Ind. En$, Chem. Process Des. Dev. 1989, 22, 687-688
Bitter are as follows: (1)The proposed equation could have been derived using “caloric concentrations” defined by Peters (1922). This was also suggested to me by Lemlich (1982) and it does result in the proposed equations. (2) The feed line is curved when the enthalpy-composition lines are straight but not parallel. However, in most cases the feed line is a short line and considering it as a straight line is an acceptable approximation. This was not emphasized in the paper (Govind, 1982) but was considered
887
in the analysis. Literature Cited Govind, R. Ind. Eng. Process Des. D e v . 1982. 21, 532-535. Lemllch, R., private communicatlon, 1982. Peters, W. A. Ind. Eng. Chem. 1922, 14, 476.
Department of Chemical Engineering University of Cincinnati Cincinnati, Ohio 45221
Rakesh Govind
Comments on “Approximate Design Equations for Reverse Osmosis Desalination by Spiral Wound Modules” Sir: In a recent article, Sirkar et al. (1982) propose a numerical approximation for the concentration polarization relationship for reverse osmosis membranes. Their method is to approximate the relationship between the solute concentration at the wall (X,) and that in the freestream (Xzl)in terms of the ratio of solute velocity to solute mass transfer coefficient, NlrVl/kl. Thus x22
= x21 e x P “ ~ l ; / ~ l l
is approximated as
in order that explicit flux expressions may be developed. The purpose of this comment is to propose an improved approximation derived from a Tchebycheff economization [cf. Dalquist and Bjorck (1974)l. For example, an approximation
over the interval [0,1.5] results in a maximum error of 2.91 90.It is not necessary to use a single approximation for the interval. Much higher levels of accuracy can be achieved using this technique if a smaller interval is chosen. The simplicity of a second-order expression is preserved even though the economization is derived from a fourthorder polynomial approximation. Thus the useful range of the approximate design equations may be considerably extended without resorting to a higher order approximation as suggested by the authors.
Literature Cited Slrkar, K. K.; Dang, P. T.; Rao, 0. H. Ind. Eng. Chem. Process D e s . D e v . 1982, 21, 517. Dalquist, G.; Bwck, A. “Numerlcal Methods”; Prentice-Hall, Engelwood Cllffs, NJ, 1974.
College of Engineering University of South Florida Tampa, Florida 33620
J. D. Jeffers 5.C. Kranc* R. P. Carnahan
Response to Comments on “Approximate Design Equations for Reverse Osmosis Desalination by Spiral Wound Modules” Sir: The improved approximation proposed by Jeffers, Kranc, and Carnahan for expressing concentration polarization in a highly rejected single solute reverse osmosis system with chopped laminar flow indeed leads to a somewhat better explicit flux expression especially in the range [1,1.5]. However, we would like to point out on the basis of further unpublished calculations that a significantly better prediction of L+ value is not necessarily achieved. This is due to the fact that a number of other assumptions and approximations were used in the deriv-
ation of the analytical result for L+. Department of Chemistry & Chemical Engineering Stevens Institute of Technology Hoboken, New Jersey 07030 Chemical Engineering Department Siddaganga Institute of Technology Tumkur-572103, Karnataka, India
K. K. Sirkar* P. T. Dang G. H. Rao
Comments on “Hydrogenation of Aromatic Hydrocarbons Catalyzed by Suifided Co0-Mo0,/y-Ai20,. Reactivities and Reaction Networks” Sir: In a recent paper, Sapre and Gates (1981) have apparently misunderstood the interpretation suggested by Patzer et al. (1979) regarding the constancy of the tetralin 0196-4305/83/1122-0687$01.50/0
(T)-to-naphthalene (N) concentration ratio observed by the latter authors in the hydroconversion of l-methylnaphthalene (M). According to Sapre and Gates, ”Patzer 0 1983 American Chemical Society
Ind. Eng. Chem. Process Des. Dev. lQ83, 22,688-689
688
