Compressibility factor chart

A chart which correlates experimental P - V - T data for all gases is included as Figure 2.1 and this is known as the generalised compressibility-factor chart.(1) Use is made of reduced coordinates where the reduced temperature Tr, the reduced pressure Pr, and the reduced volume Vr are defined as the ratio of the actual temperature, pressure, and volume of the gas to the corresponding values of these properties at the critical state. It is found that, at a given value of Tr and Pr, nearly all gases have the same molar volume, compressibility factor, and other thermodynamic properties. This empirical relationship applies to within about 2 per cent for most gases the most important exception to the rule is ammonia. 

The generalised compressibility-factor chart is not to be regarded as a substitute for experimental P — V — T data. If accurate data are available, as they are for some of the more common gases, they should be used. 

Figure 2.3 Generalized compressibility factor chart for acid gas mixtures (based on pure C02).

From a compressibility factor chart, Z = 0.86. The rate of heat input due to fire and flow rate of the vapor release can be determined by Equations 5-53 and 5-45. Table 5-12 gives the input data and results of vinyl chloride monomer. The results show that the calculated relief valve orifice area is 2.172 in. The nearest standard orifice size is L, with an orifice area of 2.853 in. ... 

Alternatively if compressibility factor charts are available, these Z factors may be used to compute the fugacity of pure component i by use of the following equation which is readily obtained by commencing with Eqs. (14-12) and (14-26)... 

Compare the results from the above equation and the generalized compressibility factor chart for natural gases shown in Fig, 3,43. Note that away from the critical point, the agreement is very good. 

Figure 3.43 Compressibility factor chart for gases from (from Standing and Katz, 1942).

At this point we may give a simple answer to the obvious question. What is the fugacity For a pure ideal gas the fugacity is identical to the pressure, and has the same dimensions as the pressure. Thus, we may think of it as a corrected pressure that enters many equihbrium calculation in place of the real pressure. Equations 7.8 and 7.10 show that we commonly show pure species fugacities as the dimensionless ratio off/P. The mathematics of Appendix C show why that occurs. For pure species, the plot of the fugacity most often seen is Figure 7.1, which is somewhat similar to the common compressibility factor chart (z chart). This plot is shown in Appendix A.5 along with the same information in an alternative format. In both//P and z charts, an ideal gas is represented by a horizontal line with value... 

FIGURE A.4 Compressibility factor chart. (From Hougen, O. A., K. M. Watson, and R. A. Ragatz, Chemical Process Principles, Part II Thermodynamics, ed. 2. 1959. New York Wiley. Reprinted by permission of the estate of O. A. Hongen.)... 

Generalized compressibility factors for gases are given in Figures 12-14A-E. These charts have been prepared to allow approximately the same accuracy in reading values over the entire range. 

Compressibility factors at low pressure for several major hydrocarbons are presented by Pfennig and McKetta. Compressibility charts for specific gases are given in Figures 12-14F-W. 

Table 12-3 lists the variation of compressibility factor, Z, with pressure as read or computed from accepted charts. 

Using the Compressibility Factor. The behavior of most pure gases can be represented adequately by a single chart of the compressibility factor Z, which has been defined above in Equation (5.55). 

As we have already seen, the universal chart of gases assumes that all gaseous species exhibit the same sort of deviation from ideal behavior at the same values of 7, and V. This fact, known as the principle of corresponding states, is analytically expressed by the deviation parameter (or compressibility factor ) Z. For n =, ... 

Generalized charts are applicable to a wide range of industrially important chemicals. Properties for which charts are available include all thermodynamic properties, eg, enthalpy, entropy, Gibbs energy, and PVT data, compressibility factors, liquid densities, fugacity coefficients, surface tensions, diffusivities, transport properties, and rate constants for chemical reactions. Charts and tables of compressibility factors vs reduced pressure and reduced temperature have been produced. Data is available in both tabular and graphical form (61—72). 

It would be convenient if the compressibility factor at a single temperature and pressure were the same for all gases, so that a single chart or table of z T, P) could be used for all PVT calculations. Nature is not that accommodating, unfortunately for example, z for nitrogen at 0°C and 100 atm is 0.9848 while z for carbon dioxide at the same temperature and pressure is... 

Figure 5.4-1 shows a generalized compressibility chart for those fluids having a critical compressibility factor of 0.27. Conditions for both gases and liquids are illustrated, although in our discussions here we only consider estimation of z for gases. Note the increasing deviations from ideal gas behavior as pressures approach Pc O-e-, when Pr 1). 

An extension of the generalized charts that provides somewhat greater accuracy also allows for a dependence of z T, P) on the compressibility factor at the critical point, which generally varies between 0.25 and 0.29,... 

Use the compressibility charts to determine the compressibility factor, and then solve for the unknown variable from the compressibility-factor equation of state (Equation 5.4-2),... 

The compressibility-factor equation of state used in conjunction with the generalized compressibility chart is not generally as accurate as a multiple-constant equation of state for PVT calculations under highly nonideal conditions. Furthermore, it lacks precision and cannot readily be adapted to computer calculations. Its advantages include relative computational simplicity and (as will be shown) adaptability to multicomponent gas mixtures. 

The compressibility factor for a gas mixture, Zm can now be estimated from the compressibility charts and the pseudoreduced properties, and V for the mixture can be calculated as... 

The basis of the generalized compressibility charts is the law of corresponding states, an empirical rule stating that the compressibility factor of a species at a given temperature and pressure depends primarily on the reduced temperature and reduced pressure, T, - T Tc and Pr = P Pc- Once you have determined these quantities, you may use the charts to determine z and then substitute the value in the compressibility-factor equation of state and solve for whichever variable is unknown. 

Calculate the reduced temperature, reduced pressure, and reduced volume, and to use any two of these parameters to obtain the compressibility factor, z, from the Nelson and Obert charts. 

Use compressibility factors and appropriate charts to predict the p-V-7 behavior of a gas, or given the required data, find compressibility factors. 

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