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7. Some economic problems of practical usage of the theory and
engineering methods of the calculation of processes of multicomponent rectification (Summary).

©     Vigdorov A.S.
Russian academy of sciences. Kurnakov's Institute of General and inorganic Chemistry. Moscow

7a. Some totals

Long-term work in the field of creation of the thermodynamically new theory of rectification processes and new engineering methods of calculating of multicomponent rectification had basically successfully completed and was published in the Internet in English under title: "Dr. Vigdorov's Home Page" and subheading "REVISION OF THEORY AND ENGINEERING METHODS OF CALCULATING RECTIFICATION PROCESSES TO ACHIEVE THE CONSISTENCY WITH THE MOST IMPORTANT CONCEPTS OF THERMODYNAMICS, IRREVERSIBLE THERMODYNAMICS AND MATHEMATICS has not only the paramount scientific significance for subsequent development of theoretical bases of chemical technology but also provides the reception of significant economic benefit." on address:

After several my references to a scientific and engineering public opinion with the help of Usernet and Chemical Engineering List:
CHEME-L@ULKYVM.LOUISVILLE.EDU with calls to familiarize with mine works, these works, published in the Internet, was subjected to anonymous examination. Soon information on works in Internet has appeared on the majority leading search machines of the world (~ 200), starting from machines of USA and finishing machines of Indium and Indonesia. The fullest list these machines is indicated on Site Google searched web for Vigdorov; Content-Location:

Scientific novelty and theoretical validity of works were exhibited in that, that the works as a result of computerized analysis in different time was recognized by the best works in the field of rectification; the information on works was included in the Internet Encyclopedia Bigtome: Search = vigdorov.
The works were twice included in number of the best works in the network of Internet on categories Science - Technology - Academy and Science - Technology - Chemical Engineering and in unique number exhibited works of my Institute and The Russian Academy of Sciences in the called categories.

Concern to the scientific contents of works exhibited that my Home Page have visited 3230 of visitors, and about 1000 persons in 2001. Although the debated works contrary to my want afects on sientific and material interest of many scientists, public oppositions on its scientific contents has not followed.

About economic significance of works, which is directly interlined to them practical usage in an industry and system education, it completely remained behind frameworks of discussion, having a places. Largely it has taken place because on the majority of search machine for a mention about economic significance of the works simply have not sufficiently a place,

In the conclusion of the unit the author considers as the debt to thank all those who within the framework of Internet has rendered him assistance in overcoming information blockade of his works, and those who has exhibited to them interest and has visited of his Home Page.

7b. Lowering of the investments because of raise of accuracy and reliability calculating of multicomponent rectification

In the given concrete case receiving of economic benefit directly is interlined with removal of serious thermodynamic and mathematical mistakes, which underlie in basis of the generally accepted now methods the engineering calculating of processes of multicomponent rectification with usage of the concept about the theoretical plates or the kinetic equations of heat- and mass-transfer with matrix factors.

To number of the major mistakes, which arise at usage traditional computational methods of continuous processes of the multicomponent rectifications should be referred at each stage of separation incorrect choice as final state of evolution of a thermodynamic system states of a stable thermodynamic equilibrium. Actually under final state of evolution of a thermodynamic system, which at invariable conditions on the borders is continuously exchanged by mass and energy with an environment, can be not equilibrium, but only the stationary disequilibrium state, which is mathematically described by other physical laws. In particular, following conception of nonequilibrium thermodynamics achievement by the thermodynamic system of a stationary disequilibrium state should be accompanied by achievement in the considered system of minimum rate of production of entropies.

To consider physical regularities of processes of phase transformations which is flowing in multicomponent mixtures, each point of phase spaces of concentrations of this mixture, found at under constant pressure and boiling point, we shall deliver in correspondence her potential defined by magnitude of free enthalpy of Gibbs[J/mol].

