Elsevier

Ecological Modelling

Volume 460, 15 November 2021, 109726
Ecological Modelling

Calibration, validation and sensitivity analysis of a surface-based ADM1 model

https://doi.org/10.1016/j.ecolmodel.2021.109726Get rights and content

Highlights

  • An ADM1-based model with a SBK approach for disintegration has been calibrated and validated.

  • Ad-hoc experimental activity on potato waste bio-conversion has been carried out.

  • A Local Sensitivity Analysis of model parameters has been carried out.

  • The analysis highlighted the goodness of the SBK modeling approach.

Abstract

A surface-based kinetic model for the anaerobic digestion of potato waste was proposed. The model was calibrated and validated, and a local sensitivity analysis was performed to investigate the most sensitive parameters. The model consisted of a modified Anaerobic Digestion Model n.1 where the disintegration process was defined through a surface-based approach able to account for the influence of the particle size on the process development. Ad-hoc experiments were carried out to calibrate and validate the model at a laboratory scale. The calibration and validation procedures accounted for the methane production and organic acid concentrations observed during experimental tests. The quality of model fitting with lab-scale data was evaluated by the Modeling Efficiency, the Index of Agreement, and the Root Mean Square Error methods. Results confirmed the high accuracy of the model for the bio-methane and organic by-products prediction during the anaerobic conversion of potato waste.

Introduction

During the last decades, the Anaerobic Digestion (AD) process has been widely used for the stabilization and the treatment of organic waste biomasses. Notable examples of AD application are the treatment of the organic fraction of municipal solid wastes and the stabilization of the sewage sludge from municipal wastewater treatment plants (De Bere, 2000, Sosnowski et al., 2003, Hartmann and Ahring, 2005). Due to the ability of specific microbial species involved in the process, AD allows the simultaneous stabilization of wastes and the production of a renewable energy source in the form of biogas (Holm-Nielsen et al., 2009, Chae et al., 2008, Lastella et al., 2002, Lokshina and Vavilin, 1999). The latter is characterized by a high methane content (40% – 75%) and can be effectively used for clean heat and electrical energy generation (Zhou et al., 2015).

The mathematical modeling of AD process has been a challenging topic for the scientific community for about half a century. Indeed, the development of predictive mathematical models plays a key role for the definition of management strategies and the designing of full scale bio-reactors. According to Xie et al. (2016), mathematical models of AD processes can be divided into three different categories: (i) kinetic, (ii) statistical, and (iii) computational fluid dynamics (CFD) based models. Kinetic models are able to account for microbial growth and substrate consumption rates to describe the system evolution. Among them, some models describe the AD process based on its limiting steps: these are usually simplified models describing the slower kinetics related to substrates and/or species involved in the process (Andrews, 1969, Andrews, 1971, Lawrence, 1971, Andrews and Graef, 1970). Other kinetic models are more complex and entirely describe the AD process without establishing a limiting step (Vavilin et al., 1994, Angelidaki et al., 1999). Statistical models are mainly focused on the link between some key parameters and the model output. These models give information about the optimum set of initial conditions able to maximize the specific process target. For instance, some of them try to find the best substrate composition by using a polynomial regression, which describes the relationship between the output and substrate components (Wang et al., 2013). CFD models numerically simulate physics phenomena occurring into bio-reactors. Given a specific reactor configuration, they are able to predict many abiotic conditions, such as the velocity field, the turbulence, the temperature distribution, and the residence time. The main aim is to study the effect of mixing conditions on the microbial population performing the AD process. Indeed, this information might be very useful at a real scale level to determine the contact time between the substrate and the microbial biomass (Yu et al., 2013). It is important to notice that CFD based models completely neglect the aspects related to the biological reactions occurring in AD. To predict the evolution of the process, a separate biological compartment constituted by a specific system of equations is required. However, CFD models are computationally more demanding than all the other models.

