April, 1941
INDUSTRIAL AND ENGINEERING CHEMISTRY
Literature Cited
485
(IO) McAdams, W. H., “Heat Transmission”, New York, McGraw-
Arnold, J. H., J . Am. Chem. SOC.,52, 3937 (1930). Conklin, L. H., Jr., and Sauer, T. C., Princeton Univ., B.S. thesis in chem. eng., 1940. Fage, A., and Townend, H. C. H., Proc. Roy. Soo. (London), A135, 656 (1932). Gilliland, E. R., and Sherwood, T. K., IND. ENQ.CHEM.,26,516 (1934). Gunness, R.C., and Baker, J. G., Ibid., 30, 497 (1938). Hall, W. T., “Textbook of Quantitative Analysis”, 2nd ed., p. 119, New York, John Wilcy & Sons, 1930. Hixson, A. W., and Crowell, J. H., IND.ENQ.CHEM.,23, 923, 1002, 1160 (1931). Hixson, A. W., and Luedeke, V. D., Ibid., 29, 927 (1937). Hixson, A. W., and Wilkens, G. A., Ibid., 25, 1196 (1933).
Hill Book Co., 1933. (11) McBain, J. W., and Liu, T. H., J . Am. Chem. SOC.,53,59 (1931). (12) Muer, H. F.,J. IND. ENQ.CHEM.,3,553 (1911). ComDounds”. (13) Seidell. Seidell, A.. A,, “Solubilities of Inorganic and Organic Compounds”, New York. D. Van Nostrand-Co.. New’ Nostrand Co.. 1919. (14) Sherwood, T; K., “Absorption and Extraction”, Chap. 2, New York, McGraw-Hill Book Co., 1937. (16) Sherwood, T. K.,and Woertr, B. B., Trans. Am. Inst. Chem. Engrs., 35, 517 (1939). (16) Walker, W. H., Lewis, W. K., McAdams, W. H., and Gilliland. E. R., “Principles of Chemical Engineering”, p. 504, New York. McGraw-Hill Book Co.. 1937. (17) White, A. M., Brenner, E., Phillips, G. A., and Morrison, M. S., Trans. Am. Inst. Chem. Engrs., 30, 570 (1934); White, A. M., and Brenner, E., Ibid., 30, 585 (1934); White, A. M., and Sumerford, S. D., Chem. & Met. Eng., 43, 370 (1936).
. ,
Rate of Absorption of Ammonia by Water in a Packed Tower ORRINGTON E. DWYER1 AND BARNETT F. DODGE Yale University, New Haven, Conn.
The rate of absorption of ammonia from air by water was studied i n a I-foot-diameter tower packed with darbon Rarchig rings. The effect of gas rate, liquor rate, temperature, size of rings, degree of humidification of inlet gas, and reproducibility of a given tower filling were invertigated. Results are expressed as over-all transfer coefficients. Individual film coefficients have also been calculated using the liquid film correlation of Sherwood and Holloway. The effect of humidity of the entering gas was found t o b e minor. Redumping of the I-inch rings had a negligible effect on the coefficient. Increase i n temperature decreased the over-all coefficient. The calculated gas film coefficient also decreased with temperature, contrary t o what was expected. The effect of flow rates was correlated by the equation,
HE rate of absorption of ammonia from air by water T has been the subject of several investigations, but at the time the present work was started there were no data on this system using Raschig ring packing. One of the subjects of this study was to remedy this deficiency and to present data on absorption coefficients for this system as a function of several of the important variables, such as rate of gas flow, rate of liquor flow, size of packing ring, and temperature. Another object was to study certain factors which, while not major variables that would appear in a correlation of results, might have an important practical bearing on the problem. The first is the reproducibility of the coefficients for different fillings of the tower with a given packing; the second is the effect of humidification of the inlet gas; and a third is the effect of length of the column of packing or, putting it another way, the inI
Present address, University of Rochester, Rochester. N. Y.
with the following values of the constants at an average temperature of 85’ F.: Ring
Size, In. ‘/a
1 1‘/2
7
0.0065 0.036 0.014
n
t
0.90 0.71 0.12
0.65 0.18 0.18
m 0.39 0.20 0.38
e
0.310 0.103 0.093
This equation indicates that both gas and liquid rates affect the gas film coefficient but only the liquid rate i s important in the case of the liquid film coefficient. Over-all coefficients varied from 3.5 to 16 pound moles/ (hour) (cubic foot) (atmosphere). The effect of packing size on the over-all coefficient was approximately as the 0.45 power of the superficial area. Gas film resistance could not be said to b e controlling under any of the conditions used, since i t varied from 40 to 90 per cent of the total resistance. The relative resistance of the two films was independent of packing size.
