在本研究中，使用Clostridium tyrobutyricum的批式醱酵實驗數據，建立非結構化的數學模型來描述細胞生長、產物生成與基質消耗。利用不同基質起始濃度醱酵的實驗數據與模型預測結果，以最小化殘餘誤差加權平方總和(Sun of the Square of Weighted Residues)的方法，來估測模型的所有參數。基於此模型，以產率與生產力最大化為目標，搜尋反應器操作模式與操作變數最適化問題。研究結果，反應器操作模式最適化為連續式模式。決定反應器模式後，針對操作變數進行最適化研究，其中操作變數則包含稀釋速率、醱酵槽分流比、進料流率比、醱酵槽體積比與基質進料濃度。在參數估計與最適化問題研究皆利用基因演算法(Genetic Algorithm)進行搜尋。

In this study, we constructed unstructured models to describe the kinetic of cell growth, product formation, and substrate consumption in the batch fermentation of Clostridium tyrobutyricum. All the parameters in the models were estimated by minimizing the sun of the square of weighted residues (SSWR) between the predictions of the models and the experimental data obtained from batch fermentation with different initial substrate concentrations. Based on this models, the optimal problem of bioreactor operation and operation variable were analyzed by maximizing the yield and productivity. The optimal model of the bioreactor operation is the continuous. The operation variables include the dilution rate, the bleed ratio, the feed flow ratio, the volume ratio, and the feed substrate concentration. The parameter estimation and the optimization problem were determined by Genetic Algorithm (GA).

[中文]
[1] 詹明峰，「生物系統建模、最適化與控制設計」，博士論文，國立台灣科技大學，台北(2012)。
[2] 林勳棟，「整合醱酵與分離程序的最適化設計研究」，博士論文，國立中正大學，嘉義(2008)。
[3] 許智凱，「研發乳酸連續醱酵製成」，碩士論文，國立台灣科技大學，台北(2010)
[英文]
[1] Aiba S., Shoda M., Nagatani M., Haldane J.B.S. Kinetics of product inhibition in alcohol fermentation. Biotechnology and Bioengineering 1968;X:845-864.
[2] Alam S., Stevens D., Bajpai R. Production of butyric acid by batch fermentation of cheese whey with Clostridium beijerinckii. Journal of Industrial Microbiology 1987;2:359-364.
[3] Andrews J.F. A mathematical model for the continuous culture of microorganisms utilizing inhibitory substrates. Biotechnology and Bioengineering 1968;X:707-723.
[4] Boonmee M., Leksawasdi N., Bridge W., Rogers P.L. Batch and continuous culture of Lactococcus lactis NZ133: Experimental data and model development. Biochemical Engineering Journal 2003;14:127-135.
[5] Bouguettoucha A., Balannec B., Amrane A. Unstructured models for lactic acid fermentation - a review. Food Technology and Biotechnology 2011;49:3-12.
[6] Canganella F., Wiegel J. Continuous cultivation of Clostridium thermobutyricum in a rotary fermentor system. Journal of Industrial Microbiology and Biotechnology 2000;24:7-13.
[7] Cascone R. Biobutanol - A replacement for bioethanol? Chemical Engineering Progress 2008;104:S4-S9.
[8] Dette H., Melas V.B., Pepelyshev A., Strigul N. Efficient design of experiments in the Monod model. Journal of the Royal Statistical Society. Series B: Statistical Methodology 2003;65:725-742.
[9] Dwidar M., Park J.Y., Mitchell R.J., Sang B.I. The future of butyric acid in industry. The Scientific World Journal 2012.
[10] Fayolle F., Marchal R., Ballerini D. Effect of controlled substrate feeding on butyric acid production by Clostridium tyrobutyricum. Journal of Industrial Microbiology 1990;6:179-183.
[11] Ge X.M., Bai F.W. Intrinsic kinetics of continuous growth and ethanol production of a flocculating fusant yeast strain SPSC01. Journal of Biotechnology 2006;124:363-372.
[12] Haldane J.B.S. Enzymes. MIT Press. Cambridge, 1965.
[13] Han K., Levenspiel O. Extended Monod kinetics for substrate, product, and cell inhibition. Biotechnology and Bioengineering 1988;32:430-437.
[14] He G.Q., Kong Q., Chen Q.H., Ruan H. Batch and fed-batch production of butyric acid by Clostridium butyricum ZJUCB. Journal of Zhejiang University: Science 2005;6 B:1076-1080.
