I
FUMITAKE YOSHIDA and TETSUSHI KOYANAGI Chemical Engineering Department, Kyoto University, Kyoto, Japan
Liquid Phase Mass Transfer Rates and Effective Interfacial Area in Packed Absorption Columns With this novel approach, costly experiments may be avoided in designing a packed column for a new system
most successful correlation for liquid phase mass transfer rates in packed columns is the Sherwood-Holloway correlation (78), confirmed by several other investigators and generally considered to be a standard. However, it lacks generality, as it is based only on data with water as the irrigating liquid. The present work was intended to obtain a more general correlation for liquid phase mass transfer rates in packed columns. Studies were made on the absorption of pure carbon dioxide into water and methanol in a column packed with spheres, Raschig rings, and Berl saddles as well as in a bead column containing spheres connected in a vertical row. Reasonable correlations among the height of a transfer unit, the Reynolds number, and physical properties of the liquid phase were obtained. The effective interfacial area id the packed column and its variation with liquid rates were determined for both water and methanol.
T H E
Basis of Interpretation
Sherwood and Holloway (78) have correlated their data on the desorption
of oxygen, carbon dioxide, and hydrogen from water in a packed column with the equation 1
where a varies from 80 to 550 and n from 0.22 to 0.46, depending upon the type and size of packings studied. Van Krevelen and Hoftijzer (73) proposed the following equation for the liquid phase mass transfer coefficients in packed columns:
in which the effective interfacial area, a,, is given by a,/a,
=
1
-
e--0.40(I,lp)
(3)
Equation 2 is dimensionally sound. Equation 3 was obtained (74)by comparing k,a values from various sources on the assumption that wetting was complete-effective area was identical with total surface area of the packing in some experiments. I t is inconceivable that the total surface of packing is effective, however good wetting may be.
Fujita and Hayakawa ( 5 ) have obtained a correlation similar to Equation 2 with an exponent of 0.5 on the Schmidt number, taking (4L/a, p ) as the Reynolds number, in which aW is the wetted area measured directly (6) by means of a dye solution. They took the effect of packed height into account. Noting that ElL equals L / k L a p , one can rearrange Equation 2 to give
An equation of this type could also be obtained directly by dimensional analysis. The exact relationships among the dimensionless groups should be studied by experimentation. Recently, Shulman and others (79) obtained the following equation for kL in packed columns. dL k d= 25.1 (%) D
045 '
(4)
The k~ value was obtained from the kLa data of Sherwood and Holloway and the effective area, which was determined by comparing the kGa data of Fellinger (4) on ammonia absorption into water VOL. 50, NO. 3
MARCH 1958
365
RESERVOl R
3 - b I
MANOMETER
WATER OUT
. BEAD LUTE VESSEL
-WATER JACKET
PUMP
STILL
CO,
PREHEATER
Entire apparatus for experiments with packed columns. When bead column was used, equipment was the same except for the column Bead column, containing steel balls sprayed with metallic aluminum, was used in developing method for calculating effective area of column
and the ko data (79) on the vaporization of naphthalene packings. Three forms of the Reynolds number appear in Equations 1, 2, 2a, and 4. The dimensional group, (Lip), i n Equation 1 is considered unsound even for a given size of packing. If the wetted area, or the effective area, varies with the liquid rate, which seems a reasonable assumption, values of ( L / p ) are no longer proportional to the true Reynolds number of the liquid stream, because the effective wetted periphery increases with the effective area. The Reynolds number for film flow of liquid is 4l?/p, where I’ is the liquid rate per unit length As the effective of wetted periphery. wetted periphery per unit cross section of a column is numerically equal to the effective area of packing per unit volume, I’ equals L/aB in the case of film flow of liquid in the packing. Therefore, the Reynolds number in Equation 2 or 2a is sounder than (L/p). The Reynolds number in Equation 4 is reasonable if the ratio of the effective area to the total surface area of packing is constant, because d,, the characteristic length for a
366
given type of packing is, in general, inversely proportional to the total surface area of the packing per unit packed volume. Kling (7 7) adopted the column diameter as the characteristic length in the Reynolds number, but this seems to have no theoretical basis. Thus, in studying the effect of liquid rates on the liquid phase mass transfer rates in packed columns use of the Reynolds number of the form, (4L/a,p), is soundest. a, is usually unknown. This led to the idea of experimenting with an apparatus with a fixed interfacial area but a liquid flow pattern similar to that in packed columns. One method would be the use of disk columns (27). However, the bead column seems to give better liquid distribution and a liquid flow pattern more like that in packed columns. When the present work was in progress, Lynn, Straatmeier, and Kramers (76) reported studies on the absorption of sulfur dioxide by water in a bead column. They applied the penetration theory of Higbie (8) to the bead column, assuming that liquid flow over the spheres is perfectly laminar, and
INDUSTRIAL AND ENGINEERING CHEMISTRY
found reasonable agreement of data with the theory when it was postulated that there was essentially no mixing of stream lines in the liquid film as it flowed from one sphere to the next. Their results, however, somewhat contradict the results of the present study. Because the actual liquid flow pattern in bead columns seemed too complicated for theoretical treatment, an attempt was made to correlate the height of a transfer unit in a bead column as a function of the liquid phase Reynolds number and to compare the correlation with a similar correlation for a packed column, to determine the effective area in the packed column. Consider a bead column, in which liquid flows down over n spheres of diameter d, connected in a vertical row. If complete wetting of spheres is assumed, the total wetted area is nnd2 and the total height is nd. Then, the average wetted periphery, b, can be defined as b =
wetted area - nrd2 - -nd = r d height
(5)
PACKED COLUMNS Table 1.
