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A Data-Driven Model of Waste Gasification and Pyrolysis: One Tailored Approach for an Experimental Facility from the Czech Republic

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16 December 2025

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18 December 2025

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Abstract

The increasing demand for sustainable energy production necessitates the development of innovative technologies for converting municipal waste into valuable energy offering a viable alternative to fossil fuels. This study presents a flexible, portable, and expandable waste-to-energy concept that integrates gasification and pyrolysis processes production of combustible gases and liquid fuels. Particular emphasis is placed on the use of transparent and interpretable modeling approaches to support system optimization and future scalability. The proposed methodology is demonstrated on two experimental systems currently operated at CEET Explorer, VSB – Technical University of Ostrava, Czech Republic: (i) a primary gasification facility equipped with a plasma torch, reactor, hydrogen separator and tank, fuel cells, and renewable grid connections; and (ii) a secondary pyrolysis unit designed to maximize pyrolysis oil production. Both systems are modeled and simulated using in-house software developed in Python, employing stoichiometric balances, symbolic regression, and polynomial regression to represent chemical reactions and energy flows. The findings demonstrate that transparent models—such as stoichiometric modeling combined with interpretable machine learning—can accurately reproduce the operational behavior of waste-to-energy processes. Gasification is optimized for hydrogen generation and electricity production via fuel cells, whereas pyrolysis favors liquid fuel yield with syngas as a by-product. Molar mass relations are applied to ensure consistent conversion between mass and volume across gasification, pyrolysis, and combustion pathways, maintaining the conservation of mass. Overall, the integration of stoichiometric balance models with symbolic and polynomial regression provides a reliable and interpretable framework for simulating real waste-to-energy systems. The current results, based on bio-wood waste from the Czech Republic, validate the proposed methodology, which is made openly available to promote transparency, reproducibility, and further advancement of sustainable waste-to-energy technologies.

Keywords: 
hydrogen
;  
pyrolysis
;  
symbolic regression
;  
syngas
;  
software
;  
waste-to-energy
Subject: 
Engineering  -   Energy and Fuel Technology

1. Introduction

The objective of this study is to create flexible, portable, durable, ecologically sustainable, and expandable technology solution for efficient transformation of waste into valuable energy forms (taking care about, e.g., evidence that plasma gasification of municipal and/or industrial waste enables hydrogen production with superior environmental and thermodynamic performance when coupled with CO2 capture [1], that catalytic pyrolysis of bio-waste enhances product yield and quality while reducing emissions [2], that pyrolysis and gasification of solid waste can be directed toward high-value outputs such as methanol, hydrogen, and electricity [3], etc.), especially in combustible gases obtained in gasification facility (primary facility) or in liquid fuel obtained in small pyrolysis facility (secondary facility, i.e. pyrolysis is auxiliary process).
Both systems are modeled and simulated using in-house software developed in Python, employing stoichiometric balances, symbolic regression, and polynomial regression to represent chemical reactions and energy flows. The interactive bilingual Python software is available at https://shinyenet.vsb.cz/. To foster transparency and ensure reproducibility of our research, we provide open-source codes, including an MS Excel tool that integrates key thermochemical processes of the Centre for Energy and Environmental Technologies – Explorer (CEETe, https://ceet.vsb.cz/en/CEETe/). The methodology is fully transparent and based on open-source resources, leveraging both regression and stoichiometric modeling. In addition, an automated reporting tool for gasification analysis is made available as open source. The tool is available as Electronic Appendix A. The present work focuses on technologies currently implemented at CEETe and complements the recent techno-economic analyses of energy supply systems (e.g., [4]). Unlike prior studies, all models introduced here are openly accessible in a public repository.
An Excel table that provides raw data sets from repeated gasification measurements to cover the uncertainty of measurements is given as Electronic Appendix B. The repository also includes a Python-based automated regression tool for gasification modeling and reporting, provided as Electronic Appendix C.

1.1. Background

A rough schema of facilities and processes in the observed waste-to-energy system is given in Figure 1.
Main products in the facilities examined are:
1. Primary facility: Gas mixture from gasification, i.e., syngas, which is mainly composed of nitrogen N2, hydrogen H2, carbon monoxide CO, carbon dioxide CO2, and methane CH4, depends on the type of waste and gasification temperature.
2. Secondary facility: Pyrolysis oil (liquid fuel) is the main product from pyrolysis.
The gasification facility (primary facility) includes a plasma torch, gasification reactor, and fuel cell unit for producing hydrogen in a main process (e.g., Aziz et al. [5] review thermochemical and biological routes for converting biomass and organic waste to hydrogen, highlighting recent progress, key technologies, and challenges for advancing a sustainable hydrogen economy), with auxiliary process for producing hydrogen in an electrolyzer. Combustion for heating (or conventional electricity generation via a turbine), or the production of liquid fuel, is used as an alternative process. This alternative process operates only when the fuel cells in the main process are turned off, or in parallel with other available gases—mainly methane and carbon monoxide, in addition to hydrogen. The entire amount of produced hydrogen is used either in the main process or in the alternative process. Other non-combustible gases are envisaged for the possible production of liquid fuel after chemical treatment. Small pyrolysis is a separate facility (secondary facility).

1.2. Literature Overview

Synthetic gases had been frequently used before the Second World War, but were later substituted with natural gas due to environmental issues. These issues have since been overcome by using cleaner technologies and by substituting the type of alternative fuel (raw material for both examined facilities), i.e. to switch from coal to communal waste. For example, dos Santos et al. [6] find that a natural gas–based hydrogen industry with CO₂ capture can aid the energy transition but depends on oil prices and CO2 storage capacity. Thomas [7] shows that the manufactured gas industry transformed lighting and safety, expanded to energy and chemicals, and became the first integrated energy network before natural gas replaced it. Melaina [8] shows that the manufactured gas industry, once central to urban lighting and heating, illustrates how innovation, competition, and adaptability shaped energy networks, offering lessons for today’s hydrogen infrastructure. Wehrer [9] reviews how legacy manufactured gas plant sites still threaten groundwater with toxic organic and inorganic contaminants, highlighting knowledge gaps in pollutant behavior and the need for improved risk assessment and remediation. Hamper [10] reviews the history of U.S. manufactured gas plants, their decline with the rise of natural gas and electricity, and details how different production processes generated distinct gases and residuals, knowledge essential for assessing former plant sites. Albertazzi et al. [11] highlight biomass gasification as a renewable, CO2-neutral energy source and explore challenges in reforming high-sulfur and alkali-rich gas streams for liquid fuel production. Liebs [12] gives an overview about town gas), e.g., different carbon footprint is for hydrogen production from coal, from waste, from water, or from hydrocarbons. Maksimov et al. [13] analyze water use and carbon footprints in hydrogen production, showing that nearly half of the hydrogen from steam reforming originates from water with lower emissions, highlighting water and energy balances as key factors for sustainable hydrogen development. Also, pyrolysis was not always popular because it can form unwanted and toxic hydrocarbons if the process is not controlled with care. For example, Lyu et [14] al. show that biochars produced at higher pyrolysis temperatures (>400oC) are less toxic and have lower dioxin-like potencies, making them more suitable as soil adsorbents, and Rutkowski and Lewin [15] show that thermal decomposition of certain plastics produces toxic gases, mainly carbon monoxide and hydrogen cyanide, with hazards comparable to other common polymers.
Syngas (gases from gasification or as byproduct of pyrolysis) is different compared to natural gas in which hydrocarbons and especially methane is dominant. Among others, Rahimpour et al. [16] give an extensive overview about syngas production, and Odel [17] overviews facts relating to the production and substitution of manufactured gas for natural gas). Hydrogen from syngas can be used for blending with natural gas as demonstrated in Erdener et al. [18], who examine the potential of blending hydrogen into natural gas grids, highlighting technical, safety, and regulatory challenges while identifying research gaps for wider integration, and in Ozturk et al. [19], who show that blending hydrogen with natural gas improves combustion efficiency and reduces CO2 and CO emissions, though NOx trends fluctuate and some environmental impacts slightly increase. Composition of syngas from pyrolysis is very different from that of syngas from gasification.
This article is organized into two main parts, namely modeling and description of in-house developed software based on developed models which can be used for various testing. A data-driven digital model of waste gasification and pyrolysis includes machine learning methods [20,21,22,23]. Ascher et al. [20] apply machine learning to model biomass and waste gasification, showing gradient boosting as most accurate and demonstrating that interpretability methods improve trust and insights for process design. Li et al. [21] use machine learning to model biomass gasification, showing gradient boosting predicts product yields accurately and identifies optimal feed and temperature conditions for maximizing H2-rich syngas. Lee et al. develop an Artificial Neural Network (ANN)-based model for steam methane reforming using extensive operational data, achieving high prediction accuracy and optimizing process conditions to reach 85.6% thermal efficiency. Chu et al. develop regression and neural network models to predict syngas characteristics in plasma gasification of municipal waste, showing key roles of input power, feedstock, and gas flow rates in determining efficiency and composition.
Waste is alternative fuel used instead of fossil fuels, while hydrogen is used here as energy source as a predominant alternative for fossil fuels as presented in Kaheel et al. [24], who review the hydrogen energy landscape, identifying technical, policy, logistical, and infrastructure challenges affecting production, distribution, and deployment of hydrogen energy, and underscores the importance of public–private partnerships, regulation, and strategic planning to accelerate blue and green hydrogen adoption globally.

2. Waste-to-Energy Experimental Facilities — Models of the System

Gasification and pyrolysis are two complementary thermochemical conversion routes for valorizing waste and low-rank fuels. Gasification, particularly in co-gasification setups, has shown strong potential to address global waste challenges while enhancing hydrogen-rich syngas production and process efficiency [25]. Plastic waste, for example, is increasingly recognized as an energy resource, with co-gasification improving gas yield, cold gas efficiency, and fuel quality compared to single-feed processes [26]. Similarly, blending low-rank coals with refuse-derived fuels has been demonstrated as a feasible strategy to produce hydrogen-rich syngas and improve feedstock usability [27]. Pyrolysis, on the other hand, enables the thermal decomposition of plastics and biomass into liquid fuels, syngas, and char, thereby complementing gasification in integrated waste-to-energy and resource recovery systems.
The main difference between pyrolysis (a secondary facility) and gasification (a primary facility) is that pyrolysis takes place without access to oxygenators, while gasification takes place in presence of ambient air.
The temperature in both examined facilities is set [28] in order to:
1. maximize hydrogen production from syngas from gasification [29], i.e., from the primary facility for use in fuel cells (main process in the primary facility); alternatively, if fuel cells are out of order, the goal is to maximize the energy value of syngas for combustion and heating purposes (alternative process of the primary facility),
2. maximize the production of liquid fuel (pyrolysis oil) [30,31,32], which is the main optimization goal to achieve in pyrolysis, i.e., in the secondary facility.
Gasification (primary facility) takes place in a reactor with a temperature ranging from 750 °C to 1100 °C, while pyrolysis from 300 °C to 800 °C.

