In many applications, complex biological phenomena can be reproduced via structured mathematical models, which depend on numerous biotic and abiotic input parameters, whose effect on model outputs can be of paramount importance. The calibration of model parameters is crucial to obtain the best fit between simulated and experimental data. Sensitivity analysis and uncertainty quantification constitute essential tools in the field of biological systems modeling. Despite the significant number of applications of sensitivity analysis in wet anaerobic digestion, there are no examples of global sensitivity analysis for mathematical models describing the dry anaerobic digestion in plug-flow reactors. For the first time, the present study explores the global sensitivity analysis and uncertainty quantification for a plug-flow reactor model. The investigated model accounts for the mass$ / $volume variation that takes place in these systems as a result of solid waste conversion in gaseous value-added compounds. A preliminary screening based on the Morris' method allowed for the definition of three different groups of parameters. A surrogate model was constructed to investigate the relation between input and output parameters without running demanding simulations from scratch. The obtained Sobol' indices allowed to perform the quantitative global sensitivity analysis. Finally, the uncertainty quantification results led to the definition of the probability density function related to the investigated quantity of interest. The study showed that the net methane production is mostly sensitive to the values of the conversion parameter related to the particulate biodegradable volatile solids in acetic acid $ k_1 $ and to the kinetic parameter describing the acetic acid uptake $ k_2 $. The application of these techniques led to helpful information for model calibration and validation.
Citation: Daniele Bernardo Panaro, Andrea Trucchia, Vincenzo Luongo, Maria Rosaria Mattei, Luigi Frunzo. Global sensitivity analysis and uncertainty quantification for a mathematical model of dry anaerobic digestion in plug-flow reactors[J]. Mathematical Biosciences and Engineering, 2024, 21(9): 7139-7164. doi: 10.3934/mbe.2024316
In many applications, complex biological phenomena can be reproduced via structured mathematical models, which depend on numerous biotic and abiotic input parameters, whose effect on model outputs can be of paramount importance. The calibration of model parameters is crucial to obtain the best fit between simulated and experimental data. Sensitivity analysis and uncertainty quantification constitute essential tools in the field of biological systems modeling. Despite the significant number of applications of sensitivity analysis in wet anaerobic digestion, there are no examples of global sensitivity analysis for mathematical models describing the dry anaerobic digestion in plug-flow reactors. For the first time, the present study explores the global sensitivity analysis and uncertainty quantification for a plug-flow reactor model. The investigated model accounts for the mass$ / $volume variation that takes place in these systems as a result of solid waste conversion in gaseous value-added compounds. A preliminary screening based on the Morris' method allowed for the definition of three different groups of parameters. A surrogate model was constructed to investigate the relation between input and output parameters without running demanding simulations from scratch. The obtained Sobol' indices allowed to perform the quantitative global sensitivity analysis. Finally, the uncertainty quantification results led to the definition of the probability density function related to the investigated quantity of interest. The study showed that the net methane production is mostly sensitive to the values of the conversion parameter related to the particulate biodegradable volatile solids in acetic acid $ k_1 $ and to the kinetic parameter describing the acetic acid uptake $ k_2 $. The application of these techniques led to helpful information for model calibration and validation.
