt’eekman and Myers 11964, 1965) Larkins (1959, 1961) Larkins 11959, 1961)
X
Data f o r heat transfer through column wall to gas-liquid
VOL. 6
NO.
4
OCTOBER 1967
487
completely recycling flow, or a combination of each, where a fraction of the recycling water flow was continuously replaced by fresh make-up water. Provisions were made far mixing ammonia with the incoming air Stream and for saturating the recycling water stream with oxygen. Temperature control was provided by cooling coils located in the sump, Pressure loss was measured across various segments of the packed bed by pressure taps located a t different points around the column circumference a t each elevation. Gas-phase and liquid-phase samplers were located a t various axial and radial positions within the packed bed.
I;; -
. r
Packed
Taps
mop
.
vgnt
i
U
I
Sump Tank
Cooling water
I
Drain
Figure column
'
'
Genera'
"Ow
diagram
I n the small columns quick-dosing valves were arranged so that holdup of liquid could be measured. The technique for holdup measurement was similar to that ofLarkins (1959). Packing. T h e packing used in this study was predominantly thin-walled polyethylene R a x h i g rings ranging from '/z to 3 inches. The packed beds were made by both stacking and dumping the rings. One series of experiments utilized a bed of dumped 1-inch Intalox saddles. The packing data are summarized in Table 11. The beds of stacked 1- and 3-incb rings were ~iiaocuy sracking the polyethylene rings on triangular centers. A layer of packing was offset from the layer below, so that every third layer was identically oriented. The rings were held together in an array by fusing their points of contact with 'a warm soldering iron. After the array was properly oriented and assembled, it was cut to fit the inside diameter of the 4- or 16-inch column. As a result, there were fractional segments of rings next to the column wall, and in effect, these packed beds were merely a core from a larger bed. A core of 1-inch rings from the 4-inch column is shown in Figure 3. Figure 4 shows the stacked array of '/$-inch rings in a section of the 3inch column. For this case only, whole rings were stacked in randomly offset layers. The resulting radial distribution of voidage was not uniform. Radial Liquid Distribution. The 16-inch column was equipped to measure the radial liquid distribution. A liquid collector was assembled with individual compartments as -. . was ,mcatea . ~oirecriy 1. , ., O ~1~ O W mown m Figure 3. i n e couecmr the packing, so that each compartment received the liquid falling from the packing immediately above it. T h e outlet from each compartment was connected to a two-way, 13-port valve. T h e gas-liquid flaw through each compartment could flow directly to the sump tank or be diverted for a short interval to 13 individual collecting drums (see Figure 2). The liquid flow through each compartment could he measured by determining the volume of water in each drum after a short interval of diverted flaw. The gas and liquid inlet distributor is shown in Figure 6. Air and water could be introduced bv a series of concentric air jets with water in the surraundihg annulus. This distributor configuration was known as the water-in-annulus distributor. The discharge of the concentric nozzles was about 2 inches above the packed bed. A large-scale single-concentric nozzle is shown in Figure 7. Measurements of liquid distribution for this nozzle were made to evaluate its performance, as its dimensions are similar to a single nozzle which might he used as part of a waler-in-annulus distributor a n a commercial scale. A scaled-down version of the water-in-annulus distributor was used in the 3- and 4-inch columns.
Of
packed
'Ocurrent
~
-.
?*
.
Mass Transfer. In establishing the technique for masstransfer measurements, two objectives were kept in mind. First, the measurements of concentration should be made within the packed bed to give a profile along the bed length and not just inlet and outlet concentrations. This eliminates "entry effects" resulting from mass transfer in the inlet and outlet of the packed column. Second, measurements of concentration should be continuous and instantaneous. This ensures that conditions are a t steady state when measurements are made.
Figure 2. 488
16-inch diameter cocwrent packed column
l&EC PROCESS DESIGN A N D DEVELOPMENT
T o accomplish the first objective, small gas-liquid separators were made from individual rings in the packed bed. To obtain a liquid-free gas sample, a ring was located with its axis parallel to the column axis and the upper end capped off. A hypodermic tube was introduced through the ring wall just under the capped-off end; the other end of the tube extended out through the column wall. For dumped beds these ring samplers were installed in the empty column and the packing was carefully dumped around them. Far stacked packing, one of the rings in the array was used directly as a sampler. The rate of gas flow through these samplers was carefully controlled so that no liquid was entrained. Thus a continuous liquid-free gas sample could be withdrawn from any point in the bed. jvithout mass transieer taking place in the sample line. l o obtain a liquid sample the whole packed bed was simply inverted so that the ring samplers had their bottoms capped off.
Figure 3. 4-inch core stacked 1-inch Raschig rings
of
I'igure 4.
3-inch cob
Jmn with stacked
%-
irich Roschig rings
@ @ I @ @
tigure 6.
Gas-liquid inlet distributor
W
Figure 5.
Wall ring First ring
Second ring Center ring
Collector for 16-inch column Radius, Inches
Fractional Area of Individual Comportment
8.00 7.47 5.28 2.71
0.0321 0.1089 0.0802 0.1150
Figure 7.
