Stagewise models

Although the stagewise model is not physically reaUstic for differential contactors, it is sometimes used. The number of equivalent theoretical stages N can be determined graphically usiag the stepwise constmction illustrated ia Figure 7. For the case where both the equihbrium and operating lines are linear, it can be shown that ... 

A wide variety of extraction column forms are used in solvent extraction applications and many of these, such as rotary-disc contactors (RDC), Oldshue-Rushton columns, and sieve-plate column extractors, have rather distinct compartments and a geometry, which lends itself to an analysis of column performance in terms of a stagewise model. As the compositions of the phases do not come to equilibrium at any stage, however, the behaviour of the column is therefore basically differential in nature. 

At the prevailing high levels of dispersion normally encountered in such types of extraction columns, the behaviour of these essentially differential type contactors, however, can be represented by the use of a non-equilibrium stagewise model. 

The stagewise model with backmixing is an essential component of any model representation of a stagewise extraction column. As shown in Sec. 3.3.1.5 the non-ideal flow behaviour is represented by the presence of the N stages in... 

The simulation program CHROMPLATE uses the plate model for the same column conditions as the simulation model CHROMDIFF. The results obtained are very similar in the two approaches, but the stagewise model is much faster to calculate. 

As explained in Section 4.4.4, there exists an equivalency between tubular dispersion models and stagewise or tank in series models. The stagewise model, used in CHROMPLATE considers the chromatographic column to consist of a large number of well-mixed stirred tanks, arranged in series and thus represents an alternative modelling approach to that of the tubular dispersion model CHROMDIFF. The same two-component separation process is modelled and simulated in both cases. 

Write a program for this stagewise model using transfer rates as in CHROM-DIFF. 

Batch Decomposition of Acetylated Castor Oil 243 Dispersion Model for Chromatography Columns 483 Stagewise Model for Chromatography Columns 486 Complex Reaction 237 Continuous Flow Tank 406... 

For contactors in which discrete well-mixed compartments can be identified, for example sieve-plate columns, axial mixing effects are incorporated into the stagewise model by means of the backflow ratio a which is defined as the fraction of the net interstage flow of one phase which is considered to flow in the reverse direction. For a contactor in which there are many compartments, the axial dispersion coefficient and the backflow ratio, a, are interrelated as follows ... 

Series-of-stirred-tanks model The series-of-stirred-tanks model (often referred to as the cell model) is perhaps the simplest type of stagewise model for the backmix reactor. In this model, the reactor is represented by a series of perfectly mixed stages. The degree of backmixing is characterized by the number of stages the... 

Three-parameter mixing-cell model (Van Swaaij et aL106) This is a stagewise model for liquid-phase backmixing in a trickle-bed reactor. According to this model, an elementary mixing pattern for trickle flow is expressed as106... 

Stagewise models in which the mass balance is applied to staged regions, i.e. represented by algebraic equations. The basic model in this class is the perfectly mixed cell model. 

This remark introduces the problem of the comparison between differential and stagewise models. The cell in series model (Figure 2a) and the axial dispersion model (Figure 1b)... 

B - Stagewise models packing with its voids is regarded as a series of cells. Ordinary differential equations are used for mass and heat balances. 

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