Pure acentric factor

Basic pure component constants required to characterize components or mixtures for calculation of other properties include the melting point, normal boiling point, critical temperature, critical pressure, critical volume, critical compressibihty factor, acentric factor, and several other characterization properties. This section details for each propeidy the method of calculation for an accurate technique of prediction for each category of compound, and it references other accurate techniques for which space is not available for inclusion. 

Figure 8 depicts how the three popular equation-of-state methods cited previously perform on pure steam. From a theoretical viewpoint, none of the methods has the foundation to handle mixtures of polar/non-polar components. Although the agreement with experimental data is not very satisfactory for any of the methods, the Lee-Kesler equation-of-state does best. It was also found that by slightly adjusting the acentric factor of water, improvement in the representation of the enthalpy of steam can be obtained by this method at 598 K, the conditions of the experimental mixture data, and at other temperatures as well. 

In Figure 10 are shown comparisons of the equation of state methods with the experimental data. The Lee-Kesler methods represent the data the best. Again, if the water acentric factor determined to best represent the pure steam enthalpy data is applied to the mixtures, further improvement is noted for the predictions by the Lee-Kesler method. Use of interaction constants within the Lee-Kesler, or other models, would undoubtedly provide even better representation of the data. 

To design a supercritical fluid extraction process for the separation of bioactive substances from natural products, a quantitative knowledge of phase equilibria between target biosolutes and solvent is necessary. The solubility of bioactive coumarin and its various derivatives (i.e., hydroxy-, methyl-, and methoxy-derivatives) in SCCO2 were measured at 308.15-328.15 K and 10-30 MPa. Also, the pure physical properties such as normal boiling point, critical constants, acentric factor, molar volume, and standard vapor pressure for coumarin and its derivatives were estimated. By this estimated information, the measured solubilities were quantitatively correlated by an approximate lattice equation of state (Yoo et al., 1997). 

The acentric factor, u, is a constant. Each pure substance has a different value of acentric factor. 

Values of a-pj and bj for each component of the mixture are obtained with Equations 15-9 through 15-12 from a knowledge of the critical properties and acentric factors of the pure components. 

To estimate the pure component parameters, we used the technique of Panagiotopoulos and Kumar (11). The technique provides parameters that exactly reproduce the vapor pressure and liquid density of a subcritical component. Table II presents the pure component parameters that were used. For the supercritical components, the usual acentric factor correlation was utilized. 

The acentric factor for a pure chemical species is defined with reference to its vapor pressure. Since the logarithm of the vapor pressure of a pure fluid is approximately linear in the reciprocal of absolute temperature, we may write... 

The Pitzer acentric factor is a property of pure fluids and has been widely tabulated (for example, see Ref. [ ]). It can be estimated in several ways, one of w hich [5] is given in the Nomenclature. 

Listed here for various chemical species are values for the molar mass (molecular weight), acentric factor >, critical temperature Tc, critical pressure Pc, critical compressibilityfactor Z., critical molar volume Vc, and normal boilingpoint T . Abstracted from Project 801, DIPPR , Design Institute for Physical Property Data of the American Institute of Chemical Engineers, they are reproduced with permission. The full data compilation is published by T. E. Daubert, R. P. Daimer, H. M. Sibul, and C. C. Stebbins, Physical and Thermodynamic Properties of Pure Chemicals Data Compilation, Taylor Francis, Bristol, PA, 1,405 chemicals, extant 1995. Included are values for 26 physical constants and regressed values of parameters in equations for the temperature dependence of 13 theniiodynamicand transport properties. 

Fugacity coefficient, pure species i Fugacity coefficient, species i in solution Functions, generalized fugacity-coefficientcorrelation Constants, cubic equations of state Acentric factor... 

For the calculations presented in this paper, we first elected to use three simple cubic equations of state PR-EOS SRK-EOS and RK-EOS. For the pure components, critical properties (Pq, Tq) and Pitzer s acentric factor (ci>) are needed to obtain a and b . Critical properties have been measured for most of the low molecular weight components and are reported by Reid et al. 

