Bubble-Point BP Methods

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. 

An alternative is to use the tridiagonal method for calculating compositions, but to calculate the new temperatures directly, without iterating on the bubble-point equation, These new temperatures are approximate but as long as the internal compositions are properly corrected during each column trial, the temperature profile will continue to move toward the solution. This is the basis of the theta method of Holland (7, 9, 26). With either alternative, the energy balances are used to find the total flow rates. 

The BP methods generally work best for narrow-boiling, ideal or nearly ideal systems, where composition has a greater effect on temperature than the latent heat of vaporisation, 

The theta method. This method has been primarily applied to the Thiele-Geddes equations but a form of the theta method equation has also been applied to the equations of the Lewis-Matheson method. The main independent variable of the method is a convergence promoter, theta (or 6). The convergence promoter 0 is used to force an overall component and total material balance and to adjust the compositions on each stage. These new compositions are then used to calculate new stage temperatures by an approximation of the dew- or bubble-point equation called the Kb method. The power of the Kb method is that it directly calculates a new temperature without the sort of failures that occur when iteratively solving the bubble- or dew-point equations. 

The theta function. This function begins with the component balance for a conventional column  

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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... 

BP Method for Distillation The bubble-point method for distillation, particularly when the components involved cover a relatively narrow range of volatihty, proceeds iteratively by the following steps, where k is the iteration index for the entire distillation column. 

BP (bubble-point) 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 13.16 and described in the next section. The availability of a FORTRAN program was cited earlier in this section. 

Figure 13.16. Algorithm of the BP (bubble-point) method for distillation separations [Wang and Henke, Hydrocarbon Processing 45(5, 155-166 1963)) Seader and Henley, 1998].

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