Exergoeconomic Assessment of a Cogeneration Unit Using Biogas

Abstract

Biogas, a promising fuel for present and future generations, is produced from the anaerobic digestion of organic waste generated by the condominium itself. Therefore, this work aims to evaluate the exergoeconomic performance of a biogas cogeneration unit designed to meet the electrical and thermal energy demands of a residential condominium in the city of Teresina, Piauí, Northeast Brazil. The cogeneration unit consists of an internal combustion engine (ICE) coupled to an electric generator (genset) to produce electricity, and a heat exchanger that recovers part of the exhaust-gas heat to heat water. The analysis was conducted based on the concepts of Thermodynamics and Exergoeconomics, using the SPECO (Specific Exergy Costing) methodology to define the exergetic costs of the system. The novelty of the work lies in applying the SPECO exergoeconomic analysis to a small-scale biogas cogeneration unit fueled by residential organic waste. The achieved electricity production was 167.40 kW, and the heat transfer rate at the exchange rate was 51.55 kW. The results revealed that the exergy destroyed in the internal combustion chamber (ICE) was 223.65 kW, whereas that in the heat exchanger was significantly higher at 45.67 kW. The exergy efficiency of the ICE reached 39.19%, and the heat exchanger efficiency was around 9%. In financial terms, the cost of exergy destroyed in the ICEC was USD/h 135, but in the heat exchanger, it was dramatically higher at USD/h 158.40. The cost of producing hot water (product) was considered extremely high (USD/GJ 38.98). The relative difference parameter in the heat exchanger also has a value much higher than expected (10.240). This is because the product’s cost (USD/GJ 38.98) is well above the cost of fuel (USD/GJ 3.468). This study concludes that the cogeneration unit is more justifiable by the savings generated through thermal energy production than by electricity production alone, since the cogeneration system significantly enhances performance, raising both the energetic and exergetic efficiencies to 55% and 48%, respectively, thereby confirming the added value of the simultaneous utilization of heat and power.

1. Introduction

Cogeneration is the use of a single energy source to produce two useful forms of energy [1,2]. This is a way of rationalizing energy resources, which is essential because, in current times, energy demand is high and resources are increasingly scarce [3]. In this scenario, it is also important to use alternative energy sources. Solar and wind energy are widely used, but biomass energy generation has also gained importance in recent years [4].

Biomass energy is an energy source that can be burned to make heat or electricity. There are various types of biomass, such as wood, sugarcane bagasse, rice straw, and corn. Biomass, in turn, is the organic material used as a raw material for the production of biogas, a gaseous fuel generated by its anaerobic decomposition. In essence, biomass is the “food” and biogas is the energy “product” resulting from its transformation [5]. In this work, biogas, a mixture of gases resulting from the degradation of organic matter, was used as a fuel.

As previously explained, biogas is an end product of the Anaerobic Digestion (AD) process, in which organic material, including food waste, is converted into energy in the absence of oxygen [6]. This degradation can occur in domestic waste, sanitary landfills, effluent treatment plants, agricultural or industrial waste [7]. The use of biogas transforms an environmental liability into an energy asset, something that already exists and pollutes the environment, which can then produce useful energy [8].

Biogas is widely used for energy generation through internal combustion engines or gas turbines [9]. The authors in [10] performed thermodynamic and thermoeconomic analyses and optimization of a waste heat recovery system integrated with an Afyon biogas power plant that produces biogas from chicken manure. The integrated system is an Organic Rankine Cycle (ORC). As a result of the analyses, integrating the waste heat recovery system into the power plant greatly improves the system’s performance parameters and economic cost savings.

The authors conducted a case study on the sustainability of a large-scale biogas plant operating in Nepal in [11]. Analyses of operating conditions, financial situation, and benefits were conducted using real data from the installation. The results were compared with the design parameters for this type of installation and showed lower feedstock and digester efficiency values than expected. This led to reductions in biogas and biofertilizer production. In addition, the plant showed an undetermined internal rate of return (IRR) under actual operating conditions, as the net present value was negative across all discount rates. However, reductions of up to 274 tons of CO₂ equivalent per year were estimated under actual operating conditions. Based on these results, it is recommended to improve the operational performance of large-scale biogas plants under operating conditions similar to those in this work. An energetic and economic analysis of a cogeneration plant using biogas was carried out in [12]. The authors estimated a production of 1.72 MW of electricity and 57.81 GJ of heat.

The production of biogas from food waste was analyzed in Al-Wahaibi et al. [13]. An experimental analysis of biogas production and a theoretical one were carried out. In the economic analyses, the net present value method was used, with an estimated payback period of 6 years for the proposed system. Pochwatka et al. [14] show that the energy and economic effects of an investment in an on-demand biogas cogeneration plant (CHP) were compared with those of a conventional plant installed in modern medium-scale dairy farm facilities [14]. The economic analysis of the biogas plant indicated a payback period of 3.41 years, making the investment profitable. In terms of energy analysis, the plant, operating as a cogeneration unit, could produce up to 2126 MWh/year.

The energy of biogas is due to its methane content. The higher the percentage of this gas, the greater the fuel’s energy potential. Therefore, purification processes are used to reduce CO₂ levels and increase methane content [15]. The authors in [16] provide a review of the biogas production chain with an emphasis on cleaning and purification processes. The authors realized that there are several types of processes, but the choice may depend on the source of the biogas, the quality of the raw biogas, and the intended application.

