Optimizability of Biogenic Hydrogen Production

Abstract

The biogenic hydrogen production by dark fermentative digestion of biomass shows excellent potential for solving the recent energy difficulties. To augment the efficiency of this process, the biochemical degradation needs to be understood better. The physical optimum (PhO) method was found to be particularly suitable to illustrate the maximum potential of the process. It is based on a theoretical, ideal reference state. For this purpose, the dark fermentation was modeled mathematically using Petri nets, a modeling language based on graph theory. The Petri net model was developed based on the biochemical reactions system of anaerobic digestion. All degradative steps relevant to hydrogen production were included. Then the modeled metabolic rates were analyzed to be used as a reference base in evaluating the process’s efficiency. This ideal reference state, the anaerobic digestion’s PhO, was compared with experimental data by the PhO factor. This factor summarizes the efficiency of the whole process.

1. Introduction

Hydrogen technologies, combined with sector coupling, can decarbonize sectors that cannot be electrified (e.g., the chemical industry, steel industry, etc.) [1].

In 2030, hydrogen will account for 0.5% of the electricity mix, according to studies by DNV. In 2050, DNV expects it to be 5%. However, according to the Paris Agreement, at least 15% hydrogen is required in the electricity mix [1]. Yet, expanding renewable energy and electrolysis technologies at the necessary pace will be nearly impossible. Both renewables and electrolysis-ready water are critical resources that could lead to supply insecurities [2].

For this reason, we need new technologies for the production of hydrogen in the course of decarbonization.

1.1 Biological hydrogen as an alternative to electrolysis

In 2021 bioenergy covered about 55 % of global renewable energy supply (6 % of total energy supply) which makes it the largest source of renewable energy [3]. According to Net Zero Emissions by 2050 the use of bioenergy will increase rapidly by 2030 [4].

The conversion of biomass can take place via three routes: thermo-chemical (pyrolysis, gasification), physicochemical (e.g., chemical conversion), or biochemical (anaerobic fermentation, alcoholic fermentation). All three approaches can produce gaseous and liquid fuels, with the first two having high energy requirements. Biochemical transformation, on the other hand, proceeds essentially in a self-determined manner and with a lower external energy requirement. [5, 6]

A general advantage of biomass conversion is the sensible use of biological waste products (e.g., from agriculture) [6]. A significant disadvantage is the current inefficiency of the hydrogen production method [7]. The resulting biogas contains only small amounts of hydrogen since, in most cases, hydrogen is directly decomposed to form methane [8].

This effect can be reduced by so-called dark fermentation, an anaerobic fermentation without light. Methanogenesis is suppressed using bacterial cultures in which few hydrogen-consuming microorganisms (MOs) are present [8]. The process’s main advantages are the simple reactor configuration and the ability to produce hydrogen continuously regardless of ambient conditions.

1.2 The efficiency of hydrogen via dark fermentation

Dark fermentation has not yet been investigated on a large scale at the current stage. Laboratory studies suggest substantial production variations depending on inoculum, substrate, and substrate pretreatment. Values between 27 L H₂/kg TVS (Total Volatile Solids) [9] and 125 L H₂/kg TVS [10] were measured for continuously operated biogas plants. This corresponds to a maximum of one-third of converted initial biomass [11].

1.3 Challenges in optimizing biological processes

Efficiency assessment is essential, especially for sector coupling processes, but it is also difficult. Depending on the (sub)process of the overall process under consideration, there are various methods and key figures for efficiency evaluation. This makes a holistic, objective comparison of the impossible processes. However, this is indispensable if the optimizability of the overall process is to be determined [12]. While the efficiency of purely technical processes can at least be described thoroughly, biological (sub)processes are even more difficult to describe due to their complexity. Biological processes can hardly ever be considered completely isolated since they usually interact with many other processes and are thus dependent on them. On the one hand, this makes it challenging to draw balance boundaries. On the other hand, not all interaction partners are known, so a complete consideration of the isolated process is impossible. Thus, a comprehensive efficiency assessment of these processes is (almost) impossible, even if the state of knowledge yields new information.