et al. attributed this result to an equilibrium limitation". At the outset, we would like to point out that nowhere in their paper did Patzer et al. interpret their resulta in terms of thermodynamic equilibrium. The precise interpretation proposed by Patzer et al. is that the constancy of the T-to-N ratio is due to "an apparent steady-state kinetic limitation" which may result from the reversibility of naphthalene hydrogenation-whether the reaction is a t equilibrium or not. Patzer et al. tabulated two sets of data on space velocity effect with two different catalysts a t two different temperatures (Table I1 of their paper). These data are plotted here as Figures 1and 2 for the present discussion. (The concentrations of decalin are not shown for clarity.) As can be seen from Figure 1,the concentration of M falls rapidly and the formations of N and T are nearly parallel (T-to-N ratio -0.54) for contact times at least in the range of 0.25-0.5 h. This behavior would not be caused by simple irreversible reactions. It is therefore logical to attribute the apparent constancy of the T-to-N ratio to the reversible character of the reaction between N and T. Figure 1also suggests that the hydrogenation of T to D is slower than the dehydrogenation of T to N. While Patzer et al. did not claim "equilibrium product distribution", it is reasonable to assume that these product distributions, more than likely, are not far from equilibrium because of the high temperature employed (343 "C). Sapre and Gates' critique is solely based on the low temperature (316 "C) data shown in Figure 2. They extrapolated the data to regions of extremely high contact times (-10 h) by using the rate constants suggested by their catalyst and conditions, which were different from those used by Patzer et al. It is not surprising that they can get a reasonably good fit because in this case the extent of the reaction is rather low and the range of the experimental conditions is relatively narrow (contact times between 0.41 and 0.61 h), as shown in Figure 2. The low extent of reaction also explains why the formations of naphthalene and Tetralin shown in Figure 2 are approximately linear with contact time. Consequently, the product distribution a t high contact times calculated by Sapre and Gates reported in their Figure 6 may be totally irrelevent to the catalysts and conditions used by Patzer et al. In other words, we feel that the extrapolation may just be too bold. Due to the low temperature employed, the data shown in Figure 2 were likely obtained a t kinetics-controlled conditions. Even though not discussed in the paper, it should be pointed out that an equilibrium argument is permissible at high temperatures, such as 343-399 "C employed by Patzer et al. in their studies. There are two opposing effects at high temperatures: while increasing temperature tends to inhibit the formation of T from N, the enhanced hydrogenation of T to D shifts the N-T equilibrium to the right. As a result, the concentrations
lOOh
I
i
I
1
T-343'C P = 6.09 MPo
1
0
1
M
L,'
I
I
0.2
I
(LHN)-',
I
0.6
0.4
ht
Figure 1. Concentration vs. contact time in catalytic hydroconversion of 1-methylnaphthalene,catalyst B in Patzer et al. (1979).
'.
I
I
I T = 316'C P = 6.89 MPo
I
1
'\ ' \ \
Relative Concentrotion 1%)
(LHW-',
hi
Figure 2. Concentration va. contact time in catalytic hydroconversion of 1-methylnaphthalene,catalyst A in Patzer et al. (1979).
of N and T decline simultaneously but slightly, thereby resulting in an apparent constant T-to-N ratio. The data presented in Table IV of Patzer et al. (1979) are in line with this argument.
Registry No. 1-Methylnaphthalene,90-12-0; Tetralin, 11964-2; naphthalene, 91-20-3.
Literature Cited Sapre, A. V.; Gates, 0. D. Ind. Eng. Chem. Process Des. Dev. 1981, 20, 60. Patzer, J. F., 11; Ferrauto, R. J.; Montagna, A. A. Id.€ng. chem. Process Des. Dev. 1079, 18, 625.
Exxon Research & Engineering Co. Linden, New Jersey 07036
Teh C. Ho* Angelo A. Montagna
Response to Comments on "Hydrogenationof Aromatic Hydrocarbons Catalyzed by Sulfided C ~ M o 0 , / y - A i , 0 3 . Reactlvlties and Readlon Networks"
Sir: The basis for our reinterpretation (Sapre and Gates, 1981) of the results of Patzer et al. (1979) is our belief that one of the conclusions emphasized in their paper is misleading. Patzer et al. stated the following: "...Although the reaction sequence of 1-methylnaphthalene naphthalene tetralin decalin proved not to be amenable
-
-
-
0196-4305/83/1122-0688$01.50/0
to further kinetic analysis with the data obtained, we noted (Tables 11, 111, and IV) a surprising phenomenological result that the ratio of the concentration of tetralin to the concentration of naphthalene in the product remained almost constant a t about 0.49 f 0.03 (95% confidence interval) for all catalysts studied over the temperature 0 1983 American Chemical Society
