A new methodology for early BMP assessment using a mathematical - - PowerPoint PPT Presentation

A new methodology for early BMP assessment using a mathematical model

Sabrina Gu´ erin 2 St´ ephane Mottelet 1 Sam Azimi 2 Jean Bernier 2 Laura Andr´ e 3 Thierry Ribeiro 3 Andr´ e Pauss 1 Vincent Rocher 2

1Universit´

e de Technologie de Compi` egne, FRANCE

2SIAAP Direction D´

eveloppement et Prospective, Colombes, FRANCE

3UniLaSalle Beauvais, FRANCE

15th Anaerobic Digestion 2017 Conference

Sabrina Gu´ erin , St´ ephane Mottelet , Sam Azimi , Jean Bernier , Laura Andr´ e , Thierry Ribeiro , Andr´ e Pauss , Vincent Rocher (UTC/SIAAP/UniLaSalle) BMP , methodology and modeling 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´ e , Thierry Ribeiro , Andr´ e Pauss , Vincent Rocher (UTC/SIAAP/UniLaSalle) BMP , methodology and modeling 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, no 397

Sabrina Gu´ erin , St´ ephane Mottelet , Sam Azimi , Jean Bernier , Laura Andr´ e , Thierry Ribeiro , Andr´ e Pauss , Vincent Rocher (UTC/SIAAP/UniLaSalle) BMP , methodology and modeling AD15, 17/10/2017 3 / 19

Experimental device

500 ml reactors,I/S ratio=3 CO2 trapping Mean flow measurement by ≈ 10ml throttles AMPTS 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´ e , Thierry Ribeiro , Andr´ e Pauss , Vincent Rocher (UTC/SIAAP/UniLaSalle) BMP , methodology and modeling AD15, 17/10/2017 4 / 19

Experimental study

36 batchs in triplicates MS, MV, DCO, DBO measurement BMP obtained after 20 days No evident correlation between BMP and a priori measurements! Could a model of AD digestion help to make an early assessment of BMP?

2 4 6 8 10 t (day) 1 2 3 CH4 flow (g COD/L/day) 2 4 6 8 10 t (day) 1 2 3 CH4 flow (g COD/L/day) 2 4 6 8 10 t (day) 1 2 3 CH4 flow (g COD/L/day) 2 4 6 8 10 t (day) 1 2 3 CH4 flow (g COD/L/day) 2 4 6 8 10 t (day) 1 2 3 CH4 flow (g COD/L/day) 2 4 6 8 10 t (day) 1 2 3 CH4 flow (g COD/L/day) 2 4 6 8 10 t (day) 1 2 3 CH4 flow (g COD/L/day) 2 4 6 8 10 t (day) 1 2 3 CH4 flow (g COD/L/day) 2 4 6 8 10 t (day) 1 2 3 CH4 flow (g COD/L/day) 2 4 6 8 10 t (day) 1 2 3 CH4 flow (g COD/L/day) 2 4 6 8 10 t (day) 1 2 3 CH4 flow (g COD/L/day) 2 4 6 8 10 t (day) 1 2 3 CH4 flow (g COD/L/day)

Sabrina Gu´ erin , St´ ephane Mottelet , Sam Azimi , Jean Bernier , Laura Andr´ e , Thierry Ribeiro , Andr´ e Pauss , Vincent Rocher (UTC/SIAAP/UniLaSalle) BMP , methodology and modeling 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

S0

r0

− − − − → S1, (Hydrolysis) S1

r1

− − − − → YX1X1 + (1 − YX1)S2 + k4CO2, (Acidification) S2

r2

− − − − → YX2X2 + (1 − YX2)CH4 + k5CO2, (Methanogenesis) S0 : insoluble organic molecules, S1 : simple compounds (fatty acids, peptides, amino acids, . . .), S2 : volatile fatty acids Warning : we use the ≪ batch ≫ version of this model!

Sabrina Gu´ erin , St´ ephane Mottelet , Sam Azimi , Jean Bernier , Laura Andr´ e , Thierry Ribeiro , Andr´ e Pauss , Vincent Rocher (UTC/SIAAP/UniLaSalle) BMP , methodology and modeling AD15, 17/10/2017 6 / 19

Modified AM2 model

Differential equations system

Perfectly mixed batch reactor, states of the sytem : S0, S1, S2, X1, X2 S0′ = −r0, S1′ = r0 − r1, S2′ = (1 − YX1)r1 − r2, X1′ = YX1r1, X2′ = YX2r2, CH4′ = (1 − YX2)r2 initial conditions : S0(0) = S0

0, S1(0) = S0 1, X1(0) = X 0 1 , X2(0) = X 0 2 .

reaction rates : r0 = µ0S0, r1 = µmax

1

S1X1 S1 + KS1 , r2 = µmax

2

S2X2 S2 + KS2 + S2

2/KI

· Parameters θ = (YX1, YX2, µ0, µmax

1

, µmax

2

, KS1, KS2, KI

• θc : kinetic parameters

, X 0

1 , X 0 2 , S0 0, S0 1, S0 2

• θb : batch parameters

)

