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Ind. Eng. Chem. Fundam. 1984, 23, 153-158
while, beginning with the onset of flow separation a t Reynolds numbers of about 150, higher values are required for higher Reynolds number flows. The trends are consistent with physical arguments and the model is expected to prove useful in the study of Titer performance, especially since many additional effects such as electrostatic enhancement can be examined by the simple addition of force terms to the equation of motion.
7' = single-sphere collection efficiency 8, = angular position defining critical trajectory p = gas viscosity, kg s-l p g = gas density, kg rn-, pp = fine particle mass density, kg rn-, \k = stream function, rn-, s-l
Nomenclature
Alexander, J. C. Ph.D. Thesis, Department of Electrical Engineering, MIT, Cambridge, MA, 1978. Chandrasekhara, B. C.; Vortmeyer D. Waerme Stoffubemrag. 1979, 72, 105-1. 1. 1. Davies, C. N. Proc. Phys. SOC. 1945, 5 7 , 259-270. Dietz, P. W. J . Aerosol Sci. 1981, 72, 27. Fanhein, R. W.; Stankovic, L. M. Chem. Eng. Sci. 1979, 3 c , 1350. Happel, J. AlChE J . 1958, 4(2), 197. Jollis, K. R.; Hanratty, T. J. Chem. Eng. Sci. 1988, 27, 1185-1190. Kallio, G. A.: Dietz, P. W. Presented at the 7th TDFM Convention on "Gas Borne Particles", Oxford, England, June 1981. Kallio, G., Dietz, P. W.;Gutfinger, C. "Proceedings of the Symposium on the Transfer and Utilization of Particulate Control Technology", Denver, CO. 1979. Karabelas, A. J.; Wagner, T. H.; Hanratty, T. J. Chem. Eng. Sci. 1973, 28, 673-682. Kuwabara, S. J . Phys. SOC.Jpn. 1959, 74, 527. Lamb, H. "Hydrodyamics", 6th ed.; Cambridge University Press; Cambridge, England, i932.Leclair, B. P.; Hameliec, A. E. Ind. Eng. Chem. Fundam. 1988, 7 , 542. Ranz, W. E.; Wong, J. 8. Ind. Eng. Chem., 1952, 44(6), 1371. Sorensen, J. P.; Stewart, W. E. Chem. Eng. Sci. 1974, 29, 819. Tardos, G. I.; Abuaf, N.; Gutflnger, C. J . Air Pollut. Control Assoc. 1978, 28(4\. 355. .,~ Vander Merwe, D. F.; Gauvin, W. H. AiChE J . 1971, 17(3), 5-19. Zahedi, K.; Melcher, J. R. Ind. Eng. Chem. Fundam. 1977, 76, 240. Zahedi. K.; Melcher, J. R . J . Air Pollut. Control Assoc. 1978, 26(4). 345.
= velocity potential, m2s-l s-l 4 = angle defining edge of step velocity profile L i t e r a t u r e Cited
A,, B, = constants used in eq 9 and 15 c = correction factor for noncontinuous effects L = granular bed length, m P, = nth-order Legendre polynomial Re = Reynolds number S t = Stokes number Uo = superficial/face gas velocity, m s-l a = bed granule radius, m 1 = unit-cell radius, m no = inlet concentration of fine particles, mW3 r, 8 = polar coordinates rp = fine particle radius, m t = time, s u = local gas velocity, m s-l ur, ug= radial and tangential components of local gas velocity, m s-l u = fine particle velocity, m s-l ur, ug = radial and tangential components fine particle velocity, m 1*, r*, u*, etc. = normalzied parameters
~
Greek Letters = bed void fraction @ = intesification factor r = single-sphere collection rate, s-l 7 = total bed collection efficiency
Received for review May 6, 1982 Accepted August 25, 1983
CY
This work was performed under the U S . Department of Energy Contract No. DE AC01-79-ET15490.
