# Optimization of Biomethane Productivity of an Industrial Anaerobic Digestion Process

Julien Thuillier, Sihem Tebbani, Cristian Puentes, Didier Dumur

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Julien Thuillier, Sihem Tebbani, Cristian Puentes, Didier Dumur. Optimization of Biomethane Productivity of an Industrial Anaerobic Digestion Process. Joint 9th IFAC Symposium on System Structure and Control, 19th IFAC Workshop on Time Delay Systems and 2nd IFAC Workshop on Control of Complex Systems, Jun 2025, Gif sur Yvette, France. hal-05110042

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# Optimization of Biomethane Productivity of an Industrial Anaerobic Digestion Process

J. Thuillier* S. Tebbani* C. Puentes** D. Dumur*

**Abstract:** This study aims to determine the optimal operating conditions of an industrial agriculture digester to maximize the biomethane productivity. This involves identifying key decision variables, such as the input substrate feed rate and digestate recirculation flow, while ensuring compliance with critical operational constraints, including command saturation, biomethane production, Organic Loading Rate (OLR), and Hydraulic Retention Time (HRT) limits. Advanced optimization techniques, specifically genetic algorithms, are considered to fine-tune process parameters to achieve the specifications. Additionally, multiple scenarios are explored regarding the premix feeding strategy of input materials, ensuring an optimized and adaptive approach to enhance overall system performance and efficiency. The proposed solution leads to about 11 % increase of the biomethane production over a month in comparison to an existing initial solution.

**Keywords:** Agriculture biodigester, Anaerobic digestion, Optimization, Genetic Algorithms.

## 1. INTRODUCTION

In sustainable energy, the production of biogas and its subsequent injection into the distribution network is a relatively mature technology and one of the strategies for decarbonizing the gas sector in Europe (Brémond et al. (2021)). This endeavor involves generating energy and continuously integrating this green gas into the pre-existing methane infrastructure. Such an integration requires meticulous regulation and stabilization of biogas production based on the anaerobic digestion process. Anaerobic digestion (AD) has emerged as the standard for biogas production, employing a complex decomposition process where microorganisms convert various organic materials into biogas. The numerous advantages of this process are linked to its impact on waste management and energy production, especially for clean mobility. The produced biogas can be upgraded to biomethane ($CH_4$). When the latter is used as a fuel, greenhouse gas emissions are significantly reduced, and in general, it contributes to the mitigation of climate change and the improvement of air quality. The advantages of anaerobic digestion extend far beyond the simple production of biogas. This process generates multiple energy forms; for instance, the heat generated can be harnessed to produce electricity, enhancing energy efficiency. In addition, it transforms wastes into high-quality fertilizers that enrich agricultural soils, closing the loop in our resource cycle. The core of anaerobic digestion is a complex biological process coordinated

by various groups of bacteria living in symbiosis within the substrate. Like an ecological microcosm, this balance can be easily disturbed if one group of bacteria does not perform as expected. Maintaining this equilibrium in an anaerobic digester requires constant monitoring and adjustment to keep the process in tune. This involves navigating through complex biochemical reactions - from hydrolysis to methanogenesis - each of which is crucial in producing biomethane. The performance of AD units consists in maximizing biomethane productivity (Ward et al., 2008). However, maintaining the biomethane production at its optimal value is challenging due to several factors such as non-ideal mixing (Singh et al., 2020) and limitation/inhibition phenomena because of feed overload/overload (Jimenez et al., 2015). AD optimization is an active research field that have been addressed with both experimental and analytical approaches. Experimental studies have highlighted several key operating parameters such as temperature, pH, feed mixture, and reactor mixing (Ward et al. (2008); Liu and Liu (2017); Zhang et al. (2020); Gunes et al. (2021)). Ensuring the smooth running of the AD process requires carefully monitoring and controlling these key operational parameters. In this context, the organic loading rate, the hydraulic retention time and pH levels need to be accurately monitored and controlled, ensuring that every aspect of the process contributes to the system's overall efficiency and stability. Model-based monitoring and optimal control of such systems involve models to simulate the internal dynamics of the process. The

