本論文主要推導在薄膜透析器中伴隨著非均勻濾速之超過濾質量傳送分析。透析伴隨超過濾於並流式之矩形透析器的研究是基於假設通道中均勻的流速和濃度所做出的質量平衡。考量到過程中濃度極化現象的增加與透膜壓差的遞減效應，並為了更加接近與符合實際的物理現象，我們不再假設均勻的超過濾通量，而是一隨距離增加而遞減的指數函數。在本研究的結果數據與圖表中可發現，提高超過濾通量以及進料體積流率可使溶質與溶劑的分離更加良好，也使得分離效率有著顯著的提升。此外，對於質量傳送而言，增加透餘相中的體積流率會比增加透析相的體積流率來的更有效益。而在透析系統中導入超過濾對於分離效率是有著顯著的成效的，特別是對於有著低質量傳送係數的系統。

Dialysis coupled with ultrafiltration in parallel-flow rectangular membrane modules was investigated, based on mass balances with the assumption of uniform velocity and concentration within the cross sections of flow channels. The declination of ultrafiltration flux along the membrane module due to the increase of concentration polarization and the declination of transmembrane pressure, is also taken into consideration. Considerable improvement in separation efficiency is achievable if the effect 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.

目錄
誌   謝	I
中文摘要	II
英文摘要	III
目錄	IV
圖目錄	VI
表目錄	X
第一章  緒論	1
1.1 前言	1
1.2 薄膜分離的驅動力	2
1.3 研究動機與目的	3
第二章 文獻回顧	5
第三章  薄膜透析器合併超過濾操作之理論分析	8
3.1 順流式平板型薄膜透析器	8
3.1.1 濃度分佈	8
3.1 2總質量傳送速率	13
3.1.3 超過濾效應所提昇分離效率	14
3.2 逆流式平板型薄膜透析器	15
3.2.1 濃度分佈	15
3.2.2總質量傳送速率	20
3.2.3 超過濾效應所提昇的分離效率	23
第四章 結果與討論	24
4.1 範例計算	24
4.2 順流平板型薄膜透析器伴隨超過濾濾速遞減效應之影響	25
4.2.1 透餘相之出口濃度	25
4.2.2 質量傳送速率	26
4.2.3 超過濾效應所提昇的分離效率	26
4.3 逆流平板型薄膜透析器伴隨超過濾濾速遞減效應之影響	46
4.3.1 透餘相之出口濃度	46
4.3.2 質量傳送速率	46
4.3.3 超過濾效應所提昇的分離效率	47
4.4 順流型與逆流型薄膜透析器之比較	58
第五章 結論	75
符號說明	77
參考文獻	79




圖目錄
圖 1順流式平板型薄膜透析伴隨超過濾系統	9
圖 2逆流式平板型薄膜透析伴隨超過濾系統	16
圖 3順流透析器之總質量傳送速率對透餘相體積流率作圖(Qd,i=2×10^-6 m3/s,CB,i=0.5 kg/m3,CD,i=0,f=0.5)	28
圖 4順流透析器之總質量傳送速率對透餘相體積流率作圖(Qd,i=2×10^-6 m3/s,CB,i=0.5 kg/m3,CD,i=0,f=1.0)	29
圖 5順流透析器之總質量傳送速率對透餘相體積流率作圖(Qd,i=4×10^-6 m3/s,CB,i=0.5 kg/m3,CD,i=0,f=0.5)	30
圖 6順流透析器之總質量傳送速率對透餘相體積流率作圖(Qd,i=4×10^-6 m3/s,CB,i=0.5 kg/m3,CD,i=0,f=1.0)	31
圖 7順流透析器之總質量傳送速率對透餘相體積流率作圖(Qd,i=8×10^-6 m3/s,CB,i=0.5 kg/m3,CD,i=0,f=0.5)	32
