-------------------------------------------------------------------- Valeri Kiva: Comments on Russian work on multiple steady states in distillation (Personal communication, June 1998) -------------------------------------------------------------------- From kiva@cc.nifhi.ac.ru Thu Jun 11 09:04:30 1998 To: skoge@chembio.ntnu.no Subject: Re: Russian works Dear Sigurd, Really, I am fine but have a lot of work now. Sometimes I think it is too much for a old, sick and tired man as I am. Some words about Russian works on the multiplicity of the steady states at continuous distillation of ternary azeotropic mixtures. 1) Possibility of the multiple steady states at "infinite efficiency of separation" (N=infinity, R=infinity, D/F from 0 to 1) was first noted by Balashov, M.I., A.V.Grishunin, L.A.Serafimov, "On the investigation of the regions of continuous and batch distillation"(in Russian), in the book "Physical and Chemical Foundations of Rectification", Moscow, Moscow Lomonosov Institute of Fine Chemical Technology, 1970, pp 205-215. They considered the feasible separations of the mixture of Class 1.0-1b by Serafimov's classification with max.boiling azeotrope formed between light and heavy components(type 003 by Matsuyama or elementary U-cell) and noticed that for these mixtures there are multiple separations at the same value of parameter D/F. However, they did not analyse in more details this multiplicity. This book is available only in the central libraries of Russian and it can't have an influence on the works of other investigators. 2) Later Petlyk F.B. and Avetjan, V.S., Theoretical Foundations of Chemical Engineering, 1971, v.5 No 4, pp 499-507 (pages from Russian edition, there is English edition of this journal, but it's possible with another numbers of pages) had analysed the problem in more details. This analysis was included in the book by Petlyuk and Serafimov "Multicomponent Distillation. Principles and Design Procedure", Moscow, Chemistry Publishing Co, 1983. I left this book to Katrine and you can use the figures from this book. Now I try to give the translation of some fragments from it with the references to the figures. Petlyuk use the concepts "region of distillation" and "subregion of distillation". Term "region of distillation" means a part of the composition space which is filled in with one family of the distillation lines (in Stichlmair's sense) [p.18 in the book, original references:Petlyuk, Kievski, Serafimov, Russ.Journ.Phys.Chem,1975, v.49 (12), pp 3102-3104; Theor.Found. of Chem.Engng., 1977, 11 (1), pp 3-10. Term "subregion of distillation" for a three component mixture means two dimensional polyhon, the vertexes of which correspond to all singular points of one main tie chain of mximum longitude connecting the unstable and stable nodes of the distillate lines. For example: the mixture of Class 1.0-1a ( Matsuyama's type 030 has one region of distillation and two subregions of distillation). He writes: "The existence of more than one saddle at the main tie chain of distillation lines going from unstable node to stable node ("excessive subregion of distillation") leads tomultiplicity of the separation products at the same feed composition and the same value of parameter D/F" [Book, pp99-100, original reference: Petlyuk, Avetjan, 1971]. My comments: The mixture as example is shown in Fig.III-3,v(Cyrillic) at page 95 (the upper line, the third triangle from the left). Subregion 12-1-3-23 at this triangle (the main tie chain 12-1-3-23 has two saddles, namely, 1 and 3) is excessive. There is multiplicity for all feed compositions belonging to this subregion. Further Felix writes: "The correspondence between the distillate composition and the parameter D/F for the case of the feed composition F from Fig.III-3v is shown in Fig III-4." (page 100). Translation of legend: Fig.III-4. Dependence of the parameter D/F on the distillate composition at the rectification of ternary azeotropic mixture at the infinite efficient separation (ambiguity of separation) I, II, III - three variants of the distillate composition that can be obtained at D/F=0.5; x2- mole fraction of component 2 at the distillate for the mixtures 2-3 and 2-1. Text under X-axis: Mixture 2-3: Mixture 2-1 My comments: As one can see, it's typical bifurcation curve, and the case of three steady states is underlined in this graph. Further he writes: "For the values of D/F in the range between extremums there are three dufferent sets of the separation product composition (points I, II, III in Fig.III-4). Thus at these values of parameter there are three steady states of the process. Realization of some of these steady states depends on the start-up procedure. Existence of several saddles in the region of distillation can lead to situation when the product regions of distillate and of bottom products can be partially intersected (see Fig.III-3,e at page 95). It means that at the fixed feed composition X(F) the same composition can