Exergoeconomics is an important tool for the study of thermal systems; it allows for defining the exergetic costs of the system by combining concepts from thermodynamics with those of economics [17,18,19,20]. The authors in [21] used the SPecific Exergy COsting (SPECO) methodology to carry out an exergoeconomic assessment of a compact electricity-cooling cogeneration system. The system consisted of an internal combustion engine and an absorption cooling system. The internal combustion engine has the highest exergy destruction rate, and the cost to produce electricity is USD/h 10.52. The authors conducted an exergoeconomic analysis of a biogas plant for the anaerobic digestion of municipal solid waste in [22]. A cogeneration cycle powered by biomass and natural gas was analyzed using the exergoeconomic method [23]. In this system, a steam Rankine cycle (SRC), a single-effect absorption chiller (SEAC), and an organic Rankine cycle (ORC) are employed as bottoming cycles for the utilization of waste heat from a natural gas–biomass dual-fuel gas turbine. The system achieved a thermal efficiency of 75.69% and an exergy efficiency of 41.76%. The combustion and post-combustion chambers contribute significantly to exergy destruction costs. The SPECO method was used in [24] to analyze an ORC and a Kalina cycle, comparing both cycles in terms of power production. Another combined cycle was investigated by the SPECO method by [24]. The authors in [24] analyzed the Brayton cycle and CO₂ recompression systems with an absorption cooling system. The results show that the combined system has 26.12% higher first-law efficiency and 2.73% higher second-law efficiency than the simple system. Several recent studies have explored the optimization and evaluation of cogeneration systems [20,25,26]. Sendek et al. [27] propose an optimized biomass-powered system for energy production and refrigeration, achieving 32.31% exergy efficiency and an optimized net present value (NPV) of $14.28M. However, the high exergy destruction rate in the combustion chamber was a limitation. In a study of a solar-fossil system for energy, freshwater, and H₂/O₂, Caglayan et al. [28] used 6E analyses (Energy, Exergy, Economic, Environmental, Exergoeconomic, and Exergoenvironmental) and multi-objective optimization. The optimization increased the exergy efficiency to 37.55% and identified the duct burner (DB) as the most significant contributor to exergy destruction.

On the other hand, Hajabdollahi et al. [29] conducted an exergoeconomic analysis to optimize the operating modes of a sugar factory, revealing that the most excellent profitability occurs when both the factory and the electrical grid are served (Scenario I). The turbines were the largest source of irreversibility, and avoidable exergy losses of up to 9.63 MW were identified. Considering the evaluation of an improved tCO₂ cycle and using a vortex tube, Raiyan et al. [30] showed a maximum EUF (Energy Utilization Factor) of 70.44% through the use of exergoeconomic analysis, highlighting the turbine and reactor as the main factors in the system cost, and noting that the limitation in the system was attributed to single-level cooling. Finally, Su [31], focusing on an industrial natural gas cogeneration system (CC, GT, AC and tile dryers), employed advanced exergoeconomic analysis (ADEXEC), where the study identified the tile dryers (WD and GD) as the components with the greatest potential for avoidable improvement, despite the combustion chamber (CC) having the highest exergy destruction cost rate.

A new configuration of four cycles, such as steam–gas cycles and an organic Rankine cycle, a biogas Brayton cycle, and a solar Brayton cycle, for the recovery of energy from hot exhaust gas, as well as their simulation and optimization, are discussed in [32]. Exergy, energy, economic exergy, and environmental exergy (5E) evaluations were conducted for the defined configuration. The exergetic efficiency is 61.7% at the optimum point, and the electricity generation cost is 6.36 cents per kilowatt-hour. The addition of Rankine cycles to the gas cycles increases the exergetic and energy efficiencies to 73.7 and 71.8, respectively.

The growing global demand for sustainability drives the rigorous evaluation of energy and desalination systems. In this context, 4E Analysis (Energy, Exergy, Exergoeconomic, and Exergoenvironmental) emerges as a robust and comprehensive diagnostic tool [33]. In integrated systems, dynamic exergy analysis has been essential for evaluating Hybrid Renewable Energy Systems (HRES) in buildings, given fluctuations in environmental conditions and energy demand, as shown in the literature [34]. In this sense, advanced exergy analysis provides greater accuracy [35], as it decomposes exergy destruction into avoidable/unavoidable and endogenous/exogenous components, thereby providing a more accurate diagnosis for economic and environmental optimization. The application of these methodologies has proven essential in polygeneration systems, where integrating renewable energy with desalination is an efficient option for remote locations [36].

Additionally, improvements in components, such as the incorporation of Phase Change Materials (PCMs) into Solar Air Heaters (SAHs), have demonstrated increased efficiency and reduced payback time, thereby conferring greater economic viability [37]. Aiming at a cutting-edge application, Moharram et al. [38] propose and thermodynamically analyze a multigeneration plant employing supercritical zero-liquid discharge (ZLD) desalination. Although the system presents high efficiency and multiple products, the study highlights practical limitations related to materials and operational safety under supercritical conditions. This underscores that, despite theoretical advances in exergoeconomic methodologies, the industrial implementation of innovative technologies still faces technical and cost barriers that must be overcome. Regarding methodological differences, conventional exergoeconomic analysis identifies the component with the highest inefficiency cost.

In contrast, advanced analysis can estimate the avoidable portion of this inefficiency and discern whether the cause is internal to the component or due to poor integration with the system. This enhanced diagnostic capability, discussed in Fallah et al. [35] and Faizan et al. [33], is crucial for identifying the real potential for system improvement. Despite their effectiveness, these analyses are predominantly used in thermoelectric power plants and are limited to systems that utilize renewable energy. The application of 4E Analysis as an alternative for evaluation and feasibility in polygeneration systems represents a gap in the literature, as does its use in small-scale systems, such as residential systems, which remain unexplored, as existing studies focus on medium- and large-scale systems.

The novelty of this study lies in its unprecedented scale shift, since it adapts the well-established SPECO (Specific Exergy Costing) methodology conventionally used for industrial-grade systems to a distributed residential cogeneration unit. The transition directs a neglected niche in exergoeconomic literature, which is the urban micro-utility. Consequently, by developing a detailed exergy-costing map of a decentralized biogas system powered by residential waste, this work provided a unique benchmark for the feasibility of waste-to-energy solutions in high-density urban environments. The main contributions are as follows:

• Conducting an exergoeconomic assessment of a small-scale cogeneration system powered by biogas from organic waste in a residential building;
• Transforming an environmental liability (organic waste) into an energy asset, aiming to replace high-energy-consuming equipment (electric showers) with more sustainable water heating;
• Detailed component analysis and optimization that not only calculate the exergetic efficiency and exergy destroyed by components, by quantifying the costs of exergy destroyed and other exergoeconomic parameters, but also perform sensitivity analysis, offering clear guidelines for system optimization.

