European Green Deal: Justification of the Relationships between the Functional Indicators of Bioenergy Production Systems Using Organic Residential Waste Based on the Analysis of the State of Theory and Practice

Abstract

Based on the analysis conducted on the state of theory and practice, the expediency of assessing the relationships between the functional indicators of bioenergy production systems using the organic waste of residential areas is substantiated in the projects of the European Green Deal. It is based on the use of existing results published in scientific works, as well as on the use of methods of system analysis and mathematical modeling. The proposed approach avoids limitations associated with the one-sidedness of sources or subjectivity of data and also ensures complete consideration of various factors affecting the functional indicators of the bioenergy production system from the organic waste of residential areas. Four types of organic waste generated within the territory of residential areas are considered. In our work, we used passive experimental methods to collect data on the functional characteristics of bioenergy production systems, mathematical statistics methods to process and interpret trends in the functional characteristics of bioenergy production systems using municipal organic waste, and mathematical modeling methods to develop mathematical models that reflect the patterns of change in the functional characteristics of bioenergy production systems. The results indicate the presence of dependencies with close correlations. The resulting dependencies can be used to optimize processes and increase the efficiency of bioenergy production. It was found that: (1) yard waste has the highest volume of the total volume of solid organic substances but has a low yield of biogas and low share of methane production; (2) food waste has the highest yield of biogas and, accordingly, the highest share of methane production; (3) mixed organic waste has the lowest volume of the total volume of solid organic substances and the lowest content of volatile organic substances. The amount of electricity and thermal energy production varies by type of organic waste, with mixed organic waste having a higher average amount of electricity production compared to other types of waste. It was established that the production volume of the solid fraction (biofertilizer) is also different for different types of organic waste. Less solid fraction is produced from food waste than from yard waste. The obtained research results are of practical importance for the development of sustainable bioenergy production from organic waste in residential areas during the implementation of the European Green Deal projects. They provide further research on the development of effective models for determining the rational configuration of bioenergy production systems using organic waste for given characteristics of residential areas.

1. Introduction

Organic waste is one of the most widespread sources of environmental pollution and resource expenditure of individual communities for its primary treatment and disposal. Every year, about 2.01 billion tons of organic waste is generated in the world, of which only 12% is collected and recycled. The remaining 88% is subject to disposal in landfills where it emits methane, a greenhouse gas with a high global warming potential [1,2,3]. At the same time, the European Commission has set an overall goal of making the European continent climate neutral by 2050 [2]. This indicates the feasibility of implementing European Green Deal projects (EGDPs) in the area of bioenergy production from residential waste.

The relevance of bioenergy production from organic waste generated in residential areas is growing as the population grows and the amount of waste generated increases. In addition, in many countries of the world, in particular in Ukraine, governments are taking measures to stimulate the production of renewable energy, including bioenergy [4,5,6]. The utilization of organic waste through the production of bioenergy is one of the effective scenarios for solving this problem, both for residents of residential areas and for communities and regions. This makes it possible to reduce the amount of organic waste disposed of through the implementation of EGDPs, which helps reduce methane and other greenhouse gas emissions. In addition, bioenergy can be used to produce heat and electricity, leading to a reduced dependence on traditional energy sources such as oil and gas.

To substantiate effective scenarios for the creation of bioenergy production systems using organic waste in residential areas, it is necessary to perform simulations based on the disclosure of relationships between various functional indicators of individual processes [7,8,9]. Such indicators characterize the volume, type, and quality of organic waste, which determine the volume and quality of bioenergy production. They also characterize the technological processes of organic waste processing, which determine the type of bioenergy produced, as well as its quality and volume. The characteristics of the infrastructure for the collection and processing of organic waste determine the cost and efficiency of bioenergy production systems using the organic waste of residential areas under the given scenarios of their operation.

In separate scientific works [10,11,12,13,14,15], the authors conducted research on determining the indicators of organic substrates for calculating the productivity of modular anaerobic systems for biogas production. However, the performed studies relate only to the given conditions of biogas production and a separate type of organic waste. At the same time, there are no scientific works in which the regularities of changes in functional indicators of bioenergy production systems using the organic waste of residential areas due to changes in conditions and type of organic waste are substantiated. This makes it impossible to create accurate models for determining the rational configuration of bioenergy production systems using the organic waste of residential areas [16,17,18,19,20,21].

There is a need to study the interrelationships between the functional indicators of bioenergy production and the organic waste of residential areas using modular plants. This article considers four types of organic waste that are generated within the territory of residential areas: (1) food waste (FW); (2) yard waste (YW); (3) mixed food and yard waste (FYW); and (4) mixed organic waste (MOW). For each of the indicated types of organic waste in residential areas, the relationships between the functional indicators of bioenergy production were evaluated. The results of this study can be used to model bioenergy production systems using organic waste to determine their effective configuration within the territory of given residential areas.

The scientific novelty of the performed work consists in substantiating the patterns of changes in the functional indicators of bioenergy production systems using the organic waste of residential areas. The obtained research results have practical value, as they ensure the creation of models for the optimization of bioenergy production systems using organic waste for the given characteristics of residential areas.

2. Analysis of Literature Data and Problem Statement

In recent years, more and more scientific works have been published which are devoted to the production of bioenergy from organic waste [22,23,24,25,26,27]. These studies cover a wide range of issues, including technologies for processing organic waste, the economic efficiency of bioenergy production, environmental aspects, and social consequences.

One important area of research is the study of relationships between functional indicators of bioenergy production systems. The relationships between these indicators are complex and multifactorial. They depend on many factors [28,29,30,31,32]. The study of these relationships is an important scientific and applied task for the design of efficient bioenergy production systems using organic waste from residential areas during the implementation of the EGDPs [3,25].

