The Difference Point Equation DPE

The design in Figure 9.12a can be divided into CSs as shown in Figure 9.12b. Each of the distillation column sections (DCSs 1 3) has its own unique profile described by the difference point equation (DPE) refer to Section 3.3. As previously discussed, the DPE describes how the liquid composition changes down the length of a DCS. The profile for each DCS depends on the X - and r -values for that particular section. With these values set, a CPM can be generated. 

The original development of the difference point equation (DPE) relied upon an assumption of constant molar overflow (CMO). This assumption can be relaxed with the inclusion of the appropriate energy balance. Although this was never shown in the text, it is hoped that the reader can infer this by the methods shown in Chapter 9 on membrane permeation, for example, where this assumption is not justified. Thus, with the necessary modeling, the DPE and hence the CPM method show great versatility and adaptability. 

Notice that the DPEs describing the scenarios in Cases 1 and 2 (Equations 9.18 and 9.20) are mathematically similar to each other. Each comprise of the addition of two vectors, namely the separation vector, S = x —y, and the mixing vector, M = Xa — X. The only difference between the two cases is that the difference point (Xa) is equal to the composition of the product being removed in Case 1. To avoid repetition, these two cases will be discussed simultaneously, due to the similar nature of their equations. 

DODS-ProPlot. This is a comprehensive profile plotting package which allows the user to plot single profiles, entire CPMs and ROMs, and their associated pinch points. There are 13 systems to choose from, each of which may be modeled either with a modified Raoult s law and the NRTL activity coefficient model, or with the ideal Raoult s law (does not model azeotropes), or with a constant relative volatility approximation where the software automatically determines the relative volatilities between components (this model also cannot account for azeotropic behavior). One also has the option to insert one s own constant volatilities. It is possible to plot the full DPE, the shortened DPE at infinite reflux (shown in Chapter 7) or the classic residue curve equation. Depending on the equation chosen, the user is free to specify any relevant parameters such as an R value, difference points, system... 

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