| [1] |
G. Esposito, L. Frunzo, F. Liotta, A. Panico, F. Pirozzi, Bio-methane potential tests to measure the biogas production from the digestion and co-digestion of complex organic substrates, Open Environ. Eng. J., 5 (2012), 1–8. https://doi.org/10.2174/1874829501205010001 doi: 10.2174/1874829501205010001
|
| [2] |
G. Esposito, L. Frunzo, A. Giordano, F. Liotta, A. Panico, F. Pirozzi, Anaerobic co-digestion of organic wastes, Rev. Environ. Sci. Bio/Technol., 11 (2012), 325–341. https://doi.org/10.1007/s11157-012-9277-8 doi: 10.1007/s11157-012-9277-8
|
| [3] |
V. Luongo, M. R. Mattei, L. Frunzo, B. D'Acunto, K. Gupta, S. Chellam, et al., A transient biological fouling model for constant flux microfiltration, Math. Biosci. Eng., 20 (2023), 1274–1296. https://doi.org/10.3934/mbe.2023058 doi: 10.3934/mbe.2023058
|
| [4] |
Y. Li, S. Y. Park, J. Zhu, Solid-state anaerobic digestion for methane production from organic waste, Renewable Sustainable Energy Rev., 15 (2011), 821–826. https://doi.org/10.1016/j.rser.2010.07.042 doi: 10.1016/j.rser.2010.07.042
|
| [5] |
O. Karthikeyan, C. Visvanathan, Bio-energy recovery from high-solid organic substrates by dry anaerobic bio-conversion processes: A review, Rev. Environ. Sci. Bio/Technol., 12 (2013), 257–284. https://doi.org/10.1007/s11157-012-9304-9 doi: 10.1007/s11157-012-9304-9
|
| [6] |
P. Vandevivere, New and broader applications of anaerobic digestion, Critical Rev. Env. Sci. Technol., 29 (1999), 151–173. https://doi.org/10.1080/10643389991259191 doi: 10.1080/10643389991259191
|
| [7] |
G. Policastro, V. Luongo, L. Frunzo, N. Cogan, M. Fabbricino, A mechanistic mathematical model for photo fermentative hydrogen and polyhydroxybutyrate production, Math. Biosci. Eng., 20 (2023), 7407–7428. https://doi.org/10.3934/mbe.2023321 doi: 10.3934/mbe.2023321
|
| [8] |
A. Donoso-Bravo, C. Sadino-Riquelme, D. Gómez, C. Segura, E. Valdebenito, F. Hansen, Modelling of an anaerobic plug-flow reactor. process analysis and evaluation approaches with non-ideal mixing considerations, Bioresour. Technol., 260 (2018), 95–104. https://doi.org/10.1016/j.biortech.2018.03.082 doi: 10.1016/j.biortech.2018.03.082
|
| [9] |
I. Białobrzewski, K. Waszkielis, K. Bułkowska, The application of Anaerobic Digestion Model No. 1 for the optimization of biogas production from maize silage, pig manure, cattle manure, and digestate in a full-scale biogas plant, Fuel, 357 (2024), 129789. https://doi.org/10.1016/j.fuel.2023.129789 doi: 10.1016/j.fuel.2023.129789
|
| [10] |
R. Kothari, A. Pandey, S. Kumar, V. Tyagi, S. Tyagi, Different aspects of dry anaerobic digestion for bio-energy: An overview, Renewable Sustainable Energy Rev., 39 (2014), 174–195. https://doi.org/10.1016/j.rser.2014.07.011 doi: 10.1016/j.rser.2014.07.011
|
| [11] |
D. J. Batstone, J. Keller, I. Angelidaki, S. Kalyuzhnyi, S. Pavlostathis, A. Rozzi, et al., The iwa anaerobic digestion model no 1 (adm1), Water Sci. Technol., 45 (2002), 65–73. https://doi.org/10.2166/wst.2002.0292 doi: 10.2166/wst.2002.0292
|
| [12] |
C. De Crescenzo, A. Marzocchella, D. Karatza, S. Chianese, D. Musmarra, Autogenerative high-pressure anaerobic digestion modelling of volatile fatty acids: Effect of pressure variation and substrate composition on volumetric mass transfer coefficients, kinetic parameters, and process performance, Fuel, 358 (2024), 130144, https://doi.org/10.1016/j.fuel.2023.130144 doi: 10.1016/j.fuel.2023.130144
|
| [13] | C. De Crescenzo, A. Marzocchella, D. Karatza, A. Molino, P. Ceron-Chafla, R. E. Lindeboom, et al., Modelling of autogenerative high-pressure anaerobic digestion in a batch reactor for the production of pressurised biogas, Biotechnol. Biofuels Bioprod., 15 (2022). https://doi.org/10.1186/s13068-022-02117-x |
| [14] |