2. System Description

The cogeneration unit was designed to meet the energy demand for power and heat of a residential condominium located in the city of Teresina, Piauí, Brazil. The complex, consisting of 288 apartments across three buildings (approximately 1150 inhabitants), required a system specifically sized to meet its combined power and heat demand. A biodigester, fed by organic matter from the condominium’s food waste, produces the biogas needed to power the cogeneration unit. This unit consists of an internal combustion engine that drives an electric generator set [39,40]. The heat contained in the engine’s exhaust gases is used to heat water in a heat exchanger [41]. Figure 1 shows the cogeneration unit under study.

The internal combustion engine and the generator are evaluated as a single component, hereinafter referred to as ICE. The analysis will be restricted to the engine generator and the heat exchanger. In the geographical region under study, residential water heating is carried out using electric showers, equipment characterized by high energy consumption. Therefore, the hot water produced by the cogeneration unit will replace the use of these electric heaters, making biogas heating a more sustainable option.

In this work, the substrate used to produce biogas was defined as kitchen organic waste. The selected building is being designed. Therefore, the amount of waste generated was estimated based on data from the Teresina Municipal Integrated Solid Waste Management Plan [42]. According to this report, the average amount of Urban Solid Waste generated in Teresina is 1.53 kg/inhab/day. Also, according to the report, the residential waste has an organic fraction of 51.40%. Solid waste is composed of a dry mass and water. Biogas is produced from the dry mass. Volatile solids content represents the portion of the matter that can be used to generate biogas. The values of moisture content and volatile solids content were estimated based on [43]. These values are shown in

Table 1. The initial parameters for the calculation of biogas production (Based on [32]).

Waste Characterization	Value
Volatile solid content	90%
Moisture content	80%
Theoretical Biogas Generation Potential	316.6 NL biogas/kgSV

.

Biogas production can be estimated from volatile solids. In this study, an average of four people per apartment was considered.

3. Thermodynamic Analysis

The thermodynamic analysis begins by defining the biogas energy potential (Teresina, PI, Brazil). For this study, the Lower Heating Value (LHV) of biogas was determined from its methane content. For a methane composition of 65%, the average LHV is 6.4 kWh/m³. The assumed methane concentration of 65% is crucial for determining the LHV and exergy of the system, as it aligns with critical sensitivity parameters widely recognized in several studies from the literature [44]. Vitazek et al. [45] presented a thermodynamic study using biogas as a fuel, considering methane (CH4) and carbon dioxide (CO₂) as the primary components. They confirmed that the LHV of methane is approximately 9.94 kWh/m³ (100%). Consequently, the assumption of 65% concentration conducted to approximate of 6.40 kWh/m³ value, the same used in the work presented by Gartner [44]. In the same context, Krou et al. [46] confirmed a significant production of biogas characterized by a methane content of over 65%. The dependence of thermodynamic efficiencies (First and Second Laws) on fuel composition is an established premise in energy systems, as demonstrated in the work of Yang et al. [47], where the overall exergy efficiency and exergy flows of a cogeneration system depend directly on the molar fraction and LHV of the fuel mixture. Similarly, Wang et al. [48], through exergoeconomic and sensitivity analyses, found that the supplementary use of methane significantly impacts energy and exergy efficiencies, establishing an economic sensitivity linked to the fuel consumption rate. Furthermore, the 65% concentration is supported by the literature analyzing the variability of the raw material, as Ruwa and Abbaso [49] confirmed that increasing the methane content of biogas from 40% to 60% substantially reduces substrate demand (from about 42% to 4%), confirming the correct hypothesis of 65%. The energy potential can be calculated by Equation (1).

$$E_{total}=LHV·V$$

(1)

where $E_{total}$ is the total energy available from the combustion of biogas, in kWh/day, and V is the daily volume of biogas produced; LHV is the Lower Heating Value in kJ/kg. To calculate the energy available in a day, Equation (2) must be applied:

$$E_{av}={\displaystyle \frac{LHV}{\mathrm{86,400}}}$$

(2)

$E_{av}$ The energy is in kW, and 86,400 is the number of seconds in a day. The energy generated by combustion is not fully converted into electrical energy. The exhaust gases and cooling water still contain usable thermal energy. Another part of the energy is lost due to process irreversibilities.

The characteristic curves of the generator motor, such as rotational speed, exhaust gas temperature, and fuel flow rate as functions of workload, are shown in Equations (3) through (6) [39,40].

Table 2. Definitions of variables for the generator and motor characteristic curves.

Variables	Description
$RPM$	Rotation speed
$T_{exau}$	Thermal energy contained in the exhaust gases
${\dot{m}}_{fuel}$	Fuel mass flow rate
${Power}_{ele}$	Electrical power

lists the definitions of variables for the generator and motor characteristic curves.

$$RPM=31.99061897Load-0.06337754$$

(3)

$$T_{exau}=2.37207607Load+499.98932763$$

(4)

$${\dot{m}}_{fuel}=0.11141555Load+0.8377921$$

(5)

$${Power}_{ele}=-0.00014702{Load}^3+0.01973421{Load}^2+1.00516323Load+16.59757459$$

(6)

The electrical power (${Power}_{ele}$), the thermal energy contained in the exhaust gases ($T_{exau}$), rotation speed (RPM, and the fuel mass flow rate (${\dot{m}}_{fuel}$) are shown as the characteristic curves of the engine. The rest of the thermal energy is considered to include losses, such as cooling water, as well as other losses.