<footnote>* Université Paris-Saclay, CentraleSupélec, CNRS, Laboratoire des Signaux et Systèmes, Gif sur Yvette, France</footnote>

<footnote>(e-mail:julien.thuillier@centralesupelec.fr;</footnote>

<footnote>sihem.tebbani@centralesupelec.fr; didier.dumur@centralesupelec.fr).</footnote>

<footnote>** Université Paris-Saclay, CentraleSupélec, Laboratoire de Génie des Procédés et Matériaux, France</footnote>

<footnote>(e-mail:cristian.puentes@centralesupelec.fr)</footnote>
Anaerobic Digestion Model No.1 (ADM1) (Batstone et al. (2002); Rosen and Jeppsson (2005)) has been widely used for the AD modeling. This model demystifies the complex biochemical and physico-chemical reactions and provides a framework for understanding and simulating the process. Several studies have considered the optimization of the AD operation, mainly based on the ADM1 model (Feldman et al. (2018)), using several optimization approaches such as extremum seeking (Dimitrova and Krastanov (2014); Lara-Cisneros et al. (2015)) or evolutionary algorithms (Enitan et al. (2017); Awhangbo et al. (2024)). Finding these optimal conditions is the first step in mastering the control of AD systems. It sets the stage for a future where biogas can play an even more significant role in our sustainable energy landscape, contributing to a cleaner, more circular economy.

In this paper, an industrial biodigester fed by agricultural waste (from rye and maize wastes) is under study. Due to confidentiality concerns, the name of this specific site is not disclosed. This AD unit is a continuous stirred tank reactor (CSTR) of about 2270 $m^3$ volume and fed with a mixture of maize and rye silage. The objective is to determine the biodigester's optimal operating conditions to maximize biomethane production while respecting numerous operational constraints. The challenges in this case are linked to stability issues due to acidification risks (Zhang et al. (2022)) and the size of the biodigester, where the assumption of a well-stirred homogeneous system is no longer valid. This leads to the need for modeling and optimization tools that can capture the highly complex nonlinear behavior of the system. A black-box model (Pradel et al. (2025)), based on machine learning approaches, is used in our case. The paper focuses on optimizing the biodigester operation to maximize biomethane productivity. For the considered black-box model, and based on operational specifications and constraints, the optimization problem to be solved is modeled by determining the cost function, the decision variables, and the constraints to be fulfilled. Then, due to the problem's complexity and size, Genetic Algorithms (GA) were chosen to solve the determined optimization problem. The developed optimization strategy is then assessed through realistic data in the case of constant and time-varying waste feeding strategies.

The paper structure is as follows. Section 2 is dedicated to the problem statement, including the model definition. Then, Section 3 outlines the optimization problem to be addressed and the Genetic Algorithm-based optimization approach. Finally, Section 4 will showcase the simulation of a biodigester in an open-loop configuration, examining two scenarios: optimizing conditions with a fixed premix, followed by a variable premix. Finally, conclusions are presented, and future perspectives are discussed.

## 2. PROBLEM STATEMENT AND SYSTEM MODELING

### 2.1 System description

As mentioned above, the studied plant is an AD industrial agriculture unit (Megue Kamkeng et al. (2024)). Its schematic representation is given in Fig. 1. The digester tank is a cylindrical vessel with a diameter of 23 $m$, a

<figure><img src="image_2.png" /><figcaption>Fig. 1. Schematic representation of the studied plant.</figcaption></figure>

liquid height of 5.5 $m$, and a total working volume of about 2270 $m^3$. The tank was equipped with two eccentric two-bladed impellers for mixing the digestate. Their speed of rotation is fixed. The biodigester is fed with a mixture of fresh maize and rye silage with a flow rate, denoted $Q$. The mass proportion of maize and rye is a degree of freedom that can be controlled. The biological wastes composition depend, in general, on the season and the nature of the wastes. They are supposed to be known in this study. The biodigester is operated in a continuous mode, i.e., output feed rate, denoted $Q_{out}$, equals the input one, denoted $Q_{in}$, leading to a constant operating volume (denoted $V_R$, $V_R = 2270 m^3$). The input $Q_{in}$ is given by adding to the fresh silage flow rate, $Q$, a recirculated digestate with a flow rate, denoted $Q_{rec}$:

$$Q_{in} = Q + Q_{rec} \quad (1)$$

Through the recirculation, a part of the digestate output is reintroduced at the input of the biodigester (see Fig. 1). The recirculation flow $Q_{rec}$ can be controlled independently from the outlet flow rates (with $Q_{rec} \le Q_{out}$). In this paper, it will be modeled through a recirculation ratio, denoted $R \in [0, 1]$, as:

$$Q_{rec} = R Q_{out} = R Q_{in} \quad (2)$$

Recirculation allows for the retreatment of the digestate (especially if it has not been completely degraded) and consequently maximizes its potential for biomethane production. The produced biogas of the biodigester can be upgraded to biomethane, which is injected into the energy grid. However, there are limitations on the maximal value of possible injected biomethane. The objective is to produce a gaseous biomethane flow rate, denoted $Q_{CH4}$, as stable as possible and lower than a maximal allowed value (here 3000 $Nm^3/day$, to be respected over a month). The outlet digestate could be treated again before being used in the fields and valorized as fertilizer so as to respect environmental specifications. This subsequent treatment process is not considered in this paper.

### 2.2 Biodigester model

The considered system is complex and highly nonlinear. The AD process is commonly modeled through the ADM1 model. The latter assumes a well-stirred homogeneous CSTR and provides a good representation of the biochemical phenomena occurring in the biodigester. From inlet flow rate and the silage inputs composition, it can predict several biological variables, such as biogas, volatile fatty acids, biomass concentrations and pH, etc.
However, considering the volume and the rheology of the liquid phase within the biodigester, the homogeneity assumption is not valid since hydrodynamics and mixing induce variation in the system behavior. A Computational Fluid Dynamics (CFD) model was proposed and validated by Megue Kamkeng et al. (2024) from experimental data for the studied process. This study showed the existence of two caverns inside the reactor, around the agitators, whereas there are non well-mixed zones outside the caverns. This phenomena limits the validity of the ADM1 model. In order to model the system more accurately, a more complex model, based on considering the whole tank as the association of 15 compartments, was developed by Megue Kamkeng (2023). For each compartment, an ADM1 model for the kinetic behavior was developed and identified. The hydrodynamical-biochemical coupled model is more accurate that the classical ADM1 model, but it is very complex, and its numerical simulation is time-consuming, making it not suitable for optimization and for real-time process control. In order to address the limits of the previous model, a surrogate model based on machine learning (ML) was developed to represent the system (Pradel et al. (2025)). With a sampling time set to 1 day, this ML model provides a prediction of the process states and outputs over 210 days. The coupled mechanistic model was used to generate the training and validation data of the machine learning model. This black-box model is based on the Encoder-Decoder approach. It has 23 inputs (e.g. proportion of maize and rye in the mixture, dry matter pourcentage, flow rates, kinetic constants, etc) and predicts about 255 outputs at each sampling time (17 variables for each compartment), over an horizon of 210 days, with a sampling frequency of 1 day.

The machine learning model (denoted $ML_{digeste}$ hereafter) is considered as a black-box model in this study to perform simulations based on the chosen input data. After analysis of the global machine learning model and its behavior considering the specifications, only a part of its inputs and outputs was considered for the optimization study, as illustrated by Fig. 2. More precisely, considered model inputs and output are:

### Model Inputs:

* fresh materials inflow rate, $Q$, in $m^3/day$,

* recirculation ratio, $R$,

* percentage of premix (the percentage of maize in the fresh feeding mixture). It is represented by a variable *premix* (in %, 100% representing a mixture containing only maize),

* initial conditions of the states (concentrations inside the reactor), denoted $x_0$.

<figure><img src="image_3.png" /><figcaption>Fig. 2. Inputs and output of the machine learning model (liquid flow rates in solid line, gaseous flow rate in dashed line).</figcaption></figure>

* the volatile matter percentage in the input substrate, denoted $V_S$. It depends on the composition of the fresh silage.