Crystallization of Calcium Carbonate Accompanying Chemical Absorption Hideharu Yagi, Akira Iwazawa, Rikio Sonobe, Toshinao Matsubara, and Haruo Hikila +
Department of Chemical Engineering, University of Osaka Prefecture, 4-804 Mozu-Umemachi, Sakai, Osaka, 59 I , Japan
Crystallization of CaCO, accompanying chemical absorption of COP as a single gas and as a mixture with SO, into aqueous solutions of Ca(OH), was studied in a stirred vessel with a flat gas-liquid interface. The nucleation and growth rates determined by CSD analysis of crystals formed in a MSMPR crystallizer were related to several operating conditions. The type and shape of the crystals varied with the concentration of Ca(OH),, but their mean size was only slightly influenced by the concentration of Ca(OH), and by the mean residence time of suspension. The presence of SO, considerably reduced the growth rate of CaCO, crystals under the conditions of a slight decrease in the rate of COPabsorption.
crystals produced by the gas-liquid reaction. In spite of its importance, little information is available on the characteristics of this process. The present work deals with the crystallization of calcium carbonate, CaC03, produced by the chemical absorption of a single or mixed gas in an aqueous solution of calcium hydroxide, Ca(OH),. Although many theoretical and experimental works on gas absorption have been reported and CaC0, is known to form different crystal varieties in different circumstances, the crystallization kinetics and the behavior of CaCO, crystals produced by this process have not been studied. A stirred vessel with a flat
Introduction
The gas-liquid reaction which produces a sparingly soluble material is an important process in the chemical, electronic, and metallugical industries. Well-known examples of its large-scale use include wet gas desulfurization, the production of calcium carbonate as a rubber filler, and ferrite production by the goethite method. The control of crystal size and shape is important for the subsequent separation process (Sohnel and Matejckova, 1981) and the quality of the product. It is probable, though it has not been confirmed experimentally, that the rate of gas absorption influences, and is influenced by, the habit of 0196-4313/84/1023-0 153$01.50/0
0
1984 American Chemical Society
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Ind. Eng. Chem. Fundam., Vol. 23,No. 2, 1984 Table I. Concentration of CaSO,. ' / l H , O ain t h e Suspension, mol/m3
C O : + N,
_ _ so:
a COi'S02*Ni
Figure 1. Schematic diagram of experimental apparatus: (1) crystallizer; (2) temperature-controlled bath; (3) motor; (4) flow meter; (5) heat exchanger; (6) gas tank (7) liquid tank (8) pump; (9) thermometer; (10) liquid level controller; (11)COz cylinder; (12) N2 cylinder.
gas-liquid interface, a similar type of absorber commonly used for study on gas-liquid reactions in the laboratory, was used as a mixed-suspension mixed-product removal (MSMPR) crystallizer. Rates of crystal nucleation and growth were obtained from the steady-state crystal-size distribution and the population balance equation (CSD analysis) as proposed by Randolph and Larson (1971). The relations of crystallization kinetics to the reactant concentration, the mean residence time of suspension, and the partial pressure of SO2 absorbed simultaneously were studied. The enhancement factor for gas absorption was measured and compared with the theoretical estimate. The effect of crystal particles produced by the reaction on the rate of gas absorption was also examined.
