Properties, estimation critical

The compilations of CRC (1-2), Daubert and Danner (3), Dechema (15), TRC (13-14), Vargaftik (18), and Yaws (19-36) were used extensively for critical properties. Estimates of critical temperature, pressure, and volume were primarily based on the Joback method (10-12) and proprietary techniques of the author. Critical density was determined from dividing molecular weight by critical volume. Critical compressibility factor was ascertained from application of the gas law at the critical point. Estimates for acentric factor were primarily made by using the Antoine equation for vapor pressure (11-12). 

Lydersen, A.L. (1955), Estimation of critical properties of organic compounds by the method of group contributions . Uniu. Wisconsin Coll., Eng. Exp. Stn. report No. 4, Madison, Wl. 

A. L. Lydersen, Estimation of Critical Properties of Organic Compounds, Report 3, College Engineering Experiment Station, University of Wisconsin, Madison, Wis., Apr. 1955. 

Critica.1 Properties. Several methods have been developed to estimate critical pressure, temperature, and volume, U). Many other properties can be estimated from these properties. Error propagation can be large for physical property estimations based on critical properties from group contribution methods. Thus sensitivity analyses are recommended. The Ambrose method (185) was found to be more accurate (186) than the Lyderson (187) method, although it is computationally more complex. The Joback and Reid method (188) is only slightly less accurate overall than the Ambrose method, and is more accurate for some specific substances. Other methods of lesser overall accuracy are also available (189,190) (T, (191,192) (T, P ),... 

D. Ambrose, Correlation and Estimation ofVapor-Eiquid Critical Properties. I. Critical Eemperatures of Organic Compounds,NMoa-A Physical Laboratory, Teddington, UK, NPL Report 92 (1978, corrected 1980). 

Critical properties, if not available, can be estimated from tbe methods of tbe previous section. T,. is tbe reduced temperature at tbe temperature of interest, while Tr is tbe reduced temperature at tbe normal boiling point. 

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. 

Table 2. Weighting Method for Estimating Critical Properties of Organics...

Also useful, and convenient to use, are prediction methods based on the use of reduced properties (corresponding states) providing that values for the critical properties are available, or can be estimated with sufficient accuracy see Sterbacek et al. (1979). 

Development of ANN model for estimating VLE is less cumbersome than methods based on EOS. It does not require parameters such as the critical properties of the components or the... 

Would anyone pretend that our current (or future methods) of estimating the critical properties of an undefined component are accurate to 10°C ... 

Since most synthetic and natural gas systems will contain some amount (however small) of heavy undefined components, we have been searching for improved methods of predicting critical properties and an equation of state which does not use critical constants (or quasi critical constants) to determine the parameters for the equation. Development of improved critical property prediction methods appears to be a waste of time. Wilson and Cunningham (6) have presented an equation—the Parameters From Group Contributions (PFGC) equation of state which satisfies our needs. As the name implies, the parameters in this equation of state are estimated by group contribution rather... 

The basic equations used to predict the thermodynamic properties of systems for the SRK and PFGC-MES are given in Tables I and II, respectively. As can be seen, the PFGC-MES equation of state relies only on group contributions--critical properties etc., are not required. Conversely, the SRK, as all Redlich-Kwong based equations of states, relies on using the critical properties to estimate the parameters required for solution. 

Solutions in hand for the reference pairs, it is useful to write out empirical smoothing expressions for the rectilinear densities, reduced density differences, and reduced vapor pressures as functions of Tr and a, following which prediction of reduced liquid densities and vapor pressures is straightforward for systems where Tex and a (equivalently co) are known. If, in addition, the critical property IE s, ln(Tc /Tc), ln(PcVPc), and ln(pcVPc), are available from experiment, theory, or empirical correlation, one can calculate the molar density and vapor pressure IE s for 0.5 < Tr < 1, provided, for VPIE, that Aa/a is known or can be estimated. Thus to calculate liquid density IE s one uses the observed IE on Tc, ln(Tc /Tc), to find (Tr /Tr) at any temperature of interest, and employs the smoothing relations (or numerically solves Equation 13.1) to obtain (pR /pR). Since (MpIE)R = ln(pR /pR) = ln[(p /pc )/(p/pc)] it follows that ln(p7p)(MpIE)R- -ln(pcVpc). For VPIE s one proceeds similarly, substituting reduced temperatures, critical pressures and Aa/a into the smoothing equations to find ln(P /P)RED and thence ln(P /P), since ln(P /P) = I n( Pr /Pr) + In (Pc /Pc)- The approach outlined for molar density IE cannot be used to rationalize the vapor pressure IE without the introduction of isotope dependent system parameters Aa/a. 

The method described above can be applied to isotopomer pairs for which critical property IE data exists or can be estimated. Calculated values of ln(p7p) are insensitive to IE s on the acentric factor, Aoo/oo (equivalently Aa/a). The VPIE, on the other hand, is strongly dependent on Aoo/oo. For 3He/4He and H2/D2 critical property IE data are complete and MpIE and VPIE are available across the entire liquid range, are one to two orders of magnitude larger, and known to better precision than for other pairs (save perhaps H2O/D2O). For heavier pairs critical property IE data are usually incomplete or uncertain, and often data on MpIE and VPIE exist only over a limited temperature range. 

