THERMODYNAMIC MODELING,
COMPUTATIONAL THERMODYNAMICS,
THERMODYNAMIC PROPERTIES OF SUBSTANCES
Glushko Thermocenter, IVTAN Association of Russian Academy of Sciences
Methods of computational thermodynamics have been successfully used for the investigation of various processes and the development of new technologies for many years. Now there is no need to prove the practical value of calculation of equilibrium composition and properties of thermodynamic systems. A number of examples illustrating how thermodynamic calculations may be used as a basic tool in the development and optimization of materials and processes are presented in the excellent book
Hack, K. (ed). Thermodynamics at Work. Institute of Materials, London, 1996.
Below are listed some field of science and technology where thermodynamics works bestThe basic concept of thermodynamics is thermodynamic equilibrium. Thermodynamic equilibrium is some final state of a thermodynamic system insulated from the external medium, i.e., there exists thermal, mechanical and chemical equilibrium in each point of the system and there are no flows. In practice the requirement of isolation means that the processes leading to equilibrium occur faster than the changes on the system’s boundaries (external change of pressure, temperature and chemical composition, etc.) take place. For example when thermodynamic examination of the combustion process is accomplished the adiabatic assumption is usual, i.e. heat losses are not taken into consideration. When the processes in chemical reactor are modeled the common assumption is that the rates of chemical reactions are much higher than the velocity of flow, so, while the flow is in the reactor the chemical equilibrium is reached. Now, there are many evidences that the equilibrium model is valid for the high temperature processes (T > 1500 K) or when there is enough time to reach the equilibrium. Two examples of equilibrium systems are combustion products in the rocket engine chamber where equilibrium is reached in approximately 0.00001 s; some parts of the earth crust where millions of years required to reach equilibrium.
The components of thermodynamic model are
Often the question arise, can we believe the results of modeling? There is no definite answer to this question, it depends. The best way to get the answer is the comparison of results of calculations with the experimental data when possible. The researcher should have the answer to the following questions:
So, one may conclude that thermodynamic modeling is science and the art simultaneously. The researcher should "feel" the system that he/she investigate.
The famous study
Gibbs J.W. On the Equilibrium of Heterogeneous Substances. Trans. Connect. Acad., 1876, 3, pp. 108-248; 1878, 3, pp. 343-524.
provided the theoretical background for thermodynamic examination of complex chemically reacting system. The next remarkable book
Lewis G.N., Randall M. Thermodynamics and the Free Energy of Chemical Substances. NY. McGraw-Hill, 1923.
provided the bridge from the theory to practice. But only the appearance of computers allowed to develop appropriate instruments for thermodynamic modeling. One of the first algorithms of calculation of equilibrium composition was developed by S.R. Brinkley and H.J. Kandiner
Brinkley, S.R. Calculation of Equilibrium Composition of Systems of Many Constituents. J. Chem. Phys., 1947, v. 15, No 2, pp.107-110.
Kandiner H.J., Brinkley, S.R. Calculation of Complex Equilibrium Problem. Ind. Eng. Chem., 1950, v. 42, No 5, pp. 850-855.
The described algorithm used the concept of equilibrium constants. Then another algorithm based on minimization of the Gibbs energy appeared
White W.B., Johnson S.M., and Dantzig G.B. Chemical Equilibrium in Complex Mixtures. J. Chem. Phys. 1958, v. 28, No 5, pp.751-755.
The first "serious" computer program supplied with the database on thermodynamic properties of substances has been developed by F.J. Zeleznik, S. Gordon and B.J. McBride
Zeleznik F.J., Gordon S. A General IBM 704 or 7090 Computer Program for Computation of Chemical Equilibrium Compositions, Rocket Performance, and Chapman-Jouget Detonations. NASA TN D-1454, 1962.
Gordon S., McBride B.J. Computer Program for Calculation of Complex Chemical Equilibrium Composition, Rocket Performance, Incident and Reflected Shocks and Chapman-Jouget detonations. NASA, 1971, SP-273.
The similar program has been developed in Russia, seeAlemasov V.E., Dregalin A.F., Tishin A.P. et al. Thermodynamic and Thermophysical Properties of Combustion Products. Moscow, 1971.
One should admit that the intensive development of the methods of thermodynamic modeling was caused by the development of the rocket engines. It would be impossible to create the modern rocket engines without the preliminary theoretical investigation of the combustion processes and the processes of the combustion products expansion where hundreds of simultaneous chemical reactions occur.
