本篇論文主要在探討逆流型透析器中伴隨超過濾或回流以提高質量傳送之操作。在理論的推導過程中為了數學上的簡便我們假設超過濾通量並未隨著質量傳送而遞減。由本次研究結果可知在透析伴隨超過濾情況下對於質量傳送速率會有明顯地的提升，值得一提的是當溶質質傳係數較小時，增加超過濾操作會大量提高質量傳送速率。由進料體積流率來看，提高透餘相的體積流率會比提高透析相的體積流率還要更好。最後我們發現提高超過濾通量以及進料體積流率可使溶質與溶劑分離效率更佳的良好。由於數學推導過程的假設，其研究結果可能僅適用於輕微的濃度極化現象及輕微的透膜壓差遞減之情形。
    在逆流型交流式透析器伴隨內回流操作中，我們假設流體於通道橫切面的速度和溶質濃度為均一。由本次研究結果可知在透析伴隨內回流情況下對於質量傳送速率也會有明顯地的提升。也因為多了回流裝置使得溶質進料體積流率會比無回流裝置的進料體積流率還大，如此一來便可降低裝置內的質傳阻力。由整理出的圖表可看出提高回流比與提高進料體積流率和進料濃度可大幅增加質傳效率。

The effect of application of either ultrafiltration or recycle operation to dialysis in countercurrently rectangular membrane modules was investigated. For the dialysis coupled with the application of ultrafiltration operation in a countercurrrently parallel-flow device, the assumption of uniform ultrafiltration flux was made for operation with slight concentration polarization and declination of transmembrane pressure. Considerable improvement in mass transfer is achievable if the operation of ultrafiltration is applied, especially for the system with low mass transfer coefficient. The enhancement in separation efficiency is significantly increased with increasing ultrafiltration flux, as well as with increasing the volumetric flow rates. Furthermore, increasing the volumetric flow rate in retentate phases is more beneficial to mass transfer than increasing in dialysate phase. 
  For dialysis with internal recycling operation in countercurrently cross-flow device, the uniform velocities and concentrations in the cross sections of flow channels were assumed. In contrast to a device without reflux, considerable mass transfer is achievable if the dialyzers are operated with internal recycling, which provides an increase in fluid velocity, resulting in a reduction of mass-transfer resistance. The improvement increases with reflux ratio, especially for large flow rate and feed concentration.

中文摘要	I
英文摘要	II
目錄	IV
圖目錄	VII
表目錄	IX
第一章 緒論	1
  1-1	 前言	1
  1-2	 薄膜分離之驅動力	2
  1-3	 薄膜透析應用	4
  1-4	 研究目的	6
第二章 文獻回顧	7
第三章 理論分析	10
  3-1	 質量傳送係數	12
  3-2	 單行程逆流型並流式平板薄膜透析伴隨超過濾系統	15
3-2-1	濃度分佈	16
3-2-2	總質量傳送速率	22
3-2-3	超過濾分離效率	23
