Pseudocritical property

Critical properties of gaseous compounds are useful in determining the P-V-T (Pressure-Volume-Temperalure) properties at nonideal conditions. The compressibility faetor Z is defined by the following relationship  

When the compounds involved are gaseous mixtures, a weighting method is used to arrive at the eritieal properties of the mixture. 

The example provided in Table 2 is for a four eomponent mixture of hydroearbons (methane, ethane, propane, and n-oetane). The weighting method is a eommon ealeulation procedure that proeess engineers will encounter many times. Computations for simple systems can be easily set up on an Exeel spreadsheet. 

Compound Mole Fraction Critical Press. (atm) Critical Temp. ( R) Pseudocritical Press. Pseudocritical Temp.  

The following formulas can be used to calculate critical properties  

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For hydrocarbon and nonpolar gas mixtures, the Pitzer pure component method can be used to predict vapor density by replacing the true critical properties with pseudocritical properties defined in... 

No specific mixing rules have been tested for predicting compressibility factors for denned organie mixtures. However, the Lydersen method using pseudocritical properties as defined in Eqs. (2-80), (2-81), and (2-82) in place of true critical properties will give a reasonable estimate of the compressibihty faclor and hence the vapor density. 

For mixtures, the pseudocritical properties of the mixture should be used to obtain the compressibility factor. 

These pseudocritical properties were devised simply for use in correlating physical properties. Pseudocritical properties are not equal to the actual critical properties of a gas mixture. Equations 3-42 are often called Kay s mixture rules.5 A somewhat more accurate method of calculating pseudocritical properties is given in Appendix B. 

Often the composition of a natural gas is unknown. However, specific gravity, being more easily measured, is usually available for a gas of interest. In this situation the correlation presented in Figure 3-11 can be used to determine the pseudocritical properties of the gas.8... 

The accuracy of the compressibility equation bf state is not any better than the accuracy of the values of the z-factors used in the calculations. The accuracy of Figures 3-7 and 3-8 was tested with data from 634 natural gas samples of known composition.8 Experimentally determined z-factors of these gases were compared with z-factors obtained from the charts using Kay s rules for calculating the pseudocritical properties and Figure 3-10 for properties of heptanes plus. 

However, the presence of hydrogen sulfide and carbon dioxide causes large errors in compressibility factors obtained by the methods previously discussed. The remedy to this problem is to adjust the pseudocritical properties to account for the unusual behavior of these acid gases.10 The equations used for this adjustment are... 

Pseudocritical properties obtained by either of the methods described previously are adjusted in this manner. These adjustments bring the accuracy of calculated compressibility factors to within the limits expressed above. 

First, determine value of pseudocritical properties in the usual manner. 

Second, determine the value of e and adjust the pseudocritical properties. 

First, estimate pseudocritical properties, calculate pseudoreduced properties, and get a value of z-factor. 

The volume of the gas in the reservoir may be calculated using the compressibility equation of state. This calculation is based on 1 lb mole of gas using Equation 3-39. The composition of the gas in the reservoir calculated by the recombination method can be used to compute the pseudocritical properties so that the compressibility factor may be obtained in the same manner as illustrated in Examples 3-10 and 3-12. 

An alternative to Kay s method for calculating pseudocritical properties when gas composition is known is given below. This method provides pseudocritical properties which give more accurate values of z-factors when used with Figure 3-7 or 3-8. 

The units of the critical and pseudocritical properties are psia and °R. Figures, 3-7 and 3-8, pages 112-413, Compressibility Factors of... 

Sutton and Whitson evaluated several methods for estimating the pseudocritical properties of heptanes plus.2,5 The Kessler Lee equations are recommended.6... 

Figure 3-11, page 119, Pseudocritical Properties of Natural Gases... 

Sutton derived equations for pseudocritical properties of natural gases based on measured z-factors for 264 natural gas samples.2 He used the Dranchuk Abou-Kassem equation for z-factors and the Wichert Aziz adjustment for nonhydrocarbon components.4,7,8 Sutton s equations are... 

For mixtures, pseudocritical properties are used for the evaluation of the reduced properties. For use with Figure 7.28, Kay s rules are applicable, namely,... 

Here pc is in pP (micropoises), Pc in atm, Tc in K, and Vc incm3/mol. Figure 2.4 can also be used to approximate viscosities of mixtures with the pseudocritical properties defined by... 

Here is the mole fraction of species i in a mixture. We may use Figure 2.4 for fluid mixtures, with pseudocritical properties instead of critical properties. This procedure yields reasonable accuracy for mixtures of chemically similar substances. 

Reduced properties are then calculated for the mixture based on the pseudocritical properties. 

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