Introduction

Residential, industrial, transportation, and manufacturing are the four economic sectors that consume much energy. Heating and cooling our homes, lighting office buildings, driving cars and transporting freight, and producing the goods we rely on in our daily lives are all energy-intensive functions. It is purely evident that a human's life is entirely dependent on energy. The rapid population increase, political instabilities, geographical diffusion, policy difussion has put a strain on the energy supply from fossil fuel resulting in disruption of the energy supply. Therefore, it is with a great need for future sustainable development that alternative energy sources are established [1]. Rapid population growth has not only increased energy demand, but waste generation has also increased and introduced emerging pollutants or contaminant into waste streams, posing sanitary, environmental and economic risks. These pollutants end up in landfills and water sources, contaminating the environment and creating a negative impact to the economy, social services, and health care systems. The significant growth in trash generation necessitates broadening the present waste management system to include sustainable digital waste management technology requirements, innovative treatment alternatives, and technologies [2].

The global digital waste management market, especially in urban areas, is rapidly expanding. In recent years, waste management technology has advanced significantly to collect, measure, monitor, dispose, and manage waste produced by various end-use industries and across the end-to-end value chain. In addition, the expansion of the healthcare, food, manufacturing, and retail sectors is generating a significant amount of waste. Various digital strategies, design and innovation, enterprise resource planning (ERP), waste management technologies, policies and metrics (regulations and standards) such as extended producer responsibilities (EPR), Circular Economy Action Plan (EU-CEAP), ecodesign for sustainable products regulation (ESPR), life cycle assessments (LCA), ISO TC 323, and plastics acts have been introduced to the global market to support the shift from a linear to a circular economy. Garbage cans are installed with active sensors. Containers with sensors capture data such as container location and fill level. This information is sent to a central cloud platform, where it is used to improve procedures such as pick-up routes [3]. The digital waste management system illustration in reference [4].

Digital waste management reduces total transportation and collection costs while also providing convenient strategies and solutions for increasing waste management and disposal rates. The large amount of waste generated by residential buildings, streets, public spaces, and commercial sectors necessitates digital waste management to maximize the waste management system's resources for collection, management, and disposal [3]. The advantages of digital waste management, such as reduced emissions, increased jobs, and revenue generation, are expected to propel the digital waste management market forward during the forecast period. Aside from that, the growing need for energy conservation is a significant factor expected to propel the global digital waste management market forward in the coming years. Furthermore, with the increasing use of waste (biomass) as an energy source in fulfillment of the circular economy cycle, the digital economy is anticipated to enhance business segment growth in the near future [4].

Due to the growing concern about environmental sustainability that results from population growth, economic development, and ecological concerns, strategies for a circular economy must be adopted to meet the Sustainable Development Goals (SDGs). Some SDGs aim to; provide affordable and clean energy, good health and well-being, clean water, and sanitation [5]. The circular economy was proposed as a model for transitioning from a linear to a circular structure (from take-make-dispose to use-make-return), as illustrated in Fig. 1. It is a system designed to reduce energy use, natural resource consumption, and waste production. The circular economy model entails reducing raw material inputs and waste outputs, preserving resource value as long as possible within the system, and reintegrating goods into the system as they reach the end of their valuable lives [6].

Fig. 1
figure 1

Linear economy vs. circular economy [7]

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Moving toward a circular economy is essential from an environmental, social and economic perspective as it lays the foundation for a sustainable and competitive economy. Creating a circular economy with better waste and materials management contributes to recovering materials from waste streams for recycling or reusing waste-to-energy technologies such as the anaerobic digestion process [8]. Anaerobic digestion involves the breaking down of organic materials by microbes in the absence of oxygen to produce biogas energy [9, 10]. Biogas-derived energy is used in fuel, heat, and electricity generation. Wide biogas usages have successfully demonstrated effective methods to use renewable energy supplies while reducing greenhouse gas emissions [11]. It is a mechanism that is environmentally friendly, tackles pollution, and helps to minimize, reuse, and recycle waste.