  3-3	 雙行程逆流型交流式平板薄膜透析伴隨內回流系統	24
3-3-1	質量傳送速率	25
3-3-2	透餘相及透析相之平均濃度	29
3-3-3	透餘相及透析相之平均濃度差	32
3-3-4	透餘相出口濃度	34
3-3-5	質量傳送係數	36
3-3-6	無回流系統之質量傳送速率	37
3-3-7	透析伴隨內回流系統所提升的分離效率	39
第四章 範例計算	40
  4-1	 單行程逆流型並流式平板薄膜透析伴隨超過濾之計算	40
  4-2	 雙行程逆流型交流式平板薄膜透析伴隨內回流之計算	41
第五章 結果與討論	42
  5-1	 透析伴隨超過濾之透餘相溶質出口濃度	42
  5-2	 透析伴隨超過濾之總質量傳送速率	43
  5-3	 透析伴隨超過濾之藉由超過濾所提升的分離效率	44
  5-4	 透析伴隨內回流之效應	45
第六章 結論	69
  6-1	 單行程逆流型並流式平板薄膜透析伴隨超過濾之總結	69
  6-2	 雙行程逆流型交流式平板薄膜透析伴隨內回流之總結	70
符號說明	71
參考文獻	74

圖目錄
圖1 影響薄膜分離程序之因素及其應用範圍	3
圖2 薄膜透析質量傳送方向	11
圖3 薄膜透析濃度分佈示意圖	11
圖4 單行程逆流型並流式平板薄膜透析伴隨超過濾之系統	15
圖5 雙行程逆流型交流式平板薄膜透析伴隨內回流之系統	24
圖6 雙行程逆流型交流式平板薄膜透析伴隨內回流系統俯視圖	26
圖7 單行程逆流型交流式平板薄膜透析系統俯視圖	38
圖8 總質量傳送速率對透餘相體積流率作圖 (Qb,i=2×10-6 m3/s, Ca,i=0.5 kg/m3, Cb,i=0)	46
圖9 總質量傳送速率對透餘相體積流率作圖 (Qb,i=4×10-6 m3/s, Ca,i=0.5 kg/m3, Cb,i=0)	47
圖10 總質量傳送速率對透餘相體積流率作圖 (Qb,i=6×10-6 m3/s, Ca,i=0.5 kg/m3, Cb,i=0)	48
圖11 總質量傳送速率對透餘相體積流率作圖 (Qb,i=8×10-6 m3/s, Ca,i=0.5 kg/m3, Cb,i=0)	49
圖12 透析提高率對透餘相體積流率作圖 (Qb,i=2×10-6 m3/s, Ca,i=0.5 kg/m3, Cb,i=0)	50
圖13 透析提高率對透餘相體積流率作圖 (Qb,i=4×10-6 m3/s, Ca,i=0.5 kg/m3, Cb,i=0)	51
圖14 透析提高率對透餘相體積流率作圖 (Qb,i=6×10-6 m3/s, Ca,i=0.5 kg/m3, Cb,i=0)	52
圖15 透析提高率對透餘相體積流率作圖 (Qb,i=8×10-6 m3/s, Ca,i=0.5 kg/m3, Cb,i=0)	53
圖16 總質量傳送速率對回流比作圖 (Qb,i=1×10-7 m3/s, Ca,i=1 kgmol/m3, Cb,i=0)	60
圖17 總質量傳送速率對回流比作圖 (Qb,i=5×10-7 m3/s, Ca,i=1 kgmol/m3, Cb,i=0)	61
圖18 總質量傳送速率對回流比作圖 (Qb,i=1×10-6 m3/s, Ca,i=1 kgmol/m3, Cb,i=0)	62
圖19 總質量傳送速率對回流比作圖 (Qb,i=1×10-7 m3/s, Ca,i=5 kgmol /m3, Cb,i=0)	63
圖20 總質量傳送速率對回流比作圖 (Qb,i=5×10-7 m3/s, Ca,i=5 kgmol /m3, Cb,i=0)	64
圖21 總質量傳送速率對回流比作圖 (Qb,i=1×10-6 m3/s, Ca,i=5 kgmol/m3, Cb,i=0)	65
圖22 透析提升率對回流比作圖 (Ca,i=1 kgmol/m3, Cb,i=0)	66

表目錄
表1 用於人工腎臟的透析薄膜	5
表2 透析伴隨超過濾之提升率 (Ca,i=0.5 kg/m3, Cb,i=0, Qb,i=2×10-6 m3/s)	54
表3 透析伴隨超過濾之提升率 (Ca,i=0.5 kg/m3, Cb,i=0, Qb,i=4×10-6 m3/s)	55
表4 透析伴隨超過濾之提升率 (Ca,i=0.5 kg/m3, Cb,i=0, Qb,i=8×10-6 m3/s)	56
表5 透析伴隨超過濾之提升率 (Ca,i=1 kg/m3, Cb,i=0, Qb,i=2×10-6 m3/s)	57
表6 透析伴隨超過濾之提升率 (Ca,i=1 kg/m3, Cb,i=0, Qb,i=4×10-6 m3/s)	58
表7 透析伴隨超過濾之提升率 (Ca,i=1 kg/m3, Cb,i=0, Qb,i=8×10-6 m3/s)	59
表8 透析伴隨內回流之提升率 (Ca,i=1 kgmol/m3, Cb,i=0)	67
表9 透析伴隨內回流之提升率 (Ca,i=5 kgmol/m3, Cb,i=0)	68

