Pressure real gases, effect

In practical open circuit gas turbine plants with combustion, real gas effects are present (in particular the changes in specific heats, and their ratio, with temperature), together with combustion and duct pressure losses. We now develop some modifications of the a/s analyses and their graphical presentations for such open gas turbine plants, with and without heat exchangers, as an introduction to more complex computational approaches. 

The Hawthorne and Davis analysis is first generalised for the [CBT]i open circuit plant, with fuel addition for combustion,/ per unit air flow, changing the working fluid from air in the compressor to gas products in the turbine, as indicated in Fig. 3.11. Real gas effects are present in this open gas turbine plant specific heats and their ratio are functions off and T, and allowance is also made for pressure losses. 

The [CBT]ig efficiency is replotted in Fig. 3.14, against (Tt,ITx) with pressure ratio as a parameter. There is an indication in Fig. 3.14 that there may be a limiting maximum temperature for the highest thermal efficiency, and this was observed earlier by Horlock et al. [8] and Guha [9]. It is argued by the latter and by Wilcock et al. [10] that this is a real gas effect not apparent in the a/s calculations such as those shown in Fig. 3.9. This point will be dealt with later in Chapter 4 while discussing the turbine cooling effects. 

For high gas pressures, ideal gas law predictions can become inaccurate and real gas effects have to be taken into account. More details on high-pressure effects can be found in Ohe [34]. 

At extreme conditions (low temperature and high pressure), real gas behavior deviates from ideal behavior because the volume of the gas molecules and the attractions (and repulsions) they experience during collisions become important factors. The van der Waals equation, an adjusted version of the ideal gas law, accounts for these effects. 

At higher pressures it may be necessary to take real gas effects of the sorptive medium into account. A simple way to do this is, to replace the... 

The exponential function in this expression mirrors the influence of the other components (k i) on the adsorption of component (i). The series expansions (7.55, 7.59) can be derived from equivalent virial expansions of the thermal equation of state (EOS) of the single- or multicomponent adsorbate by standard thermodynamic methods. Details are given in [7.2, 7.3]. Real gas effects of the sorptive gas mixture can be taken into account by replacing the partial pressures (pi, i = 1...N) in (7.60) by the (mixture) fugacities (fi = fi (pi... pN, T)) of the system [7.17]. 

Figure 15.6 Sizing coefficient versus reduced inlet stagnation pressure calculated according to EN-ISO 4126-7 and a nozzle flow model including real gas effects for ethylene at inlet stagnation temperatures of 300 and 443 K.

A set of calculations using real gas tables illustrates the performance of the several types of gas turbine plants discussed previously, the [CBT]ig, [CBTX]ig, [CBTBTX]ig, [CICBTXIig and [CICBTBTX]ig plants. Fig. 3.15 shows the overall efficiency of the five plants, plotted against the overall pressure ratio (r) for = 1200°C. These calculations have been made with assumptions similar to those made for Figs. 3.13 and 3.14. In addition (where applicable), equal pressure ratios are assumed in the LP and HP turbomachinery, reheating is set to the maximum temperature and the heat exchanger effectiveness is 0.75. 

We will start by imagining that we have a cylinder with a piston at one end that can move without any frictional losses. (We told you would get sick of cylinders and pistons ) Then each collision of the perfectly elastic particles of the gas would move that piston a little bit. Of course, a real gas has an enormous number of atoms or particles, so the net effect of all the collisions is felt like a continuous force, rather than individual impulses. We want to calculate the force necessary to keep the piston stationary. The pressure is then this force divided by the cross-sectional area of the piston. To calculate this, we will need to sum up all the impulse forces delivered to the piston. Recalling our classical mechanics, we can write Equation 10-8. 

The next step is to account for the attractions that occur among the particles in a real gas. The effect of these attractions is to make the observed pressure P0bs smaller than it would be if the gas particles did not interact ... 

For discussion of intramolecular forces it is essential to remove from consideration effects due to intermolecular forces, that is, to have heats of formation referring to the ideal gas state. In general the correction of heats of formation of real gases at 1 atmosphere pressure to the ideal gas state is very small compared with the accuracy to which heats of formation are known for example, approximately 0-002 kcal mole for methane and 0-02 kcal for methyl chloride. This means that for all purposes connected with bond energies, a knowledge of the heat of formation of the real gas is adequate. Thus for substances whose heat of formation is known directly for the liquid or solid, a knowledge of the heat of vaporization at the appropriate temperature is required. Strictly, however, the quantity concerned is the heat of vaporization to the ideal gas state. 

The fugacity and partial pressure of a gas are related in the same way as activities and concentrations in solution. Interaction of molecules with each other in a real gas diminishes the reactivity of an individual gas shghtly, creating an effective partial pressure called the godly. As the gas pressure approaches zero, the pressure and fugacity are equal. The interference effect on gases in the atmosphere, however. 

We could regard/as the effective pressure just as activities were introduced as effective concentrations . As all gases tend to perfect behaviour as P - 0, under these conditions/will tend to become equal to P. The standard state is strictly the state of the perfect gas at one atmosphere pressure where P = 1 atm and / = 1 atm. This is illustrated in Fig. 8.4. For practical purposes, as many gases are virtually ideal at 1 atm, no great error is introduced if the standard state is characterized by the properties of the real gas at 1 atm. 

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