Waste to resources (circular economy of waste to energy) is a biological process sustainable value chain of carbon cycle. The anaerobic digestion procedure is done in bioreactors or biodigesters with monitored conditions, including temperature, pH level, macro- and micronutrients, organic loading rates (OLR), microbes, and humidity content. These conditions provide a suitable environment for the growth of microbes and aid the degradation process to yield biogas, bioliquid, and fibre digestate [9]. The inhibitory factors that contribute to the growth and production of the biomethane consist of the following: type of microbes, temperature variation, lower or higher pH, choking of the biodigester, macro- or micronutrients, formation of compounds (ammonia and carboxylic acid), etc. Firstly, the feedstock for anaerobic digestion is prepared by passing the waste through sorting, segregation, and shredding i.e. waste quantification and pre-treatment. To begin the anaerobic digestion process, relevant environmental factors such as temperatures between 35–70 °C and pH up to 6.7 are then sustained in the reactor. The materials (substrates) are then blended well for a specific retention time and heated for more extended periods at low temperatures, and the gas components are captured, isolated, and preserved. The digestate anaerobic digestion residue serve as a bio-fertilizer to enhance soil nutrients [12, 13]. The anaerobic digestion process occurs in 5 consecutive phases. Figure 2 displays the different phases of biomass degradation to biogas.

Fig. 2
figure 2

Anaerobic digestion degradation phases [1]

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Disintegration

Extracellular processes, often known as disintegration, are the breakdown of composites. Particulate natural carbon and dead biomass converted to polymeric components, followed by enzymatic hydrolysis to dissolvable monomers, are examples. Depolymerisation enzymes outside the cell depolymerise a pool of accessible organic material into smaller molecules. Disintegration is a non-natural interaction that occurs when complex natural materials are broken down and dissolved in solvent substrates. The end products, which act as a substrate for the hydrolysis process, are complex composite particulates and polymeric carbohydrates, lipids, and proteins. Other disintegration products include particulate inertia and soluble inertia content [14].

The International Water Association (IWA) task committee chose disintegration as the first approach because it allows for various applications and the lysis of biological sludge and complicated organic material. The disintegration process was also described in the composite organic material set description. This is especially crucial in waste-activated and primary sludge digestion, where whole-cell lysis and composite partition are required for disintegration[14].

Hydrolysis

"hydrolysis" refers to breaking down a given particulate or macromolecular substrate into soluble monomers. Hydrolysis is a chemical process for smaller macromolecules and a surface mechanism for particles (biopolymers). Polysaccharides are converted to basic sugars, proteins to amino acids, and lipids to long-chain fatty acids during hydrolysis processes (LCFA). This function is carried out by heterotrophic microorganisms attached to particles. They generate the enzyme around the molecule, and this advantage from solvent items is delivered by the enzymatic response [15]. As a result, the microorganisms developing on the particle surface should be considered the effective catalyst rather than the enzyme. Acidogenic bacteria can easily enter the products of hydrolysis [16].

Acidogenesis

Acidogenesis is a microbial process in which anaerobic acid is generated without the use of an electron acceptor. During acidogenesis, heterotrophic bacterial cells pick up small soluble molecules such as amino acids and simple sugars (hydrolysis products) across the cell membrane and ferment or aerobically oxidize them. The degradation of LCFA occurs when it is oxidized with an internal electron acceptor (H+). During fermentation, substrate-level phosphorylation releases energy (ATP) directly from an energy-rich intermediate. Electron equilibrium is achieved by either substrate internal electron translocation (where another replaces one part of the fermented molecule) or external electron translocation (where another replaces one part of the fermented molecule) (where another replaces one part of the fermented molecule). Electrons may also be transferred to cytoplasmic electron acceptors (most commonly H+ or pyruvate) [16]. It is common for neutral compounds like sugars and proteins to be converted to acidic compounds like carboxylic acids (also known as volatile fatty acids, VFAs). As a result, most fermentative microbes have been genetically modified to be acidifying or acidogenic, a process known as acidogenesis [15].

Acetogenesis

Acetogenesis is the bacterial synthesis of chemicals other than acetate, resulting from the fermentation process into acetate, carbon dioxide, and hydrogen gas. Propionate and butyrate are the essential acetogenic substrates, but lactate, ethanol, methanol, and H2 and CO2 are (homo) acetogenically transformed to acetate. The acetogenic bacterias are hydrogen contributors (H+ serves as an internal electron acceptor during the regeneration of intracellular electron carriers, such as NADH), and hydrogen, which results from a stoichiometric transfer reaction propionate. It inhibits their metabolism thermodynamically [15, 16].

Methanogenesis

The final stage of anaerobic organic matter oxidation to carbon dioxide and methane is completed by methanogenic bacteria. There are two types of methanogens: those that convert acetate to acetic acid (acetoclastic methanogens) and those that use hydrogen (hydrotrophic methanogens). Finally, the methanogens bacteria convert carbon dioxide, hydrogen, and acetic acid to methane and carbon dioxide in the fourth and final stage. Carbon dioxide and hydrogen are responsible for 30% of the methane generated in this step. Acetate contains the most methane (70%) of all methane produced. Only when the influent COD is transformed does COD exit the reactor system's liquid process [16].