Therefore, this chapter develops a model to describe dark fermentation’s physical optimum (PhO). Based on this model, the efficiency potentials of the process can be determined, and recommendations for improvement can be derived. An in-depth understanding of the process is required for model development. For this reason, the anaerobic degradation of biomass is described first. The dark fermentation process is then mapped using Petri nets (PNs) to create an idealized comparison process for evaluating existing processes.

2. Theoretical basics of dark fermentation

In biogas plants, biomass is converted into biogas by bacterial decomposition. Primarily methane (60% [13]) and carbon dioxide (35% [13]), but also hydrogen is produced. The biochemical conversion of biomass to biogas is divided into four reaction stages: hydrolysis, acidogenesis, acetogenesis, and acetylation [5, 13].

Dark fermentation, the anaerobic degradation of biomass without light, is the term for hydrogen formation. Dark fermentation is thus identical to anaerobic digestion up to hydrogen formation (acetogenesis). Only methanogenesis is inhibited in dark fermentation [14]. In an actual biogas plant, the degradation process does not simply stop after hydrogen formation. Instead, the resulting H₂ is further converted to methane with CO₂. Accordingly, this step must be eliminated to increase the hydrogen yield.

2.1 Degradation step 1: Hydrolysis

During hydrolysis, the complex biomass is enzymatically split into its monomers. This process divides complex carbohydrates into monosaccharides, primarily glucose, by amylases (Eq. 1 [5, 15]).

$${\left(C_6{H}_{10}{O}_5\right)}_n+n{H}_{2}O\to n{C}_6{H}_{12}{O}_6$$E1

Proteins are cleaved by extracellular proteases into shorter peptide chains (di- and tripeptides) and amino acids (AA) (Figure 1 [15]). Their degradability depends on their AA sequence, hydrophobicity, and the milieu conditions (especially acidity).

Figure 1.

Protein hydrolysis reaction scheme [15].

The peptides are subsequently cleaved intracellularly into AA. These are used for protein synthesis and energy production of the MO [16]. Lipids are cleaved by lipases into fatty acids and glycerol (Figure 2 [17, 18]). This degradation is done by anaerobic bacteria such as Bacteroides, Clostridia, or Bifidobacteria [19, 20].

Figure 2.

Reaction scheme of lipid hydrolysis.

2.2 Degradation step 2: Acidogenesis

The monomers are converted into even simpler components in the second degradation step. Here, AA and monosaccharides are metabolized, and long-chain saturated fatty acids (LCFA, e.g. C4 to C18 by Syntrophomonas spp. [21]) are converted by β-oxidation [17, 22] by facultative and anaerobic acidogenic bacteria such as Bacteroides, Clostridium, Butyribacterium, Propionibacterium, Klebsiella, Escherichia, Syntrophomonas, and Thermoanaerobacterium to various organic acids (OAs) such as propionic or butyric acid, but mainly to acetic acid (Figure 3) [13, 20, 24, 25]. Carbon dioxide, water, and hydrogen are also formed as waste products [13].

Figure 3.

Various fermentation reactions with glucose as a reactant and various organic acids as products [23].

The glycerol is converted in the glycolysis process at which hydrogen is produced [17]. Protein-rich substrates yield exceptionally high levels of butyric and valeric acids [13]. These are released as the carbon residue of the AA after deamination or transamination (loss of the amino group). The amino group is separated as an ammonia molecule at the end of the metabolic pathway. It is, therefore, the main product of protein catabolism [16].

2.3 Degradation step 3: Acetogenesis

In the third degradation step, the metabolic products of acidogenesis, mainly propionic and butyric acids, but also ethanol (Eq. 2 [19]) and lactate (eq. 3 [19]), are further degraded by anaerobic oxidation.

$$H_{3}C-C{H}_2-\mathit{OH}+H_{2}O\to H_{3}C-\mathit{\text{COOH}}+H_2$$E2

$$H_{3}C-\mathit{\text{HCOH}}-\mathit{\text{COOH}}+H_2\to H_{3}C-C{H}_2-\mathit{\text{COOH}}+H_{2}O$$E3

Butyric and other longer OAs are degraded according to the same principle during β oxidation (Eq. 3 [26]). Propionic acid is metabolized to acetic acid (Eq. 4) [13, 19].

$$H_{3}C-C{H}_2-\mathit{\text{COOH}}+3H_{2}O\to H_{3}C-\mathit{\text{COOH}}+C{O}_2+H_{2}O+3H_2$$E4

However, the butyrate degradation to acetate and H2 is, under standard conditions, an endergonic reaction [27]. For this reaction to occur, hydrogen elimination is strictly necessary. By forming so-called syntrophic communities consisting of hydrogen producers (e.g., Clostridium spp.) and hydrogen consumers (e.g., Methanoculleus spp.), the metabolization of butyrate to methane can be achieved despite being thermodynamically unfavorable.

