Ind. Eng. Chem. Res. 1987,26, 397-398 PT = recuperator pipeline air temperature in G8 measured by thermocouples in Table I1 and Figure 4 (circled points),
K N / 0 2 = 4 for air and 0 for oxygen/steam in eq 10, mol/mol of O2 q5 = H20/Oz = steam/oxygen ratio in eq 9-11, mol/mol of
q1 =
0 2
c4i = 41 + q 5 S = surface area of sample base (base of cuboid or cylinder),
cm2 TC = calculated temperature, an intermediate between CZT and link zone temperature, K V = volume of coal sample, cm3 VIa, Vza = volatile matter in coal sample before and after gasification, respectively, w/o W (E or C) = water content in product gas, v/o Wla, WZa= water content in coal before and after gasification, respectively, w/o z = amount of fixed carbon reacting with 1 mol of 02,in eq 8 and 11, mol/mol of O2 Registry No. H2, 1333-74-0.
397
Harloff, G. J.; Eddy, T. L.; Schwartz, S. H. Presented at the Proceedings of the 6th Underground Coal Conversion Symposium, Shangri-La, OK, 1980;p 111-40. Massey, L. G. Adu. Chem. Ser. 131, 1974,15. Natarajan, R.; Edgar, T. F.; Savins, J. G. Presented a t the Proceedings of the 6th Underground Coal Conversion Symposium, Shangri-La, OK 1980;p 111-15. Perry, C.; Gillott, J. E. Bull. Can. Pet. Geol. 1982,30(1),34. Rauk, J. Ph.D. Dissertation, Central Mining Institute, Katowice, Poland, 1971 (in Polish). Rauk, J. Thesis for Assistant Professorship, Central Mining Institute, Katowice, Poland, 1978 (in Polish). Rich, F. J.; Youngberg, A. D. Prepr. Pap-Am. Chem. SOC.,Diu. Fuel Chem. 1983,28(1),141. Wei, J. Ind. Eng. Chem. Process Des. Dev. 1979,18, 554. Wen, C. Y.; Lee, E. Stanley Coal Conversion Technology; AddisonWesley: Reading, MA, 1979;p 72. *Author to whom correspondence should be addressed a t Marchlewskiego 8/2,40-129Katowice, Poland.
Jerzy Mastalerz, Maciej S. Matyjaszczyk,* Jerzy Rauk Central Mining Institute 40-951 Katowice, Poland
Literature Cited Barrer, R. M. Zeolites and Clay Minerals as Sorbents and Molecular Sieves; Academic: London, 1978.
Received for review April 3, 1984 Revised manuscript received July 31, 1986 Accepted September 18, 1986
CORRESPONDENCE Comments on “Predicting the Maximum Spoutable Height in Spouted Beds of Irregularly Shaped Particles” Sir: Morgan and Littman (1982) have presented a correlation for predicting the maximum spoutable height in spouted beds of irregularly shaped particles. The correlation for spherical particles proposed by Littman et al. (1978) is modified to account for the effect of particle shape by introducing a factor g(@s),a function of particle shape factor, qbS. Hence, modified correlation
should fit both spherical and nonspherical particle data. For the nonspherical particle data given in Table I1 (Morgan and Littman, 1982) with a value of A,, > 0.014 (for 24 data points), in eq 1 the standard deviation of m is 0.226 and an average deviation 37.4%. To improve the accuracy of the fit and to retain similarity with the correlation for spherical particles, Morgan and Littman, using data for both spherical and nonspherical particles, have made an asymptotically similar fit to eq 1 to get the quadratic m = 0.218 + 5.13
10-3A,;1 + 2.54 A,, > 0.014 X
X
10-5A,,-2 (2)
Equation 2 fits the nonspherical partical data mentioned above with a standard deviation of m of 0.185 and an average deviation of 27.1% . Introduction of the third parameter has not resulted in any substantial improvement in accuracy of the fit, while simplicity is lost. Also, eq 1 and 2 differ with regard to the effect of variables on H,. 0888-5885 / 87/ 2626-0397$01.50/ 0
For example, the effect of di on H, in eq 1 and 2 is different. In view of the above observations, the significance of parameters in eq 1 and the need to retain them in the development of an equation for nonspherical particles are checked. In the process, it is observed that nonspherical particle data of Malek and Lu (1965) for air-polyethylene and air-brucite systems were used along with the data for spherical particles by Littman et al. (1978), without any correction factor for shape as proposed by Morgan and Littman (1982), in order to get the correlation m = 0.218 + 0.005/A (3) for spherical particles. Littman et al. (1979) have given additional data on maximum spoutable height in spouted beds of spherical particles and a mA vs. A plot. The data for A > 0.02 in that plot are said to fit eq 3 within about 12% average deviation. The 62 data points identified from the plot include those for air-polythene and air-brucite systems also and fit eq 3 with a multiple correlation coefficient squared (R2)of 0.636, a standard deviation of m of 0.053, and an average deviation of 12.25%. Based on a leastsquares estimation, the same data give m = 0.180 + 0.00645/A (4) with R2 = 0.68, a standard deviation of m of 0.05, and an average deviation of 11.6%. The above analysis indicates that no significance can be attached to the parameters in eq 3, as the data used for 0 1987 American Chemical Society
398
Ind. Eng. Chem. Res. 1987,26, 398-399