Commercial scale water in annulus nozzle VOL. 6
NO. 4
OCTOBER 1 9 6 7
489
Liquid collected in these samplers and was slowly drained off, giving a gas-free liquid sample. Ammonia absorption was chosen to represent a gas-phase resistance controlling mass transfer system and oxygen desorption was used for liquid-phase controlling transfer. Therefore, to satisfy the second objective, procedures for continuous analysis of ammonia in air and oxygen in water were required. Ammonia concentrations were first analyzed by a @ray ionization probe which utilized the principle of cross-section ionization (Deal et al., 1956; Lovelock, 1961; Otvos and Stevenson, 1956). A cross-section ionization probe was constructed using tritium foil as a source of 0 radiation to ionize the sample. The ammonia-air sample flowed through a gap in this probe, across which a potential of 120 volts was imposed. The small electrical current flowing through the gap of ionized gas was measured with a Keithley Model 417 picoammeter. This probe was calibrated with known ammonia-air samples, so that the current flow was a direct continuous measurement of the ammonia concentration. This technique was adequate in the range 0.001 to 0.1 mole fraction of ammonia in air. An improved technique for ammonia-air analysis was developed which extended the range of concentration down to 0.000050 to 0.010 mole fraction (50 to 10,000 p.p.m.), enabling large scale experiments to be operated safely with the gas discharge directly to atmosphere. This technique utilized the ultraviolet absorption characteristics of ammonia a t 204.3 mp (Gunther et al., 1956, 1958; Kolbezen, 1964). A Beckman Model D U R recording spectrophotometer was used with flow through ultraviolet quartz sample cells of 10- and 100mm. optical length. Temperature control assured that the sample and cell temperature remained constant a t 24.5’ =k 0.5’ C. Standard ammonia-air samples were used for calibration and the per cent light transmittance, which could be continuously recorded, deviated only slightly from the LambertBeer law over the whole range of concentration. The concentration of dissolved oxygen in the water was continuously measured by means of a Beckman Model 260 physiological gas analyzer. The macroprobes supplied with this instrument were inserted in special flow through probe holders which were attached to the discharge lines of the liquid samplers. Reference baths of saturated water solutions of Nz, air, and O2held a t column temperature were used for calibration. Experimental Results
Single-phase Pressure Loss. Single-phase pressure loss was measured with both air and water flowing singly in the small columns, while air alone was used in the 16-inch column. T h e experimental data were expressed in the form of the Ergun (1952) equation
where
Constants a and p were determined by least squares and the
Table II.
Packing Ring height, inches Ring o.d., inches Ring wall thickness, inch Column i.d., inches E
a,, sq.
D,,ft. 01
P
490
ft./cu. ft.
values are tabulated in Table I1 along with the packed bed properties. The constants in the Ergun equation have different values for each packing material. This is i n agreement with the results of Larkins (1959) ; however, Ergun (1952) suggested that a and p were constant for all packed beds of granular material. Two-Phase Pressure Loss. The method proposed by Larkins (1959) for correlating two-phase pressure loss data in packed columns was used to correlate the two-phase pressure loss data obtained in this investigation. Larkins reduced the momentum equation for steady two-phase vertical downflow to
(3)
The effective density, p m , for vertical two-phase flow in packed beds may not be described as simply as expressed by Equation 4, in that Equation 4 assumes that all downflowing liquid contributes to the effective density or “head.” I n a packed column much of this liquid is not free falling but runs over the packing surface. Consequently, only a small fraction of the total liquid holdup actually is contributing to the effective density or head. As a result, the effective density may be smaller than given by Equation 4 and indeed the “head” term gpnl/gC in Equation 3 may be small compared to the other two terms. The maximum numerical value of the effective density calculated by Equation 4 for total holdup values measured in packed beds is about 0.12 p.s.i. per foot. Hence, if ( h P / A Z ) , , is greater than ca. 0.6 p.s.i. per foot the effective density term or head effect can be neglected without serious error. A careful review of Larkins’ data (1959) shows that the measured pressure loss was less than 0.6 p.s.i. per foot for only four out of 190 runs. Hence, there is no conclusive evidence as to the correctness of applying Equation 4 to calculate the effective density of gas-liquid cocurrent downflow in packed beds. For the two-phase pressure loss data of this study, the effective density or head effect was neglected for all runs. For large liquid flow rates where liquid was observed to be freefalling, the effective density could possibly be given by Equation 4. But the measured pressure loss for these cases usually exceeded 0.6 p.s.i. per foot. For lower liquid flow rates where the pressure loss was less than 0.6 p.s.i. per foot the liquid was observed to flow mainly over the packing surface, and Equation 4 is probably not valid. These conclusions have also been reported by Weekman and Myers (1964). The form of the Larkins (1959) pressure drop formula may be expressed as
Dimensions of Packing and Properties of Packed Beds
‘/*-inch dumped
‘/*-inch stacked
’12
‘12
‘ I 2
‘/2
3/84
3
0.783 117 0.0105 110
2.04
1-inch dumped
1-inch stacked
1
1 1
1 1/16
1/~6
3
16
0.726 153 0.0105 83.8 0.234
0.883 47.8 0.0147
4 and 16 0:787 86.7 0,0147 129 0.117
3/84
l & E C PROCESS D E S I G N A N D DEVELOPMENT
920
5.51
3-inch stacked 3 3 3i16
I-inch Intalox
16
16
0.787 28.9 0.0442 122
0.682 78.0 0.0245 135 2.00
0.108
where
x
= (6L/6,)"2