The biogas generated contains 20–40% carbon dioxide (CO2) and 60–80% methane, along with traces of ammonia and sulphide (CH4). Biogas can generate heat and electricity using microturbines, combustion engines, and combined heat and power plants. Digestate can also be used as a fertilizer to help soil grow [12, 17]. Biogas and biofertilizer (digestate) are the two types of products produced by the anaerobic digestion process.Scientists have been redesigning and refining anaerobic digestion models for organic substances for over 40 years. For accurate prediction of biomethane production, the development of appropriate models is essential for optimization of the AD production and efficiency. This will also help minimize experimental costs and save on industrial time. In this study, simulation-modeling of biomethane production was completed by using different kinds of computational tools, which were [18]:

Using the non-linear curve (regression) fitting with Gompertz, Logistic, and Richards models and supporting graphs, conventional mathematical modeling with Microsoft Excel 365 was used to calculate cumulative biogas production prediction 18. Jupyter Notebook (Anaconda 3) – simulation-modelling with machine learning (Python) – was used to plot graphs of prediction vs. trained data of biogas production using Gompertz, Logistic, and Richards models [21].

Mathematical modelling is an effective tool for predicting the behavior of the mechanism when tests are either too unreliable or too costly. Modeling may also assist in the understanding of a system's fundamental mechanisms. Biogas production is predicted using modified Gompertz, Richards, Logistic, Stannard, Schnute, and other growth models [18]. However, this study aimed to compare the Gompertz, Logistic, and Richards models for the growth curve of biomethane production to ascertain which model better matched the actual curve. Given that biomethane production is a bacterial growth function, i.e., a composite function, the mathematical parameters were enhanced into biological parameters in the original function [20]. The Modified Gompertz, Logistic, and Richards Equations can respectively be given by Eq. 1 to Eq. 3:

$$\mathrm{y}=\mathrm{Aexp}\{-\mathrm{exp}[\frac{{\upmu }_{\mathrm{m}}\mathrm{e}}{\mathrm{A}}\left(\uplambda -\mathrm{t}\right)+1]$$
(1)
$$\mathrm{y}=\frac{\mathrm{A}}{\{1+\mathrm{exp}[\frac{4{\upmu }_{\mathrm{m}}}{\mathrm{A}}\left(\uplambda -\mathrm{t}\right)+2]\}}$$
(2)
$$\mathrm{y}=\frac{\mathrm{A}}{{\{1+\mathrm{d exp}\left(1+\mathrm{d}\right)\mathrm{exp}[\frac{{\upmu }_{\mathrm{m}}}{{\mathrm{A}\left(1+\mathrm{d}\right)}^{\left(1+ \frac{1}{\mathrm{d}}\right)}(\uplambda -\mathrm{t})\}}]\}}^{(\frac{1}{\mathrm{d}})}}$$
(3)

where: y = Cumulative biogas production (ml), A = Ultimate biogas production potential (ml), µ = Maximum biogas production rate (d−1), λ = Lag phase period or minimum time to produce biogas (d), t = Cumulative time for biogas production (days), e = Mathematical constant (2.718282), d = Constant (1).

Artificial intelligence, in general terms, is the ability of a machine to replicate intelligent human behavior. One subfield of artificial intelligence is machine learning. To complete complex jobs in a manner akin to how humans solve problems, artificial intelligence systems are deployed. Machine learning is the process of extracting information from data [21]. It is a topic of study at the convergence of statistics and artificial intelligence (AI) that focuses on designing computer algorithms that learn from data and improve their accuracy over time without being taught. In machine learning, algorithms are "trained" to recognize trends and features in massive amounts of data to make judgments and predictions based on the incoming data. As more data is processed, the algorithm's conclusions and predictions will become more exact. Some of the steps involved in the process are acquiring data, pre-processing it, building, training, and testing the model [22].

Examples of machine learning may now be found all over the internet. Digital assistants scan the web and play music in response to our spoken instructions. Websites make recommendations for products, movies, and songs based on what we've already bought, watched, or listened to. While we do something more constructive with our time, robots vacuum our floors. Unwanted emails are kept out of our inboxes by spam filters. Medical image recognition algorithms let doctors spot tumors that would otherwise go undetected. In addition, the first self-driving cars have begun to appear on public roads [22]. When we look at a complex website like Facebook, Amazon, or Netflix, we expect to find multiple machine learning models that can predict bioprocess technologies [21].