Thus is arising the potential field , which allows at the specification of the position of one points of a trajectory in a phase space of concentrations to define by a numerical integration a appearance and position of all trajectory quasistatic process of free evaporation, proceeding from a condition, that at variation of the system along this of trajectories should be did maximal "useful work". 1.


1 In thermodynamic under maximal "useful work" understand summary value of work without work, produced against constant pressure of environment, A'  =  S A  - p D V[1,2]. For processes that are flowing in multicomponent mixtures, such work is the work of separation.
  1. Dodge Barnett F. Chemical Engineering Thermodynamic. First Edition. New York, London, 1944.
  2. Prigogine I.R., Defay R. Thermodynamique Chimique Liège, 1950. Translated into English.

Told directly follows from consideration of the system of parametric material balance equations, which mathematically describe elementary process of a free phase change D N / N   relative molecular ratio of multicomponent liquid with the regard of limitations, following from conservation laws of mass.
N xi  =   D N yi * + (N - D Nxi*                     i  =  1, 2, ... n
Utillizing a correlation
D N / N ®  0 
(xi -  xi *®d xi®  0   by simple

transformations of the system of equations (1i) can be represent in a view of the autonomous system of ordinary differential equations (2i).

d xi
d t¢
 = yi*   - xi*

Here d t¢  =  d ln N - so named dimensionless time;  N - initial quantity of evaporating solution, mol; xi* and y i*- contents i-ts component in liquid and vapor to be in equilibrium at the end of elementary process, mol/mol;
d  x1d x2,..., d xn - projections of a gradient on axis of coordinates, mol/mol.

In a right part of these equations as independent variable not enters the time and they will be used only for the description of different stationary processes.
Major property of solutions of received system of equations is that. that they can be given kinematic interpretation, namely is put in correspondence movement of a point on a trajectory, disposed in phase space, on axis of which in considered case in quality coordinates are utilised the concentrations of components of a mixture. In course of mathematics 2 are adduce evidences, that trajectory , received in quality, solutions of the called equations can be only of three grades:


2 § 15. Autonomous systems of differential equations and their phase spaces.
In book L.S. Pontryagin: Ordinary differential equations.
translated from the Russian by Leonas Kacinskas and Walter B.Counts
Adiwes international series in mathematics, v. VI, 298 s. Publisher: Reading (Mass.): Addison-Wesley, 1962.

The following Fig. 1. shows that the traditional methods of multicomponent rectification calculations, based on the theoretical plates conceptions lead to the intercrossing of the calculated trajectories at changes of the reflux ratio or vapor ratio. It directly contradicts the above mentioned conclusions of the mathematical theory about allowed solutions of autonomous systems the differential equation.


Fig. 1. Reciprocal intersections of calculated trajectories in the concentration phase space with the alteration of reflux ratio or the vapor ratio. The calculations were based on the theoretical plates conception.

That circumstance, that a final condition of evolution of system in considered elementary process evaporating is a condition of thermodynamic equilibrium between heated up temperature of boiling of liquid and formed sated vapor at which the size of free enthalpy of Gibbs of systems accepts minimal means of all possible value, that on a distance of phase space connecting points of the beginning and the end of process the maximal loss free enthalpy systems takes place or in conditions quasi-static process the maximal useful work is made.

In a case adiabatic process of rectification in each elementary volume columns at the moment of achievement of a stationary state should proceed such change of a liquid phase at which in a limit takes place the maximal loss free enthalpy of liquids and is made maximal "useful work". In other words the trajectory of change of composition of a liquid phase in stationary process of multicomponent rectification in a limit should coincide with a trajectory of change of composition of a liquid in quasi-static process of free evaporation.

For this reason the described above potential fields which properties are determined only by composition of a divided mixture in continuous stationary processes of multicomponent rectification, define an opportunity of reproduction of division and physical modelling of processes in devices of the different sizes and designs. At the same time it is necessary to mean, that in real processes of rectification there is a set of the reasons (cross movement of phases, their hydrodynamics instability etc.), which aspire to reject a real trajectory from theoretical on size of possible indignations in conditions when the thermodynamic system aspires all accessible ways to reduce size of these indignations.