Most of the existing scientific works are focused on the study of relationships between individual functional indicators of bioenergy production systems [33,34,35,36,37]. For example, some studies study the influence of the quantity and quality of organic waste on the efficiency of the recycling process [38,39,40,41]. Other studies were conducted to study the impact of organic waste processing technology on the quality of the obtained bioenergy [42,43,44,45,46].

These studies are important for understanding certain aspects of the relationships between functional indicators. However, they do not allow us to get a complete picture of these relationships using different types and quality of organic waste from residential areas, which makes it impossible to create effective models for determining the rational configuration of bioenergy production systems using organic waste for given characteristics of residential areas.

The main drawback of the existing scientific works is their focus on the general issues of bioenergy production from organic waste in residential areas. They do not take into account the specific features of the formation of organic waste in the territory of given residential areas. These features include the diverse composition of organic waste generated in residential areas, its variable quantity and quality, as well as the possibility of producing various types of bioenergy (electrical and thermal) and biofertilizers. Taking these features into account is important for creating models for determining efficient bioenergy production systems using organic waste from residential areas.

In many existing scientific works, authors quite often use statistical methods to study the relationships between functional indicators [43,44,45,46]. These methods do not take into account the dynamics of these relationships. To substantiate the interrelationships between the functional indicators of bioenergy production systems and the organic waste of residential areas, it is necessary to conduct research that takes into account the specific features of this production. These studies should be based on methods that allow taking into account the dynamics of interrelationships between functional indicators of bioenergy production systems using the organic waste of residential areas.

To carry out research with the aim of a quantitative assessment of the relationships between functional indicators of bioenergy production systems using the organic waste of residential areas, it is proposed to develop a methodology based on the use of existing results published in scientific works [3,25,47,48,49,50]. In our work, passive experiment methods were used to collect data on the functional indicators of bioenergy production systems, mathematical statistics methods for processing and interpreting trends in the functional indicators of energy production systems from organic waste in residential areas, as well as mathematical modeling methods to develop mathematical models that reflect regularity changes in functional indicators of bioenergy production systems. These methods allow taking into account the complexity and multifactorial relationships between functional indicators. In addition, they allow taking into account the dynamics of these relationships.

The purpose of this work is to substantiate the methodology for determining the interrelationships between functional indicators of bioenergy production systems using the organic waste of residential areas, which is based on an analysis of literary sources and conducting passive production observations, which ensures consideration of the complexity and multifactorial nature of functional indicators, as well as the development of qualitative models for their forecasting.

To achieve this goal, it is necessary to solve the following tasks:

–

To propose a methodology for evaluating the interrelationships between functional indicators of bioenergy production systems using the organic waste of residential areas.

–

Based on the use of the proposed methodology, to substantiate the dependencies between functional indicators of bioenergy production systems using the organic waste of residential areas and their mathematical models.

3. Methodology for Evaluating Relationships between Functional Indicators of Bioenergy Production Systems Using the Organic Waste of Residential Areas

Assessing the relationships between the functional indicators of bioenergy production systems using the organic waste of residential areas is an important scientific and applied task, the solution of which ensures the creation of models and, based on them, the justification of effective bioenergy production systems using the organic waste of residential areas. These models can be used to optimize the configuration of EGDPs. In particular, this applies to determining the parameters of bioenergy production systems in the territory of given residential areas, taking into account their characteristics, calculating the economic efficiency of bioenergy production, and comparing different scenarios of EGDPs.

For each of the stages of modeling bioenergy production, a selection of mathematical models is made for the analysis of various scenarios of bioenergy production processes from the organic waste of residential areas (Figure 1).

Models can include thermodynamic equations, reaction kinetics, mass balance, and other mathematical expressions [51,52,53,54]. During the modeling of bioenergy production processes, technical parameters of the anaerobic system, such as power, reactor volume, temperature, pressure, etc., are taken into account. For each scenario of bioenergy production, calculations using mathematical models and analysis of the data obtained are carried out to evaluate the functional indicators of each scenario.

Modeling of harvesting organic raw materials involves forecasting the volumes $\left(Q_{owk}^p\right)$ of organic waste generation of k types, taking into account the components of the expression

$$Q_{owk}^p=f\left(T_{ri},T_{bi},N_{bi},N_{hi},S_{ti},N_{ri},L_{ri},q_{dk}\right)$$

(1)

where $Q_{owk}^p$—predicted amount of generation of k types of organic waste; $T_{ri}$—type of residential area; $T_{bi}$, $N_{bi}$—number and type of houses in the i-th housing estate; $N_{hi}$—the number of households in each house of the i-th residential massif; $S_{ti}$—area of the territory of the i-th residential massif; $N_{ri}$—the number of residents in households of the i-th housing estate; $L_{ri}$—income level of residents of households of the i-th housing estate; and $q_{di}$—daily amount of k types of organic waste generation per inhabitant in the i-th housing estate.

For each type $\left(T_{owk}\right)$ of organic waste, separate models are created, which are based on machine learning algorithms [3].

It is known [48,49] that the collection of waste at the place of its direct processing provides the highest amount of biogas output. At the same time, the highest yield of biogas is observed in pre-sorted organic waste, while mechanical sorting leads to an increase in the duration of waste storage and, accordingly, a decrease in available energy [55,56,57,58]. Pre-sorted organic waste in households ensures an increase in the efficiency of bioprocesses and, accordingly, an increase in the volume of biogas production [10,11,12,13,14,15,16,17,18,19]. Accordingly, in our work, the condition is accepted that residents of residential areas independently sort waste and deliver it to the appropriate container, which is installed in the territory of their residential areas.

