J. P. Boltz, E. Morgenroth, and D. Sen, Mathematical modelling of biofilms and biofilm reactors for engineering design, Water Science & Technology, vol.62, issue.8, pp.1821-1836, 2010.
DOI : 10.2166/wst.2010.076

H. Brouwer, A. Klapwijk, and K. J. Keesman, Identification of activated sludge and wastewater characteristics using respirometric batch-experiments, Water Research, vol.32, issue.4, pp.1240-1254, 1998.
DOI : 10.1016/S0043-1354(97)00334-5

G. H. Chen, J. C. Huang, and I. M. Lo, Removal of rate-limiting organic substances in a hybrid biological reactor, Water Science and Technology, vol.35, issue.6, pp.81-89, 1997.
DOI : 10.1016/S0273-1223(97)00098-X

S. Chen, D. Sun, and C. J. , Simultaneous removal of COD and ammonium from landfill leachate using an anaerobic???aerobic moving-bed biofilm reactor system, Waste Management, vol.28, issue.2, pp.339-346, 2008.
DOI : 10.1016/j.wasman.2007.01.004

E. H. Choi, B. Klapwijk, A. Mels, and H. Brouwer, Evaluation of wastewater characterization methods, Water Science and Technology, vol.52, pp.10-11, 2005.

J. Choubert, Analyse et optimisation du traitement de l'azote par les boues activées à basse température, 265 pp, Louis Pasteur, 2002.

J. M. Choubert, C. Druilhe, F. Beline, and S. Gillot, Techniques de fractionnement de la matière organique des déchets liquides pour la modélisation des bioprocédés, 2010.

P. Christiansen, L. Hollesen, and P. Harremoës, Liquid film diffusion on reaction rate in submerged biofilters, Water Research, vol.29, issue.3, pp.947-952, 1995.
DOI : 10.1016/0043-1354(94)00206-M

O. Cinar, G. T. Daigger, and G. S. , Evaluation of IAWQ Activated Sludge Model No. 2 using steady-state data from four full-scale wastewater treatment plants, Water Environment Research, vol.70, issue.6, pp.1216-1224, 1998.
DOI : 10.2175/106143098X123552

J. B. Copp and M. K. , Estimation of the active nitrifying biomass in activated sludge, Water Research, vol.29, issue.8, pp.1855-1862, 1995.
DOI : 10.1016/0043-1354(94)00347-A

H. Eberl, E. Morgenroth, D. Noguera, C. Picioreanu, B. Rittmann et al., Mathematical modeling of biofilms, 2006.

M. Ferrai, G. Guglielmi, and G. Andreottola, Modelling respirometric tests for the assessment of kinetic and stoichiometric parameters on MBBR biofilm for municipal wastewater treatment, Environmental Modelling & Software, vol.25, issue.5, pp.626-632, 2010.
DOI : 10.1016/j.envsoft.2009.05.005

N. Frössling, Über die verdunstung fallender Tropfen. (About the evaporation of falling drops) Gerlands beiträge zur geophysik, pp.52170-215, 1938.

C. Grunditz and G. Dalhammar, Development of nitrification inhibition assays using pure cultures of nitrosomonas and nitrobacter, Water Research, vol.35, issue.2, pp.433-440, 2001.
DOI : 10.1016/S0043-1354(00)00312-2

L. J. Hem, B. Rusten, and H. Ødegaard, Nitrification in a moving bed biofilm reactor, Water Research, vol.28, issue.6, pp.1425-1433, 1994.
DOI : 10.1016/0043-1354(94)90310-7

M. Henze, G. Jr, C. P. Gujer, and W. , A general model for single-sludge wastewater treatment systems, Water Research, vol.21, issue.5, pp.505-515, 1987.
DOI : 10.1016/0043-1354(87)90058-3

