基于渗流理论的生物膜传质模拟及实验研究
摘要
基质在生物膜内的质量传递过程是生物膜法污水处理技术的重要研究内容,是生物膜技术理论的本质和基础。随着科技的发展与理论的更新,这一领域被不断赋予新的研究内容。在前人研究成果的基础上,本文以生物膜多孔介质为研究对象,在生物膜传质模型中引入渗流理论,细化模型结构,通过数值模拟和实验研究的手段,对生物膜的传质过程进行了深入的研究,数值模拟结果与实验测试结果吻合较好。
本文主要内容包括：
1.将渗流理论引入生物膜内的质量传递过程,建立生物膜“对流-扩散-反应”模型。对生物膜模型进行分层处理,使模型物性参数更接近实际生物膜内的真实状态。采用Runge-Kutta法对传质模型进行数值求解,从而研究了不同进料液浓度和渗流速度,不同生物膜孔道弯曲因子和孔隙率条件下的生物膜内传质规律。结果表明：随着各参数值的逐渐增大,基质在生物膜内的渗透深度逐渐增加；进水浓度、生物膜孔隙率和渗流速度对传质影响较大,弯曲因子对基质的渗透影响较小。分层生物膜模型中基质渗透深度大于均一化生物膜模型的结果,分层模型对基质的传质阻力比均一化生物膜模型小。
2.建立了一套10L的固定床好氧生物膜反应器实验装置,研究反应器中水力停留时间(HRT)、进水COD浓度和曝气量等参数对COD去除率的影响,同时利用微电极技术检测了不同参数条件下溶解氧在生物膜内的浓度分布规律。结果表明：较小的液相流速对生物膜内的传质过程影响不大,较高的COD浓度会增大生物膜内的耗氧速率,当COD=800 mg/L时,微生物生长不再受COD浓度的影响；实验测得反应器的最佳运行条件为：HRT=6-8 h,进水COD=600 mg/L,曝气量Qg=0.1 m3/h；
3.根据批实验数据,拟合出反应器内底物基质的生物反应速率方程,得到氧的最大消耗速率为0.0099 min-1,半饱和浓度为6.94 mg/L；葡萄糖的最大降解速率为0.0095min-1,半饱和浓度为485.71 mg/L。用实验测得的参数对生物膜“对流-扩散-反应”传质方程进行分层处理并求解,得到生物膜内基质浓度的分布,计算值与实验值的误差在1.91%-18%之间,表明分层生物膜模型比均一化模型更符合实际传质情况,该模型可用于预测生物膜内的传质过程。
The process of the substrates mass transfer in the biofilm plays a very important role in wastewater treatment technology using biofilm, which is the essence or basis of biofilm theory. With technology development and theory updates, this research field is constantly given new contents. Basing on previous work in this area, this thesis added percolation theory to mass transfer model within biofilm porous medium and make an intensive research of mass transfer process in biofilm by means of numerical simulation and experiment. The results of numerical simulation agree well with experimental results.
The contents of this study include:
1. Introduce percolation theory to the process of mass transfer within biofilm and build a "convection-diffusion-reaction" model. The model was stratified so that physical parameters of biofilm can be closer to actual situation, and numerically calculated by Runge-Kutta method. The influence of substrate concentration and seepage velocity, tortuosity and porosity to mass transfer within biofilm was investigated accordinglly. The numerical results showed that as the value of each parameter increased, the substrate penetration depth increased. Besides, most of these parameters had significantly influence on mass transfer within biofilm except the tortuosity. The substrate penetrates deeper into stratified biofilms than it does into homogeneous biofilms, the stratified biofilm model shows the lower mass transfer resistance to the substrate penetrate.
2. A fixed-bed aerobic biofilm reactor of 10 L was established. The COD of effluent was monitored with HRT、COD of influent and aeration rate changing. The results show that smaller liquid flow rate has little effect on mass transfer within biofilm and higher COD influent concentration will increase the oxygen consumption rate of aerobic biofilm. When the value of COD reached to 800 mg/L, the COD was no longer the limiting factor for microbial growth.The best operating conditions in this experiment are listed as follows: HRT=6-8 h,COD in influent=600 mg/L, the aeration rate Qg=0.1m3/h.
