Ind. Eng. Chem. Process Des. Dev. 1985, 24, 261-264
a = gas-liquid interfacial area based on aerated liquid or slurry volume, cm2/cm3 C = concentration of dissolved oxygen in liquid phase, mol/dm3 CAi= concentration of absorbing gas component in the gasliquid interface, mol/dm3 C, = concentrationof liquid-phasereactant in the bulk liquid, mol/dm3 CBs = saturation concentration of liquid-phase reactant species, mol/dm3 c = concentration determined by D.O. meter, mol/dm3 D, = diameter of the bubble column, cm DA = molecular diffusivity of absorbing gas component in liquid phase, cm2/s = molecular diffusivity of liquid-phase reactant species D n! liquid phase, cm2/s d = average diameter of solid particles, pm If=D.O. meter reading, % g = gravitational acceleration, cm/s2 H = Henry's law constant, (MPa m3)/mol KGu = overall volumetric mass transfer coefficient based on gas phase, mol/(MPa m3 s) kca = volumetric gas-side mms transfer coefficient, mol/(MPa m3 s) kLa = volumetric liquid-side mass transfer coefficient, l / s 12, = mass transfer coefficient for solid dissolution, cm/s k2 = second-order reaction rate constant, dm3/(mol s) L = height of dispersion in the bubble column, cm M =~~CB~DA/~L" M' = k&&A/kLo2 N = kSA,zL2/DB 9=
2cAi/cBs
DP/DB
T = time constant of D.O. meter, s UG = dimensionless gas velocity defined by eq 11 UG = superficial gas velocity, cm/s u = liquid volume per unit gas-liquid interface, cm3/cm2 w = solid concentration, wt % x = dimensionless distance into liquid phase from gas-liquid interface YA= dimensionless concentration of absorbed gas species in liquid phase relative to the interfacial concentration = CA/CAi YB = dimensionless concentration of dissolved solid species in liquid phase relative to the saturation concentration = CB/CBs YBo = YB in the bulk liquid phase
261
zL = thickness of liquid film, cm
Greek Symbols tG = gas holdup pG = gas density, g/cm3 pL = liquid density, g/cm3 u = surface tension of liquid, dyn/cm 4 = enhancement factor $ = parameter defined by eq 4 Superscripts * = equilibrium with the gas phase = without chemical reaction Registry No. COz, 124-38-9;Ca(OH)z, 1305-62-0. Literature Cited Akita, K.; Yoshida, F. Ind. Eng. Chem. Process Des. D e v . 1974, 13, 84. Astarita, G. "Mass Transfer wlth Chemlcal Reactlon", Eisevier: Amsterdam, 1967; p 145. Botton, R.; Cosserat, D.; Charpentier, J. C. Chem. Eng. J . 1980, 20, 87. Calderbank, P. H.; Moo-Young, M. B. Chem. Eng. Sci. 1961, 16, 39. Deckwer, W.-D.; Burckhart, R.; Zoii, G. Chem. Eng. Sci. 1974, 29, 2177. Deckwer, W.-D.; Louisi, Y.; Zaidi, A.; Ralek, M. Ind. Eng. Chem. Process D e s . Dev. 1980, 19, 699. Dhanuka, V. R.; Stepanek, J. 8. AIChE J . 1980, 2 6 , 1092. Gestrich, W.; Esenweln, H.; Krauss, W. Int. Chem. Eng. 1978, 18, 38. Hughmark, G. A. Ind. Eng. Chem. Process Des. Dev. 1987, 6 , 219. Kato, Y. Chem. Eng. Jpn. 1983, 27, 7. Kato, Y.; Nishiwakl, A.; Kago, T.; Fukuda, T.; Tanaka, S. Int. Chem. Eng. 1973, 13, 562. Kim, S.D.; Baker, C. G. J.; Bergougnou, M. A. Can. J . Chem. Eng. 1972, 50,695. Kumar, A.; Oegaleesan, T. E.; Laddha, G. S.;Hoelscher, H. E. Can. J . Chem Eng . 1974, 5 4 , 503. Oels, U.; Lucke, J.; Buchholz, R.; Schugerl, K. Ger. Chem. Eng. 1978, 1 , 115. Ratcliff, G. A.; Holdcroft, J. G. Trans. Inst. Chem. Eng. 1963, 4 1 , 315. Sada, E.; Kumazawa, H.; Lee, C. H. Chem. Eng. Sci. 1983, 3 8 , 2047. Schumpe, A.; Serpemen, Y.; Deckwer, W.-D. Ger. Chem. Eng. 1979, 2 , 234. Schumpe, A.; Deckwer, W.-D. Chem. Eng. Sci. 1980, 35, 2221. Schumpe, A.; Deckwer, W.4. Chem. Eng. Commun. 1982, 17, 313. Schugerl, K.; Lucke, J.; Oels, U. "Advances in Biochemical Engineering"; Ghose, T. K., Fiechter, A.; Blakebrough, N., Ed.; Springer-Verlag: Berlin, 1977; Vol. 7, p 60. Sharma, M. M.; Mashelkar, R. A. Institution of Chemical Engineers, London, International Chemical Engineering Symposium Series, 1968; No. 28, p 10. Sittig, W. Verfahrenstechnik 1977, 1 1 , 730. Yoshida. F.; Akita, K. AIChE J . 1965, 1 I , 9.