Modeling of biogas production is carried out according to the method presented in [18,19,20,21,50]. It is based on the disclosure of general relationships during the biological decomposition of organic waste in a reactor. At the same time, stationary conditions for obtaining biogas in a modular anaerobic system are assumed. The consideration of the organic waste decomposition process in the reactor is based on the biogas balance, which can be expressed in terms of biogas based on the expression

$$C=C^{\prime }-C^{″}$$

(2)

where $C$—carbon in biogas, which was formed in a methane tank; $C^{\prime }$—carbon that enters the methane tank and is further decomposed into biogas; and $C^{″}$—carbon that decomposes into biogas and leaves the methane tank.

The biogas balance represented by Expression (2) in terms of biogas can be written as:

$$GPR=Q\cdot TV{S}_f\cdot G_o-Q\cdot TV{S}_r\cdot G_o^{\prime }$$

(3)

where $GPR$—performance of a modular anaerobic system during biogas production, m³/day; $Q$—submission of organic waste, m³/day; $TV{S}_f$—total amount of volatile substances in organic waste, kg/m³; $TV{S}_r$—the total amount of volatile substances in the methane tank, kg/m³; and $G_o,G_o^{\prime }$—respectively, the final yield of biogas from the submitted organic waste and removed wastewater, m³ biogas/kg $TVS$.

Dividing Expression (3) by $\left(Q\cdot TV{S}_f\right)$ gives the specific production of biogas, $SGP$:

$$SGP=G_o-\left(1-f_{TVS}\right)\cdot G_o^{\prime }$$

(4)

where $SGP$—specific production of biogas, m³ biogas/kg $TVS$; and $f_{TVS}$—the fraction $TV{S}_f$ that separates in the reactor.

It is assumed where $f_{TVS}=1$ that all volatile substances have been removed from the organic waste, and, at the same time, the specific production of biogas will be equal to the final output of biogas from organic waste. If not all volatile substances decompose, then it is observed that −$f_{TVS}<1$. At the same time, the case when $G_o^{\prime }=0$, which is typical for a considerable retention time of organic waste in the methane tank, then under this option it will be observed that $SGP=G_o$.

The above indicates that the yield of biogas also depends on the kinetic aspects of the biogas formation process. The rate of carbon decomposition will be proportional to the concentration of carbon decomposed in the methane tank, which is described by the kinetic equation

$$C_d=k\cdot V\cdot D_C$$

(5)

where $V$—methane tank volume, м³; and $D_C$—concentration of decomposed carbon.

If we replace the concentration of decomposed carbon with biogas production, Equation (5) for determining the productivity of a modular anaerobic system during biogas production will look like this:

$$GPR=k\cdot V\cdot TV{S}_r\cdot G_o^{\prime }$$

(6)

After dividing Expression (6) by $\left(Q\cdot TV{S}_f\right)$ we get the specific production of biogas:

$$SGP=k\cdot HRT\cdot \left(1-f_{TVS}\right)\cdot G_o^{\prime }$$

(7)

Substituting the values $G_o^{\prime }$ from Equation (4) and making the appropriate reductions, we get:

$$SGP=\frac{G_o}{1+1/\left(k\cdot HRT\right)}$$

(8)

where $HRT$—hydraulic retention time of biomass in methane tanks, days.

The values of indicators of organic substrates known in literary sources for calculating the productivity of a modular anaerobic system during biogas production are presented in

Table 1. The value of indicators of organic substrates for calculating the productivity of a modular anaerobic system during bioenergy production.

Option	Description/Literary Source	Total Volume of Solid Organic Substances, TS (kg/m3)	The Content of Volatile Organic Substances, TVS (% from TS)	Biogas Output, SGP, (m3/kg TVS)	Methane Output, SMP, (m3/kg TVS)	Kinetic Constant of Methane Production, km
Food waste (FW)
VFW1	Kitchen waste/[12]	214.1	88.1	1.035	0.642	1.611
VFW2	Household waste/[13]	280.0	86.1	0.657	0.353	1.857
VFW3	Food waste/[14]	266.0	93.4	0.885	0.560	1.580
VFW4	Food waste/[15]	239.0	91.3	0.862	0.526	1.637
VFW5	Food waste/[19]	278.0	93.6	0.672	0.375	1.788
VFW6	Food waste/[20]	226.0	93.8	0.970	0.590	1.644
Average		250.5	91.1	0.847	0.508	1.686
Yard waste (YW)
VYW1	Yard waste/[12]	504.0	92.0	0.215	0.103	2.087
VYW2	Yard waste/[15]	973.0	91.1	0.329	0.167	1.970
VYW3	Yard waste/[18]	600.0	90.5	0.134	0.065	2.062
VYW4	Yard waste/[20]	895.0	87.3	0.364	0.189	1.926
VYW5	Yard waste/[21]	943.0	91.7	0.349	0.177	1.972
Average		783.0	90.5	0.278	0.140	2.003
Mixed food and yard waste (FYW)
VFYW1	FW + YW (1:1)/[15]	606.0	91.2	0.466	0.286	1.629
VFYW2	FW + YW (1:3)/[15]	790.0	91.2	0.271	0.165	1.642
VFYW3	FW + YW (1:5)/[21]	688.0	90.8	0.223	0.143	1.559
VFYW4	FW + YW (1:10)/[21]	668.0	90.4	0.212	0.127	1.669
VFYW5	FW + YW (3:1)/[15]	422.0	91.3	0.562	0.346	1.624
VFYW6	FW + YW (5:1)/[17]	335.0	90.5	0.742	0.483	1.536
Average		585.0	90.9	0.413	0.258	1.606
Mixed organic waste (MOW)
VMOW1	Sorted from house/[10]	200.0	88.2	0.637	0.379	1.680
VMOW2	Sorted from house/[11]	181.9	73.5	0.454	0.263	1.726
VMOW3	Sorted from house/[16]	260.0	87.0	0.645	0.388	1.668
VMOW4	Sorted from house/[16]	310.0	91.0	0.802	0.489	1.640
VMOW5	Sorted from house/[16]	280.0	87.0	0.781	0.473	1.650
VMOW6	Sorted from house/[16]	300.0	80.0	0.652	0.392	1.660
VMOW7	Sorted from house/[16]	340.0	87.0	0.858	0.515	1.666
Average		267.0	85.0	0.690	0.414	1.670

.

