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Contribution to improve the dynamic control of a binary distillation column

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Abstract

Conventionally, steady state design for distillation column is often completed before dynamics and control issues are considered. The aim of this paper is to use the design issues as a tool to improve dynamic behavior of binary distillation column. The idea is augmenting the liquid holdup in the feed plate through a middle vessel. The degree of interactions between the loops are examined for five well known control schemes by considering different quantities of liquid holdup in the feed plate. Simulation results show that augmenting the hold-up in the feed plate will lead to minimize the interactions between the loops in all cases particularly for DV control scheme where a total decoupling is achieved.

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Authors and Affiliations

  1. Laboratory of Signals and Systems, Institute of Electrical and Electronic Engineering, Boumerdes University, Boulevard de l’independance, 35000, Boumerdes, Algeria

    Riad Bendib & Hamid Bentarzi

Authors
  1. Riad Bendib
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  2. Hamid Bentarzi
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Corresponding author

Correspondence to Riad Bendib.

Appendix: The used column

Appendix: The used column

It consists of seven plates, a reboiler, and a condenser. The column separates a mixture of Benzene–Toluene. The feed is entering at plates 4 numbering from the base. Measurements are the compositions of liquid on plate 7 and reboiler. The manipulated variables are reflux, distillate flow, bottom flow, and reboiler steam valve position. Vapor flow into the column responds quickly to changes in steam valve position. The linear model for this column in state space representation given by

$$x^{ \bullet } = Ax + Bu$$
$$y = Cx$$
$$A = \left[ {\begin{array}{*{20}l} { - 0.0135} \hfill & {0.0063} \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill \\ 0.0290 \hfill &-0.0436 \hfill & 0.0168 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & -0.0490\\ 0\hfill & 0.0290\hfill & -0.0457\hfill & 0.0212\hfill & 0\hfill & 0\hfill &0\hfill & 0\hfill & 0\hfill & 0\hfill & -0.0908\\0\hfill & 0\hfill & 0.0290\hfill & -0.0502\hfill & 0.0290\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & -0.0396\\0 \hfill & 0 \hfill & 0 \hfill & {0.0270} \hfill & { - 0.0626} \hfill & {0.0346} \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & { - 0.1176} \hfill \\ 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & {0.0356} \hfill & { - 0.0702} \hfill & {0.0446} \hfill & 0 \hfill & 0 \hfill & 0 \hfill & { - 0.1369} \hfill \\ 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & {0.0356} \hfill & { - 0.0802} \hfill & {0.0548} \hfill & 0 \hfill & 0 \hfill & { - 0.1240} \hfill \\ 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & {0.0356} \hfill & { - 0.0904} \hfill & {0.0628} \hfill & 0 \hfill & { - 0.0892} \hfill \\ 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & {0.0081} \hfill & { - 0.0157} \hfill & 0 \hfill & { - 0.0123} \hfill \\ 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & { - 15.240} \hfill & { - 5.0086} \hfill & {299.42} \hfill \\ 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & {0.0004} \hfill & {0.0283} \hfill & {0.0084} \hfill & { - 0.6868} \hfill \\ \end{array} } \right]$$
$$B = \left[ {\begin{array}{*{20}l} 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill \\ {0.0533} \hfill & { - 0.0005} \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill \\ {0.0988} \hfill & { - 0.0009} \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill \\ {0.1520} \hfill & { - 0.0014} \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill \\ {0.1653} \hfill & { - 0.0019} \hfill & { - 0.1169} \hfill & { 0. 0 0 8 6} \hfill & 0 \hfill & 0 \hfill \\ {0.1129} \hfill & { - 0.0011} \hfill & {0.1129} \hfill & 0 \hfill & 0 \hfill & 0 \hfill \\ {0.1023} \hfill & { - 0.0010} \hfill & {0.1023} \hfill & 0 \hfill & 0 \hfill & 0 \hfill \\ {0.0736} \hfill & { - 0.0007} \hfill & {0.0736} \hfill & 0 \hfill & 0 \hfill & 0 \hfill \\ {0.0102} \hfill & { - 0.0001} \hfill & {0.0102} \hfill & 0 \hfill & 0 \hfill & 0 \hfill \\ 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & {0.6229} \hfill & {1.4409} \hfill \\ {0.0005} \hfill & 0 \hfill & {0.0005} \hfill & 0 \hfill & 0 \hfill & 0 \hfill \\ \end{array} } \right]$$
$$C = \left( {\begin{array}{*{20}l} 0 \hfill & 1 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill \\ 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 1 \hfill & 0 \hfill & 0 \hfill \\ \end{array} } \right)$$

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Bendib, R., Bentarzi, H. Contribution to improve the dynamic control of a binary distillation column. Int J Syst Assur Eng Manag 8 (Suppl 2), 663–675 (2017). https://doi.org/10.1007/s13198-016-0503-6

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