A new methodology for early BMP assessment using a ...mottelet/AD15/slides.pdf · Modiﬁed AM2 model O. Bernard, Z. Hadj-Sadok, D. Dochain, A. Genovesi, J. P. Steyer (2001),Dynamical

A new methodology for early BMP assessment using amathematical model

Sabrina Guerin 2 Stephane Mottelet 1 Sam Azimi 2 Jean Bernier 2

Laura Andre 3 Thierry Ribeiro 3 Andre Pauss 1 Vincent Rocher 2

1Universite de Technologie de Compiegne, FRANCE

2SIAAP Direction Developpement et Prospective, Colombes, FRANCE

3UniLaSalle Beauvais, FRANCE

15th Anaerobic Digestion 2017 Conference

Sabrina Guerin , Stephane Mottelet , Sam Azimi , Jean Bernier , Laura Andre , Thierry Ribeiro , Andre Pauss , Vincent Rocher (UTC/SIAAP/UniLaSalle)BMP, methodology and modeling AD15, 17/10/2017 1 / 19

MOCOPEE Program (Modeling, Control and Optimization of Wastewater TreatmentProcesses, www.mocopee.com)

The Mocopee research program aims to build the metrological and mathematicaltools (signal processing, treatment processes modeling, regulation) required toimprove the control and the optimization of water and sludge treatment plants.

R&D actions on the AD process :

I validate at industrial scale sewage sludge BMP estimation methods

I build predictive models of AD process


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 Gresillons)Inoculum sampled at the output of the digester

preliminary work :

S. Guerin et al. (2016), Cartographie des boues de STEP et reduction du temps de mesure du potentielmethanogene : � couplage experimentation en reacteur / modelisation �, L’eau, l’industrie, lesnuisances, no 397


Experimental device

500 ml reactors,I/S ratio=3CO2 trappingMean flow measurement by ≈ 10mlthrottles

AMPTS

Full compliance with experts recommendations :C. Holliger et al. (43 auteurs) (2016), Towards a standardization of biomethane potential tests, WaterScience &Technology


Experimental study

36 batchs in triplicatesMS, MV, DCO, DBOmeasurementBMP obtained after 20 days

No evident correlation betweenBMP and a priori measurements !

Could a model of AD digestion helpto make an early assessment ofBMP?

0 2 4 6 8 10t (day)

0

1

2

3

CH4

flow

(g C

OD/

L/da

y)

0 2 4 6 8 10t (day)

0

1

2

3

CH4

flow

(g C

OD/

L/da

y)

0 2 4 6 8 10t (day)

0

1

2

3

CH4

flow

(g C

OD/

L/da

y)

0 2 4 6 8 10t (day)

0

1

2

3

CH4

flow

(g C

OD/

L/da

y)

0 2 4 6 8 10t (day)

0

1

2

3

CH4

flow

(g C

OD/

L/da

y)

0 2 4 6 8 10t (day)

0

1

2

3

CH4

flow

(g C

OD/

L/da

y)

0 2 4 6 8 10t (day)

0

1

2

3

CH4

flow

(g C

OD/

L/da

y)

0 2 4 6 8 10t (day)

0

1

2

3

CH4

flow

(g C

OD/

L/da

y)

0 2 4 6 8 10t (day)

0

1

2

3

CH4

flow

(g C

OD/

L/da

y)

0 2 4 6 8 10t (day)

0

1

2

3

CH4

flow

(g C

OD/

L/da

y)

0 2 4 6 8 10t (day)

0

1

2

3

CH4

flow

(g C

OD/

L/da

y)

0 2 4 6 8 10t (day)

0

1

2

3

CH4

flow

(g C

OD/

L/da

y)


Modified AM2 modelO. Bernard, Z. Hadj-Sadok, D. Dochain, A. Genovesi, J. P. Steyer (2001), Dynamical model developmentand parameter identification for an anaerobic wastewater treatment process, Biotechnology andbioengineering

R. Fekih Salem, N. Abdellatif, T. Sari, and J. Harmand (2012), On a three step model of anaerobicdigestion including the hydrolysis of particulate matter, MATHMOD 2012

A. Donoso-Bravo, S. Perez-Elvira and F. Fdz-Polanco (2014), Simplified mechanistic model for thetwo-stage anaerobic degradation of sewage sludge, Environmental Technology

S0r0−−−−→ S1, (Hydrolysis)

S1r1−−−−→ YX1X1 + (1− YX1)S2 + k4CO2, (Acidification)

S2r2−−−−→ YX2X2 + (1− YX2)CH4 + k5CO2, (Methanogenesis)

S0 : insoluble organic molecules, S1 : simple compounds (fatty acids, peptides, aminoacids, . . .), S2 : volatile fatty acids

Warning : we use the � batch � version of this model !


