In this study  the visualization  system AVS  (Application Visualization System) is  applied. 
This  tool  is  provided  with  a  module  library  for  userfriendly  modelling  of systems  under 
study.  Three data viewers  are  implemented:  Image Viewer, Graph Viewer  and Geometry 
Viewer allowing  the graphical  representation of multidimensional data fields  as the boiling 
and  dew  temperatures  as  a  function  of  the  composition.  By  using  special  modules  the 
graphical  representations can  be characterized by colours, brightness and other effects;  by 
the  zoom  module  the  scale  can  be  varied;  there  are  also  possibilities  for  the  animation 
of the objects  under study,  the  representation  of isolines,  for  example of temperature or 
driving  forces,  as  well  as  the  calculation  and  representation  of vector  fields.  The  last 
option  makes  it  possible  to  construct  representation  combining  information  about  the 
residue  curve map and  the temperature surface

Haase, Hans-Joachim

Hartmann, Klaus

English

Periodica Polytechnica (Budapest University of Technology and Economics)

PERIODICA POLYTECHNICA SER. CHEM. ENG. VOL. 38, NOS. 1-i!, PP. 57-68 (1994,) VISUALIZATION METHODS FOR EVALUATION OF FEASIBLE SEPARATIONS OF AZEOTROPIC MIXTURES Klaus HARTMANN and Hans-Joachim HAASE Technische Universitat Berlin Institut fUr ProzeB- und Anlagentechnik Arbeitsgruppe Systemverfahrenstechnik im WIP Rudower Chaussee 5, 12484 Berlin, Germany Received: July 23, 1994 Abstract In this study the visualization system AVS (Application Visualization System) is applied. This tool is provided with a module library for userfriendly modelling of systems under study. Three data viewers are implemented: Image Viewer, Graph Viewer and Geometry Viewer allowing the graphical representation of multidimensional data fields as the boiling and dew temperatures as a function of the composition. By using special modules the graphical representations can be characterized by colours, brightness and other effects; by the zoom module the scale can be varied; there are also possibilities for the animation of the objects under study, the representation of isolines, for example of temperature or driving forces, as well as the calculation and representation of vector fields. The last option makes it possible to construct representation combining information about the residue curve map and the temperature surface. Keywords: separations of azeotropic mixtures. 1. Introduction Highly nonideal mixtures are characterized by strong interactions between the molecules of components as hydrogen bonding, dispersion forces, dipole-dipole interaction which cause deviations from Raoult's law and result in such phenomena as homogeneous or heterogeneous azeotropes. Azeotrope forming compounds are quite common. There was published recently a two-volume compilation with data of more than 18 800 azeotropic systems involving about 1700 compounds (GMEHLING, 1994). There are different types of azeotropes as binary azeotropes, ternary, quaternary and even two quinary azeotropes, further minimum, maximum or saddle azeotropes. The topology of binary azeotropic mixtures appears in various graphic representations in the following way : Minimum or maximum boiling temperatures under constant pressure conditions, Minimum or maximum total vapor pressure at constant temperature, 58 K. HARTMANN and H.-l. HAASE The vapor-liquid equilibrium diagram is such that an intersection between the equilibrium curve and the 45°-line can be observed. 2. Ternary and Higher Dimensional Azeotropic Mixtures In binary systems the situation and the topology is simple and obvious and the synthesis of optimal separation schemes can be carried out without complications. But the separation of binary azeotropic mixtures needs often the involving of a third compound - an entrain er - and this results finally in a ternary mixture. The complications in the process synthesis are connected with ternary and higher dimensional systems. Depending on the number of components involved in a mixture and on the order of azeotropic points a great vari-ety of topologies studied by many investigators appears, see for example (MATSUYAMA and NISHIMURA, 1977). In Fig. 1 a ternary system is presented showing the great variety of topologies in the boiling temperature vs. composition diagrams of such mixtures as binary and ternary azeotropic points, distillation boundaries and saddle points. The composition of a mixture containing N species with Li (i = 1,2, ... ,N) moles of each is uniquely defined by a state vector of N 1 mole fractions x = (Xl, ... , xN-d and can be represented as a point in a (N -1)- dimensional composition simplex or concentration plane called a composition (or Gibbs) diagram. For the graphical representation of the behavior of an azeotropic sys-tem, on the following constructions can be used: 1. The residue curve map representation based on the residue curve approach, 2. The boiling (and dew) temperature surfaces based on the repre-sentation of the boiling (and dew) temperatures vs. mixture composition. The concept of the residue curve was introduced by SCHREINEMAKERS (1901). Let us assume that an amount of dL moles of composition Yi (i = 1,2, ... , N) is vaporized in equilibrium with the liquid. The amount of the residual liquid, L - dL will have the composition Xi + dXi. The ma-terial balance for the i-th component gives: LXi = YidL + (L - dL)(Xi + dXi). (1) By ignoring the second-order differential, this becomes LXi = dL(Xi Yi). (2) VISUALIZATION METHODS Methanol 64,rC bAZ bAz C-M A-M o 53,4°C 55,rC min min 56,2°C Acetone bAzA-C 64,4°C max 61,2°C Chloroform 59 Fig. 1. Azeotropic points and their characteristics, distillation regions, boundaries and their approximation by the konovalov's rule (B - bottom product, D - distillate product, bAz - binary azeotrope, tAz - ternary azeotrope) The mole fractions in Eq. (2) are not all independent since they must satisfy the conditions: N LXi=li i=l N LYi = l. i=l Setting dt = dL/ L this can be rewritten as (3) (4) The compositions in the vapor and liquid phase are determined by the thermodynamic equilibrium relationship y = f(x). 60 K. HARTMANN and H.-J. HAASE Methanol Acetone Chloroform Fig. 2. Residue curve map for the mixture acetone-chloroform-methanol (1 bar, azeotrope points are designed by.) Pure components and azeotropes are singular points of the vector field defined by the right hand side of Eq. (4), which vanishes simultaneously at pure and azeotropic compositions, i.e. satisfying Xi = Yi. MATSUYAMA (1977) and DOHERTY (1978) have shown that these singular points are elementary (saddles or nodes) and isolated in the composition space. The residue curve is defined as an integral curve of the set of simul-taneous nonlinear differential equations (4). The continuous distillation profiles are constrained to lie within certain subregions of the composition simplex, and it is precisely this fact which distinguishes azeotropic distil-lation from ideal distillations. According to the Konovalov's second rule a residue curve runs monotonously in the direction of rising temperature (at constant pressure). Therefore, knowing the boiling temperatures of the pure components and the azeotropes it is possible to indicate approximately the subregions and the boundaries between them. In Fig. 1 the azeotropic points and the connecting lines between them are shown. Each subregion represents a new distillation region (a so-called simple distillation region, SDR) with the properties of an ideal mixture. The azeotropic mixture plays the role of VISUALIZATION METHODS 61 a new or pseudocomponent. That means a feed lying in a given subregion can be separated only into the components representing the corners of this subregion (accounting the boiling temperatures of the components). The separatrices representing special residue curves divide the different simple distillation regions. Fig. 2 shows the total reflux distillation paths (or residue curves) for one of the most investigated systems, the homogeneous azeotropic mixture methanol-acetone-chloroform. Residue curves and rectification trajectories coincide only in the case of total reflux. Under distillation conditions the rectification trajectories can differ from the residue curves (VOGELPOHL 1993). 3. Process Syste:ms for the Separation of Azeotropic Mixtures For the separation of azeotropic mixtures different approaches can be used, see for example (SIMMROCK): a) methods without external components (entrainers) Two-pressure rectification (in some mixtures the azeotrope can be broken by changing system pressure); For systems showing minimum azeotropic behaviour and two liquid phases (with no miscibility gap) a combination of column and decanter can be applied; b) methods with external components (entrainers) Azeotrope rectification: Using an external component forming a new azeotrope with one of the components with the highest or lowest boil-ing temperature of the system. The entrainer recovery can be car-ried out either by a decanter for heterogeneous azeotropic mixtures or by additional separation operations for homogeEeous azeotropic mix-tures. Extractive rectification: Adding an entrainer with a high boiling tem-perature which overcomes the azeotrope it is possible to recover the entrainer after separation in an additional column. Reactive rectification: Combining the separation process with a chem-ical reaction in some cases high efficient separation schemes can be obtained. For the optimal choice of the separation scheme the identification and loca-tion of the continuous azeotropic distillation region boundaries (which are boundaries only in the case of distillation with total reflux, in other cases the rectification lines can cross these boundaries) is one of the most impor-tant aspects for the synthesis. 62 K. HARTMANN and H.