1.	Cheryan M., (1998), “Ultrafiltration and Microfiltration,” Handbook, Technomic, 245.
2.	Blatt W.F., A. Dravid, A.S. Michaels and L. Nelson, (1970), “Solute Polarization and Cake Formation in Membrane Ultrafiltration: Causes, Consequences, and Control Techniques,” in Membrane Science and Technique, J. E. Flinn ed., Plenum Press, New York.
3.	Grimsurd, L. and Babb, A.L., (1966), “Velocity and concentration profiles for laminar flow of Newtonian fluid in a dialyzer,” Chem. Eng. Prog. Symp. Ser., 62, 20.
4.	Cooney, D.O., Kim, S.S. and Davis, E.J., (1974), “Analysis of mass transfer in hemodialyzers for laminar blood flow and homogeneous dialysate,” Chem. Eng. Sci., 29, 1731.
5.	Lipps, Ben J., Stewart, Richard D., Perkins, Herbert A., Holmes, George W., McLain, Earl A., Rolfs, Mary R., Oja, Phyllis D., (1967), “The Hollow Fiber Artificial Kidney,” Trans. Amer. Soc. Artif, Intern. Organs., 13, 200.
6.	Colton C.K., Henderson L.W., Ford C.A., Lysaght M.J., (1975), “Kinetics of hemodiafiltration. I. In vitro transport characteristics of a hollow-fiber blood ultrafilter,” J. Lab. Clin. Med., 85, 355.
7.	Heinz D. Papenfuss, Joseph F. Gross, Steven T. Thorson, (1979), “An analytical study of ultrafiltration in a hollow fiber artificial kidney,” AIChE J., 25, 170.
8.	Gostoli, C. and Gatta, A., (1980), “Mass transfer in a hollow fiber dialyzer,” J. Membr. Sci. 6, 133.
9.	Popovich, R.P., Christopher, T.G., and Babb, A. L., (1971), “The effect of membrane diffusion and ultrafiltration properties on hemodialyzer design and performance,” Chem. Eng. Prog. Symp. Ser., 67, 105.
10.	Jagannathan, R. and Shettigar, U.R., (1977), “Analysis of a tubular hemodialyzer-effect of ultrafiltration and dialysate concentration,” Med. Biol. Eng. Comput., 15, 134.
11.	Park J.K. and Chang H.N., (1986), “Flow distribution in the fiber lumen side of a hollow-fiber module,” AIChE. J., 32 1937.
12.	Masataka Tanigaki, Tetsuo Shiode, Shinsuke Okumi and Wataru Eguchi, (1975), “Facilitated Transport of Zinc Chloride Through Hollow Fiber Supported Liquid Membrane. Part 3. Module Operation,” Sep. Sci., 30, 877.
13.	Bruining, W. J., (1989), “A General Description of Flows and Pressures in Hollow Fiber Membrane Modules,” Chem. Eng. Sci., 44, 1441.
14.	Tharakan John P. and Pao C. Chau, (1986), “Operation and Pressure Distribution of Immobilized Cell Hollow Fiber Bioreactors,” Bioeng., 28, 1064.
15.	Yang, M.C. and Cussler E.L., (1989), “Artificial gill”, J. Membr. Sci, 42, 273.
16.	Yang, M.C. and Cussler E.L., (1986), “Design Hollow-Fiber contactors,” AIChE. J., 32, 1910.
17.	Sherwood, T., P. Brian, R. Fisher, and L. Dresner, (1965), “Salt Concentration at Phase Boundaries in Desalination by Reverse Osmosis,” Ind. Eng. Chem. Fundamentals, 4, 113.