values of the number of liquid phase transfer units for the same system a t a given temperature. The spheres in the bead column are of the same size as the packings in the packed -column. Then, the liquid phase Reynolds number in the effective area in the packed column should be equal to the Reynolds number in the bead column:
Comparative Data on Packings Used" No. of Pieces Total in No.of Surface, Free Vertical Pieces Sq. Ft./ Space, DirecPackedb Cu. Ft. %" tiond
Packing Spheres 1-inch 306 41 43 16.5 0.5-inch 2580 86 40 33.5 Rascbig rings 59 70 15.1 236 25-mm. 106 63 25.5 1130 15-mm. Berl saddles 25-mm. 336 82 66 17.0 12-mm. 2200 198 64 31.8 0 Packed height, 16.0 inches (40.6 om.). Inside diameter of column, 12.0 om. b Counted. Observed. Calculated.
where a, is usually unknown. 7 can be written as
Equation
( 4 L l a t p ) ( a d a d = 4Wl4.4
(7a)
in which at is the total surface area of the packing per unit packed volume. Now, the superficial Reynolds number on the basis of the total surface area is defined as ( 4 L / a t p ) and is employed temporarily in plotting the number of liquid phase transfer units for the packed column against ( 4 L / a , p ) . For the bead column the number of liquid phase transfer units are plotted us. 4 W/ndp. Then, aB/at can be calculated by comparing the values of 4L/a,p and those of 4 W / ~ d pa t given values of the number of transfer units. The effective area thus obtained is not identical with the wetted area of the packing nor with the total interfacial area between gas and liquid. In the method proposed, the effects of liquid velocity distribution over packing pieces and existence of semistagnant liquid pockets are automatically taken into account. Considering the splitting of kLa into kL and a, the local value of k L should vary from one point to another even on a piece of packing, and the value of effective area should depend on the value of kL taken as the average; no effective area can be defined unless an average kL value is specified. The effective area obtained here has the average value of kL in a bead column as the criterion of comparison. It seems reasonable to assume that the height of a liquid phase transfer unit and, accordingly, k ~values . are approximately equal for a bead column and for the effective surface in a packed column under comparable conditions,
Accordingly, the average Reynolds number for the liquid stream in a bead column is 4r/p = 4W/rdp
(7)
4L/a,p = 4 W / r d p
(6)
where W is the total mass rate of liquid flow. The liquid flow pattern in the packed column might be more complicated than in the bead column. However, it may be assumed that the value of the number of liquid phase transfer units or the liquid phase mass transfer coefficient in a packed column and in a bead column are equal if three conditions are identical: Reynolds number in the effective part of the liquid stream, number of times and degree of mixing of liquid stream lines, and length of liquid travel over each piece of packing. Conversely, if the last two conditions are satisfied, the values of the Reynolds number should be equal if the values of the number of transfer units are equal in packed and bead columns. The last two conditions seem to be nearly satisfied, if each piece of packing in a packed column and the spheres in a bead column are of the same size and columns are equal in height. Table I shows that in such cases the number of spheres in the bead column approximately equals the number of packing pieces in the vertical direction in the packed column. The packed volume was divided by the total number of packing pieces, which were counted individually, giving the average volume occupied by a piece of packing. Then, to obtain the number of pieces in the vertical direction, the packed height was divided by the length of a side of the cube having a volume equal to the average volume for a piece of packing. The determination of effective interfacial area in the packed column is based on the following principle. Suppose a packed column and a bead column of an equal height show equal
Table II.
I
Run Series BW-1 BW-2 BW-3 BW-4 BW-5 BW-6 BW-7 BW-8 BM-1 BM-2
No. of Runs 10 14 8 10 8 12 7 8 9 8
and to extend application of this method to determination of the effective areas in packings such as Raschig rings and Berl saddles with use of k~ value's in bead columns as the criteria of comparison, on the assumption that the average k~ values on the effective surface of such packings approximate that of a bead column under comparable conditions. The effective area in absorption columns determined by Shulman and others (79) or the effective area in a water vaporization column estimated by Weisman and Bonilla (22) offer somewhat similar problems. The values they obtained are based on the average values of ka in naphthalene Raschig rings or in all-wet packings. Such average ka values might not be equal to the average values of kc on the effective surface in irrigated packings, and liquid velocity might affect ka values. According to Shulman and others (ZO), the effective areas in packed columns used for vaporization are larger than those for absorption columns, because semistagnant liquid pockets may be effective for vaporization but relatively ineffective for absorption. I t might be more appropriate, however, to distinguish between the effective area for gas phase, a in koa, and the effective area for liquid phase, a in kLa. T h e effective area obtained in the present work is that for liquid phase. Experimental When the bead column was used, the setup was the same as with the packed column, except for the column proper. Most parts of the equipment which came into contact with liquids were of glass; some were of stainless steel. The packed column, 12 cm. in inside diameter, was made of glass and was packed with 1- and 0.5-inch glass spheres, 25- and 15-mm. ceramic Raschig rings, and 25- and 12-mm. ceramic Berl saddles to heights of 8 and 1G inches. The glass spheres were frosted by emery powder in a rotating ball mill. The packing was supported by a stainless steel wire netting of coarse mesh. The
Runs with Bead Column Sphere Diam., Inch 1 1 1
1 0.5 0.5 0.5 0.5 1 0.5
No. of Spheres 16 16 16 8 32 32 32 16 16 32
Temp., Liquid Water Water Water Water Water Water Water Water Methanol Methanol
VOk. 50, NO. 3 4
O
c.