### Model Output:

* total biomethane gas flow ratio, denoted $Q_{CH4}$, in $m^3/day$ (produced by considering all the compartments).

The black-box model can be represented by the following equation:

$$Q_{CH4} = ML_{digeste}(x_0, Q, R, premix, V_S) \quad (3)$$

In this study, $Q$ and $R$ will be the control inputs, whereas premix and $V_S$ are considered as disturbances. The initial state is assumed to be known and fixed. Ongoing work considers the impact of this parameter on the optimal control strategy.

In addition to the model output, other key operational variables are determined, namely the Organic Loading Rate (OLR) and the Hydraulic Retention Time (HRT). The Organic Loading Rate (OLR) is a key variable to avoid process failure and ensure its performance and stability. It is given by:

$$OLR = \frac{Q.V_S}{V_R} \quad (4)$$

The hydraulic retention time (HRT), or residence time, corresponds to the average time spent by the material in the reactor, and is a key factor to ensure the performance of biogas production. It is given by:

$$HRT = \frac{V_R}{Q} \quad (5)$$

## 3. PROPOSED OPTIMIZATION APPROACH

The objective of the study is to determine the fresh material flow rate $Q$ and the recirculating rate, $R$, to maximize the biomethane gas flow rate produced by the biodigester over a period of time (from $t_s$ to $t_f$, here a prediction horizon of 45 days), while respecting operational specifications (limitations on $Q_{CH4}$, HRT and OLR over the horizon). The sampling time is set to $T_e=1$ day, in adequacy with machine learning model and operational constraints. The control horizon, denoted $N_c$ is set to 30 days (corresponding to the specifications). After these 30 days, the last control action will be maintained until day 45 (corresponding to the end of the prediction horizon, denoted $N_p$). Considering a control horizon different from prediction horizon leads to better performances and is in adequacy with specifications. In addition, due to system dynamics and to the recirculation, the impact of an input can take several days to impact the output (depending on the value of flow rate). The inputs and outputs are given at time instants $t_i = t_s + iT_e$, for $0 \le i \le N_c \le N_p$, $N_c = 30$, $N_p = 45$.

The optimization problem is modeled by:
$$
\begin{array}{ll}
\min_{(\mathbf{Q}, \mathbf{R})} & - \sum_{i=1}^{i=N_p} Q_{CH4}(t_i) \\
\text{s.t.} & Q_{CH4}(t_i) - Q_{CH4,Max} \le 0, 1 \le i \le N_p, \\
& HRT_{min} \le HRT(t_i) \le HRT_{max}, 0 \le i \le N_p - 1, \\
& OLR_{min} \le OLR(t_i) \le OLR_{max}, 0 \le i \le N_p - 1, \\
& Q_{min} \le Q_i \le Q_{max}, 0 \le i \le N_c - 1, \\
& R_{min} \le R_i \le R_{max}, 0 \le i \le N_c - 1, \\
& |R_i - R_{i-1}| \le \delta_R, 2 \le i \le N_c - 1, \\
& |Q_i - Q_{i-1}| \le \delta_Q, 2 \le i \le N_c - 1
\end{array}
\qquad (6)
$$

where the decision variables are given by $\mathbf{Q} = (Q_i)_{1\le i\le N_c-1}$ and $\mathbf{R} = (R_i)_{1\le i\le N_c-1}$, recalling that the last control inputs are maintained constant over time interval $[N_c T_e, N_p T_e]$. In the problem (6), lower and upper bounds are set for variables $Q_{CH4}$, $OLR$ and $HRT$ and on decision variables $\mathbf{Q}$ and $\mathbf{R}$. These bounds are given by the operating conditions. In addition, the two last constraints in (6) are added to smoothen the control variations over the simulation horizon, in order to reduce energy consumption of actuators. It can be noted from (4) and (5), that the constraints on $OLR$ and $HRT$ can be converted into constraints on $\mathbf{Q}$.