M. Henze, W. Gujer, T. Mino, V. Loosdrecht, and M. C. , Activated Sludge Models ASM1, ASM2, 2000.

M. Henze, W. Gujer, T. Mino, V. Loosdrecht, and M. C. , Activated sludge models ASM1, 2000.

M. Henze, P. Harremoës, J. La-cour-jansen, and A. E. , Wastewater treatment, 1996.

H. Horn and H. D. , Growth and decay in an auto-/heterotrophic biofilm, Water Research, vol.31, issue.9, pp.2243-2252, 1997.
DOI : 10.1016/S0043-1354(97)00081-X

A. Khlebnikov, F. Samb, and P. Péringer, Use of a dynamic gassing-out method for activity and oxygen diffusion coefficient estimation in biofilms, Water Science and Technology, vol.37, issue.4-5, pp.4-5, 1998.
DOI : 10.1016/S0273-1223(98)00100-0

G. Koch, M. Kühni, W. Gujer, and H. Siegrist, Calibration and validation of activated sludge model no. 3 for Swiss municipal wastewater, Water Research, vol.34, issue.14, pp.3580-3590, 2000.
DOI : 10.1016/S0043-1354(00)00105-6

Y. Lee and O. J. , Effects of predation and ORP conditions on the performance of nitrifiers in activated sludge systems, Water Research, vol.37, issue.17, pp.4202-4210, 2003.
DOI : 10.1016/S0043-1354(03)00341-5

M. Levstek and I. Plazl, Influence of carrier type on nitrification in the moving-bed biofilm process, Water Science & Technology, vol.59, issue.5, pp.875-882, 2009.
DOI : 10.2166/wst.2009.037

M. Levstek, I. Plazl, and R. J. , Estimation of the specific surface area for a porous carrier, Acta Chimica Slovenica, vol.57, issue.1, pp.45-51, 2010.

Y. H. Lin, Kinetics of nitrogen and carbon removal in a moving-fixed bed biofilm reactor, Applied Mathematical Modelling, vol.32, issue.11, pp.2360-2377, 2008.
DOI : 10.1016/j.apm.2007.09.009

G. Mannina, D. Trapani, M. Torregrossa, and G. Viviani, Modelling of hybrid moving bed biofilm reactors: a pilot plant experiment, Water Science & Technology, vol.55, issue.8-9, pp.237-246, 2007.
DOI : 10.2166/wst.2007.264

J. P. Mcquarrie and J. P. Boltz, Moving Bed Biofilm Reactor Technology: Process Applications, Design, and Performance, Water Environment Research, vol.83, issue.6, pp.560-575, 2011.
DOI : 10.2175/106143010X12851009156286

G. Munz, C. Lubello, and O. J. , Modeling the decay of ammonium oxidizing bacteria, Water Research, vol.45, issue.2, pp.557-564, 2011.
DOI : 10.1016/j.watres.2010.09.022

R. Nogueira, L. F. Melo, U. Purkhold, S. Wuertz, and M. Wagner, Nitrifying and heterotrophic population dynamics in biofilm reactors: effects of hydraulic retention time and the presence of organic carbon, Water Research, vol.36, issue.2, pp.469-481, 2002.
DOI : 10.1016/S0043-1354(01)00229-9

D. R. Noguera and E. Morgenroth, Introduction to the IWA task group on biofilm modeling, Water Science and Technology, vol.49, pp.11-12, 2004.

L. Novák, L. Larrea, and J. Wanner, Estimation of maximum specific growth rate of heterotrophic and autotrophic biomass: A combined technique of mathematical modelling and batch cultivations, Water Science and Technology, vol.30, issue.11, pp.171-180, 1994.

H. Ødegaard, B. Gisvold, and J. Strickland, The influence of carrier size and shape in the moving bed biofilm process, Water Science and Technology, pp.41383-391, 2000.

H. Ødegaard, B. Rusten, and J. Siljudalen, The development of the moving bed biofilm process-from idea to commercial product, European Water Management, vol.2, issue.3, pp.36-43, 1999.

H. Ødegaard, B. Rusten, and T. Westrum, A new moving bed biofilm reactor applications and results, Water Science and Technology, vol.29, pp.10-11, 1994.