The available energy is generated through the chemical reaction of combustion. Equation (7) shows the unbalanced chemical reaction. The coefficients a, b, c, d, e, g, h, i, j, k, and l are the number of moles of each component of the reaction.

a CH₄ + b CO₂ + c (O₂ + 3.76 N₂) + d H₂ + e H₂S + f O₂ + g N₂ = h H₂O + i CO₂ + j H₂SO₄ + k N₂ + l O₂

(7)

3.1. Energy Analysis

The First Law of Thermodynamics for control volumes can be written as in Equation (8), with the kinetic and potential energy terms neglected. The steady state is considered.

$${\dot{Q}}_{in}+{\dot{W}}_{in}+{\sum }_{in}\dot{m}·h={\dot{Q}}_{out}+{\dot{W}}_{out}+{\sum }_{out}\dot{m}·h$$

(8)

$\dot{Q}$ is the heat transfer rate entering or leaving the control volume, $\dot{W}$ the power, ṁ the mass flow, and h the enthalpy. For the internal combustion engine (ICE) control volume, the energy balance is given by Equation (9):

$${\dot{Q}}_{ice}={\dot{W}}_{ice}+\dot{m}(h_p-h_r)$$

(9)

where the subscript P indicates the products of the combustion reaction and the R indicates the reactants. The Equations (10) through (13) model the heat exchanger (HX):

$${\dot{Q}}_{hx}={\dot{m}}_{exa,g}·{cp}_{exa,g}·\left(T_{exa,g,ice}-T_{exa,g,hx}\right)$$

(10)

$${\dot{Q}}_{hx}={\dot{m}}_{water}·{cp}_{water}·\left(T_{water,out}-T_{water\_in}\right)$$

(11)

$${\dot{Q}}_{hx}={UA}_{hx}·{∆T}_{lm,hx}$$

(12)

$${∆T}_{lm,hx}={\displaystyle \frac{\left(T_{exa,g,ice}-T_{water\_in}\right)-(T_{exa,g,hx}-T_{water,out})}{\mathit{ln}\left(\frac{\left(T_{exa,g,ice}-T_{water\_in}\right)}{(T_{exa,g,hx}-T_{water,out})}\right)}}$$

(13)

where the (${\dot{Q}}_{hx}$) represented the heat from the heat exchanger, ($T_{exa,g,ice}$, $T_{exa,g,hx}$), represents the exhaust temperature from the ICE and the HX, $T_{water,out}, T_{water\_in}$, represents the water temperatures, the (${\dot{m}}_{exa,g},{\dot{m}}_{water}$) represents the water flow mass, and the (${UA}_{hx}$) the UA product from the heat exchanger.

3.2. Exergy Analysis

For the exergetic analysis, physical exergy (Equation (14)) and chemical exergy were considered. The exergy of the fuel and exhaust gases is defined by Equation (15). The total specific exergy is given by Equation (16).

$${ex}_{ph}=\left(h-h_0\right)-T_0\left(s-s_0\right)$$

(14)

$${Ex}_{ch}=\dot{n(}\sum _i{y}_i·{\overline{ex}}_i^{ch,0}+\overline{R}·T_0·\sum _i{y}_i·\ln y_i)$$

(15)

$${ex}_{tot}={ex}_{ph}+{ex}_{ch}$$

(16)

Properties with subindex 0 are properties in the dead state, which is a reference state in a default condition. For the working fluids under study, this state is defined at 25 °C and 101 kPa; s is the entropy, and y_i is the molar fraction. The standard chemical exergy is obtained in the literature [42].

Destroyed exergy and exergetic efficiency were calculated according to Equations (17) and (18), respectively:

$${\dot{Ex}}_{dest}=\sum {\dot{m}}_{out}{ex}_{out}-\sum {\dot{m}}_{in}{ex}_{in}$$

(17)

$${\eta }_{ex}={\displaystyle \frac{\sum _{out}\dot{m}·{ex}_{tot}}{\sum _{in}\dot{m}·{ex}_{tot}}}$$

(18)

For ICE, the exergy destroyed is obtained from Equation (19), and the exergetic efficiency from Equation (20). For the heat exchanger effectiveness (ε_HX), the values are determined by Equations (21) and (22).

$${Ex}_{dest, ice}={Ex}_{fuel}-{\dot{W}}_{ice }-{Ex}_{exa,g}-{Ex}_{loss}$$

(19)

$${\eta }_{ex,ice}={\displaystyle \frac{{\dot{W}}_{ice }+{Ex}_{exa,g}}{{Ex}_{fuel}}}$$

(20)

$${Ex}_{dest,hx}={\dot{m}}_{exa,g}·\left({ex}_{tot,exa,g,ice}-{ex}_{tot,exa,g,hx}\right)+{\dot{m}}_{water}.\left({ex}_{tot,water,out}-{ex}_{tot, water\_in}\right)$$

(21)

$${\eta }_{ex,hx}={\displaystyle \frac{{\dot{Q}}_{ex\_real}}{{\dot{Q}}_{ex\_max}}}$$

(22)

3.3. Exergoeconomic Analysis

Exergoeconomic analysis combines thermodynamics, exergy, and economics. Through this analysis, it is possible to define costs for the exergetic flows and, thus, determine the costs of the processes. There are many methodologies of exergoeconomic analysis. The one chosen for this work was often used in the literature [2,24,50]. This methodology is called SPECO (Specific Costing). The SPECO methodology can be defined in four steps:

• The identification of exergy flows;
• The definition of fuel F and product P;
• The allocation of costs to exergetic flows;
• Definition of auxiliary equations by the F and P principles.

Exergy is contained in workflows, heat flows, or mass flows entering and leaving the control volume. For each exergy flow, there is an associated cost. In Equation (23), there is the exergy costing associated with the exergy flow that enters the control volume, in Equation (24), the cost of exergy related to the outgoing flow, in Equation (25), the cost associated with power (w), and in Equation (26), the cost associated with the rate of heat transfer (q).

$${\dot{C}}_{in}=c_{in}{\dot{E}}_{in}=c_{in}{\dot{m}}_{in}{ex}_{tot,in}$$

(23)

$${\dot{C}}_{out}=c_{out}{\dot{E}}_{out}=c_{out}{\dot{m}}_{out}{ex}_{tot,out}$$

(24)

$$\dot{C_w}=c_w\dot{W}$$

(25)

$$\dot{C_q}=c_q{\dot{E}}_q$$

(26)

$c_q, c_w, c_{out},c_{in}$ are the average costs per unit of exergy, while Ċ_q, Ċ_w, Ċ_in, Ċ_out are the monetary costs associated with the flow of exergy and extot the specific exergies. For each component, there is a cost balance including all its exergetic flows, as we can see in Equation (27), costs associated with the investment capital, operation, and maintenance of the components (Ż).

$$\sum _e{\left(c_e{\dot{E}}_e\right)}_k+c_{w,k}{\dot{W}}_k=c_{q,k}{\dot{E}}_{q,k}+\sum _i{\left(c_i{\dot{E}}_i\right)}_k+{\dot{Z}}_k$$

(27)

Ż is the cost associated with the c capital, operation, and maintenance of the components of each k component. The exergy cost balance can then be summarized as in Equation (28):

$${\dot{C}}_{p,tot}={\dot{C}}_{f,tot}+{\dot{Z}}_{tot}$$

(28)

${\dot{C}}_{p,tot}$ is the cost required to generate the product, Ċ_f,tot is the fuel cost rate, and Ż_tot is the sum of the costs associated with installation, maintenance, and operation. The unit of these rates is USD/h.