12
20 30 20 12 20
30 20
15 15
MARCH 1958
367
3
2
1.0
k
8
6
f 4
12'C. 20'C. 30'C.
0.2
IO
2
4
6
8
100
4
2
6
8 1000
4P -
r
Figure 1.
Effects of temperature and sphere diameter on
Figure 2.
Effects of number and diameter of spheres on
0 16 @
4r -
32
HL for bead column
HL for
I-IN
bead column
SPHERES
1/2-IN. SPHERES
6
r
Figure 3.
368
HL for
carbon dioxide-methanol in bead column
INDUSTRIAL AND ENGINEERING CHEMISTRY
8 1000
liquid distributor consisting of 1 9 glass nozzles extended down to the top of the packing. For fine adjustment of temperature, the column was enclosed in a water jacket made of transparent plastic. For the bead column shown, vertical rows of 8 and 16 spheres of 1-inch diameter and 16 and 32 spheres of 0.5inch diameter were used. The spheres were steel balls coated with sprayed metallic aluminum, to prevent slight dissolving of iron into water containing carbon dioxide. They were drilled through and connected in line by a stainless steel wire with clearances of 4 mm. between adjacent spheres for 1inch spheres and 2-mm. clearances for 0.5-inch spheres. The column wall consisted of two concentric glass cylinders, the annular space being used as a water jacket. Observations through the glass jacket ensured complete and uniform wetting of the spheres in all the runs. Presence of ripples at high Reynolds number and of pulse waves a t moderate Reynolds number was observed. Procedure. Carbon dioxide gas (9970 purity from a gas cylinder) was first passed through the gas preheater, a glass coil immersed in a thermostated bath, and then bubbled through the liquid in the jacketed humidifier, where the gas was saturated with the vapor of water or methanol. Thus the cooling of liquids in the column due to vaporization was prevented. The temperature of the gas entering the column was controlled within 0.5" C. of the liquid temperature a t the bottom of the column bottom. The rate of the gas introduced to the columns was not measured exactly, but it was always greater than 10 times the rate of gas absorbed in the column. Thus, the effect of the presence of inert gas stripped from liquid in the column was considered negligible. The gas not absorbed $vas purged from the column top. Because pressure in the column was slightly above atmospheric, the pressure difference was taken for each run and was added to the barometer reading to obtain absolute pressure. The solvents used, tap water and methanol, contained negligible amounts of carbon dioxide or any other substance which consumes barium hydroxide. The solvents were first preheated in the liquid preheater with electric heating elements, and then fine temperature adjustment was made at the temperature regulator by a thermostat. The temperature of the water to the jackets enclosing the columns was also regulated by a thermostat. The temperature of the solvent water a t the bottom of the column was adjusted to within 0.1' C. of 12', 20", or 30" C. The temperature of methanol at the bottom was kept a t 15" C., as reliable equilibrium data were available only at that temperature for the latter system. When water was used as the solvent, the top and bottom tempera-
PACKED COLUMNS tures agreed within 0.4' C. In the $uns with methanol the bottom temperature was slightly higher than the top temperature, owing to the heat of solution of carbon dioxidein methanol (3' C. a t most in packed column runs and less than O X 0 C. in bead column runs). The flow rates of liquids leaving the column were measured by measuring bulbs installed a t the exit piping and a stop watch. The methanol from the column containing carbon dioxide was pumped to a continuous distillation unit, in which carbon dioxide was stripped off, and then recycled. Each run took from a few to 90 minutes, depending upon liquid rate, to reach steady conditions. For liquid analysis, 20 ml. of sample were taken from the calibrated sampling buret connected to the liquid exit piping and run into a flask containing O.lh1 barium hydroxide solution, the excess base being titrated with standard hydrochloric acid and phenolphthalein indicator. In the methanol solution the reaction between carbon dioxide and barium hydroxide was so slow that titration was done after the sample was shaken for 5 to 12 hours. For determination of carbon dioxide in alcohols, the procedure of de Kiss, Lajtai, and Thury was used (70). The equilibrium data used in the calculations were those of Bohr (7) for carbon dioxide-water and of Kosakewitsch (72) for carbon dioxidemethanol. Discussion of Results
Tables I1 and I11 summarize runs made with the bead column and the packed column, respectively. The total number of runs was 238. Experimental results for each run are given in Tables I V to VI1 (Tables IV and V deposited with ADI). Generally speaking, the accuracy of the data was satisfactory. Reproducible data were obtained even after the packings were redumped. The values of H L were computed on the assumption that the resistance to mass transfer was wholly in the liquid phase HL
=
i
Z In
c* - c, c* - cz
~
(8)
where C, the concentration of entering liquid, was always zero. Values of C*, equilibrium liquid concentration, were obtained on the assumption that the gas was 99% pure. So far as the present data are concerned, the effect of the variation of C*, due to the change of the temperature of liquid as it flowed down, on the value of the number of transfer units is negligible, provided the value of C* for the bottom liquid temperature is taken. (H.T.U.), for Bead Column. HL values for the absorption of carbon dioxide by water in the bead column are
Table 111. Run Series
No. of Runs
PW-1
12 11 9
PW-2 PW-3 PW-4 PW-5 PW-6 PW-7 PW-8 PW-9 PW-10 PW-11 PW-12 PM-1 PM-2 PM-3 PM-4 PM-5 PM-6
9
8 7
8 7 8 6
7 7
5 6 9 8 10 7
Table VI. Liquid Rate, Ml./Sec.
Runs with Packed Column
Packing
Packed Height, Inches
Liquid
' c.