Most data on VPIE s for heavier pairs are at or below the normal boiling point, Tr-0.7. Of the critical property IE s, ln(Tc /Tc) is the easiest to measure and the most reliably known. Often lnlPc /Pd, and very often ln(pc /pc), are unknown or imprecisely known, and IrHp /p) has been measured only at or near room temperature or must be estimated. 

In the data collection, a literature search was conducted to identify data source publications (1-40). The publications were screened and copies of appropriate data were made. These data were then keyed into the computer to provide a data base of critical properties for compounds for which experimental data are available. The data base also served as a basis to check the accuracy of the estimation methods. 

Upon completion of data collection, estimation of the critical properties for the remaining compounds was performed using the group contribution method of Joback as given by Reid, Prausnitz and Poling (24). A comparison of the estimates with experimental data was favorable with average absolute errors of only 0.9%, 6.3 %, and 4.4% for critical temperature (465 compounds), pressure (453 compounds) and volume (345 compounds). 

To model the solubility of a solute in an SCF using an EOS, it is necessary to have critical properties and acentric factors of all components as well as molar volumes and sublimation pressures in the case of solid components. When some of these values are not available, as is often the case, estimation techniques must be employed. When neither critical properties nor acentric factors are available, it is desirable to have the normal boiling point of the compound, since some estimation techniques only require the boiling point together with the molecular structure. A customary approach to describing high-pressure phenomena like the solubility in SCFs is based on the Peng-Robinson EOS [48,49], but there are also several other EOS s [50]. 

Poling et al. [6] also describe methods for estimation of additional properties, such as critical properties, P-V-T properties, and phase equilibria. 

Recently, Rebelo and coworkers [172] presented a method to estimate the critical temperatures of some ILs based on fhe temperature dependence of fheir surface tension and liquid densities. The molar enfhalpies of vaporization of a series of commonly used ILs were also determined for fhe firsf fime. The molar enfhalpies of vaporization of [C Cilm][Tf2N] ILs in fhe function of the alkyl chain length have been presented [214]. The critical properties (T(, P(, Vf), the normal boiling temperatures, and the acentric factors of 50 ILs were determined as well for fhe firsf fime [215]. 

Klincewicz, K. M., and R. C. Reid, Estimation of Critical Properties with Group Contribution Methods. AIChE, 1984 30, 137-142. 

I he critical properties of phosgene have been determined expert menially. , x M The method of Vow les has been used to esilmatr the other critical temperatures with a probable ei for of less than 5 C. and live critical densities within 0.01 gramcmilliliter The critical pressures w-erc estimated by the method ol Lvdeison. C [Pg.26]

Kobe and co-workers have measured the critical properties and sapor pressures of all four compounds 0 Additional data are available from several other sources.The cntical density of MIBK was estimated by the method of Vowlcs. with a probable error ol less than 1%. Figure 26-2 presents the boiling point of aqueous acetone solutions (sec also Table 26-11. 

The cntical properties of methyl acetate and ethyl acetate have been reported in the literature.Estimation methods were used to calculate the critical properties or butyl and vinyl acetate.1 The probable error is d C on the critical temperature. 15-25 psi on the critical pressure, and U.002 grams-milliliter on (he critical density. 

The critical properties of turun. I HK und dioxane are available in the literature. 1 2 the critical temperature und pressure of turfural were estimated by (he method of Riedel. When compaivd with die expert me tit at data on die other three compounds, the method gave an error of about KPC o the critical temperature und Ms 40 psi on the cntKal pressure... 

The critical properties of all four compounds have been reported in the litcraturc.(,IR> 5 The method of Vowlcs was used to estimate the critical density of butyronitrile. 

The critical properties of hydrazine and nitro-methane 7 are available in the literature. Thermodynamic properties for hydrazine, A arc available from 27 C to 727T. Thermodynamic properties of niirrancihanc are also available.161 The other critical properties have been estimated by the me thod ol Lvdersen.1... 

The critical properties of styrene arc available from the literature 253 254 Except for the critical temperatures of cyclo-peniene and cyclohexene,VJ, M the critical properties of these compounds were estimated by the method proposed by Ly-dersen. ... 

The critical properties have been experimentally measured for bromobenzcnc, chlorobenzene, and fluorobcn-Mnc s.s.iuj.w Lydcrsen s method wus used U calculate the critical properties of benzyl chloride 1 Literature data arc reported for the vnpnr pressure ot bru-mobenzene, chlorobenzene, and fluorobcn/ertc up to the critical point, -1" 271 Stull has compiled the vapor pressure data on benzyl chloride up to its boiling point J Ashcroft pce cms data from 48T to I I C. 275 The vapor pressure above the boiling point was estimated ... 

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