應用數學規劃法於熱質傳交換網路之合成與改良

Mathematical Programming Approach for Heat/Mass Exchange Networks Synthesis and Retrofit

洪平松(Ping-Sung Hung)

指導教授 ： 陳誠亮

國立臺灣大學/工學院/化學工程學研究所/博士(2005年)

https://doi.org/10.6342/NTU.2005.02611

摘要

本研究之主旨在於透過數學規劃法來探討質傳交換網路中的合成與改良問題，參考Yee and Grossmann (1990a,1990b)所提出之熱交換網路階層超結構，本文首先提出質傳交換網路階層式超結構，此一超結構可以涵蓋所有可能發生的的質傳交換配對情形，不僅同時可以直接處理多成分和採用反應離劑的問題，也可以延伸至包含再生再利用之問題。根據此超結構，吾人可以將質傳交換網路之合成問題，轉換成為一個混合整數非線性規劃問題，此法不同於狹點技術需使用經驗法則，而是直接根據所提出之超結構，建立一個完整的最適化模式，因此可以同時考量任何能數學化之目標。

在本論文中也提出兩個新的策略來合成符合經濟要求且兼顧操作彈性的熱質傳交換網路， 也就是能容忍不確定的進口溫度/組成和流率，第一個為有效群組法，此策略將問題可以被 分成三的主要的步驟：(1)合成具最小年總成本(TAC)之熱或質傳交換網路；(2)使用操作彈性分析 去測試該網路結構在所要求之不確定範圍內是否可行；(3)透過整數切除方程式排除不合格之網路結構。第二個則為隨機取點法，此策略有三個主要部份；(1)合成具最小年總成本(TAC)之熱或質傳交換網路；(2)隨機取點之操作彈性測試I(尚未考慮單元大小)；(3)隨機取點之操作彈性測試II(考慮單元大小)。此兩策略皆需反覆的重複上述三個步驟直到得到所要求的網路結果。

本研究也使用一個多目標的合成方法，此方法能同時考量最少能源使用量以及最大化進口溫度變化之彈性，甚至最少單元數，這類的彈性熱交換器網路能被建立成一個多目標的混合整數線性規劃問題，為了處理這些設計目標，採用一個兩階段的模糊多目標方法，用以得到一個最好的妥協解。

本論文也將上述的合成改良模式與所提出之策略應用於文獻中常見的實例中，用以驗證所提之模式與策略之可行性。

關鍵字

質傳交換網路 ； 合成 ； 改良 ； 數學規劃法

並列摘要

This dissertation deals with the synthesis and retrofit problems of mass exchange networks (MENs) by adopting a mathematical programming approach based on the stage-wise superstructure representation of the MENs. It is analogous to the one introduced by Yee and Grossmann (1990a,1990b) for synthesis of heat exchange networks (HENs). This stage-wise superstructure-based representation can not only handle multiple transferable components and reactive separating agents directly, but also be extended to include regeneration networks straightforwardly. Not using any heuristics that are based on the concept of pinch points, the proposed superstructure-based representation for MEN's is formulated as a mixed-integer nonlinear programming (MINLP)
optimization model. Therefore, any objects can be minimized simultaneously.

Also, two novel strategies for the synthesis of cost effective flexible heat/mass exchanger networks that involves specified uncertainties in the source-stream temperatures/compositions and flow rates is presented. The first strategy is active set strategy that is decomposed into three main iterative steps: (1) the simultaneous HEN or MEN synthesis to attain a network configuration with a minimum total annual cost (TAC); (2) the flexibility analysis to test whether the network obtained from the synthesis step is feasible or not in the full disturbance range; and (3) the integer cuts to exclude disqualified network configurations. The second strategy is random simulation that is also decomposed into three main steps:
(1) the simultaneous HEN or MEN synthesis to attain a network configuration with a minimum total annual cost (TAC); (2) flexibility test without consideration of the size restrictions to verify whether the current network candidate is feasible or not for a large number of corrected uncertain parameters; and (3) with consideration of the size restrictions that have been ignored previously, execution of flexibility test of the network qualified in step (2), with an increase of the size of individual exchange units if necessary. A few iterations of these three steps for the two strategies are required to secure the desirable results.

In addition, a multi-criteria synthesis strategy for heat-exchanger networks (HENs) simultaneously considering minimum utility consumption, maximum source-stream temperature flexibility, and even minimum number of matches is also proposed. The flexible HEN synthesis problem is formulated as a multi-objective mixed-integer linear programming (MO-MILP). For handling the multiple conflict design targets, a two-phase fuzzy multi-criteria decision-making method is presented to attain a best compromised solution.

Final, several examples from literatures are supplied to demonstrate the applicability of the proposed MENs synthesis and retrofit models and the efficiency of the proposed strategies.

並列關鍵字

Mass Exchange Networks ； Synthesis ； Retrofit ； Mathematical Programming Approach

參考文獻

Aaltola, J.

"Simultaneous synthesis of flexible heat exchanger network," Appl. Therm. Eng., vol. 22, p. 907, 2002.

"Decision making in a fuzzy enviroment," Management Sci., vol 17, p. 141-164, 1970

"Global optimization of heat exchanger network synthesis problems with and without the isothermal mixing assumption," Comput. Chem. Eng., vol. 26, p. 1581, 2002.

"Simultaneous Synthesis of Flexible Heat-Exchange Networks with Uncertain Source-Stream Temperatures and Flow Rates,"