Parameters


The calculation of vapor and liquid fugacities in multi-component systems has been implemented by a set of computer programs in the form of FORTRAN IV subroutines. These are applicable to systems of up to twenty components, and operate on a thermodynamic data base including parameters for 92 compounds. The set includes subroutines for evaluation of vapor-phase fugacity  [c.5]

The data base contains provisions for a simple augmentation by up to eight additional compounds or substitution of other compounds for those included. Binary interaction parameters necessary for calculation of fugacities in liquid mixtures are presently available for 180 pairs.  [c.5]

To use Equation (10b), we require virial coefficients which depend on temperature. As discussed in Appendix A, these coefficients are calculated using the correlation of Hayden and O Connell (1975). The required input parameters are, for each component critical temperature T, critical pressure P,  [c.29]

Guide for Estimating Unknown Parameters  [c.36]

Since parameters for many fluids of interest are not given in this monograph, it may be necessary to estimate the required parameters T, P, R, y, and n.  [c.36]

The parameters r, q, and q are pure-component molecular-structure constants depending on molecular size and external surface areas. In the original formulation (Abrams and Prausnitz, 1975), q = q. To obtain better agreement for mixtures containing water or alcohols, q for water and alcohols has here been obtained empirically to give an optimum fit to a variety of systems containing these components. For alcohols, the surface of interaction q is smaller than the geometric external surface q, indicating that for alcohols, intermolecular attraction is determined primarily by the OH group. Appendix C presents values of these structural parameters.  [c.42]

For each binary combination in a multicomponent mixture, there are two adjustable parameters, t 2 21 turn,  [c.42]

Parameters a 2 21 found from binary experi-  [c.43]

Since the accuracy of experimental data is frequently not high, and since experimental data are hardly ever plentiful, it is important to reduce the available data with care using a suitable statistical method and using a model for the excess Gibbs energy which contains only a minimum of binary parameters. Rarely are experimental data of sufficient quality and quantity to justify more than three binary parameters and, all too often, the data justify no more than two such parameters. When data sources (5) or (6) or (7) are used alone, it is not possible to use a three- (or more)-parameter model without making additional arbitrary assumptions. For typical engineering calculations, therefore, it is desirable to use a two-parameter model such as UNIQUAC.  [c.43]

The most reliable estimates of the parameters are obtained from multiple measurements, usually a series of vapor-liquid equilibrium data (T, P, x and y). Because the number of data points exceeds the number of parameters to be estimated, the equilibrium equations are not exactly satisfied for all experimental measurements. Exact agreement between the model and experiment is not achieved due to random and systematic errors in the data and due to inadequacies of the model. The optimum parameters should, therefore, be found by satisfaction of some selected statistical criterion, as discussed in Chapter 6. However, regardless of statistical sophistication, there is no substitute for reliable experimental data.  [c.44]

When there are sufficient data at different temperatures, the temperature dependence of the parameters is reflected in the confidence ellipses (Bryson and Ho, 1969 Draper and Smith,  [c.44]

Temperature Dependence of UNIQUAC Parameters for Ethanol(1)/Cyclohexane(2) Isothermal Data (5-65°C) of Scatchard (1964)  [c.46]

Calculated with temperature-independent UNIQUAC parameters.  [c.47]

Calculated with temperature-dependent UNIQUAC parameters.  [c.47]

In the first, both components strongly associate with themselves and with each other. In the second, only one of the components associates strongly. For both systems, representation of the data is very good. However, the interesting quality of these systems is that whereas the fugacity coefficients are significantly remote from unity, the activity coefficients show only minor deviations from ideal-solution behavior. Figures 6 and 7 in Chapter 3 indicate that the fugacity coefficients show marked departure from ideality. In these systems, the major contribution to nonideality occurs in the vapor phase. Failure to take into account these strong vapor-phase nonidealities would result in erroneous activity-coefficient parameters, a 2 21  [c.51]

Equation (15) requires only pure-component and binary parameters.  [c.53]

Table 3 shows results obtained from a five-component, isothermal flash calculation. In this system there are two condensable components (acetone and benzene) and three noncondensable components (hydrogen, carbon monoxide, and methane). Henry s constants for each of the noncondensables were obtained from Equations (18-22) the simplifying assumption for dilute solutions [Equation (17)] was also used for each of the noncondensables. Activity coefficients for both condensable components were calculated with the UNIQUAC equation. For that calculation, all liquid-phase composition variables are on a solute-free basis the only required binary parameters are those for the acetone-benzene system. While no experimental data are available for comparison, the calculated results are probably reliable because all simplifying assumptions are reasonable the  [c.61]