Similarly, lactate degradation can be performed by several members of the genus Clostridium, resulting in the formation of acetate, propionate, and carbon dioxide. In sulfate-limited and hydrogen-consuming milieus, Desulvovibrio vulgaris is furthermore able to generate H2, besides acetate and CO2, from lactate, making it a desirable species for dark fermentation [28]. Additionally, lactate seems to be cometabolized by syntrophic acetate oxidizers such as Syntrophaceticus schinkii [29].

2.4 Degradation step 4: Methanogenesis

In the last fermentation step, methane is formed. There are two possible metabolic pathways.

On the one hand, there are hydrogenotrophic methanogenic MO, such as Methanoculleus, which produces methane from hydrogen and carbon dioxide (Eq. 5 [30]). On the other hand, there are acetoclastic methane producers, such as Methanosaeta, which form methane based on acetate (Eq. 6 [20, 30]. The hydrogenotrophic methane formation is energetically preferred.

$$4H_2+C{O}_2\to C{H}_4+C{O}_2$$E5

$$H_{3}C-\mathit{\text{COOH}}\to C{H}_4+C{O}_2$$E6

This changes as soon as the critical hydrogen partial pressure is below a certain threshold. A peculiarity is that the transforming MO is now exclusively Archeans, in contrast to the previous bacteria [19]. These exhibit two temperature optima: at 32–42°C in the mesophilic [20] and at 48–55°C in the thermophilic range [20], as well as a pH optimum at pH 7 to 7.5 [13, 20]. If the pH value falls below a critical threshold, e.g., to pH 6.5, short OAs and acetate accumulate because methanogenesis is inhibited, further lowering the pH [20].

Archaea activity shows a stronger inhibition by lower pH values than bacteria in the previous degradation steps [13].

2.5 Inhibition of methanogenesis in favor of hydrogen production

Methanogenesis is the final step in the anaerobic degradation of biomass. In this step, methane is formed from H₂ and CO₂ on the one hand (hydrogenotrophic) and from acetate on the other (acetoclastic). Since hydrogenotrophic methane formation is H₂-consuming, this step must be inhibited for a higher hydrogen yield and the H₂-producing reactions must be enabled [20, 30].

Hydrogen partial pressure is the most crucial factor influencing H₂ formation and consumption. According to Ahlert, this must be below 50,66 Pa [19] so that H₂ can be formed. According to Cazier, a value of 101,33 Pa [31] is sufficient to inhibit acetogenesis. A higher value inhibits production [13, 24]. At the same time, methanogenesis is inhibited by a low H₂ partial pressure (below 6,48 Pa [19]). Then, acetoclastic methanogenesis is favored instead of hydrogenotrophic methanogenesis, so no H₂ is consumed but acetate.

Another possibility to inhibit hydrogenotrophic methanogenesis is the removal of CO₂ from the reactor air [31]. However, this does not solve the problem of H₂ formation inhibition when the H₂ partial pressure becomes too high, so this method should be used as a supplement, but not alone.

Two other important influencing factors are temperature and pH. Methanogenic MO is archaea, which are more susceptible to stress than bacteria. They can better withstand temperature fluctuations and survive somewhat lower pH values, whereas methanogenic archaea can withstand higher pH values. Methanogenic archaea are strongly inhibited at a pH below seven, already in the slightly acidic range [13, 19, 20]. Therefore, to inhibit methanogenesis, a slightly acidic pH value such as 6.5 would be advantageous for inhibiting methanogenesis.