.
Received for review August 26, 1983 Revised manuscript received April 16, 1984 Accepted April 26, 1984
Solubility and Diffusivity of Carbon Dioxide in Aqueous Slurries of Kaolin Haruo Hlklta, Kosaku Ishlml, Ken-lchl Ueda, and Sadatoshi Koroyasu Department of Chemical Engineering, University of Osaka Prefecture, Sakai, Osaka 59 1, Japan
Solubility and diffusivity of carbon dioxide in 10-43 wt % aqueous kaolin slurries were measured at 15, 25, and 35 O C and at atmospheric pressure. The effects of the addition of electrolytes (sodium chloride, sodium sulfate, and magnesium chloride) in 15-44 wt % aqueous kaolin slurries on carbon dioxide solubility and diffusivity were determined at 25 OC. The electrolyte concentration ranged from 0.5 to 1.7 kmol/m3. The carbon dioxide solubilities in aqueous slurries of 12-42 wt % zircon and 7-21 wt % sulfur were also measured at 25 OC. All the solubility and diffusivity data could be correlated well by simple correlations proposed here.
Introduction
Gas absorption into slurries is often encountered in the chemical process industry. Some typical examples of industrial importance are the flue gas desulfurization process using lime/limestone slurry as the scrubbing medium and 0196-4305/85/1124-0261$01.50/0
the Fischer-Tropsch slurry process for the production of hydrocarbons from carbon monoxide and hydrogen. For the rational design of absorbers or reactors in such processes, knowledge of the solubilities and diffusivities of gases in slurries is required. However, there are few data 0 1985 American Chemical Society
262
lnd. Eng. Chem. Process Des. Dev., Vol. 24, No. 2, 1985
Table I. Experimental Conditions Used in Solubility Measurements and Carbon Dioxide Solubility in Aqueous Slurries of Kaolin. Zircon. and Sulfur at Partial Pressure of 1.013 X lo5 Pa slurrv, wt %
solid vol fraction, 6
10.3 15.8 20.3 30.5 41.0 30.7 30.7 17.0 31.0 42.6 31.0 33.3 15.2 30.0 43.7 16.9 32.0 41.7
0.0407 0.0649 0.0861 0.140 0.205 0.141 0.141 0.0735 0.149 0.223 0.146 0.165 0.0614 0.143 0.233 0.0717 0.152 0.213
42.7 27.7 12.3
0.139 0.0772 0.0297
7.16 14.2 20.7
0.0358 0.0735 0.112
electrolyte
NaCl NaCl NaCl NaCl NaCl NazSOl Na2S04 Na2S04 MgC12 MgC12 MgC12
electrolyte concn, kmol/m3 temp, " C Kaolin ( p , = 2690 kg/m3) 25 25 25 25 25 15 35 1.04 25 1.05 25 1.04 25 0.518 25 1.69 25 0.441 25 0.448 25 0.433 25 0.355 25 0.339 25 0.320 25 Zircon ( p , = 4560 kg/m3) 25 25 25 Sulfur
(p.
on the solubilities and diffusivities of gases in slurries, and no method for predicting these physicochemical properties is available in the literature. In this paper, new data for the solubility and diffusivity of carbon dioxide in aqueous kaolin slurries are reported, and simple empirical correlations which permit the estimation of the solubilities and diffusivities of gases in aqueous slurries are also presented.