3. According to batch test data, the aerobic biofilm reaction rate equation was fitted, namely the largest oxygen consumption is 0.0099 min-1, half-saturation 6.94 mg/L, Glucose maximum degradation rate 0.0095 min-1, half-saturation 485.71 mg/L. Substrate concentration distribution within biofilm can be determined by numerically calculating mass transfer equcation with above-mentioned parameters. The error of the result between that obtained by stratified biofilm model and the convection-diffusion-reaction equation is 1.91%-18%. It was also verified that the stratified biofilm model is more suitable for actual mass transfer than the homogeneous biofilm model, thus can be used to predict the mass transfer process within the biofilm.
本文主要内容包括：
1.将渗流理论引入生物膜内的质量传递过程,建立生物膜“对流-扩散-反应”模型。对生物膜模型进行分层处理,使模型物性参数更接近实际生物膜内的真实状态。采用Runge-Kutta法对传质模型进行数值求解,从而研究了不同进料液浓度和渗流速度,不同生物膜孔道弯曲因子和孔隙率条件下的生物膜内传质规律。结果表明：随着各参数值的逐渐增大,基质在生物膜内的渗透深度逐渐增加；进水浓度、生物膜孔隙率和渗流速度对传质影响较大,弯曲因子对基质的渗透影响较小。分层生物膜模型中基质渗透深度大于均一化生物膜模型的结果,分层模型对基质的传质阻力比均一化生物膜模型小。
2.建立了一套10L的固定床好氧生物膜反应器实验装置,研究反应器中水力停留时间(HRT)、进水COD浓度和曝气量等参数对COD去除率的影响,同时利用微电极技术检测了不同参数条件下溶解氧在生物膜内的浓度分布规律。结果表明：较小的液相流速对生物膜内的传质过程影响不大,较高的COD浓度会增大生物膜内的耗氧速率,当COD=800 mg/L时,微生物生长不再受COD浓度的影响；实验测得反应器的最佳运行条件为：HRT=6-8 h,进水COD=600 mg/L,曝气量Qg=0.1 m3/h；
3.根据批实验数据,拟合出反应器内底物基质的生物反应速率方程,得到氧的最大消耗速率为0.0099 min-1,半饱和浓度为6.94 mg/L；葡萄糖的最大降解速率为0.0095min-1,半饱和浓度为485.71 mg/L。用实验测得的参数对生物膜“对流-扩散-反应”传质方程进行分层处理并求解,得到生物膜内基质浓度的分布,计算值与实验值的误差在1.91%-18%之间,表明分层生物膜模型比均一化模型更符合实际传质情况,该模型可用于预测生物膜内的传质过程。
The process of the substrates mass transfer in the biofilm plays a very important role in wastewater treatment technology using biofilm, which is the essence or basis of biofilm theory. With technology development and theory updates, this research field is constantly given new contents. Basing on previous work in this area, this thesis added percolation theory to mass transfer model within biofilm porous medium and make an intensive research of mass transfer process in biofilm by means of numerical simulation and experiment. The results of numerical simulation agree well with experimental results.
The contents of this study include:
1. Introduce percolation theory to the process of mass transfer within biofilm and build a "convection-diffusion-reaction" model. The model was stratified so that physical parameters of biofilm can be closer to actual situation, and numerically calculated by Runge-Kutta method. The influence of substrate concentration and seepage velocity, tortuosity and porosity to mass transfer within biofilm was investigated accordinglly. The numerical results showed that as the value of each parameter increased, the substrate penetration depth increased. Besides, most of these parameters had significantly influence on mass transfer within biofilm except the tortuosity. The substrate penetrates deeper into stratified biofilms than it does into homogeneous biofilms, the stratified biofilm model shows the lower mass transfer resistance to the substrate penetrate.
2. A fixed-bed aerobic biofilm reactor of 10 L was established. The COD of effluent was monitored with HRT、COD of influent and aeration rate changing. The results show that smaller liquid flow rate has little effect on mass transfer within biofilm and higher COD influent concentration will increase the oxygen consumption rate of aerobic biofilm. When the value of COD reached to 800 mg/L, the COD was no longer the limiting factor for microbial growth.The best operating conditions in this experiment are listed as follows: HRT=6-8 h,COD in influent=600 mg/L, the aeration rate Qg=0.1m3/h.