Our experience with multicomponent vapor-liquid equilibria suggests that for system temperatures well below the critical of every component, good multicomponent results are usually obtained, especially where binary parameters are chosen with care. However, when the system temperature is near or above the critical of one (or more) of the components, multicomponent predictions may be in error, even though all binary pairs are fit well.  [c.61]

For all calculations reported here, binary parameters from VLE data were obtained using the principle of maximum likelihood as discussed in Chapter 6, Binary parameters for partially miscible pairs were obtained from mutual-solubility data alone.  [c.64]

To illustrate, predictions were first made for a ternary system of type II, using binary data only. Figure 14 compares calculated and experimental phase behavior for the system 2,2,4-trimethylpentane-furfural-cyclohexane. UNIQUAC parameters are given in Table 4. As expected for a type II system, agreement is good.  [c.64]

Figure 4-14. Predicted liquid-liquid equilibria for a typical type-II system shows good agreement with experimental data, using parameters estimated from binary data alone. Figure 4-14. Predicted liquid-liquid equilibria for a typical type-II system shows good agreement with experimental data, using parameters estimated from binary data alone.
Parameters for Ternary Liquid-Liquid Systems  [c.65]

UNIQUAC equation with binary parameters estimated by supplementing binary VLE data with ternary tie-line data.  [c.66]

Figure 15 shows results for a difficult type I system methanol-n-heptane-benzene. In this example, the two-phase region is extremely small. The dashed line (a) shows predictions using the original UNIQUAC equation with q = q. This form of the UNIQUAC equation does not adequately fit the binary vapor-liquid equilibrium data for the methanol-benzene system and therefore the ternary predictions are grossly in error. The ternary prediction is much improved with the modified UNIQUAC equation (b) since this equation fits the methanol-benzene system much better. Further improvement (c) is obtained when a few ternary data are used to fix the binary parameters.  [c.66]

Unfortunately, good binary data are often not available, and no model, including the modified UNIQUAC equation, is entirely adequate. Therefore, we require a calculation method which allows utilization of some ternary data in the parameter estimation such that the ternary system is well represented. A method toward that end is described in the next section.  [c.66]

To illustrate the criterion for parameter estimation, let 1, 2, and 3 represent the three components in a mixture. Components 1 and 2 are only partially miscible components 1 and 3, as well as components 2 and 3 are totally miscible. The two binary parameters for the 1-2 binary are determined from mutual-solubility data and remain fixed. Initial estimates of the four binary parameters for the two completely miscible binaries, 1-3 and 2-3, are determined from sets of binary vapor-liquid equilibrium (VLE) data. The final values of these parameters are then obtained by fitting both sets of binary vapor-liquid equilibrium data simultaneously with the limited ternary tie-line data.  [c.67]

As indicated in Chapter 6, and discussed in detail by Anderson et al. (1978), optimum parameters, based on the maximum-likelihood principle, are those which minimize the objective function  [c.67]

In most cases only a single tie line is required. When several are available, the choice of which one to use is somewhat arbitrary. However, our experience has shown that tie lines which are near the middle of the two-phase region are most useful for estimating the parameters. Tie lines close to the plait point are less useful, since no common models for the excess Gibbs energy can adequately describe the flat region near the  [c.68]

The method described here is based on the high degree of correlation of model parameters, in this case, UNIQUAC parameters. Thus, although a certain set of binary parameters may be best for VLE data, we are able to find other sets of binary parameters for the miscible binaries which significantly improve ternary LLE prediction while only slightly decreasing accuracy of representation of the binary VLE. Fitting ternary LLE data only, may yield unrealistic parameters that predict grossly erroneous results when used in regions not identical to those employed in data reduction. By contrast, fitting ternary LLE data simultaneously with binary VLE data, effectively provides constraints on the binary parameters, preventing them from attaining arbitrary values of little physical significance. Determination of a single set of parameters which can adequately represent both VLE and LLE is particularly important in three-phase distillation.  [c.69]

Using the method outlined above, calculations were performed for ten ternary systems. All binary parameters are shown in Table 4. Some typical results are shown in Figures 16 to 19.  [c.69]