Among kinetic models, in 2002 the International Water Association (IWA) Task Group for Mathematical Modeling of Anaerobic Digestion Processes developed a comprehensive mathematical model known as Anaerobic Digestion Model no.1 (ADM1) (Batstone et al., 2002), which was based on experiences acquired over the previous years in modeling and simulating the AD process. Although some processes involved in the AD are neglected, ADM1 was the first real attempt to create a common framework in the AD modeling field. From its publication in 2002, almost 2000 works have been inspired on ADM1 structure. The model was proposed for the AD of sewage sludge and it considered different biochemical (e.g. substrate decomposition, biomass growth etc.) and physico-chemical (e.g. gas-transfer, acid–base equilibrium etc.) processes taking place in an AD reactor. It is based on mass balance equations for different state variables (particulate, soluble and gaseous substance concentrations) and it reproduces the conversion of complex organic matter to a methane rich biogas. The ADM1 can be applied to a Continuous Stirred Tank Reactor (CSTR), where a perfect mixing is implemented. In this case, the derived mass balance equations represent a system of nonlinear Ordinary Differential Equations (ODE) where the state variables only depend on time and the non-linearity is due to the source terms. The model schematizes the process in five main phases: disintegration, hydrolysis, acidogenesis, acetogenesis and methanogenesis. In its first edition of 2002, ADM1 neglected crucial processes involved in AD: reduction of sulfate and nitrates, oxidation of acetate, homoacetogenesis, precipitation of solids, inhibition due to sulfide, nitrates, long chain fatty acids (LCFAs) and weak acids and bases. Over the years, many modifications have been proposed to the original ADM1 to take into account some of these processes overlooked by the model. For instance, in 2008 Esposito et al. (2008) proposed a modified ADM1 based model to study the effect of the solid particle size on the production of methane. The authors modeled the disintegration process with a Surface-Based Kinetic (SBK) approach. They introduced a kinetic constant depending on two terms: the specific disintegration rate (Ksbk) and the overall surface area of the treated complex organic particles per unit mass (a). The first term was influenced by the nature of the substrate, the latter was affected by the particle size. In particular they considered spherical shape particles fed to the bio-reactor. In another work (Esposito et al., 2011), the same authors calibrated and validated the model considering a small particle size range (0.5 – 2.5 mm) of the fed particles, and the calibration was performed with AD experimental data obtained from the conversion of a synthetic cheese and pasta substrate. Other authors used a SBK approach for modeling the disintegration process of AD. Momoh and Saroj studied the applicability of both surface-based and water-based-diffusion kinetic models for biogas production from cow manure (Momoh and Saroj, 2016). They found that both approaches can be successfully applied to model the kinetics of hydrolysis and the biogas production. Dawei Li et al. focused on the effects of porphyritic andesite on the hydrolysis and the acidogenesis phases of solid organic wastes AD (Li et al., 2009). They proved that particulate substrate degradation is enhanced by the addition of porphyritic andesite, and they showed that the proper dose of this additive compound is able to adsorb volatile acids, increase local pH levels and accelerate solids degradation. This resulted in the use of an increased value of the Ksbk rate. Liotta et al. investigated the role of Total Solids (TS) content in the AD of selected complex organic matters, using a mathematical model based on a modified version of the ADM1 (Liotta et al., 2015). The authors linked the Ksbk kinetic constant to the TS content through a linear function introducing two new parameters to be calibrated. They found a good agreement between numerical and observed data of AD of food waste and rice straw in batch conditions.

In the present study, a modified version of ADM1 has been calibrated and validated for a wider range of particle size, using potato waste as substrate. A local sensitivity analysis was performed to obtain information about the influence of all model parameters on the numerical output of the mathematical model. The calibration was based on experimental data of the cumulative methane production and acidic byproducts concentrations achieved with lab scale bio-reactors. The experimental tests were performed using potato waste with particle size lower than one millimeter. Finally, the validation of the model was carried out with other experimental data-sets related to the AD of potato waste with particle sizes of 4 and 20 mm, respectively.

Section snippets

Mathematical modeling

The mathematical model is based on a modified version of the ADM1 proposed by Esposito et al. (2008). The model accounts for the effect of particle size distribution during the disintegration process by using a SBK approach. In addition, ADM1 discrepancies in both carbon and nitrogen balances are removed according to Blumensaat and Keller (2005). These authors highlighted that, due to the decay of microbial biomass involved in the process, additional balance terms are required to close carbon

Sensitivity analysis

The aim of AD is to maximize the production of methane from a given substrate with a stable biological process. On the other hand, VFAs concentration during the anaerobic conversion may be a useful index to avoid bio-reactor acidification and decreased conversion efficiency. The cumulative methane production was chosen as the model output to perform the sensitivity analysis. The results of the sensitivity indexes for each investigated parameter are shown in Fig. 1. The sensitivity analysis was

Conclusions

The aim of the present work was to calibrate and validate a surface-based kinetic model for the anaerobic digestion process of potato waste. The model consisted on a modified ADM1 model where the disintegration kinetic was able to account for the particle size of the organic substrate. Modifications concerning the kinetic parameters of the microbial species involved in the AD process have been discussed. A local sensitivity analysis highlighted the importance of choosing the correct set of

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work has been developed in the context of D.D. n. 1377 on June 5, 2017, additional PhD fellowships for 2017/2018 academic year, course XXXIII within the framework of the “Programma Operativo Nazionale Ricerca e Innovazione (PON RI 2014/2020) Action I.1 - Innovative PhDs with industrial characterization”.

The authors also acknowledges the support from: CARIPLO Foundation (progetto VOLAC, Grant number: 2017-0977); Progetto Giovani G.N.F.M. 2019 “Modellazione ed analisi di sistemi microbici

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