3. According to batch test data, the aerobic biofilm reaction rate equation was fitted, namely the largest oxygen consumption is 0.0099 min-1, half-saturation 6.94 mg/L, Glucose maximum degradation rate 0.0095 min-1, half-saturation 485.71 mg/L. Substrate concentration distribution within biofilm can be determined by numerically calculating mass transfer equcation with above-mentioned parameters. The error of the result between that obtained by stratified biofilm model and the convection-diffusion-reaction equation is 1.91%-18%. It was also verified that the stratified biofilm model is more suitable for actual mass transfer than the homogeneous biofilm model, thus can be used to predict the mass transfer process within the biofilm.
引文
[1]钱正英,张光斗.中国可持续发展水资源战略研究综合报告及各专题报告[M].北京：中国水利水电出版社,2001.
[2]杨晓明.我国水资源的可持续利用与环境教育[J].甘肃科技,2008,2(7)：94-96.
[3]孙建民,于丽青,孙汉文.重金属废水处理技术进展[J].河北大学学报,2004,24(4)：438-443.
[4]吴会中,单欣,赵琛琛.生物膜处理技术的研究进展[J].技术交流,2005,(11)：52-54.
[5]董德明,李鱼,花修艺,等.自然水体中生物膜的主要化学组分与水体中相关化学物质的关系[J].高等学校化学学报,2002,(8)：1507-1509.
[6]Headley J, Gandrass J, Kuballa J, et al. Rates of sorption and partitioning of contaminants in river biofilm [J]. Environmental Science & Technology,1998,32(24): 3968-3973.
[7]刘雨,赵庆良,郑兴灿.生物膜法污水处理技术[M].北京：中国建筑工业出版社,2000.
[8]沈耀良,黄勇,赵丹.固定化微生物污水处理技术[M],北京：化学工业出版社,2002.
[9]Zbigniew Lewandowski, Derek Webb, Martin Hamilton. Quantifying biofilm structure[J]. Wat. Sci. Tech.,1999,39(7):273-278.
[10]温沁雪,施汉昌,陈志强.生物膜微环境和传质现象研究进展[J].环境污染治理技术与设备,2006,7(6)：1-5.
[11]Massol-Deya A A, Whallon J, Hickey R F, et al. Dhannel structures in aerobic biof ilms of fixed-film reactors treating contaminated groundwater[J]. Applied Environmental Microbiology,1995,61(3):769-777.
[12]Stoodley P, De Beer D, Lewandowski Z. Liquid flow in biofilm system[J]. Apple Envior Microbio,1994,60(8):2711-2716.
[13]Tijhuis L, Van Bentham W A J, Van Loosdrecht M C M, et al. Solids retention time in spherical biofilms in a biofilm airlift suspension reactor[J]. Biotechnol Bioeng,1994,44(8):867-879.
[14]王文军,张学林,王文华,等.天然水体中生物膜及悬浮颗粒物的元素含量研究[J].应用生态学报,2002,13(8)：1001-1006.
[15]余国忠,高长海,贾吕虎等。一种异养生物膜密度分布的分型特征[J],信阳师范学院学报：自然科学版,2008,21(1)：61-63.
[16]Okabe S, Kuroda H, Watanabe Y. Significance of biofilm structure on transport of inert particulates in the biofilms[J]. Water Science and Technology,1998,38(8-9): 163-170.
[17]Gjaltema A, Arts P A M, Van Loosdrecht M C M. Heterogeneity of biofilms in rotating annular reactors:occurrence, structure, and consequences[J]. Biotechnol Bioeng, 1994,44(2):194-204.
[18]SurenWi jeyekoon, TakashiMino, Hiroyasu Satoh, Tomonori Matsuo. Effects of substrate loading rate on biofilm structure[J]. Wat. Res.,2004,38:1479-1488.
[19]Okabe S., Oozawa Y., Hitrata K., et al. Relationship between population dynamics of nitrifiers in biofilms and reactor performance at various C/N ratios[J].Wat. Res.,1996,30(7):1563-1572.
[20]Villasefior J C, van Loosdrecht M C M,Picioreanu C, et al. Influence of different substrates on the formation of biofilms in a biofilm airlift suspension reactor[J]. Water Science and Technology,2000,41(4):323-330.
[21]Alma Masic, Jessica Bengtsson, Magnus Christensson. Measuring and modeling the oxygen profile in a nitrifying Moving Bed Biofilm Reactor[J],Mathematical Biosciences,2010, (227):1-11.
[22]Gialtema A, Ti jhuis L, Van Loosdrecht MCM, et al. Detachment of biomass from suspended nongrowing spherical biofilms in airlift reactors [J]. Biotechnol. Bioeng.,1995,46: 258-269.