correspond to the distillate or to the bottom product de[pending on the value of parameter D/F." {Book, p.100] Faktisk, it is all that is written in the "old" Russian papers. Now we have some reinessance of the interest to this problem after the papers by Morari. I think you need not a fax of these pages because you have the book itself and can use my translation of the relevant fragments of the text and the legendsof the graphs. Translation of Legend for Fig.III-3 (p.95): Fig.III-3. The diagrams of the feasible separation products for three component azeotropic mixtures at the infinite efficiency of separation. a-e - variants of diagram - - - - lines of mass balance at the marginal values of D/F continuous bold lines - multitudes of the product compositions at the various values of D/F continuous thin lines - the borders of the composition triangles. I hope this is what you want. Regards, Valeri Dr.Valeri N.Kiva Head of Laboratory Laboratory on Mixture Separation Karpov Institute of Physical Chemistry Vorontsovo Pole St., 10 Moscow, 103064 Russia e-mail : kiva@cc.nifhi.ac.ru fax (095)-975-2450 phone (private) (095)-240-0711 --------------------------------------------------------- From skoge@chembio.ntnu.no Mon Jun 29 09:27:06 1998 Date: 29 Jun 1998 11:27:01 +0200 To: Morari@aut.ee.ethz.ch, ekh@chembio.ntnu.no, guetti@aut.ee.ethz.ch, jacobsen@elixir.e.kth.se, sbj@home.kt.dtu.dk, skoge@chembio.ntnu.no Subject: Kiva on Russian work on MSS in distillation Hello, Please find enclosed a copy of some further commens from Valeri Kiva on Russian work on multiple steady states. -Sigurd >>From kiva@cc.nifhi.ac.ru Wed Jun 17 08:20:40 1998 >From: "Valeri N. Kiva" >Subject: Re: Russian works Dear Sigurd, I am glad that I can be useful. Misssing of some Russian works is a common, so it is not a great fault. ----------------------------------- On your follow-up questions: ----------------------------------- >1. Was there any reason why only the 003-class was considered? No, it is only the simplest example. >2. Was it believed that MSS also could hold for other classes? Surely. Felix wrote that MSS could hold for all classes which RCs map includes an "excessive subregion of distillation", or in the other words, "U-cell" of residue curves or distillation lines. He considered also 130-class as another example. >3. Did you teach these things to your students? Yes. Usually PhD students on distillation should learn these things. Serafimov's team at Lomonosov Institute of Fine Chem.Technology teach these things even to their undergraduated students in the course on non-ideal mixture separation. --------------------------------------- Further follow up to Questions 1 and 2. --------------------------------------- >>From kiva@cc.nifhi.ac.ru Wed Jun 24 11:24:04 1998 >4. And: did he consider the 001 class (which I think is simpler than 003)? Class 001 is totally symmetrical (distillate contra bottom product and vice versa) to Class 003 and no more complex that this class. >5. About references: 1. Possibility of multiple steady states was firstly discovered by Balashov et al. in 1970 (Balashov M.I., A.V.Grishunin, A.V.Ryazanova, L.A.Serafimov, "On the investigation of the regions of batch and continuous rectification", in "Physical-Chemical Foundations of Rectification" (in Russian), Moscow, Lomonosov Institute of Fine Chemical Technology, pp 205-215). They considered the mixtures of Class 1.0-1b by Serafimov's classification (or type 003 by Matsuyama) and of Class 2.0-1 (103) and discovered the multiplicity at infinity/infinity for these mixtures. --- According to Russian approach on the antipodal diagrams, multiplicity --- for mixture 003 means automatically the multiplicity for mixture of --- type 001. We all know it but nobody had wrote that in the papers. 2. Later the problem was considered in more detail by Petlyuk and Avetjan (Petlyuk F.B., V.S.Avetjan, "Investigation of ternary rectification at total reflux", Theoretical Foundation of Chemical Engineering, 1971, v. 5 (4), pp 499-507). This paper is available in English. They considered 13 model mixtures with various VLE obtained by the alteration of Wilson equation parameters and ratios P(I)/P(J). Hence, they did not some systematical investigation of all feasible structures, and their choice of mixtures was in some degree occasional. Considering the the lines of rectification (or the composition profiles) and the regions of rectification (the regions where the lines of rectification have the same initial and final points), they showed that there are two type of rectification regions: a)regions including two nodes and one saddle, or "triangular" regions, and , b) regions including two nodes and two saddles. These regions may be triangular or "quadrangle". The type of rectification region determines the product areas for the fixed feed composition. The first type of region is more common. However, we can find the quadrangle regions in Fig. 4c, 4e, 4f,4h, 4l (Classes 4b by