I n d . Eng. Chem. Res. 1988, 27, 1557-1558
increase in hydrogen treat rate increased the coal residence time in the reactor due to vaporization of the solvent and liquid products from coal. The increased coal residence time in the reactor resulted in higher liquid yield from coal. Qualitative relationships between the increase in extent of coal conversion with an increase in coal residence time resulting from vaporization of liquid in the reactor are correct. However, it is very important to understand that Strobel and Friedrich (1987) used high volatile solvents (ASTM D86 50% below 222 and 340 “C) which along with the light and middle distillates from coal were vaporized in the reactor. The vehicle (solvent) for slurrying of coal in the studies of Singh and Carr (1987) and Singh (1987) consisted of the heavy ends (Figure 1 in Singh and Carr (1987)). The composition of heavy ends was almost identical with that of the slurry in the reactor. A study of the effect of variations in vaporization equilibrium constant for a large range of extent of coal conversion in the SRC-I1 process showed that the effect of the latter on the slurry residence time in the reactor was small (Singh and Carr, 1983). A large effect of hydrogen treat rate on coal (slurry) residence time observed by Strobel and Friedrich (1987) resulted from the use of high volatile materials as vehicle (solvent). It appears that all the comments and supportive references have been used to conclude (last paragraph, last line) that an indirect effect such as hydrogen sulfide partial pressure is unimportant, if not irrelevant, and our studies should conform with the direct (measured) effect of hydrogen treat rate on the mean coal residence time. Use
1557
of inappropriate terms (direct vs indirect effects in place of physical and reaction or chemical effects) or citations for differences in reported results cannot support the above erroneous conclusions. The latter merely reflect the difficulties one may have in dealing with complex systems such as coal liquefaction. A scientific approach to the development of an understanding of such complex processes requires that each chemical and physical aspect of the process be given due consideration. In all likelihood an overzealous attempt to generalize the results of one study to all related studies can only limit the scope of the possible developments. It is obvious that all the comments on studies of Singh and Carr (1987) and Singh (1987) are a result of such an effort to generalize the observed relationship between hydrogen treat rate and slurry residence time (Strobel and Friedrich, 1987). Literature Cited Singh, C. P. P. Znd. Eng. Chem. Res. 1987, 26, 1565-1573. Singh, C. P. P.; Carr, N. L. Znd. Eng. Chem. Process Des. Dev. 1983, 22, 104-118. Singh, C. P. P.; Carr, N. L. Znd. Eng. Chem. Res. 1987,26,501-511. Strobel, B. 0.;Friedrich, F. Proceedings of the 1987 International Conference on Coal Science; Moulin, J. A., et al., Eds.; Elsevier Science: New York, 1987; pp 395-398.
Chandra P. P. Singh Aristech Chemical Corporation Research Laboratory 1000 Tech Center Drive Monroeville, Pennsylvania 15146
Comments on “The Axial Laminar Flow of Yield-Pseudoplastic Fluids in a Concentric Annulus” Sir: Hanks (1979) published an article on laminar flow of a Herschel-Bulkley fluid in a concentric annulus in which 900 computed values of the parameter X were reported. X is the basic parameter for the solution of the problem, namely, the value of the dimensionless radial coordinate for which the ICZ component of momentum flux tensor 7, = 0. About 10% of these values was chosen to check a computer program developed for the evaluation of a more general case of laminar flow: Herschel-Bulkley fluid with Newtonian slip layers in a concentric annulus (Buchtelovl, 1984). No differences in Hanks’ published values and my values of X were found for any cases where the power law index of the Herschel-Bulkley model m L 0.2; however, for m = 0.1, the values did not agree in several cases. The whole set of Hanks’ value of X for m = 0.1 was then checked, and 24 differences were found (Table I). The reasons for publishing the corrected values