[23]王宝贞.水污染控制工程[M].北京：高等教育出版社,1990.
[24]Hunt A P, Parry J D. The Effect of Substratum Roughness and River Flow Rate on the Development of a Freshwater Biofilm Community[J]. Biofouling,1998,12(4):287-303.
[25]师存杰.生物膜技术在水处理中的应用[J].青海大学学报：自然科学版,2001,19(5)：32-34.
[26]常晓雷.废水处理中SRB生物膜微观结构及传质动力学研究[D].天津：天津大学化工学院,2007.
[27]LaMotta E J. Internal diffusion and reaction in biological films[J]. Envior Sci Tech,1976,10(8):765-769.
[28]Benefield, Molz. Mathematical simulation of a biofilm process[J]. Biotechnol Bioeng, 1985,27(7):921-931.
[29]Fan L-S, Leyva2Ramos, Wisecarver R, et al. Diffusion of phenol through a biofilm grown on activated carbon particles in a drafttube three-phase fluidized-bed bioreactor [J]. Biotechnol Bioeng,1990,35(3):279-286.
[30]Harald Horn, Dietmar C, Hempel. Modeling mass transfer and substrate utilization the boundary layer of biofilm systems[J]. Wat. Sci. Tech.,1998,37(4-5):139-147.
[31]Dirk de Beer, Andreas Schramm. Micro-environments and mass transfer phenomena in biofilms studied with microsensors[J]. Wat. Sci. Tech.,1999,39(7):173-178.
[32]Dirk de Beer, Paul Stoodley, Zbigniew Lewandowski. Liquid flow and mass transport in heterogeneous biof ilms[J]. Wat. Res.,1996,30(11):2761-2765.
[33]Dirk de Beer, Paul Stoodley. Relation between the structure of an aerobic biofilm and transport phenomena[J]. Wat. Sci. Tech.,1995,32(8):11-18.
[34]Sizgerist H, Gujer W. Mass transfer mechanisms in a heterotrophic biofilm[J]. Wat Res,1985,19(12):1969-1985.
[35]Stoodley P, De Beer D, Lewandowski Z, Relationship between mass transfer coefficient and liquid flow velocity in heterogeneous biofilms using microelectrodes and confocal microschopy[J]. Biotech. Bioeng,1997,56(5):681～688.
[36]Bungartz H J, Kuehn M, Mehl M. Fluid f lowand transport in defined biofilm:Experiments and numerical simulation on a microscale[J]. Wat. Sci. Technol.,2001,41:33.
[37]Atkinson B, Davies I J. Overall rate of substrate uptake (reaction) by microbial films.1. biological rate equation[J]. Transactions of the Institution of Chemical Engineers,1974,52(3):248-259.
[38]Rittmann B. E., McCarty P.L.. Model of steady-state-biofilm kinetics[J]. Biotechnology and Bioengineering,1980,22:2343-2357.
[39]Rittmann B. E., McCarty P. L., Evaluation of steady-state-biofilm kinetics. Biotech-nology and Bioengineering,1980,22:2359-2373.
[40]尚倩倩,方红卫,何国建.水利工程中的生物膜研究进展[J].中国科技论文在线,2010,5(7)：563-568.
[41]Wimpenny J. W. T., Colasanti R.. A unifying hypothesis for the structure of microbial biofilms based on cellular automaton models. Fems Microbiology Ecology,1997,22: 1-16.
[42]Wimpenny J. W. T., Colasanti R.. A more unifying hypothesis for biofilm structures-a reply [J]. Fems Microbiology Ecology,1997,24:185-186.
[43]Picioreanu C, van Loosdrecht M. C. M, Hei jnen J. J. Effect of diffusive and convective substrate transport on biofilm structure formation:a two-dimensional modeling study[J]. Biotechnology and Bioengineering,2000,69(5):504-515.
[44]Eberl H. J., Picioreanu C., Hei jnen J. J., et al. A three-dimensional numerical study on the correlation of spatial structure, hydrodynamic conditions, and mass transfer and conversion in biofilms[J]. Chemical Engineering Science,2000,55:6209-6222.
[45]施雯.基于陶瓷载体的生物膜与废水处理效果之间关系的研究[D].上海：上海师范大学生命与环境科学学院,2010.