1-in. spheres 1-in. spheres 1-in. spheres 1-in. spheres 0.5-in. spheres 0.5-in. spheres 25-mm. rings 25-mm. rings 15-mm. rings 15-mm. rings 25-mm. saddles 12-mm. saddles 1-in. spheres 0.5-in. saddles 25-mm. rings 15-mm. rings 25-mm. saddles 12-mm. saddles
16 16 16 8 16 8 16 8 16 8 16 16 16 16 16 16 16 16
Water Water Water Water Water Water Water Water Water Water Water Water Methanol Methanol Methanol Methanol Methanol Methanol
12 20 30 20 20 20 20 20 20 20 20 20 15 15 15 15 15 15
Absorption of Carbon Dioxide by Methanol in Bead Columns Liquid Concn.,
lo-* G. COdM1. Bottom
Equilib.
No. of Transfer Units
Liquid Raw, Ml./Sec.
16 I-Inch Spheres, 15' C. (Series BM-1)
5.1
7.25 7.72 7.88 7.58 7.01 8.04 7.49 7.40 7.95
2.06 1.27 3.37 5.8 0.53 3.32 3.94 1.03
Table VII. Liquid Rate, Ml./Sec.
8.18 8.18 8.18 8.18 8.18 8.18 8.18 8.18 8.18
Liquid Concn., G. C o d M 1 . Bottom Equilib.
No. of Transfer Units
32 0.5-Inch Spheres, 15' C. (Series BM-2)
2.17 2.88 3.31 2.62 1.94 4.07 2.47 2.35 3.57
3.54 2.71 2.12 1.37 1.14 0.92 0.71 0.441
7.11 7.38 7.48 7.68 7.80 7.79 7.88 7.99
8.12 8.12 8.12 8.12 8.12 8.12 8.12 8.12
2.08 2.40 2.54 2.92 3.24 3.21 3.52 4.14
Absorption of Carbon Dioxide by Methanol in Packed Columns" Liquid Concn.,
lo-' G. COdM1. Bottom
Equilib.
Liquid Rate, Ml./Sec.
No. of Transfer Units
1-Inch Spheres (Series PM-1) 8.12 2.77 21.1 7.61 8.12 2.77 9.5 7.61 7.82 8.12 3.30 3.85 7.82 8.12 3.30 3.20 12.4 7.52 8.12 2.61 7.62 7.69 7.50 7.37 7.16 7.80
8.05 8.05 8.05 8.05 8.05 8.05
'
2.93 3.11 2.69 2.48 2.20 3.47
25-Mm. Raschig Rings (Series PM-3) 8.11 3.48 3.33 7.86 8.11 3.12 4.54 7.75 3.20 7.78 8.11 6.9 8.11 2.99 10.3 7.70 8.11 2.71 16.0 7.57 8.11 2.53 21.7 7.46 8.11 2.37 25.3 7.35 8.11 2.08 33.9 7.19 8.11 2.06 41.7 7.08
a Column diameter, 12 cm.; packed height, 16 inches; temperature, 15' C.
Liquid Concn., G. COdM1. Bottom Equilib.
No. of Transfer Units
15-Mm. Raschig Rings (Series PM-4)
0.5-Inch Spheres (Series PM-2) 11.8 15.2 27.4 38.5 55 10.4
Temp.,
'
4.11 5.8 7.4 9.6 20.0 23.5 31.3 41.7
7.90 8.00
7.97 7.79 7.79 7.68 7.52 7.36
8.17 8.17 8.17 8.17 8.17 8.17 8.17 8.17
3.41 3.87 3.71 3.07 3.07 2.81 2.53 2.31
25-Mm. Berl Saddles (Series PM-5) 3.10 4.21 5.2 7.7 10.5 12.9 16.1 18.5 26.7 37.0
8.00 7.91 7.91 7.87 7.82 7.86 7.64 7.60 7.37 7.37
8.15 8.15 8.15 8.15 8.15 8.15 8.15 8.15 8.15 8.15
3.99 3.53 3.53 3.37 3.21 3.34 2.77 2.70 2.35 2.35
12-Mm. Berl Saddles (Series PM-6) 5.0 6.9 12.7 15.2 20.0 25.0 56
7.99 7.95 7.94 7.86 7.92 7.84 7.54
VOL. 50, NO. 3
8.13 8.13 8.13 8.13 8.13 8.13 8.13
MARCH 1958
4.06 3.81 3.76 3.41 3.66 3.34 2.63
369
9
a 4~ ob
4 =“4> d
IV2-lN
PACKED COLUMN PACKEO HEIGHT 16
SPHERE
IN
0 25-MM. RASCHIC RING I 15-MM. RASCHIC R I N G A
25-MM
BERL
A 12-MM
SADDLE
BERL SADDLE
r r--i
--
-
HO ,
ZO’
C
‘A----
6 4
u
GI-
20
4
’
6
_____ I 8 100
2
LIQUID R A T E ,
Figure
plotted on a logarithmic scale against the average Reynolds number of water stream (Figure 1). KO effect of gas velocity on H L was seen for several runs, a t a constant liquid rate with gas velocities varying about sixfold. I n calculating H L values the clearances between the spheres were not included in the column height, because the absorption on the surface of the thin wire between the spheres was considered negligible. The curves in Figure 1 flatten out in the range of low Reynolds number. This may be partly due to experimental errors. The slope of the straight parts of the lines is 0.5. The temperature of liquid has a marked effect on HL. probably because of the change of liquid viscosity and diffusivity. Figure 1 also shows that 16 spheres of 1-inch diameter give HL values somewhat higher than 32 0.5-inch spheres a t given Reynolds number, although time of liquid-gas contact and total length of liquid travel are substantially equal in both cases. This seems to imply that stream lines are mixed a t the points of juncture between the spheres, in contrast to the conclusion of Lynn, Straatmeier, and Kramers (76). If no mixing took place, the liquid phase mass transfer coefficients or H L values for both sizes of spheres should be equal for a given contact time. That mixing a t the points
I COLUMN
-~ I 1
WATER
i -
z i j T i PACKING
01
2
DlAM
4
6
810
,
1 I
-,, --
1 i, 120” 12’
c
30’ C
2
4
6 8 l O O
2
4
Figure 6. Effect of temperature on HLfor carbon dioxidewater (sphere packings)