Many data science and analytical applications now use Python as their primary language. It includes libraries for data loading, visualization, statistics, natural language processing, and image processing, among other things. Data scientists may use the enormous toolbox to access a wide range of general and particular purpose features. One of the most appealing features of Python is the ability to communicate directly with the code through the terminal or other resources such as Jupyter Notebook. Data analytics and machine learning are essentially iterative systems through which the data guides the analysis. Tools that allow fast and easy interaction are critical for these processes. As a general-purpose programming language, Python also enables the development of complex graphical user interfaces (GUIs) and web services for system integration [21].

Modeling machine learning is achieved by using the Python coding language in a Jupyter notebook (Anaconda). Jupyter Notebook is an interactive tool for running code in the browser. It supports many programming languages and makes it easy to incorporate code, text, and images. The Python coding program consists of a group of scientific libraries used in modeling with machine learning. scikit-Learn is a well-known machine learning library developed among other Python scientific libraries such as NumPy, SciPy, matplotlib, and pandas [25].

The study intends to assess the sustainability of biomass as a source of energy through biomass characterization and biomethane potential tests. The data-driven circularity of waste management is applied to predict bioenergy production.

The goal of this study was to look into sustainable waste-to-energy on integrated waste management and digitalization of biomethane production using the anaerobic digestion (AD) process, i.e., waste-to-resources (data-driven circular economy of waste-to-energy) as a biological process across the carbon cycle value chain (transition from take-make-dispose to use-make-return) through waste quantification, characterization, and the biomethane potential. To predict biomethane production using conventional modeling such as Modified Gompertz, Logistic, and Richards models for the biomethane production growth curve and determine which model best matched the actual curve, as well as using predictive simulation by artificial intelligence (AI) and machine learning with Python.

Methodology

Waste Quantification and Characterisation

Figure 3 demonstrates a flow diagram of waste quantification, waste characterization, and biogas/biomethane production analysis.

Fig. 3
figure 3

Flow diagram of the biomass quantification, biomass characterization and biogas production

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Waste Quantification

The biomass (waste substrate) used in this study was obtained in South Africa, Gauteng Province. Food waste was gathered from local kitchen garbage in Johannesburg, cow dung from a farm at Springdale in Johannesburg, sewage sludge from the wastewater treatment plant in Pretoria, and poultry manure from a farm in Soweto, South Africa. The substrate/feedstock collection was done following ASTM D5231-92 requirements [26]. These biomasses were kept in the fridge at 4 °C until they were needed to feed the digester. Personal protection equipment (PPE) was necessary during the investigation to reduce occupational hazard exposure. PPE such as safety gloves, nasal masks, overalls, and protective shoes was required. Biomass was measured and weighed, and the data was recorded before categorization.

Waste Characterization

The composition of the biomass was determined by substrate characterization. Chemical and physical structure for proximate analysis: moisture content (MC), total solids (TS), volatile solids (VS), and ultimate analysis; elemental analysis for carbon, nitrogen, sulphur, and hydrogen were determined according to the standard methods (APHA 2012) [27]. Table 1 displays the substrate characterization methods and equipment that met standards.

Table 1 Standards methods and equipment for biomass characterization
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Automatic Methane Potential Test System II (AMPTS II) Set-Up for Biomethane Potential (BMP) Test

A bioprocess control (BPC) AMPTS II automated set up was used for the biomethane potential test of biogas and biomethane generated by anaerobic digestion of any biologically degradable substrate (both solid and liquid form) at a laboratory scale. A substrate and an inoculum were required to start this experiment. The inoculum was prepared at 14 days to supply the nutrients (substrates) to the microbes and kick-start the experiment by eliminating the lag phase. The sludge from the full-scale biogas plant was usually an inoculum. The inoculum used was suited to the existing substrate (sample), and the substrate was stored at 4 °C in the refrigerator to keep it as fresh as possible. Waste characterization and biogas research were carried out at the University of Johannesburg, Department of Chemical Engineering, Department of Applied Chemistry, and Process, Energy, and Environmental Technology Station (PEETS).

The procedure was as follows:

With their lids, each of the 15 digesters (500 ml) was labeled. The rate of organic loading was based on the volatile solid composition. The feeding rate was measured three times and the average was taken. Inoculum and substrate were fed to all of the digesters. Inoculum was used to reduce the lag phase with the due diligence supply of the microbes. The digester had a total volume of 500 ml, with an organic input rate of up to 400 ml and a headspace of 100 ml. The pH was adjusted to 7 using a solution of 8 g NaOH, 100 mL water, and sulphuric acid. Silicone spray was used to lubricate the rubber stoppers on the bottle's contact side, which were then firmly closed. The air in the digester was flushed out with nitrogen gas, which made the process anaerobic. The thermostatic water bath was filled with deionized water to maintain a mesophilic temperature of 37 °C in the digester.