[46]DE BEER D. Measurement of nitrate gradients with an ion-selective microelectrode [JJ.Analytica Chimica Acta,1989,219:351-356.
[47]De Beer D, Stoodley P.Relation between the structure of an aerobic biofilm and transport phenomena[J]. Water Science and Technology,1995,32(8):11-18.
[48]H. Horn, D. C. Hempel. Growth and decay in an auto-/heterotrophic biofilm[J]. Water Research,1997,31:2243.
[49]KJETIL RASMUSSEN M, ZBIGNIEW LEWANDOWSKI. The accuracy of oxygen flux measurements using microelectrodes[J]. Wat. Res.,1998,32(12):3747-3755.
[50]A. Hille,T. Neu, D. C. Hempel, et al. Oxygen profiles and biomass distribution in biopellets of Aspergillus niger[J]. Biotechnology and Bioengineering,2005,92:614.
[51]YU T, ROSA C DE LA, LU R.Microsensor measurement of oxygen concentration in biofilms:from one dimension to three dimensions[J].Water Science and Technology, 2004,49 (11-12):353-358.
[52]邱玉琴,周小红,施汉昌.基于氧微电极的生物膜内异养菌衰减系数的原位测定[J].环境科学,2008,29(11)：3110-3113.
[53]邱玉琴.基于氧微电极的生物膜内反应动力学参数的原位测定研究[D].北京：清华大学环境科学与工程系,2008.
[54]周小红,施汉昌,何苗.采用微电极测定溶解氧有效扩散系数的研究[J].环境科学,2007,28(3)：558-602.
[55]仵彦卿.多孔介质污染物迁移动力学[M].上海：上海交通大学出版社,2007.
[56]陶斌斌.多孔介质对流干燥传热传质机理的研究及其数值模拟[D].河北：河北工业大学热能工程,2004.
[57]Daniel R. Noguera, Satoshi Okabe, Cristian Picioreanu. Biofilm model ing:Present status and future directions[J]. Wat. Sci. Tech.,1999,39(7):273-278.
[58]Wanner O, ReiehertP. Mathematical modeling of mixed-culture biof ilms[J]. Bioteehnol Bioeng,1996,49:172-184.
[59]Pereival Letal. Biof ilm Development on Stainless Steel in Mains [J]. Water. Wat. Res., 1996,32(1):243-253.
[60]李宇.内环流生物膜反应器传质过程模拟及实验研究[D].辽宁：大连理工大学流体机械及工程,2007.
[61]Beyenal H., Lewandowski Z..Internal and external mass transfer in biofilms grown at various flow velocities[J]. Biotechnology Progress,2002,18:55-61.
[62]邓洪权,潘永亮,杨平.内循环生物流化床反应器数学模型分析[J].四川大学学报,2001,33(2)：54-55.
[63]Zhang T. C., Bishop P. L..Density, porosity, and pore structure of biofilms[J]. Water Research,1994,28:2267-2277.
[64]Zbigniew Lewandowski. Notes on biofilm porosity[J]. Wat. Res.,2000,9(34):2620-2624.
[65]顾国维.水污染治理技术研究[M].上海：同济大学出版社,1997.
[66]吴为中,王占生.水库水源水生物陶粒滤池预处理中试研究[J].环境科学研究,1999,12(Ⅰ)：10-14.
[67]俞汉青.生物膜反应器挂膜方法的试验研究[J].中国给水排水,1992,8(13)：54-58.
[68]赵冰怡,陈英文,沈树宝.C/N比和曝气量影响MBR同步硝化反硝化的研究[J].环境工程学报,2009,3(3)：400-404.
[69]李探微,彭永臻.活性污泥法的生物泡沫形成和控制[J].中国给水排水,2001,4(17)：73-76.
[70]韩晓云.低温生物膜及其微生物特性的研究[M].黑龙江：黑龙江大学出版社,2009.
[71]Nazira Khabibor Rahman, Monhamad Zailani Abu Bakar, Mohamad Hekarl Uzir,et al. Modelling on the effect of diffusive and convective substrate transport for biofilm[J]. Mathematical Biosciences,2009, (218):130-137.
[72]Rittman B E, Manem J A. Development and experiment evaluation of steadystate multispecies biofilm model[J]. Biotechnol Bioeng,1992,39(9):914-922.
[73]Hirata A, Takemoto T, Ogawa K, Auresenia J, et al. Evaluation of kinetics parameters from concentration step change response of three-phase fluidized bed biofilm reactor for wastewater treatment[J]. Biochemical Engineering Journal,2000,5(2): 165-171.
