Differential Flow and Reaction Applications

The main process variables in differential contacting devices vary continuously with respect to distance. Dynamic simulations therefore involve variations with respect to both time and position. Thus two independent variables, time and position, are now involved. Although the basic principles remain the same, the mathematical formulation for the dynamic system now results in the form of partial differential equations. As most digital simulation languages permit the use of only one independent variable, the second independent variable, either time or distance, is normally eliminated by the use of a finite-differencing procedure. In this chapter, the approach is based very largely on that of Franks (1967), and the distance coordinate is treated by finite differencing. 

In this procedure, the length coordinate of the system is divided into N finite-difference elements or segments, each of length AZ, where N times AZ is equal to the total length or distance. It is assumed that within each element any variation with respect to distance is relatively small. The conditions at the midpoint of the element can therefore be taken to represent the conditions of the element as a whole. This is shown in Fig 4.1, where the average concentration of any element n is identified by the midpoint concentration Cn- The actual continuous variation in concentration with respect to length is therefore approximated by a series of discontinuous variations. 

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Differential Flow and Reaction Applications Simplifying the above equation gives... 

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