As it was shown by realization of comparative calculations of division of three-component mixes which results are given on Home Page in the text of my work, mistakes of definition of number of theoretical plates or steps of division, and, accordingly, the constructive sizes of columns at approach reflux ratio to the minimal value reach hundred and more percents.

There is no necessity to prove, that elimination of mistakes in methods of engineering calculation of processes of rectification in view of the big individual size of capital investments and frequency of use of these processes in different branch industries of many states, in scales of economic annually results in unreasonable many million's losses in dollars of USA.

In the given concrete case economic benefit of elimination of mistakes will be received in spite of the fact that make more exact methods of calculation have phenomenological character, There are weighty bases to believe, that at the first stage of practical development in the industry of new methods of kinetic calculations of processes of multicomponent rectification the level of admitted mistakes will be lowered up to a level of mistakes which now take place at calculation of division of binary mixes. The basis for such optimistic statement is that circumstance, that by use of new theoretical representations kinetics of process of rectification binary and multicomponent mixes in columns devices with counterflow movement of phases it should be described the same by the form the kinetic equation that includes the same independent driving force - a difference of temperatures of pair and liquids and one independent phenomenological coefficient while kinetics of process is put in conformity movement of a point on a trajectory of process in phase space of concentration.

The further increase of accuracy of calculation of the constructive sizes rectification columns mostly will depend on accumulation and generalization of experimental data on kinetic of process, received after elimination of the thermodynamic mistakes of the kinetic equations. Simplicity and severe physical validity of the new kinetic equations allows considerably to reduce the price of process of generalization of experimental data and to receive the criterions equations with coefficients that should have the statistical importance by criterion of Fisher.

7c. Reorganization of programs of training of engineers - chemists

Practical use of new engineering methods of calculation of processes of the multicomponent rectification, based on consecutive use of methods of nonequilibrium thermodynamics, should inevitably result in change of the status of this area of a science, existing now in system of higher education.

Earlier this status was defined by an opportunity to explain in chemical technology many physical phenomena, that were open and mathematically described without actual use of nonequilibrium thermodynamics or even before its legalization in independent area of a science. Today this status should be changed in view of that many laws formulated and the sciences investigated in this area should lie in a basis of the mathematical description of many processes of chemical technology just so as they have underlie in a basis of the theory and the mathematical description of multicomponent rectification.

At that not poorly important value has the same circumstance, that overwhelming majority of processes of chemical technology, also process of rectification, proceeds in nonequilibrium thermodynamic systems, which final condition of evolution at all is not the condition of steady thermodynamic equilibrium. In particular, to them are referred all areas of chemical technology, where are anyhow used conception about theoretical plates or stages and many other.

Development new the theory and engineering methods of calculation of processes of rectification will demand the certain expansion of mathematical knowledge of students. In particular, in the program of training of the future engineers - chemists in mathematics. should be included the new sections devoted to autonomous systems of the ordinary differential equations and the mathematical theory of a field.

7d. Algorithms and programs - initial point of practical usages of the new theory and new engineering computational methods

The key question determining the beginning of practical use of developed new methods of calculation and physical modelling of processes of binary and multicomponent rectification is presence of algorithms and programs necessary for the decision of the named problems.

Developed in Institute essentially new algorithms of calculation allows to determine not only the general number of units of heattransfer or steps of division (thermal plates), but also to thermodynamically optimize these numbers in rectifying and stripping parts of a column with consider of efficiency of each step, i.e. by direct calculation to find thermodynamically optimal section of input of feed, not resorting at determination of number of stages to selection of these magnitudes with usage of a trial and error method. Besides the developed algorithm at echivement of the general convergence of calculation reduces dimension of a task on unit, that essentially reduces the general duration of the decision of a task especially at division of complex mixes.