[74]邓洪权,潘永亮,杨平.内循环生物流化床反应器数学模型分析.四川大学学报,2001,33(2)：54-55.
[2]杨晓明.我国水资源的可持续利用与环境教育[J].甘肃科技,2008,2(7)：94-96.
[3]孙建民,于丽青,孙汉文.重金属废水处理技术进展[J].河北大学学报,2004,24(4)：438-443.
[4]吴会中,单欣,赵琛琛.生物膜处理技术的研究进展[J].技术交流,2005,(11)：52-54.
[5]董德明,李鱼,花修艺,等.自然水体中生物膜的主要化学组分与水体中相关化学物质的关系[J].高等学校化学学报,2002,(8)：1507-1509.
[6]Headley J, Gandrass J, Kuballa J, et al. Rates of sorption and partitioning of contaminants in river biofilm [J]. Environmental Science & Technology,1998,32(24): 3968-3973.
[7]刘雨,赵庆良,郑兴灿.生物膜法污水处理技术[M].北京：中国建筑工业出版社,2000.
[8]沈耀良,黄勇,赵丹.固定化微生物污水处理技术[M],北京：化学工业出版社,2002.
[9]Zbigniew Lewandowski, Derek Webb, Martin Hamilton. Quantifying biofilm structure[J]. Wat. Sci. Tech.,1999,39(7):273-278.
[10]温沁雪,施汉昌,陈志强.生物膜微环境和传质现象研究进展[J].环境污染治理技术与设备,2006,7(6)：1-5.
[11]Massol-Deya A A, Whallon J, Hickey R F, et al. Dhannel structures in aerobic biof ilms of fixed-film reactors treating contaminated groundwater[J]. Applied Environmental Microbiology,1995,61(3):769-777.
[12]Stoodley P, De Beer D, Lewandowski Z. Liquid flow in biofilm system[J]. Apple Envior Microbio,1994,60(8):2711-2716.
[13]Tijhuis L, Van Bentham W A J, Van Loosdrecht M C M, et al. Solids retention time in spherical biofilms in a biofilm airlift suspension reactor[J]. Biotechnol Bioeng,1994,44(8):867-879.
[14]王文军,张学林,王文华,等.天然水体中生物膜及悬浮颗粒物的元素含量研究[J].应用生态学报,2002,13(8)：1001-1006.
[15]余国忠,高长海,贾吕虎等。一种异养生物膜密度分布的分型特征[J],信阳师范学院学报：自然科学版,2008,21(1)：61-63.
[16]Okabe S, Kuroda H, Watanabe Y. Significance of biofilm structure on transport of inert particulates in the biofilms[J]. Water Science and Technology,1998,38(8-9): 163-170.
[17]Gjaltema A, Arts P A M, Van Loosdrecht M C M. Heterogeneity of biofilms in rotating annular reactors:occurrence, structure, and consequences[J]. Biotechnol Bioeng, 1994,44(2):194-204.
[18]SurenWi jeyekoon, TakashiMino, Hiroyasu Satoh, Tomonori Matsuo. Effects of substrate loading rate on biofilm structure[J]. Wat. Res.,2004,38:1479-1488.
[19]Okabe S., Oozawa Y., Hitrata K., et al. Relationship between population dynamics of nitrifiers in biofilms and reactor performance at various C/N ratios[J].Wat. Res.,1996,30(7):1563-1572.
[20]Villasefior J C, van Loosdrecht M C M,Picioreanu C, et al. Influence of different substrates on the formation of biofilms in a biofilm airlift suspension reactor[J]. Water Science and Technology,2000,41(4):323-330.
[21]Alma Masic, Jessica Bengtsson, Magnus Christensson. Measuring and modeling the oxygen profile in a nitrifying Moving Bed Biofilm Reactor[J],Mathematical Biosciences,2010, (227):1-11.
[22]Gialtema A, Ti jhuis L, Van Loosdrecht MCM, et al. Detachment of biomass from suspended nongrowing spherical biofilms in airlift reactors [J]. Biotechnol. Bioeng.,1995,46: 258-269.
[23]王宝贞.水污染控制工程[M].北京：高等教育出版社,1990.
[24]Hunt A P, Parry J D. The Effect of Substratum Roughness and River Flow Rate on the Development of a Freshwater Biofilm Community[J]. Biofouling,1998,12(4):287-303.
