A new methodology for early BMP assessment using a mathematical model erin 2 ephane Mottelet 1 Sam Azimi 2 Jean Bernier 2 Sabrina Gu´ St´ e 3 Thierry Ribeiro 3 e Pauss 1 Vincent Rocher 2 Laura Andr´ Andr´ 1 Universit´ e de Technologie de Compi` egne, FRANCE 2 SIAAP Direction D´ eveloppement et Prospective, Colombes, FRANCE 3 UniLaSalle Beauvais, FRANCE 15 th Anaerobic Digestion 2017 Conference Sabrina Gu´ erin , St´ ephane Mottelet , Sam Azimi , Jean Bernier , Laura Andr´ BMP , methodology and modeling e , Thierry Ribeiro , Andr´ e Pauss , Vincent Rocher (UTC/SIAAP/UniLaSalle) AD15, 17/10/2017 1 / 19
MOCOPEE Program (Modeling, Control and Optimization of Wastewater Treatment Processes, www.mocopee.com) The Mocopee research program aims to build the metrological and mathematical tools (signal processing, treatment processes modeling, regulation) required to improve the control and the optimization of water and sludge treatment plants. R&D actions on the AD process : ◮ validate at industrial scale sewage sludge BMP estimation methods ◮ build predictive models of AD process Sabrina Gu´ erin , St´ ephane Mottelet , Sam Azimi , Jean Bernier , Laura Andr´ BMP , methodology and modeling e , Thierry Ribeiro , Andr´ e Pauss , Vincent Rocher (UTC/SIAAP/UniLaSalle) AD15, 17/10/2017 2 / 19
The different substrates considered in the study Primary, biologic (nitrification, denitrification), floated, mixed and thickened sludge, from different plants of SIAAP (Seine centre, Seine aval, Seine Gr´ esillons) Inoculum sampled at the output of the digester preliminary work : S. Gu´ erin et al. (2016), Cartographie des boues de STEP et r´ eduction du temps de mesure du potentiel m´ ethanog` ene : ≪ couplage exp´ erimentation en r´ eacteur / mod´ elisation ≫ , L ’eau, l’industrie, les nuisances, n o 397 Sabrina Gu´ erin , St´ ephane Mottelet , Sam Azimi , Jean Bernier , Laura Andr´ BMP , methodology and modeling e , Thierry Ribeiro , Andr´ e Pauss , Vincent Rocher (UTC/SIAAP/UniLaSalle) AD15, 17/10/2017 3 / 19
Experimental device AMPTS 500 ml reactors,I/S ratio=3 CO 2 trapping Mean flow measurement by ≈ 10ml throttles Full compliance with experts recommendations : C. Holliger et al. (43 auteurs) (2016), Towards a standardization of biomethane potential tests, Water Science &Technology Sabrina Gu´ erin , St´ ephane Mottelet , Sam Azimi , Jean Bernier , Laura Andr´ BMP , methodology and modeling e , Thierry Ribeiro , Andr´ e Pauss , Vincent Rocher (UTC/SIAAP/UniLaSalle) AD15, 17/10/2017 4 / 19
Experimental study 3 3 3 CH4 flow (g COD/L/day) CH4 flow (g COD/L/day) CH4 flow (g COD/L/day) 2 2 2 36 batchs in triplicates 1 1 1 0 0 0 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 MS, MV, DCO, DBO t (day) t (day) t (day) 3 3 3 CH4 flow (g COD/L/day) CH4 flow (g COD/L/day) CH4 flow (g COD/L/day) measurement 2 2 2 BMP obtained after 20 days 1 1 1 0 0 0 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 t (day) t (day) t (day) 3 3 3 CH4 flow (g COD/L/day) CH4 flow (g COD/L/day) CH4 flow (g COD/L/day) No evident correlation between 2 2 2 BMP and a priori measurements! 