Method of Wang and Henke

The stage temperatures are determined from the calculated stage compositions by bubble point calculations. The calculations are carried out iteratively using Muller s algorithm (Wang et al., 1966). The authors have determined that convergence by this method is more reliable than the Newton-Raphson technique. 

The method has been successfully employed for many column types, although convergence problems can occur for nonideal mixtures where the A -values are strongly composition dependent or for highly complex columns. The method is also limited in the types of performance specifications it can handle. 

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Perhaps the best-known example of this approach for multi-component distillation is the method of Wang and Henke (JL). 

BP (bubblepcdnt) methods. Temperatures are corrected iteratively by determinations of bubblepoints. The method is satisfactory for mixtures with relatively narrow ranges of volatilities. The parent program of this type is that of Wang and Henke (1966) which is flowsketched on Figure 13.17 and described in the next section. The availability of a FORTRAN program was cited earlier in this section. 

The iterative calculation procedure is outlined in Figure 14.10. The method is an adaptation to extraction by Tsuboka and Katayama (1976) of the distillation calculation procedure of Wang and Henke [Hydrocarb. Proc. 45(8), 155-163 (1967)]. It is also presented by Henley and Seader (1981, pp. 586-594). 

The BP methods use a form of the equilibrium equation and summation equation to calculate the stage temperatures, The first BP method, by Wang and Henke (24), included the first presentation of the tridiagonal method to calculate the component flow rates or compositions. These are used to calculate the temperatures by solving the bubble-point equation but this temperature calculation can be prone to failure. 

There are several valuable references to developing and applying a multicomponent distillation program, including Holland [26, 27,169], Prausnitz [52, 53], Wang and Henke [76], Thurston [167], Boston and Sullivan [6], Maddox and Erbar [115], and the pseudo-K method of Maddox and Fling [116]. Convergence of the iterative trials to reach a criterion requires careful evaluation [114]. There are sever-... 

The rigorous methods thus convert a column to a group of variables and equations. The equations were first referred io as the MESH equations by Wang and Henke (24). The MESH variahles are often referred to as state variables. These are... 

Calculating the component flow rates. The tridiagonal matrix method introduced by Wang and Henke (24), is a fast and accurate technique for calculating the component and total flow rates. This method for calculating the component flow rates is used in most of the following rigorous methods. 

Figure 13.17. Algorithm of the BP (bubblepoint) method for distillation separations [Wang and Henke, Flydrocarbon Processing 45(S), 155-166 (1963) Henley and Seader, 1981],...

Frequently, distillation involves species that cover a relatively narrow range of vapor-liquid equilibrium ratios (X-values). A particularly effective solution procedure for this case was suggested by Friday and Smith and developed in detail by Wang and Henke. It is referred to as the bubble-point (BP) method because a new set of stage temperatures is computed during each iteration from... 

On page 162 of their article, Wang and Henke claim that their method of solving the tridiagonal matrix for the liquid-phase mole fractions does not involve subtraction of nearly equal quantities. Prove or disprove their statement. 

To solve (15-12) for X( by the Thomas method, Ky values are required. When they are composition dependent, initial assumptions for all xy and yy values are also needed unless ideal K-values are employed for the first iteration. For each iteration, the computed set of xy values for each stage will, in general, not satisfy the summation constraint given by (15-4). Although not mentioned by Wang and Henke, it is advisable to normalize the set of computed xy values by the relation... 

Analog computers may be employed in many ways in process engineering for the calculation of material and heat transfer processes [255]. In the last 10 years chiefh those methods have been further developed which can only be used by means of electronic computers [6]. These are, above all, the so-called matrix methods as evolved by Wang and Henke [256], Sargent and Murtagh [257] and Stainthorp et al. [258]. 

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