Experimental data for all packing types except 3-inch rings are shown i n Figure 8 in comparison with Equation 5. T h e + 5 0 ~ 0lines are ale7 shown and the majority of the data lie within these limits. The experimental data on stacked 3-inch rings showed large deviations when corrrelated i n this fashion. T h e contribution of the effective density is more important for 3-inch stacked rings than for any other packing types investigated, because measured values of two-phase pressure loss are small and the packing surface area is lower than for other types used. Hence, for any liquid flow rate, the fraction of free-falling liquid will be larger and the effective density contribution probably cannot be neglected. As holdup could not be measured in the 16inch column, the effective density could not be evaluated. T h e actual experimental pressure loss data for stacked 3-inch rings are shown in Figure 9. Liquid Holdup. Liquid holdup measurements were made in the small 3- and 4-inch columns by sudden closing of ball valves on the liquid and gas inlets and the column outlet. End effect corrections were estimated by bolting the inlet and outlet flanges together with the packed bed sections removed. T h e liquid held up in the entry and exit sections was subtracted from total holdup when the column was in place. Holdup data from stacked and dumped '/'-inch rings and stacked 1-inch rings are shown in Figure 10. T h e Larkins (1959) holdup correlation log h = -0.774
+ 0.525 (log x) - 0.109 (log x ) ~
IO-'
Stacked
%" %"
I
I
I I l l 1
I
I
I
I I I I I
10
Figure 9. Two-phase pressure drop for stacked 3-inch Raschig rings
Establishing a good initial liquid distribution resolves only part of the liquid distribution problem. As the flow proceeds through the bed, liquid migrates toward the wall. If this is severe, liquid redistributors may be required. As a result, liquid distribution after flow through various bed lengths of stacked 1-inch rings was also measured. To evaluate the performance of initial distributors and measure distribution after flow through the bed, a quantitative definition of distribution is required. The definition is, of course, determined by the design of the collecting device. T h e collecting device i n this case consisted of 13 compartments made from concentric rings partitioned off into quarters as shown in Figure 5. The area of each of the nine compartments in the central part was designed to be 10% of the total area, with the four-wall compartment totaling the remaining
(6)
0 Dumped
I
Vg,f t / s e c
is also shown. Most (data points are within &5070 limits shown. T h e largest deviations are with stacked 1-inch rings a t high liquid rates. (Caution should be exercised if Equation 6 is used for stacked packing much greater than l-inch rings. No data are available on larger rings, because of the impossibility of making holdup measurements with the 16-inch column. Radial Liquid Distrilbution. A rather pragmatic investigation of a number of different inlet distributor configurations was carried out in the 16-inch column. T h e water-in-annulus configuration (Figure 6) proved to give adequate results and was used for the majority of the pressure drop and masstransfer experiments. 0
d
v
1
Rings
Rings
0 A
S t a c k e d 1" Rings D u m p e d 1" Rings -0 D u m p e d I" "Intalox"
-
4-
Figure 8. Two-phase pressure Larkins correlation A*------
0
1
-50% 4 , I
'.
r
'k.
0
I
I
I
I
I
I
I
I
1
I
I
T-,. I
I
I
X
VOL. 6
NO. 4
OCTOBER 1 9 6 7
491
1.
150%
lo-'[
I
J 10-1
I
I
1 I I I I / I
I
I
I
I
0
Stacked
Ib"
Rings
0
Dumped
'b"
Rings
0
Stacked 1" Rings
I
I
I I I I
I
10
I l l l l 1
x
Figure 10.
Liquid holdup correlation
10%. T o simplify construction from standard parts the actual areas of the compartments are as indicated i n Figure 5. A fractional standard deviation of the liquid superficial velocity is defined as follows :
(7) T h e fraction of the superficial liquid velocity in the nth compartment is
where Qn is the liquid collected from the nth compartment with area A n and Q I as the total liquid collected in all 13 compartments with total area A , . Another more graphic means of displaying liquid distribution is using smoothed distribution profiles. The average velocity for each of the three annular rings and for the center compartment was calculated by (9) where Q r is the total liquid collected from all four quadrants of one annular ring of area A , (or the liquid collected from the single center compartment). These average velocities were
plotted against the center radius of the respective ring and a smooth curve was drawn through the points. The fractional standard deviation could be plotted as a function of the two-phase parameter x (see Equation 5) and the data for different gas and liquid rates were reduced to a single curve. Figure 11 shows this type of plot for the initial distribution and for the liquid distribution after flow through three different lengths of packed bed. A fractional standard deviation of 0.2 was arbitrarily chosen as "good" liquid distribution. Figure 12 shows the smoothed profiles for a value of x = 0.44. For this case, a good initial distribution deteriorates somewhat, because of water migration to the wall as the flow proceeds down through the packed bed. For values of x greater than 1 the initial distribution was poor, because of high liquid flow near the column center and almost no liquid near the wall. The distribution improved with flow down through the bed because of migration of liquid to the wall. H a d the bed been longer than 7 5 inches, the distribution would tend to worsen because of increased liquid flow near the wall. The performance of a single commercial-scale nozzle (Figure 6) can be seen from the smoothed profile in Figure 13. For these tests the nozzle sprayed into empty column sections 26 and 49 inches long. Figure 13 shows that a t these flow rates this type of nozzle could be spaced on about 10-inch centers if
:::; 0.6
1 L
Figure 1 1 . Liquid d i s t r i b u t i o n for s t a c k e d 1-inch Raschig rings W a t e r in annulus dirtributor, standard deviation
0.4
-
f
B e d Length, inches
0 0 26
c
0
.- .
0.2 -
49 75
/
0.1
492
I
I
1
I
I I I I I
I & E C PROCESS D E S I G N A N D D E V E L O P M E N T
I
1
I
I
I 1 1 1
the distance of nozzle to packing is about 2 feet and a reasonably flat profile would result from the overlapping of successive nozzle spray patterns. Further increasing the gas velocity causes wider spreading of the liquid to the point where there is very little liquid below the gas jet center line.
x
9
Mass Transfer. Mass-transfer data for packed beds are usually presented either in the form of a capacity coefficient, the product of the mass-transfer coefficient, and the interfacial area per unit volume of packing, or koa or kla,or as the height of a transfer unit, H T U , or HTUI, where
0.44
These quantities were calculated from the experimental ammonia absorption data based on Equation 12.