370
HL
of juncture is not complete is shown in Figure 2. Run series BW-2 with 16 1inch spheres shows higher H L values than BW-4 with eight spheres of the same diameter, and BW-6 with 32 0.5-inch spheres gives H L values greater than BW-8 with 16 spheres of the same diameter. If complete mixing of stream lines took place at the juncture points, the mass transfer coefficients or HL values should be independent of the number of spheres. Another possible explanation for the variation of HL with the number of spheres could be the existence of end effects. However, to attribute the variation of H L with the number of spheres solely to end effects, one must assume the existence of end effects equivalent to the action of several spheres, which is unlikely in the bead column used. Although end effects are conceivable, the variation of H L in the bead column with height seems, a t least partly, intrinsic as in wetted-wall columns. In short, some mixing of stream lines occurs a t the points of juncture between spheres, but the mixing is not complete, and the higher the column, the greater the H L values. H L values calculated from the data of Lynn, Straatmeier, and Kramers (16) on the absorption of sulfur dioxide by water are also plotted in Figure 2. The slight
3 SPHERE-PACKED
5.
INDUSTRIAL AND ENGINEERING CHEMISTRY
, I
6 8 I000 LB./SQ FTHR
4
A7
MeOH AT 15” C
2
4
6
8 IO000
vs. I for packed column 16 inches high
difference between the diffusivities of sulfur dioxide-water and carbon dioxide-. water systems cannot account for the surprisingly large difference between the data of Lynn and coworkers and the present data. Lynn’s large H L values might be due to the addition of a surface active material to water in all runs with the bead column, although it had no observable effect on the mass transfer rates in the short wetLed-wall column (75). Addition of a surface active material might change the liquid flow pattern in a bead column, especially in the vicinity of juncture points, thus affecting mass transfer rates. The effects of liquid physical properties such as viscosity and diffusivity or of the Schmidt number on HL can be studied by either varying liquid temperature or using various liquids. Dimensional analysis leads to the following equation :
which is of the same type as Equation 2a. The value of the exponent on the Schmidt number cannot be determined by a simple cross plot from the graph of H L vs. the Reynolds number, unless p and p are constant. I n the case of a packed column one cannot determine the exact value of the exponent on the Schmidt number without knowledge of effective
PACKED COLUMNS 3
3
I
RASCHIG RING - PACKED COLUMN WATER A T 20' C
10
+
k 6 2 -
AT
20'
c
I
1.0
8
c
WATER
I
I I ;
I
2
E
1.6
I4
4
2
2
01
4 L -
0.11
! !6b
Pat
Figure 8. H L for carbon dioxide-water with Raschig rings, 16 and 8 inches high
interfacial area, because this is involved in the Reynolds number. Thus, the bead column is useful for determining the effect of the Schmidt number, because it has a known interfacial area and a liquid flow pattern similar to that in packed columns. The data for two series of runs, BM-1 and BM-2, with methanol as solvent are plotted in Figure 3. The HL values for carbon dioxide-methanol are considerably lower than those for carbon dioxidewater, because the Schmidt number for the former system is much smallerbthan for the latter a t a given temperature. I n computing the Schmidt number, liquid diffusivities were estimated by the Wilke correlation (23). The value of the exponent on the Schmidt number in Equation 9 was determined by cross plots from the graph of HL/(p2//p2g)'la us. the Reynolds number, by carbon dioxidewater data a t various temperatures and carbon dioxide-methanol data at 15' C. The value of q is 0.5 in the range of Reynolds numbers above 100 but smaller than 0.5 in the range of low Reynolds numbers. This might appear strange, but it means that the effect of diffusivity
= G
4L
Figure 9. HL for carbon dioxide-water with Berl saddles, 16 inches high
[(Re) (Sc)]OJ
(9a)
where the value of c is 18.2 for 16 spheres of 1-inch diameter, 17.0 for eight spheres of 1-inch diameter, 16.5 for 32 spheres of 0.5-inch diameter, and 14.7 for 16 spheres of 0.5-inch diameter.
