Real Gas Properties

We know from experience that a rapid decrease in pressure will lead to a decrease in the temperature of the fluid. This is why frost is formed on the exhaust from a gas reUef pipe. 

Can we describe this process using our knowledge of thermodynamics We rewrite the first law of thermodynamics for an open system and, recognizing that there is no work being done on the fluid and no heat being added to the system, we find that 

For real fluids, the enthalpy ean also be a function of pressure. Under these circumstances, we need a new method of evaluating the thermodynamic properties of the fluid. There are several alternatives  

Assume ideal gas behavior (not very helpful in many cases). 

Use an alternate equation of state that adequately models the real gas properties. 

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The discussion of the performance of gas turbine plants given in this chapter has developed through four steps reversible a/s cycle analysis irreversible a/s cycle analysis open circuit gas turbine plant analysis with approximations to real gas effects and open circuit gas turbine plant computations with real gas properties. The important conclusions are as follows ... 

The choice of these values is arbitrary. In practice, the cooling fraction will depend not only on the combustion temperature but also on the compressor delivery temperature (i.e. the pressure ratio), the allowable metal temperature and other factors, as described in Chapter 5. But with ip assumed for the first nozzle guide vane row, together with the extra total pressure loss involved (k = 0.07 in Eq. (4.48)), the rotor inlet temperature may be determined. These assumptions were used as input to the code developed by Young [11] for cycle calculations, which considers the real gas properties. 

The relationship to the earlier discussion of real gas properties (Section 2.4.1) can be demonstrated by re-expressing the Van der Waals equation in terms of Z. To obtain Zvdw for the Van der Waals gas, we first rewrite (2.13) in expanded form as... 

None of the equations discussed so far in this chapter adequately represents the properties of gases over the ranges of temperature and pressure of interest to the petroleum engineer. These equations are given here to illustrate the various semitheoretical schemes researchers have used in an attempt to modify the ideal gas equation of state to describe real gas properties. 

The true worth of the equations for ideal gases is now evident. They are important because they provide a convenient base for the calculation of real-gas properties. 

Essentially there are four methods of getting or predicting real gas properties ... 

For design calculations involving Refrigerant 500, a minimum-boiling azeotrope of 39.4 mol % of 1,1-difluoroethane and 60.4 mol % of difluorodichloromethane, reliable real gas thermodynamic properties are required which have been calculated from 0.2 to 100 bar and from 220 to 540 K using the recently proposed Boublik-Adler-Chen-Kreglewski equation of state and the PVT data reported in the literature. This equation of state has 21 universal constants and only five adjustable constants which have been calculated for R-500 from the PVT data, saturated vapor pressure and liquid density, and the critical constants. In order to calculate the absolute values of the real gas properties, the reference state properties, which are also reported here, are required. All properties are given in SI units. 

The equation of state data in the recommendations is given in terms of second virial coefficients for the pure substances, Bi(T), and their interaction coefficients with methane, Bjj(T). (Because of the low pressmes used in the industry, the simple equation PV/RT=1+ B(T)/V is sufficiently accurate). There are very few hydrocarbons for which there are measmed virial coefficient data in the temperature range of interest, and appreciable extrapolations are needed. Also some of the virial coefficients are based on indirect methods, and may be of marginal reliability. To overcome these problems, a correlation developed by K.R.Hall for virial coefficients for all of the hydrocarbon data has been used. It is valid for the range 0 to 25 °C and is based on a reduced equation of state. A computer program in GPA 2172-1985 [13], uses this correlation to calculate real gas properties. 

Significant errors in thermodynamic properties calculated as previously described may arise from the uncertainty in the specific-heat data. These errors may be reduced significantly by using zero-pressure specific heats calculated by the methods of statistical mechanics with spectroscopic data, since ideal-gas properties are generally about an order of magnitude more accurately known than the real-gas properties determined by calorimetric methods. ... 

The heat balance over the steam reformer itself is thus almost unchanged when real gas properties are used. The reason is the moderate pressure and the high temperature, but at a higher pressure or for mixtures close to the dew point the difference increases. 

In these equations, the real-gas properties are expressed relative to the standard state values, H°, S°, and G°, which are, respectively, the molar enthalpy, the molar entropy, and the molar Gibbs energy values which the gas would have at a standard pressure p° (1.013 25 bar) if it were ideal. 

The data of IVTANTHERMO are used mainly by the branches of industry connected with high temperatures, and by research institutes which deal with calculation of real-gas properties and need data on their prc rties in the ideal-gas state. 