Since the quantitative values of FW and YW have variable values [10], the composition of household organic waste is taken as the average according to the literature data presented in Table 1.

The coefficient $k_m$ that characterizes the kinetic constant of waste decomposition is used to estimate the rate of biological decomposition of organic substances in the process of anaerobic transformation during the formation of biogas.

The coefficient $k_m$ indicates the relative volume of methane formation from biogas and is determined by the formula

$$k_m=\frac{SGP}{SMP}$$

(9)

where $SGP$—biogas yield in cubic meters per kilogram of volatile organic substances in solid high-carbon substances (m³/kg TVS); and $SMP$—yield of methane in cubic meters per kilogram of volatile organic matter in solid high-carbon matter (m³/kg TVS).

The essence of the coefficient $k_m$ is to determine how effectively organic substances in the process of anaerobic decomposition are transformed from biogas into methane.

A great value $k_m$ indicates a high rate and efficiency of biomethane formation, while a smaller value $k_m$ indicates a less efficient process of methane formation from biogas.

The volume of electricity production from biogas of organic waste can be determined using the following formula:

$$E=V_{\mathrm{biogas}}\cdot G\cdot LH{V}_E\cdot {\eta }_{EY}$$

(10)

where $E$—volume of electricity production kWh; $V_{\mathrm{biogas}}$—volume of biogas, m³; $G$—methane content in biogas, %; $LH{V}_E$—lower heat of combustion of methane, MJ/m³; and ${\eta }_{EY}$—efficiency factor of the power plant, %.

Given the data in Table 1, you can determine the appropriate volume of biogas $V_{\mathrm{biogas}}$ and methane content $G$ by the following formulas:

$$V_{\mathrm{biogas}}=\frac{TVS}{TS}$$

(11)

$$G=\frac{SMP}{SGP}$$

(12)

The lower heating value (LHV) for methane obtained from various organic waste sources is estimated in MJ/m³. However, quantitative values largely depend on the type and composition of waste, as well as on the conditions of their decomposition. In our research, the average values of the LHV for the use of different types of organic waste are taken [11,12,13,14,15,16,17,18,31]: (1) food waste (FW)—25…35 MJ/m³; (2) yard waste (YW)—20…30 MJ/m³; (3) mixed food and yard waste (FYW)—22…32 MJ/m³; and (4) mixed organic waste (MOW)—20…30 MJ/m³. These values may also vary depending on factors such as the composition of the waste and its processing technology.

The efficiency factor of the power plant ${\eta }_{EY}$ during electricity generation depends on many factors, including the efficiency of methane and organic waste conversion processes. Typically, power plants using biogas (including methane derived from organic waste) may have ${\eta }_{EY}=25\dots 35\%$ and even more, depending on technology, equipment, and gas purification processes. In our calculations, we assume that ${\eta }_{EY}=35\%$. It is important to understand that the exact value ${\eta }_{EY}$ will depend on the specifications of a specific power plant, its technical characteristics, and operating conditions. Therefore, to obtain accurate data regarding ${\eta }_{EY}$, manufacturers of modular anaerobic systems with cogeneration equipment should be consulted.

To determine the amount of thermal energy production $Q$ from organic waste methane, use the formula

$$Q=V_{\mathrm{methane}}\cdot LH{V}_Q\cdot {\eta }_{QY}$$

(13)

where $Q$—volume of thermal energy production, kCal; $V_{\mathrm{methane}}$—volume of produced methane, m³; $LH{V}_Q$—thermal energy capacity in methane, MJ/m³; and ${\eta }_{QY}$—thermal energy production efficiency factor.

The volume of methane produced is determined by the formula

$$V_{\mathrm{methane}}=V_{\mathrm{biogas}}\cdot G.$$

(14)

In general, one kilogram of the solid fraction of organic waste can give the calorific value of methane $LH{V}_Q$ = 20–35 MJ/m³ under standard conditions (25 °C and atmospheric pressure).

Usually, the coefficient of efficiency ${\eta }_{QY}$ of thermal energy production from various fuel sources can lie in a range from 0.3 to 0.9 (30% to 90%). The value of the coefficient depends on the technology, equipment, and production conditions. Given the wide variety of technologies and approaches to using organic waste for energy production, the exact value of the coefficient ${\eta }_{QY}$ efficiency will depend on a number of factors. In our further calculations, we accept the value ${\eta }_{QY}=0.6$.

Volumes of production of the solid fraction (biofertilizer) during the production of biogas from organic waste can be determined using the following formula:

$$F=TS\cdot \left(1-TVS\right)$$

(15)

where $F$—production volume of solid fraction (biofertilizer), kg/m³; $TS$—total volume of solid organic substances, kg/m³; and $TVS$—content of volatile organic substances, % from TS.

Equation (8) is useful for evaluating the biological decomposition of organic waste, which is carried out during the given hydraulic retention time of biomass in methane tanks.

At the same time, the equation can be used to estimate the achieved biogasification as a fraction of the maximum possible:

$$f_b=\frac{SGP}{G_o}=\frac{1}{1+1/\left(k\cdot HRT\right)}$$

(16)

Thanks to Equation (16), it is possible to estimate the efficiency of the bioprocess during the production of biogas in a modular anaerobic system within the territory of a residential area.