圖 8順流透析器之總質量傳送速率對透餘相體積流率作圖(Qd,i=8×10^-6 m3/s,CB,i=0.5 kg/m3,CD,i=0,f=0.5)	33
圖 9順流透析器之超過濾效應所提昇的分離效率對透餘相體積流率作圖(Qd,i=2×10^-6 m3/s,CB,i=0.5 kg/m3,CD,i=0,f=0.5)	34
圖 10順流透析器之超過濾效應所提昇的分離效率對透餘相體積流率作圖(Qd,i=2×10^-6 m3/s,CB,i=0.5 kg/m3,CD,i=0,f=1.0)	35
圖 11順流透析器之超過濾效應所提昇的分離效率對透餘相體積流率作圖(Qd,i=4×10^-6 m3/s,CB,i=0.5 kg/m3,CD,i=0,f=0.5)	36
圖 12順流透析器之超過濾效應所提昇的分離效率對透餘相體積流率作圖(Qd,i=4×10^-6 m3/s,CB,i=0.5 kg/m3,CD,i=0,f=1.0)	37
圖 13順流透析器之超過濾效應所提昇的分離效率對透餘相體積流率作圖(Qd,i=8×10^-6 m3/s,CB,i=0.5 kg/m3,CD,i=0,f=0.5)	38
圖 14順流透析器之超過濾效應所提昇的分離效率對透餘相體積流率作圖(Qd,i=8×10^-6 m3/s,CB,i=0.5 kg/m3,CD,i=0,f=1.0)	39
圖 15逆流透析器之總質量傳送速率對透餘相體積流率作圖(Qd,i=2×10^-6 m3/s,CB,i=0.5 kg/m3,CD,i=0,f=0.5)	48
圖 16逆流透析器之總質量傳送速率對透餘相體積流率作圖(Qd,i=2×10^-6 m3/s,CB,i=0.5 kg/m3,CD,i=0,f=1.0)	49
圖 17逆流透析器之總質量傳送速率對透餘相體積流率作圖(Qd,i=8×10^-6 m3/s,CB,i=0.5 kg/m3,CD,i=0,f=0.5)	50
圖 18逆流透析器之總質量傳送速率對透餘相體積流率作圖(Qd,i=8×10^-6 m3/s,CB,i=0.5 kg/m3,CD,i=0,f=1.0)	51
圖 19逆流透析器之超過濾效應所提昇的分離效率對透餘相體積流率作圖(Qd,i=2×10^-6 m3/s,CB,i=0.5 kg/m3,CD,i=0,f=0.5)	52
圖 20逆流透析器之超過濾效應所提昇的分離效率對透餘相體積流率作圖(Qd,i=2×10^-6 m3/s,CB,i=0.5 kg/m3,CD,i=0,f=1.0)	53
圖 21逆流透析器之超過濾效應所提昇的分離效率對透餘相體積流率作圖(Qd,i=8×10^-6 m3/s,CB,i=0.5 kg/m3,CD,i=0,f=0.5)	54
圖 22逆流透析器之超過濾效應所提昇的分離效率對透餘相體積流率作圖(Qd,i=8×10^-6 m3/s,CB,i=0.5 kg/m3,CD,i=0,f=1.0)	55
圖 23順流與逆流透析器在θ = 1.0之總質量傳送速率比較圖(Qd,i=2×10^-6 m3/s,CB,i=0.5 kg/m3,CD,i=0,f=0.5)	59
圖 24順流與逆流透析器在θ = 1.0之總質量傳送速率比較圖(Qd,i=2×10^-6 m3/s,CB,i=0.5 kg/m3,CD,i=0,f=1.0)	60
圖 25順流與逆流透析器在θ = 1.0之總質量傳送速率比較圖(Qd,i=8×10^-6 m3/s,CB,i=0.5 kg/m3,CD,i=0,f=0.5)	61
圖 26順流與逆流透析器在θ = 1.0之總質量傳送速率比較圖(Qd,i=8×10^-6 m3/s,CB,i=0.5 kg/m3,CD,i=0,f=1.0)	62
圖 27順流與逆流透析器在θ = 0.61之總質量傳送速率比較圖(Qd,i=2×10^-6 m3/s,CB,i=0.5 kg/m3,CD,i=0,f=0.5)	63
圖 28順流與逆流透析器在θ = 0.61之總質量傳送速率比較圖(Qd,i=2×10^-6 m3/s,CB,i=0.5 kg/m3,CD,i=0,f=1.0)	64
圖 29順流與逆流透析器在θ = 0.61之總質量傳送速率比較圖(Qd,i=8×10^-6 m3/s,CB,i=0.5 kg/m3,CD,i=0,f=0.5)	65
圖 30順流與逆流透析器在θ = 0.61之總質量傳送速率比較圖(Qd,i=8×10^-6 m3/s,CB,i=0.5 kg/m3,CD,i=0,f=1.0)	66