By removing CO2 with NaOH, carbon dioxide fixation was set up to remove/upgrade/clean biogas to biomethane. The digesters were stirred on a regular basis under an automated stirrer to achieve a homogenous substrate mixture and consistent temperature distribution (30 s on and off). An automated approach was used to connect the various motors and the gas volume metering device. The sensors' downward displacement mechanism was used to measure the biomethane produced using an ethernet cable connected to the local network. The gas volume monitoring system and the outlet were both connected to the power supply. The acquired biomethane data was entered into the AMPTS II program. The program was utilized to ensure that each cell functions properly. Daily accumulated biochemical methane values were obtained using AMPTS II software. The biochemical methane potential (BMP) test set-up composed of 15 bio-digesters in a water bath, 15 carbon removers, 15 downward displacement gas collectors, and internet of things-data logger, analytics, and reporting system using AMPTS II software.

Modelling Method using Computational Tools

Conventional Mathematical Modelling

The daily accumulated biomethane production results recorded on the AMPTS II software were used to calculate and plot actual growth curve graphs against the growth curve graphs obtained from the Modified Gompertz (Eq. 1), Logistic (Eq. 2), and Richards (Eq. 3). With distinct to the four different substrates: food waste, cow manure, sewage sludge, and chicken manure. The plotted curves were used to determine which model better matched the actual curve. A Microsoft Excel sheet was used to carry out these calculations and plots.

Modelling with Machine Learning (Python)

Modeling with machine learning was achieved using the Python coding program in the Jupyter Notebook (Anaconda) software. Jupyter Notebook user interfaces when it first opened. A new Python 3 folder was created and renamed "Biogas Prediction with Python." To start programming, the libraries were imported into the Jupyter notebook. These libraries were used to import data using Sklearn, load the dataset with Pandas, train test split function (splits the arrays of data into training and testing subsets), and use matplotlib (used to plot graphs and scatterplots in Python). By using pandas, a library in Python and the dataset were imported. The dataset was in an excel file. The coding process was then used to plot the prediction graph vs trained data of biomethane production using modified Gompertz, logistic, and Richards models.

Results and Discussions

Waste Characterization

The substrates were characterized by proximate analysis: moisture content (MC), total solids (TS), volatile solids (VS), and ultimate analysis; elemental analysis for carbon, nitrogen, sulphur, and hydrogen using standard methods.

Proximate Analysis

Figure 4 illustrate the characterization of food waste, cow manure, sewage sludge, and chicken manure substrates used during the proximate analysis Fig. 5.

Fig. 4
figure 4

Proximate analysis results in weight percent of the substrates used

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Fig. 5
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Ultimate analysis results in weight percent of the substrates used

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Analyzing the MC, TS, and VS% helped to characterize the four distinct substrates. Fig. 6 represents the results of the proximate analysis of all the collected substrate samples. Before and after substrate characterisation, the pH was observed to be between 6 and 8 for all four substrates, suitable for the AD process. A high pH level creates a favourable environment for the methanogenic bacteria, thus increasing biomethane production. According to the observed results, food waste, sewage sludge, and chicken manure had a higher MC% of 87 wt%, while cow manure had an MC% of 60.32 wt%. The results meant that the substrates had sufficient moisture content for AD, with the cow manure having the lowest MC, showing that it was slightly dry when the sample was taken. Moisture content assisted with the disintegration (breakdown of substrates), hydrolysis, acidogenesis and medium for acetogenesis and methanogenesis in the AD processes. Sewage sludge substrate was observed to have had the lowest TS% of 1.13 wt% followed by food waste and chicken manure substrates, with the TS% of 13.07 wt% and 14.03 wt%, respectively. Cow manure substrate had a TS% of 39.68 wt%, which was the highest compared to the other substrates, which meant cow manure contained the highest organic solid content. VS% content in biomass was important to loading rate, pH regulation, and determining the amount of nutrients. VS% was 12.16 wt%, 24.41 wt%, 2.86 wt%, and 13.93 wt% regarding food waste, cow manure, sewage sludge, and chicken manure substrates.

Fig. 6
figure 6

Biomethane potential test for biomasses: (a) BMP mono-digestion and (b) BMP co-digestion

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According to the proximate analysis results, the characteristics of the biomasses were in the optimum range. High MC%, TS%, and VS% in biomasses indicate that they are easily biodegradable and suitable for anaerobic digestion to produce biomethane. According to Zhang et al. (2012) [28], this also means that the substrates had a high organic solid content that was to be converted to biomethane. A comprehensive substrate characterization was important in the design of the biodigesters and especially in the prediction (modeling) of BMP from different biodegradable biomasses related to waste-to-energy (WtE) applications.