Table 3. Exergoeconomic equations.

Component	Fuel	Product	Auxiliary Equation	Exergoeconomic Balance
Internal Combustion Engine +Generator	${\dot{C}}_2$	${\dot{C}}_w+{\dot{C}}_3$	-	$\begin{array}{l}{\dot{C}}_w+{\dot{C}}_3=\\ {\dot{C}}_2+{\dot{Z}}_{ice}\end{array}$
Heat Exchanger	${\dot{C}}_3-{\dot{C}}_4$	${\dot{C}}_6-{\dot{C}}_5$	${\dot{C}}_3={\dot{C}}_4$	${\dot{C}}_6-{\dot{C}}_5={\dot{C}}_3-{\dot{C}}_4+{\dot{Z}}_{hx}$

presents the equations for the exergetic costs of the product and the components’ fuel, the exergoeconomic balance, and the auxiliary equations. Auxiliary equations are necessary for all costs to be determined and are guided by the F and P principles according to the literature [32]. For exergoeconomic analysis, it is important to define which flow is the product and which is the fuel. Mass flows that have increased exergy and are part of the component’s objective are considered products. If the mass flows have decreased exergy or have increased exergy but are not part of the component’s objective, they are regarded as products.

The costs of installation, operation, and maintenance (Ż) are defined as input parameters for exergoeconomic analysis. The acquisition and installation costs of the equipment were calculated using the economic analysis methodology proposed by Kotas [43]. The calculation of the installation, operation, and maintenance cost rate was based on Lazzaretto and Tsatsaronis [50]. This rate can be defined by Equation (29):

$${\dot{Z}}_k={\dot{Z}}_k^{CI}+{\dot{Z}}_k^{OM}$$

(29)

${\dot{Z}}_k$ is the investment and installation cost, and ${\dot{Z}}_k^{OM}$ the operation and maintenance, defined by Equations (30) and (31), respectively:

$${\dot{Z}}_k^{CI}={\displaystyle \frac{CRF}{{\eta }_h}}{Z}_k$$

(30)

$${\dot{Z}}_k^{OM}={\displaystyle \frac{\phi }{{\eta }_h}}{Z}_k$$

(31)

CRF is the capital recovery factor, defined by Equation (32), η_h the number of hours of annual operation, set to 8000 h, $\phi$ the maintenance factor, determined with the value of 5%, i the annual interest rate of 10%, and n_annual the useful years of the plant operation considered by 10 in this study. Those values were chosen from the literature [21,27,33]. The USD quotation was made on 5 August 2025 (rate of exchange used: 1 USD = BRL 5.46, Central Bank of Brazil [51]).

$$CRF=i· \left({\displaystyle \frac{{\left(1+i\right)}^{n_{annual}}}{{\left(1+i\right)}^{n_{annual}}}}\right)$$

(32)

The acquisition costs of the cogeneration system equipment, the generator motor (USD 23,065.39), and the heat exchanger (USD 6458.31) were selected from the literature [39] and updated using Equation (33) from Bejan et al. [52]

$$Update cost=original cost \left({\displaystyle \frac{{CI}_{RY}}{{CI}_{PY}}}\right)$$

(33)

where CI_RY is the cost index in the reference year (2025), and CI_YP is the cost index in the year the equipment was originally acquired. These indices were selected according to what is established in the literature [53]

In addition to the exergetic cost balance for each component, exergoeconomic parameters can be calculated to evaluate equipment performance. These are: the average cost per unit of energy input (c_f,k), the average cost per unit of product exergy (c_p,k), the relative cost difference (r_k) the exergoeconomic factor (f_k) and the cost rate associated with the destroyed exergy (Ċ_d,k) given by Equations (34)–(38), respectively.

$$c_{f,k}={\displaystyle \frac{\dot{c_{f,k}}}{{\dot{Ex}}_{f,k}}}$$

(34)

$$c_{p,k}={\displaystyle \frac{\dot{c_{p,k}}}{{\dot{Ex}}_{p,k}}}$$

(35)

$$r_k={\displaystyle \frac{\dot{{\dot{c}}_{p,k}}-{\dot{c}}_{f,k}}{{\dot{c}}_{f,k}}}$$

(36)

$$f_k={\displaystyle \frac{{\dot{Z}}_k}{{\dot{C}}_{d,k}+{\dot{Z}}_k}}$$

(37)

$${\dot{C}}_{d,k}={\dot{c}}_{f,k}.{\dot{Ex}}_{d,k}$$

(38)

4. Results and Discussion

This section presents the results obtained from the energy, exergy, and exergoeconomic analyses of the biogas cogeneration unit. Following this, the parametric analysis is presented, including thermal power and heat flow rate, exhaust and water temperatures, efficiencies based on the first and second Law of Thermodynamics, and the exergoeconomic analysis, and finally, a consolidated critical discussion of the goal of the study is presented.

4.1. Energetic, Exergetic, and Exergoeconomic Results

Balanced biogas combustion used 15% excess air for combustion, as it was used in the literature [39,40]. From this balance of the reaction equation, it was possible to calculate the enthalpies of the fuel and exhaust gases.

Table 4. Values of biogas production and energy potential.