[25]师存杰.生物膜技术在水处理中的应用[J].青海大学学报：自然科学版,2001,19(5)：32-34.
[26]常晓雷.废水处理中SRB生物膜微观结构及传质动力学研究[D].天津：天津大学化工学院,2007.
[27]LaMotta E J. Internal diffusion and reaction in biological films[J]. Envior Sci Tech,1976,10(8):765-769.
[28]Benefield, Molz. Mathematical simulation of a biofilm process[J]. Biotechnol Bioeng, 1985,27(7):921-931.
[29]Fan L-S, Leyva2Ramos, Wisecarver R, et al. Diffusion of phenol through a biofilm grown on activated carbon particles in a drafttube three-phase fluidized-bed bioreactor [J]. Biotechnol Bioeng,1990,35(3):279-286.
[30]Harald Horn, Dietmar C, Hempel. Modeling mass transfer and substrate utilization the boundary layer of biofilm systems[J]. Wat. Sci. Tech.,1998,37(4-5):139-147.
[31]Dirk de Beer, Andreas Schramm. Micro-environments and mass transfer phenomena in biofilms studied with microsensors[J]. Wat. Sci. Tech.,1999,39(7):173-178.
[32]Dirk de Beer, Paul Stoodley, Zbigniew Lewandowski. Liquid flow and mass transport in heterogeneous biof ilms[J]. Wat. Res.,1996,30(11):2761-2765.
[33]Dirk de Beer, Paul Stoodley. Relation between the structure of an aerobic biofilm and transport phenomena[J]. Wat. Sci. Tech.,1995,32(8):11-18.
[34]Sizgerist H, Gujer W. Mass transfer mechanisms in a heterotrophic biofilm[J]. Wat Res,1985,19(12):1969-1985.
[35]Stoodley P, De Beer D, Lewandowski Z, Relationship between mass transfer coefficient and liquid flow velocity in heterogeneous biofilms using microelectrodes and confocal microschopy[J]. Biotech. Bioeng,1997,56(5):681～688.
[36]Bungartz H J, Kuehn M, Mehl M. Fluid f lowand transport in defined biofilm:Experiments and numerical simulation on a microscale[J]. Wat. Sci. Technol.,2001,41:33.
[37]Atkinson B, Davies I J. Overall rate of substrate uptake (reaction) by microbial films.1. biological rate equation[J]. Transactions of the Institution of Chemical Engineers,1974,52(3):248-259.
[38]Rittmann B. E., McCarty P.L.. Model of steady-state-biofilm kinetics[J]. Biotechnology and Bioengineering,1980,22:2343-2357.
[39]Rittmann B. E., McCarty P. L., Evaluation of steady-state-biofilm kinetics. Biotech-nology and Bioengineering,1980,22:2359-2373.
[40]尚倩倩,方红卫,何国建.水利工程中的生物膜研究进展[J].中国科技论文在线,2010,5(7)：563-568.
[41]Wimpenny J. W. T., Colasanti R.. A unifying hypothesis for the structure of microbial biofilms based on cellular automaton models. Fems Microbiology Ecology,1997,22: 1-16.
[42]Wimpenny J. W. T., Colasanti R.. A more unifying hypothesis for biofilm structures-a reply [J]. Fems Microbiology Ecology,1997,24:185-186.
[43]Picioreanu C, van Loosdrecht M. C. M, Hei jnen J. J. Effect of diffusive and convective substrate transport on biofilm structure formation:a two-dimensional modeling study[J]. Biotechnology and Bioengineering,2000,69(5):504-515.
[44]Eberl H. J., Picioreanu C., Hei jnen J. J., et al. A three-dimensional numerical study on the correlation of spatial structure, hydrodynamic conditions, and mass transfer and conversion in biofilms[J]. Chemical Engineering Science,2000,55:6209-6222.
[45]施雯.基于陶瓷载体的生物膜与废水处理效果之间关系的研究[D].上海：上海师范大学生命与环境科学学院,2010.
[46]DE BEER D. Measurement of nitrate gradients with an ion-selective microelectrode [JJ.Analytica Chimica Acta,1989,219:351-356.
[47]De Beer D, Stoodley P.Relation between the structure of an aerobic biofilm and transport phenomena[J]. Water Science and Technology,1995,32(8):11-18.