fluence of entrance and exit effects. I n the present paper data only on the first two of these factors are reported. The ideal goal toward which investigators in the field of gas absorption have been striving is an assemblage of data on rate coefficients for the two individual films and a correlation of these data with the main variables assumed t o affect the individual fXm resistance, such as gas flow, liquor flow, diffusivity, viscosity, density, and possibly surface tension. When this program is completed, it is assumed t h a t the over-all coefficient for any case not complicated by chemical reaction may be calculated from the correlations and used to determine the necessary tower size for a specific duty. This relatively simple picture of the mechanism of absorption, based largely on an analogy t o heat transfer, may be an oversimplification of the true situation. Absorption is a more complex process than heat transfer, and no one has been able to devise a truly satisfactory way of determining film
486
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 33, No. 4
Johnstone and Williams (12) reported on the absorption from air by single drops of water. Kowalke, Hougen, and Watson (13) and Hixson and Scott (9) reported results for spray towers. The principal studies on packed towers, with which we are more particularly concerned, are summarized in Table I. The results of these various investigations are in fair agreement on some points and a t variance on others. The following discussion is an attempt to depict in brief form the state of our previous knowledge on the absorption of ammonia. RELATIVERESISTANCE OF THE Two FILMS.The work Scope of Investigation on wetted-wall towers indicated that practically all of the The variables studied and their limits of variation may be resistance to absorption was in the gas film, even a t high gas summarized as follows: velocities. Most of the investigators who have studied absorption of ammonia in spray towers, in single drops of liquid, GASFLOW RATE. 100 to 1000 pounds/(hour) (square foot) at in stirred or quiescent batches of liquid, and in packed constant liquor rate of approximately 500. towers have either assumed that the gas film was controlling LIQUORFLOWRATE. 100 t o 1000 pounds/(hour) (square foot) at constant gas rate of approximately 500. or interpreted their results as indicating that such was the PACKING. l / ~ - ,1-, and l'jn-Raschig rings; 48-inch depth of case. Johnstone and Singh (11), however, had added acid packing used in all runs. to the absorbing water to ensure that the gas film would conTEMPERATURE. Average gas temperature varied from 74' to trol. Practically the only dissenting voice prior to very recent 88" F. and liquor temperature from 74" t o 98.5" F. The variation in gas temperature was not systematic but wm a chance one investigations was that of Whitman and Davis (19) whose caused by conditions not under control, whereas some systematic experiments indicated that there was an appreciable resistvariation was attempted in the case of the liquor. ance in the liquid film. The results recently reported by HUMIDIFICATION AND REFILLING.Two series of runs were Sherwood and Holloway (16), on absorption both in acid and made with 1-inch rings on each of two fillings of the tower with the same lot of rings. In one of each series the entering gas had in water, confirm this fact. Much more remains to be done the humidity of the revailing laboratory air, and in the other before any definite conclusions are warranted. the air was humidifiezto such a point that the liquor temperature EFFECT OF GAS FLOW RATE. All investigators agree that remained substantially constant. the gas rate has considerable effect on the gas film absorption coefficient but there is disagreement on the quantitative efPrevious Work on Ammonia Absorption from fect. Most of the work in wetted-wall towers indicated that Gases by Water and by Dilute Acids the coefficient was proportional to the 0.8 power of the gas rate, which was consistent with the analogy between heat Whitman and Davis (19),Monaweck and Baker (14),and transfer and mass transfer. The extensive work of Hollings Hanks and McAdams (6) investigated the absorption of and Silver (IO), however, gave an exponent of 0.56. Sherammonia from air by a stirred body of water. Haslam, wood (16) accounts for the lower value by the fact that they Hershey, and Kean ( Y ) , Cogan and Cogan (S), Hanks and used a helix in their gas inlet line to promote turbulence in the McAdams (6),and Hollings and Silver (IO) absorbed amtower. On the other hand, on this basis the exponent for a monia from air by water in a wetted-wall tower. Hanks and packed tower should be still less, but the data of Kowalke, McAdams also used hydrogen and butane as the carrier gas Hougen, and Watson (IS) were correlated by Sherwood and Hollings and Silver used city gas as well as air. The (16) using an exponent of 0.8. Furthermore, the extensive latter two also used dilute sulfuric acid as absorbent. Whitdata of Johnstone and Singh on air humidification, interman, Long, and Wang @O), Hatta, Ueda, and Baba (8) and preted by them as absorption coefficients through the use of the Chilton-Colburn analogy (11), gave values of 0.8 for most of their packings and 0.95 for 1-inch Raschig rings. However, their depth of packing was only 6 inches, and entrance and exit effects must have been appreciable, though it is by no means clear how this would affect the exponent. The recent work reported by Sherwood and Holloway (16) indicated exponents of G of 0.5 to 0.55 for 1-inch rings. I n this discussion of effect of gas rate, one should distinguish between the effect on the gas film coefficient and on the over-all coefficient; but in the present confused state of our knowledge on the relative resistances of the two films in any given case, this cannot be done. All measurements have been made on over-all coefficients, but many of the authors have interpreted their results in such a way as to give what they considered to be the effect on the gas film coefficient. EFFECT OF LIQUOR FLOWRATE. Liquor flow rate has an effect on the over-all coCourteay. American Hard Rubber Company efficient for ammonia absorption in a packed tower but it is generally agreed t o be less than AMMOWLA STORAGE TANKS coefficients. Until recently most workers in this field have assumed that in most cases of ammonia absorption in water the gas film controlled, and that the over-all coefficient, KG, was equal t o the gas film coefficient, kG. Recent work has cast doubt on the validity of this assumption, at least for a packed tower. The results of this investigation will be reported as over-all coefficients, but analysis of the results will involve the two-film concept and some of the common relations resulting from it.
