Shortcut methods profiles

To begin the calculations the column variables must be first initialized to some estimated values. Simple methods can be used for this purpose, based on the column specifications and possibly supplemented by shortcut methods. The column temperature profile may be assumed linear, interpolated between estimated condenser and reboiler temperatures. The values for Lj and Vj may be based on estimated reflux ratio and product rates, assisted by the assumption of constant internal flows within each column section. The compositions Xj- and T, may be assumed uniform throughout the column, set equal to the compositions of the liquid and vapor obtained by flashing the combined feeds at average column temperature and pressure. The other variables to be initialized are Rf,Rj, and Sj, which are calculated from their defining equations. The values for Qj may either be fixed at given values (zero on most stages) or estimated. 

Against this background, both precise and straightforward shortcut methods for model parameter determination are presented below. Based on the individual task users have to decide specifically which procedures are most adequate. In this context it must be mentioned that the adsorption equilibrium has clearly the largest influence on the position and shape of chromatographic profiles and, therefore, the isotherms deserve the greatest care. 

A shortcut method for estimating furnace gas exit temperature is offered by the graph of figures 2.20 and 5.3, adapted by coauthor Shannon from radiant tube data, and extrapolated above 1800 F (1255 C). Also refer to Estimating Furnace temperature profile for calculating heating curves in chapter 8. 

This technique, combined with Fenske shortcut calculations for generating initial estimates of temperature profiles and stage liquid or vapor flow rates, is a robust method that can solve a large percentage of different types of separation processes. The algorithm also has provision for handling inequality specifications (Brannock et al., 1977). For each inequality specification, an alternate equality specification is required to ensure a unique solution. In this manner, the so-called over-constrained problems may be solved since inequality specifications are not subject to degrees of freedom restrictions. 

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