有機朗肯循環（Organic Rankine Cycle, ORC）為提升工業製程能源效率並減少環境影響提供了一種極具潛力的技術。本研究旨在發展一套完整的數學方法，以最適化方法將ORC系統整合至釋放低品位廢熱的既有工業製程中。透過代數與目標設定找出最佳解，本研究試圖識別並有效利用廢熱，以提升ORC與製程整合的可行性並最大化軸功輸出。本方法包含透過分析工業製程的總複合曲線（Grand Composite Curve, GCC）來辨識可回收的熱量，選出能達成高效率的工作流體。ORC設計可置於挾點之上或之下，以有效回收廢熱。研究中會辨識 ORC 的蒸發與冷凝溫度，並將其對應至總複合曲線上，以驗證系統整合的可行性，ORC 的最佳化設計涉及尋找一種同時最大化廢熱回收與軸功輸出的系統設置，以確保在節能與成本效益上達到最佳效果。本研究提出一種代數方法來優化 ORC 設計，運用數學方程式，透過解析推導進行最佳化，該方法能夠優化 ORC 設計，以提升低品位熱源發電應用中的經濟可行性與競爭力。本研究亦探討如何透過挖掘GCC中的「口袋區域」（pocket）來最大化能源回收與軸功輸出，並進一步降低冷公用流體用量。透過實際案例研究進行驗證，結果顯示 ORC 系統在挾點上下的不同配置均可有效實現熱回收與發電，這些案例顯示在能源回收、軸功輸出與冷公用流體用量減少方面皆有顯著改善。

This study develops an algebraic optimization method for integrating Organic Rankine Cycle (ORC) systems into industrial processes to enhance energy efficiency and recover low-grade heat. The proposed approach analyzes the Grand Composite Curve (GCC) to identify available heat sources and determine optimal evaporation and condensation temperatures for ORC design. Three integration scenarios are investigated: sub-pinch integration without absorption limits, sub-pinch with absorption constraints (in and out of pockets), and supra-pinch integration. Results show that the proposed method achieves comparable or superior performance to traditional pinch-based iterative methods and mathematical programming approaches. The ORC system is modeled using unified phase-change heat exchangers to minimize equipment count and improve cost-effectiveness. For cases involving pocket integration, the method effectively reduces cooling utility demand while maximizing shaft work. A graphical algebraic approach simplifies the optimization process by solving linear equations without iterative drawing of new GCCs, significantly lowering the entry barrier compared to conventional methods. The results validate that the proposed strategy is suitable for heat-to-power integration and provides a systematic, visual, and practical framework for improving process energy utilization.

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