本研究主要是探討以中空纖維模組應用在薄膜氣體吸收系統之解析解與實驗之驗證。針對中空纖維模組的部份，導入Happel’s free surface模式，以建立其速度分佈式及邊界條件。而在薄膜氣體吸收系統中，氣體溶質於氣、液兩相內之質傳屬於共軛格拉茲問題，利用正交性質展開法建立二維濃度分佈式，並配合分離變數法及級數展開可求得系統之解析解。研究中也進一步推導出氣體溶質在氣-液薄膜接觸器內，於氣、液兩相中之平均濃度分佈、質傳係數、吸收速率及吸收效率等物理量之數學表示式。
以本文所推導之理論為基礎，改變氣、液兩相之進料流量與混合氣體進料的濃度，對二氧化碳之物理吸收作廣泛的討論，並以實驗結果印證理論分析之準確性。
本研究之主要價值在於無需經過冗長費時的實驗即可求得整個吸收系統之質傳係數及氣體溶質的二維濃度分佈式，進一步可討論各種變因對吸收效率的影響。

The effects on solute mass transfer for a laminar gas absorption process were investigated theoretically and experimentally in this study. A mathematical formulation was developed in a hollow fiber gas-liquid membrane contactor that independently regulates gas and liquid flows. The analytical solution for such a conjugated Graetz problem is obtained by using the separated variable method with an orthogonal expansion technique extended in power series. Physical carbon dioxide absorption in water was studied.
The theoretical predictions show that a higher absorbent flow rate has a positive effect producing better absorption efficiency in the case when the CO2 concentration in gas feed is specified. The absorption efficiency in the countercurrent-flow device is better than that in the concurrent-flow device in the same operating conditions. The experiments of hollow fiber module are set up to confirm the accuracy of the theoretical results.

目 錄
中文摘要 ...................................................................................................... II
英文摘要 ..................................................................................................... III
目錄 ............................................................................................................. IV
圖目錄. ...................................................................................................... VII
表目錄 ......................................................................................................... IX
符號說明 ...................................................................................................... X
第一章 緒論 ................................................................................................. 1
1-1 簡介 ............................................................................................. 1
1-1-1薄膜氣體吸收 ........................................................................... 1
1-1-2 格拉茲問題(Graetz problems) ................................................. 3
1-2 研究動機、目的與方向 ............................................................. 4
第二章 文獻回顧 ......................................................................................... 6
2-1 格拉茲問題(Graetz problems) .................................................... 6
2-2薄膜氣體吸收之研究 .................................................................. 7
第三章 中空纖維型順流式氣-液薄膜接觸器 ......................................... 10
3-1 基本理論 ................................................................................... 10
3-2 平均濃度與質傳係數 ............................................................... 18
3-3 吸收速率與吸收效率 ............................................................... 19

3-4 計算範例、結果與討論 ........................................................... 20
第四章 中空纖維型逆流式氣-液薄膜接觸器 ......................................... 30
4-1 基本理論 ................................................................................... 30
4-2 平均濃度與質傳係數 ............................................................... 35
4-3 吸收速率與吸收效率 ............................................................... 37
4-4 計算範例、結果與討論 ........................................................... 37
第五章 薄膜吸收實驗 ............................................................................... 48
5-1 實驗設備 ................................................................................... 48
5-2 實驗流程 ................................................................................... 49
5-3 結果與討論 ............................................................................... 51
第六章 結論 ............................................................................................... 60
參考文獻 ..................................................................................................... 63
附錄A 套管型氣-液薄膜接觸器 .............................................................. 70
附錄B 正交性質證明 ............................................................................... 76
附錄C 積分公式證明 ............................................................................... 80
C-1 中空纖維模組順流系統積分公式 .......................................... 81
C-2 中空纖維模組逆流系統積分公式 .......................................... 84
附錄D 展開係數求解過程 ....................................................................... 86
D-1 中空纖維模組順流展開系數 .................................................. 92
D-2 中空纖維模組逆流展開系數 .................................................. 95
附錄E 平均濃度 ....................................................................................... 98
E-1中空纖維模組順流系統平均濃度 ............................................ 99
E-2 中空纖維模組逆流系統平均濃度 ......................................... 100