18.	Evangelista F., (1988), “An Improved Analytical Method for the Design of Spiral-wound Modules,” Chem. Eng. J., 38, 33.
19.	Costanzo, M.R., Saltzberg, M., O'Sullivan, J., and Sobotka, P., (2005), “Early ultrafiltration in patients with decompensated heart failure and diuretic resistance,” J. Am. Coll. Cardiol., 46, 2047.
20.	Costanzo, M.R., Guglin, M.E., Saltzberg, M.T., Jessup, M.L., Bart, B.A., Teerlink, J.R., Jaski, B.E., Fang, J.C., Feller, E.D., Haas, G.J., Anderson, A.S., Schollmeyer, M.P. and Sobotka, P.A., (2007), “Ultrafiltration versus intravenous diuretics for patients hospitalized for acute decompensated heart failure,” J. Am. Coll. Cardiol., 49, 675.
21.	Bourge, R.C. and Tallaj, J.A., (2005), “A new approach toward mechanical diuresis in heart failure,” J. Am. Coll. Cardiol., 46, 2052.
22.	Kazory, A. and Ross, E.A., (2008), “Contemporary trends in the pharmacological and extracorporeal management of heart failure: a nephrologic perspective,” Circulation, 117, 975.
23.	Yeh, H.M., Cheng, T.W. and Chen, Y.J., (2000), “Mass transfer for dialysis with ultrafiltration flux declined in cross-flow membrane modules,” J. Chem. Eng. Jpn., 33, 440.
24.	Yeh, H.M. and Chang, Y.H., (2005), “Mass transfer for dialysis through parallel-flow double-pass rectangular membrane modules,” J. Membr. Sci., 260, 1.
25.	Yeh, H.M., (2009), “Numerical analysis of mass transfer in double-pass parallel-plate dialyzers with external recycle,” Comput. Chem. Eng., 33, 815.
26.	Yeh, H.M., (2009), “Analysis of dialysis in cross-flow parallel-plate membrane modules with feed-stream recycle for improved performance,” Chem. Eng. Comm., 179, 445.
27.	Yeh, H.M., (2010), “Dialysis in countercurrent-flow rectangular membrane modules with external reflux for improved performance,” Membrane Water Treatment, 1(2), 159.
28.	Yeh, H.M. (2011), “Mass transfer in cross-flow parallel-plate dialyzer with internal recycle for improved performance,” Chem. Eng. Comm., 198, 1366.
29.	Yeh, H.M. (2011), “Effect of external recycle on mass transfer in countercurrent double-pass cross-flow rectangular dialyzers,” Sep. Sci. Technol., 46, 1068.
30.	Yeh, H.M., (2011), “Dialysis in double-pass cross-flow rectangular membrane modules with external recycle for improved performance,” Membrane Water Treatment, 2(2), 75.
31.	Kiani, A., Bhave, R.R., Sirkar, KK., (1984), “Solvent extraction with immobilized interfaces in a microporous hydrophobic membrane,” J. Membr. Sci., 20, 125.
32.	Porter, M.C., (1990), “Handbook of Industrial Membrane Technology,” Noyes Publications, New Jersey, 175, 1.
33.	Yeh, H.M. and Chen, Y. K., (2000), “Membrane Extraction through Cross-Flow Rectangular Modules,” J. Membr. Sci., 170, 235.
34.	Kunitomo, T., Kirkwood, R.G., Kumazawa, S., Lazarus, J.M., Gottlieb, M.N. and Lowrie, E.G., (1978), “Clinical evaluation of postdilution dialysis with a combined ultrafiltration hemodialysis system,” Trans. Am. Soc. Artif. Intern. Organs., 24, 169.
35.	Sakai, K. and Mineshima, M., (1984), “Performance evaluation of a module in artificial kidney system,” J. Chem. Eng. Jpn., 17, 198.
36.	Yeh, H.M., (2006), “Effect of Reflux and Reflux-Barrier Location on Solvent Extraction through Cross-Flow Flat-Plate Membrane Modules with Internal Reflux,” J. Membr. Sci., 269, 133.