Similarly, it is possible to evaluate the efficiency of specific methane production in a modular anaerobic system within the territory of a residential area [50]:

$$f_b=\frac{SMP}{B_o}=\frac{1}{1+1/\left(k\cdot HRT\right)}$$

(17)

where $SMP$—specific production of methane, m³; and $B_o$—final yield of methane from organic waste, m³ CH₄/kg TVS.

On the basis of the above, it is possible to determine the loading speed of the methane tank with organic waste of residential areas. However, not all volatile solid organic waste is degradable, and to accurately determine the volumes of their loading into methane tanks, it is necessary to consider the part of these solids that can be converted into biogas. The loading rate of organic waste is determined by the formula

$$OLR=\frac{TV{S}_f}{HRT}$$

(18)

where $TV{S}_f$—total amount of volatile substances in organic waste, kg/m³; and $HRT$—hydraulic retention time of biomass in methane tanks, days.

Taking into account the above, in [50,59,60,61,62,63], in order to determine the real speed of loading the methane tank with organic waste of residential areas, it is proposed to replace Expression (18) with the expression

$$OL{R}_r=\frac{TV{S}_f\cdot G_o}{HRT\cdot 1.87}$$

(19)

where $OL{R}_r$—potential production of biogas, gram of carbon/m³ per day; and $1.87$ is a constant characterizing the amount of conversion of 1 m³ of biogas into grams of carbon.

Based on the transformation of Expressions (18) and (19), we obtain:

$$OL{R}_r=\frac{OLR\cdot G_o}{1.87}$$

(20)

It is known [4] that the actual energy consumption of anaerobic systems during bioenergy production depends on their annual productivity and is accordingly described by the equations:

–

electrical energy $\left(E_{oe}\right)$:

$$E_{oe}=4107\cdot m_{ow}^{-0.369}$$

(21)

where $m_{ow}$—volume of processing of organic raw materials, t/year.

–

thermal energy $\left(E_{ot}\right)$:

$$E_{ot}=6628.9\cdot m_{ow}^{-0.501}$$

(22)

As a result of modeling bioenergy production, functional indicators are obtained for each scenario, such as the amount of biogas production, the amount and composition of by-products, energy efficiency, the cost of bioenergy production, the rate of utilization of organic waste, etc.

4. Results of Substantiation of Dependencies between Functional Indicators of Bioenergy Production Systems Using the Organic Waste of Residential Areas

On the basis of the data in Table 1, the dependencies of indicators of organic substrates were constructed for calculating the productivity of a modular anaerobic system during bioenergy production (Figure 2, Figure 3, Figure 4 and Figure 5).

The obtained dependencies (Figure 2) of the yield of biogas SGP (m³/kg TVS) on the total volume of solid organic substances TS (kg/m³) in organic waste are described by the following equations:

–

food waste (FW)

$$SG{P}_{FW}=-0.0051\cdot TS+2.1145, R^2=0.85$$

(23)

–

yard waste (YW)

$$SG{P}_{YW}=0.0004\cdot TS-0.0366, R^2=0.76$$

(24)

–

mixed food and yard waste (FYW)

$$SG{P}_{FYW}=-0.0011\cdot TS+1.0829, R^2=0.86$$

(25)

–

mixed organic waste (MOW)

$$SG{P}_{MOW}=0.002\cdot TS+0.148, R^2=0.74$$

(26)

The obtained dependencies (Figure 3) of SGP biogas yield (m³/kg TVS) on the total volume of solid organic substances TS (kg/m³) in organic waste and the content of volatile organic substances (% TVS of TS) are described by the following equations:

–

food waste (FW)

$$SG{P}_{FW}^{\prime }=-0.0051\cdot TS+0.0068\cdot TVS+1.4949, R^2=0.87,$$

(27)

–

yard waste (YW)

$$SG{P}_{YW}^{\prime }=0.0004\cdot TS-0.0049\cdot TVS+0.4198, R^2=0.77,$$

(28)

–

mixed food and yard waste (FYW)

$$SG{P}_{FYW}^{\prime }=-0.0011\cdot TS+0.1064 \cdot TVS- 8.5669, R^2=0.89,$$

(29)

–

mixed organic waste (MOW)

$$SG{P}_{MOW}^{\prime }=0.002\cdot TS+0.0108\cdot TVS- 0.624, R^2=0.92.$$

(30)

The obtained dependencies (Figure 4) of the SMP methane output (m³/kg TVS) on the SGP biogas output (m³/kg TVS) are described by the following equations:

–

food waste (FW)

$$SM{P}_{FW}=0.6886\cdot SGP-0.0675, R^2=0.96$$

(31)

–

yard waste (YW)

$$SM{P}_{YW}=0.5372\cdot SGP-0.0092, R^2=0.99$$

(32)

–

mixed food and yard waste (FYW)

$$SM{P}_{FYW}=0.6525\cdot SGP-0.0109, R^2=0.99$$

(33)

–

mixed organic waste (MOW)

$$SM{P}_{MOW}=0.6326\cdot SGP-0.0223, R^2=0.99$$

(34)

The obtained dependencies (Figure 5) of the kinetic constant of methane production on the output of SMP methane (m³/kg TVS) are described by the following equations:

–

food waste (FW)

$$k_{mFW}=-0.8637\cdot SMP+2.1246, R^2=0.85$$

(35)

–

yard waste (YW)

$$k_{mYW}=-1.1611\cdot SMP+2.1662, R^2=0.84$$

(36)

–

mixed food and yard waste (FYW)

$$k_{mFYW}=-0.3410\cdot SMP+1.7142, R^2=0.89$$

(37)

–

mixed organic waste (MOW)

$$k_{mMOW}=-0.278\cdot SMP+1.7851, R^2=0.74$$

(38)

On the basis of the research conducted, the trends of changes in the average values of indicators of the use of organic substrates in modular anaerobic systems during the production of bioenergy were established, which are presented in Figure 6.