G. Pastorelli, G. Andreottola, R. Canziani, C. Darriulat, E. De-fraja-frangipane et al., Organic carbon and nitrogen removal in moving-bed biofilm reactors, Water Science and Technology, vol.35, issue.6, pp.91-99, 1997.
DOI : 10.1016/S0273-1223(97)00099-1

I. Pasztor, P. Thury, and P. J. , Chemical oxygen demand fractions of municipal wastewater for modeling of wastewater treatment, International Journal of Environmental Science & Technology, vol.33, issue.12, pp.51-56, 2009.
DOI : 10.1007/BF03326059

E. Paul, J. C. Ochoa, Y. Pechaud, Y. Liu, and A. Line, Effect of shear stress and growth conditions on detachment and physical properties of biofilms, Water Research, vol.46, issue.17, pp.5499-5508, 2012.
DOI : 10.1016/j.watres.2012.07.029
URL : https://hal.archives-ouvertes.fr/hal-00914360

J. Pérez, C. Picioreanu, V. Loosdrecht, and M. , Modeling biofilm and floc diffusion processes based on analytical solution of reaction-diffusion equations, Water Research, vol.39, issue.7, pp.1311-1323, 2005.
DOI : 10.1016/j.watres.2004.12.020

H. Pham, S. Viswanathan, and K. R. , Evaluation of Plastic Carrier Media Impact on Oxygen Transfer Efficiency with Coarse and Fine Bubble Diffusers, Proceedings of the Water Environment Federation, vol.2008, issue.11, 2008.
DOI : 10.2175/193864708788805378

C. Picioreanu, J. U. Kreft, V. Loosdrecht, and M. C. , Particle-Based Multidimensional Multispecies Biofilm Model, Applied and Environmental Microbiology, vol.70, issue.5, pp.3024-3040, 2004.
DOI : 10.1128/AEM.70.5.3024-3040.2004

C. Picioreanu, M. C. Van-loosdrecht, and H. J. , Effect of diffusive and convective substrate transport on biofilm structure formation: A two-dimensional modeling study, Biotechnology and Bioengineering, vol.22, issue.5, pp.504-515, 2000.
DOI : 10.1002/1097-0290(20000905)69:5<504::AID-BIT5>3.0.CO;2-S

M. Plattes, E. Henry, and P. M. Schosseler, A zero-dimensional biofilm model for dynamic simulation of moving bed bioreactor systems: Model concepts, Peterson matrix, and application to a pilot-scale plant, Biochemical Engineering Journal, vol.40, issue.2, pp.392-398, 2008.
DOI : 10.1016/j.bej.2008.01.011

M. Plattes, E. Henry, P. M. Schosseler, and A. Weidenhaupt, Modelling and dynamic simulation of a moving bed bioreactor for the treatment of municipal wastewater, Biochemical Engineering Journal, vol.32, issue.2, pp.61-68, 2006.
DOI : 10.1016/j.bej.2006.07.009

H. J. Pöpel and A. Fischer, Combined influence of temperature and process loading on the effluent concentration of biological treatment, Water Science and Technology, vol.38, issue.8-9, pp.129-136, 1998.
DOI : 10.1016/S0273-1223(98)00686-6

W. Rauch, H. Vanhooren, and P. A. Vanrolleghem, A simplified mixed-culture biofilm model, Water Research, vol.33, issue.9, pp.2148-2162, 1999.
DOI : 10.1016/S0043-1354(98)00415-1

P. J. Roeleveld, V. Loosdrecht, and M. C. , Experience with guidelines for wastewater characterisation in the Netherlands, Water Science and Technology, vol.45, issue.6, pp.77-87, 2002.

P. N. Rowe, K. T. Claxton, and L. J. , Heat and mass transfer from a single sphere in an extensive flowing fluid, Trans. Inst. Chem. Eng, pp.4314-4345, 1965.

B. Rusten, B. Eikebrokk, Y. Ulgenes, and E. Lygren, Design and operations of the Kaldnes moving bed biofilm reactors, Aquacultural Engineering, vol.34, issue.3, pp.322-331, 2006.
DOI : 10.1016/j.aquaeng.2005.04.002

B. Rusten, B. G. Hellström, F. Hellström, O. Sehested, E. Skjelfoss et al., Pilot testing and preliminary design of moving bed biofilm reactors for nitrogen removal at the FREVAR wastewater treatment plant, Water Science and Technology, vol.41, pp.4-5, 2000.

