Ind. Eng. Chem. Process Des. Dev. 1984, 23, 341-343
= solid density, g/cm3 Literature Cited ps
BrBtz, W. Chem. Ing. Techn. 1958, 28, 165. Chang, C. C.; Fan, L. T.; Rong, S. X. Can. J . Chem. Eng. 1982, 6 0 , 272. Davldson, J. F.; Harrison, D. “FiuMlzation”; Academic Press: London, 1971; Chapter 14. Fen, L. T.; ToJo, K.; Chang, C. C. Ind. €47. Chem. RocessDes. Dev. 1979, 78. 333. Fan, L. T.; Chang. C . C. ACS Symp. Ser. lS81, No. 768, 95-115. Gabor, J. D. A I C M J . 1864, 10. 345. Geldart. D. Powder Techno/. 1973, 7 , 285. (Lace, J. R. ACSSymp. Ser. 1981, No. 168, 1-18.
341
Highley, J.; Merrick, D. AICMSymp. Ser. 1971, 67(116), 219. Hlrama, T.; Ishida, M.; Shlrai, T. Kageku Kogaku Ronbushi 1975, 7 , 272. Kunli, D.: LevensDlei. 0. “Fluidization Enaineerina”: Wilev: New York, 1969; p 130. M e v ,J. M. D.; Davidson, J. F. Trans. Inst. Chem. Eng. 1973, 51, 361. Morl, Y.; Nakamura, K. Kagaku Kogaku 1985, 29, 866. Rowe, P. N. Chem. Eng. S d . 1976, 3 1 , 285. Whitehead, A. B.; Gartskle, G.; Dent, D. C . Chem. Eng. J . 1970, 7 , 175. Whitehead A. B. Chem. Eng. Scl. 1879, 3 4 , 751.
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Received for review December 28, 1982 Accepted July 18, 1983
Particle Size Distribution Analysis of Blended Solids by a Modified Andreasen Pipet Method Robert W. Farmer and James R. Beckman’ Chemical and Bio Engineering Department, Arizona State Unlverslfy, Tempe, Arizona 85287
A method to determine independent, sub-sieve particie size distributions for two or more blended species is described. An illustrative example is given for a blend of gypsum (CaS0,.2H20) and calcium hydroxide (Ca(OH),) which is of interest in’ nonregenerabie desulfurization processes. Data scatter is reduced by using a modified Andreasen pipet apparatus in conjunction with a quantitative chemical analysis.
In certain instances it is necessary to determine independent particie size distributions for two or more blended solid species. An example would be a crystallization process in which the effluent stream contains inert or byproduct particulates as well as the desired product crystals (Farmer, 1982). A sub-sieve range (10-80 pm) particle sizing method is described for a particular pair of blended crystal species: gypsum (CaSO4.2H2O)and calcium hydroxide (Ca(OH)2). This combination is of interest in nonregenerable desulfurization applications such as the lime/limestone wet-scrubbing and dual alkali processes. Methods for particle size analysis and interpretation of the results have been surveyed in texts by Allen (1968) and by Irani and Callis (1963). The means of particle sampling and indication of crystal size distribution (CSD) may dictate the suitability of a given method. In this study, methods which offered only visual or gravimetric indications of size distribution were not feasible, since no distinction could be made between the two solids present. The approach adopted utilizes a modified version of the Andreasen pipet in conjunction with a quantitative chemical analysis to indicate the relative amounts of each solid compound present. The Andreasen pipet belongs to the class of sedimentation techniques termed incremental methods. Such methods consist of periodically determining the concentration of solids at a given depth in a vertical settling tube (Berg, 1959,1965). The chemical analysis employed makes use of the differing acid solubilities of the two compounds of interest. For other applications of this method, various chemical or physical property differences may be used to distinguish the amount of each species present. The key point which makes the Andreasen technique so well suited is that discrete particle samples are obtained, each of which correspond to a calculable mean particle dimension. 0796-4305/84/ 1723-0347$01.50/0
Theoretical Considerations The practical range of particle size which may be measured by sedimentation in water is from about 0.1 to 100 pm. Stokes’ law, which is the basis of all sedimentation procedures, describes the steady-state settling of spherical particles. An upper limit of the validity of Stokes’ law has been given in terms of the particle Reynolds number, Re, P*dpVt
Re, = -I1.0 9
(1)
The constant terminal velocity may be written in terms of a distance, h, traversed over an elapsed settling time, At, and if Brownian motion is neglected, the gravitational force may be equated to the frictional force. This leads to the well-known Stokes equation for laminar particle settling
where p and ps are the mass densities of the fluid medium and a particular solid species, respectively. Assuming a uniform initial suspension and laminar settling an elapsed time At may be calculated from eq 2 which will correspond to a Stokes particle diameter, d,, that has settled a distance, h. An aliquot sample taken at this depth would thus contain only particles with Stokes diameter less than d,. So the concentration of solids present, C , as a fraction of the initial uniform concentration, Co, will correspond to the cumulative weight fraction undersize for diameter d, (3)
where { (L) is a general size distribution function of mean 0 1984 American Chemical Society
342
Ind. Eng. Chem. Process Des. Dev., Vol. 23,No. 2, 1984
tMODIFIED ANDREASEN SEDIMENTAm CYLINDER
CALIBRATED lOml MARK
I
HDfFMANN CLAMP SAMPLING PIPETTE
Figure 1. Experimental apparatus for particle size analysis.