Based on the obtained research results, it can be said that the highest amount of organic solids (TS) is observed in the food waste (FW) category, with a value of 783.0 kg/m³, which significantly exceeds the amount in other categories. The smallest volume was recorded in the mixed organic waste (MOW) category—267.4 kg/m³.

The average content of volatile organic substances (TVS) relative to the total volume of waste is almost the same in all categories. The values range from 84.8% to 91.05%, where the mixed organic waste (MOW) category has the lowest TVS content and the food waste (FW) category has the highest.

The yield of biogas (SGP) relative to the mass of TVS is the highest in the food waste (FW) category (0.847 m³/kg TVS) and the lowest in yard waste (YW) (0.278 m³/kg TVS). This may indicate that most of the biogas is produced from solid food waste.

The values of the kinetic constant (k) are quite close between all categories. They range from 1.606 to 2.003. This may indicate the similarity of kinetic properties of different types of waste.

In general, certain conclusions about trends can be drawn:

–

yard waste (YW) has the highest volume of TS but a low biogas yield and share of methane production;

–

food waste (FW) has the highest yield of biogas and, accordingly, the highest share of methane production;

–

mixed organic waste (MOW) has the lowest TS volume and the lowest TVS content.

Based on the use of the data in Table 1 and Formulas (10)–(15), appropriate calculations were performed, and quantitative values of the production volumes of electricity and thermal energy from organic waste biogas were obtained. The obtained results are presented in

Table 2. The value of indicators of the volume of production of electricity and thermal energy from the biogas of organic waste.

Option	Volume of Biogas, ${\mathit{V}}_{\mathbf{biogas}}$, m3/kg TS	Methane Content G in Biogas, %	Volume of Methane Produced, ${\mathit{V}}_{\mathbf{methane}}$, m3	Volume of Electricity Production, E, kWh	Volume of Thermal Energy Production, Q, kWh	Production Volume of the Solid Fraction (Biofertilizers), F, kg/m3
Food waste (FW)
VFW1	0.411	0.620	0.255	5.666	5.932	25.478
VFW2	0.308	0.537	0.165	3.668	3.262	38.920
VFW3	0.351	0.633	0.222	4.932	5.174	17.556
VFW4	0.382	0.610	0.233	5.175	4.860	20.793
VFW5	0.337	0.558	0.188	4.171	3.465	17.792
VFW6	0.415	0.608	0.252	5.604	5.452	14.012
Average	0.363	0.600	0.218	4.840	4.694	22.420
Yard waste (YW)
VYW1	0.183	0.479	0.087	1.941	0.952	40.320
VYW2	0.094	0.508	0.048	1.055	1.543	86.597
VYW3	0.151	0.485	0.073	1.624	0.601	57.000
VYW4	0.098	0.519	0.051	1.124	1.746	113.665
VYW5	0.097	0.507	0.049	1.095	1.635	78.269
Average	0.116	0.504	0.058	1.292	1.294	74.385
Mixed food and yard waste (FYW)
VFYW1	0.150	0.614	0.092	2.050	2.643	53.328
VFYW2	0.115	0.609	0.070	1.560	1.525	69.520
VFYW3	0.132	0.641	0.085	1.879	1.321	63.296
VFYW4	0.135	0.599	0.081	1.800	1.173	64.128
VFYW5	0.216	0.616	0.133	2.957	3.197	36.714
VFYW6	0.270	0.651	0.176	3.904	4.463	31.825
Average	0.155	0.625	0.097	2.155	2.384	53.235
Mixed organic waste (MOW)
VMOW1	0.441	0.595	0.262	5.825	3.502	23.600
VMOW2	0.404	0.579	0.234	5.196	2.430	48.204
VMOW3	0.335	0.602	0.201	4.469	3.585	33.800
VMOW4	0.294	0.610	0.179	3.973	4.518	27.900
VMOW5	0.311	0.606	0.188	4.178	4.371	36.400
VMOW6	0.267	0.601	0.160	3.559	3.622	60.000
VMOW7	0.256	0.600	0.154	3.410	4.759	44.200
Average	0.318	0.600	0.191	4.240	3.825	40.050

.

The obtained data in Table 2 indicate that the amount of electricity production (kWh) and thermal energy (kWh) varies depending on the type of organic waste. Mixed organic waste (MOW) has a higher average amount of electricity production compared to other types of waste. Similarly, it is observed that the production volume of solid fraction (biofertilizer) (kg/m³) is also different for different types of organic waste. Based on the data in Table 2, the dependencies of the indicators of the production volumes of electricity and thermal energy from the biogas of organic waste were constructed (Figure 7, Figure 8, Figure 9 and Figure 10).