Description of System Possible reactions of C02in aqueous solution of Ca(OH), are COz + OH- = HC03-
(1)
HC03- + OH- = C032-
(2)
Ca2++ C032- = CaC03
(3)
Since the solubility of CaC03 is very low and the equilibrium constants for these reactions are very large, the effective reaction proceeds irreversibly as COz + Ca(OH)2= CaC03 + H,O (4) When the concentration of CaC03 exceeds its solubility, the nucleation and growth of crystals take place. In the simultaneous absorption of the mixture of C 0 2 and SOz, parallel to the reaction of eq 4, the following reaction occurs
SO2 + Ca(OH), = CaS03.1/2H20+ '/2Hz0
(5)
Experimental Section Figure 1 shows the experimental apparatus schematically. The crystallizer was a stirred vessel with a flat gas-liquid interface. The vessel consisted of a Pyrex cylinder, top and bottom covers, and two six-blade turbine stirrers. The vessel was 10.3 cm in diameter and 15 cm high, with a liquid depth of 10.3 cm. Four vertical baffles, 1cm wide, were oriented 7r/2 rad and fitted from 1 cm to 9 cm above the bottom. The stirrers, 5 cm and 8 cm in diameter, were positioned at the middle of liquid and gas phases and set at 5 s&. The bottom cover, the liquid-phase stirrer and the shaft were made of stainless steel. The top cover and the gas-phase stirrer were made of acrylic resin. The liquid reactant was prepared by dissolving Ca(OH), (guaranteed grade) in distilled water, filtering through
viv, 7c
Psop Pa x 10''
0.5
0.51
1 2
1.01 2.02
mean residence time, s
210
120
840
0.51
0.51 1.02 2.05
2.05
Solubility of CaSO;I/,H,O is 0.42 mo1/m2.
Tohoroshi No. 5C filter paper until even trifling muddiness had disappeared, then diluting to the desired concentration with distilled water. This solution was continuously fed to the crystallizer at a constant flow rate. The suspension was removed from the crystallizer via a liquid level controller. In the single-gas absorption, COz and N2 gases from cylinders were mixed in the desired ratio by use of two flow meters and fed into the crystallizer. In the simultaneous absorption, the mixture of C02and SOz, balanced with N2 to the desired concentration, had been previously saved in a bag; then it was squeezed out the bag and fed into the crystallizer a t the constant flow rate of 5 cm3/s. To start a run, the crystallizer was filled with pure N2, the reactant liquid was fed to the crystallizer a t a given flow rate, and stirring was started. The liquid was withdrawn continuously through the level controller to maintain a constant volume in the crystallizer. Then, the flow of reactant gas was begun. The concentrations of Ca(OH), in the inflow and outflow liquids were determined by the titration with standard solution of HCl. Crystal sizes were measured by the microphotographic technique. Since the crystals were not spherical, the size of an individual crystal was defined as the Feret diameter, the perpendicular projection, onto a fixed direction, of the tangents to the extremities of the particle profde (Perry and Chilton, 1973). Samples were taken after the crystallizer had run for 5 , 7,10, and/or 12 residence times. Steady state was assessed by constant CSD and Ca(OHIz concentration in the product suspension.
Calculation The calculation method is described for the case of simultaneous absorption, but in case of Pso, = 0, the following equations give the values for the single-gas absorption. Since SO2is very soluble in water and the gas flow rate was slow, most of the supplied SOz was absorbed in the liquid; the gas chromatographic analysis could not detect SO2 in the exit gas. The rate of SOz absorption was given by Nsoz = pso, V~/(298R) (6) where Pso, was the partial pressure of SO2 in the feed gas and VG was the gas flow rate. The rate of COPabsorption was obtained from the difference in Ca(OH), concentration between inflow and outflow liquids and the rate of SO2 absorption
NCO,= W
i n
- Bout) - N S O ~
(7)
The experimental value of enhancement factor for C 0 2 absorption was given by
P = Nco,/(k~*AAi)
(8)
Table I shows the concentrations of [CaS03J/zH20]in the outflow suspension obtained from eq 9 [CaSO3.1/,1 = N s o , / ~
(9)
Ind. Eng. Chem. Fundam.. VoI. 23, No, 2. 1984
0
5 cry5101 *,ze,
155
IO pnl
Fieure 2. Crystal size diatribution in single-gas absorption plotted an semilogarithmic coordinates.
Although these values exceeded the solubility, SO3*- ion was not detected in the crystals. Therefore CaS02- had left the crystallizer as a supersaturated solute or before its crystals grew to the size caught by a submicron fdter paper. Therefore, our study was focused on the crystallization of CaCO,. For a perfectly mixed MSMPR crystallizer operated under steady-state condition, the population density for size-independent crystal growth is given by
n = no exp(-L/GT)
-
1
0
10
5 cry51.21 size.
