1.2.3 Computer K-Value Prediction Methods for Hydrocarbon-Type Systems

ICHAO-SEATZR (12) This method uses:

I (i) The Redlich and Kwong equation for the vapor phase rugacity coefficient.

(ii) An empirical expression based on the generalized j corresponding states PVT correlation of Pitzer el al (26) ! I for the liquid phase fugacity coefficent. j j I

(iii) The Scatchard-Hildebrand (solubility parameter) for liquid j phase activity coefficients. j j j

I (iv) Empirical mixing rules, based on pseudo-critical j properties. j

| (v) The Poynting correction is neglected. j

¡The advantages of this method are (i) simplicity and low computation ¡cost, (ii) it only needs pure component data, and does, not need ¡mixture data.

¡The disadvantages of this method are (i) poor accuracy (4), especially if calculations are performed at conditions remote from ¡those used to establish the correlation parameters, (ii) predictions j are poor at high pressure, because the effect of pressure is {neglected.

| The Grayson-Streed method (13) is a variation of the Chao-Seader ¡method which uses different correlation constants. This method has j been recommended over the original Chao-Seader correlation (14).

' One interesting application of the Chao-Seader correlation was I described by Newman (15). This application involves adding a |parameter to the Chao-Seader equation, which enables correlating jK-values for the main components from experimental data. This method | was successfully applied to predicting K-values for c3 splitters, in which accuracy is critical.

j SOAVE-REDLICH-KWONG (16) This procedure uses the Redlich and Kwong equation of state for predicting K-values. The original Redlich and Kwong equation has been modified by Soave to obtain a better temperature dependence of the pure component vapor pressure data. The original Redlich and Kwong mixing rules have been retained in the Soave correlation. In the case of polar components, the mixing rule j is often modified to include an additional parameter which is used to j fit experimental data. The additional parameter describes the polar interaction and is independent of temperature.

The main advantages of the Soave-Redlich-Kwong (SRK) correlation are I (i) it gives reliable predictions of K-values for light hydrocarbon mixtures (but often erraneous liquid densities) (4,17), (ii) it is reasonably simple.

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The main disadvantages of the equation are (i) some empirical corrections are required when the system contains significant auan.ti.ties of hydrocen. -arbon dioxide, hydrogen sulfide and other i polar coniponer. _ 3 , (ii) it ii i^suf f iciently accurate to predict k-values for close separations (15), (iii) The application of the SRK equation involves a solution to a cubic equation, which may give bad K-values if th? wrong root is used. '

The SRK equation, often with some modification, generally gives good ! accuracy and has been recommended for K-value prediction for non-polar , compounds in the reduced temperature range of 0.5 to 1 (18,19). I Figure 1-17 demonstates the ability of this equation to predict good j K-values even at pressures approaching the convergence pressure of the ! mixture.

I The Peng-Robinson equation (20) is similar to the SRK equation, but is j i slightly more complex. It was developed to improve prediction of : liquid densities. The mixing rule used by this equation is similar to J the SRK equation, but it uses slightly different constants. Comments ! made regarding the accuracy and applicability of the SRK equation also ! : apply to the Peng-Robinson equation (17,18).

! A large amount of work in presently underway to improve the SRK and PR i ; equations predictions, with the main objective being to extend their !

application to polar components and to small components (eg hydrogen, | : helium). Soave (19) recently modified his mixing rule and the temperature dependence of the molecular attraction term, thus generating an expression which included two adjustable interaction parameters which are fitted to experimental data. Soave successfully applied this formulation to predict alcohol-water data. Another • successful application of Soave's new version for a multicomponent j chlorinated hydrocarbon system was also described (61).

Recent versions use a single, temperature independent interaction |

parameter (66), others have a single interaction parameters correlated ; with temperature (67,70) and others two temperature-independent | interaction parameters (19,61,66). The importance of using a good set j 1 of interaction parameters with polar systems is well-illustrated in j j reference 68. Reference 69 provides temperature-independent values of j ! binary interaction prameters to be used with the Soave equation of : state.

1 BENEDICT-WEBB-RUBIN (21) This method is based on the I Benedict-Webb-Rubin (BWR) equation of state. This is a multi-constant | equation, which uses empirical mixing rules. The constants are mostly | obtained from fitting experimental data at low and moderate ! pressures. Several tabulations of the constants and modified versions | of the correlation are available, some of the more notable being in : references 22 to 24. The method is primarily suited for light j i hydrocarbons.

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