Binding Liquid Requirements for Agglomeration by Tumbling’ C. Edward Capes,* Rene J. Germain, and Richard D. Coleman Division of Chemistry, National Research Council of Canada, Ottawa K I A OR9 Canada
The interior pores of agglomerates formed in balling drums and disks can be considered to be approximately saturated with binding liquid. With this assumption, the following equation can readily be derived: W = 1/[1 ((1 - t)ps)/(tpL)]. W is the weight fraction of liquid in the agglomerate, t is its void fraction, and ps and p~ are the particle and liquid densities, respectively. The purpose of the work reported here was to derive a correlation for binding liquid requirements based on this simple equation. A wide variety of data from both the patent and scientific literature were used in the study. Solid density ranged from about 1 to 6 g cm-3 while liquid density was generally close to 1 g ~ m - The ~ . effects of both feed particle and product agglomerate size on balling liquid requirements were assessed and it was found that the former effect was much stronger than the latter. The following equations were derived to estimate the binding liquid level for agglomeration by tumbling: for particle diameter 30 p , W = 1/[1 2.17(ps/pL)].
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Downloaded by UNIV OF NEBRASKA-LINCOLN on August 30, 2015 | http://pubs.acs.org Publication Date: October 1, 1977 | doi: 10.1021/i260064a014
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Introduction The agglomerates formed in balling drums and disks are generally considered to have their internal pores saturated with binding liquid (Bhrany e t al., 1962; Butensky and Hyman, 1971; Capes and Danckwerts, 1965; Sherrington, 1968). In quantitative terms, this model of a saturated structure yields eq 1 for the liquid content of an agglomerate on a wet basis CPL
W= WL
+ (1- t ) P S
(1)
W is the weight fraction of liquid in the agglomerate, t is its void fraction, and p s and p~ are the particle and liquid densities, respectively. In practical systems, however, the prediction of the liquid requirements for balling by eq 1 is complicated by a number of factors. Agglomeration occurs over a narrow range of liquid contents and not simply a t one value as inferred above. Equation 1 may thus be assumed to predict the average or “optimum” level. Solubility of any of the solid components will increase the effective amount of liquid in the mix so that the quantity of the binding phase is then greater than the volume of liquid added (Hardesty, 1955; Hardesty et al., 1956). Part of the internal voids contain trapped air and the complete capillary liquid state is not reached. Even if the agglomerate interiors are essentially filled with liquid, the surfaces are relatively dry since the liquid menisci are withdrawn into it in developing the capillary binding forces. Thus smaller agglomerates are expected to contain less liquid than larger ones due to their larger surface/volume ratios (Sherrington, 1968). In addition, variations in liquid properties such as viscosity, surface tension, and wetting characteristics, in solid properties such as particle shape, size, roughness and wettability, and in operating variables such as drum speed, size and loading all mitigate against development of a simple relationship to predict the binding liquid requirements for a wide range of agglomeration systems. Nevertheless, it is worthwhile to determine the extent to which the simple approach embodied in eq 1 may be used to represent actual agglomeration data; this was the objective of the present study. Testing the Model Literature data were used exclusively to test eq 1 and this presented a number of problems due to incomplete information. As a minimum, a report had to state the amount and type NRCC No. 16191.
of binding liquid as well as the type of solids treated. Often, liquid and solid densities were not indicated in which case these were estimated with reference to standard handbooks. Since the effect on liquid requirement of both the particle size and the agglomerate diameter were to be examined, it was desirable that the source should contain information on these two variables. Where this information was not given, an estimate based on knowledge of similar feed materials and products was made. A total of 47 different reference sources from the scientific, patent, and trade literature up to the end of 1973 were found to contain sufficient information for use in the study (Germain, 1973). These sources provided 92 sets of data for materials ranging from fertilizers, iron ore, and sand through to cement mix, glass batch mix, and fly ash. The sets included repetitive data from different sources for some of the more commonly agglomerated materials such as iron ore. Since product density was rarely given in the literature sources, it was assumed that the agglomerate void fraction, t , could be considered constant. In addition, since most agglomeration data pertains to water as the bridging liquid, measurements for other liquids were converted to the weight fraction of water equivalent to the volume of the actual liquid used. With these simplifications, eq 1 becomes W=- 1 l+ke PL
where h is a parameter given by (1- t ) / ( c p ~ ) Equation . 2 was fitted to the data by a nonlinear least-squares procedure. Five different groupings of the data were used: (1)all the data sets; (2) data for particle diameter less than 30 k ; (3) data for particle diameter greater than 30 k ; (4) data for agglomerates smaller than 5 mm; ( 5 ) data for agglomerates larger than 5 mm. For each grouping of the data, the least squares procedure was repeated several times with rejection of all points outside two standard deviations from the fitted relationship a t each stage. This resulted in rejection of an average of 24% of the data over the five data groupings used (see Table I).
