Nonequilibrium stage model solution

Krishnamurthy, R. and Taylor, R., A Nonequilibrium Stage Model of Multicomponent Separation Processes. I—Model Development and Method of Solution, AIChE J, 31, 449-456 (1985a). 

Among several analytical methods for the prediction of movement of dissolved substances in soils, one model (Leij et al., 1993) was developed for three-dimensional nonequilibrium transport with one-dimensional steady flow in a semi-infinite soil system. In this model, the solute movement was treated as one-dimensional downward flow with three-dimensional dispersion to simplify the analytical solution. Another model (Rudakov and Rudakov, 1999) analyzed the risk of groundwater pollution caused by leaks from surface depositories containing water-soluble toxic substances. In this analytical model, the pollutant migration was also simplified into two stages predominantly vertical (one-dimensional) advection and three-dimensional dispersion of the pollutants in the groundwater. Typically, analytical methods have many restrictions when dealing with three-dimensional models and do not include complicated boundary conditions. 

It should be stated that the number of equations in this approach is very large, and specialized computer programs have been developed far their solution. Our objective here is very limited, namely to provide an idea of the basis of these equations. The basic set of equations in such rate based or nonequilibrium models of a distillation plate/ stage is sometimes referred to as the MERSHQ equations (Taylor et id., 2003), with each letter representing equations for a particular aspect of the problem for any plate n of the n-component system. 

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