2.1. Gasification Facility – Primary Facility of the Observed Waste-to-Energy System

The gasification is the primary facility in the examined waste-to-energy system, with a diagram given in Figure 2.
Air is used as the gasification medium in the gasification facility. Fuel (alternative fuel) for the system is waste, mostly municipal waste, which consists mainly of organic materials (biomass or combustibles from communal garbage and industry). It is used to produce synthetic gas – syngas. The main process within the facility goes through a hydrogen separator and tank [33] and fuel cells to produce electricity from hydrogen. It is connected to a battery, electric grid with integrated photovoltaic and wind turbine [34]. An electrolyzer which can produce hydrogen from water through electrolysis, is also part of the system as a support to the main process as an auxiliary process. In addition, a combustion unit (with an envisaged alternative to produce liquid fuel through Fischer-Tropsch synthesis) is added to the gasification system as an alternative process, which operates only when the main process is turned off (i.e., when fuel cells are turned off), and vice versa. For the moment, the entire amount of hydrogen produced goes entirely or in the main process or in alternative process. Alternatively, combustion as a variant of the alternative process can work without hydrogen only with methane and carbon monoxide in parallel with the main process. Combustion can be replaced with the production of liquid fuel where non-combustible compounds of syngas possibly can be used.
Gasification is characterized by the following parameters: Fuel cells with the installed capacity of 40kW (with 5 stacks of 8 kW), an electrolyzer 14 kW, battery with capacity of 500 kWh with an inverter of 250 kVA, connections to photovoltaic with the capacity of up to 170 kW, and wind power up to 10 kW. Waste is used as an alternative fuel with an input of 60-80 kg/hour with calorific values of 21.1 and 27.12 MJ/kg where the energy required for the separation of H2 from syngas is missing, for example, biomass) [35]. The energy required for compression from 1 to 200 bars at a flow rate of 0.39 kg/h is about 11.98 kWh if the efficiency of the compressor is 50%.
The input/output relations within the processes of the gasification facility are identified in Table 1.
The components of the gasification facility, such as Alternative fuel, Gasification reactor, Plasma torch, Hydrogen separation and tank, Fuel cells, Electrolyzer, Combustion or production of liquid fuel, Photovoltaics, and wind turbine, will be explored in more detail in the following text.
Input of waste for gasification is estimated to 20 kg per hour, which can give around 17.6-18.33 normal m3 of syngas (or for 100 kg of waste it can give around 88 normal cubic meters of syngas; initially about 150 normal m3 of syngas were estimated for 100 kg of waste production; however, it was extremely ambitious, knowing that mass of waste plus reactants from ambient air need to be equal to the mass of the produced syngas) while further details are given in Table 2.
Based on Boyle's law (Boyle–Mariotte law), Charles’ law, and Gay-Lussac’s law, pV=nRT, where p is pressure in Pa, V is volume in cubic meters, n is number of mol, T is temperature in K, and the universal gas constant is R=8.3144598 m3·Pa/(mol∙K). The following can be concluded, as given in Table 3.

2.1.1. Alternative Fuel

Fuel for gasification and pyrolysis should be communal waste or combustible residuals from industry and biomass (Figure 3). The waste is mechanically preprepared before being sent to the gasification reactor.

2.1.2. Plasma Torch

A plasma torch enables gasification of municipal waste in the gasifier reactor [36]. A plasma torch is a device for generating a stream of plasma with an appropriate temperature [37]. In this case, the middle plasma torch temperature T [K], which depends on the required power of plasma torch P [kW], the base constant of nozzle k [dimensionless], and the filling pressure fp [bar], is given in Equation (1):
T = 700 + 19050 · P k · f p
The plasma torch from this study provides low-temperature plasma with a middle plasma torch temperature T ranging from min. 1295.3K to max. 19750.0K based on real physical experiments [38,39,40,41]. Equation (1), based on symbolic regression [38], gives very accurate predictions only in this range, where it is well correlated with experimental data with the relative error that remains below 0.283‰ (0.0283%) [42].

2.1.3. Gasification Reactor - Amount and Composition of Syngas Based on Temperature

Gasification is performed in a reactor in the presence of air while heat is provided by the low-temperature plasma torch. In the model, the composition of syngas depends on the temperature in the gas reactor from Equation (1) as given in Table 4. The gasification facility with the reactor in its core is given in Figure 4.
Waste gasification is performed in a reactor with temperature t ranging from 750 °C to 1100 °C in the presence of air that is used as the gasification medium. The plasma torch, which is used for this study, provides plasma with a middle plasma torch temperature T ranging from min. 1295 K to max. 19750 K based on real physical experiments which further should be reduced to the required temperature prescribed for the gasification reactor as given in Equation (2):
t=(T-273.15)·0.01917+726.59
Where t is the middle temperature in the gasification reactor in [°C], and T is the temperature of the plasma torch in [K] as seen in Equation (1). The values of the temperature are expressed in different units—T [K] vs. t [°C]—solely because of the available structure’s raw parameters from the available datasets. An additional reference for the syngas composition for comparisons is Hasanzadeh et al. [43], where the composition of syngas in air gasification is reported: H2≈18%, CO≈15%, CH4≈3-4%, CO2≈10%, and N2≈60%. While in steam gasification it is as follows: H2≈62%, CO≈21%, CO2≈3-4%, and CH4≈1-2%.
The composition of syngas depends mostly on the temperature in the gasification reactor, oxidation medium, and the composition of waste, while the most desired component is hydrogen because the main purpose of the facility is to produce electrical energy from hydrogen in fuel cells. The desired components of syngas are also methane and carbon monoxide, which can be further used for direct combustion (for heating or for the production of electricity) or for the production of liquid fuels through Fisher-Tropsch synthesis [44,45]. Carbon dioxide can also be used for carbon production [46].
Gasification is simulated using two types of regression, symbolic and polynomial (based on a similar analysis as in [47], polynomial formulations can be recommended for use in this case1). Symbolic regression is a technique based on artificial intelligence with the ability to explore appropriate mathematical expressions for identifying the best-fit models for a given dataset [48].
Based on data from Table 4 and using regression, both symbolic and polynomial, continual functions of five gases with largest volumetric percentage in syngas in dependence of temperature t [°C] in the gasification reactor are established (these five gases give in sum around 100%).
Symbolic regression functions for gasification are developed using the open-source tools AI Feynman [49]—previously applied in gasification modeling [50]—and PySR (High-Performance Symbolic Regression in Python and Julia) [51], alongside polynomial expressions. The resulting formulas are presented in Table 5.
The maximum production of hydrogen is around 900 °C in the reactor, while the temperature of the plasma torch is around T=10887.2 K. The goal is to maximize the production of hydrogen for further use in fuel cells. It is discovered after entropy analysis through Occam’s Razor [47] that the results obtained in the AI Feynman software from [50] are not stabile, i.e., these symbolic regression formulas show oscillatory behavior between the points given in Table 4 as shown in Figure 5. In Figure 5a, the red line presents expected behavior, while in Figure 5b, the green line presents oscillatory behavior between the black dots. In both Figure 5a and Figure 5b, these black dots represent real data from Table 4.
Suitable formulas for volumetric percentages are given in Figure 6 and Figure 7.
According to the symbolic regression models obtained in PySR, for t=928 °C, an unrealistic peak for hydrogen occurs which is not confirmed in practice. An unreliable amount of hydrogen is predicted by PySR between 897°C and 955°C. However, this peak does not appear in polynomial regression models, where the sum of the entire amount of the produced syngas always remains below 100 %, as can be seen in Figure 8. Therefore polynomial models maintain the conservation of syngas volume better compared to symbolic models.
Models obtained in symbolic regression – PySR and polynomial regression can be combined with the exception hydrogen, for which only polynomial regression model should be used. In more detail:
  • Polynomial regression: For the middle temperature in the gasification reactor t ranging from 879 °C and 966 °C, the production of hydrogen is maximal with an amount larger than 15% and never reaches 16%. The absolute peak for the production of H2 is for t=923 °C. For t=923 °C, CO2 11.87 %, CO 19.76 %, CH4 2.11 %, and N2 49.3 %, which gives a total of 98.78 % while the rest are other gases.
  • Symbolic regression – PySR: A model for all components of syngas can be used except for hydrogen, for which polynomial regression formulation should be used instead.
Polynomial regression models perform better than symbolic regression models as confirmed by statistical and entropy analyses grounded in Occam’s Razor [47]. Therefore, the polynomial regression approach will be further developed in more detail:
  • Hydrogen H2
The recommended model for hydrogen H2 is a polynomial of degree 4, as given in Table 6. Its mean squared error is as low as 0.3.
Figure 9 shows optimized models of volumetric percentage of H2 in dependence on temperature t [°C] in the gasification reactor obtained in polynomial regression.
  • Carbon dioxide CO2
The recommended model for carbon dioxide CO2 is a polynomial of degree 4, as given in Table 7. Its mean squared error is as low as 0.4.
Figure 10 shows optimized models of volumetric percentage of CO2 in dependence on temperature t [°C] in the gasification reactor obtained in polynomial regression.
  • Carbon monoxide CO
The recommended model for carbon monoxide CO is a polynomial of degree 4, as given in Table 8. Its mean squared error is as low as 0.21.
Figure 11 shows optimized models of volumetric percentage of CO in dependence on temperature t [°C] in the gasification reactor obtained in polynomial regression.
  • Methane CH4
The recommended model for methane CH4 is a polynomial of degree 4, as given in Table 9. Its mean squared error is as low as 0.04.
Figure 12 shows optimized models of volumetric percentage of CH4 in dependence on temperature t [°C] in the gasification reactor obtained in polynomial regression.
  • NitrogenN2
The recommended model for nitrogen N2 is a polynomial of degree 4, as given in Table 10. Its mean squared error is only 0.49.
Figure 13 shows optimized models of volumetric percentage of N2 in dependence on temperature t [°C] in the gasification reactor obtained in polynomial regression.
In summary, recommendations for the optimized models obtained in polynomial regression are presented after analyzing regression polynomials of degrees 2, 3, 4, 5, and 6 with respect to maximum absolute error, maximum relative (percentage) error, and mean squared error, as given in Table 11.