INDUSTRIAL A N D ENGINEERING CHEMISTRY
April, 1941
OF INVESTIQATIONS ON THE ~ TABLEI. SUMMARY
Citation Column Packed No. Diam. Height Investigators Inchee Inches Sherwood & Kilgore (18) 4 42
T OFE
Packing Material Inches Coke, 0.35-0.63
Solvent Water
ABSORPTION OF AMMONIA IN PACKED TOWERS Liquor Rate Gas Rate Lb./(hr.)(UP. ft.) Constant 149-507 at 323
Temp. O F.
(13)
16
41
Quarta, 1.25-1.75
Water
(13)
16
41
Water
Same Johnstone & Sin&
!;:{
.:I
41
Spip! tile 3 &partition An&, 4 Wood grids Wood grids
Spheres, I/a, stone, 1/4, Same Spheres a/& Rings, i
Water
500
400-550
72.81
Water Water Water
600 495 570-830
72-81 72-81 77
660-710, 1750 1520-1850
400-550 400-550 55-530 65-700
Chilton, Duffeu, & Vernon Same Same Sherwood & Holloway
(16)
10
Same
(16)
10
Same
(26)
Same
(18)
(5')
3
(d
6
(81
11.3
100 48-54 45 19-31
SI4, 1; 1/a
Water
0.3 N HAo
Rings, 1
Water
10
19-31 19-31
Rings, 1
10
19-31
Rings and Berl saddles, 0.5,1
0.5-4.5N Has01 3.5-4.5N HoSOc
t h a t of gas rate. Kowalke, Hougen, and Watson (IS) found t h a t for certain packings the coefficient increased a t first but soon reached a constant value, whereas for other packings the coefficient continued to increase up to the highest rates they used, 900 pounds/(hour) (square foot). Hollings and Silver (IO) found no effect of liquor rate on ammonia absorption in a wetted-wall tower. The data reported by Sherwood and Holloway (16) showed t h a t for absorption in water KQu varied as L to the 0.35-0.40 power, but experiments with sulfuric acid as absorbent showed the coefficient t o be almost independent of liquor rate in the range of L from 1200 t o
$600. The effect of liquor rate has been variously interpreted as influencing principally the liquid film coefficient, to a lesser extent the gas film coefficient, and sometimes as being due chiefly to an effect on the distribution over the packing and hence on the active surface of packing. EFFECT OF DIFFUSIVITY, D,OF THE GAS. This is of consequence primarily when comparing the absorption of ammonia from air with some other system, but it does have a definite bearing on the present discussion. For example, t h e extensive work of Johnstone and Singh (11) was mainly concerned with heat transfer in air humidification, and the correlation with absorption depended on the diffusivity. The Chilton-Colburn analogy equation assumes that k~ varies as the power of D; Gilliland and Sherwood (6)correlated their results on vaporization of liquids in a wetted-wall tower o n the basis of kQ proportional to the 0.56 power of D; the results of Hollings and Silver (IO) gave the same exponent. T h e recent results of Mehta and Parekh reported by Sherwood and Holloway (16)indicate that in a packed tower the diffusivity has much less effect and the exponent is about 0.17. The effect of D in a packed tower is deilnitely an open question. The effect of temperature on EFFECT OF TEMPERATURE. 'the over-all coefficient, KQ,is composed of three individual , on b,and effect on the solubility effects: effect on k ~ effect (measured by H ) . Sherwood (16)concludes t h a t bo is proportional to the square root of the absolute temperature a t a given Reynolds number. From the Gilliland-Sherwood equation for film thickness based upon the vaporization of liquids in a wetted-wall tower-namely
-d
=
constant
16-570
25-800 21-670 1100
75-480
6-240
6-240 19-240 1180-2780
211
68-110 68-110
.... ....
54 77
....
3300
Remarks Desorption also studied
70-90
Kowalke, Hougen, & Watson Same
...
487
............... .................. ..................
Heat transfer data for humidification of air using the same and othkr packings (jnoluding 1-in Rasehi rings). correlated well w.ttt: the absorption data using Chilton-Colburn Analogy relation
..................
.................. ..................
Work of Borden and Squires, first work on Rasohig rings Work of Doherty and Johnson
Work of Doherty and Johnson Work of Withers
and from the definition of the gas film coefficient based upon the Maxwell diffusion concept-namely k~ = DP/RTx P B M
(2)
and the fact t h a t p is proportional to 1/T and D is proportional to T1.6,we can derive T0.28
k~ = constant
--p
(3)
for a given mass velocity, pressure, and size of packing, assuming ideal gases and low concentration of solute gas. Since ,u of air is approximately proportional to we may conclude that kG should be nearly independent of 1 46 the temperature. I- 4 4 If we change the exponents in Equation 1 to 0.60 and 0.20, re$ 36 spectively, in accordance with 34 the recent work on packed towers, the con' 88 c l u s i o n is un% 70 75 80 90 # changed. I TEMPERATURE 'F. H&lam, HerFIGURE 1. EBFECTOF TEMPERATURE shey, and Kean ON LIQVID FILMCONDUCTANCE (7) found that KQ for absorption of ammonia in water decreased as temperature increased and from their results deduced the fact t h a t k~ varied inversely as P4.Kowalke, Hougen, and Watson (IS) confirmed the fact that KQ decreases as temperature increases. There is little doubt that k~ increases with temperature but H decreases, and the net result on the liquid film resistance, 1 / H k ~may , be either an increase or a decrease. I n the case of the ammonia-water system the liquid film conductance (reciprocal of resistance) decreases with increase in temperature as shown in Figure 1. The method by which the values in this figure were calculated will be explained later under LLDiscussionof Results". If the gas f ilm were con-
2
5 :E
-
ma
INDUSTRIAL AND ENGINEERING CHEMISTRY
trolling, KG should be practically independent of temperature. The fact that it decreases would appear to be good evidence that gas 'dm is not, in general, controlling for the absorption of ammonia in water.