7e, Economic benefit of the prompt development of the theory and new methods of engineering calculation of processes of rectification in the Higher school

The big economic benefit can be received in the Higher school, because of the termination of non-productive expenditure for teaching the thermodynamically erroneous theory of processes of rectification that dooms tens if not hundred thousand, present students and post-graduate students, and the future engineers - chemists on necessity in the near future to pass repeated theoretical retraining.

Speed of mastering of the new theory and new methods of engineering calculation in the higher school it is limited now by absence of textbooks, curriculums and examples of calculation. Thus it is required to consider, that urgently it is required to carry out retraining of the big number of the specialists working in the industry and the Higher school.

Under this circumstances paramount value gets a question on a choice so-called free or closed way of distribution of a software. At a choice of the closed way of distribution mathematical algorithms and program they are kept and are sold as the codes received after translation of the program and an environment that were originally written in language of a high level and allow to adapt the program for the decision of the fixed number of variants of the task given in the menu. Thus the algorithm of the decision of each variant of a task remains closed for the end user and for the improvement first demands decoding of the used algorithm of the decision.

Use of the closed way of distribution is connected to the big expenditure of means for the costs, connected to protection of rights to the intellectual property as expenses for creation of the software become covered, as a rule, with the help of the mechanism of the purchase and sales. Completely clearly, that use of this way of distribution of a software in itself brakes his wide development in the Higher school as from the very beginning assumes necessity of an expenditure of means for its purchase.

The free way of distribution of the software assumes free-of-charge transfer under the first requirement of the software, and the information necessary for his use to any user. The transmitted software written in the programming language of the high level, if should allow to the user to bring anyone, including essential improvements in algorithm of the decision of practical tasks. At such approach the software under influence of very big number of users, each of which solves own tasks, very quickly will get a kind most convenient for practical use. Thus, I hope, possible to overcome the obstacles connected to existence of different platforms for programming (Windows, Unix, Linux etc.), different variants of technological circuits for division of complex mixes, and with necessity of the coordination of new thermodynamic programs with other programs that are used for calculation of phase balance and other thermodynamic sizes, for hydrodynamics calculations, definition of the constructive sizes and mechanical calculations rectification columns, and others adjacent technological calculations.

Now advantages and lacks of use of the open and closed software from the point of view of economic expenditure of a society are enough well-known , as both ways are rather widely used in practice and in each concrete case can be subjected to the authentic economic analysis. A stumbling-block at the decision of this question is the question on financing creation of the new open software.

In the West creation of the open software is financed by the largest firms, such as IBM, that under the words of the represents this firm in Moscow madams Natalia Iron ( has spent for these purposes about 1 billion dollars. In particular this money were spent for installation by firm IBM openly is distributed operational system Linux as the basic on the New York stock exchange. Not casually the prestige of this operational system continuously grows also she becomes freqvently more and more significance of the standard de facto .

Other known sponsor of financing of the open software is Japanese corporation Sun Microsystems ( http:/ that participated in creation initially free-of-charge language Java, operational system Solaris, and office package StarOffice.

The facts stated above were promulgated by firm IBM and corporation Sun Microsystems at a working meeting "The Free software: business models and corporate initiatives" 28.11.2001 (, organized Higher school of economy ( and Publishing house "Computerru" ( Within the framework of actions of the Federal target program "Electronic Russia" which priority is realization of the tender on delivery in rural schools of Russia of computers and the software.

Texts of statements quoted under the report on a working meeting in transmission on radio "Svoboda" of Alexander Kostinskiy
( 401.asp).

Dr.Ph. A.S.Vigdorov
Kurnakov Institute of General
and Inorganic Chemistry RAS
Leninskiy prospekt 31,
117009, GSP-1, Moscow, Russia
Tel/Fax:7 095-954-1279

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