Real gas factor

For real gases, especially at high pressure, the design equations must be corrected with the real gas factor (Figure 3.1.2-1, Chapter 3). 

Real gas factor r = pVfRT of dry air at different temperatures an pressures. 

Fig. 2.1-27 Fugacity coefficient dependent on the reduced pressure, parametrized with the reduced temperature, at critical real gas factor Z, = 0.27...

Furthermore, at the discussed high pressures the real gas behavior of hydrogen comes into the play. Hydrogen has a real gas factor > 1. This means, that the density increases more slowly than the pressure. In the contrary, natural gas has a real gas factor <1 over a wide range of pressure levels, which means the density increases more rapidly than the pressure. Therefore, an optimal pressure level of 200 bar is resulting as an optimal pressure level for storage of natural gas. For hydrogen tanks... 

In case of mixtures of components which do not strongly or differently associate in the vapor phase, the separation factor aij can be approximated by Qfij = Pf/P[ Ki/vj. In other cases the ratio of the real gas factors has to be taken into account. Calculate the ratio of the pure component vapor pressures, the activity coefficients (calculated using the UNIQUAC model) and the real gas factors for the system water (1)-acetic acid (2) at 80 °C as function of concentration. Discuss the results. 

Here we assume that the real gas factor or compressibility (Z) of the sorptive gas in the adsorption equilibrium state considered. 

As can be recognized from eqs. (3.55a, b, 3.56a, b) accurate measurements of gas concentrations (y, yf) or, equivalently (w, wf) are very important in order to get small dispersions of adsorbate s mass mfgg. Due to experience it also can be said that accurate measurements of the system s pressure (p) and temperature (T) are essential, whereas the influence of the real gas factor (Z) and its uncertainly often is rather small. Given MSDs of gas concentrations =ayjf <10, of microbalance measurement (on/f2)<10 and of all the... 

Real gases deviate from ideal gas behavior at higher pressures and lower temperatures, which has to be accounted by real gas equations and the real gas factor z. 

Figure 3.1.2 Real gas factor versus pressure of selected gases at 300 K (a) and for N2 at different temperatures (b). Tfie data for CO2 pertain to 313 K as it liquefies at 300 K (p = 67 bar).

The fugacity coefficients yjj can be approximated by the real gas factor Z (Section 3.1.1), which is unity for ideal gases, and for real gases is defined as Zi = pVmou/RT. The equation to determine [Pg.191]

The specific volume at stagnation conditions in Eq. (15.2) should be determined not for ideal gases but rather for a real gas. No method is recommended in EN-ISO 4126-7 for computing the real gas factor. 

Typical values for the velocity coefficient in a frictional nozzle flow are 0.9-1 -Sigloch ([5], S. 392) gives an average value of 0.97. Numerical calculations on a high-pressure safety valve lead to the conclusion that the velocity coefficient is close to 1, [14, chapter 5]. The real gas factor is generally determined with a suitable equation of state. 

The real gas factor Z is calculated from the equation of state by adjustment of Eq. (15.22) with the specific volume v = ZRTfp. Eor example, for the Soave-Redlich-Kwong equation, we have... 

Figure 15.2 Real gas factor Z for ethylene, methane, and nitrogen as functions of reduced stagnation pressure and reduced stagnation temperature.

The equation for computing the real gas factor Z and the derivatives Kj und Kp can be derived analytically. Figure 15.2 shows the real gas factor calculated by the Soave-Redlich-Kwong equation of state for methane in the pressure range between 0.01 and 250 MPa at temperatures of 200, 300, and 450 K, for nitrogen at a temperature of 300 K, and for ethylene at 296.4 and 443.1 K. Pressure and temperature are based in all cases on the critical data of the fluid as reduced pressure and reduced temperature T ... 

Nearby the thermodynamic critical temperature (T, = 1.05), the real gas factor drops off, at first very strongly, reaches a minimum at a reduced pressure of somewhat over 1, and then increases again. The further away the temperature of the gas is from the thermodynamic critical point, the less strongly pronounced the minimum is. 

The real behavior of a gas essentially depends on how far away the actual pressure and temperature are from the thermodynamic critical point and not on the absolute values of pressure or temperature of the gas. The assumption that a gas behaves ideally (Z = 1) may lead to significant errors in the sizing of safety valves. Basically, the required cross-sectional area of the valve seat is rather underestimated if a too small real gas factor is assumed. 

As an alternative, the analytic solution based on Eq. (15.17) may be used for sizing a valve. Arithmetic averages between the inlet and the throat of the nozzle for the isentropic exponent, the real gas factor, and its gradients can only be recommended if the change of the isentropic coefficient and the real gas factor is almost linear that is, pressure and temperature are far from the thermodynamic critical condition. 

Discharge coefficient of a safety valve for gases/vapors Pressure gradient of the real gas factor... 

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