obtaining them are a mix of values for spherical and nonspherical particle systems and also, because of large scatter, different parameters give an equally good fit. So, making an asymptotically similar fit to retain the parameters 0.218 and 0.005 is not necessary. In view of the above reasoning, an attempt is made to obtain a two-parameter correlation to replace eq 2 using the data given in Littman et al. (1978), Littman et al. (1979),and Morgan and Littman (1982). Of the 102 data points (A,, > 0.014) given in the above three references, 85 points were used to obtain m = 0.167 + 0.0078/A,, (5)
For these 85 data points, eq 1,2, and 5 compare as shown in Table I. For the 24 nonspherical particle data points used to test eq 1 and 2 earlier, eq 5 gives a standard deviation of m of 0.179 and an average deviation of 25.8%, which shows that the simpler two-parameter eq 5 is as good or even slightly better than the three-parameter eq 2 of Morgan and Littman. Further, Morgan and Littman (1982) have extended to nonspherical particles the criterion proposed by Littman et al. (1979),for finding the maximum inlet tube diameter in a bed of height H,, for which the fluidization of annular solids causes the spout termination mechanism. It is claimed that for spherical particles there is excellent agreement with the experimental data and for nonspherical particles there are no data to test the modified criterion. The source of the maximum inlet tube diameter data presented in Table I11 of Littman et al. (1979) is given as Littman et al. (1978). But materials and their particle diameters match those used in Malek and Lu (1965), and even this reference does not give any data on maximum inlet diameter in a bed of height H,. Figures 8 and 9 of this reference, which depict the effect of orifice diatneter on maximum spoutable depth, also do not contain the data given in Littman et al. (1979). Table IV in Malek and Lu
Table I eq no. 1 2 5
R2
std dev of m
av dev, 90 ’
0.678 0.781 0.795
0.076 0.063 0.061
15.3 13.1 12.0
(1965) shows that the maximum values of di used for each of the materials correspond to di/D, of 0.3125 for wheat-3, 0.33 for polystyrene, and 0.29 for millet, whereas Littman et al. (1979) give experimental values of (di/Dc)max as 0.35, 0.396, and 0.313, respectively. Moreover, polystyrene particles are nonspherical with a shape factor ds = 0.84. So, only the lone data point of Grbavcic for a bed of glass beads spouted with water reported in Littman et al. (1979) is available for testing this criterion even for spherical particles. For spouting with gases, data are needed for both spherical and nonspherical particles. Literature Cited Littman, H.; Morgan, M. H., 111; Vukovic, D. V.; Zdanski, F. K.; Grbavcic, Z. B. “Proceedings of the 2nd Engineering Foundation Conference on Fluidization, 1978, Cambridge”; Davidson, J. F., Keairns, D. L., Eds.; Cambridge University Press: Cambridge, England, 1978; pp 381-386. Littman, H.; Morgan, M. H.; 111; Vukovic, D. V.; Zdanski, F. K.; Grbavcic, Z. B. Can. J. Chem. Eng. 1979,57, 684-687. Malek, M. A.; Lu, B, C. Y.Ind. Eng. Chem. Process Des. Dev. 1965, 4,123-128. Morgan, M. H., 111; Littman, H. Ind. Eng. Chem. Fundam. 1982,21, 23-26.
K. Babu Rao Chemical Engineering Division Regional Research Laboratory Hyderabad 500 007, India
Reply to Comments on “Predicting the Maximum Spoutable Height in Spouted Beds of Irregularly Shaped Particles” Sir: This will reply to K. B. Rao’s comments on our paper (Morgan and Littman, 1982) concerning the prediction of the maximum spoutable height in spouted beds. 1. We found during our initial investigations (Littman et al., 1978, 1979) that the equation m = Hmdi/D,2= 0.218 + 0.005/A; A
> 0.02
(1)
fit experimental data for the maximum spoutable height in beds of coarse spherical particles with an average deviation of 12%. Rao has recorrelated the data we used and obtains the correlation m = 0.180 + 0.00645/A. His recorrelation reduces the average deviation from 12.25% to 11.6%. This is hardly significant since errors in measuring H , are at the very least 10%. 2. Rao is concerned that in Littman et al. (1978) Malek and Lu’s data were used in developing eq 1 without any correction factor for shape. The average deviation of the data from eq 1is about 12% both with and without Malek and Lu’s data.
3. In Morgan and Littman (1982), we reported on the effect of particle shape and presented the equations = 0.218 5.13 X 10-3A,;1 + 2.54 X 10-5A,,-2; A > 0.014 (2) and m = 1.75(A,, - 0.010); 0.010 C A,, 5 0.014 (3)
+
where A,, = Ag(h). For spherical particles, A,, = A . Retaining the same form as eq 1, Rao correlated the data for both spherical and nonspherical particles and obtained m = 0.167 + 0.0078/A,, (4) Comparing the fit of eq 2 and 4, he finds that eq 4 reduces the standard deviation from 0.063 to 0.061 and the average deviation from 13.1% to 12.0%. Considering the scatter of the data (Figure 1, Morgan and Littman, 1982), such an improvement in the correlation is again hardly significant.
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