The next stage of the development of thermodynamic modeling is linked with metallurgy. Traditional metallurgical chemistry was based on investigation of the leading (or dominating) reactions. But this approach is very unreliable, as variation of parameters (temperature, pressure, source composition) often changes the list of the leading reactions. So, computational thermodynamics appeared helpful for the examination of metallurgical processes, see
Eriksson G. Thermodynamic Studies of High Temperature Equilibria. Acta
Chem. Scand., 1971, v.25, No 7, pp.2651-2658.
Eriksson G., Hack K. ChemSage - a Computer Program for the Calculation of
Complex Chemical Equilibria. Metallurgical Trans. B, 1990, v. 21B, pp.1013-1023.
Siniarev, G.B., Vatolin, N.A., and Trusov B.G. Primenenie EVM dlia
termodinamicheskih raschetov metallurgicheskih processov (Thermodynamic Modeling
of Metallurgical Processes with Computer). Nauka, Moscow, 1982.
The last book (Siniarev et al.) contains FORTRAN source codes of the powerful computer program for the calculation of complex chemical equilibrium developed by Prof. B.G. Trusov (Bauman Moscow State Technical University). Now, there exists hundreds of algorithms and computer programs intended for the calculation of equilibrium composition of thermodynamic systems. A detailed review of many of them is presented in
Van Zeggeren F., Storey S.H. The Computation of Chemical Equilibria.
Oxford: Cambridge Univ. 1970.
Holub R., Vonka P. The Chemical Equilibria of Gaseous Systems. Dordrecht:
Reidel Pub. Comp. 1976.
Smith W.R., Missen R.W. Chemical Reaction Equilibrium Analysis: Theory
and Algorithms. NY, John Wiley, 1982.
There are two reasons for the existence of this lot of algorithms. The first one is the great variety of thermodynamic systems with their specific features (e.g. combustion processes and the processes in the earth crust). The second reason is caused by "limited" mathematics of the computer, which can accomplish calculations with limited number of significant digits. So, even if mathematics guarantees the solution for some algorithm the computer version of the algorithm will fail in some cases.
Calculation of the equilibrium composition of the system may be accomplished through the solution of a set of the nonlinear equations. The questions of existence and uniqueness of the solution are reviewed in many sources, see Smith W.R., and Missen R.W. for example. It is shown that if the gas phase behavior is described by the ideal gas equation of state and the condensed mixtures are ideal the target function is convex and there usually exists a unique solution.
The basis, the intrinsic part of any serious computer system, intended to accomplish thermodynamic modeling, is a database on thermodynamic properties of individual substances. The main sources of this information are the reference books
Gurvich, L.V., Veitz, I.V., et al. Thermodynamic Properties of Individual
Substances. Fourth edition in 5 volumes, Hemisphere Pub Co. NY, L., Vol 1 in 2
parts, 1989, etc.
Chase M.W., Curnutt J.L., Hu A.T., Prophet H., et al. JANAF
Thermochemical Tables. Third Edition, 1985.
Barin I., Knacke O., Kubaschewski O. Thermochemical Properties of Inorganic
Substances. Springer-Verlag, Berlin, 1977.
Iorish V.S., Belov G.V. On Quality of Adopted Values in Thermodynamic Databases. Netsu Sokutei, 1997, 24 (4), pp. 199-205. The last references contains information about other data sources.
In Thermocenter of the Russian Academy of Science during many years is being carried out a theoretical study of thermodynamic properties of individual substances and accumulation of this information in form of the reference book and a database. This information is intended for scientists and engineers who work in various branches of science and engineering and it must be delivered them in an easy-to-handle form.
The most characteristic feature of IVTANTHERMO is that the stored information is not borrowed from any other data bases or reference books. This information is obtained by means of critical analysis and treatment of the original data available in literature. Primary information analysis and all necessary calculations have been performed with the use of original methods, algorithms and software, developed for the ‘Thermodynamic Properties of Individual Substances’ handbook and updated by its authors for the IVTANTHERMO database. Now the database contains information about approximately 2500 substances formed by 96 chemical elements.
To enable the researchers and engineers to investigate thermodynamic systems of various kinds the software IVTANTHERMO has been developed. Recently a new version of the software appeared, which consists of six programs and the database on thermodynamic properties of individual substances. The software has an intelligible interface, which does not require from user special computer knowledge. All six programs with the database represent one complex - IVTANTHERMO for Windows. The programs are
Prof. Trusov B.G. (Bauman Moscow State Technical University, e-mail: trusov@iu7-head.bmstu.ru) participated in the development of the software IVTANTHERMO for Windows.