Modified AM2 modelDifferential 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) = S00 , S1(0) = S0

1 , X1(0) = X 01 , X2(0) = X 0

2 .

reaction rates :

r0 = µ0S0, r1 = µmax1

S1X1

S1 + KS1

, r2 = µmax2

S2X2

S2 + KS2 + S22/KI

·

Parameters θ = (YX1 ,YX2 , µ0, µmax1 , µmax

2 ,KS1 ,KS2 ,KI︸︷︷︸θc : kinetic parameters

,X 01 ,X

02 ,S

00 ,S

01 ,S

02︸︷︷︸

θb : batch parameters

)


Modified AM2 modelIdentifiability

Knowing CH4(t), ∀t > 0 can we uniquely identify parameters?

I O. Bernard et al. (2001), R. Fekih Salem et al. (2012) model : no

I A. Donoso et al. (2014) : a priori no , but certain algebraic expressions areidentifiable :

CH4(∞) = (1− YX2)((1− YX1)(S

00 + S0

1) + S02

)Other interesting expressions (relative proportions of substrates) :

S00∑2

i=0 S0i

,S0

1∑2i=0 S0

i

,S0

2∑2i=0 S0

i


Modified AM2 modelPractical identification

Goals :1 obtain 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 :

I No identifiability of parameters =⇒ numerical problems !I Important mass of data (108 experiences to assimilate)


Identification of parametersAvailable measurements, simulations

For each batch #i we haveI (t i

k )k=1...mi the times of throttle switchsI (Di

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

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

d ik (θc , θb) =

(CH4(t i

k )− CH4(t ik−1)

)/(t i

k − t ik−1),

and the function

Ji(θc , θb) =

mi∑k=2

(t ik − t i

k−1)(Dik − d i

k (θc , θb))2

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


Identification of parametersStrategy

1 Learning phase : minimize with respect to ξ = (θc , θ1b . . . , θ

69b ) ∈ R353

ξ = argminξ

J(ξ) =∑

i=1...69

Ji(θc , θib) + λ‖ξ‖2,

We obtain θc ∈ R8 which is used for the predictionI Optimization : interior points method (fminc, MATLAB)I Moderate computation time (computer with 20 processors Xeon E5-2660-v2)

2 Prediction/validation phase at T = 4 days : minimize with respect to θib ∈ R5

θib = argmin

θbJi

T (θc , θb), i = 70 . . . 108

JiT (θc , θb) =

∑k=2

tk≤T

(t ik − t i

k−1)(Dik − dk

i (θc , θb))2


ResultsLearning on batchs #1 to #69

Kinetic parameters θc

YX1 0,58

YX2 0,12

µ0 0,29

µmax1 3,63

µmax2 2,67

KS1 1,02

KS2 3,45

KI 1,440 200 400 600 800 1000 1200 1400

true BMP (NmL)

0

200

400

600

800

1000

1200

pre

dic

ted

BM

P (

Nm

L)

Model-3


ResultsLearning, primary sludge

0 5 10 15

t (days)

0

100

200

300

400

flow

(N

mL/d

)

Model-3 - batch n°5 (Manip 20130717, cell=8)

0 5 10 15

t (days)

0

500

1000

Vol (

Nm

L))


0 5 10 15

t (days)

0

5

10

g.C

OD

/L


S0

S1

S2

0 5 10 15

t (days)

0

5

10

15

g.C

OD

/L


X1

X2


ResultsLearning, nitrification sludge

0 5 10 15

t (days)

0

100

200

300

400

flow

(N

mL/d

)


0 5 10 15

t (days)

0

500

1000

Vol (

Nm

L))


0 5 10 15

t (days)

0

5

10

g.C

OD

/L


S0

S1

S2

0 5 10 15

t (days)

0

2

4

6

8

g.C

OD

/L


X1

X2


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

0 200 400 600 800 1000 1200 1400

true BMP (NmL)

0

200

400

600

800

1000

1200

pre

dic

ted B

MP

(N

mL)

Model-3


ResultsPrediction, floated sludge

0 5 10 15

t (days)

0

100

200

300

400

flow

(N

mL/d

)


0 5 10 15

t (days)

0

500

1000

Vol (

Nm

L))


0 5 10 15

t (days)

0

5

10

g.C

OD

/L


S0

S1

S2

0 5 10 15

t (days)

0

5

10

g.C

OD

/L


X1

X2


ResultsPrediction, thickened sludge

0 5 10 15

t (days)

0

100

200

300

400

flow

(N

mL/d

)


0 5 10 15

t (days)

0

500

1000

Vol (

Nm

L))


0 5 10 15

t (days)

0

5

10

g.C

OD

/L


S0

S1

S2

0 5 10 15

t (days)

0

5

10

g.C

OD

/L


X1

X2


Trends and conclusions

Results :

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

Planned improvements :

I Theoretical study of identifiability of parameters in learning phaseI DBO and VSS measurements should be taken into accountI Coupling between triplicates has to be consideredI Confidence intervals should be computed for the predicted BMPI Actual model should be simplified and compared with other models


Thanks for your attention !


Documents

A new methodology for early BMP assessment using a ...mottelet/AD15/slides.pdf · Modiﬁed AM2 model O. Bernard, Z. Hadj-Sadok, D. Dochain, A. Genovesi, J. P. Steyer (2001),Dynamical