Vol. 33, No. 4
CORRELATIONS. Sherwood (16) correlated most of the data for the case where the gas film was assumed to be controlling by the relation, Koa =
yGQ.8
(4)
where y is a function of liquor rate, packing, and temperature. For room temperature and liquor rate of 500 pounds/ (hour) (square foot) y varied between the limits 0.057 and 0.147, depending on the packing. Sherwood and Holloway (16) combined the effects of both gas and liquor rate in the relation : Kaa = y G n L m
(5)
The data of Borden and Squires gave n = 0.5 and m = 0.4 for 1-inch carbon rings.
Experimental Procedure
FIGURE 2. DIAGRAM OF APPARATUS
SIZE AND TYPEOF PACXIKG. The effect of different packings is not so great as might be expected on the basis of their superficial area per unit of tower volume. Sherwood compared eleven different packings, for which results were reported in the literature, on absorption of ammonia from air by water, and the over-all coefficients KG a t G = L = 500 varied from 8.2 to 21.3 or 2.5 fold, whereas the area ratio was 5.6. Furthermore, there mas no correlation between the area and the coefficient as might be expected since the shape is also varying. For similar shapes Chilton, Duffey, and Vernon ($) found that K,u increased as the 0.5-0.6 power of the superficial packing area per unit volume. At G = L = 500 they obtained Kca values of 10-12 for packing (clay spheres and crushed stone) of an area of 60 square feet per cubic foot. Sherwood and Holloway (16) reported Koa of about 12 for 1-inch carbon Raschig rings, which also have an area of about 60 square feet per cubic foot. For absorption of ammonia in acid, 1/2- and 1-inch Berl saddles and 1-inch rings gave approximately the same coefficients, but '/&ch rings gave results about 70 per cent higher, for some unexplained reason. HUMIDIFICATION. Chilton, Duffey, and Vernon ( 2 ) made runs with and without a saturator for the inlet air and concluded that there was little difference. It is believed that these authors are the only ones who have investigated this point. REDUMPING OF PACKING.Chilton, Duffey, and Vernon ( 2 ) tested the reproducibility of different fillings of the same packing, and in one set of comparable runs little difference was found between the two fillings.
ABSORPTION SYSTEM. The column was constructed of 16-gage iron having an inside diameter of 12.0 inches; it consisted of three flanged sections, two %foot sections above a 2-foot section, All 'oints in each section were welded. *he liquor distributor was of the low-head variable-orifice type designed to permit a sensitive regulation of wide flow variations without materially increasing the head on each individual effluent stream of liquor. I t consisted of a horizontal 2-inch brass pipe containing a large number of $/le-inch copper tubes attached at various points along it3 length and at different points on the circumference. All the tubes were bent down and around, so that each discharged its stream at approximately the same level. The number of tubes discharging at any time depended on the height of the liquor in the brass pipe which served as a reservoir. The pipe was connected to a feed tank from which it received its liquor supply by gravity. The tubes were connected to the pipe at seven different levels, permitting a liquor rate varying from 100 to 1200 pounds/(hour) (square foot) of tower cross section. Each level contained three tubes except the bottom level, which contained seven. It was felt that less than seven tubes would not provide adequate liquor distribution across the tower at very low liquor rates. The distributor was given a protective coating of rubber paint to withstand corrosion. Gas flow through the tower was handled by a centrifugal gas booster connected t o the outlet line. We originally intended to force the gas mixture through the tower, but the slow steady increase in temperature which occurred was undesirable and the simplest way to avoid it was to suck the gas through the tower. The fact that the tower was under a slight vacuum caused no difficulty. The inlet gas could be humidified by injecting saturated steam into the gas stream at the base of the tower. The temperature increase thus produced in the gas stream was not more than 2' F. OPERATION.The method of operating the absorption apparatus is shown in Figure 2. The air supply was furnished by the gas booster, A , the inlet side of which was connected by a 4-inch pipe line to the top of absorption column C. After passing through the blower, the exit gas stream from the tower was dischar ed t o the atmosphere, The rate of gas flow wa3 controlled f ~ ay 4-inch gate valve, B , placed immediately after the tower in the exit as line. Air from the room entered the system at the left end o?pipe D,which was welded steel pipe of 5-inch inside diameter. Ammonia for mixing with the inlet air was supplied as liquid by a 150-pound cylinder! E, and was throttled by a diaphragm regulatin valve. Immedlately after throttling, the liquid ammonia passefthrough a double-pipe heat exchanger, F, where it was vaporized and heated to room temperature with condensing steam. From the heat exchanger Dhe gaseous ammonia flowed through a surge tank, G, t o damp out