curve and k2 is read from the other. Appendix D gives tables of values for the Vi, k1 and k2 which are spaced such that linear interpolation is adequate in both variables (i.e., temperature or molecular weight). The k factors in Appendix D have been obtained graphically from the multicomponent PVTX data of Hiza and Haynes [15] and Miller and Hiza [25] as well as densities calculated from the extended corresponding states method of section 2.

The limits of compositions of the revised Klosek and McKinley method are the most severe of any of the methods given here. This method should not be used for mixtures other than LNG like mixtures and for LNG like mixtures only when they

contain at least 60% methane, less than 4% nitrogen, less than 4% each of iC4H10 nC4H10 and less than 2% total and nC5H12°

of ic

iC5H12

The

There are 40 experimental PVTX points from the original set of 285 which may be considered LNG like and fall within the composition limits outlined above. Figure 4 shows all of the deviations between calculated and experimental densities in this 40 point comparison set which exceeds the 0.1% criterion. deviation trends for the revised Klosek and McKinley method (fig. 4) are very similar to those of the hard sphere method (fig. 2) and in fact all of the deviations in fig. 4 occur at temperatures at or above 115 K, therefore the method can only be considered as accurate as the others for LNG like mixtures at temperatures below 115 K.

5. THE CELL MODEL

The cell model considered here was originally proposed by Renon,

et al. [32]. In a paper by the same three authors which appeared simultaneously (Eckert, et al. [7]), the cell model was applied to mixtures via Scott's [36] two-fluid theory and a three parameter corresponding states theory. Albright [2] further modified the method by modifying the mixing rules on the basis of a

TEMPERATURE, K

points)

proposal by Yuan [38] and by inserting a pressure dependence based on the experimental liquid ethane data by Pope [31].

The optimization of this method was carried out by M. Albright [1] at Phillips Petroleum Company in Bartlesville, Oklahoma and the details of this work will be published elsewhere. The model is included here because it was optimized to the same data set as the others and therefore the comparisons between experimental and calculated densities given here in fig. 5 together with figs. 1, 2 and 4 provide a common basis of comparison with the other three methods. A listing of the computer program is given in Appendix F.

The same data set as was used in the hard sphere method for comparison has been used here, i.e., all of the data points for mixtures containing nitrogen at temperatures 120 K and above have been taken out of the original 285 points leaving a total of 251 data points.

As in the case of the other methods fig. 5 shows all of the points for which the calculated and experimental densities differ by more than 0.1%.

6. USE OF THE METHODS

When the project started in 1972, the atomic weights of nitrogen, carbon and hydrogen were taken from the 1961 carbon 12 scale, IUPAC [16]. During the course of the investigation a revision, Atomic Weights of the Elements [3], to this scale appeared. The revision changed slightly the atomic weights of carbon and hydrogen, but since the changes were small (the maximum difference in any of the densities used here is 0.003%), and because changing the atomic weights would not change the relative results, the changes were not made. Therefore when using the tables and programs in the appendices, the molecular weights given in the tables and programs should be used to maintain consistency.

Figure 5.

TEMPERATURE, K

Deviations greater than 0.1% between experimental and calculated
densities using the Cell model. The comparison set is all of the data
in Appendix A except those data points for mixtures containing N2 at
temperatures above and including 120 K. (251 data points)

The critical parameters used here are from: CH4, McCarty [22]; C2H6, Sliwinski [37]; C2Hg, Das, et al. [4]; iC4H10, Das, et al. [5]; nC4H10, Das, et al. [6]; iC5H12, Kudchadker, et al. [19]; and N2, Jacobsen, et al. [17].

Errors in the input variables will of course, cause errors in the density predicted by the models. In general, the error in density caused by an error in the input varibles is a function of those input variables, and must be treated on an individual basis. However, for LNG like mixtures certain general trends are found. An error in the pressure must be at least 50% before it will have any effect at all on the resulting density. An error in composition, unless it is of the order of several percent, will cause the same relative error in density as it will cause in the molecular weight of the mixture, i.e., if an error in composition causes a 0.1% error in the resulting molecular weight, it will also cause a 0.1% error in the predicted density.

The error in the calculated density due to an error in the input temperature is a function of the composition and the temperature. Table 1 gives resulting errors in density for a 1% error in temperature, for three hypothetical LNG like mixtures.

In general the errors in density caused by an error in temperature are the largest for mixtures containing a high concentration of the most volatile fluids, CH4 and N2, and correspondingly the errors decrease as the concentration of the heavier hydrocarbons increases in the mixture. These errors are not a function of which model is being used.

When using the extended corresponding states method, one should keep in mind that twelve significant figures are required by the methane equation of state. The hard sphere model also uses the methane equation from McCarty [22] and the nitrogen equation of Jacobsen, et al. [17] to calculate compressibilities and