[15] Huang J., Cai J., Wang J., Zhu X., Huang L., Yang S.T., Xu Z. Efficient production of butyric acid from Jerusalem artichoke by immobilized Clostridium tyrobutyricum in a fibrous-bed bioreactor. Bioresource Technology 2011;102:3923-3926.
[16] Jo J.H., Lee D.S., Kim J., Park J.M. Effect of initial glucose concentrations on carbon and energy balances in hydrogen-producing Clostridium tyrobutyricum JM1. Journal of Microbiology and Biotechnology 2009;19:291-298.
[17] Kong Q., He G.Q., Chen F., Ruan H. Studies on a kinetic model for butyric acid bioproduction by Clostridium butyricum. Letters in Applied Microbiology 2006;43:71-77.
[18] Kumar S., Dheeran P., Singh S.P., Mishra I.M., Adhikari D.K. Kinetic studies of ethanol fermentation using Kluyveromyces sp. IIPE453. Journal of Chemical Technology and Biotechnology 2013;88:1874-1884.
[19] Levenspiel O. The Monod equation: a revisit and a generalization to product inhibition situations. Biotechnology and Bioengineering 1980;22:1671-1687.
[20] Lobry J.R., Flandrois J.P., Carret G., Pave A. Monod's bacterial growth model revisited. Bulletin of Mathematical Biology 1992;54:117-122.
[21] Luedekingt R., Piret E.L. A kinetic study of the lactic acid fermentation. Batch process at controlled pH. Biotechnology and Bioengineering 2000;67:642-644.
[22] Mandli A.R., Modak J.M. Evolutionary algorithm for the determination of optimal mode of bioreactor operation. Industrial and Engineering Chemistry Research 2012;51:1796-1808.
[23] Michel-Savin D., Marchal R., Vandecasteele J.P. Butyrate production in continuous culture of Clostridium tyrobutyricum: Effect of end-product inhibition. Applied Microbiology and Biotechnology 1990a;33:127-131.
[24] Michel-Savin D., Marchal R., Vandecasteele J.P. Butyric fermentation: Metabolic behaviour and production performance of Clostridium tyrobutyricum in a continuous culture with cell recycle. Applied Microbiology and Biotechnology 1990b;34:172-177.
[25] Michel-Savin D., Marchal R., Vandecasteele J.P. Control of the selectivity of butyric acid production and improvement of fermentation performance with Clostridium tyrobutyricum. Applied Microbiology and Biotechnology 1990c;32:387-392.
[26] Mitchell R.J., Kim J.S., Jeon B.S., Sang B.I. Continuous hydrogen and butyric acid fermentation by immobilized Clostridium tyrobutyricum ATCC 25755: Effects of the glucose concentration and hydraulic retention time. Bioresource Technology 2009;100:5352-5355.
[27] Modak J.M., Lim H.C. Optimal mode of operation of bioreactor for fermentation processes. Chemical Engineering Science 1992;47:3869-3884.
[28] Patel G.B., Agnew B.J. Growth and butyric acid production by Clostridium pupuleti. Archives of Microbiology 1988;150:267-271.
[29] Phisalaphong M., Srirattana N., Tanthapanichakoon W. Mathematical modeling to investigate temperature effect on kinetic parameters of ethanol fermentation. Biochemical Engineering Journal 2006;28:36-43.
[30] Sarkar D., Modak J.M. Optimisation of fed-batch bioreactors using genetic algorithms. Chemical Engineering Science 2003;58:2283-2296.
[31] Song H., Eom M.H., Lee S., Lee J., Cho J.H., Seung D. Modeling of batch experimental kinetics and application to fed-batch fermentation of Clostridium tyrobutyricum for enhanced butyric acid production. Biochemical Engineering Journal 2010;53:71-76.
[32] Song H., Jang S.H., Park J.M., Lee S.Y. Modeling of batch fermentation kinetics for succinic acid production by Mannheimia succiniciproducens. Biochemical Engineering Journal 2008;40:107-115.
[33] Van Den Heuvel J.C., Beeftink H.H. Kinetic effects of simultaneous inhibition by substrate and product. Biotechnology and Bioengineering 1988;31:718-724.
[34] Zhang C., Yang H., Yang F., Ma Y. Current progress on butyric acid production by fermentation. Current Microbiology 2009;59:656-663.
[35] Zigova J., SturdIk E. Advances in biotechnological production of butyric acid. Journal of Industrial Microbiology and Biotechnology 2000;24:153-160.
[36] Zigova J., SturdIk E., Vandak D., Schlosser S. Butyric acid production by Clostridium butyricum with integrated extraction and pertraction. Process Biochemistry 1999;34:835-843.