of X are that the evaluation of velocity profiles is very sensitive to the correctness of the X value, especially for highly plastic and pseudoplastic materials (Buchtelovl, 1986), and that the Herschel-Bulkley model or the power law model with a low value of m is often used for approximation of material behavior (for instance, in drilling technology). We should keep in mind, however, that in some cases nonregistered or incorrectly measured behavior could be hidden behind the low power law index. Justification of my values of X is presented below. Table I of Hanks (1979) lists values of X for various values of annulus aspect ratio, u; the rheological parameter in yield power law, m; and the parameter To= ( 2 r 0 ) / ( P R ) (ro being the yield stress, P the total head loss, and R the
Table I 0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
2mJPR 0.75 0.80 0.85 0.65 0.70 0.75 0.55 0.60 0.65 0.45 0.50 0.55 0.35 0.40 0.45 0.25 0.30 0.35 0.15 0.20 0.25 0.05 0.10 0.15
values of A, according to Hanks (1979) Buchtelova (1984) 0.3211 0.3215 0.3195 0.3259 0.3179 0.3349 0.4515 0.4525 0.4501 0.4589 0.4487 0.4700 0.5512 0.5520 0.5501 0.5616 0.5489 0.5765 0.6353 0.6359 0.6344 0.6488 0.6334 0.6624 0.7095 0.7093 0.7247 0.7086 0.7314 0.7079 0.7767 0.7762 0.7757 0.7865 0.7752 0.7882 0.8378 0.8380 0.8412 0.8374 0.8428 0.8371 0.8951 0.8954 0.8949 0.8954 0.8960 0.8947
radius of the outer pipe of the annulus). In all columns of that table, the values of X for each u start with the highest value at the top-for To = 0.0-and change in relatively even steps to the lowest value at the bottom for the highest value of To.This holds for all values of m, with the exception of m = 0.1; for it (for all u from 0.1 to 0.8),
0888-5S8~/88/2627-1557$01.50/0 0 1988 American Chemical Society
Figure 2. Schematic velocity profile; coordinates are in dimensionless form.
Figure 1. Values of X as tabulated in Hanks (1979) and here for annulus aspect ratio u = 0.5 and all tabulated values of m: ( X ) m = 0.1; (0) m = 0.2; (e) m = 0.3; ( 0 )m = 0.4; (*) m = 0.5; (V) m = 0.6; (0) m = 0.7; (+) m = 0.8; (6)m = 0.9; (A)m = 1.0.
two or three values at the bottom of each column suddenly depart from the above-mentioned tendency and jump to the higher values, in some cases above the value for To = 0.0. This peculiar behavior of h values is quite obvious from the table in its numerical form but can perhaps be better discussed in a graphical representation. Figure 1 shows one part of that table-for u = 0.5; other parts of Table I of Hanks (1979) would give similar results. To the values tabulated in Hanks (1979), the point TL is added. This point shows the limit of the function X = X(m, To) for a given u if toi u and too 1(to& = value of coordinate C; for which T,, = -T,,; too= value of t for which T,, = + T ~ (see Figure 2); and T , ~being the r-z component of momentum flux tensor). TLis not given in Table I o f Hanks (1979) but can be easily found from eq 15 and 16 of his article. Values of coordinates of TL for a given u are [ (1 - 0);01'2]and are independent of m. Figure 1 also shows the three values of A, which were evaluated by my program
-
-
differently than in Table I of Hanks (1979) and therefore are included in Table I here. Without knowing the details of the numerical methods used by Hanks to evaluate A, I cannot be certain why some of his values are in error. One possibility is that in computing the 24 erroneous values of h cited here he prematurely halted the iterations required to evaluate the integrals (see Hanks' eq 19) leading to the determination of A.
Literature Cited Buchtelovi, M. Report of Institute of Hydrodynamics No. 638/D/84, 1984; Czechoslovak Academy of Sciences, Prague. Buchtelovi, M. "The Axial Laminar Flow of Bulkley-Herschel Fluid with the Slip Effect in a Concentric Annulus". Vodohosp. Cas. 1986,34(4), 381-398 (in Czech, Abstract in English and Russian). Hanks, R. W. "The Axial Laminar Flow of Yield-Pseudoplastic Fluids in a Concentric Annulus". Ind. Eng. Chem. Process Des. Dev. 1979, 18(3), 488-493.
Marie B u c h t e l o v g Institute of Hydrodynamics Czechoslovak Academy of Sciences Podbabskd 13, 166 12 Prague 6, Czechoslovakia