Figure 4-16. Representation of ternary liquid-liquid equilibria using the UNIQUAC equation is improved by incorporating ternary tie-line data into binary-parameter estimation. Representation of binary VLB shows small loss of accuracy. ---- Binary Figure 4-16. Representation of ternary liquid-liquid equilibria using the UNIQUAC equation is improved by incorporating ternary tie-line data into binary-parameter estimation. Representation of binary VLB shows small loss of accuracy. ---- Binary
Figure 4-17. Representation of ternary liquid-liquid equilibria using the UNIQUAC equation is improved by incorporating ternary tie-line data into binary-parameter estimation. Representation of binary VLB shows some loss of accuracy. Figure 4-17. Representation of ternary liquid-liquid equilibria using the UNIQUAC equation is improved by incorporating ternary tie-line data into binary-parameter estimation. Representation of binary VLB shows some loss of accuracy.
Vapor-liquid and liquid-liquid equilibria depend on the nature of the components present, on their concentrations in both phases, and on the temperature and pressure of the system. Because of the large number of variables which determine multi-component equilibria, it is essential to utilize an efficient organizational tool which reduces available experimental data to a small number of theoretically significant functions and parameters these functions and parcimeters may then be called upon to form the building blocks upon which to construct the desired equilibria. Such an organizational tool is provided by thermodynamic analysis and synthesis. First, limited pure-component and binary data are analyzed to yield fundamental thermodynamic quantities. Second, these quantities are reduced to obtain parameters in a molecular model. That model, by synthesis, may be used to calculate the phase behavior of multicomponent liquids and vapors. In this way, it is possible to "scale up" data on binary and pure-component systems to obtain good estimates of the properties of multicomponent mixtures of a large variety of components including water, polar organic solvents such as ketones, alcohols, nitriles, etc., and paraffinic, naphthenic, and aromatic hydrocarbons.  [c.2]

The accuracy of our calculations is strongly dependent on the accuracy of the experimental data used to obtain the necessary parameters. While we cannot make any general quantitative statement about the accuracy of our calculations for multicomponent vapor-liquid equilibria, our experience leads us to believe that the calculated results for ternary or quarternary mixtures have an accuracy only slightly less than that of the binary data upon which the calculations are based. For multicomponent liquid-liquid equilibria, the accuracy of prediction is dependent not only upon the accuracy of the binary data, but also on the method used to obtain binary parameters. While there are always exceptions, in typical cases the technique used for binary-data reduction is of some, but not major, importance for vapor-liquid equilibria. However, for liquid-liquid equilibria, the method of data reduction plays a crucial role, as discussed in Chapters 4 and 6.  [c.5]

Activity-coefficient data at infinite dilution often provide an excellent method for obtaining binary parameters as shown, for example, by Eclcert and Schreiber (1971) and by Nicolaides and Eckert (1978). Unfortunately, such data are rare.  [c.43]

To illustrate, UNIQUAC parameters were obtained for the ethanol/cyclohexane system using the extensive isothermal data of Scatchard and Satkiewicz (1964). Figure 2 shows parameters for 5, 35, and 60°C along with the confidence ellipses. These regions indicate that it is possible to choose a single value of 322 appropriate for all temperatures a single value of a2 (e.g. 1300) can be included in all three confidence ellipses, implying that in the range 5-65 C parameter a2 is temperature independent. For 3., however, there is no single value which can intercept all three confidence ellipses. Therefore, parameter a 2 must be represented by a function of temperature as shown in Table 1 where the estimated variance of the fit, a, provides a measure of how well the data are represented. The first line shows results obtained when fitting two UNIQUAC parameters, a 2 21 ii ispendent of temperature. The next two  [c.45]

Figure 4-2. UNIQUAC parameters and their approximate confidence regions for the ethanol-cyclohexane system for three isotherms. Data of Scatchard and Satkiewicz, 1964. Figure 4-2. UNIQUAC parameters and their approximate confidence regions for the ethanol-cyclohexane system for three isotherms. Data of Scatchard and Satkiewicz, 1964.

See pages that mention the term Parameters : [c.29]    [c.29]    [c.44]    [c.44]    [c.45]    [c.45]    [c.45]    [c.46]    [c.48]    [c.48]    [c.57]    [c.57]    [c.65]    [c.67]   
Computational chemistry using the PC (2003) -- [ c.97 , c.117 , c.251 ]