B. Rusten, L. J. Hem, and H. Odegaard, Nitrification of municipal wastewater in moving-bed biofilm reactors, Water Environment Research, vol.67, issue.1, pp.75-85, 1995.
DOI : 10.2175/106143095X131213

B. Rusten, C. H. Johnson, S. Devall, D. Davoren, and C. B. , Biological pretreatment of a chemical plant wastewater in high-rate moving bed biofilm reactors, Water Science and Technology, vol.39, issue.10-11, pp.10-11, 1999.
DOI : 10.1016/S0273-1223(99)00286-3

B. Rusten, M. Mccoy, R. Proctor, and S. J. , The innovative moving bed biofilm reactor/solids contact reaeration process for secondary treatment of municipal wastewater, Water Environment Research, vol.70, issue.5, pp.1083-1089, 1998.
DOI : 10.2175/106143098X123435

B. Rusten, J. G. Siljudalen, and N. B. , Upgrading to nitrogen removal with the KMT moving bed biofilm process, Water Science and Technology, vol.29, issue.12, pp.185-195, 1994.

S. Salem, M. S. Moussa, V. Loosdrecht, and M. C. , Determination of the decay rate of nitrifying bacteria, Biotechnology and Bioengineering, vol.86, issue.2, pp.252-262, 2006.
DOI : 10.1002/bit.20822

R. Salvetti, A. Azzellino, R. Canziani, and L. Bonomo, Effects of temperature on tertiary nitrification in moving-bed biofilm reactors, Water Research, vol.40, issue.15, pp.2981-2993, 2006.
DOI : 10.1016/j.watres.2006.05.013

. Eker-ª, H. Beyenal, and A. Tanyolaç, The effects of biofilm thickness on biofilm density and substrate consumption rate in a differential fluidizied bed biofilm reactor (DFBBR), Journal of Biotechnology, vol.41, issue.1, pp.39-47, 1995.

D. Sen and R. C. , Improved computational model (AQUIFAS) for activated sludge, integrated fixed-film activated sludge, and moving-bed biofilm reactor systems, Part I : Semi-empirical model development, Water Environment Research, vol.80, issue.5, pp.439-453, 2008.

D. Sen and R. C. , Improved Computational Model (AQUIFAS) for Activated Sludge, Integrated Fixed-Film Activated Sludge, and Moving-Bed Biofilm Reactor Systems, Part II: Multilayer Biofilm Diffusional Model, Water Environment Research, vol.80, issue.7, pp.624-632, 2008.
DOI : 10.2175/106143008X268434

D. Sen and R. C. , Improved Computational Model (AQUIFAS) for Activated Sludge, Integrated Fixed-Film Activated Sludge, and Moving-Bed Biofilm Reactor Systems, Part III: Analysis and Verification, Water Environment Research, vol.80, issue.7, pp.633-646, 2008.
DOI : 10.2175/106143008X268443

H. C. Sena, Recebimento de lodo de eta em ete por lodo ativado operando com midia plastica no tanque de aeraçao (MBBR), 2011.
DOI : 10.11606/t.3.2011.tde-31082011-161023

P. Servais, A. Barillier, and J. Garnier, Determination of the biodegradable fraction of dissolved and particulate organic carbon in waters, Annales de Limnologie - International Journal of Limnology, vol.31, issue.1, pp.75-80, 1995.
DOI : 10.1051/limn/1995005

D. H. Shin, W. S. Shin, Y. H. Kim, M. H. Han, and S. J. Choi, Application of a combined process of moving-bed biofilm reactor (MBBR) and chemical coagulation for dyeing wastewater treatment, Water Science & Technology, vol.54, issue.9, pp.54181-189, 2006.
DOI : 10.2166/wst.2006.863

