I n d . Eng. C h e m . R e s . 1989,28, 1571-1572
1571
CORRESPONDENCE Letter to the Editor Sir: By chance, the recent letter to the editor of your journal written by Rakesh Govind, Chemical Engineering Department, University of Cincinnati (Govind, 1988),came to my attention. In his letter, Govind apologizes for not having cited the work of Fisher (1963) in one of his publications (Govind, 1982). He also mentions his correspondence (Govind, 1983) with me (Bitter, 1983) on this subject, saying that again Fisher’s contribution was not mentioned by either author. This is correct, but as far as I am concerned, there was no reason for citing Fisher. The publication of Fisher (1963) is of concern in conjunction with Govind (1982) only because in his derivations he used equations as given by Fisher (1963). But since I used the method of Smoker (1938) for calculating the number of theoretical stages directly (by creating the needed straight operating lines with the concept of “caloric units” suggested by Peters (1922)), I did not need these equations for the curved operating lines. Emphasizing, this was the intention of my letter! (Fisher called Peter’s method “confusing”.) Besides this, much earlier publications tried to solve, or even solved, the problem Fisher dealt with, among them the works of Hausen (1942), Thum (1957), and Billet (1958), the latter cited, e.g., also by Kirschbaum (1960). I myself realized this in 1967 after having prepared a set of equations for the operating lines of systems with straight but not parallel phase lines, accounting for heat losses and pressure drop. After setting the respective terms to zero and performing some tedious transformations, I could show that the equations of Billet (1958) and Fisher (1963) are identical (a special case of my equations (Bitter, 1968)) and may be written in a far simpler form. Up to that time, it had not been recognized that Billet (1958) implicitly used straight phase lines in his model, as Fisher (1963) did explicitly. Furthermore it could be shown that assuming a straight intersection line, as Fisher (1963) (like Govind (1982)) did, is inconsistent with the model used, though of minor numerical interest in most cases. In my letter, I used the above-mentioned special case of my equations for curved operating lines to remind the readers of this fact. Therefore, I did not see any reason for citing Billet (1958) (not to mention Fisher (1963)) again, as I already did in 1968. As it is, Govind (1982) not only missed citing the deciding contributions of Fisher (1963) but also Lemlich
(1982) and Peters (1922) in his original publication. Moreover, he did not make clear that he considered in his analysis the above-mentioned inconsistency. I take this opportunity to emphasize that, although I used the concept of “caloric units” together with the method for calculating theoretical stages proposed by Smoker (1938) for a long period, I did not publish on this subject prior to Govind, because I thought the application to be obvious. The same applies to the extension for use with nonsaturated feeds that I made (Bitter, 19831, which resulted from my cited publications. Due tQ this familiarity with the problem, I readily had available the consistent set of equations given in my first letter, now referred to be Govind.
Literature Cited Billet, R. Berechnung der Austauschlinien fuer die Rektifikation binaerer Gemische. Chem.-1ng.-Tech. 1958,30, 513-515. Bitter, R. Rektifikation von Zweistoffgemischen. Chem.-Ing.Tech. 1968, 40, 651-656. Bitter, R. Comments on “Analytical Form of the Ponchon-Savarit Method for Systems with Straight Enthalpy-Composition Phase Lines. Ind. Eng. Chem. Process Des. Deu. 1983, 22, 684-686. Fisher, G. T. Modification of the McCabe-Thiele Method for Systems of Unequal Heats of Vaporization. Ind. Eng. Chem. Process Des. Deu. 1963, 2, 284-288. Govind, R. Analytical Form of the Ponchon-Savarit Method for Systems with Straight Enthalpy-Composition Phase Lines. Ind. Eng. Chem. Process Des. Deu. 1982,21, 532-535. Govind, R. Response on Comments on “Analytical Form of the Ponchon-Savarit Method for Systems with Straight EnthalpyComposition Phase Lines. Ind. Eng. Chem. Process Des. Dev. 1983, 22, 686-687.
Govind, R. Letter to the Editor. Ind. Eng. Chem. Res. 1988, 27, 1957.