Optimization problems can be solved using various algorithms available in the literature, such as derivative-free algorithms and gradient-based methods. The choice of an optimization algorithm depends on the characteristic of the problem to be solved. In the case of problem (6), the problem in a constrained one, with no analytical formulation, and with several possible local minima. These considerations led us to adopt a derivative-free approach and, more specifically, a genetic algorithm. Genetic algorithms optimize solutions by evolving an initial population over successive generations. This evolution is driven by mechanisms such as reproduction, mutation, and selection, which define the GA (Genetic Algorithm) approach (Whitley (1994) and Lambora et al. (2019)). One of their advantages is their robustness to initial guess (which is difficult to have in the considered problem) and their capacity to handle a large number of variables. The constraints can be handled through penalty approaches in the cost function. However, the main drawback of this type of algorithm is the computational time required to reach the final solution, which heavily depends on the tuning of its parameters. Nevertheless, GA proves particularly effective in overcoming the challenge of local minima in highly complex systems. In addition, the large sampling time (here one day) allows the use this kind of algorithm. The genetic algorithm was used in this work to achieve the aimed production objectives (using Matlab GA algorithm). It should be mentioned that other optimization strategies, mainly local ones, were tested and failed to find a feasible solution (data not shown).

## 4. NUMERICAL RESULTS

This section presents numerical results for two scenarios with different premix compositions: First, a fixed premix was considered (constant percentage of maize in the feeding materials), and then, a time-varying one, based on realistic data for agriculture waste. The time horizon is set to 45 days ($t_f - t_s = 45$ day), and the sampling time to $T_e = 1$ day. The values of the considered bounds

<table><caption>Table 1. Parameters bounds</caption><thead><tr><td>Parameter</td><td>Units</td><td>Value</td></tr></thead><tbody><tr><td>$Q_{CH4,Max}$</td><td>$Nm^3/day$</td><td>3000</td></tr><tr><td>$[OLR_{Min}, OLR_{Max}]$</td><td>$gV_S/L/day$</td><td>$[2, 5]$</td></tr><tr><td>$[HRT_{Min}, HRT_{Max}]$</td><td>$day$</td><td>$[38, 227]$</td></tr><tr><td>$[Q_{Min}, Q_{Max}]$</td><td>$m^3/day$</td><td>$[10, 60]$</td></tr><tr><td>$[\delta_R, \delta_Q]$</td><td>-, $m^3/day$</td><td>$[0.05, 20]$</td></tr><tr><td>$[R_{Min}, R_{Max}]$</td><td>-</td><td>$[0.8, 0.9]$</td></tr></tbody></table>

are given in table 1. They are provided from operational considerations and constraints. It could be noted that these bounds are, in some cases, more restrictive than the physically possible bounds (e.g. for $R$ where only values between 0.8 and 0.9 are considered). The process state, $\mathbf{x}_0$ is initialized with initial conditions corresponding to a realistic operating regime that corresponds to a lower level of biomethane production than the upper limitation.

### 4.1 Case 1: Constant premix

First, a scenario with a constant premix is studied. The premix is fixed at 42% for maize and 58% for rye. The system behavior with constant inputs (designed as basic solution) and with the obtained optimal solution are compared. The basic solution is set to classical values of decision variables ($Q = 42Nm^3$ and $R = 0.85$), usually considered to operate the plant. It should be mentioned these constant input values over all the prediction horizon failed to provide good performances (especially for varying premix). GA parameters as population size and number of generation are numerically 50 and 200, running in 4 minutes with a 24 cores CPU. The solutions (in blue) obtained ($Q$ and $R$) using GA are presented in Figure 3. Solutions for $Q$ over 30 days slightly oscillate close to $39 m^3/day$ while recirculation solutions $R$ varies between 0.80 and 0.89. The recirculation ratio variations are more pronounced than those of flow rate. Indeed, recirculated digestate is better degraded than fresh one, leading to better biomethane production. This fluctuation of recirculation ratio should be further analyzed since it could be linked to solution suboptimality, ML model accuracy or biological constraints.