Ultimate Analysis

Figure 5 shows the characterization of food waste, cow manure, sewage sludge, and chicken manure substrates used during the ultimate analysis.

The results of the ultimate analysis were illustrated in Fig. 7, where the carbon (C), hydrogen (H), nitrogen (N), and sulphur (S) content of substrates was expressed as a percentage by weight. Since the anaerobic digestion system took place without oxygen, the oxygen content by weight was not included in the nutrients analysed. Sewage sludge dominated the C content of the substrate, accounting for 47.64 wt%. The substrates were found to have a partial distribution of nitrogen and sulphur. Sewage sludge also outperformed the other substrates in terms of hydrogen content, with 6.66 wt%. Carbon was discovered to be the dominant element in the final study of the substrate, followed by hydrogen, nitrogen, and finally sulphur. According to Chan et al. (2016) [30], organic matter is responsible for the majority of the CHNS composition. The final study findings can be used to determine the biomass's molecular formula. This aids in calculating and predicting process input and output (gases, carbonates, sulphates, and nitrates), and the modeling and simulation of waste-to-energy technologies.

Fig. 7
figure 7

Modified prediction modelling of food waste BMP using (a) Gompertz, (b) Logistic, (c) Richards

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In the anaerobic digestion (AD) process, the C/N ratio was critical to bacterial stability and nutrient balance. The C/N ratios of food waste, cow manure, sewage sludge, and chicken manure are displayed in Fig. 7. It was observed that food waste, cow manure, sewage sludge, and chicken manure substrates had a C/N ratio of 30.77 wt%, 20.69 wt%, 15.57 wt%, and 13.29 wt%, respectively. The C/N ratio for all substrates was within the ideal range of 15–30; this indicated a balanced nutrient (C/N) that microorganisms required during AD. Since high carbon content provides the nutrients needed for bacterial development, a C/N ratio of 15–30 promotes high digestion stability and thus increased biomethane production [2].

Biomethane Potential (BMP) Test

Figures 6 illustrate the biomethane potential (BMP) test results for biomass mono-digestion and co-digestion, respectively.

It was observed that BMP mono-digestion test results for cow manure substrate produced the highest levels of biomethane compared to food waste, sewage sludge, and chicken manure. According to the proximate analysis, cow manure had the highest TS% and VS% of 39.68 wt% and 24.41 wt%, which meant that it had the most organic solid content that was easily biodegradable and converted to biomethane. The pH level for the cow manure substrate was at a high level of 7.2, which created a favourable environment for the methanogenic microbes and a maximum biomethane production. In terms of ultimate analysis, the C/N ratio for cow manure was 20.69 wt%, which promoted high digestion stability and thus increased biomethane production. Since the C/N ratio was critical in the AD, optimizing it in the co-digestion of several substrates was crucial to obtain consistent, high-level control of process variables, improved AD efficiency over time, and optimal biomethane generation. Based on these findings, it was suggested that waste-to-energy (WtE) conversion technology pathways (thermochemical and biochemical) could be performed on biomass with a high C/N ratio outside of the ideal range of 30:1.

Modified Modelling of Biomethane Production

Figure 7 illustrates simulation modelling of the cumulative biomethane yield comparison between the AD experimental results and the fitted results obtained from food waste modified models.

Figure 7 illustrates the cumulative biomethane yield comparison between the AD experimental results and the fitted results obtained from the modified Gompertz, Logistic, and Richards models, using food waste as the substrate. All three models provided a satisfactory sigmoidal curve fit to the experimental data, and the coefficient of determination (R2) values were all greater than 0.9. It was observed that the Logistic model was the best fit compared to the other models with an R2 value of 0.9439, followed by the Gompertz model, with the R2 value of 0.9473, and lastly, the Richards model with the R2 value of 0.9704.

The lag phase (λ) period or time (d) was the amount of time it took for micro-organisms to adapt to their environment and substrate, allowing them to grow and produce biomethane. The lag phase period observed from all three models was 5, 3, and 2 days, respectively. The lag phase period was shortened due to the inoculum added to the food waste sample, supplemented with microbes. Thus, it resulted in quicker biomethane production. Additionally, R2 and lag phase time (λ) were significant indicators of substrate biodegradability and its consumption rate [31]. After the lag phase, the accumulative biomethane production began to significantly rise for all model curves. This indicated that the micro-organisms had suitably adapted to their environment, food waste substrate and were at the peak of their lives. The µ-maximum biomethane production rate (d−1) was a stationary phase in which the rate stabilised, and biomethane production reached equilibrium [32]. This behaviour was observed as 120, 130, 1500 Nml/day, respectively, for the Gompertz, Logistics, and Richards models. The biomethane accumulative curve reached the stationary phase of equilibrium, which formed a sigmoidal shape. Which indicated that the microorganisms had reached the end of their life span or there was no more substrate to feed on; hence they died.