'H
(H.T.U.)L for Packed Columns Figure 5 shows HL values plotted against superficial mass liquid rates, L, on a logarithmic paper for carbon dioxidewater at 20" C. and cai-bon dioxidemethanol at 15" C. The values for carbon dioxide-methanol are considerably lower than those for carbon dioxidewater, mainly owing to the difference in the Schmidt number. At given temperatures and liquid rates, HL values increase in the order of 12-mm. saddles, 15-mm. rings, 0.5-inch spheres, 25-mm. saddles, 25-mm. rings, and 1-inch spheres for carbon dioxide-methanol. The order of the last two packings is reversed for carbon dioxide-water. HL values of carbon dioxide-water are in good agreement with the Sherwood-Holloway data. The effect of temperature on H L can be seen from Figure 6. The curves are shaped somewhat like those for the bead column but have smaller slopes. Difference in slopes is due to variation of effective interfacial area in the packed column with liquid rdtes. The effect of gas velocity on HL values or effective area was not studied with
RASCHIG RING-PACKED WATER
COLUMN
I 2 LIQUID RATE, CU. FT./SQ. FT. HR. Figure 10. Fractional effective area in sphere-packed column irrigated with water
,
6 io L
Pat
on k L is greater where the Reynolds number is small. The exponent on the Reynolds. number is also small in the range of low Reynolds number. A tentative plot was made with HA/ (pz/lpzg)l~~ as ordinate and the product of the Reynolds and the Schmidt numbers as abscissa on a logarithmic scale (Figure 4). The data points for both systems at various temperatures come roughly on a single line, although the points for eight spheres lie slightly below the line, as would be expected. Surface tension appears to have little effect on liquid phase mass transfer rates in bead columns, although there is considerable difference in surface tension between water and methanol. The correlation for H L in bead columns in the range where the product of R e and Sc is greater than 40,000 can be expressed by i7L/($)1'8
L
! -
4
LIQUID
6
RATE,
8 IO
2
CU.FT./SQ.FT
4
I 6
I
1
8100
I
200
HI.
Figure 1 1. Fractional effective area in Raschig ring-packed column irrigated with water VOL. 50, NO. 3
MARCH 1958
371
'
BERL SADDLE- PACKED C O L U M N WATER I
4
I
,
I
1
I l l
I
I
1
/ , I
~
-
aat e !
1
1
~
,
{ I
I
1
I 2
+-
,
I
I
a
___
. I -~
y'
,O/i0
A
01 8
6
'
4
I
/o
I
SIZE MM
o'T/G / I
Q
I
2
4
I
6
-
P A C K I N G PACKED -
-1
2
OO'bs
I
/e-
/
HEIGHT
0
25
IN 16
___A
12
16
2
6 IO
4
6
I
8 100
7
200
Figure 12. Fractional effective area in Bed saddle-packed column irrigated with water
the packed column but was assumed negligible in view of the results of Sherwood and Holloway (78). Gas velocities in the present experiments were far below the velocities corresponding to loading conditions. Gas velocity might affect H L values in the region of loading or at very high liquid rates, as shown by Cooper, Christl, and Peery (2). Figure 7 shows the HL values for carbon dioxide-water at 20' C. plotted against superficial Reynolds number. As in the bead column, the deeper the packing, the greater the H L values. To attribute the variation of H L IO end effects alone one must assume end effects equivalent to about 6 inches of packed height. This value seems to be too large in view of the value obtained with a column of similar size (24)-i.e., about 2 inches. The difference in HL values with packed heights results partly from end effects and partly from the intrinsic variation of HL with heights as in the bead column. However, the variation of HL in the packed column with height is slightly larger than in the bead column. This may be attributed partly to larger
8
I
I
I
R I N G - P A C K E D COLUMN METHANOL AT 15 ' C
RASCHIG
end effects and partly to the fact that the deeper the packing, the poorer the liquid distribution. Although definite conclusions cannot be drawn from the data for only two packed heights, in deep packings used in industrial equipment HLvalues should be considerably higher than in experimental columns. Sherwood and Holloway (78) state that no effect of packed height was seen with a column in which end effects were eliminated. Nevertheless, a careful examination of their unplotted data reveals some trend with packed heights. Figure 8 is a plot of HL us. the superficial Reynolds number for carbon dioxide-water. The H L values for two sizes of Raschig rings fall on common lines when plotted against the superficial Reynolds number, but this seems to be a mere coincidence. Figure 9 shows HL values for carbon dioxide-water a t 20' C. Comparison of Figures 7, 8, and 9 shows the relative magnitude of HL values for three types of packings at given values of the superficial Reynolds number. Similar plots were obtained for carbon dioxidemethanol but are not shown.
-1
Figure 13. Fractional effective area in sphere-packed column irrigated with methanol
-'--I
--
'1-I
Effective Interfacial Area in Packed Columns
The effective interfacial areas in the packed column were determined on the principle outlined. The HL value for a run of series PW-2 (packed column, carbon dioxide-water at 20" C., I-inch spheres, 16 inches deep) is 0.728 foot at the superficial Reynolds number of 23.2. Then, by use of the correlation of HL u'. the true Reynolds number (Figure 1 or 2) for run series BW-2 (bead column, carbon dioxide-water at 20' C., 19 spheres of 1-inch diameter), the true Reynolds number which gives the HL value of 0.728 foot is found to be 112. The fractional effective interfacial area is computed by Equation 7a. n,/at =
23.2/112 = 0 207
Thus, values were calculated for all the runs with the packed column. The effective areas for 1-inch spheres, 25mm. Raschig rings, and 25-mm. Berl saddles were obtained from comparison with data for the 1-inch bead columns of equal heights, and the effective areas for 0.5-inch spheres, 15-mm. Raschig rings,
- PACKED
BERL SADDLE METHANOL
AT
LIQUID
COLUMN 15 'C
RATE,
CU.FT./SQ.
FT.
HR.
Figure 15. Fractional effective area in Berl saddle-packed column irrigated with methanol
372
INDUSTRIAL AND ENGINEERING CHEMISTRY
PACKED COLUMNS a 6
100 8
PACKED COLUMN WATER
METHANOL
6
AT
15' C
4
c LA. a e 2 L c
v7 a
10
' 8
d
6 4
2
LIQUID
Figure 16. water
RATE
,
6
8
1
2
CU.FT.ISQ.FT.HR.