·J. HAASE 4. The Temperature Surface and the Residue Curve Map Approach for the Separation Scheme Synthesis Although a qualitative overview of the different subregions and the bound-aries can be obtained applying the second Konovalov's rule, this informa-tion is only necessary but not sufficient for a synthesis procedure. For a more exact analysis of the distillation regions more sophisticated tools are needed: the residue curve map, the temperature surfaces and their deriva-tives. A numerical procedure for the exact calculation of the separatrices has been proposed recently (MEKIFFER, HARTMANN, 1992). The residue curve map approach allows to determine the SDR and the separatrices between them approximately. For this aim a user-friendly t~ol was invented which solves the following operations: Integration of the system of differential Eqs. (3)-(4) for mixtures of arbitrary dimension and pressure Graphical representation of the residue curves map and various pro-jections for higher dimensional systems Calculation of the azeotropic points Determination of the character of the azeotropic points (in the sense of Lyapunov) Computation of the pinch points The representation of the boiling and dew temperature surfaces of azeotropic mixtures gives some other insights into the topology than the residue curve map. It implies more information about the complex rela-tionships in these systems including subregions of distillation, distillation boundaries, driving forces, temperature surface isotherms, minimum sep-aration work as a function of the composition and distillation course in a column. Although the valleys and ridges on the temperature surface are not the boundaries (separatrices) of simple distillation regions and can be crossed by rectification trajectories, they join approximately the singulary points of the mixture (Fig. 3). The valley and/or ridge lines arise in each binary positive or binary negative azeotrope. They arrive at a binary point on another edge of the system being is not an extremum. In the case of a ternary azeotrope the valley and/or ridge lines cross the point of the ternary azeotrope. For a comprehensive overview of these very complicated relationships one needs a sophisticated graphical representation tool allowing different user-friendly operations with the boiling (and dew) temperature surfaces. For this aim different computer-aided graphic tools can be used. Graphical based design and representation environments are exten-sively used in different fields of chemical engineering. The design of chem-VISUALIZATION METHODS 63 Methanol Acetone Chloroform Fig. 3. Azeotropic points, valleys and ridges of the boiling temperature surface for the mixture acetone-chloroform-methanol (1 bar) ical process systems, especially the separation sequence synthesis for mul-ticomponent mixtures with nonideal behaviour requires a deep insight in the topology of distillation regions, the course of the distillation boundaries and their dependence on pressure, the influence and choice of external com-pounds as entrainers, etc. It requires the ability to interpret the complex relationships, to represent special views what concerns isolines of the tem-peratures or other variables, peaks and valleys of the surfaces, boundaries, vector fields and interconnection of different surfaces, further the anima-tion of the graphical representations for better views in the multidimen-sional space, the projections on given planes, zooming of interesting areas and so on. The aim of presenting information in this way is to provide in-struments of exploring all the relevant details and connections so as to be able to extract data for synthesizing optimal process systems . 64 Maximum Azeotrope Chloroform K. HARTMANN and H.·J. HAASE Methanol Dew Temperature Surface Boiling Temperature Surface Minimum Azeotrope Fig. 4. Equilibrium diagram for the ternary mixture acetone- chloroform-methanol (1 bar) The use of colours for the representation of different levels of values (for example of temperatures), for highlighting of regions of interest as well as for the construction of contour values is a necessary component of a computer-aided graphical tool. The use of such techniques as graphical po-tentiometers to specify a range of smooth parameter change an animated observation of different shapes and states of a system under study is pos-sible. Thus, the chemical engineer is able to generate a much more rapid graphical representation of the actual state and situation of the parameter space. A wider and deeper knowledge of the variety of behaviour is pos-sible because the tools allow to acquire information more readily and in a manner more suitable for knowledge retention (MCGREAVY 1991). In this study the visualization system AVS (Application Visualization System) is applied. This tool is provided with a module library for user-friendly modelling of systems under study. Three data viewers are imple-mented: Image Viewer, Graph Viewer and Geometry Viewer allowing the graphical representation of multidimensional data fields as the boiling and dew temperatures as a function of the composition. By using special mod-VISUALIZATION METHODS 65 ules the graphical representations can be characterized by colours, l bright-ness and other effects; by the zoom module the scale can be varied; there are also possibilities for the animation of the objects under study, the rep-resentation of isolines, for example of temperature or driving forces, as well as the calculation and representation of vector fields. The last option makes it possible to construct representation combining information about the residue curve map and the temperature surface. 