2.1.4. Hydrogen Separation

Separation of hydrogen is very important because fuel cells require very clean fuel.
The maximum production of hydrogen is achieved for different combinations of inputs for the plasma torch as given in Table 12. Different combinations of the input parameters can give the same output values.
The actual physical method used for separating hydrogen and its purification is not relevant for this evaluation.

2.1.5. Hydrogen Tank

After separation and compression, the hydrogen is stored in bundles of high-pressure cylinders forming a hydrogen tank. The hydrogen tank attached to the gasification facility has the volume of 2.2 m3, with pressure of 20 MPa (200 bar), and with the temperature in the tank of 298 K. In this tank with these parameters, n≈17758 mol can be placed inside, which means ~ 35.52 kg of hydrogen. If the production of hydrogen is 0.39 kg/hour, then around 92 hours or around 3.84 days are needed to fill the tank [52]. This tank is shown in Figure 14; the white bottles are filled with hydrogen produced in the facility, while the red bottles are filled with pure hydrogen with certified cleanliness bought on the market for comparison with the produced one.
An example of the filling duration of a hydrogen tank is given in Table 13.

2.1.6. Fuel Cells and Electrolyzers

2.1.6.1. Fuel Cells

Fuel cells are electrochemical devices that convert the chemical energy of a fuel, typically hydrogen, directly into electricity through a reaction with oxygen (from ambient air), producing water and heat as byproducts. They are highly efficient and environmentally friendly, with applications ranging from powering vehicles to providing electricity for buildings and portable devices.
It is estimated that around 0.3 kg of hydrogen which can be produced per hour from the gasification facility can give around 10.2 kWh of electrical energy (lower heating value - LHV) or 12.2 kWh of electrical energy (higher heating value - HHV). These values are for 100% fuel cell efficiency. When used as part of a fuel cell, 1 kg of hydrogen can produce 33 kWh/kg of electrical energy (lower heating value - LHV) for high-temperature fuel cells if the product is steam, or 39.38 kWh/kg (higher heating value - HHV) for low-temperature fuel cells if the product is water in liquid phase. In a low-temperature fuel cell, where the product is liquid water, the HHV should be employed in efficiency calculations, while for high-temperature fuel cells, it may be permissible to use the LHV if the product steam is put to good use [53]. Efficiency (35 %-60 %): 3.57 kWh of electrical energy (lower heating value - LHV), 4.26 kWh of electrical energy (higher heating value - HHV) - Both in real conditions [54]2.
The installed fuel cells are in 5 stacks of 8 kW and are connected directly to the electric grid.
The examples of work of fuel cells installed within the observed gasification facility are given in Table 14.
The installed fuel cells are shown in Figure 15.

2.1.6.2. Electrolyzer

An electrolyzer is a device that uses electricity to split water into hydrogen and oxygen through a process called electrolysis [55,56]. The technology in fuel cells and electrolyzers is related but operates in reverse mod. While fuel cells generate electricity by combining hydrogen and oxygen, producing water as a byproduct, electrolyzers use electricity to split water into hydrogen and oxygen.
Typically, 52 kWh are required to produce 1 kg of hydrogen3. Therefore, 3.57 kWh produced typically per hour in fuel cells can produce 0.069 kg of hydrogen. This means that around 22.21% of hydrogen can be recovered if the hydrogen is used to produce electricity in fuel cells and then to use this produced electricity to produce hydrogen in the electrolyzer.
The implemented models are general and, therefore, offer calibration according to the requirements of researchers.
The electrolyzer has the power of 14 kW. It is shown in Figure 16. The installed electrolyzer is not connected to the electric grid, but the electric energy is instead supplied through photovoltaics of 170kW and wind turbines of 10kW.
The installed electrolyzer is used as an auxiliary process for producing hydrogen in addition to the gasification of waste, which is the main process for producing hydrogen. The examples of work of the electolyzer are given in Table 15.

2.1.6.3. Purge Process of Fuel Cells and Electrolyzers

The purge process for fuel cells has also been developed (it is valid for electrolyzers as well). Validation of fuel cells and electrolyzers was performed in R programming language, and a script for fuel cell validation (detection and prediction of purge) and a script for electrolyzer validation (detection and prediction of pressurization and hydrogen generation) were implemented in-house4.
The purge is a cleaning process whereby the short-term opening of the hydrogen valve at the output of the fuel cell modules washes away impurities from the anode side of the cells, thus stopping the gradual drop in their operating voltage.
Pressurization occurs in the production of hydrogen, when a constant increase in pressure is sharply reduced at some point. In addition to finding where this reduction occurred, the total amount of hydrogen produced between two moments of pressurization is also of interest. In both cases, it is a problem of detecting changes in time series. In order to automate and facilitate the work, it was also necessary to create a set of custom scripts in the R language to ensure that the results could be easily retrieved and converted into a user-friendly form and saved to a disk.
The selected methods for both fuel cell purge time detection and electrolyzer pressurization detection are of two types, with the first one being based on the use of sliding windows and the calculation of the average values in these windows. The difference of these values in two adjacent windows is then used to identify the change. The second method relies on the widely used Bayesian approach and the use of Markov Chain Monte Carlo (MCMC) simulation. This modern method produces a probabilistic time series profile based on the input data and using MCMC simulation. From this profile, the change points are extracted using the created scripts, which are then displayed to the user.
Figure 17 shows the results of the algorithm for detecting fuel cell purges. The results show that the fuel cell purge detection is highly reliable for the detection task, as it produces only three false positives.
Table 16 shows the comparison of the known values with the values predicted by the algorithm electolyzers.
The calculated absolute error shows that the algorithm can predict the values of hydrogen produced quite accurately: out of 16 intervals, in 12 cases the algorithm predicted the amount of hydrogen produced with an absolute error of less than 0.54 dm3/min (cases are shown in green). The maximum error of the algorithm was in 11 intervals: the algorithm predicted the amount of hydrogen produced to be 28.53 dm3/min, while the reality was 26.28 dm3/min. This corresponds to an absolute error of 2.64 dm3/min.

2.1.7. Combustion or Production of Liquid Fuel — An Alternative Process in the Gasification Facility

The synthesis gas produced can be used in two ways. The first is its energy recovery. That is, it is burned in a suitable energy device (burner, turbine, boiler, etc.) and thus, the chemical energy is converted into chemical energy.
Table 17 shows the amount of gases and related energy if all combustible components of syngas produced from 60kg of waste per hour (if the entire produced amount of all combustible compounds of gas, including hydrogen, go into combustion).
The second option is to use syngas to produce liquid fuel. The liquid fuel is most often prepared by the synthesis of CO and H2 on a suitable catalyst [58,59,60]. Since syngas contain components other than CO and H2, these components must be suitably separated from the gas and subsequently transformed to CO and H2 using reforming (steam or dry). The N2 component, which comes from the gasification medium, must be separated as it has no energy value.

2.1.8. Photovoltaics and Wind Turbine

Photovoltaics of up to 170 kW and wind power of up to 10 kW are installed to provide power for the electrolyzer. Surpluses of electric energy are stored in the PYLONTECH LiFePO4 battery with the capacity of 500 kWh.
The installed photovoltaics and wind turbines are shown in Figure 18. Time to fill up the battery from such photovoltaics and wind turbines is given in Table 18.

2.2. Small Pyrolysis

An additional separate facility, i.e., the secondary facility in the examined waste-to-energy system includes small pyrolysis, the diagram of which is given in Figure 19. The main product of pyrolysis is liquid fuel - pyrolysis oil [61,62,63], while the byproduct is gas and char, the composition of which is very different compared with the gas produced in the gasification facility, i.e., in the primary facility.
Pyrolysis oil is a very heterogeneous substance consisting of many compounds [64], which can be dangerous for the environment and humans [65,66]. However, with appropriate handling, this danger can be eliminated so that pyrolysis liquid can be a valuable source of raw materials [67].
Small pyrolysis is designed for 2-5 kg of waste per hour with the maximum outputs for 5 kg of waste: Char up to 1.9 kg/hour, liquid fuel, i.e., pyrolysis oil 1.6 kg/hour, and gases 1.5 kg/hour (very different composition of gas compared with gasification). The volume of this produced gas under normal conditions of pressure and temperature is around 0.9 m3.
The diagram of the installed small pyrolysis is shown in Figure 19 and a photo of the installed small pyrolysis is in Figure 20.
The input/output relations within the processes of the pyrolysis facility are identified in Table 19.
t=(p+1.5591)/0.0425
Where t is temperature [°C] (from 300 °C to 800 °C), and p is energy consumed in pyrolysis [MJ] (from 3.6MJ to 36MJ).
Five kg of waste gives 3.06m3 of gas in pyrolysis if all mass is transformed into gas (it is based on the logic from gasification for mass balance) – 100% of mass in gas is not possible in practice because gas is a by-product. Based on [31], this amount of gas is corrected giving 0.91m3 of gas: CO=0.287m3, CO2=0.548m3, CH4=0.075m3, and H2=0.0006102m3. 1.489 kg of the total mass of input waste is transformed into gas.
Mass percentage of gas G is given in Equation (4):
G%mass = 11.3943 + 0.059×t
Where t is pyrolysis temperature [°C].
Mass percentage of gas compounds is given in Table 20.
mass percentage of liquid fuel (pyrolysis oil) L is given in Equation (5):
L%mass = 30.2507+0.0246×t-0.000057833×t2
Where t is pyrolysis temperature [°C], while the rest, aside from the liquid and gas part, is biochar.
The examples from small pyrolysis are given in Table 21.
Table 22 examines, in more detail, Examples 1 and 2 from Table 21 for by-product Gas G.

