Nomograph procedure

A trial-and-error procedure is required with any K-value correlation that takes into account the effect of composition. One cannot calculate K values until phase compositions are known, and those cannot be known until the K values are available to calculate them. For K as a function of T and P only, the DePriester charts provide good starting values for the iteration. These nomographs are shown in Fig. 13-14/7 andZ . SI versions of these charts have been developed by Dadyburjor [Chem. Eng. Prog., 74(4), 85 (1978)]. 

Figure 3. Nomograph to determine the optimum number of replications in the second stage of a two-stage procedure.

The procedure by which the nomograph is generated is not limited to the WLF equation. Since it is based on the reduced variable concept, any superposition equation that results in the calculation of a temperature shift factor may be used to calculate the needed data to create the master curve and subsequent nomograph. The software can easily be modified to calculate and display a master curve on some other superposition equation. 

Figure 2 is a reduced temperature nomograph which demonstrates the procedure for reading the nomograph as follows Select a combination of temperature and frequency, for example, 1000 Hz and 75 C. Find the point for 1000 Hz on the right-hand frequency axis. Proceed horizontally to the temperature line for 75 C. At this intersection, draw a vertical line. Then, read the modulus and loss factor values from the appropriate data curve, at the point of intersection with the vertical line. In this example, modulus G(1000 Hz, 75 C) = 8 x 10° U/wr and loss factor (1000 Hz, 75 C) = 1.96. 

The temperature scale at the top of the reduced temperature nomograph shows increasing temperature from right to left. Labeling of the temperature lines is done in a uniform temperature increment. The temperature increment is identified at the top of the nomogram. The nomograph presentation and data reduction procedure have been described in earlier publications (6.71. 

Following this procedure, a master curve is converted to a nomograph by plotting fjaip as a function of fj using the same abscissa as for the plots of modulus and loss tangent vs. fa. ... 

Data Reduction Procedure. The nomograph lends itself readily to reduction of viscoelastic data and is particularly convenient for computerized procedures. If one selects the proper position for Tq and the interval At between Tq and Ti, T2, etc., then the grid of lines can be used to place the test data in position. 

Figure 4-7 is a nomograph based upon the area of the segment of a circle [5]. The nomograph converts the height (rise) over diameter ratios directly to percent of area. The procedure in using the nomograph is ... 

The calculated sets of temperatures, flow rates, and compositions obtained by the calculational procedure developed below are presented in Tables 4-14 through 4-16. These results were obtained by use of the data of Cecchetti et al. for the K values and enthalpies of the pseudo components. Curve fits of these data are presented in Tables B-14 and B-16. The K values for water / = 35 was taken from nomographs given by Hadden and Grayson,12 and the enthalpies from the steam tables given by Smith and Van Ness.21 In the condenser, the was taken equal to its vapor pressure (as given in the steam tables) divided by the total pressure in the condenser. 

Figure 5-4 is used to fix the trial diameter. To use this nomograph, follow this procedure ... 

Once is selected. Equation 5-3 can be solved for the drum diameter. Figure 5-7 is the nomograph to use for this calculation. Follow this procedure ... 

Generally, adequate computational procedures are not available for predicting equilibrium data for gas-liquid systems bas entirely on the physicochemical pn ities of the individual components. However, correlations have been proposed which can provide approximate values for simple systems. Osborne and Maikovic," for example, present a nomograph that relates the solubilities of conunon gases in oiganic liquids to the iiquid surface tension and molar volume. 

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