Parameter	Value
Organic matter	17.56 kg·hab·day
Total organic matter	20251.72 kg·day
Mass of solids	4046.01 kg·day
Mass of volatile solids	3644.20 kg·day
Volume of biogas produced	1152.66 Nm3/day
Total energy available from burning biogas	407.39 kW
Generated electrical power	167.40 kW
Heat in the exhaust gases	51.55 kW
Heat in the cooling system	51.55 kW
Losses in transmission and heat to the environment	64.75 kW

presents the calculated biogas production values. Based on the estimated waste volume, 1153 Nm³/h of biogas is produced. The electricity produced is 167.4 kW, considering 100% of the engine load. The value of the heat contained in the exhaust gases does not include the heat exchanger for heating water, but rather the energy that would be lost, along with the losses associated with its irreversibilities. The electricity (BRL/kWh 1.4) and the Biogas (BRL/m³ 0.9) tariffs were selected by the local companies [54,55]

Table 5. Thermodynamic properties of the points of the cogeneration unit under study.

Points	Fluid	Temperature (°C)	Enthalpy (kJ/kg)	Mass Flow (kg/s)	Entropy (kJ/kg·K)
1	Air	25.00	298.6	0.1665	5.695
2	Biogas	25.00	−5781	0.0119	9.435
3	Exhaust Gases	737.20	−1741	0.1784	8.314
4	Exhaust Gases	512.20	−2023	0.1784	7.998
5	Water	25.00	104.9	0.2000	0.367
6	Water	86.37	361.7	0.2000	1.150

shows the thermodynamic properties of the working fluids of the system. The hot-water inlet temperature to the heat exchanger was set to 25 °C. As the water is intended for bathing use, this is an adopted average temperature. The exhaust gas temperature was adopted based on the characteristics curve [39,40].

Table 6. Exergetic properties and exergy costs.

Points	Fluid	Physical Exergy (kJ/kg)	Chemical Exergy (kJ/kg)	Total Specific Exergy (kJ/kg)	Total Exergy (kW)	Average Specific Cost (USD/GJ)	Exergy Costing (USD/h)
1	Air	0.00	0.00	0.00	0.00	0.0000	0.0000
2	Biogas	0.00	54520	35669	427.3	0.01312	47.2500
3	Exhaust Gases	357.40	102.9	460.3	82.13	0.02443	87.9400
4	Exhaust Gases	75.21	102.9	178.1	31.78	0.00945	34.0300
5	Water	0.00	49.96	49.96	9.99	0.00000	0.0000
6	Water	23.36	49.96	73.32	14.66	0.01527	54.9800

shows the exergy values and the respective exergetic costs. The air is in dead state conditions and has no exergy. Biogas is also in a dead state, so its physical exergy is zero, but it has a considerable chemical exergy value. The heat transfer rate between the exhaust gases and the water exceeds 100.00 kW. If there were no cogeneration, this energy potential of the exhaust gases would be lost.

Table 7. Results of energetic and exergetic analyses.

Component	Electrical Power (kW)	Heat transfer Rate (kW)	Exergy Destroyed (kW)	Energetic Efficiency (%)	Exergetic Efficiency (%)
ICE + Generator	167.40	163.20	223.65	42.00	39.19
Heat exchanger	-	51.55	45.67	31.39	9.29

shows the values of the energetic and exergetic analyses. It can be observed that the energetic and exergetic efficiencies were 42% and 31%, respectively, for the ICE unit, and 39% and 9%, respectively, for the heat exchanger. It can be observed that the energetic and exergetic values from the heat exchanger are low due to the energy lost during the heating process. This loss signals an opportunity for reuse that could be better exploited, such as using this residual thermal energy to power an absorption system. However, the overall performance of the cogeneration system was significantly positive with the implementation of this heat exchanger. Its inclusion increased the system’s energy and exergy efficiency by almost 40% (energetic efficiency) and 23% (exergetic efficiency), respectively, compared to the scenario of exclusive electricity production.

Table 8. Results of exergoeconomic parameters.

Component	Cost of Product (USD/GJ)	Cost of Fuel (USD/GJ)	Cost of Exergy Destroyed (USD/h)	Monetary Costs (USD/h)	Relative Difference	Exergoeconomic Factor (%)
ICE + Generator	1.141	0.6038	135.00	4.913	0.8902	16.58
Heat exchanger	38.980	3.468	158.40	1.376	10.240	4.53

shows the exergoeconomic results. It is interesting to note that although the exergy destroyed from the internal combustion engine (223.65 kW) is greater than that from the heat exchanger (45.67 kW), the cost of the exergy destroyed (USD/GJ 158.40) is greater in the heat exchanger than in the internal combustion engine (USD/h 135). The relative difference parameter in the heat exchanger also has a value much higher than expected (10.240). This is because the product’s cost (USD/GJ 38.98) is well above the cost of fuel (USD/GJ 3.468). When a device has a high rk and a low f_k, it indicates a need for improvement [24]. This is observed in the heat exchanger. It was found that the cost of the product, that is, the cost to produce hot water, is higher than that of others.

4.2. Parametric Analysis

The selection of parameters for the sensitivity analysis focused on the variables that most impact the performance and economic viability of the biogas cogeneration unit. The ICE load was chosen because it represents the system’s actual operation, linked to the Biogas mass flow rate as the engine’s starting input (fuel), and is therefore directly linked to the available energy and, consequently, to the generated electrical power (the engine’s main product). Variations in engine load directly influence the viability of the proposed cogeneration unit. Regarding the use of residual heat, the gas temperature in the heat exchanger is essential, as it directly determines the energy reused for water heating and is a critical parameter for the process’s efficiency. The last two parameters represent the thermal product. The water outlet temperature is linked to the quality of the thermal product (hot water) generated by the cogeneration system (the secondary product). It also showed the performance of the ICE, HX, and cogeneration system in terms of energy efficiency. These parameters should be impacting the electric and thermal energy produced for the residence. Several studies in the literature used the same analogy [20,39,56,57].

Figure 2 shows a significant increase in thermal power as the cogeneration system’s load increases. A notable aspect is the energy potential of biogas, which serves as a renewable source powering the system. Obviously, the increased energy released during biogas combustion results in greater hot water production and greater heat loss to the environment. It is important to note that the heat loss includes the portion extracted by the engine’s cooling water, which is not being used in this study. The available useful heat for water heating can be used for various purposes in residential complexes, such as powering absorption chillers for air conditioning and supplying water for daily tasks (cleaning, cooking, etc.).