Gurikov's classification or 001 by Matsuyama, 8a or 102, 8b or 203, 9 or 103, 14b or 441). Authors considered some pecularities of separation for the regions of the first type. Considering the regions of the second type they wrote: "The shape of tis type of rectification region can be not only triangular, but qudrangle as well. This leads to such interesting phenomena as ambiguity of the product composition at the same feed composition and the same value of parametrer D/F. For example, the dependence of the product composition on the parameter D/F is shown in Fig.6 for the mixtures belonging to the regions marked by asteric in Fig.4. There is a range of parameter where three various product compositions correspond to the same value of parameter D/F." [The typical bifurcation curve is given in Fig.6. However, it is not clear which namely asteric in Fig. 4 relates to the example of Fig.6.] has the [mixtures of Class 8b or 201 by Matsuyama, c - tertathat the region of rectification can be tetragonae possibility of . Really, the possibility of multiple steady states. 3. The quadrangle regions and multiplicity of the steady states for all classes of ternary mixtures is clearly seen in Fig.4 in the paper by Serafimov et al (Serafimov L.A., Zharov V.T., Timofeev V.S.,"Rectification of multicomponent mixtures, 1" in Acta Chim.Sci.Hung., 1971, 69 (4), pp 383-396. However, authors did not write about this phenomena. Katrine has a copy of this paper. 4. Later, Petlyuk and Serafimov wrote in their book [Petlyk F.B., L.A.Serafimov, "Multicomponent Rectification. Theory and Design", 1983, Moscow, Chemistry Publishing Co, pp.98-100] about the multiplicity of steady states for the systems with excessive sub-region of distillation. In other words it means multiplicity for the mixtures with quadrangle rectification regions or with U-cells. They give as example the mixture of Class 2.0-1 by Serafimov or 130 by Matsuyama. For us there is not difference between Class 130 and Class 103 - both mixtures have the same topological structure of RC map. Katrine has this book (in Rissian), but you can have a look at p.95 (Fig.III-3 Upper line, the second triangle) and p. 100 (Fig. III-4, bifurcation curve of the dependence X(D) on parameter D/F. That's all I can say you about Russian references. Regards, Valeri ---------------------------------------------------------------- A third comment from July 1998 based on a remark from Guttinger ---------------------------------------------------------------- From kiva@cc.nifhi.ac.ru Fri Jul 17 07:57:09 1998 To: skoge@chembio.ntnu.no Subject: Re: Distillation and summer >I was a bit puzzled by the email from Thomas Guttinger. He writes: > >The "quadrangle condition" of Petlyuk and >Avetyan (and also in the other references) is neither necessary nor >sufficient for multiplicities in the infinf case. >Not necessary since (in the formulation of Petlyuk and Avetyan) > there must not be two saddles in a region to fulfill the > geometrical condition of Bekiaris et al., e.g. highly curved > boundaries will lead to MSS as in the Acetone, Methanol and > Chloroform mixture or in the MTBE reactive distillation process. >Not sufficient since not all "quadrangles" as considered by the >russians lead to MSS. MSS, and I think that the Russian DO know >that (it was just not precisely analysed in the papers), only exist >if a "quadrangle" fulfills the geometrical condition, i.e., they >depend on the location of the singular points forming the quadrangle ! >Hence, the geometrical condition of Bekiaris is the only precise, >necessary and sufficient condition for MSS in the infinf case. > >Do you have any comments? > Yes, at first I was a bit puzzled by this e-mail from Guettinger too. But later I understood that Guettinger is quite right. My comments: (1) MSS in reactive distillation has another nature than MSS in usual distillation, and I am not sure that it's possible to find "general" condition of MSS at reactive and usual distillation. (2) I agree that Petlyuk's condition is not necessary, because it does not include the case of MSS at the strong curvature of the separatrix. Furhermore, I agree that it is not a sufficient condition too, because this U-shape cell not always leads to MSS. UN---------S1 I I I I I I SN--------- S2 If the edges UN-S1 and/or S2-SN are curved in a certain way, the geometric conditions for MSS can not be satisfyied. A propos, Felix did not write that this condition is sufficient, he wrote that MSS is possible at these cells. (3) I am not sure that ">the Russian DO know that<", as Thomas wrote (he is very polite), because till now nobody (including Felix) analyzes this problem in details. I wish you good rest. My and Alla's regards to Anne-Lise. Hilsen, Valeri Dr.Valeri N.Kiva Head of Laboratory Laboratory on Mixture Separation Karpov Institute of Physical Chemistry Vorontsovo Pole St., 10 Moscow, 103064 Russia e-mail : kiva@cc.nifhi.ac.ru fax (095)-975-2450 phone (private) (095)-240-0711