C. Fall, J. Loaiza-Navía, Design of a tracer test experience and dynamic calibration of the hydraulic model for a full-scale wastewater treatment plant by use of AQUASIM, Water Environ. Res., 79 (2007), 893–900. https://doi.org/10.2175/106143007X176068 doi: 10.2175/106143007X176068
|
| [15] | Y. Muslu, Numerical approach to plug-flow activated sludge reactor kinetics, Comput. Biol. Med., 30, (2000), 207–223. https://doi.org/10.1016/S0010-4825(00)00009-3 |
| [16] |
V. Vavilin, L. Lokshina, X. Flotats, I. Angelidaki, Anaerobic digestion of solid material: Multidimensional modeling of continuous-flow reactor with non-uniform influent concentration distributions, Biotechnol. Bioeng., 97 (2007), 354–366. https://doi.org/10.1002/bit.21239 doi: 10.1002/bit.21239
|
| [17] |
B. Wu, Integration of mixing, heat transfer, and biochemical reaction kinetics in anaerobic methane fermentation, Biotechnol. Bioeng., 109 (2012), 2864–2874. https://doi.org/10.1002/bit.24551 doi: 10.1002/bit.24551
|
| [18] |
D. B. Panaro, M. R. Mattei, G. Esposito, J. P. Steyer, F. Capone, L. Frunzo, A modelling and simulation study of anaerobic digestion in plug-flow reactors, Commun. Nonlinear Sci. Numer. Simul., 105 (2022), 106062. https://doi.org/10.1016/j.cnsns.2021.106062 doi: 10.1016/j.cnsns.2021.106062
|
| [19] |
Y. Han, Z. Du, X. Hu, Y. Li, D. Cai, J. Fan, et al., Production prediction modeling of food waste anaerobic digestion for resources saving based on SMOTE-LSTM, Appl. Energy, 352 (2023), 122024. https://doi.org/10.1016/j.apenergy.2023.122024 doi: 10.1016/j.apenergy.2023.122024
|
| [20] |
A. Saltelli, K. Aleksankina, W. Becker, P. Fennell, F. Ferretti, N. Holst, et al., Why so many published sensitivity analyses are false: A systematic review of sensitivity analysis practices, Environ. Modell. Software, 114 (2019), 29–39. https://doi.org/10.1016/j.envsoft.2019.01.012 doi: 10.1016/j.envsoft.2019.01.012
|
| [21] |
A. Donoso-Bravo, J. Mailier, C. Martin, J. Rodríguez, C. A. Aceves-Lara, A. V. Wouwer, Model selection, identification and validation in anaerobic digestion: A review, Water Res., 45 (2011), 5347–5364. https://doi.org/10.1016/j.watres.2011.08.059 doi: 10.1016/j.watres.2011.08.059
|
| [22] |
B. Tartakovsky, S. Mu, Y. Zeng, S. Lou, S. Guiot, P. Wu, Anaerobic digestion model No. 1-based distributed parameter model of an anaerobic reactor: II. Model validation, Bioresour. Technol., 99 (2008), 3676–3684. https://doi.org/10.1016/j.biortech.2007.07.061 doi: 10.1016/j.biortech.2007.07.061
|
| [23] |
N. Noykova, M. Gyllenberg, Sensitivity analysis and parameter estimation in a model of anaerobic waste water treatment processes with substrate inhibition, Bioprocess. Eng., 23 (2000), 343–349. https://doi.org/10.1007/s004499900169 doi: 10.1007/s004499900169
|
| [24] |
O. Bernard, Z. Hadj-Sadok, D. Dochain, A. Genovesi, J. P. Steyer, Dynamical model development and parameter identification for an anaerobic wastewater treatment process, Biotechnol. Bioeng., 75 (2001), 424–438. https://doi.org/10.1002/bit.10036 doi: 10.1002/bit.10036
|
| [25] |
V. Vavilin, S. Rytov, S. Pavlostathis, J. Jokela, J. Rintala, A distributed model of solid waste anaerobic digestion: Sensitivity analysis, Water Sci. Technol., 48 (2003), 147–154. https://doi.org/10.2166/wst.2003.0241 doi: 10.2166/wst.2003.0241
|
| [26] |
Y. Lin, C. Wu, Sensitivity analysis of phenol degradation with sulfate reduction under anaerobic conditions, Environ. Model. Assess., 16 (2011), 213–225. https://doi.org/10.1007/s10666-010-9243-1 doi: 10.1007/s10666-010-9243-1
|
| [27] |
K. Solon, X. Flores-Alsina, K. V. Gernaey, U. Jeppsson, Effects of influent fractionation, kinetics, stoichiometry and mass transfer on $CH_{4}$, $H_{2}$ and $CO_{2}$ production for (plant-wide) modeling of anaerobic digesters, Water Sci. Technol., 71 (2015), 870–877. https://doi.org/10.2166/wst.2015.029 doi: 10.2166/wst.2015.029
