以數學規畫法作多效蒸餾系統設計

Abstract

由於能源價格不斷上漲，而新興能源卻仍處於發展階段，因此，如何有效率地使用能源已然成為工業製程上相當重視的議題。在一般化工廠中，蒸餾程序扮演著高耗能的角色，自然而然也成為專家學者們重點探討之對象。其主要目的在於設計出適當的蒸餾塔操作方式來達成節約能源之效果，如此既可降低操作成本以符合經濟效益，亦能減低對環境所造成之衝擊。多效蒸餾塔（Multi-effect Distillation Columns）之概念早於1950年由Robinson與Gilliland所提出；藉由增加某些蒸餾塔的操作壓力造成塔與塔之間的溫度差，並進一步針對多根蒸餾塔進行熱整合，達到能量再利用及減少能量消耗之目的。 以超結構為基礎，本研究將提出一套完整的數學模式來描述多效蒸餾系統，並針對該系統進行最適化設計。其中設計目標包含了最小化能量使用以及最小化年總成本，依據不同的目標則可決定出不同之最佳操作情況。於本文中，由所提出之數學模式得到的設計結果將先與underwood’s method的結果比較，以確認其可靠性，再與傳統蒸餾系統做詳細之成本比較，以說明多效蒸餾系統確實能夠有效地節省能量使用並降低年總成本。另外，透過一系列例子的討論與分析，可歸納出不同進料狀態與最適蒸餾架構之間的關係。

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 normal chemical works, the distillation process plays the most part in consuming energy and naturally turns into the major subject to be investigated by many savants. The main objective is to design an applicable mode for the manipulation of distillation columns which achieves the energy saving. Therefore, not only the operating cost can be reduced but the environmental impact will be also lowered. The concept of multi-effect distillation columns had been introduced in 1950 by Robinson and Gilliland: The temperature differences (for heat exchange) between distillation columns can be produced by increasing the pressure in some columns, and heat integration within the distillation system is then carried out for the purpose of energy recovery and energy saving. 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 multi-effect distillation system, where design objectives include the minimization of energy consumption and the minimization of total annual cost (TAC). Accordingly, optimal operating conditions can be obtained with different design objectives. For one thing, results from the proposed mathematical formulation will be compared with the results from Underwood’s method to confirm its validness. For the next, the results of multi-effect distillation system are also compared with the results of conventional distillation system to illustrate that the multi-effect distillation columns are actually capable of reducing the energy consumption and the total annual cost. Furthermore, the correlation between feed condition and resultant framework of distillation can be generalized through discussions on a series of examples.