In Eq. (164), Xj is the thermodynamic force. It indicates that all the main sub-matrixes are always positive, or the self-coefficient Lu is positive while the inter-coefficient may be either positive or negative.

(2) In terms of the separation principle of partial vaporization and partial condensation, component A (as the heavy component) should be transferred, as a whole, from vapor phase to liquid phase in the distillation process. On the contrary, it should be from liquid phase to vapor phase for component B (as the heavy component). So, if it is assumed that the positive direction is from vapor phase to liquid phase, then

The first requirement ensures that the separation process can occur, and the second requirement goes a further step to ensure that the direction of mass transfer is from vapor phase to liquid phase for component A and from liquid phase to vapor phase for component B. Therefore, this separation process is able to be put into practice. For the common extractive distillation, the above analysis will certainly be applicable, but, of course, only three components, i.e. A, B and S, are involved and there is no component E formed by reaction.

The mathematic model of entropy generation in the common distillation process has been reported by Liu et al. [74], in which, however, it is only suitable for the vapor phase and not extended to the whole of the vapor and liquid phases on the tray. Moreover, it isn't suitable for special distillation processes.

For reactive extractive distillation, by using Eqs. (146) - (152), entropy generation is given by a = JAV

By using the linear driving force equation of nonequilibrium thermodynamics, one obtains:

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