1 1 1 0 0 0 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 Could a model of AD digestion help t (day) t (day) t (day) 3 3 3 CH4 flow (g COD/L/day) CH4 flow (g COD/L/day) CH4 flow (g COD/L/day) to make an early assessment of 2 2 2 BMP? 1 1 1 0 0 0 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 t (day) t (day) t (day) Sabrina Gu´ erin , St´ ephane Mottelet , Sam Azimi , Jean Bernier , Laura Andr´ BMP , methodology and modeling e , Thierry Ribeiro , Andr´ e Pauss , Vincent Rocher (UTC/SIAAP/UniLaSalle) AD15, 17/10/2017 5 / 19
Modified AM2 model O. Bernard, Z. Hadj-Sadok, D. Dochain, A. Genovesi, J. P . Steyer (2001), Dynamical model development and parameter identification for an anaerobic wastewater treatment process, Biotechnology and bioengineering R. Fekih Salem, N. Abdellatif, T. Sari, and J. Harmand (2012), On a three step model of anaerobic digestion including the hydrolysis of particulate matter, MATHMOD 2012 A. Donoso-Bravo, S. P´ erez-Elvira and F. Fdz-Polanco (2014), Simplified mechanistic model for the two-stage anaerobic degradation of sewage sludge, Environmental Technology r 0 − − − − → S 1 , S 0 (Hydrolysis) r 1 S 1 − − − − → Y X 1 X 1 + ( 1 − Y X 1 ) S 2 + k 4 CO 2 , (Acidification) r 2 S 2 − − − − → Y X 2 X 2 + ( 1 − Y X 2 ) CH 4 + k 5 CO 2 , (Methanogenesis) S 0 : insoluble organic molecules, S 1 : simple compounds (fatty acids, peptides, amino acids, . . .), S 2 : volatile fatty acids Warning : we use the ≪ batch ≫ version of this model! Sabrina Gu´ erin , St´ ephane Mottelet , Sam Azimi , Jean Bernier , Laura Andr´ BMP , methodology and modeling e , Thierry Ribeiro , Andr´ e Pauss , Vincent Rocher (UTC/SIAAP/UniLaSalle) AD15, 17/10/2017 6 / 19
Modified AM2 model Differential equations system Perfectly mixed batch reactor, states of the sytem : S 0 , S 1 , S 2 , X 1 , X 2 S 0 ′ = − r 0 , S 1 ′ = r 0 − r 1 , S 2 ′ = ( 1 − Y X 1 ) r 1 − r 2 , X 1 ′ = Y X 1 r 1 , X 2 ′ = Y X 2 r 2 , CH 4 ′ = ( 1 − Y X 2 ) r 2 initial conditions : S 0 ( 0 ) = S 0 0 , S 1 ( 0 ) = S 0 1 , X 1 ( 0 ) = X 0 1 , X 2 ( 0 ) = X 0 2 . reaction rates : S 1 X 1 S 2 X 2 r 0 = µ 0 S 0 , r 1 = µ max , r 2 = µ max · 1 2 S 2 + K S 2 + S 2 S 1 + K S 1 2 / K I Parameters θ = ( Y X 1 , Y X 2 , µ 0 , µ max , µ max , X 0 1 , X 0 2 , S 0 0 , S 0 1 , S 0 , K S 1 , K S 2 , K I ) 1 2 2 � �� � � �� � θ b : batch parameters θ c : kinetic parameters Sabrina Gu´ erin , St´ ephane Mottelet , Sam Azimi , Jean Bernier , Laura Andr´ BMP , methodology and modeling e , Thierry Ribeiro , Andr´ e Pauss , Vincent Rocher (UTC/SIAAP/UniLaSalle) AD15, 17/10/2017 7 / 19
Modified AM2 model Identifiability Knowing CH 4 ( t ) , ∀ t > 0 can we uniquely identify parameters? ◮ O. Bernard et al. (2001), R. Fekih Salem et al. (2012) model : no ◮ A. Donoso et al. (2014) : a priori no , but certain algebraic expressions are identifiable : � � ( 1 − Y X 1 )( S 0 0 + S 0 1 ) + S 0 CH 4 ( ∞ ) = ( 1 − Y X 2 ) 2 Other interesting expressions (relative proportions of substrates) : S 0 S 0 S 0 0 1 2 , , � 2 � 2 � 2 i = 0 S 0 i = 0 S 0 i = 0 S 0 i i i Sabrina Gu´ erin , St´ ephane Mottelet , Sam Azimi , Jean Bernier , Laura Andr´ BMP , methodology and modeling e , Thierry Ribeiro , Andr´ e Pauss , Vincent Rocher (UTC/SIAAP/UniLaSalle) AD15, 17/10/2017 8 / 19