Download the manual, about 0.4 MB.
The ideal gas equation of state is most frequently used in thermodynamic calculations. And this assumption is valid for many cases. However if the density of the gas phase is high enough (e.g., temperature is low or pressure is high) a real gas equation of state should be used. Click here for more details.
The appearance and wide spreading of the world wide nets mark the new stage in development of thermodynamic modeling. Now one can use the remote computers for the calculations. However the standalone computers still keep their positions and it is more comfortable to have own software on the table.
Below are listed the references to some interesting sites where thermodynamic and thermochemical information can be found. The list inevitably is not full and contains only those references that I have managed to find. The brief description is borrowed from the URL sources.
The NIST JANAF Thermochemical Tables provide a compilation of critically evaluated thermodynamic properties of approximately 1800 substances over a wide range of temperatures. Recommended temperature-dependent values are provided for inorganic substances and for organic substances containing only one or two carbon atoms. These tables cover the thermodynamic properties with single-phase and multi- phase tables for the crystal, liquid, and ideal gas. The properties tabulated are:
MTDATA is a software/data package for the calculation of phase equilibria in multicomponent multiphase systems using, as a basis, critically assessed thermodynamic data. It has numerous applications in the fields of metallurgy, chemistry, materials science, and geochemistry depending only on the data available. Problems of mixed character can be handled, for example equilibria involving the interaction between liquid and solid alloys and matte, slag and gas phases. The thermodynamic models necessary to describe the properties of a wide range of phase types are incorporated in the software and database structures.
MALT2 is a comprehensive Materials-oriented Little Thermodynamic Database for Personal Computers. The task group of the thermodynamic database was organized in the Japan Society of Calorimetry and Thermal Analysis. MALT2 stores thermodynamic data such as the standard enthalpy change for formation, DfH(298.15 K), the standard Gibbs energy change for formation, DfG(298.15 K), the standard entropy, S(298.15 K), the heat capacity, Cp, and the transition temperature and the enthalpy change for transition, if any, for 4931 species; this covers those compounds important to ceramic materials, semiconductors, inorganic /organic gasses for plasma processes in semiconductors, transition metal oxides, nuclear fuels, nuclear reactor materials etc. From such stored data, the thermodynamic tables and the equilibrium constants at any temperatures can be calculated. In addition, molecular mass, coefficient of heat capacity equation, and references for data can be also available.
HSC Chemistry is made in Outokumpu Research Oy. However, many of the important calculation options are based on the code and ideas from other sources. The aim of this software is to simulate the chemical reaction equilibrium and processes in the personal computer in order to develop new processes and improve the old ones. HSC Database is a compiled database on thermodynamic properties of individual substances. The number of species in the database is more than 10000. These data are not critically evaluated, but give a fast access to data and references which can be found from the literature. The database also has fields for Structural Formula, Chemical Name, Common Name, CAS number, melting point, boiling point, color and solubility to H2O. The data in these fields are not yet complete but even now they can help, for example, to identify organic substances.
Thermodynamic Data and Property Calculation Sites on the Web.
EQS4WIN is a powerful and easy-to-use software package that solves a wide range of problems related to the calculation of the reaction and phase equilibrium composition of complex chemical systems. EQS4WIN incorporates up-to-date technology in numerical analysis, programming, and thermodynamics. It was written under the supervision of Dr. W. R. Smith, senior author of a classic text in the field (see Ref. above). EQS4WIN solves equilibrium problems by minimizing the overall Gibbs free energy of systems involving up to 4 multi-species ideal-solution phases (a gas phase and up to 3 condensed liquid or solid solutions) and any number of pure (condensed) phases. Calculations can be performed for several different types of thermodynamic conditions, either at a single state point, or for up to two simultaneously varying parameters. All versions of EQS4WIN incorporate a thermochemical database based on the species listed in the JANAF Tables.
ThermoChemical Calculator
F*A*C*T - Facility for the Analysis of Chemical Thermodynamics F*A*C*T-Web - provides the free access to the pure substances database, chemical reactions, and Gibbs energy minimization calculations. WEB Servers - similar WWW sites in inorganic chemical thermodynamics.
Feedback:gbelov@iname.com.
Last modified May, 03 1998
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