Experimental Section Materials. Aqueous kaolin clay slurries containing or not containing electrolytes were employed for both the solubility and diffusivity measurements. Sodium chloride, sodium sulfate, and magnesium chloride were used as electrolytes. Aqueous kaolin clay slurries were prepared from commercial kaolin clay. The commercial kaolin clay used in the present work contains alkaline impurities and holds the adsorbed alkaline earths on its surface. Consequently, when carbon dioxide dissolves into the commercial kaolin slurry, it reacts with alkali. Therefore, in the present work, aqueous kaolin slurries were prepared as follows; after commercial kaolin clay was added to distilled water, the resulting kaolin slurry was contacted with strong acidic ion-exchangeresin beads to remove alkali in kaolin slurry. For the solubility measurements, aqueous zircon and sulfur slurries were also used. Solubility Measurements. The solubilities of carbon dioxide in the aqueous slurries were measured by a gravimetric method. The principle of this method is to bring a solute gas into contact with a weighed quantity of gasfree liquid, to agitate the liquid until equilibrium is established, and to measure the increase in weight of the liquid. The absorption vessel was of a volume of about 100 cm3 and a test liquid of about 70 cm3 was put into it. Before pure carbon dioxide was introduced into the absorption vessel the liquid in the vessel was deareated by boiling under vacuum. The vessel containing the liquid was weighed and the liquid in the vessel was then agitated by a magnetic stirrer. After equilibrium was established, the vessel containing the liquid was weighed again and the
= 2070 kg/m3) -.
25 25 25
slurry density p , kg/m3
solub in slurry C*, mol/m3
solub in cont. phase, Co*, mol/m3
1066 1107 1143 1234 1344 1237 1233 1160 1284 1407 1261 1332 1158 1287 1427 1143 1275 1377
32.6 31.8 30.5 29.4 27.0 39.4 22.9 24.3 22.1 20.4 26.0 18.9 23.2 21.2 19.6 28.6 26.0 23.9
33.9 33.9 33.9 33.9 33.9 45.5 26.4 26.8 26.8 26.8 30.2 23.1 25.1 25.0 25.2 30.0 30.1 30.3
1492 1272 1103
28.8 32.1 32.2
33.9 33.9 33.9
1035 1076 1117
32.7 31.1 29.9
33.9 33.9 33.9
amount of the dissolved carbon dioxide was determined from the change in the weight of the liquid before and after the experimental run. The experimental conditions used in the solubility measurements are given in Table I. Diffusivity Measurements. The diffusivities of carbon dioxide into aqueous kaolin slurries were determined by measuring the steady-state diffusion rate of carbon dioxide through a thin layer of kaolin slurries. The experimental apparatus was similar to that used by Otto and Quinn (1971). The diffusion cell consisted of two compartments separated by a liquid film holder. The upper and lower compartments had volumes of about 12 cm3and 6 cm3, respectively. The liquid film holder was composed of a vinyl chloride resin spacing ring (90.0 mm o.d., 30.9 mm i.d., and 1.5 mm thick) and two thin Teflon membranes (Millipore filter, type LS; 125-150 pm thick), which were supported by vinyl chloride resin supporting rings. The thin layer of kaolin slurry was held between two Teflon membranes, and its thickness was about 1.7 mm. The lower compartment was flushed with pure carbon dioxide saturated with water vapor for about 1.5 h preceding a run, while air was continuously passed through the upper compartment to sweep away the carbon dioxide transported through the liquid film. After the lower compartment was flushed, the additional carbon dioxide was fed into the compartment to maintain the pressure at atmospheric pressure. The steady-state diffusion rate of carbon dioxide across the liquid film was determined by measuring the feed rate of carbon dioxide to the lower compartment with a soap film meter. Assuming that carbon dioxide does not react with kaolin clay and that mass transfer through the thin layer of kaolin slurry takes place by molecular diffusion, the diffusivity D of carbon dioxide in aqueous slurries was calculated from the following equation D = NG/A(CI - C,) (1) where N is the steady-state diffusion rate of carbon di-
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 2, 1985 263 Table 11. Experimental Conditions used in Diffusivity Measurements and Carbon Dioxide Diffusivity in Aqueous Kaolin Slurries
slurry, w t 70 15.0 30.1 42.8 30.2 30.0 16.7 30.2 41.4 30.0 30.0 14.6 28.8 42.8 14.7 29.4 40.1
solid vol fraction, d 0.0614 0.137 0.217 0.138 0.137 0.0715 0.143 0.214 0.139 0.144 0.0622 0.316 0.226 0.0614 0.136 0.203
electrolyte
electrolyte concn, kmol/m3
NaCl NaCl NaCl NaCl NaCl Na2S04 NazS04 Na2S04 MgC12 MgCl, MgCl2
1.00 1.00 1.00 0.496 1.51 0.418 0.416 0.416 0.300 0.299 0.300
slurry density, p , kdm3 1101 1230 1364 1233 1227 1155 1273 1390 1250 1293 1150 1272 1418 1123 1248 1359
temp. "C 25 25 25 15 35 25 25 25 25 25 25 25 25 25 25 25
oxide, 6 is the liquid film thickness, A is the cross-sectional area of the liquid film, and C1 and Co are the carbon dioxide concentrations at boundaries of the liquid film.The value of C1 was taken to be equal to the saturated concentration of carbon dioxide in aqueous kaolin slurry at a total pressure of 1.013 X lo5 Pa (atmospheric pressure) and the value of Cowas assumed to be zero. The resistance of the Teflon membrane to carbon dioxide diffusion was neglected. The experimental conditions employed in the diffusivity measurements are listed in Table 11.