The low pH must not be caused by LCFA enrichment, as this inhibits hydrolysis and acidogenesis in addition to methanogenesis, which is essential for H₂ formation. Methanogenic MO is the first to be inhibited by LCFA accumulation, starting at 1.0–2.9 kg COD/m³ biomass [32]. Acidogenic MO is inhibited from 2.1–7.9 kg COD/m³ biomass [32] and hydrolytic ones only from 2.6–9.4 kg COD/m³ biomass [32]. Thus, if the concentration of LCFA is between 1.0–2.1 kgCOD/m³ biomass, methanogenesis should be inhibited, not the other two degradation steps.

3. Development of an efficiency evaluation method for dark fermentation hydrogen production

To develop a model for evaluating the efficiency of dark fermentation, the system must first be defined and limited as a process. This process is to be worked out as a PN. The results of the modeled biomass conversion will then be compared with experimental data, and the efficiency of the process will be summarized based on an efficiency factor.

3.1 Definition of the system under consideration

Before a system can be considered mathematically, its accounting limits must first be defined. The system of dark fermentation in a biogas plant must be represented mathematically. In particular, changes in the process flow leading to hydrogen production are relevant. The balance space must contain all desired processes and structures [33]. This work focuses solely on the biodegradation of biomass without technically required secondary components (Figure 4).

Figure 4.

Schematic illustration of the accounting process.

The input is the already prepared biomass, and the output is the end products of the reaction pathways during fermentation, mainly hydrogen and methane formation. The material balance is formed based on the effluents described. Here, all material flows have to be considered, which influence the considered target substances, in this case, the hydrogen formation [33].

Figure 5 shows the transit-adjusted distribution of the chemical reactions considered. It is a highly simplified representation of the relevant reactants and products. This figure focuses on classifying the products and intermediates to the degradation steps of anaerobic digestion. It should be noted that the degradation steps are not strictly sequential. To simplify matters, overlaps have not been considered in this figure.

Figure 5.

Schematic illustration of the four steps of biomass degradation to methane —Hydrolysis, acidogenesis, acetogenesis, and methanogenesis—Their intermediates and their interactions (transit-adjusted balance area; green: Contributes positively to H₂ formation; red: Contributes negatively to H₂ formation; blue: Does not contribute directly to H₂ formation; and black: Does not contribute at all to H₂ formation).

Each reaction is divided into “contributes positively” (green), “negatively” (red), “not directly” (blue), or “not at all” (black) to hydrogen formation. In the red reactions, H₂ is consumed, whereas H₂ is formed in the green reactions. Undesired by-products, which are formed independently of the desired H₂, but do not negatively influence the yield of the main product, are shown in orange.

There are two transit streams: the inert biomass parts, e.g., lignin, and the inert AA. These are hardly or not at all degraded. The desired main product is H₂; the undesired by-products are CH₄, CO₂, and NH₄. Ammonia is formed during AA degradation. Carbon dioxide is produced during sugar fermentation and acetoclastic methanogenesis.

It is striking that the sugar fermentation shows red and green reactions, while the AA fermentation and fat degradation show only green reactions. In particular, the lactate and ethanol pathways are H₂-consuming, whereas in the other reaction pathways, H₂ is produced during the further metabolism of OAs.

By definition, methanogenesis is no longer part of dark fermentation. Since it is the primary H₂ consumer, it is nevertheless considered.

3.2 Development of a Petri net

PNs are mathematical structures based on graph theory. They function as a formal modeling language with strict syntax [34]. PNs are directed bipartite multigraphs. They are constructed from two types of nodes (bipartite): places and transitions. Places describe states, which can be, e.g., molecular species and physical parameters like temperature. They are graphically represented as circles. Transitions are state changes and represent, e.g., chemical reactions, changes of location, or an interaction. They are graphically represented as squares. So-called tokens mark places. The terminology used for the developed model is shown in Figure 6.

Figure 6.

Graphical representation of the elements that can be used in a Petri net [35].

With PNs, causal processes can be represented particularly well, although they can also run independently. Thus, PNs are well suited for describing complex biochemical systems, such as gene regulation or metabolism. The exact syntax of PNs prevents mathematically nonsensical models, and the graphical representation allows an intuitive application that hardly requires mathematical or computer science knowledge.