圖 31順流與逆流透析器在θ = 1.0之分離效率提昇率比較圖(Qd,i=2×10^-6 m3/s,CB,i=0.5 kg/m3,CD,i=0,f=0.5)	67
圖 32順流與逆流透析器在θ = 1.0之分離效率提昇率比較圖(Qd,i=2×10^-6 m3/s,CB,i=0.5 kg/m3,CD,i=0,f=1.0)	68
圖 33順流與逆流透析器在θ = 1.0之分離效率提昇率比較圖(Qd,i=8×10^-6 m3/s,CB,i=0.5 kg/m3,CD,i=0,f=0.5)	69
圖 34順流與逆流透析器在θ = 1.0之分離效率提昇率比較圖(Qd,i=8×10^-6 m3/s,CB,i=0.5 kg/m3,CD,i=0,f=1.0)	70
圖 35順流與逆流透析器在θ = 0.61之分離效率提昇率比較圖(Qd,i=2×10^-6 m3/s,CB,i=0.5 kg/m3,CD,i=0,f=0.5)	71
圖 36順流與逆流透析器在θ = 0.61之分離效率提昇率比較圖(Qd,i=2×10^-6 m3/s,CB,i=0.5 kg/m3,CD,i=0,f=1.0)	72
圖 37順流與逆流透析器在θ = 0.61之分離效率提昇率比較圖(Qd,i=8×10^-6 m3/s,CB,i=0.5 kg/m3,CD,i=0,f=0.5)	73
圖 38順流與逆流透析器在θ = 0.61之分離效率提昇率比較圖(Qd,i=8×10^-6 m3/s,CB,i=0.5 kg/m3,CD,i=0,f=1.0)	74

表目錄
表 1順流透析器伴隨超過濾濾速遞減效應計算結果(Qd,i=2×10^-6 m3/s,CB,i=0.5 kg/m3,CD,i=0,f=0.5)	40
表 2順流透析器伴隨超過濾濾速遞減效應計算結果(Qd,i=2×10^-6 m3/s,CB,i=0.5 kg/m3,CD,i=0,f=1.0)	41
表 3順流透析器伴隨超過濾濾速遞減效應計算結果(Qd,i=4×10^-6 m3/s,CB,i=0.5 kg/m3,CD,i=0,f=0.5)	42
表 4順流透析器伴隨超過濾濾速遞減效應計算結果(Qd,i=4×10^-6 m3/s,CB,i=0.5 kg/m3,CD,i=0,f=1.0)	43
表 5順流透析器伴隨超過濾濾速遞減效應計算結果(Qd,i=8×10^-6 m3/s,CB,i=0.5 kg/m3,CD,i=0,f=0.5)	44
表 6順流透析器伴隨超過濾濾速遞減效應計算結果(Qd,i=8×10^-6 m3/s,CB,i=0.5 kg/m3,CD,i=0,f=1.0)	45
表 7逆流透析器伴隨超過濾濾速遞減效應計算結果(Qd,i=4×10^-6 m3/s,CB,i=0.5 kg/m3,CD,i=0,f=0.5)	56
表 8逆流透析器伴隨超過濾濾速遞減效應計算結果(Qd,i=4×10^-6 m3/s,CB,i=0.5 kg/m3,CD,i=0,f=1.0)	57

[1]	L. E. Applegate, “Membrane Separation Processes”, Chem. Eng., 91, 64 (1984).
[2]	P. M. Bungay, H. K. Lonsdale and M. N. De Pinho, “Synthetic Membrane: Science, Engineering and Applications,” D. Redel Publishing Company, Holland, 1986.
[3]	P. S. Kumar, J. A. Hogendoorn, P. H. M. Feron and G. F. Versteeg, “New Absorption Liquids for the Removal of CO2 from Dilute Gas Streams Using Membrane Contactors,” Chem. Eng. Sci., 57, 1639 (2002).
[4]	Y. S. Kim and S. M. Yang, “Absorption of Carbon Dioxide through Hollow Fiber Membranes Using Various Aqueous Absorbents,” Sep. Purif. Technol., 21, 101 (2000).