Modified AM2 model Practical identification Goals : obtain a mathematical model allowing to reproduce the methane rate of our 108 1 experiences, without necessarily uniquely describe state variables ( X 1 , X 2 , S 1 , S 2 , S 0 ) . being able to use this model to predict the BMP from new data measured after 4 days 2 Pitfalls to bypass : ◮ No identifiability of parameters = ⇒ numerical problems! ◮ Important mass of data (108 experiences to assimilate) Sabrina Gu´ erin , St´ ephane Mottelet , Sam Azimi , Jean Bernier , Laura Andr´ BMP , methodology and modeling e , Thierry Ribeiro , Andr´ e Pauss , Vincent Rocher (UTC/SIAAP/UniLaSalle) AD15, 17/10/2017 9 / 19
Identification of parameters Available measurements, simulations For each batch #i we have ◮ ( t i k ) k = 1 ... m i the times of throttle switchs ◮ ( D i k ) k = 2 ... m i the mean CH 4 flow rate measured at t = t i k , k = 1 . . . m i For θ = ( θ c , θ b ) we can simulate the mean flow of CH 4 : � � d i CH 4 ( t i k ) − CH 4 ( t i / ( t i k − t i k ( θ c , θ b ) = k − 1 ) k − 1 ) , and the function m i � ( t i k − t i k − 1 )( D i k − d i k ( θ c , θ b )) 2 J i ( θ c , θ b ) = k = 2 evaluates the misfit between measurements of batch #i and the simulation with parameters θ = ( θ c , θ b ) Sabrina Gu´ erin , St´ ephane Mottelet , Sam Azimi , Jean Bernier , Laura Andr´ BMP , methodology and modeling e , Thierry Ribeiro , Andr´ e Pauss , Vincent Rocher (UTC/SIAAP/UniLaSalle) AD15, 17/10/2017 10 / 19
Identification of parameters Strategy Learning phase : minimize with respect to ξ = ( θ c , θ 1 b . . . , θ 69 b ) ∈ R 353 1 � ˆ J i ( θ c , θ i b ) + λ � ξ � 2 , ξ = arg min ξ J ( ξ ) = i = 1 ... 69 θ c ∈ R 8 which is used for the prediction We obtain ˆ ◮ Optimization : interior points method (fminc, MATLAB) ◮ Moderate computation time (computer with 20 processors Xeon E5-2660-v2) Prediction/validation phase at T = 4 days : minimize with respect to θ i b ∈ R 5 2 θ i ˆ T (ˆ b = arg min J i θ c , θ b ) , i = 70 . . . 108 θ b � T (ˆ ( t i k − t i k − 1 )( D i k − d k i (ˆ θ c , θ b )) 2 J i θ c , θ b ) = k = 2 t k ≤ T Sabrina Gu´ erin , St´ ephane Mottelet , Sam Azimi , Jean Bernier , Laura Andr´ BMP , methodology and modeling e , Thierry Ribeiro , Andr´ e Pauss , Vincent Rocher (UTC/SIAAP/UniLaSalle) AD15, 17/10/2017 11 / 19
Results Learning on batchs #1 to #69 Model-3 Kinetic parameters ˆ 1200 θ c 1000 Y X 1 0 , 58 Y X 2 0 , 12 predicted BMP (NmL) 800 µ 0 0 , 29 600 µ max 3 , 63 1 µ max 2 , 67 2 400 K S 1 1 , 02 200 K S 2 3 , 45 K I 1 , 44 0 0 200 400 600 800 1000 1200 1400 true BMP (NmL) Sabrina Gu´ erin , St´ ephane Mottelet , Sam Azimi , Jean Bernier , Laura Andr´ BMP , methodology and modeling e , Thierry Ribeiro , Andr´ e Pauss , Vincent Rocher (UTC/SIAAP/UniLaSalle) AD15, 17/10/2017 12 / 19
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