3. Conclusions

This study developed and deployed open-source regression-based software tool for simulating compact, mobile, and user-friendly waste-to-energy facilities. The objective was to support planning, development, management, and optimization of waste management in the Czech Republic and beyond.
Key quantitative findings
  • Gasification: Regression methods provided interpretable and robust approximations of thermochemical processes of transforming waste to syngas, contrasting with black-box deep learning approaches. Furthermore, polynomial regression models perform better in this case compared to symbolic regression models. Optimal reactor temperature range was determined as 879–966 °C, with a peak hydrogen yield at 923 °C (H2 = 15.1%, CO2 = 11.87%, CO = 19.76%, CH4 = 2.11%, N2 = 49.3%, total 98.78%).
  • Pyrolysis: the developed model identified an optimal power of 3.3 kW, converting 3 kg/h of waste input into 0.97 kg/h of liquid fuel.
Limitations
  • Current validation is limited by the availability of experimental datasets.
  • The results are based on wood pallets typical of Central Europe; feedstock variability may affect accuracy when extending to other waste types.
  • Scaling up from laboratory to industrial operation may introduce additional uncertainties related to reactor performance, energy efficiency, and emissions.
  • Potential environmental and health impacts of different waste-to-energy processes require further investigation.
Practical and technical implications
  • The developed tools are open-source (Python, MS Excel) and accessible through web browsers, enabling interactive scenario analysis.
  • The software supports community-scale applications, including industrial enterprises and municipalities, and may be integrated with renewable energy sources (PV, wind) or fuel cell systems.
Future work
  • Extend datasets and validation across different waste feedstocks to improve generalizability.
  • Conduct a comprehensive techno-economic analysis (similar as Rizqi [5]) to assess feasibility at different scales. Integrate cost analysis.
  • Integrate environmental impact assessments (e.g., life-cycle analysis, emission control studies) into the modeling framework.
  • Facilitate further transparency by releasing additional open-source data and codes.

Funding

The authors received support from: 1. the Ministry of Education, Youth and Sports of the Czech Republic through the e–INFRA CZ (ID: 90254) project, 2. the EU funds under the project “Increasing the resilience of power grids in the context of decarbonisation, decentralisation and sustainable socioeconomic development”, CZ.02.01.01/00/23_021/0008759, through the Operational Programme Johannes Amos Comenius, and 3. the Technology Agency of the Czech Republic through the CEET project—“Center of Energy and Environmental Technologies” TK03020027. Dejan Brkić additionally wants to acknowledge: This work has been supported by the Ministry of Science, Technological Development and Innovation of the Republic of Serbia, grant number: 451-03-136/2025-03/200102.

Author Contribution Roles

Dejan Brkić: Conceptualization, Data curation, Formal Analysis, Funding acquisition, Investigation, Methodology, Software, Supervision, Validation, Visualization, Writing – original draft, Writing – review & editing; Pavel Praks: Conceptualization, Data curation, Formal Analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Software, Supervision, Validation, Visualization, Writing – original draft, Writing – review & editing; Judita Buchlovská Nagyová: Conceptualization, Data curation, Software, Validation, Visualization, Writing – original draft, Writing – review & editing; Michal Běloch: Conceptualization, Data curation, Formal Analysis, Methodology, Software, Validation, Writing – original draft, Writing – review & editing; Martin Marek: Conceptualization, Data curation, Formal Analysis, Methodology, Software, Validation, Visualization, Writing – original draft, Writing – review & editing; Jan Najser: Conceptualization, Data curation, Formal Analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Software, Supervision, Validation, Writing – original draft, Writing – review & editing; Renáta Praksová: Conceptualization, Data curation, Formal Analysis, Methodology, Software, Validation, Visualization, Writing – original draft, Writing – review & editing; Jan Kielar: Conceptualization, Data curation, Formal Analysis, Methodology, Software, Supervision, Validation

Data availability

All data required to repeat this research is provided in the text. Open-source codes to foster transparency and encourage reproducibility of this research are available under the CC BY 4.0 license at Zenodo; https://doi.org/10.5281/zenodo.17411891.

Electronic Appendices

All described files are given in Zenodo: https://doi.org/10.5281/zenodo.17367399

Electronic Appendix A

It includes an MS Excel tool that integrates key thermochemical processes of the Centre for Energy and Environmental Technologies – Explorer (CEETe, https://ceet.vsb.cz/en/CEETe/), which is used as a basis for https://shinyenet.vsb.cz/

Electronic Appendix B

It is given as an Excel table, which provides raw data sets from repeated gasification measurements. For example, for 750 oC gasification, results of four independent measurements are provided, in columns C, D, E, F. This article provides detailed regression analyses of the top six syngas components (O2, CO2, H2, CO, CH4, N2), which cover approximately 98% of syngas, the line ‘Sum of O2, CO2, H2, CO, CH4, N2’, i.e. B26 of the table. The absolute error of gasification measurements does not exceed 3.08 %, see the line ‘Absolute error (0 % in theory)’, the cell B28.

Electronic Appendix C

The Python file polynom.py is added to provide full reproducibility of results, which are related to bio-wood waste from the Czech Republic. However, the Python file, thanks to its general regression approach, can be applied to various alternative fuels for various countries. The Python file provides automated regression analyses and is accessible in the open repository, which automatically generates MS Word reports with color plots and tables given as a separate Word file. The Python file and the regression report provide a detailed analysis of the important syngas components (CO2, H2, CO, CH4, and N2) for regression models of degree 2 to 6, where the total of 5 times 5, i.e. 25, regression models are constructed and analyzed. The performance of these models is analyzed by various statistical metrics: max. absolute error, max. percentage error and mean squared error (MSE). Finally, the Python code and report include the most valuable regression models according to MSE. Interestingly, automated regression results clearly show that the winning (recommended) regression model for all analyzed syngas components is always represented by a polynomial of degree 4. In contrast to symbolic regression, which provides the overfitted models with artificial oscillations and non-physical peaks, classical regression models are very useful for modeling, Figure 9, Figure 10, Figure 11, Figure 12 and Figure 13. Moreover, it can be seen that MSE is very close to zero and did not exceed 1.09, as can be seen in the Table on Page 6 of the file. Finally, each gas is tested using 5-fold cross-validation, see the Python file polynom_cross_validation.py. Degree 4 polynomials generally offer the best trade-off between bias and variance for most gases, except for N₂, where degree 2 polynomials generalize slightly better: The average MSE for the degree 2 polynomial is 0.8335, whereas for the degree 4 polynomial it is 0.965.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Declaration of generative AI in scientific writing

Not used.

Nomenclature (main text)

T - middle plasma torch temperature [K],
P - power of plasma torch [kW],
k - base constant of nozzle [dimensionless],
fp - filling pressure [bar],
t - middle temperature in the gasification reactor [°C],
p - energy consumed in pyrolysis [MJ].
V – volume [m3],
G%mass - mass percentage of gas [%],
L%mass - mass percentage of liquid fuel (pyrolysis oil) [%].

Appendix A - Evaluation of gasification models using entropy

An extended analysis for new models based on [47] is given here.
This Appendix A summarizes validation of the developed gasification models by approximation and sample entropy methods.
Various approaches, such as classical polynomial regression and alternative symbolic regression using artificial intelligence elements, were developed and tested. Despite subsequent validation of the models on new data, it appears that statistical criteria such as mean square error (MSE) or Pearson correlation coefficient are not sufficient to select the appropriate model. Therefore, a new model selection methodology was developed based on the measurement of system complexity using entropy.
A new tool was developed using open-source libraries to identify appropriate (“quality”) models. The research aimed at developing software that automatically identifies and discards "unsuitable" models. The developed software was tested on gasification models, but due to its generality, it can be tested and used on other models as well.
The developed software identifies "suspicious" models that are of “low quality” according to dynamical systems theory (among others, by using approximation and sample entropy).

A.1 Approximation and sample entropy

The main tools in the software under development to detect model fit are approximation ( E a p p or A p E n ) and sample entropy ( E s a m p or S a m p E n ). In this work, the open-source EntropyHub package [69] for the Python programming language was used for the computation. These methods have already been investigated and applied by many authors for measuring and comparing complexity [70,71,72,73].
The entropy values reflect the presence of repeating patterns in the time series. A time series containing many repeating patterns has a small entropy value; data from a less predictable process has a higher entropy value.

A.2 Calculation of approximate entropy

Two parameters are chosen to calculate the approximate entropy:
  • m - window length or dimension,
  • r - area diameter or tolerance.
Given an input data vector X = x 1 , x 2 ,   … , x N , an m -dimensional space is constructed using the elements:
u m i = [ x i , x i + 1 , … , x ( i + m − 1 ) ] .
The number C i m r is then determined, which is the number u m ( j ) such that d ( u m i , u m ( j ) ) ≤ r , divided by N − m + 1 .
The maximum metric is used, thus d p , q = max a | p a − q ( a ) | .
The next step is to determine Φ m r = ( N − m + 1 ) ∑ i = 1 M − m + 1 l n ( C i m ( r ) ) .
The approximate entropy is finally calculated as E a p p X , m , r = Φ m r − Φ m + 1 r .

A.3 Calculation of sample entropy

Sample entropy uses the same parameters m and r as the approximation entropy. The algorithm begins in the same way - for the input vector is computed with the m -dimensional elements u m i = [ x i , x i + 1 , … , x ( i + m − 1 ) ] .
Sample entropy is defined as E s a m p X , m , r = ln A B , where:
  • A is the number of pairs of vectors such that d c u m + 1 i , u m + 1 j < r ,
  • B is the number of pairs of vectors such that d c u m i , u m j < r ,
  • d c is the Chebyshev distance.