fluctuations in pressure caused by unsteady throttling. From this tank the ammonia passed through a 1-inch pipe line to inlet air line D. The exit end of the ammonia line extended about 8 inches inside the 5-inch air line and had a four-point distributor t o aid in mixing the ammonia with the air. The concentration of the ammonia in the inlet gas during all runs was approximately 2.0 per cent by volume. The absorbent water for the tower was furnished by the regular water supply of the laboratory, its temperature being controlled by the addition of steam from a steam mixer, H , placed in the line. Small fluctuations in temperature were eliminated in tlie feed tank, I , where a constant level was maintained by an overflow pipe. The water passed t o the column through a 1-inch pipe
INDUSTRIAL A N D ENGINEERING CHEMISTRY
April, 1941
line, and its rate of flow was re lated by two needle valves and a lobe valve connected in para!% Before the water entered the iistributor at the top of the column, its rate of flow was determined by rotameter J . Since no recirculation of the liquor was attempted, the exit liquor from the column passed to the drain. The steam su ply was enerated at a pressure of 10 pounds per s uare inch%y a gas-&ed boiler, K , the steam lines L,M , and I? supplying the steam mixer, the ammonia heater, and the humidification nozzle, respectively. MEASUREMENT OF GAS RATE. For measuring the rate of gas flow to the tower, a sharp-edged orifice, 0, was installed in accordance with the s ecifications of the A. s. M. E. (1) in gas inlet line D. The origce was located 63 inches from the left-hand end of the straight 5-inch pipe. This 63-inch section contained a 20-inch section of straightening vanes located 18 inches from the end of the pipe and 25 inches upstream from the orifice plate. The vanes consisted of seven len ths of 16/8-inch, 20-gage Shelby seamless steel tubing, the ends ofwhich were sharpened to a knife edge to minimize turbulence. Throat pressure t a s made of standard l/s-inch wrought iron p p e were installed! The upstream ta was located 1 pi e iameter from the orifice plate and the cfownstream tap, 0 3 diameter from the plate. Two orifice plates made of 0.0022-inch stainless steel and having orifices of 1.000- and 2.000-inch diameter, respectively, were used throughout the course of the investigation. SAMPLING AND ANALYTICAL METHODS. Since the tower operated under a vacuum, the inlet and exit gas samples were sucked out by a water jet pump. The sampled gas was slowly bubbled through two absor tion bottles containing measured volumes of standardized s&uric acid solution which quantitatively absorbed the ammonia from the as. The inlet tube of each absorption bottle terminated in a gitted Jena glass disk which broke up the gas stream into minute bubbles and thus produced a large contact area between the gas and the acid solution. The deammoniated gas was collected and measured in a special one-liter flask under known temperature and pressure conditions. The concentration of the ammonia in the gas was then determined bv titrating the excess acid left in the absorotion bottles. The exit liquor was sampled by drawing off a portion of the liquor from the bottom of the tower, and its ammonia content was determined by direct titration with standard sulfuric acid. The indicator solution used consisted of a mixture of methyl red and methvlene blue dissolved in ethvl alcohol. It gave a sham color cha6ge at the end point even" when titratini dilute COGcentrations. I
where
Ka
489
= transfer coefficient, lb. moles/(hr.) (sq. ft.) (atm.)
effective interfacial area per unit volume of tower, sq. ft./cu. ft. N = rate of ammonia absorption, lb. moles/hr. V =: active volume of tower, cu. ft. ( A P ) L M= log mean of terminal driving forces, atm. a
=
All calculated transfer coefficients were based on the liquor analyses. The use of t h e log mean A p assumes Henry's law and isothermal conditions. The ammonia-water solution was so dilute in all cases t h a t the first assumption is entirely valid. In most of the runs conditions were not exactly isothermal, but t h e departure is not believed to be great enough to have any important effect on the mean driving force. In runs where either the gas rate or the liquor was held constant, the constant rate was approximately 500 pounds/ (hour) (square foot) of tower cross section. The calculated results were not only corrected to this constant rate basis, b u t they were also corrected to a common temperature basis of 85" F. These corrections were, for the most part, quite small and were made by means of relations based on data obtained during the present investigation. Representing the ammonia balance around the tower b y the expression, lb. ammonia given up by gas per hr. lb. ammonia taken up by liquor per hr.
x
100
i t may be stated that 51 runs showed a balance of less than 100 per cent with a n average of 97.8 per cent, while 50 runs showed a balance of 100 per cent or over with an average of 101.8 per cent. The two extreme balances were 90.0 and 108 per cent. The extent to which i t was possible to check experimental results is indicated by the following data (using ll/rinch rings) : Run No.