Figure 8 demonstrates a cumulative biomethane yield comparison between the AD experimental results and the fitted results obtained from cow manure modified models.

Fig. 8
figure 8

Modified prediction modelling of cow manure BMP using (a) Gompertz, (b) Logistic, (c) Richards

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Figure 8 demonstrates the cumulative biomethane yield comparison between the AD experimental results and the fitted results obtained from the Modified Gompertz, Logistic, and Richards models, using cow manure as the substrate. Both the Gompertz and Logistic models provided a visually pleasing sigmoidal curve fit to the experimental data, whereas the Richards model presented a fit that was not so satisfactory. However, according to the observations, they had R2 values of 0.9247, 0.9269, and 0.9764, respectively, for the Gompertz, Logistics, and Richards models. The observations further showed that the Richards model had a lag phase period of 7 days, whereas the Gompertz and Logistic models had a lag phase of 6 days. The lag phase indicates that the microorganisms were still adapting to the substrate and environmental conditions. The addition of inoculum to the cow manure substrate provided it with microbes, which shortened the lag phase and increased the biomethane production rate.

After the lag phase, the accumulative biomethane rose on all model curves, indicating that the microorganisms were suitably adapted to their environment and were well fed. The maximum biomethane production rate was 300 Nml/day for both the Gompertz and Logistic models, and it was 2500 Nml/day for the Richards model. The biomethane accumulative curves reached the stationary phase of equilibrium, forming a sigmoidal shape. Which indicated that the microorganisms had no more substrate to feed on or that the environmental conditions were no longer favourable; hence, they died.

Figure 9 illustrates a cumulative biomethane yield comparison between the AD experimental results and the fitted results obtained from sewage sludge-modified models.

Fig. 9
figure 9

Modified prediction modelling of sewage sludge BMP using (a) Gompertz, (b) Logistic, (c) Richards

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Figure 9 illustrates the cumulative biomethane yield comparison between the AD experimental results and the fitted results obtained from the modified Gompertz, Logistic, and Richards models, using sewage sludge as the substrate. All three models had a good fit for the experimental data. The R2 values were observed to be 0.934, 0.9175, and 0.9065, respectively. The observations continued to illustrate that the Gompertz model had a lag phase period of 8 days. In contrast, the Logistic and Richards models had a lag phase period of 7 and 8 days, respectively. Therefore, the lag phase for all model curves was between 7 and 8 days, and during this period, microorganisms were still adapting to the substrate and environmental conditions. The addition of inoculum to the sewage sludge substrate supplemented it with microbes, resulting in quicker biomethane production.

After the lag phase, the accumulative biomethane began to significantly rise on all model curves, forming an "S"-shaped curve (sigmoidal), indicating that the microorganisms had suitably adapted to their environment and were being well fed. According to Table 4, the maximum biomethane production rate was 120 Nml/day for the Gompertz model, 150 Nml/day for the Logistic model, and 2500 Nml/day for the Richards model. Once the maximum biomethane production was reached, the curve reached a stationary phase of equilibrium. This indicated that the microorganisms had no more substrate to feed on for survival and could no longer produce biomethane; hence they died.

Figure 10 demonstrates a cumulative biomethane yield comparison between the AD experimental results and the fitted results obtained from the modified models using chicken manure.

Fig. 10
figure 10

Modified prediction modelling of chicken manure BMP using (a) Gompertz, (b) Logistic, (c) Richards

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Figure 10 shows the cumulative biomethane yield comparison between the AD experimental results and the fitted results obtained from the modified Gompertz, Logistic, and Richards models, using chicken manure as the substrate. The Logistic model was observed to be the best fit to the experimental data compared to other models. The R2 value for the Logistic model was 0.9639, and it was 0.9694 and 0.9750 for the Gompertz and Richards models, respectively. The observations further showed that the Gompertz model had a lag phase of 6 days, the Logistic model was 8 days, and the Richards model was 7 days. The initial phase, known as the "Lag Phase," was marked by cellular activity but not growth. Cells were physiologically active but not yet growing exponentially during the lag phase. The time period shown that while the bacterial population adapted to the environmental factors of the growth medium into which it was introduced, the population remained constant. Therefore, the lag phase for all model curves was between 6 – 8 days; during this period, microorganisms were still adapting to the substrate and environmental conditions. The lag phase could be reduced by provided inoculation during the initial stage.