Results and Discussion Table I summarizes the values of the parameter k in eq 2 and their standard deviations obtained in grouping the data according to both feed particle size and product diameter. I t is evident that the feed particle size has a stronger effect on bridging liquid requirements than does the agglomerate size. Ind. Eng. Chern., Process Des. Dev., Vol. 16, No. 4, 1977
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Table I. Least-Squares Results in Fitting Eq 2
Grouping of data All data Data for particles
2.09 (.07) 1.85 (.07)
26% 28%
36%
From the results of this study, it is recommended that the following equations be used to calculate the binding liquid level required for agglomeration by tumbling; for fine particles ( 4 0 1 W= (3) ' 1 1.85&
2.17 (.lo)
16%
29%
for coarse particles (>30 p)
2.08 (.09)
22%
32%
W=
2.18 (.09)
27%
24%
Parameter % Std dev of k % of data calcd W from (std dev in rejected "Experibrackets) (outside f 2 a ) mental" W 27%
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PL
30 p Data for agglomerates 5 mm
1
Recalling the inverse relationship between W and 12 in eq 2, comparison of the values of k for particle diameters 30 p show that greater bridging liquid amounts are required for the finer particles. This may be explained in terms of the larger surface/volume ratios of the fine particles and the relatively greater surface forces existing between them. Agglomerates of the finer particles would therefore be expected to exhibit higher void fractions, and hence larger amounts of bridging liquid to fill these voids, than the agglomerates of the coarser particles. The relative amounts of data rejected because they were outside two standard deviations from the final correlating relationship are also given in Table I. The greatest rejection level occurred with the fine feed particle grouping and this possibly reflects the fact that with very fine particles (e.g., carbon black), forces other than capillary, such as electrostatic and van der Waals, may contribute significantly to bonding, especially a t lower liquid saturations. Thus, the amount of capillary bridging liquid needed for agglomeration will vary according to the amount of bonding obtained by these parallel mechanisms. I t is also known that due to the large surface/ volume ratio of fine particles, their degree of packing in an agglomerate is very dependent on the time and energy expended in compacting them. These factors could not be controlled in the data used in this study. In general, another factor leading to variability in the data and to rejection of some of the points was the inclusion of patent specifications in the study. Patents would be expected to cover wide ranges of the variables to give broader coverage although the upper and lower limits of the variables (such as liquid content for balling) would seldom represent "ideal" conditions.
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Ind. Eng. Chem., Process Des. Dev., Vol. 16, No. 4, 1977
+ 2.17psPL
(4)
Conclusion Equations 3 and 4 may be used to calculate approximately the binding liquid requirements for agglomeration by tumbling where actual balling data on the material in question are not available. The considerable deviation of the values calculated by these equations from the actual data is not surprising in view of the wide variety of data sources employed, the uncontrolled nature of the system and operating variables, and the lack of complete information in the literature data. Acknowledgment The authors thank A. E. Fouda for his help in the computational work. Nomenclature k = parameter in eq 2 given by (1 - t ) / c p ~ cm3/g , W = weight fraction of binding liquid for agglomeration t = void fraction in an agglomerate p~ = density of binding liquid, g/cm3 ps = true density of particles, g/cm3 CT = standard deviation L i t e r a t u r e Cited Bhrany, U. N., Johnson, R. T., Myron, T. L.,Pelczarski, E.A,, in W. A. Knepper, Ed., "Agglomeration", p 229, Interscience, New York, N.Y., 1962. Butensky, M , Hyman, D., Ind. Eng. Chem., Fundam., 10, 212(1971). Capes, C. E., Danckwerts. P. V., Trans. Inst. Chem. Eng., 43, T116, T I 2 5 (1965). Germain, R., "Moisture Requirements for Agglomeration by Tumbling", National Research Council, Ottawa, Dec 10, 1973. (Available from C.E. Capes, National Research Council, Ottawa, Canada.) Hardesty, J. O., Chem Eng. frog., 51, 291 (1955). Hardesty, J. O., Szabo, A,, Cummings, J. G., J. Agr. Food Chem., 4, 60 (1956). Sherrington, P. J., Chem. Eng. (London), 220, 201 (1968).
Receioed f o r review October 21,1976 Accepted June 15,1977