A.4 Choice of approximation and sample entropy parameters

The approximation and sample entropy parameters are the dimensions m and tolerances r . In order to choose the appropriate parameters for the CEET models, simulations were performed for different values of these parameters. Their dependence on the length of the input data vector, in particular, was also investigated. Considering the nature of the data, the parameter values were chosen as m =   1 and r = 0.2   × S D , where S D denotes the standard deviation of the input data. Changes in the parameter r as a function of the length of the input data n are shown in Figure A.1.
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Figure A.1. The plot of the parameter 𝑟 as a function of the input data length 𝑛 for CO2 models (left) and H2 models (right). Increasing 𝑛 does not result in significant changes in the parameter values.
Figure A.1. The plot of the parameter 𝑟 as a function of the input data length 𝑛 for CO2 models (left) and H2 models (right). Increasing 𝑛 does not result in significant changes in the parameter values.
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On the tested models, it can be seen that the parameter r is not significantly influenced by the length of the tested vector (number of split points of the tested interval). Option r = 0.2   × S D , therefore, does not affect the entropy results.
Subsequently, the focus is on the values of the parameter m (dimension) and entropy values as a function of the input data vector length n . Plots showing the dependence of the approximation entropy values A p E n and sample entropy S a m p E n as a function of n are presented in Figures A.2 and A.3. Both entropies are calculated for the parameter choices m = 1 a m = 2 . From the plots, it can be concluded that the choice of the parameter m does not affect the nature of the output of the decision mechanism. There is a slowdown in convergence, but it is negligible for the increasing length of the test vector. The choice of the parameter m will therefore not affect the entropy results.
It is also observed that the outputs of both algorithms ( A p E n and S a m p E n ) are consistent, i.e., the entropy results converge to similar values starting from a certain value of n . It is noted that these are two different algorithms to calculate the same model characteristic - the complexity measure. Therefore, it is important that both algorithms (even given different parameters) give similar results. The plot of changes in entropy values against the varying length of the input vector n is shown in Figure A.2 (for CO2) and Figure A.3 (for H2).
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Figure A.2. The plot of the parameter 𝑟 as a function of the input data length 𝑛 for CO2 models (left) and H2 models (right). Increasing 𝑛 does not result in significant changes in the parameter values.
Figure A.2. The plot of the parameter 𝑟 as a function of the input data length 𝑛 for CO2 models (left) and H2 models (right). Increasing 𝑛 does not result in significant changes in the parameter values.
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A.5 Conclusions of model evaluation using entropy

Within the framework of our research, the methods of approximate entropy ( A p E n ) and sample entropy ( S a m p E n ) were used for a detailed evaluation of the following gasification models:
  • CO2 Model 1:   logm 10 ( t   e s i n ( t + 0.6718609 ) ) 2 ,
  • CO2 Model 2: logm − 0.060511474   t 2   + 2.0503674 ,
  • H2 Model 1: 8.9065269419 cos ( cos ( e sin t + 1 − 2 ) ) ,
  • H2 Model 2: logm 2 7.744805   − 9.837645 + logm t − 1.5165994 + 0.0054770974   t ,
  • H2 Model 3: 6.5368786 + logm 2 ( − 9.864973 + logm 2 t − 2.1570945 ) ,
  • H2 Model 4:   8.64427756 × 10 2 − 1.11535475 × 10 − 2   t 2 + 2.50417715 × 10 − 5 t 3 − 2.08318518 × 10 − 8 t 4 + 6.0929057 × 10 − 12 t 5 .
Symbolic regression models (i.e., all models analyzed here except “H2 Model 4”) are not numerically stable: the curves of the models are sensitive to the sample length n . The algorithms for calculating entropy themselves depend on the choice of input parameters. Therefore, both algorithms are used for different combinations of the sample length n and for different input parameters to the entropy calculation algorithms (dimension m , tolerance r ). The results of the entropy analysis clearly show that the standard algorithm settings are m = 2 ,   r = 0.2   S . The sample length n remains an important variable that affects the entropy values. Knowledge of these characteristics can be used in the future to implement automatic model evaluation.
Table A.1. Entropy values for CO2 models for n = 10 000.
Table A.1. Entropy values for CO2 models for n = 10 000.
CO2 ApEn SampEn
Model 1 0.10207402716557201 0.09283472789592226
Model 2 -1.9966127829285085e-05 0.0
Table A.2. Entropy values for H2 models for n = 10 000.
Table A.2. Entropy values for H2 models for n = 10 000.
H2 ApEn SampEn
Model 1 0.20472909404756345 0.06955908463228219
Model 2 0.003898864346688402 0.0009846446174318114
Model 3 0.0040850415534996465 0.0010645168626448073
Model 4 0.001447427615602681 0.0013493376152297486
Based on the values of the parameters and entropy (see Tables A.1 and A.2), the models can be evaluated as follows.
For CO2, Model 1 is more “complex” than Model 2, as can be seen from the higher values of standard deviation (SD) and entropy.
As for H2, Model 1 shows the highest complexity (approximate entropy of about 0.2). The complexity of Models 2 and 3 is approximately identical, as indicated by the entropy curves, which are very similar. In terms of the lowest complexity, Model 4 (created by polynomial regression) is the best performing one. It achieves the lowest value of approximation entropy, while the value of sample entropy is comparable to Models 2 and 3, see Table A.2. The results for Model 4 are least dependent on the choice of the algorithm (approximation or sample entropy), the parameter m, and the model achieves the lowest value of standard deviation. This is also evident from the plot, see Figure A.3 - Model 4 H2, where we see all four curves having almost identical forms for both approximation and sample entropy (depending on the length of the input data n and the dimension parameter m ). Thus, the best model describing hydrogen gasification is Model 4. For this reason, modeling hydrogen gasification using polynomial regression is recommended.
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Figure A3. The plot of dependence of A p E n and S a m p E n values on the length of the input vector n for two choices of the parameter m (dimension) for H2 models.
Figure A3. The plot of dependence of A p E n and S a m p E n values on the length of the input vector n for two choices of the parameter m (dimension) for H2 models.
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A Python script showing these entropy results for hydrogen gasification (H2 Model 4) is described below. The Python script leverages the open-source EntropyHub library. A modification for the other gasification models can be easily provided by a modification of the function “gasification_model(x)”.
##### Python script for entropy results for hydrogen gasification (H2 Model 4) #####
### Requirements: python 3.11, EntropyHub 2.0, numpy 2.0.0, matplotlib 3.9.1 ###
import EntropyHub as ehfrom numpy import linspaceimport matplotlib.pyplot as pltdef gasification_model(x): ## modify the expression of the gasification model here return 8.64427756e+02 + 0.00000000e+00 * x + ( -1.11535475e-02) * x ** 2 + 2.50417715e-05 * x ** 3 + ( -2.08318518e-08) * x ** 4 + 6.09290570e-12 * x ** 5start_t = 750.0end_t = 1100.0apen1 = []apen2 = []sampen1 = []sampen2 = []for count in range(500, 10001, 500): t = linspace(start_t, end_t, count) v = list(map(gasification_model, t)) Ap1, Phi1 = eh.ApEn(v, m=1) apen1.append(Ap1[1]) Ap2, Phi2 = eh.ApEn(v, m=2) apen2.append(Ap2[2]) Samp1, A, B = eh.SampEn(v, m=1) sampen1.append(Samp1[1]) Samp2, A, B = eh.SampEn(v, m=2) sampen2.append(Samp2[2])fig, ax = plt.subplots()ax.plot(range(500, 10001, 500), apen1, 'C5', linestyle='solid', linewidth=1.5)ax.plot(range(500, 10001, 500), apen2, 'C5', linestyle='dashed', linewidth=1.5)ax.plot(range(500, 10001, 500), sampen1, 'C5', linestyle='solid', alpha=0.4, linewidth=1.5)ax.plot(range(500, 10001, 500), sampen2, 'C5', linestyle='dashed', alpha=0.4, linewidth=1.5)ax.set_xlabel('n')ax.set_ylabel('entropy')ax.grid(True)ax.legend(['ApEn dim=1', 'ApEn dim=2', 'SampEn dim=1', 'SampEn dim=2'])plt.title('Model 4 H\u2082')plt.show()
#############################################################

Appendix B

A fuel cell script in the R language related to detection and prediction of purge and an electrolyzer, and the R script related to detection and prediction of pressurization and hydrogen generation are given as follows:
-Fuel cells:
##### R script for purge detection of fuel cells #####
### Requirements ###
needed.packages = c("readxl", "zoo","bcp")new.packages = needed.packages[!(needed.packages %in% installed.packages()[,"Package"])]if(length(new.packages)) install.packages(new.packages)
require(readxl)require(zoo)require(bcp)source("get_highs.r")source("get_lows.r")
### Load and visualize data ###
det_purge = read_excel("purge_detection.xlsx")begend = c(4645, 4646, 4655, 4657, 4666, 4667, 4676, 4677, 4686, 4687, 4696, 4697, 4706, 4707, 4716, 4717, 4727, 4728, 4737, 4738, 4747, 4748, 4757, 4759, 4767, 4768, 4777, 4778, 4787, 4789, 4797, 4800, 4807, 4809)plot(`U actual (V)` ~ `Time (s)`, data=det_purge, type = "l")abline(v=begend, lty = "longdash", col = "red")val_shift = as.numeric(det_profuk[1,1]-1)
### Sliding window method ###
sd_purge = rollapply(det_purge$`U actual (V)`, width = 10, by = 1, FUN = sd, align = "left")plot(sd_purge, type = "l")abline(v=begend-val_shift, lty = "longdash", col = "red")getmaxpurge = get_highs(sd_purge)plot(`U actual (V)` ~ `Time (s)`, data=det_purge, type = "l")abline(v=getmaxpurge+val_shift, lty = "longdash", col = "green")
### Bayes method ###
bcp_model = bcp(det_purge$`U actual (V)`, burnin = 10000, mcmc = 100000, p0 = 0.01)plot(bcp_model$posterior.prob, type = "l", xlab = "Time (s)", ylab = "Posterior probability (-)")bcp_purge = get_lows(bcp_model$posterior.prob)plot(`U actual (V)` ~ `Time (s)`, data=det_purge, type = "l")abline(v=bcp_purge+val_shift, lty = "longdash", col = "green")
### Save data ###
write.table(getmaxpurge+val_shift, file = "Purge_prediction_windows.csv", row.names=FALSE, col.names = "Purge time prediction (s)", sep=";", append = FALSE, quote = FALSE, eol = "\n", dec = ".")write.table(bcp_purge+val_shift, file = "Purge_prediction_bayes.csv", row.names=FALSE, col.names = "Purge time prediction (s)", sep=";", append = FALSE, quote = FALSE, eol = "\n", dec = ".")
##### END SCRIPT #####
-Electrolyzers:
##### R script for pressurization detection of electrolyzers #####
### Requirements ###
needed.packages = c("readxl", "bcp")new.packages = needed.packages[!(needed.packages %in% installed.packages()[,"Package"])]if(length(new.packages)) install.packages(new.packages)
require(readxl)require(bcp)source("get_highs_p.r")source("sum_per_int.r")
### Load and visualize data ###
det_press = read_excel("pressure_detection.xlsx")pressure = c(8690, 8976, 9233, 9602, 9917, 10215, 10458, 10623, 10672, 10802, 10976, 11115, 11258, 11400, 11552)val_shift = as.numeric(det_press[1,1]-1)plot(det_press$` output hydrogen pressure (bar)` ~ det_press$`time (s)`, type = "l", ylab = "Output pressure (bar)", xlab = "Time (s)")abline(v=pressure, lty = "longdash", col = "red")
### Bayes method ###
bcp_model = bcp(det_press$`output hydrogen pressure(bar)`, burnin = 10000, mcmc = 100000, p0 = 0.01)plot(bcp_model$posterior.prob, type = "l", xlab = "Time (s)", ylab = "Posterior probability (-)")bcp_press = get_highs_p(bcp_model$posterior.prob, 0.155)plot(det_press$`output hydrogen pressure(bar)` ~ det_press$`time (s)`, type = "l", xlab = "Time (s)", ylab = "Output pressure (bar)")abline(v=bcp_press + val_shift, lty = "dotted", col = "green")sum_per_int(det_press, bcp_press)
### Save data ###
write.table(bcp_press+val_shift, file = "Pressure_detection.csv", row.names=FALSE, col.names = "Pressure time prediction (s)", sep=";", append = FALSE, quote = FALSE, eol = "\n", dec = ".")
##### END SCRIPT #####