J. L. Shore, W. S. M-'coy, C. K. Gunsch, and D. M. , Application of a Moving Bed Biofilm Reactor for Tertiary Ammonia Removal in High Temperature Industrial Wastewater, Proceedings of the Water Environment Federation, vol.2010, issue.13, 2010.
DOI : 10.2175/193864710798182150

H. Spanjers and P. Vanrolleghem, Respirometry as a tool for rapid characterization of wastewater and activated sludge, Water Science and Technology, vol.31, issue.2, pp.105-114, 1995.
DOI : 10.1016/0273-1223(95)00184-O

D. B. Spengel and D. D. , Biokinetic modeling and scale-up considerations for rotating biological contactors, Water Environment Research, vol.64, issue.3, pp.223-235, 1992.
DOI : 10.2175/WER.64.3.6

Y. M. Su, J. Makinia, and P. K. , Estimation of Autotrophic Maximum Specific Growth Rate Constant???Experience from the Long-Term Operation of a Laboratory-Scale Sequencing Batch Reactor System, Water Environment Research, vol.80, issue.4, pp.355-366, 2008.
DOI : 10.2175/106143007X221436

I. Takács, C. M. Bye, K. Chapman, P. L. Dold, P. M. Fairlamb et al., A biofilm model for engineering design, Water Science & Technology, vol.55, issue.8-9, pp.329-336, 2007.
DOI : 10.2166/wst.2007.274

R. H. Van-waveren, S. Groot, H. Scholten, F. Van-geer, H. Wösten et al., Handbook Goog Modelling Practice, 1999.

E. Vigne, Etude et modélisation dynamique d'un procédé par biofiltration en nitrification tertiaire, 2007.

E. Vigne, J. M. Choubert, J. P. Canler, A. Héduit, and P. Lessard, Toward an operational dynamic model for tertiary nitrification by submerged biofiltration, Water Science & Technology, vol.55, issue.8-9, pp.301-308, 2007.
DOI : 10.2166/wst.2007.271

E. Vigne, J. M. Choubert, J. P. Canler, A. Héduit, K. Sorensen et al., A biofiltration model for tertiary nitrification of municipal wastewaters, Water Research, vol.44, issue.15, pp.4399-4410, 2010.
DOI : 10.1016/j.watres.2010.06.005

S. Villaverde, P. A. García-encina, and F. Fdz-polanco, Influence of pH over nitrifying biofilm activity in submerged biofilters, Water Research, vol.31, issue.5, pp.1180-1186, 1997.
DOI : 10.1016/S0043-1354(96)00376-4

R. C. Wang, X. H. Wen, and Y. Qian, Influence of carrier concentration on the performance and microbial characteristics of a suspended carrier biofilm reactor, Process Biochemistry, vol.40, issue.9, pp.2992-3001, 2005.
DOI : 10.1016/j.procbio.2005.02.024

O. Wanner and W. Gujer, Competition in biofilms, Water Science & Technology, vol.17, issue.2-3, pp.27-39, 1985.

O. Wanner and E. Morgenroth, Biofilm modeling with AQUASIM, Water Science & Technology, vol.49, pp.11-12, 2004.

O. Wanner and P. Reichert, Mathematical modeling of mixed-culture biofilms, Biotechnology and Bioengineering, vol.28, issue.2, pp.172-184, 1996.
DOI : 10.1002/(SICI)1097-0290(19960120)49:2<172::AID-BIT6>3.0.CO;2-N

K. Williamson and P. L. Mccarty, A model of substrate utilization by bacterial films, Journal of the Water Pollution Control Federation, vol.48, issue.1, pp.9-24, 1976.

S. Zhu and C. S. , The impact of temperature on nitrification rate in fixed film biofilters, Aquacultural Engineering, vol.26, issue.4, pp.221-237, 2002.
DOI : 10.1016/S0144-8609(02)00022-5

N. Correspondance-entre and N. Cl, Masses molaires : N = 14 g/mol, H = 1 g/mol, Cl = 35,45 g/mol Poids de N dans NH 4 Cl, pp.14-14

. Correspondance-entre-le-glucose, 1 mg de glucose correspond à 1,06 mg de DCO filtrée Pour un ratio de DCO filtrée