Dispersed plug flow model basic differential equation

In most adsorption processes the adsorbent is contacted with fluid in a packed bed. An understanding of the dynamic behavior of such systems is therefore needed for rational process design and optimization. What is required is a mathematical model which allows the effluent concentration to be predicted for any defined change in the feed concentration or flow rate to the bed. The flow pattern can generally be represented adequately by the axial dispersed plug-flow model, according to which a mass balance for an element of the column yields, for the basic differential equation governing llie dynamic behavior,... 

From the appearance of the dispersion number DjuL in this dimensionless form of the basic differential equation of the plug-flow dispersion model it can be inferred that the dispersion number must be a significant characteristic parameter in any solution to the equation, as we have seen. 

The basic plug-flow model, with or without dispersions, is a continuous" model because the concentrations and temperature are described by differential equations. An alternative representation is by a discrete model - the so-called "cell" model (16, 17), in which it is assumed that the reactor can be broken down into several connected cells. It had long been assumed that the continuous and discrete models are equivalent ways of representing a reactor however, this assumption has recently been questioned in two different contexts (18, 19). 

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