[5]	P. Lipp, M. Witte, G. Baldauf and A. A. Povorov, “Treatment of Reservoir Water with a Backwashable MF/UF Spiral Wound Membrane,” Desalination, 179, 83 (2005).
[6]	A. W. Zularisam, A. F. Ismail and R. Salim, “Behaviours of Natural Organic Matter in Membrane Filtration for Surface Water Treatment – a Review,” Desalination, 194, 211 (2006).
[7]	R. Parasad and K.K. Sirkar, “Hollow Fibers Solvent Extraction: Performances and Design”, J. Membr. Sci., 50, 153 (1990).
[8]	H. M. Yeh, Y. Y. Peng and Y. K. Chen, “Solvent Extraction through a Double-pass Parallel-plate Membrane Channel with Recycle”, J. Membr. Sci., 163, 177 (1999).
[9]	H. C. Van Der Horst and J. H. Hanemaaijer, “Cross-flow Microfiltration in the Food Industry. State of the Art”, Desalination, 77, 235 (1990).
[10]	R. P. Popovich, T. G. Christopher and A. L. Babb, “The Effects of Membrane Diffusion and Ultrafiltration Properties on Hemodialyer Design and Performance,” Chem. Eng. Prog. Symp. Ser., 67, 105 (1971).
[11]	H. Moonen and N. J. Niefind, “Alcohol Reduction in Beer by Means of Dialysis,” Desalination, 41, 327 (1982).
[12]	B. Dutre and G. Tragardh, “Purification of Gelatin by Ultrafiltration with a Forced Solvent Stream along the Membrane Permeate Side: An Experimental Approach,” J. Food Engr., 25, 233 (1995).
[13]	T. Kannamori and T. Shinbo, “Mass Transfer of a Solute by Diffusion with Convection around a Single Hollow-Fiber Membrane for Hemodialysis,” Desalination, 129, 217 (2000). 
[14]	R. Jagannathan and U. R. Shettigar, “Analysis of a Tubular Hemodialyser-Effect of Ultrafiltration and Dialysate Concentration,” Med. & Biol. & Comput., 15, 134 (1977).
[15]	A. Wupper, F. Dellanna, C. A. Baldamus and D. Woermann, “Local Transport Processes in High-Flux Hollow Fiber Dialyzers,” J. Membr. Sci. 131, 181 (1997).
[16]	L. Grimsurd and A. L. Babb, “Velocity and Concentration Profiles for Laminar Flow of a Newtonian Fluid in a Dialyzer,” Chem. Eng. Prog. Symp. Ser., 62, 20 (1966).
[17]	D. O. Cooney, S. S. Kim and E. J. Davis, “Analysis of Mass Transfer in Hemodialyzers of Laminar Blood Flow and Homogeneous Dialysate,” Chem. Eng. Sci., 29, 1731 (1974). 
[18]	R. P. Popovich, T. G. Christopher and A. L. Babb, “The Effects of Membrane Diffusion and Ultrafiltration Properties on Hemodialyer Design and Performance,” Chem. Eng. Prog. Symp. Ser., 67, 105 (1971).
[19]	Ben J. Lipps, Richard D. Stewart, Hebert A. Perkins, George W. Holmes, Earl A. McLain, Mary R. Rolfs, Phyllis D. Oja, “The Hollow Fiber Artificial Kidney,” Trans. Amer. Soc. Artif, Intern. Organs., 13, 200 (1967).
[20]	C. K. Colton, L. W. Henderson, C. A. Ford, M. J. Lysaght, “Kinetics of hemodiafiltration. I. In vitro transport characteristics of a hollow-fiber blood ultrafilter,” J. Lab. Clin. Med., 85, 355 (1975).
[21]	Heinz D. Papenfuss, Joseph F. Gross, Steven T. Thorson, “An Analytical Study of Ultrafiltration in a Hollow Fiber Artificial Kidney,” AICHE J., 25, 170 (1979).
[22]	C. Gostoli and A. Gatta, “Mass Transfer in a Hollow Fiber Dialyzer,” J. Membr. Sci., 6, 133 (1980).
[23]	M. Abbas, and V. P. Tyagi, “Analysis of a Hollow-Fiber Artificial Kidney Performing Simultaneous Dialysis and Ultrafiltration,” Chem. Eng. Sci., 42, 133 (1987).
