Stage equations

CONTINUOUS DISTILLATION BASIC PRINCIPLES 11.3.1. Stage equations 

Material and energy balance equations can be written for any stage in a multistage process. 

Vn+i = vapour flow into the stage from the stage below, 

Sn = any side stream from the stage, qn = heat flow into, or removal from, the stage, n = any stage, numbered from the top of the column, z = mol fraction of component i in the feed stream (note, feed may be two-phase), 

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At this stage, equation (48) provides an expression for (Xm)- Continuing, if the change in mass of solute on the absorbent due to a volume flow of mobile phase Cadv is (dms), then the consequent heat evolved (dG) in the cell will be given by ... 

Sorel (1899) first derived and applied the basic stage equations to the analysis of binary systems. Figure 11.4a shows the flows and compositions in the top part of a column. Taking the system boundary to include the stage n and the condenser, gives the following equations ... 

The method starts with an assumption of the column temperature and flow profiles. The stage equations are then solved to determine the stage component compositions and the results used to revise the temperature profiles for subsequent trial calculations. Efficient convergence procedures have been developed for the Thiele-Geddes method. The so-called theta method , described by Lyster et al. (1959) and Holland (1963), is recommended. The Thiele-Geddes method can be used for the solution of complex distillation problems,... 

With the exception of this method, all the methods described solve the stage equations for the steady-state design conditions. In an operating column other conditions will exist at start-up, and the column will approach the design steady-state conditions after a period of time. The stage material balance equations can be written in a finite difference form, and procedures for the solution of these equations will model the unsteady-state behaviour of the column. 

This model is an extension of the concepts developed by Kumar and Kuloor (K16, K19). The first stage equation for this situation is... 

Their first and second stage equations, respectively, are... 

In this scheme, as always in the following, Z denotes a site on the surface of the catalyst, the arrows denote elementary reactions, and in the overall equation the equality sign is employed. Stoichiometric numbers by which the stage equations should be multiplied to obtain the overall equation are given on the right side. In this instance intermediates are Z and ZO. Another scheme equivalent to the previous one may be used ... 

It may occur that when stoichiometric numbers of stages are chosen to form a route, the cancellation of one intermediate at the summing up of the stage equations inevitably leads to the cancellation of another. Thus, in the mechanism (33) this is the case with the intermediates Z and ZO. This results from the equality... 

The Dynamit Nobel process produces dimethyl terephthalate (DMT) by a complicated series of oxidation and esterification stages (equation 241).83,84,86 In the oxidation section, p-xylene is oxidized at 150°C and 6 atm without solvent and in the presence of cobalt octoate to TPA and p-toluic acid. These oxidation products are sent to another reactor for esterification by methanol at 250 °C and 30 atm. Fiber grade DMT is purified by several recrystallizations, and monoesters are recycled to the oxidation reactor. The overall yield in DMT is about 80%, which is lower than in the Amoco process. However, this process is competitive because it is not corrosive and requires lower investments. It provides high-quality fiber-grade dimethyl terephthalate. 

For the second stage, Equation 2 (which holds for 0 < E < E ) and the diffusion equation for the outer layer m... 

SEPARATION COLUMNS (DISTILLATION, ABSORPTION AND EXTRACTION) Summary of stage equations... 

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