Effective area in packed column irrigated with
and 12-mm. Berl saddles are based on the 0.5-inch bead column data. Figure 10 shows fractional effective areas plotted against superficial volumetric liquid rates, L/p, for the water-irrigated column. The fractional effective area for a given packing is considerably larger for 8-inch than 16-inch height. This apparently large variation could be partly explained if end effects of different magnitudes-2 inches for the packed column and 0.5 inch for the bead column -were assumed. If end effects of equal magnitude were assumed for both packed and bead columns, it would make no difference in the calculated values of effective area. It is also conceivable that liquid distribution becomes worse as the packed height increases. The data for the 16-inch bed may be more reliable than for 8-inch bed, because relative end effects are less in the deeper bed. Definite conclusions could be reached only after experiments with several packed heights. The fractional effective area for 0.5inch spheres is considerably smaller than that for 1-inch spheres, probably because smaller packings have larger static holdups which exist as pockets of semistagnant liquid. Fractional effective areas for a given packing a t various liquid temperatures fall on a single line when plotted against volumetric liquid rates. In correlating effective area, there is no reason to suppose that the mass liquid rate, L, or any form of the Reynolds number should be used in preference to the volumetric liquid rate. Figure 11 is similar to Figure 10 for the column packed with 25- and 15-mm. Raschig rings. Trends with packed heights and the packing size are the same as in Figure 10. Figure 12 is a plot of fractional effective area against volumetric liquid rates for the water-irrigated column. The 12-mm. saddles show much smaller values of a,/at as compared with 25-mm. saddles. Figures 13, 14, and 15 plot fractional
4
LIQUID
6 8 IO RATE
,
4
2
6
8100
2
CU. FT./SQ.FT.HR.
Figure 17. Effective area in packed column irrigated with methanol
effective areas us. volumetric liquid rate's, for the methanol-irrigated column. Trends with the packing size are the same as in the column irrigated with water. Values of a,/at are always higher than for the water-irrigated column under comparable conditions, as was expected, since the surface tension of methanol is about one third that of water at the same temperature. Figure 16 shows the values of the effective interfacial area per unit packed volume plotted against superficial volumetric liquid rates. The values of effective area do not vary greatly with the size and type of packings, despite considerable difference in total surface area. The effective areas for 25-mm., or 1-inch, packings are greatest for Berl saddles and least for Raschig rings, with spheres intermediate. Figure 17 is similar to Figure 16, for runs irrigated with methanol. Variation of effective area with size and type of packings is relatively small. Effective areas for 25-mm. packings are greatest for Berl saddles and least for spheres, with Raschig rings intermediate. The value of the surface tension of methanol is about 25 dynes per cm. a t 20' C. This is a fair average of the values of most organic liquids, which lie in a rough range of 20 to 30 dynes per cm. Figure 17 could be used for rough estimation of effective interfacial area for most organic liquids. However, the nature of the surface of packing materials also affects wetted and effective areas. Comparison with Previous Data Figure 18 compares the present data on the effective area with the data of previous investigators on effective and wetted areas in Raschig rings irrigated with water (6, 7, 74, 77, 79). As expected, the fractional wetted areas are larger than the fractional effective areas, except the data. obtained by van Krevelen and others, which are doubtful. The effective areas obtained
in the present work are in rough agreement with those determined by Shulman and coworkers, using an entirely different method, which show a slight effect of gas rates; this effect could be neglected in practical problems. Figure 19 shows how closely the present data agree with previous data on liquid phase mass transfer rates in packed columns (3, 9). Values of effective interfacial area were estimated by use of Figure 11 or 16. Thus true Reynolds number, 4L/a,p, was computed for all runs of the previous studies. Then, the HL values were plotted against the true Reynolds number and compared with the present correlations for bead columns indicated by A , B, C, and D in Figure 19. The slight difference in the Schmidt number between oxygen-water and carbon dioxide-water systems may be neglected. Although careful check of the previous data shows some trend with packed heights and packing size, Figure 19 seems to demonstrate the general applicability of the method of correlation proposed. Conclusions Data on the absorption of carbon dioxide by water and methanol in a bead column, with absorption data for the same systems in a packed column, offer information on variation of liquid phase mass transfer rates in packed columns with liquid rates and properties of liquids and variation of effective interfacial areas in packed absorption columns with liquid rates. If effective area could be estimated by use of correlations such as presented here, experimental data on a bead column would be useful for prediction of liquid phase mass transfer rates in columns packed with packings of the same size as the spheres. Thus, if liquid phase mass transfer rates for a new system are needed for design of a packed column, costly experiments with a packed column are unnecessary and data may be obtained with a bead VOL. 50, NO. 3
0
MARCH 1958
373
r
= liquid rate per unit length of
/I
p
wetted periphery, lb./(ft.) (hr.1 = liquid viscosity, lb./(ft.) (hr.) = liquid density, Ib./cu. ft.
literature Cited (1) Bohr, C., in “International Critical Tables,” vol. 111, p. 260: McGrawHill,NewYork, 1928. (2) Cooper, C. M., Christl, R. J., Peery, L. c., Trans. Am. Inst. Chem. Engrs. 37, 979 (1941). (3) Deed, D. W., Schutz, P. W., Drcw, T. B., IKD. Exc. CHEM.39, 766
_____
0.0 1 k l
I
Figure 18.
k
L - d 6
810 LIQUID
4 ,k
RATE
1,
LIL
CU FT. /5Q.FT. HR.