BedLength 2
VP
inches
-
where
0 0.142
-.-- 264975 -----a
0.616 0.573 0.430
and
These relationships are valid because the following conditions are met by the ammonia absorption experiments. 1. Very dilute concentrations of ammonia, y < 0.05. Gas phase is an ideal gas. Ideal mixtures. Linear equilibrium relationship (Henry's law). Liquid film resistance was less than 5%; hence koa is considered to be the gas-phase resistance-controlling capacity coefficient.
2. 3. 4. 5. - 1 all
Figure rings
6
7
5
I
I
I
I
4
3
2
1
E.
Radtue, inches
1 2.
Liquid distribution for stacked 1 -inch Raschig
+
W a t e r in annulus distributor, smoothed profiles
ftlsec Air Nozzle Velocity Water Nozzle Velocity
If the ammonia concentration measurements made along the length of the column are plotted as (y - y *) us. Z on semilog paper, a straight line with slope of (1 A)kua/2.303 Vushould result (Figure 14). The measured gas phase mole fraction, y , the calculated (Equation 13) equilibrium mole fraction, y*, and the difference, y - y*, are shown. y approaches y * a t the column exit, indicating the one equilibrium stage limiting condition of cocurrent operation. Conditions 1 and 4 are shown to be valid over most of the column length. Figure 14 also shows an entry effect. The inlet concentration falls on a smooth curve, but the first sampler reads low. For most of the runs, the transfer rate in the inlet section and the upper portion of the packed bed differed significantly from that in the lower portion of the packed bed. This phenomenon could be due partially to a sampling problem and partially to a true entry effect. This again emphasizes the value of taking samples from within the packed bed away from the inlet rather than just inlet and outlet samples. Similar techniques were used for the oxygen desorption mass transfer. T h e transfer rate equations are
480 6.1
- -26" Void
- ---4?" Void *
(x
log ( x
- x*) - x*),
-
1 kza 2.303 V i
z
where x* =
-1
6
7
8
Wall
I
4
I
3
I
2
1
1
Radius, inches
Figure 1 3.
Liquid distribution, smoothed profiles
1 z* (Xl + ptg y 1 x)
However, because of the low solubility of oxygen, the amount of oxygen desorbed from the liquid phase did not affect the gas phase concentration. Hence, Equation 16 becomes x* =
Commercial scale water in annulus nozzle
VOL. 6
P2 H y1
NO. 4
OCTOBER 1967
493
h
r
loo0
800
I
1
Dumped ’1;‘ Rings V, 1.67 ftlsec v, 0.141 f t / s e c Slope 0 . 0 5 3 3 in-’ HTUp 8.15 in kea 0.207 s e B ‘
A
600
“\
Slope
0.0533
2oo/
1v‘
0
4
8
I2
16
20
24 2. inches
Z, Inches
Figure 14. tion
Concentration profiles for ammonia absorp-
Figure 15. tion
Concentration profiles for oxygen desorp-
The Beckman oxygen analyzer reads in terms of partial pressure over the liquid, which from Henry’s law is
p
= Hx
(1 8)
’ v i
A , [K gc P I
Equation 15 in terms of partial pressure is
(P - P*) l o g( -P 7- P )
=
-
1 kla 2 2.303 ~Vi
Graphs of p - p* us. 2 were prepared from experimental data and the slope on semilog paper gives -kza/2.303 V 2 . Figure 15 shows the oxygen profiles for one of the experimental runs. Many of the comments made about the ammonia profiles apply here also. ‘The entry effect can be seen as the larger slope through the first two sample points. A concept, which has been used with some degree of success, to correlate mass-transfer data is to relate the capacity coefficient to the energy dissipation per unit volume of the system. This approach has been used to correlate gas-liquid transfer data for stirred tank contactors (Calderbank and Moo-Young, 1961; Cooper et al., 1944). A similar approach was suggested for correlating the experimental transfer data from this study (Sternling, 1963). For a single-phase vertical flow system, when kinetic energy effects, heat input, and shaft work are neglected, the mechanical energy balance reduces to
T h e analogous equation for a two-phase vertical flow system derived by Standart (1 964) is 494
I&EC PROCESS DESIGN AND DEVELOPMEN1
($)zj
4-
=
El,
(21)
The fractional areas for gas, A o / A t , and liquid, A l / A , , are not simply the gas and liquid holdup, respectively, for a packed bed. As discussed previously, the liquid flows partially over the packing and partially in free fall. Hence, the terms in Equation 21 cannot be evaluated without a better understanding of the flow mechanism in the packed bed. The effective density or “head” effect was shown earlier to have negligible effect on measured pressure loss for the majority of the experimental runs. With this in mind, a modified definition of energy dissipation for each phase was made:
E , = Vo($)
gas phase lo
EI
=
Vi($)
liquid phase 20
Experimentally measured gas-phase controlling mass-transfer capacity coefficients were correlated with E, and the liquid coefficients with El. T h e two-phase pressure loss, ( A P / A Z )I,, was measured concurrently with the mass-transfer coefficients and used in evaluating the energy dissipation term. T h e mass-transfer capacity coefficients for all ammoniaabsorption runs a t 70’ F. are shown as a function of the gasphase energy dissipation in Figure 16. A dimensional equation of the following form represents these data within zk.2501,.