Results and Discussion Carbon Dioxide Solubility. The procedure of determining the gas solubility was checked by measuring the solubility of carbon dioxide in pure water. The solubilities measured at 25 "C and a carbon dioxide partial pressure of 1.013 X lo5Pa were 34.1 f 0.2 mol/m3, and the average value of the measured solubilities agreed within 0.6% with the reported value in the literature (Linke and Seidell, 1958). The carbon dioxide solubilities in aqueous slurries containing or not containing electrolytes, measured at a total pressure into those at a carbon dioxide partial pressure of 1.013 X lo5 Pa, were converted into those at a carbon dioxide partial pressure of 1.013 X lo5 Pa by correcting the water vapor pressure over aqueous slurries at the experimental temperatures. The water vapor pressure for aqueous slurries was assumed to be the same as that for pure water. The measured solubilities C* of carbon dioxide are listed in Table I. Figure 1shows all the experimental results on the carbon dioxide solubility in aqueous slurries of kaolin, zircon, and sulfur as a plot of the ratio of the solubility in the slurry to that in the continuous phase, C*/Co*, against the volume fraction $ of solid in the slurry. The value of $ was calculated from the equation
where $ is the density of the slurry, w is the mass fraction of the solid in the slurry, and ps and po are the densities of the solid particle in the slurry and of the continuous phase, respectively. For the aqueous slurries with and without electrolytes, Co* represents the carbon dioxide solubilities for aqueous electrolyte solutions and for pure water, respectively. The carbon dioxide solubility in aqueous electrolyte solutions was predicted by the method of van Krevelen and Hoftijzer (1948). The carbon dioxide
cy t
o x
A
a 0
v o
I T:mp
C 15
diffus in slurry D X io? m2/s 1.88 1.67 1.54 1.28 2.19 1.66 1.53 1.44 1.60 1.47 1.65 1.51 1.38 1.70 1.59 1.51
diffus in cont. phase, DoX los, m2/s 1.97 1.97 1.97 1.49 2.53 1.82 1.82 1.82 1.89 1.74 1.78 1.78 1.78 1.85 1.85 1.85
I I I I Slurry Electrolyte Investlgator
=:
Kaolin Kaolin Kaolln Zircon Present work Sulfur Kaohn 25 Kaolin Na2S04 25 Kaolin MgCIz I8 Bentonlte A s t a r ~ta (1965)
25 35 25 25 25
ii
1
-
. O
V
*-
V
08
-
0 Figure 1. Solubilities of carbon dioxide in aqueous slurries of kaolin, zircon, and sulfur.
solubility in pure water was taken from the literature (Linke and Seidell, 1958). The used values of Co* are also listed in Table I. As can be seen in Figure 1, the data points fall reasonably well on a straight solid line representing the equation c*/co*= 1 - $ (3) the average deviation being 1.3%. Equation 3 indicates that the reduction of gas solubility in slurries with increasing $ may be due to the decrease in the portion of continuous phase in the slurry. In Figure 1the carbon dioxide solubility data for 3.8-5.1 wt % aqueous bentonite slurries measured at 18 "C by Astarita (1965) are shown and compared with the present correlation. Although one data point falls considerably below the present correlation, two other points are in good agreement with eq 3. Carbon Dioxide Diffusivity. As a check on the precision of the measuring technique, carbon dioxide diffusivity in pure water was measured at 25 "C. The measured diffusivities were (1.94 f 0.03) X lo* m2/s and the average value of the diffusivities was in good agreement with that reported by Peaceman (1951), the maximum deviation being 1.6%. The measured diffusivities D of carbon dioxide in aqueous kaolin slurries containing or not containing electrolytes are given in Table 11.