The obtained dependencies (Figure 7 and Figure 8) of the amount of electricity production ($E$, kWh), thermal energy ($Q$, kWh), and solid fraction (biofertilizers) ($F$, kg/m³) from the specific volume of biogas ($V_{\mathrm{biogas}}$, m³/kg TS) of organic waste are described by the following equations:

–

food waste (FW)

$$E_{FW}=18.209\cdot V_{\mathrm{biogas}}-1.82, R^2=0.94$$

(39)

$$Q_{FW}=22.747\cdot V_{\mathrm{biogas}}-3.665, R^2=0.795$$

(40)

$$F_{FW}=-210.037\cdot V_{\mathrm{biogas}}+100.245, R^2=0.8$$

(41)

–

yard waste (YW)

$$E_{YW}=9.799\cdot V_{\mathrm{biogas}}+0.147, R^2=0.99$$

(42)

$$Q_{YW}=-10.336\cdot V_{\mathrm{biogas}}+2.583, R^2=0.71$$

(43)

$$F_{YW}=-610.16\cdot V_{\mathrm{biogas}}+151.196, R^2=0.76$$

(44)

–

mixed food and yard waste (FYW)

$$E_{FYW}=14.824\cdot V_{\mathrm{biogas}}-0.157, R^2=0.99$$

(45)

$$Q_{FYW}=20.327\cdot V_{\mathrm{biogas}}-1.062, R^2=0.89$$

(46)

$$F_{FYW}=-250.546\cdot V_{\mathrm{biogas}}+95.644, R^2=0.94$$

(47)

–

mixed organic waste (MOW)

$$E_{MOW}=12.557\cdot V_{\mathrm{biogas}}+0.233, R^2=0.99$$

(48)

$$Q_{MOW}=-7.619\cdot V_{\mathrm{biogas}}+ 6.624, R^2=0.83$$

(49)

$$F_{MOW}=-116.858\cdot V_{\mathrm{biogas}}+75.116, R^2=0.86$$

(50)

Based on the data obtained above and using Equation (17), the dependencies of methane production efficiency $\left(f_b\right)$ from the hydraulic retention time of biomass in methane tanks $\left(HRT\right)$, which are presented in Figure 9 can be calculated.

The obtained dependencies (Figure 9) of methane production efficiency $\left(f_b\right)$ from the hydraulic retention time of biomass in methane tanks $\left(HRT\right)$ are described by the following equations:

–

food waste (FW)

$$f_{bFW}=-0.000105\cdot HR{T}^2+0.006\cdot HRT+0.891, R^2=0.96$$

(51)

–

yard waste (YW)

$$f_{bYW}=-0.000119\cdot HR{T}^2+0.006\cdot HRT+0.903, R^2=0.94$$

(52)

–

mixed food and yard waste (FYW)

$$f_{bFYW}=-0.000087\cdot HR{T}^2+0.005\cdot HRT+0.899, R^2=0.94$$

(53)

–

mixed organic waste (MOW)

$$f_{bMOW}=-0.000105\cdot HR{T}^2+0.006\cdot HRT+0.891, R^2=0.96$$

(54)

The obtained dependencies indicate that the hydraulic retention time of biomass in methane tanks $\left(HRT\right)$ affects the efficiency of methane production in different ways $\left(f_b\right)$ for different types of waste. At the same time, all four types of organic waste have similar dependencies, where changes in the hydraulic retention time of biomass in methane tanks from 10 to 30 days reduce the efficiency of methane production, and $\left(f_b\right)$ increases from 0.94 to 0.98 due to the increase in methane production. At the same time, the coefficient of determination is within the limits $R^2=0.94\dots 0.96$, which indicates a strong connection between the hydraulic retention time of biomass in methane tanks $\left(HRT\right)$ and efficiency of methane production $\left(f_b\right)$.

On the basis of the data obtained above and using Equation (18), the dependencies of the organic waste loading rate were obtained $\left(OLR\right)$ from the hydraulic retention time of biomass in methane tanks $\left(HRT\right)$, which are presented in Figure 10.

The obtained dependencies (Figure 10) of the loading rate of organic waste $\left(OLR\right)$ from the hydraulic retention time of biomass in methane tanks $\left(HRT\right)$ are described by the following equations:

–

food waste (FW)

$$OR{L}_{FW}=0.037529\cdot HR{T}^2-2.201\cdot HRT+40.32, R^2=0.99$$

(55)

–

yard waste (YW)

$$OR{L}_{YW}=0.117949\cdot HR{T}^2-6.892\cdot HRT+125.734, R^2=0.99$$

(56)

–

mixed food and yard waste (FYW)

$$OR{L}_{FYW}=0.088316\cdot HR{T}^2-5.162\cdot HRT+94.239, R^2=0.99$$

(57)

–

mixed organic waste (MOW)

$$OR{L}_{MOW}=0.037966\cdot HR{T}^2-2.214\cdot HRT+40.304$$

(58)

The obtained results, which are presented in Figure 9, indicate a clear dependence of the loading rate $\left(OLR\right)$ of organic waste on the hydraulic retention time of biomass in methane tanks $\left(HRT\right)$ for different types of organic waste. This is confirmed by the high value of the coefficients of determination $R^2=0.99$. The resulting Equations (55)–(58) make it possible to predict the rate of loading of organic starting substances $\left(OLR\right)$ on the basis of the known hydraulic retention time of biomass in methane tanks $\left(HRT\right)$ during the optimization of bioenergy production processes from the organic waste of residential areas.

The obtained research results can be used when creating models to determine the rational configuration of bioenergy production systems using organic waste for given characteristics of residential areas. This will make it possible to develop effective strategies for managing bioenergy production processes for given residential areas that provide optimal conditions for processing specific types of organic waste. Taking into account these results contributes to increasing the production efficiency and sustainability of energy systems based on the consideration of the type and quality of organic waste.

5. Discussion of Research Results

Based on the analysis of the state of the art in theory and practice, it has been established that the implementation of EGDPs, which involve the production of bioenergy from organic waste generated in residential areas, is a rather urgent task in the world today [3,4,5,6,25,38]. This is due to the growth of the population in cities and the corresponding increase in the amount of generated waste, which negatively affects the environment due to the release of methane, a greenhouse gas with a high potential for global warming [6,25,38,39,40,41]. The utilization of organic waste through the production of bioenergy is an effective scenario for solving this problem, both for residents of residential areas and for communities and regions [64,65,66,67,68].