Physics always operates with certain models—simplified representations of real systems. The ideal gas model is one such example. Despite its variety of real gas properties, this simple model assists in understanding the behavior of more complex systems using more complex factors permitted within the model, and it provides numerical results. For example, the introduction of additional interactions leads to van der Waals s gas and allows further inclusion of virial factors, which in turn make the model more universally applicable to all gases. When using the model, the level of required accuracy has to be defined and on that basis, an appropriate model can be selected. 

This influence must be taken into consideration when calculating real gas and compressible liquid properties. 

Properties of mixtures as a real gas or as a liquid under pressure are determined starting from the properties of mixtures in the ideal gas state or saturated liquid after applying a pressure correction determined as a function of a property or a variable depending on pressure )... 

Density is the most commonly measured property of a gas, and is obtained experimentally by measuring the specific gravity of the gas (density of the gas relative to air = 1). As pressure increases, so does gas density, but the relationship is non-linear since the dimensionless gas compressibility (z-factor) also varies with pressure. The gas density (pg) can be calculated at any pressure and temperature using the real gas law ... 

A consequence of writing the partition function as a product of a real gas and an ideal g part is that thermod)mamic properties can be written in terms of an ideal gas value and excess value. The ideal gas contributions can be determined analytically by integrating o the momenta. For example, the Helmholtz free energy is related to the canonical partitii function by ... 

This technique for finding a weighted average is used for ideal gas properties and quantum mechanical systems with quantized energy levels. It is not a convenient way to design computer simulations for real gas or condensed-phase... 

The values of the thermodynamic properties of the pure substances given in these tables are, for the substances in their standard states, defined as follows For a pure solid or liquid, the standard state is the substance in the condensed phase under a pressure of 1 atm (101 325 Pa). For a gas, the standard state is the hypothetical ideal gas at unit fugacity, in which state the enthalpy is that of the real gas at the same temperature and at zero pressure. 

The 2ero and the interval of the KTTS are defined without reference to properties of any specific substance. Real measurements with real gas thermometers are much more difficult than the example suggests, and all real gases condense before 0 K is reached. 

The ideal gas is a useful model of the behavior of gases and serves as a standard to which real gas behavior can be compared. This is formalized by the introduction of residual properties. Another useful model is the ideal solution, which sei ves as a standard to which real solution behavior can be compared. This is formalized by introduction of excess propei ties. 

Although the virial equation can be used to make accurate predictions about the properties of a real gas, provided that the virial coefficients are known for the temperature of interest, it is not a source of much insight without a lot of advanced analysis. An equation that is less accurate bur easier to interpret was proposed by the Dutch scientist Johannes van der Waals. The van der Waals equation is... 

The feedstocks were prehydrogenated real gas oil fractions with different aromatic, sulphur and nitrogen contents from Hungarian and Russian crudes. Their important properties are summarized in Table 2. 

Compressing a gas brings the particles into close proximity, thereby increasing the probability of interparticle collisions, and magnifying the number of interactions. At this point, we need to consider two physicochemical effects that operate in opposing directions. Firstly, interparticle interactions are usually attractive, encouraging the particles to get closer, with the result that the gas has a smaller molar volume than expected. Secondly, since the particles have their own intrinsic volume, the molar volume of a gas is described not only by the separations between particles but also by the particles themselves. We need to account for these two factors when we describe the physical properties of a real gas. 

The standard state (and thus any standard thermodynamic property) of a pure solid refers to the pure substance in the solid phase under the pressure p of 1 bar (0.1 MPa). The standard state of a pure liquid refers to the pure substance in the liquid phase at p = 1 bar. When the substance is a pure gas, its standard state is that of an ideal gas at p = 1 bar (or, which is equivalent, that of a real gas at P = o). 

CHEMKIN REAL-GAS A Fortran Package for Analysis of Thermodynamic Properties and Chemical Kinetics in Nonideal Systems, Schmitt, R. G., Butler, P. B. and French, N. B. The University of Iowa, Iowa City, IA. Report UIME PBB 93-006,1993. A Fortran program (rglib.f and rgin-terp.f) used in connection with CHEMKIN-II that incorporates several real-gas equations of state into kinetic and thermodynamic calculations. The real-gas equations of state provided include the van der Waals, Redlich-Kwong, Soave, Peng-Robinson, Becker-Kistiakowsky-Wilson, and Nobel-Abel. 

Take, for example (12), the problem of solving for the P-V-T properties of a real gas obeying the van der Waals equation of state. 

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