4.2.1. Energetic Analysis Results

The performance of the thermal heat flow rates, varying the ICE load, was evaluated to verify cogeneration behavior. Figure 2 shows the thermal flow rates of the cogeneration system presented.

A nominal load of 100% corresponds to the operating point with the highest electrical and thermal gains, providing approximately 167 kW of electricity and 55 kW of heating, with the final average water temperature reaching 86 °C, Figure 3, which is good to activate a small absorption chiller, as the ones shown in the literature [52]. Figure 3 shows the temperature profiles of the exhaust gases and the water from the heat exchanger. It can be observed that, even at minimum partial engine load, the system is able to produce electricity and hot water at approximately 60 °C, with a cogeneration energy efficiency of 64%. This represents a viable alternative for small residential complexes, enabling daily electricity and hot water from biogas consumption.

Regarding temperatures, the maximum load (100%) maintains the water at around 86 °C, a value sufficient both for operating a small absorption chiller, as cited in the literature, and for daily household utilities [39,58]. The generated electrical power reaches its maximum at 100% load (Figure 4). At minimal engine load (30%), the system could produce around 60 kW with a 60% cogeneration efficiency.

In turn, the energy efficiency of the internal combustion engine (ICE) reaches a maximum of 40% in the 60–70% load range. This efficiency can be improved by more than 45% by using exhaust gases to heat the water (Figure 4). On the other hand, the heat exchange rate’s efficiency decreased significantly as the load increased. This is because, at higher temperatures, exergy destruction increases, reducing the heat exchanger’s efficiency to approximately 32%.

4.2.2. Exergetic Analysis Results

Figure 5 shows the parametric exergetic results of the cogeneration system. Based on the analysis of the engine and heat exchanger performance curves, the cogeneration system’s exergy efficiency peaks at partial loads (40% to 70%), indicating this range as the thermodynamically ideal operating zone. This is related to the optimized balance between irreversibilities and power production, since in this region, the Internal Combustion Engine (ICE) achieves maximum individual efficiency. However, a downward trend in overall cogeneration efficiency at full load (100%) is shown, which is linked to the exponential increase in exergy destroyed in the ICE, increasing the temperature difference and losses to the environment, leading to exergy destruction at a rate higher than the utilization of useful power, in addition to not utilizing the hot water from the engine cooling jackets, which in this case were considered as losses to the environment.

On the other hand, the Heat Exchanger (HX) exhibited a low exergy efficiency (≈9%), reflecting greater exergy destruction. This irreversibility is linked to the high temperature difference between the exhaust gases and the water. Therefore, the system exhibits better exergy efficiency at partial load, where exergy loss or destruction decreases (128 kW) relative to the utilization of residual heat (102 kW) and electricity generation (132 kW).

4.2.3. Exergoeconomic Analysis

A parametric analysis of the cogeneration system using the parametric methodology was conducted to verify the sensitivity of the exergetic costs of the ICE and HX to partial-load variations in the production of hot water and electricity. Figure 6 and Figure 7 show the exergoeconomic parameters (r_k and f_k) when the motor load and the dollar exchange rate vary. These parameters allow us to identify the need to improve the monetary costs of the system based on components that present a high relative cost difference r_k, and with high exergoeconomic factors fk (aiming at the viability of reducing capital investment in the component at the expense of component efficiency), and with low f_k values (aiming at improving component efficiency by increasing investment). It is important to note that this variation in the dollar exchange rate was selected based on the changes over the last 5 years in Brazil.

As shown in Figure 6, although the total exergy efficiency peaks at partial loads (50% to 70%), optimal savings were achieved at 100% (the system’s nominal load). From a generation perspective, this point is the most profitable, as it minimizes the cost ratio (rk), which falls from 1.5 (30% load) to 1.1 (100% load), indicating a lower cost per unit of output exergy. Furthermore, the exergoeconomic factor (fk) for both components (ICE and HX) decreases abruptly (from 0.38 to 0.16), indicating that the cost of exergy destruction becomes proportionally less relevant relative to fixed and fuel costs at full load.

On the other hand, fluctuations in the exchange rate of the dollar demonstrate the Brazilian economy’s economic vulnerability. In cases where the dollar exchange rate increases (from BRL/USD 4.00 to 6.00), there is an increase in exergoeconomic factors (from 0.13 to 0.18). This is because, as capital and maintenance (O&M) costs are economically dollarized, the implicit thermodynamic inefficiency of the engine and heat exchanger becomes relatively more expensive. Therefore, the most suitable configuration, from this point of view, is one in which the dollar exchange rate is lower, around 4, as this mitigates the impact of investment costs and preserves the competitiveness of the exergy produced.

Figure 8, Figure 9 and Figure 10 show the costs associated with exergy destruction, monetary system costs, and other factors as functions of variations in the dollar exchange rate, the interest rate used, and the ICE load. Figure 8 shows the variation in costs as a function of the dollar exchange rate (BRL/USD). A significant increase is observed in all exergy costs (c) and in the cost related to destroyed exergy (Cd) as a function of the rise in the dollar exchange rate. In reference to the product costs (cp) and the cost of destroyed exergy (C,d, HX) for the system component, these were the most sensitive. This suggests that the input cost (input exergy) and the monetary costs of investment and maintenance are closely linked to the dollar exchange rate (4.0 to 6.0), making the operation vulnerable to the economic environment, as described in Figure 7.

On the other hand, Figure 9 shows the performance of these costs relative to variations in the interest rate in the economic analysis. It can be observed that the exergy costs of the fuel and product of the MCI (cf,ICE and cp,ICE) and of the HX (cf,HX and cp,HX) are independent of the interest rate in this range, as they remain constant. Therefore, the portion of the total cost influenced by the interest rate (capital/investment costs) may be minor, and the operational share (fuel) may not have been sufficient to cause significant impacts. On the other hand, the cost of exergy destroyed (C,d,HX) and the cost of product of the HX (cp,HX) show a slight but significant increase with increasing interest rates, around 8%. This is obvious, since an increase in the interest rate raises the capital recovery factor, thereby increasing the value of the investment and, therefore, the costs of exergy destroyed and the product.