33 34 36 46
a
L
1000 970
480 480 150 150
516 525
Kaa cor. F.
t o 85'
13.7 14.0
5.6 5.5
Data and Calculations The data on 101 runs are presented in the various graphs in t h e form of over-all transfer coefficients defined by the equation:
G-LBSAHRNSQFTI AND FIGURE3. EFFECTOF GAS RATE, HUMIDIFICATION, REDUMPING
Correlations The usual two-film theory combined with Henry's law leads to the well-known relation;
L -LBS/(HWBQFT) OF LIQUOR RATE,HUMIDIFICATION, AND FIGURE 4. EFFECT REDUMPING
Vol. 33, No. 4
INDUSTRIAL AND ENGINEERING CHEMISTRY
490
If kGais assumed to be independent of liquor rate and related to gas rate by the equation, koa = aGn '
(8)
and if k ~ isa assumed to be independent of gas rate but related to liquor rate by the equation, kLU 14
(9)
Equation 7 can be written :
P
G
= p.Zr
I2
M
k
80
For all practical purposes the value of (1 - u)f for our experiments may be taken equal to unity, and hence (H. T. U.)oo may be simply calculated from the values of over-all coefficient reported in this paper. Colburn also gives the relation
lo
If gas film controls, 2 6 Koa = aGn (11) From Equation 70 75 80 85 90 95 10 a plot of 1 / K a TEMPERATURE "F. us. 1/G" will be a straight line passFIGURE 5. EFFECT OF TEMPERATURE ing through the ON TRANSFER COEFFICIENTS origin if l/HBLr . . is negligible, which means that gas film controls. This has frequently been used to that gas film is controlling, but the proof is not convincing because it depends on an assumed value of n. Quite different results are obtained whether one assumes n = 0.8 or 0.6 or even 0.7. There is no a priori reason to assume that n = 0.8, for a packed tower a t least. It seems entirely reasonable to assume that both film coefficients are affected by gas and liquor rates and Equation 7 could be put in the form, cT8
2v,
This equation also assumes that the effect of G on either film coefficient is the same a t any value of L,and vice versa, which may not be a valid assumption. One might also assume that koa was a function of both rates but that k~ was a function only of L and not of G, in which case Equation 12 becomes (13)
If gas film controls, Equations 12 and 13 both reduce to Koa = yGnL*
(5)
Sherwood and Holloway (I?') give the equation,
for the liquid film coefficient in packed towers. Nine different packings were tested, and a value of s = 0.50 was recommended for general use. a and n were found t o be functions of the packing, the particular values for 1-inch Raschig rings being CY = 100 and n = 0 . 2 2 . By using this correlation for calculation of the liquid film coefficient, values of gas film coefficient can be calculated from measured values of over-all coefficient. The results of absorption experiments may also be correlated through the concept of the transfer unit. Following the treatment of Colburn (4), the following relation is obtained between the over-all coefficient and the over-all H. T. U., both referred to the gas phase:
Assuming (H. T. U.)G and (H. T . U.)L t o be independent of gas and liquor rates, (H. T. U.)OGplotted against mG.w/L.tt on ordinary coordinates would give a straight line. Colburn found this to hold with several sets of data on absorption and extraction available in the literature; however, when our results are plotted in this way, there is decided curvature.
Discussion of Results EFFECTOF HUMIDITY OF EKTERING Gas. The effect on the over-all coefficient was found to be quite small and, in most cases, within the experimental error. This is shown in Figures 3 and 4 where runs in which the entering air was not humidified are directly compared with runs in which the air was humidified. "Not humidified" means that the air had the humidity of the air prevailing in the laboratory a t the particular time of the runs and "humidified" means that the air was humidified to such a point that the column was nearly isothermal. Without humidification the liquor decreased in temperature since the heat absorbed in vaporization of water was greater than the heat given out by the solution of the ammonia. The amount of cooling depended on the gas and liquor rates but was as great as 20-23' F. in some cases. EFFECT OF DUMPING
THE
PACKING.
The 1-inch rings were removed from the tower, cleaned, and redumped at random into the tower. Runs made before and after the refilling are also compared in Figures 3 and 4,and the effect was negligible. With a small&ratio FIGURE6. EFFECTOF GAS RATE UPON OVER-ALL COEFFICIENT of tower diameter to size of packing (12 in this case) and particularly with a smaller depth of packing (4 feet in this case), the effect would probably be much greater. EFFECT OF TEMPERATURE. Seven runs were made in which the average liquor temperature varied from 73.6" to 98.5" F. I n any given run the temperature was maintained substantially constant by humidifying the inlet air. The gas temperature was not controlled and was in most cases somewhat lower than the liquor temperature. The effect of temperature (average of the mean gas and liquor temperatures) on the over-all coefficient and the two individual film coefficients (calculated by a method discussed later in the paper) is shown in Figure 5. The effect on the over-all coefficient confirms the results of previous investigators, but
INDUSTRIAL AND ENGINEERING CHEMISTRY
April, 1941
x-
1
I
1
G'500 TEMP-85'E
the effect on kQis contrary to that expected. No good explanation can be offered to account for this. It might indicate t h a t t h e Gilliland-Sher w o o d gas film correlation does n o t apply in this case or that the Sherwood-Holloway liquid film correlation is inapplicable. The gas film correlation was based on results in a wetted-wall t o w e r , a n d kGI (or z) was assumed to be ind e p e n d e n t of liquor flow. We shall show later that our results present some e v i d e n c e of an effect of liquor rate on the gas film coefficient.
