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Dynamic modeling and parameter estimation of biomethane production from microalgae co-digestion

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Abstract

This work proposes a dynamic modeling procedure applied to biomethane production from microalgae residual co-digestion. A two-stage anaerobic digestion representation is selected, considering acidogenesis and methanogenesis as main reaction pathways. Based on the experimental database generated in the University of Mons Laboratories, several candidate models, assuming the presence or absence of biomass dynamics, are suggested, and parametric structural and local identifiability studies are performed. An original parameter estimation procedure is applied to a data-set partition used for model direct validation. The remaining experiment data are dedicated to cross-validation. The results point out how these dynamic models may serve as advanced monitoring software tools such as digital twins, even in the presence of incomplete process data.

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Abbreviations

B :

Cumulative biogas production volume

\({B_\textrm{f}}\) :

Final biogas production volume

\(\mathrm {CO_2}\) :

Carbon dioxide

\(\textrm{CO}\) :

Carbon monoxide

\(\mathrm {CH_4}\) :

Methane

\(\mathrm {H_2S}\) :

Hydrogen sulfide

\(\mathrm {NH_3}\) :

Ammonia

\(\textrm{TOC}\) :

Total organic carbon (\(\%\))

\(\textrm{TC}\) :

Total carbon (\(\%\))

\(\textrm{TIC}\) :

Total inorganic carbon (\(\%\))

\(\mathrm {NH_4^+}\) :

Ammonium cation

\(\textrm{NaOH}\) :

Sodium Hydroxide

\(\mathrm {Na^+}\) :

Sodium ion

\(\mathrm {H^+}\) :

Hydrogen ion

\(\textrm{TKN}\) :

Total Kjeldahl nitrogen

\(\mathrm {C_{NaOH}}\) :

Concentration of sodium hydroxide (mol/L)

TS:

Total solids (\(\%\))

VS:

Volatile solids (\(\%\))

VFA:

Volatile fatty acids

LCFA:

Long-chain fatty acids

C/N ratio:

Carbon over nitrogen ratio

RSD:

Relative standard deviation

I/S ratio:

Inoculum to substrate ratio

\({m_\textrm{I}}\) :

Weight of inoculum (g)

\({m_\textrm{S}}\) :

Weight of substrate (g)

\({m_\mathrm{{liq}}}\) :

Weight of liquid (g)

\(\mathrm {N_2}\) :

Nitrogen

GC:

Gas chromatography

TCD:

Thermal conductivity detector

\({V_\textrm{S}}\) :

Volume of produced biogas from the substrate (mL)

\({V_\textrm{B}}\) :

Volume of produced biogas from the inoculum (mL)

\({m_\mathrm{{I,S}}}\) :

Weight of inoculum in substrate assays

\({m_\mathrm{{I,B}}}\) :

Weight of inoculum in blank assays

\({m_\mathrm{{S,S}}}\) :

Weight of substrate in substrate assays

BVS:

Biodegradable volatile solids

\({S_i}\) :

ith Substrate concentration

\({X_i}\) :

ith Biomass concentration

\({\xi }\) :

State variable (or species) concentration vector

\({K_1}\) :

Stoichiometric matrix of the liquid components

\({K_2}\) :

Stoichiometric matrix of the gas components

\({k_i}\) :

ith Stoichiometric coefficient

r :

Reaction rate vector

\({Q_i}\) :

Gaseous output flow rate of component i

\({\mu _{i}}\) :

Specific rate of reaction i

\({\mu _{\mathrm{{max}},i}}\) :

Maximum specific rate of reaction i (constant)

\({K_{\textrm{S}_i}}\) :

Monod half-saturation constant related to the ith substrate intake

\({k_{\textrm{d},i}}\) :

ith Biomass decay rate

\({\%_i}\) :

Volumetric percentage of gas component i

\({Q_\mathrm{{exp}}}\) :

Gas flow rate measured data

\({Q_\mathrm{{model}}}\) :

Gas flow rate estimated by the model

\({\theta }\) :

Parameter vector

\({n_\textrm{S}}\) :

Number of samples during one experiment

M :

Total number of samples over the considered experiments

\({\Sigma }\) :

Covariance matrix of the measurement errors

y :

System measurement vector

u :

System input vector

\({\Re _{n}}\) :

n-Dimensional real number space

IC:

Parameter initial condition (or guess)

\({T_\mathrm{{SS}}}\) :

Total suspended solids

FIM:

Fisher Information Matrix

P :

Covariance matrix of the estimation error

\({\sigma }\) :

Scalar a posteriori estimation of the measurement error variance

\({I_\textrm{n}}\) :

Identity matrix of dimension n

J :

Cost function

\({\lambda _\textrm{f}}\) :

Weight applied to the final VS value penalty

\({\lambda _\textrm{var}}\) :

Weight applied to the biomass variance penalty

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Acknowledgements

This research is part of the AlgoTech project (convention 1510612-Algotech) supported by the Walloon Region (DGO6). The authors also thank Hana Berriche for her participation to the experimental sessions.

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Authors and Affiliations

  1. Thermodynamics and Mathematical Physics Unit, Faculty of Engineering, University of Mons, 7000, Mons, Belgium

    A. Henrotin

  2. Chemical and Biochemical Process Engineering Unit, Faculty of Engineering, University of Mons, 7000, Mons, Belgium

    A.-L. Hantson

  3. Systems, Estimation, Control and Optimization (SECO) Group, Faculty of Engineering, University of Mons, 7000, Mons, Belgium

    L. Dewasme

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Henrotin, A., Hantson, AL. & Dewasme, L. Dynamic modeling and parameter estimation of biomethane production from microalgae co-digestion. Bioprocess Biosyst Eng 46, 129–146 (2023). https://doi.org/10.1007/s00449-022-02818-5

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