The balance boundary of the considered process was drawn in the last section. The boundary encompasses all anaerobic digestion, including methanogenesis. The PN was developed based on Figure 5, which summarizes the results of the literature review on biomass degradation. Accordingly, the structure of the PN (Figure 7), created in SNOOPY (version 1.22), is similar to that of the schematic illustration of the degradation process (see Figure 5).

Figure 7.

Petri net model of the four steps of biomass degradation to methane-hydrolysis, acidogenesis, acetogenesis, methanogenesis, their intermediates, and their interactions.

The different components were treated as plates and the chemical reactions as transitions. At the arrows, there are numerical values, which reflect stoichiometry. In the model, a reaction will only occur if all necessary components are available in sufficient quantity and if the reaction rates conditional probability of a reaction is high. Once these conditions are fulfilled, the reaction takes place until the conditions are no longer fulfilled. For example, 4 H₂ molecules and 1 CO₂ molecule are required to hydrogenotrophically form 1 CH₄ molecule (see methanogenesis at the bottom of Figure 7).

3.3 Calculation of transition rates

The transition rates correspond to the stochastic probability in a stochastic PN that a transition switches. This corresponds to the reaction rate of the chemical reaction.

Initially, the biomass is added to the digester in grams per liter. The following values are specific conversion values of maize silage (see Table 1).

Conversion coefficient	Description	Value	Literature
p1	Carbohydrate content	0.546	(74)
p2	Protein content	0.1036	(74)
p3	Lipid content	0.0183	(74)
pfix	Inert content	0.3311	(74)
p4	Glucose factor	3*10^21	(75)
p5	Protein hydrolysis	1	—
p6	Lipid hydrolysis	1.64*10^20	(73,75)
p7	Glucose ➔ pyruvate	1	—
pfix2	Inert amino acids	0.2607*4581*10^22	(72,75)
p8	Butyric acid amino acids	0.0073*2019*10^22	(72,75)
p9	Propionic acid amino acids	0.0871*2208*10^22	(72,75)
p10	Valeric acid amino acids	0.1718*1977*10^22	(72,75)
p11	Acetic acid amino acids	0.4421*2272*10^22	(72,75)
p12	Glycerol➔ pyruvate	1	—
p13	Pyruvate ➔ lactate	1	—
p14	Pyruvate ➔ propionate	1	—
p15	Pyruvate ➔ butyrate	1	—
p16	Pyruvate ➔ acetate	1	—
p17	Pyruvate ➔ ethanol	1	—
p18	Lactate ➔ propionate	1	—
p19	Ethanol ➔ acetate	1	—
p20	Propionate ➔ acetate	1	—
betaOx1	β-oxidation of fatty acids	8.76	(73)
betaOx2	β-oxidation of butyric acid	1	—
betaOx3	β-oxidation of valeric acid	1	—
hydrogen	Hydrogenotrophic methanogenesis	1	—
acetogen	Acetoclastic methanogenesis	1	—

Table 1.

Data used when creating the Petri net.

Maize silage was chosen as a substrate for simplicity since the data are available. The transition rates have to be adjusted for each new substrate. First, each substrate contains a specific ratio of carbohydrates, proteins, lipids, and inert substances (those that are not degraded and thus do not contribute to the biogas yield).

In this context, a test report on maize silage from 2021 (commissioned by the Fraunhofer IFF) was used and converted into relative shares of the total dry matter (DM). As an example, this calculation is carried out in Eq. 8. Digestible carbohydrates can be found among nitrogen-free extractives. The proteins are noted as “crude proteins.” The inert substances are composed of crude ash and crude fiber. The lipids are indicated as “crude fats.”

$$\mathit{\text{protein content}}=\frac{\mathit{raw}\mathit{\text{protein}}\mathit{DM}}{\mathit{\text{total}}\mathit{DM}}=\frac{10,4\%}{92,7\%}=10,36\%\mathit{DM}$$E7

Up to this point, all values are in g DM/L. One unit corresponds to one gram DM per liter of reactor content. These must be converted into several molecules. The calculation is shown for glucose as an example in Eq. 9.

$$N_{\mathit{\text{Glucose}}}=\frac{m_{\mathit{\text{Glucose}}}}{M_{\mathit{\text{Glucose}}}}\ast N_A=\frac{1g}{\mathrm{180,906}\frac{g}{\mathit{mol}}}\ast \mathrm{6,002}\ast {10}^{23}\frac{1}{\mathit{mol}}=3,3\ast {10}^{21}$$E8

$m_{\mathit{\text{Glucose}}}$=Mass of glucose, [g].