|
| [28] | L. Benedetti, D. J. Batstone, B. De Baets, I. Nopens, P. A. Vanrolleghem, Global sensitivity analysis of biochemical, design and operational parameters of the Benchmark Simulation Model no. 2, in Proceedings of the 4th International Congress on Environmental Modelling and Software (iEMSs 2008), (2008), 1322–1330. |
| [29] |
Ž. Zonta, M. Alves, X. Flotats, J. Palatsi, Modelling inhibitory effects of long chain fatty acids in the anaerobic digestion process, Water Res., 47 (2013), 1369–1380. https://doi.org/10.1016/j.watres.2012.12.007 doi: 10.1016/j.watres.2012.12.007
|
| [30] |
F. Carrera-Chapela, A. Donoso-Bravo, D. Jeison, I. D´ıaz, J. Gonzalez, G. Ruiz-Filippi, Development, identification and validation of a mathematical model of anaerobic digestion of sewage sludge focusing on $H_{2}S$ formation and transfer, Biochem. Eng. J., 112 (2016), 13–19. https://doi.org/10.1016/j.bej.2016.03.008 doi: 10.1016/j.bej.2016.03.008
|
| [31] |
I. M. Nasir, T. I. Mohd Ghazi, R. Omar, Anaerobic digestion technology in livestock manure treatment for biogas production: A review, Eng. Life Sci., 12 (2012), 258–269. https://doi.org/10.1002/elsc.201100150 doi: 10.1002/elsc.201100150
|
| [32] |
M. D. Morris, Factorial sampling plans for preliminary computational experiments, Technometrics, 33 (1991), 161–174. https://doi.org/10.1080/00401706.1991.10484804 doi: 10.1080/00401706.1991.10484804
|
| [33] | M. Baudin, A. Dutfoy, B. Iooss, A. L. Popelin, Open TURNS: An industrial software for uncertainty quantification in simulation, preprint, arXiv: 1501.05242. https://doi.org/10.48550/arXiv.1501.05242 |
| [34] |
F. Campolongo, A. Saltelli, Sensitivity analysis of an environmental model: An application of different analysis methods, Reliab. Eng. Syst. Saf., 57 (1997), 49–69. https://doi.org/10.1016/S0951-8320(97)00021-5 doi: 10.1016/S0951-8320(97)00021-5
|
| [35] |
A. Trucchia, M. R. Mattei, V. Luongo, L. Frunzo, M. C. Rochoux, Surrogate-based uncertainty and sensitivity analysis for bacterial invasion in multi-species biofilm modeling, Commun. Nonlinear Sci. Numer. Simul., 73 (2019), 403–424. https://doi.org/10.1016/j.cnsns.2019.02.024 doi: 10.1016/j.cnsns.2019.02.024
|
| [36] |
A. Trucchia, V. Egorova, G. Pagnini, M. C. Rochoux, On the merits of sparse surrogates for global sensitivity analysis of multi-scale nonlinear problems: Application to turbulence and fire-spotting model in wildland fire simulators, Commun. Nonlinear Sci. Numer. Simul., 73 (2019), 120–145. https://doi.org/10.1016/j.cnsns.2019.02.002 doi: 10.1016/j.cnsns.2019.02.002
|
| [37] |
P. T. Roy, N. El Moçayd, S. Ricci, J. C. Jouhaud, N. Goutal, M. De Lozzo, et al., Comparison of polynomial chaos and Gaussian process surrogates for uncertainty quantification and correlation estimation of spatially distributed open-channel steady flows, Stochastic Environ. Res. Risk Assess., 32 (2018), 1723–1741. https://doi.org/10.1007/s00477-017-1470-4 doi: 10.1007/s00477-017-1470-4
|
| [38] |
D. Xiu, G. E. Karniadakis, The Wiener–Askey polynomial chaos for stochastic differential equations, SIAM J. Sci. Comput., 24 (2002), 619–644. https://doi.org/10.1137/S1064827501387826 doi: 10.1137/S1064827501387826
|
| [39] |
G. Blatman, B. Sudret, Efficient computation of global sensitivity indices using sparse polynomial chaos expansions, Reliab. Eng. Syst. Saf., 95 (2010), 1216–1229. https://doi.org/10.1016/j.ress.2010.06.015 doi: 10.1016/j.ress.2010.06.015
|
| [40] | C. K. Williams, C. E. Rasmussen, Gaussian Processes for Machine Learning, MIT press Cambridge, MA, 2 (2006). |
| [41] |
A. Trucchia, L. Frunzo, Surrogate based global sensitivity analysis of ADM1-based anaerobic digestion model, J. Environ. Manage., 282 (2021), 111456. https://doi.org/10.1016/j.jenvman.2020.111456 doi: 10.1016/j.jenvman.2020.111456