p&" 0
Stacked
0 Dumped
%" Rings vi' Rings
0 Stacked 1"
Rings
A D u m p e d 1" Rings
0
S t a c k e d 3" Rings 0 D u m p e d 1" " I n t a l o x "
Equation 24
1 10-1
1
Figure 1 6.
koa = 2.0
I
I I11111 1
I
I
I I I Ill1 1 i 10 Eg ft-lbr Force/sec f t 3
I 1 1 1 1 1 1 10'
Ammonia absorption mass transfer-energy
+ 0.91 (Eg)2/3
(24)
k,a = set.-'
E , = ft.-lb. force/sec. cu. ft. T h e gas-phase controlling transfer data measured by Wen (1963a) for absorption of water vapor i n calcium chloride solutions could possibly be comparable to the experimental results presented here for ammonia absorption. T h e Schmidt number for ammonia in air is about the same as for water vapor i n air. Hence, k , for Wen's (1 963a, b) data should be similar to k , measured for ammonia. If the interfacial area for mass transfer is similar in both experiments for similar flow rates and packing type, the capacity coefficients should be similar for each experiment. Wen's (1963a, b) data have been carefully compared with the present results. The only case where cotlditions of Wen's (1963a, b) experiments were similar to those of this work were a t his highest liquid rate, which was nearly equal to the lowest liquid rate of the present experiments. T h e values of k,a reported by Wen for dumped l / z - and 1-inch Raschig rings are considerably lower than the values reported here for similar conditions. Wen (1963a, b) noted increased channeling of liquid as liquid flow rate increased up to the maximum studied. Hence, he concluded that k,a would decrease with increasing liquid rate by virtue of less effective transfer area due to the liquid channel-
0
Stacked
0
I
1 I I I l l
dissipation correlation
ing. I n this work, improved liquid distribution was observed as liquid rates were increased. Consequently, k,a should increase with increasing liquid rate, as was observed in these experiments. T h e mechanism of liquid distribution is different in these two experiments. This could be the result of completely different ranges of liquid rates studied in the two experiments. However, the wetting characteristics of the packing become important a t low liquid rates. T h e wetting of ceramic packing by calcium chloride could be the dominant factor determining interfacial area in Wen's (1963a, b) experiments, whereas in the higher rates of this experiment wetting effects are less important. I t is concluded that the results of these two experiments are not directly comparable. Caution should be exercised in extrapolating the results of this work to liquid rates lower than studied. T h e experimental capacity coefficients for oxygen desorption a t 77' F . are shown in Figure 17. The empirical dimensional equation representing these data within +25% is kla = 0.12
kla
=
(25)
(El)1/2
sec.3
E L = ft.-lb. force/sec. cu. ft.
%" %"
Rings Rings Stacked 1" Rings S t a c k e d 3" Rings
0 Dumped
0
I
3
E a , ft-lbs F o r c e l s e c f t 3
Figure
17.
Oxygen desorption mass transfer-energy
dissipation correlation VOL. 6
NO. 4
OCTOBER 1 9 6 7
495
Data for cocurrent oxygen desorption were obtained by McIlvroid (1956) for packed beds of dumped l/r-inch Raschig rings, and dumped 4- and 6-mm. spheres. These data have been recalculated into the form of the energy dissipation correlation suggested here. The data are compared with Equation 25 in Figure 18 and the agreement is good. This appears to extend the range of packing sizes to which Equation 25 is applicable. Estimates of Effect of Physical Properties of Fluids
The scope of this investigation was limited to the study of the air-water system with packings made of polyethylene (except for the Intalox saddles, which were ceramic). T h e masstransfer measurements were made with the ammonia absorption and oxygen desorption systems. T o use the results of this investigation for design of systems involving other fluids, the effects of fluid physical properties must be known. However, it was beyond the scope of the present investigation to study the effects of physical properties of the fluids systematically. Some qualitative remarks on physical property effects can be made. The fluid properties which will probably most significantly influence the pressure drop, dynamic liquid holdup, and radial liquid distribution are gas and liquid density, gas and liquid viscosities, the surface tension of the liquid, and the contact angle between the liquid and the solid packing-Le., the wettability of the packing. All these properties and in addition the gas-phase and liquid-phase diffusivities of the transferring component will influence the mass-transfer capacity coefficient. Physical property effects have been reasonably well accounted for in the single-phase pressure-loss equation of Ergun (1952) (Equation 1) and the two-phase pressure-loss equation of Larkins (1959) (Equation 5). Effects of surface tension on two-phase pressure loss have been considered by both Larkins and Weekman and Myers (1964). The effects of liquid physical properties on liquid holdup in packed beds with no gas flow have been considered by Jesser and Elgin (1943), Shulman et al. (1955), and Standish (1964), while Larkins (1959, 1961) measured some physical property effects
Figure 1 8.