$M_{\mathit{\text{Glucose}}}$=Molecular weight of glucose, [g/mol].

$N_A$=Avogadro constant, [1/mol].

$N_{\mathit{\text{Glucoce}}}$=Number of molecules per gram of glucose, [−].

Thus, 1 g glucose corresponds to 3*10²¹ glucose molecules. Finally, the reactor volume must be considered for all molecule numbers to know the total number of molecules in the fermenter.

The other conversion factors in Table 1 were calculated analogously based on average molecular weights.

3.4 Derivation of the differential equations

The finished PN can be derived with the calculated reaction rates by SNOOPY to a differential equation system. The corresponding differential equations are formed according to the following scheme:

$$\frac{\mathit{dX}}{\mathit{dt}}=\sum _i{p}_i\ast c_{\mathit{\text{in}},m}-{\sum _j}^{\prime }t-1$$E9

$\frac{\mathit{dX}}{\mathit{dt}}$=Concentration of component X at time t, [−].

$p_i$=Stoichiometric coefficient of reaction i, [−].

$c_{\mathit{\text{in}},m}$=Concentration of input component m, [−].

SNOOPY created the complete differential equation system of the anaerobic degradation. With the help of this chemical equation system, the efficiency analysis of the degradation can be performed.

The results of the modeling of the concentration course in the reactor for the time of the total of 23 reaction steps are shown in Figure 8. By modeling each individual reaction step, it was possible to represent the idealized concentration curve of all reactants, products, and intermediates.

Figure 8.

Substance conversions of various (intermediate) products during anaerobic degradation determined by the Petri net. Left: Resulting biogases CH₄. CO₂ and H₂; right: Organic acids.

4. Efficiency assessment of laboratory data

This paper describes the development of a model characterizing an idealized reference process of dark fermentation. Based on the deviation between experimental data and the idealized reference process, the efficiency of the actual process can be quantified.

By comparing the real and the simulated concentration curves, the efficiency of the process can be mapped. At the same time, each concentration present in the reactor provides information about biodegradation via the model.

MicroPro GmbH experimentally obtained reaction rates of the components H₂ and CO₂ in a corn silage fermentation. Other components could not be measured for technical reasons.

Since the real-time process does not relate to the reaction steps in a linear matter, data points have been adopted to the respective reaction steps. At this point, there is no accurate way to measure the progress of the reaction in terms of reaction steps. The experimental data has, therefore, been adjusted to the simulated data based on H₂ and CH₄ formation.

Figure 9 compares the experimental data with the calculated reaction conversions.

Figure 9.

Comparison of the model-based and experimental reaction turnovers of hydrogen H₂ (blue) and methane CH₄ (red). The concentration is in Mol per kilogram of corn silage per liter of fermenter contents.

4.1 Performance indicator for the biological reaction

The deviation between the experimental and simulated data can be represented by the PhO factor defined by eq. 11. D. Volta first described the PhO factor, which compares an actual process and an idealized reference process, the so-called PhO [36].

$$F_{\mathit{PhO},\mathit{\text{turnover}}}=\frac{\mathit{\text{Modeled concentration}}}{\mathit{\text{Experimental concentration}}}\le 1$$E10

Figure 10 shows the course of the PhO factor over the respective reaction steps. As expected, the idealized reference process was not achieved under laboratory conditions. However, it is noticeable that the efficiency of the process fluctuates strongly over the course of the process.

Figure 10.

PhO turnover factor through comparison of experimental and modeled data for H₂ concentration in the reactor.

During the reaction, the PhO factor is a maximum of 0.79 (reaction step 9) and a minimum of 0.44 (reaction step 23). This suggests an optimization potential of the biological process of 21–56%. However, to be able to make a more precise statement as to whether this optimization potential is technically achievable, more detailed investigations must be carried out.

4.2 Discussion and outlook

A model was developed to evaluate the efficiency of the metabolism of dark fermentation on a laboratory scale, simulating the degradation and formation of all reactants, products, and intermediates.