The prograjTi KOPT is used for the evaluation of the k constant of pure fluids in the PRSV equation (see Section 3.1). The data required for this program are critical temperature (in Kelvin), critical pressure (in bar), and acentric factor of the fluid as well as data for the temperature (in Kelvin) versus vapor pressure (in any units). The program returns the Ki value, which minimizes the average difference between the estimated and experimental vapor pressures. A simplex optimization routine is used in the calculations. 

If no experimental VI. R data are available, the program can be used for predictions using internally generated liquid mole fractions of species 1 in the range from 0 to 1 at intervals of 0.1. In this case the user must provide all model parameters and temperature in addition to pure component critical temperature and pressure, acentric factor, and the kti parameter of the PRSV equation of state for each compound. An example is given below (Example D.5.C) for this mode of operation of the program. 

This example. serves to demonstrate tlie predictive mode of the program WS, which is selected with the preceding entry. This mode is used in the absence of VLE data, and therefore no data are entered to, or can be accessed from the disk in this mode. Instead, the user provides the critical temperature, critical presssure, acentric factor, and the PRSV kj parameter for each pure component, selects an excess free-energy model provides model parameters and a temperature. The program will return isothermal x-y-P predictions at the temperature entered, in the composition range X] = 0 to 1, at intervals of 0.1.)... 

For a pure component, the parameters a and b are determined from the critical temperature and critical pressure, and possibly the acentric factor. These are all tabulated quantities, and there are even correlations for them in terms of vapor pressure and normal boiling point, for example. For mixtures it is necessary to combine the values of a and b for each component according to the composition of the gaseous mixture. Common mixing rules are shown in Eqs. (2.9) and (2.10), in which the ys are the mole fraction of each chemical in the vapor phase ... 

You have solved a very simple problem to find the specific volume of a pure component or a mixture using three methods Excel, MATLAB, and Aspen Plus. Excel is readily available, and easy to use. MATLAB is a bit more difficult for beginners because it uses files, which require data transfer. It is extremely powerful, though, and is needed for other classes of problems. With both Excel and MATLAB, you must look up the critical temperature, critical pressure, and perhaps the acentric factor of each chemical. You then must carefully and laboriously check your equations, one by one. 

Equation 1.14 incorporates the definition of the acentric factor and may also be used to predict the vapor pressure, once the acentric factor has been determined. Another route for calculating the vapor pressure is via an equation of state, as described below. In the Soave equation, co is used in formulating the temperature dependency of the parameter a, which may be considered as a function of both P and co. The function fl(P,co) was determined with the objective of fitting vapor pressures calculated by the equation of state to experimental pure component vapor pressure data. 

This equation (Peng and Robinson, 1976) was developed with the goal of overcoming some of the deficiencies of the Soave equation, namely its inaccuracy in the critical region and in predicting liquid densities. The equation is similar to the Soave equation in that it is cubic in the volume, expresses its parameters in terms of the critical temperature, critical pressure, and acentric factor, and is based on correlating pure-component vapor pressure data. The equation is written as... 

Critical Constants and Acentric Factors for Pure Fluids.8... 

A prerequisite for mixture EOS calculations is reliable EOS parameters for the pure components. As discussed in Section 1.2.5, these may be obtained in a generalized way from critical constants and the acentric factor, or they may be fitted to data for the specihc fluid. Eor an accurate representation of mixture phase equilibria, the EOS must produce accurate vapor pressures for the pure components. 

Table 2 shows the pure component properties of all the substances involved in this study. Here, M is the molecular weight, Tj. is the critical temperature, 7], is the normal boiling temperature, is the critical pressure, Vc is the critical volume, and w is the acentric factor. Data were obtained from Diadem Public [17]. 

In conclusion, a new pressure-explicit equation of state has been successfully developed as intended. It is suitable for representing PVT behavior of liquid and gas phases over a wide range of temperature and pressure for pure, nonpolar compounds. Furthermore, the parameters of the proposed equation are generalized in terms of the critical properties and the acentric factor. 

The Boublik-Alder-Chen-Kreglewski augmented hard-core equation is applied to pure fluids and mixtures with special attention to the representation of phase equilibria. Equation constants are determined for twelve substances, and the three constants which are required of nonpolar, nonquantum fluids are correlated with the critical properties and acentric factor. The equation describes mixture-phase equilibria with the introduction of mixing rules and the use of up to two interaction constants for each binary system. 

---