on liquid holdup for cocurrent flow. I n none of these investigations have the important properties of surface tension and packing wettability been adequately taken into consideration. Practically no physical property effects have been accounted for in the limited experimental work on radial liquid distribution. A means of considering the effect of fluid properties on the mass-transfer capacity coefficients, koa and k la,involves separating the coefficients into the factors k and a and estimating the effect of fluid properties o n each factor. The value of k , will depend on the Schmidt and Reynolds numbers of the gas phase, while k i will be influenced by the Srhmidt and Reynolds numbers in the liquid phase. The interfacial area will be influenced mainly by the liquid density, viscosity, interfacial tension, and wettability of the packing. The mass-transfer data from this investigation as \\ell as those from previous investigations (McIlvroid, 1956; \Veri et al., 1963a) are inadequate to define these physical property effects. I t can be concluded that further experimental work is required to define adequately the effects of fluid physical properties on liquid holdup, radial liquid distribution, and masstransfer capacity coefficients for cocurrent gas-liquid flow in packed columns. Summary of Design Procedure for Cocurrenl Contacting in Packed Columns
Based on the preceding results, a design for a cocurrent packed column can be made if the Ergun constants are known for the packing material. If the packing material is not the same as, but similar to that used here, a few simple single-phase pressure loss experiments can be performed to determine these constants. When these constants are known, single-phase pressure loss for each phase as if it were flowing alone can be evaluated from Equations 1 and 2
where
Liquid phase mass transfer-energy dissipation correlation Data of Mcllvroid (1956)
496
l & E C PROCESS D E S I G N A N D D E V E L O P M E N T
x is then evaluated:
T h e two-phase parameter
x
= (61/6,)"2
and the two-phase pressure loss calculated from
0.41 6
__-
x )+ ~ 0.666
(5)
and holdup from log h = -0.774
+
0.525 log
x -
0.109 (log x)*
(6)
T h e individual phase energy dissipation terms can be evaluated from the two-phase pressure loss by
T h e gas-phase controlling mass-transfer coefficient for ammonia absorption a t 703 F. can be calculated from the dimensional equation koa
=
2.0
+ 0.91 (E,)2i3
(24)
12
k,a
C a l c u l a t e d , rec-'
Figure 19. Comparison of measured and calculated ammonia ahsorption mass transfer
where koa = set.-'
E,
=
ft.-lb. forcelsec. cu. ft.
The liquid-phase oxygen-absorption capacity coefficient a t 77' F. can be evaluated from the dimensional equation k l a = 0.12 ( E l ) 1 / 2
(25)
where kla = sec.-]
El = R.-lb. force/sec. cu. ft. Each of the above empirical equations has been determined by fitting experimental data. I n some cases the scatter of data around these individual equations is as great as =k50%. T o show that the accuracy of the over-all design procedure is not significantly different from the accuracy of the individual equations comprising it, experimentally measured gas-phase capacity coefficients are compared in Figure 19 with those calculated via the above procedure, starting from the known conditions of each ammonia absorption experiment. T h e agreement is Ivithin +507, for most cases, indicating that the fit of the experimental mass-transfer data to the over-all design procedure is no worse than the fit of the data to any individual equation comprising the design procedure. This design procedure should produce results which are accurate to within =t50%,, adequate for most preliminary designs for initial cost estimates. For more accurate design, additional pilot scale experiments may be required, especially if fluid properties are significantly different from the air-water-ammonia-oxygen systems utilized in this study. However, the similarity principle of equal energy dissipation per unit volume, shown to be valid here, can be used as a basis for mass-transfer scale-up i n cocurrent contacting in packed columns. Cocurrent and Countercurrent Gas-liquid Contacting in Packed Columns
An example of design calculation is presented here for operating conditions which are suited to cocurrent contacting.
T h e example chosen is ammonia absorption a t large liquid-togas ratio (L'IV' = 161). As a result, the liquid-phase concentration of ammonia will be very dilute and nearly constant down the length of the column, satisfying the requirement of only one equilibrium stage. The number of transfer units for this specific example will be nearly the same for both countercurrent and cocurrent flow. T h e packing chosen is dumped '/*-inch Raschig rings, as ammonia absorption data are available for this packing from the literature for countercurrent flow (Cornel1 et al., 1960) and from this report for cocurrent flow. The countercurrent design is based on operation a t 70% of flooding. The actual gas and liquid rates are calculated from the liquid-to-gas ratio using the \\fell known flooding correlation of Sher\vood et al. (see Leva, 1953). Pressure drop is determined by extrapolating design charts for '/*-inch rings (Leva, 1953) and HTC', is calculated from a generalized correlation presented by Cornell et ai. (1960). T\vo cases of cocurrent operation illustrate that there is no flooding with this mode of operation. As the column diameter is reduced, the actual velocities in the column increase if the total feed rates are kept constant. T h e result is that the column diameter is limited only by the available pressure drop. T h e pressure drop and H T U , are determined from the data presented in this paper. The number of transfer units is the same for both modes of operation; thus the column heights will be directly proportional to the H T U , and the total column pressure drop \vi11 be directly proportional to the product (HTL,) X (AP/AZ) lo. T h e two modes of operation are compared by using the countercurrent operation as a base case. The relative costs are calculated assuming that the capital cost of the column is directly proportional to the product of column diameter and column height. This assumes that the column cost is determined by the volume of the metal comprising the column shell, that the wall thickness is constant, and that the column heads and packing have a negligible cost. The results of this calculation are sho\vn in Table 111. VOL. 6
NO. 4
OCTOBER
1967
497
Table 111.
Comparison of Cocurrent Operation with Countercurrent Operation for NHs Adsorption
(Dumped '/,-inch Raschig rings) Countercurrent (cc), 70% of Flood
Cocurrent ( c o ) Case I Case 2
161
161
V', moles air/hr. sq. ft. VI, ft./sec. V,, ft./sec. (AP/AZ)l,, p.s.i./ft. HTU,, ft.
916 5.69 0.0736 0.611 0.072 0.25 1. 0 -
,680 22.8 0,294 2.44 0.52 0.12 0.50
f t.