The developed model is based on a PN, which uses defined rates and conditions for the course of a reaction for each defined step. A change in these rates and conditions directly influences the results of the PN and thus shifts the modeled optimum of the reaction. While the requirements for a reaction step are already very well described in the literature, the reaction rates can only be determined by approximating experimental data. The practical reaction rates used for the model were taken from various sources (cf. Table 1).

Since it was not technically possible to measure the concentration curves over time in the reactor, a more concrete validation had to be omitted at this point that the final product composition of the simulated process agrees with literature data and values collected in the experiment implies that most reaction rates were chosen realistically. Which reaction rates were defined too inaccurately at the current time can only be found by parameter variation and behavioral analysis of the model under comparison with experimental data.

Thus, the hydrogen and methane production rates were mapped using pressure differences and converted into concentrations for evaluation. Therefore, the pure hydrogen increase could only be measured up to reaction step 21. From then on, a comparison had to be made with combination experiments to estimate the concentration of H₂ and CH_4, separately. In these combination experiments, reactor contents were fed unchanged to methanation after dark fermentation.

Since the concentrations of the reactants, intermediates, and products cannot be monitored technically during the reaction, the temporal assignment of the experimental data to the respective reaction steps was based solely on the calculated H₂ concentrations in the reactor. Further experiments must prove the reproducibility of this assignment.

Another reason for possible inaccuracies in the model is that a change in pH was not considered in the modeling. However, these effects were deliberately neglected since the process is intended to represent an idealized reference process to identify optimization potential by comparison with an actual process.

As part of the HyPerFerment II project, the construction of a demonstration plant for dark fermentation is planned. Here, data can be collected for the first time on a small industrial scale and under nonlaboratory conditions. Further experimental data must be collected to better adapt the model of the idealized reference process of dark fermentation to actual conditions.

5. Conclusion

An idealized reference model was needed for an accurate efficiency evaluation of dark fermentation. A PN was chosen, which was modeled based on the thermodynamics of the relevant reaction pathways. A total of 27 reactions and 21 components were considered to calculate the reactor’s idealized concentration of H₂ and CH₄. Comparing the results of the PN and the experimental data showed a qualitative agreement of the graphs, which support the model’s suitability as an ideal reference state.

The model was validated using initial experimental data at a laboratory scale. Divergences between the expected and the observed reaction turnover were found. These are mainly due to experimental uncertainties. The authors plan to validate the model based on further experimental data, which will be obtained during the operation of a newly constructed demonstration plant.

Based on the existing experimental data, a substantial fluctuation in the efficiency becomes visible during the reaction. The efficiency evaluation based on the developed model suggests an optimization potential of 21–56%. Since the model is a purely theoretical idealized reference process, it can be assumed that this optimization potential cannot be achieved technically. However, the assessment method gives a better idea of where the biological process can be optimized due to the detailed analysis of separate reaction steps. By monitoring the concentrations of the reactants, intermediates, and end products in the reactor, the model can be used to identify which process steps need to be optimized in detail.

Acknowledgments

We want to extend our heartfelt appreciation to our project partners of MicroPro GmbH and Streicher Anlagenbau GmbH & Co. KG for their valuable contribution of expertise and experimental data, which greatly enhanced the quality and significance of this research. Without their support and collaboration, this study would not have been possible. We are grateful for their dedication and commitment to advancing scientific knowledge in this field.

Conflict of interest

The authors declare no conflict of interest.

Nomenclature

AA	Amino acids
DM	Dry matter
LCFA	long-chained fatty acids
MOs	Microorganisms
OA	Organic acid
PhO	Physical optimum
PN	Petri net
TVS	Total volatile solids
$c_{\mathit{\text{in}},m}$	Concentration of input component m, [−]
$\frac{\mathit{dX}}{\mathit{dt}}$	Concentration of component X at time t, [−]
$m_{\mathit{\text{Glucose}}}$	Mass of glucose, [g]
$M_{\mathit{\text{Glucose}}}$	Molecular weight of glucose, [g/mol]
$N_A$	Avogadro constant, [1/mol]
$N_{\mathit{\text{Glucoce}}}$	Number of molecules per gram of glucose, [−]
$p_i$	Stoichiometric coefficient of reaction i, [−]