圖 目 錄
圖3.1 空纖維型順流式氣-液薄膜接觸器。 ........................................... 23
圖3.2 在薄膜接觸器內不同位置，CO2於氣、液兩相中之濃度分佈圖。( Gza = 0.0941，Gzb = 400 ) ........................................................... 24
圖3.3 中空纖維型-順流式薄膜接觸器於不同Gza下，CO2於氣、液 兩相中之平均濃度變化情形。 ( Gza = 0.0627 ) ............................. 25
圖3.4 局部謝塢數於中空纖維型-順流式薄膜接觸器中之變化情形。 ( Gza = 0.0627 ) ............................................................................... 26
圖3.5 於不同Gza下，平均謝塢數與Gzb之關係。 .............................. 27
圖3.6 不同Gza下，Gzb與吸收效率之關係。 ....................................... 28
圖4.1 中空纖維型逆流式氣-液薄膜接觸器。 ....................................... 39
圖4.2 在薄膜接觸器內不同位置，CO2於氣、液兩相中之濃度分佈圖。 ( Gza = 0.0627，Gzb = 400 ) ........................................................... 40
圖4.3中空纖維型-逆流式薄膜接觸器於不同bGz下，CO2於氣、液兩相中之平均濃度變化情形。 ( Gza = 0.0627 ) ................................. 41
圖4.4 局部謝塢數於中空纖維型-逆流式薄膜接觸器中之變化情形。( Gza = 0.0627 ) ............................................................................... 42
圖4.5 於不同之Gza下，順流系統與逆流系統之平均謝塢數與液相流
率之關係。 ..................................................................................... 43

圖4.6 於不同之Gza下，順流系統與逆流系統之吸收效率與bGz之關係。 ................................................................................................. 44
圖5.1 中空纖維型順流式薄膜氣體吸收實驗裝置圖 ............................. 53
圖5.2 中空纖維模組順流系統中，理論與實驗之液相出口平均濃度與液相流率之關係。 ......................................................................... 54
圖5.3 中空纖維模組順流系統中，理論與實驗之二氧化碳吸收速率與液相流率之關係。 ( Qa = 3 cm3/s ).............................................. 55
圖5.4 中空纖維型逆流式薄膜氣體吸收實驗裝置圖 ............................. 56
圖5.5中空纖維模組順流與逆流系統中，理論與實驗之液相出口平均濃度與液相流率之關係。 ( Qa = 3 cm3/s ) ..................................... 57
圖5.6 中空纖維模組逆流系統中，理論與實驗之二氧化碳吸收速率與液相流率之關係。 ( Qa = 2 cm3/s ).............................................. 58
圖6.1 中空纖維型薄膜氣-液接觸器內，氣體溶質於氣、液兩相中的無因次濃度分佈求解流程圖。......................................................... 61
圖A.1 套管型氣-液薄膜接觸器。........................................................... 70
圖A.2套管型薄膜氣-液接觸器內，氣體溶質於氣、液兩相中的無因次濃度分佈求解流程圖。 ................................................................. 73

表 目 錄
表3.1 中空纖維型順流式氣-液薄膜接觸器特徵值數目對無因次平均出口濃度之比較。( Qa = 3 cm3/s，Qb = 6 cm3/s ) ..................... 29
表4.1 中空纖維型順流式氣-液薄膜接觸器特徵值數目對無因次平均出口濃度之比較。( Qa = 2 cm3/s，Qb = 8 cm3/s ) ..................... 45
表4.2 中空纖維順流系統於不同氣、液流率下之特徵值。 .............. 46
表4.3 中空纖維逆流系統於不同氣、液流率下之特徵值。 .............. 46
表4.4 不同氣、液流率下，中空纖維模組順流系統與逆流系吸收效效率之比較。 .................................................................................. 47
表5.1 實驗值與理論值之平均誤差 ...................................................... 59

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