particle dimension, L, presumed to be equal to the Stokes diameter for approximately spherical particles. In applying the Andreasen method, as in this study, the size distribution may be calculated directly from solids weight measurement assuming all aliquot samples are of equal volume
WL = cumulative weight fraction undersize for mean W
particle dimension, L (4)
Analytical Technique To apply the concept of differing acid solubilities, it is first recognized that the hydroxide species is subject to quantitative acid titration while the sulfate is not. In the presence of additional excess acid, the remaining gypsum solids are also driven into aqueous solution but do not consume acid in so doing. The total liquid volume must be sufficiently large so that the solubility product of either compound is not exceeded. Then the final solution pH may be adjusted as required for analytical measurement of total calcium ionic concentration. A number of analytical techniques exist for determination of ionic calcium, Ca2+,in aqueous solution. Ion-selective electrodes were successfully used for direct determination of total calcium ion concentration (Hulanicki and Trojanowicz, 1976). EDTA titration, however, was found to be impractical for the compounds under study. Interference by sulfate ions present in the solution has been noted by Diehl (1974) in both EDTA complexation and color end point clarity. Also, precipitation of calcium hydroxide was observed at the alkaline pH levels required. Experimental Section The Andreasen pipet apparatus used by Berg (1959, 1965) was simply a vertical cylinder, approximately 4 cm in diameter and 80 cm in height. Samples were to be withdrawn at measured time intervals from a horizontal port mounted near the bottom of the cylinder at some known depth below the liquid surface. After a number of trials with this device, a slightly modified version was employed for this study (Figure 1). It was found that settled particle residue in a horizontal port was picked up in subsequent samples, resulting in an inaccurate measure of solids density. By mounting the sampling port at an angle of about 30°, most of the remaining residual particles fell back out of the port after sample removal. Data scatter
and inconsistencies in the solids density measurements were markedly reduced by use of this modified apparatus. The modified Andreasen sedimentation cylinder used was constructed from translucent PVC piping, 5 cm inside diameter and 43 cm in height. A sample port tube 6.5 mm in diameter was mounted 4.5 cm above the bottom of the cylinder. The sampling port was smooth and unrestricted and extended to within 1 cm of the center line of the sedimentation cylinder. Actual withdrawal of consistent sample volumes was affected by the use of “sampling pipettes”. A number of these were made and a calibrated mark scribed for exactly 10 mL volume. These glass tubes were 6.5 mm in diameter and 64 cm in length; a Hoffmann screw clamp on the free end permitted control of the sample withdrawal rate. Typical suspension sample volume ranges between 600 and 650 mL, with solids not to exceed 1% by volume, as has been recommended to ensure uninhibited settling (Allen, 1968). If a particular sample should require dilution, a “prep solution’! saturated with all ionic species present must be used. In this way dissolution or growth that may effect sample CSD is avoided. To start the Andreasen analysis, the filled sedimentation cylinder was agitated to thoroughly suspend the particles and break up weak agglomerates. The cylinder was then mounted on a ringstand clamp and the elapsed time stopwatch was started. For particles having the density of gypsum and calcium hydroxide, the first appropriate sampling time, for about 85 pm and undersize, is 45 s from the onset of laminar settling. As dictated by the quadratic relationship between particle diameter and elapsed settling time, the intervals between samples become longer for detection of the smaller particle diameters. To remove a suspension sample, a sampling pipet was inserted into a tubing connection at the sample port. The Hoffman clamp was then opened gradually to slowly remove the 10-mL aliquot. Ideally, this should be done over as short a time span as possible, while not disturbing laminar particle setting. A consistent withdrawal time of 20 s has been recommended (Allen, 1968). After the removal of the required volume the Hoffmann clamp was shut quickly and the cylinder connection was clamped off. The sampling pipet was then detached from the port, and another one was inserted. A flexible tubing connection at the sampling port facilitates quick interchange of the pipets, as may be necessary for a rapid succession of samples. These aliquot samples were then vacuum filtered to near-dryness through Metricel, 0.8-pm pore membrane filters. Prep solution was used to rinse the solids from the sampling tubes to preclude dissolution. Solids on each filter were then washed with technical grade methanol to drive off adhering mother liquor. The entire membrane, with dried solids, was then placed in a 250-mL beaker for later chemical analysis. The analysis procedure may be divided into two tasks: fiist, a direct acid titration of the solids yielding the weight of hydroxide contained, followed by preparation of the sample for measurement of total calcium content by an ion-selective electrode. From this latter value the amount of gypsum present is obtained by difference. Since each sample treated corresponds to a calculable particle diameter for each compound, a size distribution for both species is determined in terms of cumulative weight percent undersize vs. the mean particle dimension when all of the samples are considered. To prepare the samples for ion-selective probe measurements, all of the solids must be driven into solution,
