以數學規劃法作內隔板蒸餾塔設計

Abstract

由於能源價格不斷攀升，且替代能源尚處於開發之階段，如何有效地節約能源遂成為工業界相當重視之議題。在高耗能的傳統化工產業中，是以蒸餾程序為其能源消耗之大宗。因此，專家學者們紛紛致力於蒸餾系統的改良以提高能源之使用效率。而現有的蒸餾系統相關文獻中，又以熱整合式蒸餾塔備受矚目。 內隔板蒸餾塔（Divided-wall Distillation Column）屬於一種熱整合式蒸餾塔。本研究提出一套完整且通用之數學模式，針對內隔板蒸餾系統進行最適化設計。模式的建構是以一個考慮所有可能情況之超結構為基礎，將蒸餾系統之設計表示成一個混合整數非線性規劃問題（MINLP）。設計目標包含最小化能源使用量以及最小化年總成本（TAC）。本論文中以一個具三成份之進料為例，並使用所提出之數學模式決定出不同進料狀態下之最佳內隔板蒸餾系統操作情況。而所得之設計結果將先與Underwood方法的結果比對以確認模式之正確性，再藉由與傳統蒸餾系統之結果比較來說明內隔板蒸餾系統在能源使用上以及設備投資成本方面所展現之優勢。

Owing to the rising cost of energy and the fact that new energy resources are not yet available to all, how to utilize energy in an efficient way has become an important issue for industrial processes. In high energy-consuming chemical industrials, the distillation process plays the most part in consuming energy. Therefore, all savant devote improving the distillation system to promote the energy-consuming efficiency. Until now, the relevant literature of the distillation system, the energy integration of distillation is the most interesting. Divided-wall Distillation Column (DWC) is the one of energy integration of distillation. Based on a superstructure which incorporates all possible schemes, this work aims to propose a general mixed-integer nonlinear programming (MINLP) formulation for modeling and optimizing the Divided-wall Distillation Column, where design objectives include the minimization of energy consumption and the minimization of total annual cost (TAC). For a three component feed, Optimal operating conditions can be obtained with different feed conditions according to the model of this work. For one thing, results from the proposed mathematical formulation will be compared with the results from Underwood's method to comfirm its correction. For the next, the results are also compared with the results of conventional distillation systems to illustrate that the advantages of energy-consuming and capital investment cost of Divided-wall Distillation Column (DWC).