After the lag phase, the accumulative biomethane was significantly raised on all model curves, indicating that the microorganisms have suitably adapted to their environment and are well fed. The maximum biomethane production rate was 130, 150 and 2000 Nml/day for all three models. Once the maximum biomethane production was reached, the curve reached a stationary phase, which indicated that the microorganisms had no more substrate to feed on for survival. Therefore, they could no longer produce biomethane; hence, they die.

Summary of the Biomethane Prediction Using Conventional Modelling

Table 2 is the biomethane prediction summary for Gompertz, Logistic, and Richards model. It shows a variety of substrates and some of the parameters used to plot the model curves. Where: A = Biomethane accumulation production (Nml), µ = Maximum biomethane production rate (d−1), λ = Lag phase period or minimum time to produce biomethane (d) and R2 = coefficient of determination.

Table 2 Summary of biomethane prediction
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Data in Table 2 was used to plot the biomethane experimental data curves and the biomethane model with Gompertz, Logistic, and Richards curves. It was observed that the coefficient of determination for all four substrates (food waste, cow manure, sewage sludge, and chicken manure) in all three models was greater than 0.9. This observation indicated that the model curve properly fitted the experimental curve and formed an "S"-shaped sigmoidal best fit curve. It was also observed that for all four substrates, the lag phase period was below 9 days. This indicated that the inoculum added to the substrates supplied sufficient microbes, which easily adapted to the substrates and resulted in faster biomethane production.

Modified Gompertz, Logistic, and Richards Simulation-Modelling using Machine Learning with Python Programming

Figure 11 displays prediction vs trained data of biomethane production from biomasses with Gompertz, Logistic, and Richards models using machine learning (Python).

Fig. 11
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Biomethane production prediction in Nml with Gompertz, Logistic and Richards models by using machine learning

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Figure 11 represents biomethane prediction with Gompertz, Logistic, and Richards models using machine learning (Python). Python codes were used to plot sigmoidal graphs of biomethane production against time, with all three models using biomethane production results obtained from four different substrates. The same data was then used to plot trained data, which is the dotted sigmoid curve displayed for four different substrates. Prediction vs trained data on biomethane prediction was distinguished in four different curves: a) food waste, b) cow manure, c) sewage sludge, and d) chicken manure. By the observations in cow manure (b) gave the best fit curve compared to other substrates. Whereas sewage sludge (c) substrate gave the second-best fit curve, followed by chicken manure (d) and food waste (a) being the least good fit curve. However, the R2 value was 0.99, representing high accuracy for the train data. The lag phase (days) for the trained data curve was constantly shorter than the prediction curve for all four different substrates due to constant supply of microbes.

A circular economy concept was based on the maximization of resource value indefinitely, which necessitates the absence of almost all non-recoverable waste. In terms of material products and energy provision, biomass is critical in a circular economy. The practical significance of biomass use must be grasped throughout the value chain from product design, innovation, sourcing, supply chain, logistics, production, operation, resuse-disposal to sustainable data-driven/digital waste management and develop of entire circular bioeconomy system.

Through the use of technology and digital technologies, the Industrial Revolution (IR) 4.0 offers the chance to more effectively eliminate, recover, and repurpose waste. The use of IR 4.0 technology offers encouraging prospects for enhancing the effectiveness and control of solid waste. The risk of exposing laborers to hazardous trash can be decreased by automating the segregation of waste using machine learning (ML), artificial intelligence (AI), and image recognition [33, 34].

Conclusions

This study evaluated biogas production from various substrates, such as food waste, cow manure, sewage sludge, and chicken manure. Cow manure produced the highest biomethane in the BMP mono-digestion curves as compared to other substrates. According to the proximate analysis, cow manure had the highest TS% and VS% of 39.68 wt% and 24.41 wt%, respectively, indicating that it contained the most organic solid content that was easily biodegradable and converted to biomethane. The pH of the cow manure substrate was 7.2. This pH range provided a favourable environment for methanogenic microorganisms to thrive and produce maximal biomethane. According to an ultimate analysis, the C/N ratio for cow manure was 20.69 wt%, indicating that it had good digestive stability and thus produced the most biomethane at 2500 Nml. Modified Logistic model was shown to be the best-fit curve, with a coefficient of determination (R2) > 0.9 validating the conventional mathematical modeling and simulation performance. The experimental results obtained from the cow manure substrate showed the best fitting curve to the training curve compared to other substrates, with the greatest average R2 of 0.997 for training, validation, and test data during simulation with machine learning (Python). At epoch 1, cow manure performed the best in terms of validation, with an MSE (mean squared error) of 25.3557. It should be investigated whether a real-world, comprehensive end-to-end integration can be used to optimize each step of the solid waste management chain.