d
WETTED EFFECTIVE
(1947). (4) Fellinger, L., Sc.D. thesis, hfassachusetts Institute of Technology, 1941; Perry, T. H., “Chemical
AREA AREA
8Ik-A
6
Comparison of effective and wetted areas by various investigators
column containing spheres of appropriate size. The investigation reported is preliminary and the variations in effective area and/or height of liquid phase transfer unit with height of column should be analyzed before direct applicability of this method can be established. Further studies should be made with larger packings and with various packed heights.
cz
=
C*
=
C
D
= =
d
=
dP
=
=
concentration of leaving liquid, lb. (solute)/cu. ft. (solution) equilibrium liquid concentration, Ib. (solute)/cu. ft. (solution) constant in Equation 9 liquid diffusivity, sq. ft./hr. sphere diameter, ft. diameter of sphere possessing the same surface area as a piece of packing, -- ft. acceleration due to gravity = 4.17 X 108 ft./(hr.) (hr.) (H.T.L.)L-i.e., height of a liquid phase transfer unit, ft. mass transfer coefficient for gas phase, lb. moles/(hr.) (sq. ft.) (atm.) mass transfer coefficient for liquid phase, lb./(sq. ft.) (hr.) (lb./ cu. ft.) superficial mass velocity ofliquid, lb./(hr,) (sq. ft.) exponent in Equation 1 exponent in Equation 9 exponent in Equation 9 liquid phase Reynolds number liquid phase Schmidt number liquid flow rate in bead column, lb./hr. column height. ft. constant in Equation 1 ~r
Acknowledgment
=
Thanks are due Yoshikazu Torigoe and Ryuzo Kimoto for assistance in the experimental work.
=
Nomenclature a, a, = effective interfacial area per unit packed volume, sq. ft./cu. ft. at = total surface area of packings per unit packed volume, sq. ft./ cu. ft. = wetted area of packings per unit a, packed volume, sq. ft./cu ft. b = wetted periphery, ft. C = liquid concentration, lb. (solute)/ cu. ft. (solution) C1 = concentration of entering liquid, lb. (solute)/cu. ft. (solution)
kL
=
L
=
n
= =
P Q
Re
sc
= =
=
W
=
Z
=
C Y
=
V
I
PACKED COLUMN DATA 0, DESORPTION AT 25‘ C
A SHERWOOD a HOLLOWAY
c
i
18)
i
pe
0
/
LINES A
16
B C
8 32 16
D
374
INDUSTRIAL AND ENGINEERING CHEMISTRY
FOR
BEAD
COLUMNS
I -IN. SPHERES 1 -IN.
0.5-IN. 0.5-IN.
SPHERES SPHERES SPHERES
3
Engineers’ Handbook,” 3rd ed., p. 688, McGraw-Hill, New York, 1950. ( 5 ) Fu’ita, S., Hayakawa, T., Chem. Eng. [Japan) 20, 113 (1956) (in Japanese). ( 6 ) Fu’ita, S., Sakuma, S., Zhid., 18, 64 (1954) (in Japanese). (7) Grimley, S. S., Trans. Inst. Chem. E n z s . (London) 23, 228 (1945). (8) Higbie, R., 7‘raiis. Am. Inst. Chem. Engrs. 31, 365 (1935).
( 9 ) Jones, C. H., B. Chem. Eng. thesis, Cooper Union, 1946; cited in ( 3 ) .
(IO) Kiss, A. de, Lajtai, I., Thury, G., Z. anorg. u. allgem. Chem. 233, 346 (1937). (11) Kling, G., Chem.-Zng.-Tech. 25, 557 (1953). (12) Rdsakewitsch, P. P., 2.physik. Chem. A143,216 (1929); Seidell,A.,“Solu-
bilities of Inorganic and Metalorganic Compounds,” 3rd ed., vol. I, p. 234, Van Kostrand, New York,
1940. (13) Krevelen, D.
W. van, Hoftijzer, P.
J., Chem. Eng. Progr.
44,
529
(1948).
(14) Krevelen, D. W. van, Hoftijzer, P.
J., Van Hooren, C. J., Rec. trav. chim. 66, 513 (1947). (15) Lynn, S., Straatmeier, J. R., Kramers, H., Chem. Eng. Sci. 4, 58 (1955).
(16) Ibid., p. 63. (17) Mayo, F., Hunter, T. G., Nash, -4. W., J . Sac. Chem. Znd. (faondon) 54, 375 T (1935).
(18) Sherwood, T. K., Holloway, F. A. L., Trans. Am. Inst. Chem. Engrs. 35, 39 (1940). (19) Shulman, H. L., Ullrich, C. F., Proulx, A. Z . , Zimmerman, J. O., A.I.Ch.E. Journal 1, 253 (1955). (20) Shulman, H. L., Cllrich; C. F., Wells, K., Ihid., p. 247. (21) Stephens, E. J., Morris, G. A., Chem. Eng. Progr. 47, 232 (1951). (22) Weisman, J., Bonilla, C. F., IND. ENG.CHEM.42, 1099 (1950). (23) Wilke, C. R., Chem. E n g . Progr. 45, 218 (1949). (24) Yoshida, F., Chem. Eng. Progr., Symposium Ser. No. 16, 59 (1955).
RECEIVED for review August 20, 1956 ACCEPTED April 15, 1957 Study supported in part by the Science Research Grant from the Ministry of Education, Japan. Material supplementary to this article has been deposited as Document No. 5502 with the AD1 Auxiliary Publications Project, Photoduplication Service, Library of Congress, Washington 25! D. C. A copy may be secured by citing the document number and by remitting $1.25 for photoprints or $1.25 for 35 mm. microfilm. Advance payment is required. Make checks or money orders payable to Chief, Photoduplication Service, Library of Congress.
