以數學規劃法作反應性蒸餾塔最適化設計

Abstract

本研究提出一個以逐層式模式為基礎之完整反應蒸餾系統設計。 一般在研究反應蒸餾設計時，部分的結構變數往往需要靠經驗或直覺來決定、 而操作變數則由標準的最適化技術來求得。 本文將以價格考量所有變數，建立以低廉價格為取向之目標函數， 將所有變數納入目標函數中。 因此，本研究提出一個針對反應性蒸餾塔設計方法，能對所有結構變數及操作變數 作同時最適化的階層式模式。 將處理反應性蒸餾問題的階層式模式整合成一個混合整數非線性最適化問題， 其中同時考慮原物料成本、操作成本、投資成本， 並討論多重進料對系統造成可能的影響。 本文在假設不考慮液液分相之異相系統的前提下，熱力學模式可以選擇系統適合 之模式代入超結構中，如：理想模式，Willson模式等；而對於液氣平衡的情形 使用莫菲板效率表示塔板之分離效率，使模式能夠更真實的描述反應蒸餾之行為。 並將原本只能處理均相反應系統的模式，增加考慮固相觸媒的影響，使超結構能 延伸到異相反應系統。 最後，參考文獻所提供生產乙二醇和乙酸甲酯之模擬範例，由模擬的結果可得知， 以MINLP來處理均相及異相反應之反應性蒸餾系統最適化的可行性。

A complete mathematical programming formulation based on a tray-by-tray model is presented for optimal design of homogeneous reactive distillation processes. Most of the researches on reactive distillation, some the structural details of the process are found by empiricism or intuition, and the operational variables can be determined by standard optimization techniques. An optimal model which minimize total costs with all priced structural variables and priced operational variables was set up. A tray-by-tray model was proposed for reactive distillation column design that could simultaneous optimize all structural variables and operational variables. The synthesis of reactive distillation problems can be formulated as a mixed-integer nonlinear programming (MINLP), where raw material cost, the operating costs and the investment costs are considered simultaneously and the possible benefits of multiple feed locations is emphasized. This study is supposed not considering the liquid-liquid equilibria system, the suitable thermodynamics model can be applied to the superstructure, such as: ideal model, the Willson model and so on; as for the liquid-vapor equilibria phenomena, the Murphree plate efficiency is indicated the separating efficiency of plate, and model could have the more real description of behavior reactive distillation. Apply the effect of catalyst to the model that only can handle homogeneous reaction system, make the superstructure could be extended to heterogeneous reactive distillation system. Production ethylene glycol and methyl acetate processes from literature is supplied to demonstrate the proposed simultaneous optimization approach on the homogeneous and heterogeneous reactive distillation column design by MINLP technique.