Van Winkle

In the maximum-likelihood method used here, the "true" value of each measured variable is also found in the course of parameter estimation. The differences between these "true" values and the corresponding experimentally measured values are the residuals (also called deviations). When there are many data points, the residuals can be analyzed by standard statistical methods (Draper and Smith, 1966). If, however, there are only a few data points, examination of the residuals for trends, when plotted versus other system variables, may provide valuable information. Often these plots can indicate at a glance excessive experimental error, systematic error, or "lack of fit." Data points which are obviously bad can also be readily detected. If the model is suitable and if there are no systematic errors, such a plot shows the residuals randomly distributed with zero means. This behavior is shown in Figure 3 for the ethyl-acetate-n-propanol data of Murti and Van Winkle (1958), fitted with the van Laar equation. 

Figure 6-3. Residuals for the system ethyl acetate(1)-n-propanol(2) at eooc. Data of Murti and van Winkle, 1958.

Convergence is usually accomplished in 2 to 4 iterations. For example, an average of 2.6 iterations was required for 9 bubble-point-temperature calculations over the complete composition range for the azeotropic system ehtanol-ethyl acetate. Standard initial estimates were used. Figure 1 shows results for the incipient vapor-phase compositions together with the experimental data of Murti and van Winkle (1958). For this case, calculated bubble-point temperatures were never more than 0.4 K from observed values. 

M. Van Winkle, Distillation., McGraw-Hill Book Co., Inc., New York, 1967. 

FIG. 13-41 Comparison of rigorous calcnlations with Gilliland correlation. [Henley and Seader, Eqnilihrinm-Stage Separation Operations in Chemical Engineering, Wiley, New York, 1981 data of Van Winkle and Todd, Chem. Eng., 78(21), 136 (Sept. 20, 1971) data of Gilliland, Elements of Fractional Distillation, 4th ed., McGraw-Hill, New York, 1950 data of Brown and Maiiin, Trans. Am. Inst. Chem. Eng., 35, 679 (1.93.9) ]... 

The Underwood Method will provide a quick estimate of minimum reflux requirements. It is a good method to use when distillate and bottoms compositions are specified. Although the Underwood Method will be detailed here, other good methods exist such as the Brown-Martin and Colburn methods. These and other methods are discussed and compared in Van Winkle s book. A method to use for column analysis when distillate and bottoms compositions are not specified is discussed by Smith. 

Note that the approach recommended here is not in agreement with Van Winkle [74], because he assumes the reboiler and partial condenser are included in the overall calculation for Nmin-... 

The proposal for calctdating colunrn vapor plate efficiencies by MacFarland, Sigmund, and Van Winkle [86] correlates with the Muiphree vapor plate efficiencies in percent ... 

Figure 8-49. Brown and Martin operating reflux and stages correlated with minimum reflux and sttiges. Used and adapted by permission, Van Winkle, M Oil and Gas Jour. V. 182, Mar. 23 (1953).

Van Winkle, M. and W. G. Todd, Optimum Fractionation Design by Simple Graphical Methods, Chem. Eng. Sept 20 (1971), p. 136. 

Newbold JD, Elwood JW, O Neill RV, van Winkle W (1981) Measuring nutrient spiralling in streams. Can J Eish Aquat Sci 38 860-863... 

Rill, RL Liu, Y Van Winkle, DH Locke, BR, Pluronic Copolymer Liquid Crystals Unique, Replaceable Media for Capillary Gel Electrophoresis, Journal of Chromatography A817, 287, 1998. 

Rill, RL Locke, BR Liu, Y Dharia, J Van Winkle, D, Protein Electrophoresis in Polyacrylamide Gels with Templated Pores, Electrophoresis 17, 1304, 1996. 

Rill, RL Locke, BR Liu, Y Van Winkle, DH, Electrophoresis in Lyotropic Polymer Liquid Crystals, Proceedings of the National Academy of Science, USA 95, 1534, 1998. 

Rill, RL Ramey, BA Van Winkle, DH Locke, BR, Capillary Gel Electrophoresis of Nucleic Acids in Pluronic F127 Copolymer Liquid Crystals, Chromatographia Supplement I, Vol 49, S65, 1999. 

Rill, RL Van Winkle, DH Locke, BR, Templated Pores in Hydrogels for Improved Size Selectivity in Gel Permeation Chromatography, Analytical Chemistry 70, 2433, 1998. 

Yiu, Y Locke, BR Van Winkle, DH Rill, RL, Optimizing Capillary Gel Electrophoretic Separations of Oligonucleotides in Liquid Crystalline Pluronic F127, Journal of Chromatography A817, 367, 1998. 

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