Sabrina Gu´ erin , St´ ephane Mottelet , Sam Azimi , Jean Bernier , Laura Andr´ e , Thierry Ribeiro , Andr´ e Pauss , Vincent Rocher (UTC/SIAAP/UniLaSalle) BMP , methodology and modeling AD15, 17/10/2017 7 / 19

Modified AM2 model

Identifiability

Knowing CH4(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 : CH4(∞) = (1 − YX2)

• (1 − YX1)(S0

0 + S0 1) + S0 2

• Other interesting expressions (relative proportions of substrates) :

S0 2

i=0 S0 i

, S0

1

2

i=0 S0 i

, S0

2

2

i=0 S0 i

Sabrina Gu´ erin , St´ ephane Mottelet , Sam Azimi , Jean Bernier , Laura Andr´ e , Thierry Ribeiro , Andr´ e Pauss , Vincent Rocher (UTC/SIAAP/UniLaSalle) BMP , methodology and modeling AD15, 17/10/2017 8 / 19

Modified AM2 model

Practical identification

Goals :

1

• btain a mathematical model allowing to reproduce the methane rate of our 108

experiences, without necessarily uniquely describe state variables (X1, X2, S1, S2, S0).

2

being able to use this model to predict the BMP from new data measured after 4 days 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´ e , Thierry Ribeiro , Andr´ e Pauss , Vincent Rocher (UTC/SIAAP/UniLaSalle) BMP , methodology and modeling AD15, 17/10/2017 9 / 19

Identification of parameters

Available measurements, simulations

For each batch #i we have ◮ (ti

k)k=1...mi the times of throttle switchs

◮ (Di

k)k=2...mi the mean CH4 flow rate measured at t = ti k, k = 1 . . . mi

For θ = (θc, θb) we can simulate the mean flow of CH4 : di

k(θc, θb) =

• CH4(ti

k) − CH4(ti k−1)

• /(ti

k − ti k−1),

and the function Ji(θc, θb) =

mi

• k=2

(ti

k − ti k−1)(Di k − di k(θc, θb))2

evaluates the misfit between measurements of batch #i and the simulation with parameters θ = (θc, θb)

Sabrina Gu´ erin , St´ ephane Mottelet , Sam Azimi , Jean Bernier , Laura Andr´ e , Thierry Ribeiro , Andr´ e Pauss , Vincent Rocher (UTC/SIAAP/UniLaSalle) BMP , methodology and modeling AD15, 17/10/2017 10 / 19

Identification of parameters

Strategy

1

Learning phase : minimize with respect to ξ = (θc, θ1

b . . . , θ69 b ) ∈ R353

ˆ ξ = arg min

ξ J(ξ) =

• i=1...69

Ji(θc, θi

b) + λξ2,

We obtain ˆ θc ∈ R8 which is used for the prediction

◮ Optimization : interior points method (fminc, MATLAB) ◮ Moderate computation time (computer with 20 processors Xeon E5-2660-v2) 2

Prediction/validation phase at T = 4 days : minimize with respect to θi

b ∈ R5

ˆ θi

b = arg min θb

Ji

T(ˆ

θc, θb), i = 70 . . . 108 Ji

T(ˆ

θc, θb) =

• k=2

tk≤T

(ti

k − ti k−1)(Di k − dk i (ˆ

θc, θb))2

Sabrina Gu´ erin , St´ ephane Mottelet , Sam Azimi , Jean Bernier , Laura Andr´ e , Thierry Ribeiro , Andr´ e Pauss , Vincent Rocher (UTC/SIAAP/UniLaSalle) BMP , methodology and modeling AD15, 17/10/2017 11 / 19

Results

Learning on batchs #1 to #69

Kinetic parameters ˆ θc YX1 0, 58 YX2 0, 12 µ0 0, 29 µmax

1

3, 63 µmax

2

2, 67 KS1 1, 02 KS2 3, 45 KI 1, 44

200 400 600 800 1000 1200 1400

true BMP (NmL)

200 400 600 800 1000 1200

predicted BMP (NmL) Model-3

Sabrina Gu´ erin , St´ ephane Mottelet , Sam Azimi , Jean Bernier , Laura Andr´ e , Thierry Ribeiro , Andr´ e Pauss , Vincent Rocher (UTC/SIAAP/UniLaSalle) BMP , methodology and modeling AD15, 17/10/2017 12 / 19

Results

Learning, primary sludge

5 10 15

t (days)

100 200 300 400

flow (NmL/d) Model-3 - batch n°5 (Manip 20130717, cell=8)

5 10 15

t (days)

500 1000

Vol (NmL)) Model-3 - batch n°5 (Manip 20130717, cell=8) 5 10 15 t (days) 5 10 g.COD/L Model-3 - batch n°5 (Manip 20130717, cell=8)