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1
Extended analysis is given in Appendix A.
2
Table 3 of [54] gives also specific types of low- and high-temperature fuel cells and their efficiency.
3
Electrolyzer modeling for green hydrogen: https://www.gridcog.com/blog/electrolyser-modelling-for-green-hydrogen (accessed on June 28, 2024).
4
These scripts are given in Appendix B.
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Figure 1. Schematic representation of facilities and processes in the observed waste-to-energy system: (a) Gasification, (b) Small-scale pyrolysis. In the gasification process, additional hydrogen may be supplied by an electrolyzer as part of an auxiliary system.
Figure 1. Schematic representation of facilities and processes in the observed waste-to-energy system: (a) Gasification, (b) Small-scale pyrolysis. In the gasification process, additional hydrogen may be supplied by an electrolyzer as part of an auxiliary system.
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Figure 2. Syngas production and utilization in the gasification facility as the primary waste-to-energy unit. Bold green boxes and bold text denote the main process involving hydrogen-to-electricity conversion in fuel cells.
Figure 2. Syngas production and utilization in the gasification facility as the primary waste-to-energy unit. Bold green boxes and bold text denote the main process involving hydrogen-to-electricity conversion in fuel cells.
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Figure 3. Prepared Waste Serving as an Alternative Fuel for Gasification.
Figure 3. Prepared Waste Serving as an Alternative Fuel for Gasification.
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Figure 4. Gasification facility with the reactor at the core of the process.
Figure 4. Gasification facility with the reactor at the core of the process.
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Figure 5. Hydrogen volumetric percentage vs. gasification temperature t [°C] (Black dots: experimental data from Table 4). (a) Red line: expected trend without intermediate values. (b) Green curve: oscillatory behavior from symbolic regression formulas as given in Praks et al., 2021 [50] and here in Table 5.
Figure 5. Hydrogen volumetric percentage vs. gasification temperature t [°C] (Black dots: experimental data from Table 4). (a) Red line: expected trend without intermediate values. (b) Green curve: oscillatory behavior from symbolic regression formulas as given in Praks et al., 2021 [50] and here in Table 5.
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Figure 6. PySR-derived symbolic regression models for hydrogen, carbon dioxide, carbon monoxide, methane, and nitrogen (Table 5); volumetric percentage vs. gasification temperature t [°C].
Figure 6. PySR-derived symbolic regression models for hydrogen, carbon dioxide, carbon monoxide, methane, and nitrogen (Table 5); volumetric percentage vs. gasification temperature t [°C].
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Figure 7. Polynomial regression models for hydrogen, carbon dioxide, carbon monoxide, methane, and nitrogen (Table 5); volumetric percentage vs. gasification temperature t [°C].
Figure 7. Polynomial regression models for hydrogen, carbon dioxide, carbon monoxide, methane, and nitrogen (Table 5); volumetric percentage vs. gasification temperature t [°C].
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Figure 8. Sum of all syngas components: discrepancy >100% with PySR, while polynomial model yields a sum <100%; volumetric percentage vs. gasification temperature t [°C].
Figure 8. Sum of all syngas components: discrepancy >100% with PySR, while polynomial model yields a sum <100%; volumetric percentage vs. gasification temperature t [°C].
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Figure 9. Volumetric percentage of hydrogen in the gasification reactor: Polynomial regression models valid for 750–1100 °C; volumetric percentage vs. gasification temperature t [°C]
Figure 9. Volumetric percentage of hydrogen in the gasification reactor: Polynomial regression models valid for 750–1100 °C; volumetric percentage vs. gasification temperature t [°C]
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Figure 10. Volumetric percentage of CO₂ in the gasification reactor: Polynomial regression models valid for 750–1100 °C; volumetric percentage vs. gasification temperature t [°C].
Figure 10. Volumetric percentage of CO₂ in the gasification reactor: Polynomial regression models valid for 750–1100 °C; volumetric percentage vs. gasification temperature t [°C].
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Figure 11. Volumetric percentage of CO in the gasification reactor: Polynomial regression models valid for 750–1100 °C; volumetric percentage vs. gasification temperature t [°C].
Figure 11. Volumetric percentage of CO in the gasification reactor: Polynomial regression models valid for 750–1100 °C; volumetric percentage vs. gasification temperature t [°C].
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Figure 12. Volumetric percentage of CH₄ in the gasification reactor: Polynomial regression models valid for 750–1100 °C; volumetric percentage vs. gasification temperature t [°C].
Figure 12. Volumetric percentage of CH₄ in the gasification reactor: Polynomial regression models valid for 750–1100 °C; volumetric percentage vs. gasification temperature t [°C].
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Figure 13. Volumetric percentage of N₂ in the gasification reactor: Polynomial regression models valid for 750–1100 °C; volumetric percentage vs. gasification temperature t [°C].
Figure 13. Volumetric percentage of N₂ in the gasification reactor: Polynomial regression models valid for 750–1100 °C; volumetric percentage vs. gasification temperature t [°C].
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Figure 14. Hydrogen storage tanks installed in the gasification facility
Figure 14. Hydrogen storage tanks installed in the gasification facility
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Figure 15. Installed Nedstack FCS 8-XXL fuel cell stacks as part of the system for hydrogen-to-electricity conversion
Figure 15. Installed Nedstack FCS 8-XXL fuel cell stacks as part of the system for hydrogen-to-electricity conversion
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Figure 16. Acta AES 1000 electrolyzer integrated into the facility to produce hydrogen from water electrolysis
Figure 16. Acta AES 1000 electrolyzer integrated into the facility to produce hydrogen from water electrolysis
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Figure 17. Results of the fuel cell purge detection algorithm. purple indicates the known start and end of purges, while green shows the algorithm-predicted values
Figure 17. Results of the fuel cell purge detection algorithm. purple indicates the known start and end of purges, while green shows the algorithm-predicted values
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Figure 18. Photovoltaic and wind energy systems installed in the facility
Figure 18. Photovoltaic and wind energy systems installed in the facility
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Figure 19. Diagram of the small pyrolysis unit, the secondary facility of the waste-to-energy system.
Figure 19. Diagram of the small pyrolysis unit, the secondary facility of the waste-to-energy system.
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Figure 20. Installed small-scale pyrolysis unit.
Figure 20. Installed small-scale pyrolysis unit.
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Table 1. Process input–output relations in the primary gasification facility.
Table 1. Process input–output relations in the primary gasification facility.
aMain process Input Output
Plasmatron Nozzle base constant k [dimensionless] Middle plasma torch temperature T [K]
Plasma torch power P [kW]
Filling pressure of air fp [bar]
Gasification reactor Alternative fuel – Waste Syngas
