Pseudocritical constants

When the critical constants for a pure substance or the pseudocritical constants for a petroleum fraction are known, the vapor pressure for hydrocarbons and petroleum fractions can be calculated using the Lee and Kesler equations ... 

Chueh s method gives consistently good results for mixtures except in the immediate vicinity of the critical region (T/TCml > 0.93). For the critical region, his procedure was modified by using true critical constants, rather than pseudocritical constants in Eq. (56). For this purpose, he has established a separate correlation of true critical volumes and temperatures (C3). 

Calculate the volume using Kay s method. In this method, V is found from the equation V = ZRT/P, where Z, the compressibility factor, is calculated on the basis of pseudocritical constants that are computed as mole-fraction-weighted averages of the critical constants of the pure compounds. Thus, T = Z K, 71, and similarly for Pc and Z, where the subscript c denotes critical, the prime denotes pseudo, the subscript i pertains to the ith component, and Y is mole fraction. Pure-component critical properties can be obtained from handbooks. The calculations can then be set out as a matrix ... 

TABLE 1.15 Pseudocritical Constants for Tower Bottoms in Example 1.22... 

The pseudocritical constants are simply empirical parameters that have been found useful for correlating the physical properties of a mixture. Unlike Tc and A for a single component, T. and P have no physical significance. 

To perform PVT calculations for nonideal gas mixtures, you may use Kay s rule. Determine pseudocritical constants (temperature and pressure) by weighting the critical constants for each mixture component by the mole fraction of that component in the mixture then calculate the reduced temperature and pressure and the compressibility factor as before. 

If you are faced with a complicated mixture of gases whose composition is not well known, you still can estimate the pseudocritical constants from charts such as shown in Fig. 3.8 (a) and (b) if you know the gas specific gravity. Figure 3.8 is good only for natural gases composed mainly of methane that contain less than 5% impurities (CO2, N2, H2S, etc.). 

Once this function is determined, it could be applied to any substance, provided its critical constants Pc, T, and V are known. One way of applying this principle is to choose a reference substance for which accurate PVT data are available. The properties of other substances are then related to it, based on the assumption of comparable reduced properties. This straightforward application of the principle is valid for components having similar chemical structure. In order to broaden its applicability to disparate substances, additional characterizing parameters have been introduced, such as shape factors, the acentric factor, and the critical compressibility factor. Another difficulty that must be overcome before the principle of corresponding states can successfully be applied to real fluids is the handling of mixtures. The problem concerns the definitions of Pq P(> and Vc for a mixture. It is evident that mixing rules of some sort need to be formulated. One method that is commonly used follows the Kay s rules (Kay, 1936), which define mixture pseudocritical constants in terms of constituent component critical constants ... 

These mixing rules allow for the calculation of the pseudocritical constants for the mixture and the shape factors. Combining rules were selected to be... 

Pc, Tc,and w using t ieir relation =0.291-0.OSiu. The values used for hydrogen were the pseudocritical constants recommended by Prausnitz and Gunn [14]. 

Fugacity of Mixtures. When applying the n plot and the fugacity plot to mixtures, the question arises as to the proper values to be employed for the critical temperature and the critical pressure. Mixtures have critical temperatures and critical pressures, but it has been found that these values do not give satisfactory results when used for calculating reduced temperatures and pressures to be used with the charts, but pseudocritical constants can be calculated which give better agreement. For these pseudo constants one of the best methods of... 

The pseudocritical pressure is calculated as a function of other constants ... 

EXAMPLE 3-8 Calculate the pseudocritical temperature and pseudocritical pressure of the gas given in Example 3-5. Use the critical constants given in Appendix A. 

The heat transfer to supercritical carbon dioxide was measured in horizontal, vertical and inclined tubes at constant wall temperature for turbulent flow at Re-numbers between 2300 and lxl 05. The influence of the variation of physical properties due to the vicinity of the critical point was examined, as well as the influence of the direction of flow. Therefore most of the measurements were conducted at pseudocritical points. At those supercritical points the behaviour of the physical properties is similar to the behaviour at the critical point, but to a lesser degree. At such points the heat capacity shows a maximum density, viscosity and heat conductivity are changing very fast. [1]... 

Kay s rule estimates pseudocritical properties of mixtures as simple averages of pure-component critical constants ... 

The constants Ci and Cj are both obtained from Fig. 2-40 Ci, usually from the saturated liquid fine and Cj, at the higher pressure. Errors should be less than 1 percent for pure hydrocarbons except at reduced temperatures above 0.95 where errors of up to 10 percent may occur. The method can be used for defined mixtures substituting pseudocritical properties for critical properties. For mixtures, the Technical Data Book—Petroleum Befining gives a more complex and accurate mixing rule than merely using the pseudocritical properties. The saturated low pressure value should be obtained from experiment or from prediction procedures discussed in this section for both pure and mixed liquids. 

A problem in the preceding representation occurs whenever the flux depends mainly on a mole fraction difference for the limiting or boundary condition for a pure component or a mixture of constant composition. Under this circumstance, the pseudocritical pressure remains the same. Furthermore, the flow rate or flux would be required to be zero and is not directly proportional to the pressure difference, as required for the flow of fluids through porous media. It may be assumed, therefore, that this flux relationship in terms of pseudocritical pressures is not an allowable representation. 

The specific heat of He, Na, Pb, and Pb—Bi (Fig. A2.6) is nearly constant over the whole range of operational parameters. In the case of CO2, the specific heat increases linearly and reaches the same value as Na at around 750°C. The specific heat of water goes through a peak (where its value increases almost 8 times) within the pseudocritical region. The specific heats of Pb and LBE are nearly identical and 10 times less than those of Na and CO2, and almost 40 times less than that of He. At temperatures higher than 450°C, the specific heat of He is higher than that of SCW. 

The volumetric expansivity of liquid metals is much smaller than that of the remaining coolants and stays almost constant (see Fig. A2.11). The volumetric expansivity of gases drops almost twice, in a linear fashion, from 250 to 1000°C. Remarkably, the values of volumetric expansivity for SCW at temperatures below the pseudocritical point are close to those for gases. Near the pseudocritical point, the volumetric expansivity of SCW peaks. At higher temperatures, the volumetric expansivity of SCW gradually reaches values corresponding to those of gases. 

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