Lrn
Figure 3. Crystal size distribution in mixed-gasabsorption plotted on semilogarithmic cwrdinates.
(10)
If plots of population density vs. crystal size on semilogarithmic ccadmatea give a straight line, the crystal growth rate G a t a given residence time T run can be calculated from the slope of the line -1IGT. The nucleation rate was calculated from the following relation
where the concentration C of dissolved CaC03 was negligible. If the volume-shape factor is the same for all crystals, the following relation is obtained
P
= +nOG =
2 0 ldeg)
Figure 4. Scanning electron micrograph and X-ray diffraction pattern.
- Bout - P~O,VG/(~~EFR)I/(~PC~T"/M (12) shown a reduction in crystal growth rate with decreasing In the pregent paper, the value of P,is given by eq 12, was crystal size. However, the CSDs for calcium carbonate [Bin
defined as the nucleation rate. The mean size of crystals was calculated from
Results end Discussion To prevent the precipitation a t the gas-liquid interface, the steady-state concentration of Ca(OH), was limited. Nevertheless, a t the beginning of continuous operation small particles precipitated a t the gas-liquid interface. Most of the particles, however, were soon involved into the bulk liquid by the stirring. After that, the precipitation a t the gas-liquid interface was not observed. Figures 2 and 3 show sample steady-state CSDs plotted on semilogarithmiccoordinates for two CO, partial pressures in the single-gas absorption and for different SO, partial pressures in the mixed-gas absorption. The straight line plots indicate that the crystal growth obeys McCabe's AL law. Several workers (Youngquist and Randolph, 1972; JanEiE and Garside, 1975; Sikdar and Randolph, 1976; Garaide and JanEiE, 1979; BreEevi6 and Garaide, 1981) have measured the CSD helow the limit for sieving (50pm) and
precipitated by liquid-liquid reactions (Maruscak et al., 1971; Schierholz and Stevens, 1975; Swinney et al., 1982) were linear on semilogarithmic coordinates. Linearity is also seen in the CSDs for ammonium chloride (Shadman and Randolph, 1978) and sulfamic acid (Toyokura et al., 1979) in reaction-crystallization systems. The kinetics of crystallization is generally correlated with supersaturation. In the reaction-crystallization,however, the crystallization kinetics is often correlated with different factors; the concentration of reactants (Toyokura et al., 1979), pH (Phillips et al., 1977), or the concentration of a third material (Shadman and Randolph, 1978). This is because the solubilities of crystals in reaction-crystallization are naturally low, and the measurement of supersaturation is therefore difficult. In the present work, the crystallization kinetics was related to the operating conditions and the circumstance, i.e., the mean residence time of suspension, the concentration of Ca(OH), in the outflow liquid, and the partial pressures of COz and SO2. (i) Single-Gas Absorption. Figures 4,5, and 6 show the characteristics of the crystals produced a t the mean residence time (MRT) of 420 s. Photographs were ob-
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Ind. Eng. Chem. Fundam.. Vol. 23, No. 2, 1984
n
0.1
I
c ~ ( o H )FOIICI~. ~ mol~m’
?!L
Figure 7. Growth rate of CaCO, crystals for two C02partial pressures plotted against Ca(OH), concentration.
e c
20
‘0
60
0
0.25.105
d
0.5
XI+
2 9 (deg)
Figure 5. Scanning electorn micrograph and X-ray diffraction pattern.
r 0.1
co(on),
I concn. mol 1m3
Figure 8. Nucleation rate of CsC03 crystals for two COS partial pressures plotted against Ca(OH), concentration.
-
L
-:ilL 5
f
C.l0HI1
i
0 . 3 mo,,ml
50
20
‘0
60
2 e (dpg) Figure 6. Scanning electron micrograph and X-ray diffraction pattern.
1 - 1
I 0’
lo3 MRT.
tained on a Jeol JSM 50A scanning electron microscope, and X-ray diffraction patterns were obtained on a Rigaku Denki powder X-ray diffractometer. The crystals shown in Figure 4 were produced a t low Ca(OH), concentration (