5. Applications Chloroform Methanol Acetone Fig. 5. 3D-view of the driving forces for the batch distillation of the mixture acetone-chloroform-methanol (1 bar) For an exact synthesis procedure the knowledge of the residue curve map as well as the temperature surfaces are important. In the following the lIn this paper it was impossible to include coloured figures, therefore the informa-tion level of the selected black and white figures is limited, also the animation effect can-not be reproduced. 66 K. HARTMANN and H.-}. HAASE Methanol OK~Lj~--~~~~~~~ OK Acetone o K Az. A-C Chloroform Fig. 6. Driving forces isolines for the batch distillation of the mixture acetone-chloro-form-methanol (1 bar) ternary mixture acetone-chloroform-methanol as a system characterized by one ternary azeotrope and three binary minimum azeotropes will be in-vestigated. Fig. 4 shows the boiling temperature and the dew tempera-ture surfaces as a function of the composition (equilibrium diagram for a ternary mixture). The 3D-temperature difference surface (Fig. 5) presents the driving forces for the distillation process. The driving forces vanish for the azeotropes and the pure compounds. Using filter modules it is possible to determine the 'valleys' and the 'ridges' on the temperature surface and to identify approximately the boundaries of the different distillation regions. The boundaries between the regions are highly nonlinear (curved), their knowledge is very important for the synthesis of the separation scheme. Ap-plying special slice operation isolines for example for a given temperature (Fig. 6). New and very important insights in the very complicated struc-ture of these surfaces give the inference operation carried out on the driving VISUALIZATION METHODS 67 Methanol Acetone Chloroform Fig. 7. Inference lines map for the driving forces of the mixture acetone-chloroform-methanol (1 bar) forces surfaces. Fig. 7 shows this inference response surface which is a link between the residue curve map and the driving force surface. The residue curve like representation shows clearly the different sub regions and the main directions of the residue curves as well as the azeotropic points and the separatrices. That means it is possible to transform one representation type in another using only the information about the temperature. But the tem-perature representation and the derived representations based on the tem-perature contain much more information for the synthesis than the residue curve map only: the driving forces, fine structure of the subregions, the ap-proximate location of the boundaries and their dependence on the pressure. Solving the residue curve Eq. (4) it is possible to combine this procedure with a stability analysis according Lyapunov determining the type of singu-lar points and other characteristics. Varying the system pressure it is pos-sible to investigate how the locations of the azeotropic points change. Us-ing some simple transformations new important insights can be generated for example relative volatility surfaces and minimum separation work sur-68 K. HARTMANN and H.-J. HAASE face. These graphical tools are very important for the synthesis of energy-efficient separation schemes. For mixtures containing more than three com-pounds the described procedure can be applied in the same manner using the different projections. Combining these tools with balance and flowsheet simulation packages a high-sophisticated synthesis approach is available. References 1. GMEHLING, J. - KRAFCZYK, J. - MENKE, J. - FISCHER, K. (1994): Azeotropic Data, VCH Weinheim. 2. KOHLER, J. - POLLMANN, P. - BLASS, E. (1993): Berechnung des minimalen En-ergiebedarfs nichtidealer Rektifikationen, Chem.-Ing.- Techn. Vo!. 65, pp. 143-156. 3. MATSUYAMA, H. - NISHIMURA, H. (1977): Topological and Thermodynamic Classifica-tion of Ternary Vapor-Liquid Equilibria, J. Chem. Eng. Jpn., Vo!. 10, pp. 181-187. 4. MCGREAVY, C. (1990): Graphical Representation Multidimensional Functions in Pro-cess Design and Optimization, Computer Applications in Chemical Engineering, ed. by H. T. Bussemaker and P. D. Ledema, Elsevier Publishers B. V. Amsterdam. 5. MEKIFFER, O. - HARTMANN, K. (1992): Definition and Computation of Distillation Boundaries - a New Approach, ICHEME Symposium Series No. 128, A91-A97. 6. REv, E. (1992): Crossing of Valleys, Ridges, and Simple Boundaries by Distillation in Homogeneous Ternary Mixtures, Ind. Eng. Chem. Res. Vo!. 31, pp. 893-90l. 7. SCHREINEMAKERS, F. A. H. (1901): Z. Phys. Chem. Vo!. 36, pp. 257-289. 8. SIMMROCK, K. H. - FRIED, A. WELKER, R. (1991): Beratungssystem fur die Tren-nung engsiedender und azeotroper Gemische, Chem.-Ing. Techn. Vo!. 63, pp. 593-604. 9. STICHLMAIR, J. (1988): Zerlegung von Dreistoffgemischen durch Rektifikation, Chem.-Ing. Techn. Vol. 60, pp. 747-754. 

VISUALIZATION METHODS FOR EVALUATION OF FEASIBLE SEPARATIONS OF AZEOTROPIC MIXTURES

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VISUALIZATION METHODS FOR EVALUATION OF FEASIBLE SEPARATIONS OF AZEOTROPIC MIXTURES

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Periodica Polytechnica (Budapest University of Technology and Economics)