284
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 2, 1985
I I
'
I Key T:Fp n o 2 A
+
07 ' 0
Solu;e
co2
1;
1-
7
25 C02 35 co2 NaCl -/Presentwork 25 CO? 25 COZ NaSO, I 25 CO2 MiCI, 2 0 Benzoic acld -Clough et a l
I
I
005
I
010
I 015
at 20 "C are also shown and compared with eq 4. As can be seen in this figure, the data of Clough et al. for the benzoic acid diffusivity can be correlated by the present correlation obtained for the carbon dioxide diffusivity.
I Investigator
Elect;olyte
I 020
I
1,
Conclusions From the good correlation of the experimental data observed in Figures 1 and 2, it would be expected that eq 3 and 4,respectively, can be used for the prediction of the solubilities and diffusivities of gases in aqueous slurries, regardless of solute gas and slurry, as well as temperature, although further experimentalwork with other solute gases and also other slurries is necessary to test the general applicability of these two equations. Nomenclature
025
0 Figure 2. Diffusivities of carbon dioxide in aqueous slurries of kaolin.
Figure 2 shows the measured values of the carbon dioxide diffusivity as a plot of the ratio of the diffusivity in the aqueous slurry to that in the continuous phase, DIDo, against the volume fraction 4 of solid in the slurry. For the aqueous slurries with and without electrolytes, Do represents the carbon dioxide diffusivities for aqueous electrolyte solutions and for pure water, respectively. The carbon dioxide diffusivity in aqueous electrolyte solutions was estimated by the method of Ratcliff and Holdcroft (1963). The carbon dioxide diffusivity in pure water at 25 "C was taken as 1.97 X 10" m2/s (Peaceman, 1951) and the values at 15 and 35 "C were predicted by using the Stokes-Einstein relation from the value of 1.97 X lo+' mz/s at 25 "C. The used values of Do are also given in Table 11. As can be seen in Figure 2, all the experimental data are well correlated by a solid straight line representing the equation D/Do=l-+ (4) the average deviation being 1.2%. This equation is similar to eq 3 and also indicates that the reduction of gas diffusivity in slurries with increasing 4 may be due to the decrease in the portion of continuous phase in the slurry. In Figure 2, the data of Clough et al. (1962) for the benzoic acid diffusivity in 20 wt % aqueous kaolin slurry
A = cross-sectional area of liquid film, m2 Co, C1 = carbon dioxide concentrations at boundaries of liquid film, mol/m3 C*, Co* = solubilities of carbon dioxide or solute gas in aqueous slurry and in continuous phase, mol/m3 D, Do= diffusivities of carbon dioxide or solute gas in aqueous slurry and in continuous phase, m2/s N = steady-state diffusion rate of carbon dioxide through liquid film, mol/s w = mass fraction of solid in slurry 6 = liquid film thickness, m p , p o = densities of slurry and continuous phase, kg/m3 p s = density of solid particle in slurry, kg/m3 4 = volume fraction of solid in slurry Registry No. NaC1, 7647-14-5; Na2S04,1157-82-6; MgC12, 7786-30-3;carbon dioxide, 124-38-9; zircon, 14940-68-2; sulfur, 1104-34-9.
Literature Cited Astarita, G. Ind. Eng. Chem. Fundam. 1985, 4 , 236. Clough, S.B.; Read, H. E.; Metzner, A. B.; Behn, V. C. AIChE J. 1962, 8 , 346. Linke, W. F.; Seidell, A. "Solubilities of Inorganic and Metal-Organic Compounds", 4th ed.: van Nostrand: New York, 1958; Vol. I,p 459. Otto, N. C.; Qulnn, J. A. Chem. Eng. Scl. 1971, 26, 949. Peaceman, D. W. ScD. Thesis, Massachusetts Institute of Technology, Cambridge, MA, 1951. Ratcliff, G. A,; Holdcroft, P. J. Trans. Inst. Chem. Eng. 1963, 4 1 , 315. van Krevelen, D. W.; Hoftljzer, P. J. Chim. Ind. X X I m Congr., I n t . Bruxd e s , Chim. Ind. 1948, 168.
Receiued for review December 28, 1983 Accepted April 25, 1984