Heat c (Middle plasma temperature T [K] transformed to temperature in the gasification reactor t [°C]) Waste residual
Steam, i.e., water
Hydrogen separator Syngas Pure hydrogen
Syngas without hydrogen
Hydrogen tank Hydrogen from Hydrogen separator Hydrogen
Fuel cells Hydrogen from Gasification d Electricity
Hydrogen from Electrolyzer
Auxiliary process Input Output
Electrolyzer Electricity (from Battery or Photovoltaics/Wind turbine) Hydrogen
Water (Demi water)
b Alternative process Input Output
Tank of combustible syngas without hydrogen Syngas without hydrogen Combustible syngas without hydrogen
Non-combustible compounds of syngas
Combustion Combustible syngas without hydrogen Heat
Hydrogen
Production of liquid fuel Combustible syngas without hydrogen Liquid fuel
Non-combustible components of syngas
Hydrogen
a bold letters signify/indicate the main process within the gasification facility; b when the main process operates, then the alternative process does not operate and vice versa; while combustion can alternatively work in parallel with methane and carbon monoxide; c only because the available raw parameters these values of temperature are expressed in different units: T[K] vs. t [°C]; d Grid, battery, photovoltaics, and wind turbine
Table 2. Waste-to-energy conversion estimates in the gasification facility for an amount of 20 kg of waste at the process temperature of 930°C.
Table 2. Waste-to-energy conversion estimates in the gasification facility for an amount of 20 kg of waste at the process temperature of 930°C.
Gas compound normal m3 Number of mol Mass of gas [kg] Mass % Composition Vol. %
H2 ≈ 3.5 154.5 ≈ 0.3 ≈ 1.5 19.7
CO2 ≈ 2 88.9 ≈ 3.9 ≈ 19.5 11.3
CO ≈ 3.7 163.4 ≈ 4.6 ≈ 22.8 20.8
CH4 ≈ 0.4 17.5 ≈ 0.3 ≈ 1.4 2.2
N2 ≈ 8.8 393.4 ≈ 11 ≈ 54.8 50.1
Σ ≈ 18.3 818.0 ≈ 20 100 104.1
* Volume of 1 mol of ideal gas is 0.0224 normal cubic meters at T=273.15 K and p=101325 Pa
Table 3. Amount of Produced Gas for Various Process Parameters in Gasification Facility.
Table 3. Amount of Produced Gas for Various Process Parameters in Gasification Facility.
Gas compound Number of mol n nR [m3·Pa/K] known T [K] Known V [m3] p [bar]
H2 154.5 1284.9 50 5 ≈ 0.13
CO2 88.9 739.8 50 5 ≈ 0.07
CO 163.4 1359.3 50 5 ≈ 0.14
CH4 17.5 145.7 50 5 ≈ 0.01
N2 393.4 3271.3 50 5 ≈ 0.33
Σ 818.0 6801.2 50 5 ≈ 0.68
a Gas compound Number of mol nR [m3·Pa/K] known p [bar] Known V [m3] T [K]
H2 154.5 1284.9 41.5 5 16176.8
CO2 88.9 739.8 37.3 5 25244.7
CO 163.4 1359.3 138.1 5 50801.3
CH4 17.5 145.7 19.6 5 67237.1
N2 393.4 3271.3 202.7 5 30985.7
Σ 818.0 6801.2 439.3 5 32301.0
a Gas compound Number of mol nR [m3·Pa/K] known p [bar] known T [K] V [m3]
H2 154.5 1284.9 41.5 50 ≈ 0.015
CO2 88.9 739.8 37.3 50 ≈ 0.010
CO 163.4 1359.3 138.1 50 ≈ 0.005
CH4 17.5 145.7 19.6 50 ≈ 0.004
N2 393.4 3271.3 202.7 50 ≈ 0.008
Σ 818.0 6801.2 439.3 50 ≈ 0.008
a first three columns are repeated from above
Table 4. Syngas composition dependence on temperature
Table 4. Syngas composition dependence on temperature
Gas compound in vol. %
Temperature t [°C] in gasification reactor CO2 H2 CO CH4 N2
750 8.1 9.7 29.4 4.4 45.2
800 9.8 10.9 26.0 4.0 46.2
900 11.9 16.0 20.1 2.2 48.4
1000 11.3 12.8 19.9 1.7 52.8
1050 11.5 12.3 18.8 1.2 55.0
1100 12.3 11.8 12.4 1.0 56.3
Table 5. Regression Relations Between Middle Reactor Temperature (t [°C]) and Syngas Compositiona.
Table 5. Regression Relations Between Middle Reactor Temperature (t [°C]) and Syngas Compositiona.
Gas compound in % vol. Model - Formula where t [°C] is the middle temperature in the gasification reactor
Polynomial regression 5 degree – Used in the final version of the developed waste-to-energy software
H2 8.64427756 × 10 2 − 1.11535475 × 10 − 2 t 2 + 2.50417715 × 10 − 5 t 3 − 2.08318518 × 10 − 8 t 4 + 6.0929057 × 10 − 12 t 5
CO2 7.88262261 × 10 1 − 1.42644743 × 10 − 3 t 2 + 3.66824063 × 10 − 6 t 3 − 3.38728167 × 10 − 9 t 4 + 1.07816591 × 10 − 12 t 5
CO − 7.75058073 × 10 2 + 1.12213487 × 10 − 2 t 2 − 2.59664968 × 10 − 5 t 3 + 2.22417149 × 10 − 8 t 4 − 6.70159810 × 10 − 12 t 5
CH4 − 1.35270631 × 10 2 + 1.76696155 × 10 − 3 t 2 − 3.88540841 × 10 − 6 t 3 + 3.15797384 × 10 − 9 t 4 − 9.02717242 × 10 − 13 t 5
N2 − 1.92588105 × 10 2 + 3.07852112 × 10 − 3 t 2 − 6.98410588 × 10 − 6 t 3 + 5.91052625 × 10 − 9 t 4 − 1.75956783 × 10 − 12 t 5
Symbolic regression: Models obtained in PySR – Used in the final version of the developed waste-to-energy software
H2 =LN(ABS(0.000677729241918855×t^2×ABS(LN(ABS(0.0010822109×t)+0.00000001))^(-2.6401255))+0.00000001)
CO2 =LN(ABS(-0.060511474×t^2+44.81684×t)+0.00000001)+2.0503674
CO =0.7548879×t/(0.07978012×t-40.459797)
CH4 =ABS(3.6089828-3679.8438/(t-300.00784))
N2 =ABS(0.000001013×t-0.0017925174)^(-0.5535527)
Symbolic regression: AI Feynman with oscillatory tendencies [50] – Rejected for use after reanalysis
H2 1/(0.112277210469×COS(COS(((EXP(SIN((t+1)))-1)-1))))
CO2 Model 1: 0.003263060755×(t×LN((SQRT(t)+SIN(LN(t)))))
Model 2: TAN(-29.286471691464+SQRT(((t×EXP(COS((LN(t)+1))))-1)))
CO 6.719797422959×EXP(EXP(SIN((((COS(t)-1))^(-1)+1))))
CH4 (0.946772291789×(EXP(COS((EXP(SIN((t+t)))+1)))+1))^2
N2 SQRT(-664.727896959755×((((COS(EXP(COS(t)))-1)-1)-1)-1))
Used in the evaluation in Appendix A of this article
Model 1 CO2 logm 10 ( t e s i n ( t + 0.6718609 ) ) 2 , logm 10 = l n ( t + 10 − 8 )
Model 2 CO2 logm − 0.060511474 t 2 + 2.0503674 , logm = l n ( t + 10 − 8 )
Model 1 H2 8.9065269419 cos ( cos ( e sin t + 1 − 2 ) )
Model 2 H2 logm 2 7.744805 − 9.837645 + logm t − 1.5165994 + 0.0054770974 t ,
logm 2 = l o g 2 ( t + 10 − 8 )
Model 3 H2 6.5368786 + logm 2 ( − 9.864973 + logm 2 t − 2.1570945 ) ,
logm 2 = l o g 2 ( t + 10 − 8 )
Model 4 H2 Repeated model for H2 from above in this Table from polynomial regression 5 degree
a polynomial models maintain the conservation of syngas volume better compared to symbolic models
Table 6. Optimized polynomial formulations between middle reactor temperature (t [°C]) and the amount of produced hydrogen H2.
Table 6. Optimized polynomial formulations between middle reactor temperature (t [°C]) and the amount of produced hydrogen H2.
Polynomial degree Hydrogen H2
2 -1.369 × 10 -4 t2+0.258 t-106,612
3 4.358 × 10 -7 t3-0.001 t2+1.372 t-444.415
4 7.734 × 10 -9 t4-2.828 × 10 -5 t3+0.038 t2-22.876t+5070.377
5 6.251 × 10 -12 t5-2.139 × 10 -8 t4+2.573 × 10 -5 t3-0.011t2-2.718 × 10 -5 t+890.767
6 5.077 × 10 -15 t6-1.661 × 10 -11 t5+1.865 × 10 -8 t4-7.344 × 10 -6 t3-2.149 × 10 -8 t2+4.614 × 10 -11 t+246.526
Table 7. Optimized polynomial formulations between middle reactor temperature (t [°C]) and the amount of produced carbon dioxide CO2
Table 7. Optimized polynomial formulations between middle reactor temperature (t [°C]) and the amount of produced carbon dioxide CO2
Polynomial degree Carbon dioxide CO2
2 -4.67 × 10-5 t2+0.096t-37.252
3 4.215 × 10-7 t3-0.001t2+1.173t-363.929
4 1.824 × 10-9 t4-6.35 × 10-6 t3+0.008t2-4.545t+936.676
5 1.237 × 10-12 t5-3.945 × 10-9 t4+4.359 × 10-6 t3-0.002t2-4.136 × 10-6 t+105.442
6 7.534 × 10-16 t6-2.177 × 10-12 t5+2.071 × 10-9 t4-6.422 × 10-7 t3-1.88 × 10-9 t2+4.034 × 10-12 t+6.226
Table 8. Optimized polynomial formulations between middle reactor temperature (t [°C]) and the amount of produced carbon monoxide CO.
Table 8. Optimized polynomial formulations between middle reactor temperature (t [°C]) and the amount of produced carbon monoxide CO.
Polynomial degree Carbon monoxide CO
2 1.017 × 10-4t2-0.219t+136.345
3 -5.873 × 10-7 t3+0.002t2-1.721t+591.542
4 -3.807 × 10-9 t4+1.355 × 10-5 t3-0.018t2+10.215t-2123.132
5 -2.742 × 10-12 t5+9.024 × 10-9 t4-1.036 × 10-5 t3+0.004t2+1.029 × 10-5 t-248.532
6 -1.85 × 10-15 t6+5.672 × 10-12 t5-5.85 × 10-9 t4+2.048 × 10-6 t3+5.995 × 10-9 t2-1.287 × 10-11 t-0.241
Table 9. Optimized polynomial formulations between middle reactor temperature (t [°C]) and the amount of produced methane CH4.
Table 9. Optimized polynomial formulations between middle reactor temperature (t [°C]) and the amount of produced methane CH4.
Polynomial degree Methane CH4
2 1.885 × 10-5 t2-0.045t+27.658
3 2.838 × 10-8 t3-6.012 × 10-5 t2+0.028t+5.659
4 -1.286 × 10-9 t4+4.803 × 10-6 t3-0.007t2+4.06t-911.393