1. o 1 .o 1. o
0.48
3.5 0.24
161 5550 34.5 0.450 3.70 1.7
0.058 0.41 0.23 5.4 0,094
I t may be concluded that the capital cost of a cocurrent column for these conditions is lower than the cost of a countercurrent column, but the operating cost will be higher by virtue of the increased pressure drop across the column. Conclusions
Single-phase frictional Dressure loss in packed beds can be predicted from the Ergun (1952) equation (Equation l ) , but the empirical constants are not indzpendent of packing type. The two-phase pressure drop and liquid holdup correlations of Larkins (1959, 1961) cover a wide range of packing types with an accuracy of & 50%. Radial liquid distribution is a function of packed bed height, and gas and liquid rates expressed i n the two-phase parameter X.
M iss-transfer capacity coefficients for gas-phase and liquidphase resistance-controlling transfer can be correlated with individual phase energy dissipation per unit volume, and the correlation is valid for a wide range of packing type. Further experimental work is required to evaluate the effect of flui 1 properties on liquid holdup, radial liquid distribution, and both gas-phase and liquid-phase resistance controlling mass-transfer capacity coefficients. Cocurrent columns can be designed within an accuracy of i 5 0 y o , starting with only the knowledge of the Ergun constant$for the single-phase pressure loss equation. The cocurrent mode of operation may be favored over the more conventional countercurrent operation when only one equilibrium stage is required-physical absorption a t large liquid-to-gas ratios, physical desorption a t small liquid-to-gas ratios, and chemical reaction consuming the transferring component in one of the phases; when pressure drop can be tolerated without excessive operating cost; or when capital costs of equipment are high-high pressure equipment or corrosive materials involved. Nomenclature A = cross-sectional area, sq. ft. A* = absorption factor, Equation 14 a = mass transfer interfacial area per unit volume, ft.-' = packing surface area per unit volume, ft.-l a, d = column diameter, ft. = equivalent spherical particle diameter, D, = 6(1 ZIP €),/a,, ft. 498
=
g gc
HTU h k
= = = = = =
k,a
=
H
-
L ' / V ' , moles HpO/mole air L ' , moles HsO/hr. sq.
E
l & E C PROCESS D E S I G N A N D D E V E L O P M E N T
energy dissipation per unit volume, ft.-lb. force/ sec. cu. ft. gravitational acceleration 32.2, ft./sec.? conversion constant 32.2, Ib. mass ft./lb. force sec2 Henry's law constant, atm. height of transfer unit, ft. free draining holdup, fraction of void volume mass-transfer coefficient based on individual film driving force, ft./sec. gas-phase film capacity coefficient, sec. -I liquid-phase film capacity coefficient, set.-' liquid molar velocity, solute free, moles H,O/hr. sq. ft . pressure. atm. partial pressure, mm. Hg partial pressure in equilibrium with liquid a t interface, mm. H g
27
=
P p p*
= = =
E;z
=
measured pressure gradient, p.s.i./ft.
Q Re
= =
V V'
=
volume of liquid collected, cu. ft. Reynolds number, Equation 2 superficial velocity, ft./sec. gas molar velocity solute free, moles airihr. sq. ft. liquid-phase mole fraction, moles solute/mole H20 f mole solute liquid-phase mole fraction in equilibrium with gasphase bulk concentration, moles solute/mole H20 mole solute gas-phase mole fraction, moles solute/mole air f mole solute gas-phase mole fraction in equilibrium ivith liquidphase bulk concentration, moles solute/mole air mole solute column length. ft. Ergun constant Equation 1 Ergun constant Equation 1 frictional pressure gradient, p.s.i./ft. packing void fraction fluid viscosity. 1b.jft. hr. fluid density. Ib.,/cu. ft. standard deiriation, Equation 7 two-phase parameter, x = (81/8,)'/'
=
x
= =
x*
=
y
=
y*
=
+
Z
=
cy
=
p
= = = = = = =
6 t
p p
u
x
SUBSCRIPTS = cocurrent cc = countercurrent g = gas phase 1 = liquid phase = gas-liquid phases combined or two-phase flow 1g = mean or effective (Lvith density) rn n = any compartment in collector Y = any annular ring in collector = total in cross-sectional area, pressure, etc. t 1 = column inlet co
Acknowledgment
The valuable assistance of G. H. Ackerman, J. J. Sutfin, J. M. Elliott: and \V. B. Schwenning is gratefully acknowledged. The author appreciates the permission to publish this paper granted by the Shell Development Co. literature Cited
Calderbank, P. H., Moo-Young, M. B., Chem. Eng. Sci. 16, 39 (December 1961). Cooper, C. hi., Fernstorm, G. A , , Miller, S. A., Znd. Eng. Chem. 36, 517 (1944). Cornell, D., Knapp, \V. G., Fair, J. R., Chem. Eng. Progr. 56, 6 8 i J u-l v, 19601. ~
~
Deal, C. H., b t v o s , J . I$'., Smith, V. N., Zucco, P. S., Anal. Chem. 28, 1958 (1956). Dodds, \V, S., Stutzman, I,. F., Solami, B. J . , Carter, R. J., A.Z.Ch.R. .I. 6, 197 (1960a). Dodds, \V. S., Stutzman, I,. F., Solami, B. J., Carter, R. J., A . I . Ch.E. J . 6, 390 (1960b).
-
+
Ergun, S . , Chem. Eng. Progr. 48, 89 (1952). Gunther, F. A , , Barkley, J. H., Kolbezen, M. J., Blinn, R. C., Staggs, E,. A , , Anal. Chem. 28, 1985 (1956). Gunther, F . A., Rlinn, R. C., Kolbezen, M. J., \Vilson, C. \V., Conklin, R.. A , , Anal. Chem. 30, 1089 (1958).