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 2, 1984
0 PURE CaS04*2Hp0 0 FROM BLENDED SCUDS
343
upon addition of base during pH adjustment of the samples. Titration errors and those associated with the calcium-selective probe are minimal, particularly if the acid titrant solution is carefully standardized, and electrode measurements are performed immediately after construction of a probe calibration curve. The major advantage of the modified Andreasen method applied here is that the particles are not dried prior to size analysis. This prevents possible agglomeration effects from biasing the experimental CSD, especially since calcium hydroxide and gypsum have a tendency to agglomerate upon drying. Conclusions and Applications A simple method has been demonstrated for simultaneous determination of CSD for blended solid species. By employing a modified Andreasen pipet apparatus in conjunction with a quantitative chemical analysis, it is possible to use differences in physical or chemical properties such as acid solubility, to distinguish between the compounds present. Important applications of this concept would include cases where the CSD of a single particulate product needs to be singled out from byproduct or inert solid species. It is also possible to elucidate, from a single experiment, the CSD of several materials. Acknowledgment The authors would like to acknowledge the financial assistance of Arizona State University Faculty Grant-inAid No. 520190. Nomenclature C = solids concentration CO = Initial solids concentration of a uniform suspension CSD = crystal size distribution d, = Stokes particle diameter g = gravitational acceleration h = settling distance L = mean particle dimension R e , = particle Reynolds number t = time At = elapsed settling time V , = particle terminal velocity W = solids weight in aliquot volume of initial suspension W , = solids weight of size L and undersize in aliquot volume 11 = water dynamic viscosity p = water density ps = solid density .t = size distribution function Registry No. Ca(OH)2,1305-62-0;H20, 7732-18-5; gypsum, 13397-24-5;sulfur dioxide, 7446-09-5. Literature Cited
, 1020
3 0 4 0 x ) 6 0 7 0 8 0 DWETER, L = d p ( p m l
I“
; J a
A FROM BLENDED SOClDS
4 1
20
I f 10
20
30
40
50
DIAMETER, L
60
70
80
‘dp(pml
Figure 2. Comparison o f CSD obtained f r o m p u r e materials and f r o m analysis o f blended solids; ( 0 , O ) CaS04-2H20(A,A) Ca(OH)*).
since the electrode probe will only detect solvated Ca2+ ions. This was done by further diluting the suspension to approximately 50-200 mL with deionized water and adding sufficient acid (0.4 M HC1) to cause complete dissolution. For ion-selective electrode measurements the media should be slightly basic, with pH value between 8 and 10, so a suitable base solution (0.4 M KOH) was added to adjust the solution pH. A good deal of subjective judgement must be exercised in the addition of the dilution water and acid volumes. The lower limit of linear measurement with the Orion ion-selective electrode used is a calcium ion concentration of 1 X mol/L, and accuracy improves with increasing concentration, so smaller, more concentrated samples are preferred. However, the solid compounds present are only slightly soluble in neutral water, up to 0.20 g/100 g of H20 for the hydroxide solid at 20 “C. Larger volumes will thus permit more complete and rapid dissolution. Results and Discussion Figure 2 shows an experimental determination of particle size distribution of the mixed solids using the modified Andreasen method. The figures show initial unblended samples of lime and gypsum slurries made from stock reagents. The slurries were then blended together to simulate an unknown CSD blended solids sample. The blended slurry sample was analyzed by the modified Andreasen method as described giving the individual CSD’s as shown in Figure 2. As can be seen, the CSD’s match very well with the initial unblended CSDs. This technique is an excellent procedure for elucidating the two independent solid CSD’s from a blended solids sample. The most important error in chemical analysis for solids composition is due to incomplete dissolution of the solids. Either the gypsum may not be driven completely into the solvated ion form, or calcium hydroxide may re-precipitate
Allen, T. “Particle Size Measurement”; Chapman and Hail; London, 1968. Berg, S. “Determination of Particle Slze Distribution by Examlning Oravitatbnai and Centrifugal Sedlmentatlon According to the Pipette Method and WRh Divers”, In Symposium on Particle Sire Measurement, ASTM Spec. Tech. Pub. No. 234, American Soclety for Testing and Materials, Philadelphia, 1959; pp 143-171. Berg, S. “Determination of Fineness”, I n Acta Polytechnlca Scandinavia , Chemistry Including Metallurgy Series, Chapter 43, Copenhagen, 1985; pp 9-13. Diehl, H. “Quantitative Analysis”; Oakland Street Science Press; Ames, IA, 1974; pp 280-287. Farmer, R. W. M.S. Thesis, Arizona State University, 1982. Hulanicki, A.; Trojanowicz, M. Anal. Chim. Acta 1076, 8 7 , 411. Irani, R . R.; Caiiis, C. F. “Particle Size: Measurement Interpretation and Application”; Wiiey: New York, 1983.
Received for review M a r c h 17, 1983 Accepted August 29, 1983
