Differential extraction column with axial dispersion

AXDISP - Differential Extraction Column with Axial Dispersion... 

In Sec. 4.4.3 the modelling of differential extraction columns with axial dispersion is discussed. The extractor is considered to be approximated by eight finite-difference elements as shown below. 

PHASE DIFFERENTIAL EXTRACTION COLUMN WITH AXIAL DISPERSION... 

Liquid-liquid extraction is carried out either (1) in a series of well-mixed vessels or stages (well-mixed tanks or in plate column), or (2) in a continuous process, such as a spray column, packed column, or rotating disk column. If the process model is to be represented with integer variables, as in a staged process, MILNP (Glanz and Stichlmair, 1997) or one of the methods described in Chapters 9 and 10 can be employed. This example focuses on optimization in which the model is composed of two first-order, steady-state differential equations (a plug flow model). A similar treatment can be applied to an axial dispersion model. 

Instead of the partial differential equation model presented above, the model is developed here in dynamic difference equation form, which is suitable for solution by dynamic simulation packages, such as Madonna. Analogous to the previous development for tubular reactors and extraction columns, the development of the dynamic dispersion model starts by considering an element of tube length AZ, with a cross-sectional area of Ac, a superficial flow velocity of V and an axial dispersion coefficient, or diffusivity D. Convective and diffusive flows of component A enter and leave the liquid phase volume of any element, n, as indicated in Fig. 4.24 below. Here j represents the diffusive flux, L the liquid flow rate and and Cla the concentration of any species A in both the solid and liquid phases, respectively. 

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