Ind. Eng. Chem. Res. 1987, 26, 635-637 Table I. A and B Values for Three Categories“ of Particles oarticle A B round sharp other
29.5 32.1 25.2
0.0357 0.0571 0.0672
“Lucas et al., 1986.
The work by Lucas et al. (1986) produces the following equation to calculate Remf
Remf = (A2 + BAr)l12 - A
1.00 0.50 0.25
Chen, 1986. *Lucas et al., 1986.
cellent paper of Wen and Yu (1966) commits a more serious drawing error for the same kind of representation by joining with a straight line passing through tmf = 1 from 4 = 0.2 to 0. Nevertheless, the main contribution of the paper by Lucas et al. (1986) is to show that constants A and B are in fact dependent on the shape factor 4. This is a relevant result which had not been reported by the different authors cited in Table I of Lucas et al. (1986) nor by more recent works (e.g., Thonglimp et al., 1984). In this sense, the calculation of umf becomes highly simplified, since the determination of 4 is no longer required-following the work by Wen and Yu (1966)-thus avoiding the cumbersome experimental work involved in the evaluation of the shape factor. While the use of appropriate methods (Ergun, 1952; Casal et al., 1985) gives both 4 and emf to calculate umfthrough various equations existing in the literature, eq 1 provides a practical and simplified approach to its calculation by classifying the particles into three categories, as “round”, “sharp”, and “other”; this also takes into account the variation of C, and C2 with 4. Clearly enough, Chen recognizes the interest of our work and incorporates explicitly the value of 4 into a “single” equation that uses three values of 4 according to the three categories indicated by Lucas et al. (1986). Summing it up, the situation is as follows.
(3)
where A and B are constants given in Table I, while Chen, picking up the ideas proposed by Lucas et al. (1986), presents the equation
Table 11. Shape Factor Values for Three Categories of Particles particleb d” round sharp other
635
(33.674°.1)2+
1’’
Ar - 33.674O.I (4) 24.5~pO.~~
~
where the value of 4 has been categorized as in Table 11. It should be obvious that both formulations of the problem are identical as far as they present a single equation, but while the second requires us explicitly to know the value of the shape factor to obtain Remf,the first one presented by Lucas et al. (1986) offers a practical and accurate way to calculate umfin the most general case even if 4 is unknown, by categorizing the particles in three kinds as they are commonly found in practice. Apparently, Chen, while benefiting from the relationship between C,, C2, and 4 established by Lucas et al. (1986), misses the main issue of their work: a simplified way with improved accuracy to calculate the minimum fluidization velocity while avoiding the difficulty associated in finding the value of 4. We hope that our remarks as well as Chen’s comments will help to give a further insight in this topic essential to fluidization practitioners.
Literature Cited Casal, J.; Lucas, A,; Arnaldos, J. Chem. Eng. J . 1985, 30, 155. Chen, J. J. J. Ind. Eng. Chem. Res. 1987, preceding paper in this issue. Ergun, S. Anal. Chem. 1952, 24(2), 388. Lucas, A.; Arnaldos, J.; Casal, J.; Puigjaner, L. Ind. Eng. Chem. Process Des. Deu. 1986, 25, 426. Thonglimp, V.; Hiquily, N.; Laguerie, C. Powder Technol. 1984, 38, 233.
Wen, C. Y.; Yu, Y. H. Chem. Eng. Prog., Symp. Ser. 1966,62, 100.
A. Lucas, J. Arnaldos J. Casal,* L. Puigjaner Chemical Engineering Department, U.P.C. Barcelona 08028, Spain
Comments on “Kinetic Model for Methanol Conversion to Olefins” with Respect to Methane Formation at Low Conversion Sir: Methanol conversion to gasoline-range hydrocarbons is known to be catalyzed by a range of catalysts including the pentasil zeolite H-ZSM-5 (Chang and Silvestri, 1977) and bifunctional acid-base catalysts (Olah et al., 1984). Although considerable research effort has been expounded to elucidate the mechanism of carbon-carbon bond formation, an agreement has yet to be reached. To date, both a trimethyloxonium ylide (van den Berg et al., 1980; Olah, 1981) and a surface-bound carbene species (Chang and Silvestri, 1977; Lee and Wu, 1985) have emerged as being the most likely reaction intermediates. Until now, most mechanistic research effort has been concerned solely with carbon-carbon bond formation, whilst methane formation has received comparatively scant attention. By use of the pentasil zeolite H-ZSM-5 at high methanol conversions, methane is only formed in small quantities, and most workers consider that it originates mainly from thermal cracking of higher hydrocarbons catalyzed by the highly acidic sites of H-ZSM-5. It has
been proposed (Olah et al., 1984) that some methane could originate via a radical pathway involving dimethyl ether, but the initial study (Benson and Jain, 1959) involved gas-phase reactions at a temperature in excess of 500 “C, and it is unlikely that such a reaction would contribute significantly to methane formation at temperatures normally encountered with catalysts for the methanol conversion reaction. However, at low methanol conversion, i.e.,
