AT HIGH PRESSURE AND TEMPERATURE
Moscow State University, Chemistry Department
Return to the main page.
Real Gas Equation of State
Database on Thermodynamic Properties
At the time being high pressures are often used in various branches of chemical engineering. In some cases high pressure allows to accelerate reactions velocity, in others, it helps to increase the product output. High pressures permit to enhance performance characteristics of power units, when the fuel chemical energy serves as energy source.
Experimental examination of the known processes or development of the new ones is expensive and time consuming, so accomplishing thorough computer modeling before the experiment is reasonable. Chemical reactions in the processes mentioned can involve various chemical elements, that is why the tools for modeling must be supplied with an extensive database on thermodynamic properties of substances.
The equilibrium model is successfully used for the analysis of high temperature processes. This model allows to apply methods of thermodynamics for the theoretical examination of complex chemically reacting systems. So the task is reduced to the determination of phase and chemical composition of the thermodynamic system.
If the gas density is low (pressure is less than 20 MPa and temperature is more than 1000 K) the gas phase behavior can be adequately described by the ideal gas equation of state (EOS). However in high-pressure area influence of the intermolecular forces becomes significant, and real gas EOS should be used. Detailed review of the problem and methods for its solution are given in
Baibuz V.F., Zitserman V.Yu., Golubushkin L.M., et al., ed. Yungman V.S. Chemical equilibrium in nonideal systems. Moscow, IVTAN, 1986. (In Russian).
The reference mentioned above contains some useful source codes in FORTRAN.
Freedman E., “Thermodynamic properties of military gun propellants”, in: L. Stiefel (ed), Gun propulsion technology, Washington, 1988, pp.103-132.
Smith W.R., and R.W. Missen, Chemical reaction equilibrium analysis. John Wiley, New York (1982).
To enable the researchers to accomplish the computer modeling of thermodynamic equilibrium in complex chemically reacting systems at high pressure (up to 600 - 800 MPa) and temperature (up to 6000 K) a new algorithm has been developed. The algorithm allows to take into account the intermolecular forces of the gas substances, significant at high pressure. Due to this ability the values of such parameters of the energetic materials as specific impulse, powder force and chemical composition of the combustion products may be computed more reliably than in ideal gas assumption. The developed algorithm, which is described in
Belov G.V. Thermodynamic analysis of combustion products at high pressure and temperature. Propellants, Explosives, Pyrotechnics. v.23, No 2, pp. 86-89, 1998
was derived from an older version of well known in Russia ASTRA algorithm, see
Siniarev, G.B., Vatolin, N.A., and B.G. Trusov, Computer modeling of the metallurgical processes. Nauka, Moscow, 1982. (In Russian).
On the basis of the algorithm a computer code REAL has been created. The software allows to determine the following characteristics of the energetic materials
theoretical rocket performance for both equilibrium and frozen compositions during expansion (velocity of flow, specific impulse, throat characteristics, area ratio etc.), freezing temperature can be varied;
powder characteristics (powder force, covolume, powder potential);
equilibrium and frozen sound velocity;
transport properties of the combustion products (dynamic viscosity coefficient, thermal conductivity);
partially equilibrium composition with assigned concentrations of several compounds;
heat of combustion at constant volume (in equilibrium and frozen assumptions).
The calculation of thermodynamic and other parameters is based on the following assumptions: one-dimensional form of the continuity, energy and momentum equations; complete combustion; adiabatic combustion; zero velocity in the combustion chamber; homogeneous mixing. For equilibrium expansion, composition is assumed to attain equilibrium instantaneously during expansion. For frozen expansion, composition is assumed to remain fixed at the combustion composition starting from predefined freezing temperature.
To calculate equilibrium characteristics of the system assigning of the equilibrium conditions of the system and environment is necessary. As a rule these conditions are set by values of two thermodynamic parameters, for example (P, H). Besides, the setting of the source composition of the system is necessary. REAL determines phase and chemical composition of the system and its thermodynamic properties if equilibrium conditions are specified by values of any pair of parameters from the following list: P, T, V, S, H, U.
To facilitate the apprehension of the results of calculations REAL allows to draw the charts on the screen. Possible kinds of the charts are
Concentration - Parameter,
Parameter - Parameter,
Parameter - Concentration,
Concentration - Concentration.
There are two versions of REAL - DOS-version and for Windows-version.
Now, there exist hundreds of real gas equations of state. Unfortunately, the most part of them is valid for the small groups of gases only, and the parameters of these equations of state for many gases are unavailable. So, very few of them may be used for the investigation of various classes of the gaseous combustion products. REAL allows to accomplish computer modeling using of one of three equations of state:
- ideal gas EOS: P = D*R*T,
- virial EOS: P = D*R*T*(1 + B*D + C*D2);
- Nedostup EOS: P = D*R*T*[1 + B*(T0)/(1-D/D0)],
Nedostup V.I., and E.P. Gal'kevich, “New real gas equation of state”, Dokl. Akad. Nauk SSSR, No.2A, pp.179-182 (1978).
D - density, B, C - virial coefficients, T0= T/(1-D/D0), D0 - conventional density at 0 K. The last two equations of state have strong theoretical background. Their coefficients may be obtained using Lennard-Jones 6-12 potential, the parameters of which are known or may be evaluated for many gases. Both of these equations adequately describe the gas phase behavior up to pressure values 600 - 800 MPa. This limit is rather conditional one, because sometimes calculations may be carried out at higher pressure values. Indeed, for Nedostup EOS the upper limit is defined by the relation D/D0, which must be less than 0.9. Virial EOS has not an exact upper boundary, and evaluating its reliability at pressures higher than 600 MPa or at low temperatures is difficult. From theory it follows, that virial EOS is valid if density value is lower than critical one. However, the latter is usually unknown for complex mixtures of combustion products. Being compared, these two EOS display approximately the same P(D) dependence up to pressure 300 MPa (D = 0.2 g/cm3). We consider it very useful for the researcher to have at disposal two real gas EOS for study of the high pressure systems.
No serious computer modeling is possible without reliable and extensive information about thermodynamic properties of compounds, so REAL is supplied with a database on thermodynamic properties of individual substances. The database contains information about thermodynamic and thermochemical properties of 2500 compounds made up by 79 chemical elements. Main body of the database (about 70%) consists of the information from
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.
The database welcomes improvement and expansion. There is a special service software (ASTD) for the interactive access to database information: contents review, extraction of properties of the species given, detailed reaction analysis, new data insertion or verification.
Lennard-Jones potential parameters s and e/k for the gas substances in the database were collected from various data sources. Many values of these parameters were calculated by the author from the critical point parameters (Tcr, Pcr, Vcr).
Last modified February, 2010