@MISC{LPT-pre-2008-14,
AUTHOR = {M. Stuckert and Bert Pluymers and Jobert Ludlage and W. Marquardt},
TITLE = {{The wave based model reduction applied to a binary distillation column}},
LPTKey = {LPT-pre-2008-14},
}

The wave based model reduction applied to a binary distillation column

Abstract:
A physically justified low order model of a distillation column, which considers nonlinearities and is useful for online simulation and thus for controller design, can be obtained by a transformation of column equations using the wave based model reduction. The procedure includes a resolution of the distillation column into its integral parts: condenser, reboiler, feed tray, stripping and rectifying sections. The reduction itself is actually only adopted for the both sections separately. First, the two equations describing the mass balance in a section are added and the vapour composition is excluded in favour of the liquid composition. Second, a so-called form approach H is assumed which characterises the liquid composition (a wave) in terms of parameters p1, p2, gamma and z*. An additional assumption concerning the propagation velocity of the wave is made, as well. Two further equations originate from the two boundary conditions for the section. The form approach is then substituted for liquid composition in all mentioned equations. As a result of these manipulations we get a differential-algebraic equation (DAE) of index 1 for each section. Using these DAEs we already can simulate the evolution of concentration profiles for distinct sections. Properly combined with equations for condenser, reboiler and feed tray these DAEs can then be even used to build the entire column. A variety of DAE solvers, which our obtained DAEs can be passed to, are available. Thus, numerical simulation of the process with a solver of one's own choice is possible.

Keywords:
binary distillation, model reduction, wave model