5 -1.081 × 10-12 t5+3.783 × 10-9 t4-4.659 × 10-6 t3+0.002t2+5.032 × 10-6 t-164.977
6 -9.135 × 10-16 t6+3.062 × 10-12 t5-3.525 × 10-9 t4+1.421 × 10-6 t3+4.16 × 10-9 t2-8.928 × 10-12 t-44.059
Table 10. Optimized polynomial formulations between middle reactor temperature (t [°C]) and the amount of produced nitrogen N2.
Table 10. Optimized polynomial formulations between middle reactor temperature (t [°C]) and the amount of produced nitrogen N2.
Polynomial degree Nitrogen N2
2 3.801 × 10-5t2-0.037t+51.345
3 -2.679 × 10-7 t3+0.001t2-0.722t+258.964
4 -2.412 × 10-9 t4+8.687 × 10-6 t3-0.012t2+6.841t-1461.047
5 -1.941 × 10-12 t5+6.545 × 10-9 t4-7.77 × 10-6 t3+0.003t2+8.155 × 10-6 t-222.896
6 -1.597 × 10-15 t6+5.167 × 10-12 t5-5.755 × 10-9 t4+2.271 × 10-6 t3+6.647 × 10-9 t2-1.427 × 10-11 t-34.106
Table 11. Analysis of maximum absolute error, maximum percentage error, and mean squared error for polynomial models of degrees 2, 3, 4, 5, and 6 applied to hydrogen (H2, Table 6), carbon dioxide (CO2, Table 7), carbon monoxide (CO, Table 8), methane (CH4, Table 9), and nitrogen (N2, Table 10).
Table 11. Analysis of maximum absolute error, maximum percentage error, and mean squared error for polynomial models of degrees 2, 3, 4, 5, and 6 applied to hydrogen (H2, Table 6), carbon dioxide (CO2, Table 7), carbon monoxide (CO, Table 8), methane (CH4, Table 9), and nitrogen (N2, Table 10).
Polynomial degree 2 degree 3 a degree 4 degree 5 degree 6
Max. absolute error
CO2 1.05 0.69 0.48 0.49 0.51
H2 1.9 2.09 1.07 1.13 1.18
CO 1.48 1.43 0.87 0.91 0.96
CH4 0.57 0.54 0.54 0.55 0.56
N2 1.51 1.42 1.53 1.52 1.51
Max. relative (percentage) error
CO2 13.0 9.0 6.0 6.0 6.0
H2 20.0 22.0 11.0 12.0 12.0
CO 9.0 8.0 5.0 5.0 6.0
CH4 62.0 57.9 59.0 60.0 61.0
N2 3.0 3.0 3.0 3.0 3.0
Mean squared error
CO2 0.27 0.07 0.04 0.04 0.04
H2 1.09 0.87 0.3 0.35 0.39
CO 0.75 0.35 0.21 0.22 0.23
CH4 0.06 0.06 0.04 0.04 0.05
N2 0.63 0.54 0.49 0.49 0.49
a recommended for use
Table 12. Input combinations for the plasma torch optimized for maximum hydrogen production H2.
Table 12. Input combinations for the plasma torch optimized for maximum hydrogen production H2.
Inputsa Outputs b
Combination k [[-] P [kW] fp [bar] T [K] t [°C] c Syngas produced [m³/h] vol. H2 %
1. 9.6 15 3 10621.9 925 17.6 15.9
2 5 9.9 3.8 10621.9 925 17.6 15.9
3 8.9 15 3.3 10429.3 921.3 17.6 15.9
4 5 7.5 3 10225.0 917.4 17.6 15.9
⁞ ⁞ ⁞ ⁞ ⁞ ⁞ ⁞ ⁞
a the base constant of nozzle k [no units] from 5 to 20, required power of plasma torch P [kW] from 5 to 15, and filling pressure [bar] from 3 to 8 Used unrealistic peak in symbolic regression is 22.5 % vol. of hydrogen; b T [K] is the middle temperature of the plasma torch, while t [°C] is the temperature in the gasification reactor; c for waste input 20 kg/h (e.g., waste input 5 kg/h gives 4.4 m3/h of syngas)
Table 13. Estimated filling duration of hydrogen tank connected to the gasification system.
Table 13. Estimated filling duration of hydrogen tank connected to the gasification system.
k [[-] P [kW] fp [bar] Waste input [kg/h] Syngas produced [m³/h] vol. H2 % H2 produced [m³/h] Tank
Pressure [bar] Temperature [K] Filling time [h]
9.6 15 3 20 17.6 15.9 2.79 100 200 107
5 9.9 3.8 5 4.4 15.9 0.70 160 220 623
8.9 15 3.3 10 8.8 15.9 1.40 200 250 343
8.9 15 3.3 17 15.0 15.9 2.38 200 298 169
13.4 9.4 6.4 16 14.1 10.5 1.48 200 298 276
9.7 11.3 4.9 20 17.6 12.8 2.25 200 298 182
⁞ ⁞ ⁞ ⁞ ⁞ ⁞ ⁞ ⁞ ⁞ ⁞
Table 14. Operating Inputs and Outputs of the Fuel Cell Unit.
Table 14. Operating Inputs and Outputs of the Fuel Cell Unit.
k [[-] P [kW] fp [bar] Waste input [kg/h] Mass of H2 [kg/h] a Power of fuel cells [kW] Efficiency [%] Output — Obtained electrical energy [kWh]
b LHV=33kWh/kg c HHV=39.38kWh/kg
9.6 15 3 20 0.39 40 50 6.4 7.6
5 9.9 3.8 5 0.10 40 40 1.3 1.5
8.9 15 3.3 10 0.17 40 36 2.0 2.4
8.9 15 3.3 17 0.29 40 36 3.4 4.1
13.4 9.4 6.4 16 0.13 40 60 2.6 3.1
9.7 11.3 4.9 20 0.19 32 60 3.7 4.4
⁞ ⁞ ⁞ ⁞ ⁞ ⁞ ⁞ ⁞ ⁞
a In up to 5 stacks of 8 kW; b LHV is Lower Heating Value; c HHV is Higher Heating Value
Table 15. Operating inputs and outputs of the electrolyzer unit.
Table 15. Operating inputs and outputs of the electrolyzer unit.
a Electricity input [kWh] Hydrogen produced [kg]
Photovoltaics and wind Grid From photovoltaics and wind From grid
14 54 0.27 1.04
20 20 0.38 0.38
17 7 0.33 0.13
⁞ ⁞ ⁞ ⁞
a Energy required to produce 1 kg of H₂ =52 kWh, H₂ produced from 1 kWh of electricity =0.02kg
Table 16. Electrolyzer pressurization detection: algorithm performance results.
Table 16. Electrolyzer pressurization detection: algorithm performance results.
aAmount of hydrogen produced
Interval Actual (dm3/min) Prediction (dm3/min) Absolute error (dm3/min)
1 40.73 40.73 0
2 20.69 20.63 0.06
3 19.75 19.83 0.08
4 29.84 29.84 0
5 28.02 28.01 0.01
6 28.78 28.56 0.22
7 28.40 28.68 0.28
8 30.39 32.92 2.53
9 2.62 0.09 2.53
10 26.28 28.53 2.25
11 36.70 34.06 2.64
12 29.69 30.23 0.54
13 31.39 31.18 0.21
14 30.75 31.08 0.33
15 34.79 34.79 0
16 30.23 30.23 0
a Expressed in dm3, i.e. in liters, under normal conditions of pressure and temperature
Table 17. Amounts of Gases and Associated Energy from Syngas Generated from 60 kg/h of Waste.
Table 17. Amounts of Gases and Associated Energy from Syngas Generated from 60 kg/h of Waste.
a Component of syngas Produced kg/hours Ideal theoretical 100% efficiency 35% efficiency
kWh – HHV kWh – LHV kWh – HHV kWh – LHV
H2 0.53 21.05 17.79 7.37 6.23
CO 16.88 47.63 47.63 16.67 16.67
CH4 1.39 21.34 19.21 7.47 6.72
a HHV Higher Heating Value: H2=142.08 MJ/kg, CO=10.16 MJ/kg, and CH4=55.38 MJ/kg; LHV Lower Heating Value: H2=120.08 MJ/kg, CO=10.16 MJ/kg, and CH4=49.85 MJ/kg – The higher and lower heating values are the same if their hydrogen compound content is zero because no water is produced neither in vapor nor in liquid phase [57].
Table 18. Electricity input and output of the system with the corresponding times required to fully charge the battery.
Table 18. Electricity input and output of the system with the corresponding times required to fully charge the battery.
Electricity from Battery capacity [kWh] а Consumed by
Photovoltaics [kW] Wind turbine [kW] Battery [kWh] Time to fill up the battery [hours]
120 5 500 108 4.6
60 7 500 50 10
60 7 600 50 12
120 3 700 106 6.6
⁞ ⁞ ⁞ ⁞ ⁞
a The electolyzer consumes 17kWh.
Table 19. Operational input–output relations of the pyrolysis as the secondary facility of waste-to-energy system
Table 19. Operational input–output relations of the pyrolysis as the secondary facility of waste-to-energy system
Input Output
Pyrolysis reactor Alternative fuel – Waste Hot gas
Heat (through electricity or gas) Char
Cooling Hot gas Pyrolysis oil (liquid fuel) — Main product
Syngas (different than syngas from gasification) — Byproduct
The temperature of pyrolysis is given in Equation (3):
Table 20. Mass percentage of individual gas compounds produced by pyrolysis a.
Table 20. Mass percentage of individual gas compounds produced by pyrolysis a.
Gas compound mass. %
CO2 76.631-0.0309×t-0.000070876×t2
CO 71.64571-0.18489×t+0.00018×t2
CH4 -35.957+0.1855×t-0.00014×t2
H2 -10.5349+0.0235×t+0.0000336×t2
a t is pyrolysis temperature [°C]
Table 21. Sample results from laboratory-scale pyrolysis.
Table 21. Sample results from laboratory-scale pyrolysis.
Input Output
Electricity [kWh] Waste [kg/h] Pyrolysis temperature t [°C] Pyrolysis oil (Liquid fuel) L [kg] Char [kg] Gas G [kg]
5.4 3 494.1 0.85 1.16 0.99 Example 1
3.3 5 316.2 1.61 1.50 1.89 Example 2
⁞ ⁞ ⁞ ⁞ ⁞ ⁞ ⁞
Table 22. Examples 1 and 2 demonstrating by-product gas composition from Table 21
Table 22. Examples 1 and 2 demonstrating by-product gas composition from Table 21
Example 1 Composition Vol. % Volume [m3] Mol Mass [%] Mass [kg]
CO2 44.5 0.3 14.6 65.1 0.64
CO 24.5 0.2 8.0 22.8 0.23
CH4 21.7 0.2 7.1 11.6 0.11
H2 9.4 0.1 3.0 0.6 0.01
Σ 100 0.7 32.9 100 0.99
Example 2 Composition Vol. % Volume [m3] Mol Mass [%] Mass [kg]
CO2 59.8 0.5 24.5 72.2 1.08
CO 31.2 0.3 12.7 24.0 0.36
CH4 8.7 0.1 3.5 3.8 0.06
H2 0.3 0.0 0.1 0.0 0.00
Σ 100 0.9 41.0 100 1.5
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