Developing a technique for improving the efficiency of iterative methods for the calculation of the multicomponent rectification process
DOI:
https://doi.org/10.15587/1729-4061.2016.85372Keywords:
mathematical modeling, multicomponent rectification, iteration methods, the θ-method of convergence, mobile controlAbstract
Studies of the technological base of mobile control over the processes of rectification are based on determining the concentration and temperature profiles of the installation in the established regime at different coordinates of the point of application of controlling influence.
A problem of the calculation of static characteristics of the process is in the iterative determination of such concentrations of components in the bottoms so that the bidirectional calculations, based on them, and carried out to the control section of a rectifying column, make it possible to obtain identical results. The θ-method is the effective technique for the provision of convergence of such calculations. However, when calculating multi-plate rectifying columns with several feeding inputs, in which the separation of multicomponent mixtures occurs, it is necessary to use a simple procedure for the reduction in time spent searching for the solution.
The problem of reducing the necessary number of iterations is solved by the exponentiation of coefficient θ, which is determined by the introduced tuning parameter of the algorithm. The extreme dependence of the number of iterations on this exponent is proven.
Performed calculations of the column for separating the multicomponent product of the MTBE synthesis proved that the proposed modification of the θ-method of convergence of iterative calculations of the operating modes of rectifying columns makes it possible to reduce the time, necessary for the search for the solution, by 50 %. In this case, it is not necessary to obtain high quality of initial approximations of compositions of the separation products. The method is characterized by high stability and workability in a wide range of change in the input magnitudes.
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Copyright (c) 2016 Anton Sheikus, Елена Владиславовна Белоброва, Yaroslav Dovgopoliy, Igor Levchuk, Valeriy Korsun
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