In order to substantiate effective scenarios for the creation of bioenergy production systems using the organic waste of residential areas, it is necessary to perform modeling, which is based on the disclosure of relationships between various functional indicators of individual processes [3,54,55,56,57]. At the same time, there is a need to substantiate the interrelationships between the functional indicators of bioenergy production from the organic waste of residential areas, taking into account the type and quality of organic waste, which determine the volume of bioenergy generation and the efficiency of its production.

To achieve the goal, a methodology was developed for evaluating the relationships between the functional indicators of the bioenergy production system from the organic waste of residential areas. The proposed method is based on a detailed analysis of literary sources and by conducting passive production observations. The proposed technique, which is based on the use of existing results published in scientific works [22,23,24,25,26,27,28,29,30,31,32,33], as well as on the use of methods of system analysis and mathematical modeling, ensured consideration of the complexity and multifactorial relationships between functional indicators.

In our work, four types of organic waste that are generated in the territory of residential areas were considered: (1) food waste (FW); (2) yard waste (YW); (3) mixed food and yard waste (FYW); and (4) mixed organic waste (MOW). For each of the indicated types of organic waste of residential areas, the relationships between the functional indicators of bioenergy production were evaluated. The results of the study can be used to model bioenergy production systems using organic waste to determine their effective configuration in the territory of given residential areas.

Based on the developed methodology, results were obtained which demonstrate the existing dependencies between the functional indicators of the bioenergy production system from the organic waste of residential areas. It was established that the highest volume of organic solids (TS) is observed in the category of food waste (FW) with a value of 783.0 kg/m³, which significantly exceeds the volume in other categories. The smallest volume was recorded in the mixed organic waste (MOW) category—267.4 kg/m³. At the same time, mixed food and yard waste (FYW) provide an average value of the volume of solid organic substances—585 kg/m³. The average content of volatile organic substances (TVS) relative to the total volume of waste is almost the same in all categories. The values range from 84.8% to 91.05%, where the mixed organic waste (MOW) category has the lowest TVS content and the food waste (FW) category has the highest. The yield of biogas (SGP) relative to the mass of TVS is the highest in the food waste (FW) category (0.847 m³/kg TVS), and the lowest in yard waste (YW) (0.278 m³/kg TVS). This may indicate that most of the biogas is produced from solid food waste.

The following trends were found to exist in the use of different types of organic waste for bioenergy production: (1) yard waste (YW) had the highest volume of TS, but a low biogas yield and share of methane production; (2) food waste (FW) had the highest yield of biogas and, accordingly, the highest share of methane production; (3) mixed food and yard waste (FYW) provided a lower biogas yield compared to yard waste (YW) and a higher yield compared to yard waste (YW); and (4) mixed organic waste (MOW) had the lowest volume of TS and the lowest content of TVS. At the same time, the amount of electricity and thermal energy production varied depending on the type of organic waste. Mixed organic waste (MOW) had a higher average amount of electricity production compared to other types of waste. Similarly, it was observed that the production volume of the solid fraction (biofertilizer) was also different for different types of organic waste.

The obtained research results open wide prospects for further research in the field of bioenergy production from organic waste generated within the territory of residential areas. At the same time, an important direction is the development of effective models for determining the rational configuration of bioenergy production systems using organic waste for given characteristics of residential areas.

6. Conclusions

This study substantiated the methodology and obtained results for a quantitative assessment of the relationships between the functional indicators of bioenergy production systems using the organic waste of settlements for the implementation of EGDPs. The methodology developed for assessing the relationships between the functional indicators of the bioenergy production system from municipal organic waste is based on the use of existing results published in scientific papers, as well as on the application of methods of system analysis and mathematical modeling, which made it possible to take into account the complexity and multifactorial nature of the relationships between functional indicators. This approach avoids the limitations associated with the one-sidedness of sources or subjectivity of data, and also ensures full consideration of various factors of the project environment of the EGDP that affect the functional indicators of the bioenergy production system from residential organic waste.

Using the proposed methodology, the interrelationships between the functional indicators of the bioenergy production system from the organic waste of residential areas were investigated and substantiated. We considered four types of organic waste that are generated in the territory of residential areas: (1) food waste (FW); (2) yard waste (YW); (3) mixed food and yard waste (FYW); and (4) mixed organic waste (MOW). It was established that the highest volume of organic solids (TS) was observed in the food waste (FW) category, with a value of 783.0 kg/m³, which was significantly higher than the volume in other categories. The smallest volume was recorded in the mixed organic waste (MOW) category—267.4 kg/m³. The average content of volatile organic substances (TVS) relative to the total volume of waste was almost the same in all categories. The values ranged from 84.8% to 91.05%, where the mixed organic waste (MOW) category had the lowest TVS content and the food waste (FW) category had the highest. The yield of biogas (SGP) relative to the mass of TVS was the highest in the food waste (FW) category (0.847 m³/kg TVS), and the lowest in yard waste (YW) (0.278 m³/kg TVS). This may indicate that most of the biogas is produced from solid food waste. The amount of electricity and thermal energy production varied by type of organic waste, with mixed organic waste (MOW) having a higher average amount of electricity production compared to other types of waste. It was established that the production volume of the solid fraction (biofertilizer) was also different for different types of organic waste. Less solid fraction is produced from food waste than from yard waste.

In general, the results of the work are of practical importance for the development of sustainable bioenergy production from municipal organic waste and contribute to the development of the scientific base in this area through the implementation of relevant EGDPs. The obtained results provide further research on the development of effective models to determine the rational configuration of the EGDP and the structure of bioenergy production systems using organic waste for the given characteristics of residential areas.