E F F E C TO F FLUID FLOW RATES. Figure 6 is a typical plot of the over-all coefficient against the gas rate on log-log coordinates. A straight line represents the data fairly well, but the s-shaped curve shown by the dashed line is believed to be significant because all of the results consistently give such a curve. As pointed out under "correlations" the straight-line relation would apply if gas film were controlling. If there were a liquid film resistance, the curve of log Koa us. log G would be expected to show a curvature concave to the G axis and eventually to approach a horizontal asymptote. Actually, however, the curvature reverses itself a t about G = 400. This might be due to an effect of the gas flow on the liquid film resistance or to a spray effect which would increase the effective liquid surface. For purposes of empirical correlation it appears desirable to represent the effect of G on Koa by drawing the best straight line on a log-log plot. When this is done, the following empirical equations are obtained for the three ring sizes a t a constant liquor rate of 500 and constant temperature of 85' F : l/a-inch rings: 1-inch rings: ll/a-inch rings:
Assuming that the effects of gas and liquor rates are entirely independent, we may combine the two in one equation. Thus for 1-inch rings: Koa = 0.0225 G0.5' Lo."
(21)
Sherwood and Holloway (16) reported the following equation representing the data of Borden and Squires on 1-inch rings: Kaa = 0.046
Lo.4
(22)
The equation of Borden and Squires is compared with our results in Figures 7 and 8, and the agreement is fair, their coefficients being 20-25 per cent higher than ours. The coefficients of Johnstone and Singh for 1-inch rings are about four times the values we have found. This may be due partly to the fact that their coefficients may be true gas film coefficients, whereas ours are over-all coefficients, and partly to the very short column of packing which they used. EFFECT OF PACKINU SIZE. The effect a t one gas and liquor rate [500 pounds/(hour) (square foot)] is shown in Table 11. Obviously the effective area, a, of the packing is much less than the superficial area. At this particular set of flow rates the coefficient, Koa, increases approximately as the 0.45 power of the superficial area. This agrees reasonably well with the conclusions of Chilton, Duffey, and 3
TABLE11. RELATION BETWEEN PACKING SIZEAND OVER-ALL COEFFICIENT Packing Ring size, in. '/a
Over-all Over-all Coeffiioiant Koa Coefficient KQ* Lb. Moles/(Hr.j Lb. Moles/(Hr.\ (Cu. Ft.)(Atm.) (Sq. Ft.)(Atm.) 14.0 0.12 10.2 0.18 9.0 0.24
Surface 8 9 . ft./' cu. ft. 114 57
1
37.6
11/a
* Based upon dry area of packing. 2 J
a
a
E
0
100
so
60
50 40
200
400
600
800
IO00
&a = 0.18 GO.70 Koa = 0.29 GoJT KQa = 0.26 GO.5'
The effect of liquor rate a t a constant gas rate is well r e p resented by a straight line on a log-log plot as shown in Figure 4. By locating the best straight lines through the data, the following purely empirical equations represent the effect of liquor flow a t a constant gas rate of 500 and temperature of
85" F.: l/2-inch rings: 1-inch rings: ll/.l-inch rings:
491
Koa = 0.64 Koa = 0.77 Koa = 0.48 LO.47
6\"
L - LBS.AHRl(SQ.FT1
9. EFFECTOF GAS RATE (above) AND OF LIQUORRATE(below) ON RELATIWGAS FILMREFIGURE
(20)
SISTANQE
INDUSTRIAL A N D EN G INEERING CHEMISTRY
492
Vernon ( 2 ) who found an exponent of about 0.55 from their results on solid packings.
INDIVIDUAL FILM C o E F F I C I E N T S. Liquid film coefficients kLa were calculated from Equation 14, and gas film coefficients were then calculated from Equation 7, using values of H FIGURE 10. CALCULATED vs. OBbased on the equaSERVED OVER-ALL TRANSFER tion of Kowalke, COEFFICIENTS Hourren. andWatson (IS).- The following values of the properties of a dilute ammonia solution for 85" F. were used:
D
= 9.80
p
= 1.970
p
= =
H
X 10-6
62.1 2.74 (lb. moles/cu. ft.)/atm.