Hoftyzer, P. J., Trans. ZnJt. Chem. Engrs. 42, T109 (1964). Jesser, B. W., Elgin, J. C., Trans. A.Z.Ch.E. 39, 277 (1943). Kolbezen, M. J., Eckert, J. W.,Wilson, C. W., Anal. Chem. 36, 593 (1964). Larkins, R. P., “Two-F’hase Cocurrent Flow in Packed Beds,” Ph.D. thesis, University of Michigan, 1959. Larkins, R. P., White, R. R., Jeffrey, D. W., A.Z.CI1.E. J . 7, 231 (1961). Leva, M., “Tower Packings and Packed Tower Design,” 2nd ed., pp. 28-37, U. S. Stoneware Co., 1953. Lockhart, R. W., Martinelli, R. C., Chem. Eng. Progr. 45, 39 (January 1949). Lovelock, J. E., Anal. Chcm. 33, 162 (1961). Mcllvroid, H. G., “Mass Transfer in Cocurrent Gas-Liquid Flow through a Packed Column,” Ph.D. thesis, Carnegie Institute of Technology, 1956. Otvos, J. W., Stevenson, D. P., J . A m . Chem. SOC.78, 546 (1956). Porter, K. E., Jones, M. C., Trans. Znst. Chem. Engrs. 41, 240 (1963). Shulman, H. L., Ullrica, C. F., Wells, N., Proulx, A. Z . , A.Z.Ch.E. J . 1, 259 (1955). Standart, G., Chem. Eng. Sci. 19, 227 (1964).
Standish, N., Nature 202, 587 (May 9, 1964). Sternling, C. V., private communication, 1963. Wen, C. Y., O’Brien, W. S., Fan, L. T., J . Chem. Eng. Data 8, 42 (1963a). Wen, C. Y., O’Brien, W. S., Fan, L. T., J . Chem. Eng. Data 8, 47 (1963b). Weekman, V. W., Myers, J. B., A.Z.Ch.E. J . 10, 951 (1964). Weekman, V. W., Myers, J. B., A.Z.Ch.E. J . 11, 13 (1965). RECEIVED for review December 5, 1966 ACCEPTED May 1, 1967
Material supplementary to this article has been deposited as Document 9495 with the AD1 Auxiliary Publications Project, Photoduplication Service, Library of Congress, Washington, D.C. A copy may be secured by citing the document number and by remitting $2.50 for photoprints or $1.75 for 35-mm. microfilm. Advance payment is required. Make checks or money orders payable to Chief, Photoduplication Service, Library of Congress.
C A L C U L A T I O N OF EFFECT OF V A P O R MIXING O N T R A Y EFFICIENCY D A V I D A. DIENER ESSOResearch and Engineering Co., Florham Park, N.J .
The relationship between the point efficiency and the Murphree tray efficiency has been developed for the case of partial mixing of the liquid and no mixing of the vapor. This is an extension of previous studies which have assumed the vapor entering each tray to be completely uniform in composition. The lateral concentration gradient in the vapor rising from the liquid is assumed to be similar to the longitudinal concentration gradient in the liquid flowing across the tray. This assumption probably approximates the actual physical situation best at high per cents of flood. The principal application of the results of this work is to systems where point efficiencies are greater than about 0.80. HE relationship between the point efficiency and the TMurphree tray efficiency has in general been described in terms of the degree of backmixing of the liquid as it flows across a tray. This has been done using a number of different models to characterize the liquid mixing. These models include mixed pools :in series (Gautreaux and O’Connell, 1955), eddy diffusion (Gerster et al., 1958), recycle stream (Oliver and Watson, 1956), splashing of the liquid (Johnson and Marangozis, 1958)., and measurement of residence times of liquid elements (Foss et al., 1958). In the use of each of these models to develop the relationship between point and tray efficiencies, however, the assumption has always been made that the vapor entering successive trays is well mixed. Only in ‘the extreme case of no backmixing of the liquid has the relationship between the point efficiency and the tray efficiency been developed without assuming the vapor to be completely mixed. This case, for plug flow of the liquid and unmixed vapor, has been presented (Lewis, 1936) for two different flow situations. In this work, partial mixing of the liquid with no mixing of the vapor is considered for the same two flow situations considered by Lewis in his development. T h e model used to describe the partial liquid mixing is that of eddy diffusion. In carrying out the development, it is assumed that a lateral concentration gradient exists in the vapor similar to the longitudinal concentration gradient which exists in the liquid flowing across the tray. T h e vapor is assumed to rise directly (without lateral mixing) from the point where it leaves the aerated liquid on one tray to the corresponding point on the tray above.
General Relationships
Application of the eddy diffusion model to describe the partial mixing of aerated liquid on a distillation tray yields, in terms of a material balance on a small vertical slice of liquid,
with w varying from 1 to 0 as the liquid flows across the tray. b’, and the Use of the equilibrium relationship, yn* = m x , definition of the point efficiency, Eo, = ( y , - Y n - l ) / ( Y n * ynv1), to substitute in Equation 1 then gives the relationship between the point efficiency and the vapor compositions as
+
-
T o obtain the relationship between the point efficiency and the Murphree tray efficiency, however, it is also necessary to relate the tray efficiency to the vapor compositions. This can be done by considering the definition of the Murphree tray efficiency, EIMV= (g, - gn- l)/(yo* - gn- l ) . Using this definition, the desired relationship may be expressed as
1’ (Yn
EMV =
VOL. 6
- Yn-
ddw
(3)
1
NO. 4 O C T O B E R 1 9 6 7
499