S0 S1 S2

5 10 15

t (days)

5 10 15

g.COD/L Model-3 - batch n°5 (Manip 20130717, cell=8)

X1 X2

Sabrina Gu´ erin , St´ ephane Mottelet , Sam Azimi , Jean Bernier , Laura Andr´ e , Thierry Ribeiro , Andr´ e Pauss , Vincent Rocher (UTC/SIAAP/UniLaSalle) BMP , methodology and modeling AD15, 17/10/2017 13 / 19

Results

Learning, nitrification sludge

5 10 15

t (days)

100 200 300 400

flow (NmL/d) Model-3 - batch n°64 (Manip 20140116, cell=10)

5 10 15

t (days)

500 1000

Vol (NmL)) Model-3 - batch n°64 (Manip 20140116, cell=10) 5 10 15 t (days) 5 10 g.COD/L Model-3 - batch n°64 (Manip 20140116, cell=10)

S0 S1 S2

5 10 15

t (days)

2 4 6 8

g.COD/L Model-3 - batch n°64 (Manip 20140116, cell=10)

X1 X2

Sabrina Gu´ erin , St´ ephane Mottelet , Sam Azimi , Jean Bernier , Laura Andr´ e , Thierry Ribeiro , Andr´ e Pauss , Vincent Rocher (UTC/SIAAP/UniLaSalle) BMP , methodology and modeling AD15, 17/10/2017 14 / 19

Results

Prediction/validation on batchs #70 to #108 at T = 4 days

200 400 600 800 1000 1200 1400

true BMP (NmL)

200 400 600 800 1000 1200

predicted BMP (NmL) Model-3

Sabrina Gu´ erin , St´ ephane Mottelet , Sam Azimi , Jean Bernier , Laura Andr´ e , Thierry Ribeiro , Andr´ e Pauss , Vincent Rocher (UTC/SIAAP/UniLaSalle) BMP , methodology and modeling AD15, 17/10/2017 15 / 19

Results

Prediction, floated sludge

5 10 15

t (days)

100 200 300 400

flow (NmL/d) Model-3 - batch n°92 (Manip 20140305, cell=11)

5 10 15

t (days)

500 1000

Vol (NmL)) Model-3 - batch n°92 (Manip 20140305, cell=11) 5 10 15 t (days) 5 10 g.COD/L Model-3 - batch n°92 (Manip 20140305, cell=11)

S0 S1 S2

5 10 15

t (days)

5 10

g.COD/L Model-3 - batch n°92 (Manip 20140305, cell=11)

X1 X2

Sabrina Gu´ erin , St´ ephane Mottelet , Sam Azimi , Jean Bernier , Laura Andr´ e , Thierry Ribeiro , Andr´ e Pauss , Vincent Rocher (UTC/SIAAP/UniLaSalle) BMP , methodology and modeling AD15, 17/10/2017 16 / 19

Results

Prediction, thickened sludge

5 10 15

t (days)

100 200 300 400

flow (NmL/d) Model-3 - batch n°106 (Manip 20140407, cell=13)

5 10 15

t (days)

500 1000

Vol (NmL)) Model-3 - batch n°106 (Manip 20140407, cell=13) 5 10 15 t (days) 5 10 g.COD/L Model-3 - batch n°106 (Manip 20140407, cell=13)

S0 S1 S2

5 10 15

t (days)

5 10

g.COD/L Model-3 - batch n°106 (Manip 20140407, cell=13)

X1 X2

Sabrina Gu´ erin , St´ ephane Mottelet , Sam Azimi , Jean Bernier , Laura Andr´ e , Thierry Ribeiro , Andr´ e Pauss , Vincent Rocher (UTC/SIAAP/UniLaSalle) BMP , methodology and modeling AD15, 17/10/2017 17 / 19

Trends and conclusions

Results :

◮ Well fitted kinetics in learning phase and good prediction of BMP at 4 days ◮ Ratios of S0, S1, S2 seem to be interpretable

Planned improvements :

◮ Theoretical study of identifiability of parameters in learning phase ◮ DBO and VSS measurements should be taken into account ◮ Coupling between triplicates has to be considered ◮ Confidence intervals should be computed for the predicted BMP ◮ Actual model should be simplified and compared with other models Sabrina Gu´ erin , St´ ephane Mottelet , Sam Azimi , Jean Bernier , Laura Andr´ e , Thierry Ribeiro , Andr´ e Pauss , Vincent Rocher (UTC/SIAAP/UniLaSalle) BMP , methodology and modeling AD15, 17/10/2017 18 / 19

Thanks for your attention!

Sabrina Gu´ erin , St´ ephane Mottelet , Sam Azimi , Jean Bernier , Laura Andr´ e , Thierry Ribeiro , Andr´ e Pauss , Vincent Rocher (UTC/SIAAP/UniLaSalle) BMP , methodology and modeling AD15, 17/10/2017 19 / 19