陳誠亮臺灣大學:化學工程學研究所張嘉元Chang, Chia-YuanChia-YuanChang2010-06-302018-06-282010-06-302018-06-282009U0001-1801200921443300http://ntur.lib.ntu.edu.tw//handle/246246/186935本論文試圖發展一套整合數學模型以處理化工批次排程、熱整合及水網路之問題，整體架構可分為兩大主軸，一為考量熱整合之批次排程模組，另一為批次水網路模組，兩套模組可獨立亦可合併應用。為了兼顧模組間單獨使用之效率及協同運作之相容性，在時間軸之表達方面，皆採用連續式時間點表示法為基礎，相較於傳統離散式時間點表示法具有計算效率之優勢。此外，各模組探討之範圍均完整地包含短期及週期性操作，可適用於大多數之生產狀況。研究係由Castro等人所提出之資源-任務網路數學模型(Resource-Task Network, RTN)平台架構為出發點加以擴充，為了使排程之數學模性具備熱整合之能力，本文使用新增新參數與一組新的0-1決策變數之方式，將直接熱回收之計算納入，這套新排程模型相當般化，在與文獻上之研究案例相較後，證實其具有較佳之彈性且不失效率。文接著提出一套全新水網路設計模型，可考量多污染物(成份)及多儲存槽策略下之短期與週期性操作之複雜設計，並與排程模組完全對應。由於其與排程模組唯一接合之處為固定之排程參數，因此單考慮水網路設計並無排程計算之負擔，在最小化原水消耗量之基本情況中並不需要任何之0-1決策變數，因此僅為較不複雜的非線性規劃(Nonlinear Program, NLP)問題，由研究案例與文獻之比較中可證實此設計優異性。合併前述之數學模型後，可得到一套完整之數學模型，兼具排程、熱整合及水網路之設計能力，然而不可避免須面對混合整數非線性規劃(Mixed-Integer Nonlinear Program, MINLP)求解之困難度大幅提昇之問題。一般而言，在合理計算效率下尋求可接受之解亦為重要考量，因此本研究提出符合多數情況下，排程均較水網路設計為優先考量之「兩階段計算法」，其作法為首先將水網路模組轉換為一凸包(convex hull) 之近似模型，該模型再與排程模組相結合後，可得到一容易求解之 MILP 鬆弛模型，用來求解排程之0-1決策變數；第二階段於代入第一階段之排程0-1決策變數至原模型後，可成為一較容易求解之 NLP 問題，並解得排程之外之其他變數值。為了使第一階段之鬆弛模型更貼近原模型，水網路模組中亦進行部份之延伸，在論文最後使用兩個例子說明了此計算方式的確有不錯之效果。This dissertation aims to develop an integrated mathematical formulation to solve the scheduling, heat-integration and water-reuse problems. The framework is divided into two modules: one is batch scheduling incorporated with heat recovery, whereas the other one is batch water-reuse network. The later is mainly used to work in coordination with the scheduling module. However, it can also be used individually. A continuous time formulation, which is more competitive in efficiency than traditional discrete one, is adopted as the time representation in designing each subsystem. Both short-term and periodic operation modes are considered to cover most of the production scenarios.iscussions are elaborated from a novel framework of Resource-Task Network (RTN) proposed by Castro et al. To extend the capability of scheduling toward simultaneous scheduling and direct heat-recovery, a generalized mathematical formulation is firstly proposed by introducing new parameters and a set of new binary variables in managing heat-integration. In comparison with literature examples, the new model is proven competitive with its flexibility and without the loss of compromising with efficiency.hen, a new water-reuse framework is proposed with the same continuous time concept in general scheduling model. This new formulation contains water-reuse and storage facilities for multi contaminant environment. Both single and periodic operation modes are also derived in correspondence with the scheduling model. The water-reuse module is connectable with scheduling module via the decision binary variables. However, they are regarded as predefined parameters if the water-reuse module works alone. Therefore, in the two basic scenarios of water minimization, no binary variable is required; therefore, the model is formulated in NLP, which is very competitive with the result reported in literatures.n overall model is carried out thereafter by simply combining the scheduling with water-reuse module proposed previously. However, the computational issue in handling large scaled MINLP is inevitable. Instead of global optimum, an acceptable solution might be more attractive in reasonable computation time. Since the priority in scheduling is usually higher than that in water-reuse network, a hierarchical two-step solving procedure is proposed. In the first stage, the water-reuse module is converted into a ''convex hull'' MILP model and then combined with the scheduling module. The resulting relaxed model is MILP and could be easily solved to obtain the decision binary variable in scheduling. In the second step, the overall model is solved with the fixed production schedule. Therefore, only a NLP, which is easier to solve than the original MINLP, must be solved. Several enhancements are carried out in the linearization of water-reuse module to narrow the difference between the original and relaxed model. Two examples are demonstrated to verify the performance of the solving procedure.摘要 vbstract vii圖目錄 xiii表目錄 xv號定義 xvii 批次排程設計緒論 1 1.1 排程問題之特性 2 1.1.1 排程問題之複雜度 2 1.1.2 化工廠批次排程問題之特點及分類 2 1.2 網路型批次排程之文獻回顧 3 1.3 研究動機與目的 6 1.4 章節組織 9 多功能批次製程之資源-任務網路數學模型 11 2.1 資源-任務網路表示法 11 2.2 問題敘述 13 2.3 數學模型綜述 13 2.3.1 短期排程之數學模型 14 2.3.2 週期性期排程之數學模型 19 2.4 儲存槽策略 24 2.5 應用案例 24 2.5.1 案例1:一個典型的批次網路程序 25 2.5.2 案例2:一個考慮儲存槽策略之簡易批次程序 28 2.6 本章總結 考慮熱整合之多功能批次製程之資源-任務網路數學模型 35 3.1 批次程序熱整合概述 35 3.2 問題敘述 37 3.3 數學模型 37 3.3.1 短期排程之數學模型 38 3.3.2 週期性期排程之數學模型 42 3.4 應用案例 46 3.4.1 案例1:一個簡單的連續批次程序 46 3.4.2 案例2:一個包含5階段操作之批次程序 53 3.5 本章總結 以連續式數學模型設計批次製程之水網路 59 4.1 水網路設計概述 59 4.2 問題陳述 61 4.3 數學模型 61 4.3.1 短期操作之數學模型 61 4.3.2 週期性操作程之數學模型 66 4.4 目標函數 71 4.5 應用案例 74 4.5.1 案例1:農用化學品製造程序 74 4.5.2 案例2:農用化學品製造程序 76 4.5.3 案例3:具有多成分之水網路 79 4.6 本章總結 考慮水網路設計之多功能批次製程之資源-任務網路數學模型 89 5.1 同時考慮排程雨水網路設計之數學模型 91 5.2 應用案例 101 5.2.1 案例1:具有三處理單元之排程問題 101 5.2.2 案例2:三混合槽最低廢水排放問題 106 5.3 本章總結 結論及未來展望 115 6.1 結論 115 6.2 未來展望 116考文獻 119者簡歷 1251650426 bytesapplication/pdfen-US批次程序排程熱整合水網路混合整數線性規劃混合整數非線性規劃Batch processSchedulingHeat IntegrationWater-reuse NetworkMixed-integer linear programming (MILP)Mixed-integer nonlinear programming (MINLP)thesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/186935/1/ntu-98-D89524005-1.pdf