Biomethane gas production obtained is shown in blue in Fig. 4. A ramp-up time of 10 days is observed to reach the flow rate limit of 3000 $Nm^3/day$. Stabilization of the biomethane flow rate occurs at 30 days (end of the control horizon), then the flow rate is maintained close to 3000 $Nm^3/day$ between 30 and 45 days (end of the prediction horizon). In red, the basic solution do not drive the system close to the maximum biomethane flow rate, leading to lower process productivity. The difference in production of biomethane at initial time between the two approaches is due to the ML model that considers that the part of biomethane flow rate depends instantaneously on the applied flow rate. Thus, the focus should be on transient and final values of the biomethane flow rate. In Figure 5, the time evolution of $OLR$ and $HRT$ are within bounds (for both GA and basic cases), respecting constraints as described in (6), which demonstrates that the system strictly follows the operational constraints defined in the optimization problem.

This first result validated the efficiency of the developed strategy. It also highlighted that the maximal productivity,
<figure><img src="image_4.png" /><figcaption>Fig. 3. Optimal solutions obtained for $Q$ and $R$ - case 1.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 4. Flow rate of produced $CH_4$ - case 1.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 5. Time evolution of HRT and OLR - case 1.</figcaption></figure>

in the considered case, corresponds to maintaining the produced biomethane flow rate at its upper bound.

## 4.2 Case 2: Variable premix

In the second case scenario, the premix composition fluctuates between 38% and 30%, as shown in Fig. 6. They correspond to realistic variations, depending on silage availability. The obtained control inputs given in Fig. 7 lead to the maximization of biomethane flow rate as seen in Fig. 8. The basic solution lead to lower performances than the optimal one, highlighting the advantages of the approach. The obtained behavior is similar to case 1. At the end of the control horizon, the maximum limit for the

<figure><img src="image_7.png" /><figcaption>Fig. 6. Time evolution of the maize premix - case 2.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 7. Optimal solutions for $Q$ and $R$ - case 2.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 8. Flow rate of the produced $CH_4$ - case 2.</figcaption></figure>

biomethane flow rate is reached (Fig. 7) while respecting the constraint (Fig. 9). The solutions on day 30, replicated until the end of the prediction horizon (at day 45), drive the biomethane production to remain close to the limit $3000 \text{ Nm}^3/\text{day}$, increasing methane production by 118.6 kW over a month, i.e. about 11% in comparison to the basic solution. The use of a control and prediction horizon of different sizes has allowed smoothing and stabilization of biomethane production (when compared to the solution with the same control and prediction horizons, data not shown).

# 5. CONCLUSION AND PERSPECTIVES

This study is the first step for the optimal online control of the considered industrial bioprocess. From simulation results, genetic algorithms may significantly enhanced productivity by determining optimal operating conditions, overcoming challenges from nonlinear dynamics and simplified machine learning models. Two scenar-
<figure><img src="image_10.png" /><figcaption>Fig. 9. Time evolution of HRT and OLR - case 2.</figcaption></figure>

ios were explored: a fixed input premix, which provided
insights into performance under stable conditions, and a
variable input premix, which showcased the algorithm's
effectiveness. In both cases, biomethane production was
increased while respecting operational constraints, ensur-
ing efficiency and sustainability. These results lay a strong
foundation for advanced optimal control strategies in AD
systems, offering practical guidance for managing these
complex biological processes. Future research will explore
integrating Model Predictive Control (MPC) to enable
real-time optimization and predictive adjustments based
on system dynamics, alongside validating these findings
across different feeding scenarios and initial conditions
to refine process understanding. The optimality of the
obtained control strategy will be also investigated as well
as its robustness with respect to model mismatch and
disturbances. Finally, the control strategy will be validated
on the ADM1-based model and on the real plant through
experimental campaigns.

ACKNOWLEDGEMENTS

The authors acknowledge the support of the French
Agence Nationale de la Recherche (ANR), under grant
ANR-21-CE43-0007 (project RELOAD). We also acknowl-
edge Air Liquide company for its collaboration and the
share of its operational data.

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