[48]H. Horn, D. C. Hempel. Growth and decay in an auto-/heterotrophic biofilm[J]. Water Research,1997,31:2243.
[49]KJETIL RASMUSSEN M, ZBIGNIEW LEWANDOWSKI. The accuracy of oxygen flux measurements using microelectrodes[J]. Wat. Res.,1998,32(12):3747-3755.
[50]A. Hille,T. Neu, D. C. Hempel, et al. Oxygen profiles and biomass distribution in biopellets of Aspergillus niger[J]. Biotechnology and Bioengineering,2005,92:614.
[51]YU T, ROSA C DE LA, LU R.Microsensor measurement of oxygen concentration in biofilms:from one dimension to three dimensions[J].Water Science and Technology, 2004,49 (11-12):353-358.
[52]邱玉琴,周小红,施汉昌.基于氧微电极的生物膜内异养菌衰减系数的原位测定[J].环境科学,2008,29(11)：3110-3113.
[53]邱玉琴.基于氧微电极的生物膜内反应动力学参数的原位测定研究[D].北京：清华大学环境科学与工程系,2008.
[54]周小红,施汉昌,何苗.采用微电极测定溶解氧有效扩散系数的研究[J].环境科学,2007,28(3)：558-602.
[55]仵彦卿.多孔介质污染物迁移动力学[M].上海：上海交通大学出版社,2007.
[56]陶斌斌.多孔介质对流干燥传热传质机理的研究及其数值模拟[D].河北：河北工业大学热能工程,2004.
[57]Daniel R. Noguera, Satoshi Okabe, Cristian Picioreanu. Biofilm model ing:Present status and future directions[J]. Wat. Sci. Tech.,1999,39(7):273-278.
[58]Wanner O, ReiehertP. Mathematical modeling of mixed-culture biof ilms[J]. Bioteehnol Bioeng,1996,49:172-184.
[59]Pereival Letal. Biof ilm Development on Stainless Steel in Mains [J]. Water. Wat. Res., 1996,32(1):243-253.
[60]李宇.内环流生物膜反应器传质过程模拟及实验研究[D].辽宁：大连理工大学流体机械及工程,2007.
[61]Beyenal H., Lewandowski Z..Internal and external mass transfer in biofilms grown at various flow velocities[J]. Biotechnology Progress,2002,18:55-61.
[62]邓洪权,潘永亮,杨平.内循环生物流化床反应器数学模型分析[J].四川大学学报,2001,33(2)：54-55.
[63]Zhang T. C., Bishop P. L..Density, porosity, and pore structure of biofilms[J]. Water Research,1994,28:2267-2277.
[64]Zbigniew Lewandowski. Notes on biofilm porosity[J]. Wat. Res.,2000,9(34):2620-2624.
[65]顾国维.水污染治理技术研究[M].上海：同济大学出版社,1997.
[66]吴为中,王占生.水库水源水生物陶粒滤池预处理中试研究[J].环境科学研究,1999,12(Ⅰ)：10-14.
[67]俞汉青.生物膜反应器挂膜方法的试验研究[J].中国给水排水,1992,8(13)：54-58.
[68]赵冰怡,陈英文,沈树宝.C/N比和曝气量影响MBR同步硝化反硝化的研究[J].环境工程学报,2009,3(3)：400-404.
[69]李探微,彭永臻.活性污泥法的生物泡沫形成和控制[J].中国给水排水,2001,4(17)：73-76.
[70]韩晓云.低温生物膜及其微生物特性的研究[M].黑龙江：黑龙江大学出版社,2009.
[71]Nazira Khabibor Rahman, Monhamad Zailani Abu Bakar, Mohamad Hekarl Uzir,et al. Modelling on the effect of diffusive and convective substrate transport for biofilm[J]. Mathematical Biosciences,2009, (218):130-137.
[72]Rittman B E, Manem J A. Development and experiment evaluation of steadystate multispecies biofilm model[J]. Biotechnol Bioeng,1992,39(9):914-922.
[73]Hirata A, Takemoto T, Ogawa K, Auresenia J, et al. Evaluation of kinetics parameters from concentration step change response of three-phase fluidized bed biofilm reactor for wastewater treatment[J]. Biochemical Engineering Journal,2000,5(2): 165-171.
[74]邓洪权,潘永亮,杨平.内循环生物流化床反应器数学模型分析.四川大学学报,2001,33(2)：54-55.