Hausen, H. Berechnung der Rektifikation mit Hilfe kalorischer Mengeneinheiten. 2.VDI, Beih. Verjahrenstechnik 1942,17-22. Kirschbaum, E. Destillier-und Rektijiziertechnik, 3rd ed.; Springer Verlag: Berlin, 1960; pp 192-201. Lemlich, R. Private communication to R. Govind, 1982. Peters, W. A. The Efficiency and Capacity of Fractionating Columns. Ind. Eng. Chem. 1922,14,476-479. Smoker, E. H. Analytic Determination of Plates in Rectifying Columns. Trans. AIChE 1938,34, 165-172. Thum, 0. Direkte Berechnung der theoretischen Bodenzahl. Chem.-Ing.-Tech. 1957,29,675-678. Reinhard Bitter
Kronenpuetzchen 42 D 4047 Dormagen 11, Federal Republic of Germany
Response to “Letter to the Editor” Sir: I completely disagree with Bitter with regard to his comments that in my earlier publication (Govind, 1982) I omitted citing Lemlich (1982) and Peters (1922). Firstly, Lemlich (1982) was not cited because the private communication occurred after my paper (Govind, 1982) was published. It is generally not possible to cite publi0888-5885/89/2628-1571$01.50/0
cations that have not yet been published! Secondly, Peters (1922),who used the concept of Ucaloric units”, was not cited because it was irrelevant to my analytical approach to the problem. I do not believe in littering my papers with irrelevant references. Finally, the use of a straight intersection line is an ac0 1989 American Chemical Society
1572 Ind. Eng. Chem. Res., Vol. 28, No. 10, 1989
ceptable approximation, since it is a short line. I had originally considered this point in my earlier analysis (Govind, 1982) and later realized that assuming the intersection line to be a straight line resulted in a very minor error. Hence, in my fiial analysis, I made the assumption of a straight intersection line. This fact was pointed out earlier in my response to Bitter’s comments (Bitter, 1983).
Lines”. Ind. Eng. Chem. Process Des. Dev. 1983, 22, 684-686. Govind, R. Analytical Form of the Ponchon-Savarit Method for Systems with Straight Enthalpy-Composition Phase Lines. Ind. Eng. Chem. Process Des. Dev. 1982,21, 532-535. Lemlich, R. Private communication, 1982. Peters, W. A. The Efficiency and Capacity of Fractionating Columns. Ind. Eng. Chem. 1922,14,476-479.
Rakeeh Govind
Literature Cited
Chemical Engineering Department University of Cincinnati Cincinnati, Ohio 45221
Bitter, R. Comments on “Analytical Form of the Ponchon-Savarit Method for Systems with Straight EnthalpyComposition Phase
ADDITIONS AND CORRECTIONS Analysis and Algorithms for Multistage Separation Processes [Volume 28, Number 6, page 7931. Lakshmi N. Sridhar and Angelo Lucia* Page 795. Equation 14 (Chart I) contains two incorrectly subscripted block matrices. The correct equation for the ?Jacobian matrix, G’, is
Page 796. In the left-hand column in the paragraph beginning with “To apply this theorem...”, the phrase “let Dobe the set intersection of the two-phase regions for each stage” should read “let Do be the Cartesian product of the set intersections of the two-phase regions of adjacent stages”. Page 796. Equation 25 contains an incorrect inequality associated with dLj/aTk. The correct equation is
Page 799. The condenser in Table IV is a partial condenser, and the starting values and solution on stage 1 are stage
T,K
1
328.0
starting values and solution h-’ v*, kmol h-*
y o , kmol
20.0
20.0
20.0
24.80
15.62
18.16
Page 800. The word condenser is spelled incorrectly in Table V. Page 800. In the leftihand column, second sentence after eq 53, the spectral radius of the nonnegative matrix A should be p(A) = 0.5199, which still easily satisfies the bounds given by eq 22. Page 800. The (1,l) element of J given by eq 54 should be 69.57, not 69.75. Page 801. In eq A13, the k + 2 element of the vector R should be -Pk+l(l - P k + ? ) . Page 802. The second inequality following eq A18 is aLj/aTk =
O j < k
Page 802. In the second bracketed term in eq B3, the quantity (dLk+l/VTk) should be (dLk+,/dTk).