[24]	M. Abbas, and V. P. Tyagi, “On the Mass Transfer in a Circular Conduit Dialyzer When Ultrafiltration is Coupled with Dialysis,” Int. J. Heat Mass Transfer, 31, 591 (1988).
[25]	V. Kumar and S. N. Upadhyay, “Computer Simulation of Membrane Process: Ultrafiltration and Dialysis Units,” Computers and Chem. Eng., 23, 1713(2000).
[26]	H. M. Yeh, T. W. Chen, and Y. J. Chen, “Mass Transfer for Dialysis with Ultrafiltration Flux Declined in Cross-Flow Membrane Modules”, J. Chem. Eng. Jpn., 33, 440 (2000).
[27]	Z. Liao, C.K. Poh, Z. Huang, P.A. Hardy, W.R. Clark and D. Gao, “A Numerical and Experimental Study of Mass Transfer in the Artificial Kidney,” Trans. ASME, 125, 472 (2003).
[28]	H. M. Yeh, T. W. Cheng and Y. C. Chen, “Analysis of Dialysis Coupled with Ultrafiltration in Cross-Flow Membrane Modules,” J. Membr. Sci., 134, 151 (1997).
[29]	A. S. Berman, “Laminar Flow in Channels with Porous Walls,” J. Applied Physics, 24, 1232 (1953).
[30]	S. W. Yuan, A. B. Finkelstein and N. Y. Brooklyn, “Laminar Pipe Flow with Injection and Suction through a Porous Wall,” Trans. ASME, 78, 719 (1956).
[31]	M. R. Costanzo, M. Saltzberg, J. O’Sullivan, and P. Sobotka, “Early Ultrafiltration in Patients with Decompensated Heart Failure and Diuretic Resistance,” J. Am. Coll. Cardiol., 46, 2047 (2005).
[32]	M. R. Costanzo, M. E. Guglin, M. T. Saltzberg, M. L. Jessup, B. A. Bart, J. R. Teerlink, B. E. Jaski, J. C. Fang, E. D. Feller, G. J. Haas, A. S. Anderson, M. P. Schollmeyer, and P. A. Sobotka, “Ultrafiltration Versus Intravenous Diuretics for Patients Hospitalized for Acute Decompensated Heart Failure,” J. Am. Coll. Cardiol., 49, 675 (2007).
[33]	R. C. Bourge, and J. A. Tallaj, “A New Approach Toward Mechanical Dieresis in Heart Failure,” J. Am. Coll. Cardiol., 46, 2052 (2005).
[34]	A. Kazory, and E. A. Ross, “Contemporary Trends in the Pharmacological and Extracorporeal Management of Heart Failure：A Nephrologic Perspective,” Circulation, 117, 975 (2008).
[35]	Yeh, H. M. and Chang, Y. H., “Mass transfer for dialysis through parallel-flow double-pass rectangular membrane modules,” J. Membr. Sci., 260, 1 (2005).
[36]	H. M. Yeh, T. W. Cheng, and Y. J. Chen, “Mass Transfer for Dialysis with Ultrafiltration Flux Declined in Cross-Flow Membrane Modules”, J. Chem. Eng. Jpn., 33, 440 (2000).
[37]	A. A. Kozinski, and E. N. Lighfoot, “Protein Ultrafiltration: A General Example of Boundary Layer Filtration,” AIChE. J., 19, 1030, (1972).
[38]	M. J. Clifton, N. Abidine, P. Aptel and V. Sanchez, “Growth of the Polarization Layer in Ultrafiltration with Hollow-Fiber Membranes,” J. Membr. Sci., 21, 233, (1984).
[39]	Kunimoto,T., Kirkwood, R.G., Kumazawa, S., Lazarus, J.M., Gottlieb, M.N. and Lowrie, E.G., “Clinical Evaluation of Postdilution Dialysis with Combined Ultrafiltration Hemodialysis System,” Trans. Am. Soc. Artif. Intern. Organs., 24, 169 (1978).
[40]	Sakai, K. and Mineshima, M., “Performance Evaluation of a Module in Artificial Kidney System,” J. Chem. Eng. Jpn., 17, 198 (1984).