Coefficient koa was found to be a function both of gas and liquid flows, the relations being given by the equations: JCGU = 0.127 G0.77 k c = ~ 4.12 L0.'O
( L = 500) (G = 500)
(23) (24)
These equations are based upon the over-all coefficients for 1-inch rings, first dumping with air not humidified. Combining the two effects, we obtain: koa
0.036 GO.77
L0.20
(25)
The exponent of G came out to be substantially the same as that found for wetted-wall towers, whereas a somewhat smaller value might have been expected. The data of Doherty and Johnson (16) for absorption in 3.5-4.5 N acid give an exponent of 0.63 on G, and the liquid rate was found to be without effect on koa. Sherwood and Holloway (16) also reported results on gas film coefficients in the vaporization of water which showed koa t o vary as the 0.63 power of G and 0.33 power of L. T h e relative resistance of the two Urns is indicated in Figure 9. It is of interest to note that the relative resistance is independent of packing size and that it is substantially independent of liquid rate above L = 500. This seems to indicate that the effect of liquor rate is about the same on both film resistances a t the higher liquor rates. Combination of Equations 13, 25, and 14 leads to the following relation which is believed to be the most satisfactory one for representing our data on 1-inch rings: 1 1 1 Koa 0.036 G0J7Lo.2o 0.103 H Lo.78 The agreement between the equation and the observed data is shown in Figure 10. Similar equations for the other two ring sizes are as follows:
Vol. 33, No, 4
Nomenclature effective area of packing, sq. ft./cu. ft. D = diffusivity of solute gas in carrier gas, sq. ft./hr. d = diameter of tower, ft. G = gas flow rate, lb./(hr.) (sq. ft.) GM = gas flow rate, lb. moles/(hr.) (sq. ft.) H = Henry law constant (lb. moles/cu. ft.)/atm. H. T. U. = hei h t of a transfer unit, f t . Subscript 8 G = over-all transfer units with gas phase driving force Subscript G = gas film transfer unit Subscript L = liquid film transfer unit KG = over-all absorption coefficient, Ib. moles/(hr.) (sq. ft.) (atrn.) KGU = over-all absorption coefficient, lb. moles/(hr.) (cu. ft.) (atm.) = gas film absorption coefficient, lb. moles/(hr.) (sq. ft.) (atm.) koa = gas film absorption coefficient, lb. moles/(hr.) (cu. ft.) (atm.) k~ = liquid film absorption coefficient, lb. moles/(hr.) (sq. ft.) (lb. moles/cu. ft.) k ~ a = liquid film absorption coefficient, lb. moles/(hr.) (cu. ft.) (lb. rnoles/cu. ft.) L = liquor flow rate, lb./(hr.) (sq. ft.) LM = liquor flow rate, lb. moles/(hr.) (sq. ft.) m = slope of equilibrium curve (= 1/H for Henry-law case] N = rate oi absorption, lb. moles/hr. P = ressure, atm. PBM = L g mean of inert gas pressures at film boundaries, atm. ( A P ) L M = log mean of terminal pressure differences, atm. R = gas constant T = absolute temperature, ' R. V = volume of tower, cu. f t . x = film thickness, f t . = mole fraction of solute in gas y = equilibrium value of y corresponding to x y* (1 - y)/ = log mean of 1 - y) and ( 1 - y*) p = viscosity, lb./(hr$(ft.) p = density, lb./cu. ft. a,B,y,6,e = empirical constants m,n,r,s = empirical exponents a
=
Literature Cited Sac. Mech. Engrs., "Fluid Meters, Their Theory and Application", 4th ed., Part 1 (1937). (2) Chilton, T. H., Duffey, H. R., and Vernon, H. C., IND.ENQ. CHEM.,29, 298-301 (1937). (3) Cogan, T. C., and Cogan, J. P., Mass. Inst. Tech., Thesis in Chem. Eng., 1932. (4) Colburn, A. P., Trans. Am. Inst. Chem. Engrs., 35, 211-36 (1) Am.
(1939).
(5) Gflliland, E. R., and Sherwood, T. K., IND. Exa. CHBM.,26, 516 (1934). (6) Hanks, W.V., and McAdams, W.H., Ibid., 21, 1034-9 (1929). (7) Haslam, R. T., Hershey, R. L., and Kean, R. H., Ibid., 16, 1224 (1924). (8) Hatta, S., Ueda, T., and Baba, A., J . Soo. Chem. I d . Japan, 37, Suppl. binding, 164-5 (1934). (9) Hixson, A. W., and Scott, C. E., IND.ENG.CHEM.,27, 307 (10) . .
(1935). Hollinas, H., and Silver, L., Trans. Inst. Chem. Engrs. (London), 12, 4% (1934).
Johnstone, H. F., and Singh, A. D., IND. ENO. CHEM.,29, 2%-97 - - - . 11937). ,- .. , (12) Johnstone, H. F., and Williams, Ibid., 31, 993-1001 (1939). (13) Kowalke, 0. L., Hougen, 0. A,, and Watson, K. M., Bull. Unin. Wis Eng. E&. Sta. 68 (June, 1925). (14) . . Monaweck, J. H., and Baker, E. M., Trans. Am. Inst. Chem.
(11)
Engrs., 22, 165-85 (1929).
(15) Sherwood, T. K., "Absorption and Extraction", New York, McGraw-Hill Book Co., 1937. (16) Sherwood, T. K., and Holloway, F. A. L., Trans. Am. Inst. Chem. Enars.. 36. 21-36 (19401. , .
(17) Ibid., 36, 36 (1940j. (18) . . Sherwood, T. K., and Kilgore, A. J., IND.ENQ. CHEM.,18, 744-6 (1926). (19) Whitman, W. G.,, and Davis, D. S., Ibid., 16, 1233-7 (1924). (20) Whitman, W. G., Long, L., and Wang, W. Y.,Ibid., 18, 363-7
Acknowledgment Thanks are due the National Carbon Company for the gift of the carbon Raschig rings with which the tower was packed.
(1926). TEISpaper is based on a diseertation presented by 0. E. Dwyer in June, 1940, t o the faculty of the School of Engineering, Yale University. in candidacy for the degree of doctor of engineering.