Finally, Figure 9 shows the variation in expenses with operational load. It can be observed that the exergy cost of the HX product (c_p,HX, and c_pxICE) decreases sharply with increasing load, reaching its minimum at 100% of the maximum load, indicating that the energy and exergy efficiency of the HX decrease with operational load.

Operating at partial loads below 70% implies significantly higher product costs (above USD/GJ 50). Regarding the cost of exergy destroyed (C_d,HX, and C,_d,ICE), they increase with load and reach their maximum at 100% load. This is due to the increased load, which generally involves a higher fuel flow rate and combustion gases, increasing the rate of entropy generation in the components, in this case, the combustion chamber. The fuel exergy cost (c_f) remains relatively constant throughout the range. The best operating range to minimize the monetary cost per unit of product (c_p) is at full load, where the highest exergy efficiency is achieved. In the case of HX, the cost drops from approximately USD/GJ 80 (30% load) to less than USD/GJ 40 (100% load). The 90% to 100% load range appears to be the optimal range for balancing reducing product cost with maximizing total exergy efficiency, even with the increased cost of exergy destruction.

4.3. Consolidated Critical Discussion

The study verified significant results about the cogeneration system presented, even though some findings are very low as it can be expected, as shown in the heat exchanger, where its analysis reveals a significant disparity between energy efficiency (approx. 31%) and exergy efficiency (approx. 9%), a phenomenon explained by the qualitative nature of exergy. This low exergy performance stems from the degradation of energy quality due to the large thermal gradient between the exhaust gases at 737.20 °C and the water at 25 °C. From a thermodynamic point of view, this significant temperature difference is the primary source of entropy, leading to a high rate of exergy destruction due to irreversibility. Consequently, although a considerable amount of heat is recovered (51.55kW), its usefulness is limited by the final water temperature (86.37 °C) compared to the high thermal potential available at the component’s inlet. Despite the low individual efficiency of the HX, the overall system gain is justified by the transition from a simple to a cogeneration cycle. The implementation of heat recovery increased the system’s energy efficiency to 55% and exergy efficiency to 48%, representing increases of almost 40% and 23%, respectively, compared to the exclusive electricity production scenario. Without cogeneration, the exergy potential of the gases would be entirely wasted as environmental losses; with HX, the system converts a liability into an energy asset. It can be observed that the performance could be even greater if the heat from the engine cooling water were used to drive an absorption chiller, as suggested in the literature [20,21,39]. Although the high production cost of HX (38.98 USD/GJ) and its high relative cost differential (r_k = 10.24) identify it as the efficiency bottleneck and the priority component for optimization, any use of residual heat proves superior to complete disposal.

Finally, the system demonstrates viability by serving as a technological replacement at the residential scale, the focus of this research. In the context of Teresina, Brazilian northeast, where water heating largely relies on high-consumption electric showers, the use of biogas for this purpose enables the condominium to convert organic waste into a strategic asset. This substitution directly reduces electricity bills, making cogeneration more economically attractive than isolated electricity generation. Parametric analysis confirms that the unit cost of the product is minimized when the system operates at full load (100%), at which point overall efficiency is maximized. The impact of dollar-denominated fixed costs is diluted, optimizing the relationship between production cost and thermodynamic efficiency.

5. Conclusions

The objective of this work was to perform an exergoeconomic analysis of a biogas-powered cogeneration unit to meet the energy demands of a residential condominium with 288 apartments, using organic waste for biogas production across three buildings (approximately 1150 in-habitants), required a system specifically sized to meet its combined power and heat demand. The cogeneration system consists of an internal combustion engine (ICE) coupled to an electricity generator and a heat exchanger (HX) for water heating. Among the main conclusions are:

• The electricity production was 167.40 kW, with 100% engine load and a heat transfer rate of 51.55 kW.
• The exergy destroyed in the Internal Combustion Engine (ICE) was 223.65 kW, while in the heat exchanger (HX) it was 45.67 kW. Regarding exergy efficiencies, the ICE reached 39.19%, while the HX had a low value of around 9%. The low efficiency of the heat exchanger (HX) was attributed to the significant temperature difference between the exhaust gases and the water, resulting in a small temperature and exergy difference across the product fluid (hot water). This indicated a considerable portion of exergy was being wasted.
• The inclusion of the heat exchanger (HX) resulted in a significant improvement in the overall performance of the cogeneration system, with an increase of almost 40% in energy efficiency and 23% in exergy efficiency compared to the electricity-only production scenario.
• In reference to the exergoeconomic analysis, the exergy destroyed in the MCI (223.65 kW) was greater than in the HX (45.67 kW); the cost of the exergy destroyed was significantly higher in the HX (USD/h 158.40) than in the ICE.
• The cost of producing hot water (product) was considered extremely high at USD/GJ 38.98, a value well above the cost of the input fuel at USD/GJ 3.468.
• In reference to the exergoeconomic parameters, the relative cost difference (rk) in the HX was very high (10.24) with a low exergoeconomic factor fk (4.53%), indicating that the heat exchanger represents the component in need of optimization.
• The best operating range to minimize the unit cost was at full load (100%). At this load, the HX product cost drops from approximately USD/GJ 80 (30% load) to less than USD/GJ 40. The 90% to 100% load range represents the ideal region to counterbalance the reduction in product cost and the maximization of total exergy efficiency, despite the increased cost of destroyed exergy.
• Fluctuations in the dollar exchange rate (BRL/USD) demonstrated the economic vulnerability of the system. The increase in the exchange rate (from BRL/USD 4.00 to 6.00) raised the exergoeconomic factors fk from 0.13 to 0.18, as capital and O&M costs are susceptible to dollar fluctuations. The most suitable configuration is one with a lower exchange rate (around 4.0) to mitigate the impact of investment costs.
• The study concludes that the cogeneration unit is more justifiable based on the savings from thermal energy production than from isolated electricity production, as the system demonstrated significant increases in energy and exergy efficiencies of up to 55% and 48%, respectively.
• Research data indicates that the cycle must be optimized to be technically and economically viable. For example, such a cycle should be applied in condominiums with higher waste generation, that is, with a greater concentration of people;

For future work, it is recommended that an analysis of economic factors and a new proposal for cogeneration or trigeneration using biogas in small power plants be undertaken.