Orthogonal collocation on finite elements is applied to discretize the DAE system for the simulation of multiple-fraction batch distillation processes. A detailed dynamic tray-by-tray model is used to describe batch columns more accurately which, however, leads to a set of model equations composed of nonlinear DAEs with a fairly high dimension. In addition, batch distillation operation usually takes a long period of time and therefore it costs large computational expense to simulate such processes. The use of orthogonal collocation is demonstrated to obtain a stable and highly accurate algebraic representation of the differential equations so as to improve the computational efficiency significantly. Because of the orthogonality of the polynomials introduced to approximate the state variables within a time interval, large integration steps can be taken with the collocation approximation without reducing the computational accuracy. Through simulation of two real batch distillation processes it is found that with this discretization approach 50% CPU time can be saved in comparison to the implicit Euler method normally used.
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