The Case of a Linear Equilibrium Relation

By using an equilibrium function F of this linear form in equation (6.86), we obtain 

Note that the order of the labeling of the trays or stages from 1 to. /V or in reverse order from N to 1 does not affect the problem. 

These are N equations that can be written in matrix form. For this purpose we define a vector X whose components are the state variables Xj, namely 

The matrix A is a tridiagonal Toeplitz1 matrix with constant main diagonal and codiagonal entries. 

The right-hand sides of the X equations can be combined into the constant right-hand-side vector 

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As noted in Chapter 5, the performance of a particular packing is often expressed in terms of a height equivalent to a theoretical plate (HETP) and is so reported by packing manufacturers. Performance data in terms of a HTU, or a volumetric mass transfer coefficient Ka, have a sounder theoretical basis but are relatively rare (see Table 5.6). A link between HTU and HETP can, however, be easily established for the case of a linear equilibrium relation. To show this, we start with the definitions of HTU and HETP and simply divide the two expressions. We obtain... 

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