|
| [42] |
F. Charte, I. Romero, M. D. Pérez-Godoy, A. J. Rivera, E. Castro, Comparative analysis of data mining and response surface methodology predictive models for enzymatic hydrolysis of pretreated olive tree biomass, Comput. Chem. Eng., 101 (2017), 23–30. https://doi.org/10.1016/j.compchemeng.2017.02.008 doi: 10.1016/j.compchemeng.2017.02.008
|
| [43] |
E. Ficara, S. Hassam, A. Allegrini, A. Leva, F. Malpei, G. Ferretti, Anaerobic digestion models: A comparative study, IFAC Proc. Vol., 45 (2012), 1052–1057. https://doi.org/10.3182/20120215-3-AT-3016.00186 doi: 10.3182/20120215-3-AT-3016.00186
|
| [44] | D. Panaro, L. Frunzo, M. Mattei, V. Luongo, G. Esposito, Calibration, validation and sensitivity analysis of a surface-based ADM1 model, Ecol. Modell., 460 (2021), 109726. |
| [45] |
C. Veluchamy, A. S. Kalamdhad, A mass diffusion model on the effect of moisture content for solid-state anaerobic digestion, J. Cleaner Prod., 162 (2017), 371–379 https://doi.org/10.1016/j.jclepro.2017.06.099 doi: 10.1016/j.jclepro.2017.06.099
|
| [46] |
F. Xu, Z. W. Wang, L. Tang, Y. Li, A mass diffusion-based interpretation of the effect of total solids content on solid-state anaerobic digestion of cellulosic biomass, Bioresour. Technol., 167 (2014), 178–185. https://doi.org/10.1016/j.biortech.2014.05.114 doi: 10.1016/j.biortech.2014.05.114
|
| [47] |
F. Liotta, P. Chatellier, G. Esposito, M. Fabbricino, E. D. Van Hullebusch, P. N. Lens, Hydrodynamic mathematical modelling of aerobic plug flow and nonideal flow reactors: A critical and historical review, Crit. Rev. Environ. Sci. Technol., 44 (2014), 2642–2673. https://doi.org/10.1080/10643389.2013.829768 doi: 10.1080/10643389.2013.829768
|
| [48] |
A. Marrel, B. Iooss, B. Laurent, O. Roustant, Calculations of Sobol indices for the Gaussian process metamodel, Reliab. Eng. Syst. Saf., 94 (2009), 742–751. https://doi.org/10.1016/j.ress.2008.07.008 doi: 10.1016/j.ress.2008.07.008
|
| [49] | I. Sobolprime, Sensitivity analysis for nonlinear mathematical models, Math. Model. Comput. Exp., 1 (1993), 407–414. |
| [50] | A. Saltelli, M. Ratto, T. Andres, F. Campolongo, J. Cariboni, D. Gatelli, et al., Global Sensitivity Analysis: The Primer, John Wiley & Sons, 2008. |
| [51] | M. Baudin, K. Boumhaout, T. Delage, B. Iooss, J. M. Martinez, Numerical stability of Sobol'indices estimation formula, in Proceedings of the 8th International Conference on Sensitivity Analysis of Model Output (SAMO 2016), 30 (2016), 50–51. |
| [52] |
J. Yang, L. Lu, W. Ouyang, Y. Gou, Y. Chen, H. Ma, et al., Estimation of kinetic parameters of an anaerobic digestion model using particle swarm optimization, Biochem. Eng. J., 120 (2017), 25–32. https://doi.org/10.1016/j.bej.2016.12.022 doi: 10.1016/j.bej.2016.12.022
|
| [53] |
N. Kythreotou, G. Florides, S. A. Tassou, A review of simple to scientific models for anaerobic digestion, Renewable Energy, 71 (2014), 701–714. https://doi.org/10.1016/j.renene.2014.05.055 doi: 10.1016/j.renene.2014.05.055
|
| [54] |
J. Y. X. Ling, Y. J. Chan, J. W. Chen, D. J. S. Chong, A. L. L. Tan, S. K. Arumugasamy, et al., Machine learning methods for the modelling and optimisation of biogas production from anaerobic digestion: A review, Environ. Sci. Pollut. Res., 31 (2024), 19085–19104. https://doi.org/10.1007/s11356-024-32435-6 doi: 10.1007/s11356-024-32435-6
|
Figures(6) / Tables(8)
Daniele Bernardo Panaro, Andrea Trucchia, Vincenzo Luongo, Maria Rosaria Mattei, Luigi Frunzo. Global sensitivity analysis and uncertainty quantification for a mathematical model of dry anaerobic digestion in plug-flow reactors[J]. Mathematical Biosciences and Engineering, 2024, 21(9): 7139-7164. doi: 10.3934/mbe.2024316
DownLoad: