Exergoeconomic Evaluation of a Cogeneration System Driven by a Natural Gas and Biomass Co-Firing Gas Turbine Combined with a Steam Rankine Cycle, Organic Rankine Cycle, and Absorption Chiller

Abstract

Considering energy conversion efficiency, pollution emissions, and economic benefits, combining biomass with fossil fuels in power generation facilities is a viable approach to address prevailing energy deficits and environmental challenges. This research aimed to investigate the thermodynamic and exergoeconomic performance of a novel power and cooling cogeneration system based on a natural gas–biomass dual fuel gas turbine (DFGT). 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 waste heat cascade utilization of the DFGT. The effects of main operating parameters on the performance criteria are examined, and multi-objective optimization is accomplished with a genetic algorithm using exergy efficiency and the sum unit cost of the product (SUCP) as the objective functions. The results demonstrate the higher energy utilization efficiency of the proposed system with the thermal and exergy efficiencies of 75.69% and 41.76%, respectively, while the SUCP is 13.37 $/GJ. The exergy analysis reveals that the combustion chamber takes the largest proportion of the exergy destruction rate. The parametric analysis shows that the thermal and exergy efficiencies, as well as the SUCP, rise with the increase in the gas turbine inlet temperature or with the decrease in the preheated air temperature. Higher exergy efficiency and lower SUCP could be obtained by increasing the SRC turbine inlet pressure or decreasing the SRC condensation temperature. Finally, optimization results indicate that the system with an optimum solution yields 0.3% higher exergy efficiency and 2.8% lower SUCP compared with the base case.

1. Introduction

Energy consumption has been on a long-term upward trend, paralleling the rapid advancement of societal and economic sectors. As the primary energy source, fossil fuels satisfy approximately 80% of the world’s total energy demand [1]. The global CO₂ emissions from fossil fuel combustion have increased by 2.5% annually on average in the last decade [2]. The large-scale energy consumption of fossil fuels all over the globe is responsible for the serious environmental problems, like global warming and air pollution. Additionally, the energy crisis has catalyzed a shift towards optimizing the use of non-renewable energy sources and advancing the development of renewable energy alternatives.

Biomass, characterized as a renewable energy source, produces minimal-to-zero carbon dioxide emissions and predominantly originates from sources, including forests, agricultural residues, municipal solid waste, sewage, and industrial by-products [3]. In general, biomass energy can help mitigate the environmental problems and improve the energy self-sufficiency of nations that rely on imported fossil fuels. Numerous contemporary energy strategies are in place to facilitate the adoption of biofuels. According to the survey of IEA (International Energy Agency), in China, biofuels contribute around 1.90% of the total energy supply for electricity generation [4].

There are still many problems impeding the widespread use of biomass for power generation. The energy conversion efficiencies of biomass-based power plants are relatively low, typically ranging from 15% for small plants to 30% for large ones, in comparison with the most efficient energy conversion plants, such as the natural gas combined cycles [5]. Furthermore, the use of biomass or biomass-derived fuels in the power plants has some limitations regarding fuel flexibility and system reliability, as well as economic feasibility. The investment and operational costs related to biomass processing and transport facilities are expensive for large-scale utilization [6]. To overcome these drawbacks, researchers have integrated biomass into conventional fossil fuel power generation systems, in which biomass serves as a supplementary fuel [7,8]. In particular, for a gas turbine (GT) cycle, biomass or biomass-derived fuel burns at the end of the GT cycle in a supplementary firing chamber, capitalizing on the surplus oxygen present in high-temperature combustion gases. This method not only maintains system functionality but also curtails the consumption of natural gas and CO₂ emissions, further augmenting system efficiency through the integration of bottoming heat recovery systems [9,10]. Moreover, the mechanism of biomass post-combustion provides the possibility of using commercially available components or directly combine with the commercial micro gas turbine (MGT) without major modifications [11].

In recent years, various solutions for coupling biomass with natural gas in the GT-based power plants have been proposed. Riccio et al. [11] matched an externally biomass-fired cycle with a commercial MGT and theoretically evaluated the thermodynamic performance of the plant. They found that the system could achieve a net electric efficiency of 21.8% when the biomass accounted for 70% of the total energy input. Gnanapragasam et al. [12] investigated a GT-based combined cycle with the external combustion of biomass in a supplementary firing chamber. They found that the reduction in CO₂ emissions and natural gas could reach 20 g/kWh and 1.5 kg/s, respectively. Pantaleo et al. [13] analyzed various operational approaches for a small-scale combined heat and power system using a natural gas-biomass DFGT. Their findings revealed that thermal and electrical conversion efficiencies fluctuate between 46 and 38% and 30 and 19%, respectively, with system efficacy showing an inverse relationship with the rate of biomass input. Furthermore, their research deduced that optimal investment returns are attainable when the biomass input constitutes 70%, taking into account Italy’s biomass electricity incentives, investment expenditures, and energy conversion efficiency [6]. Barzegaravval et al. [14] studied the impact of the biogas composition on both the exergetic and economic aspects of the GT cycle’s performance. They reported that the cost of generated electricity varies from 0.05 $/kWh to 0.18 $/kWh when the fuel price increases from 3 $/GJ to 14 $/GJ. Also, the idea of a biomass and natural gas co-fired combined cycle by employing the SRC as a bottoming cycle for power generation has been proposed and extensively studied [15,16,17]. Soltani et al. [18] examined a biomass-integrated fired combined cycle (BIFCC) from the viewpoints of energy and exergy. Their observations noted that, across the explored range of operational parameters, the energy efficiency varied between 46.48% and 53.16%.

Another key factor in improving the efficiency of a GT-based combined cycle is the selection of proper energy conversion techniques based on the heat source characteristics to reduce the irreversible losses. Recently, many researchers combined various waste heat recovery systems with GT cycles using biofuels for multi-generation. Gholizadeh et al. [19] conducted an exergoeconomic evaluation of a bi-evaporator power and cooling cogeneration system with a topping biogas-powered GT cycle. They reported achieving overall thermal and exergy efficiencies of 62.69% and 38.75%, respectively, with a total unit cost of 7.75 $/GJ. Yilmaz et al. [20] evaluated a biomass-solar multi-generation system from the techno-economic perspective. In the study, the GT cycle was driven by biogas, with its waste heat being utilized for a Kalina cycle, an SEAC, and a heat pump cycle (HPC). The findings revealed overall energy and exergy efficiencies of 63.84% and 59.26%, respectively. Zhang et al. [21] assessed a multi-generation system consisting of a biogas-fueled GT, a compressed air energy storage (CAES), and a ground source heat pump (GSHP) from thermodynamic and economic viewpoints. They defined the round trip efficiency and exergy efficiency to evaluate the system operation characteristics, and their values were calculated to be 90.06% and 31.52%, respectively. Asgari et al. [22] thermodynamically evaluated a GT-based trigeneration system fed by both natural gas and syngas derived from municipal solid waste. In this system, the waste heat from the GT cycle and the gasification unit is used as the heat source of two heat recovery steam generators (HRSGs), while an SEAC and a heating unit are driven by the steam. The outcomes showed that the annual energy utilization factor and exergy efficiency of the overall system are 71.25% and 30.79%, respectively. Zoghi et al. [23] undertook exergoeconomic and environmental examinations of a biomass-solar multi-generation system. This system utilizes the waste heat from a GT cycle as a heat source for an SRC, a domestic water heater, and a LiCl-H₂O SEAC. Their findings indicated that, in the base scenario, the overall exergy efficiency reached 43.11%, marking an increase of 9.04% over the exergy efficiency of a standalone GT cycle.

Previous research findings have demonstrated that combining biomass energy with waste heat recovery systems in the GT cycle stands as a highly effective approach to improve energy conversion efficiency and meet the various energy demands of users. Steam Rankine cycles, widely recognized as a leading technology for waste heat recovery, are typically employed to recover medium- or high-temperature waste heat due to the advantages of the working fluid with a high decomposition temperature, non-toxicity, environmentally friendliness, and cost-effectiveness [24]. However, in most studied SRCs, a considerable volume of thermal energy is released into the atmosphere, remaining unutilized, throughout their condensation processes. One effective way to recover the condensation latent heat is using LiBr/H₂O absorption refrigeration systems, which are available to utilize the heat source with a temperature ranging from 50 °C to 200 °C [25]. Liang et al. [24,26] investigated a cogeneration system by coupling an SRC and an SEAC to recover the waste heat of a marine engine. Their research indicated that the exergy efficiency of the cogeneration system increases by 84% compared with the basic SRC under conditions of a condensation temperature at 323 K and superheat at 100 K. Sahoo et al. [27] analyzed a solar-biomass multi-generation system, utilizing the residual heat from the SRC to power an SEAC. Their study demonstrated that the system’s energy and exergy efficiencies could achieve 49.85% and 20.94%, respectively. Ahmadi et al. [28] performed an exergo-environmental analysis of a GT-based trigeneration system integrated with an SRC and a steam-driven SEAC. They reported the thermal and exergy efficiencies of 75.5% and 47.5%, respectively. Anvari et al. [29] applied advanced exergetic and exergoeconomic concepts to assess a GT-based trigeneration system using a dual pressure HRSG and a steam-driven SEAC as bottoming cycles. They identified that nearly 29% of the exergy destruction in the cycle and the corresponding cost rates are endogenously avoidable. Nondy et al. [30] thermodynamically evaluated four GT-based cogeneration systems, in which the SEAC is driven by the heat from the SRC or exhaust gas. They concluded that the system with two SEACs driven, respectively, by steam and exhaust heat is the most appropriate from the viewpoints of energy and exergy.

A comprehensive examination of the aforementioned research suggests that the natural gas combined with biomass energy is a practicable scheme for GT-based multi-generation systems from the technical and economic aspects, which can help to reduce the fossil fuel consumption and mitigate the environmental impact. The literature review also reveals that the coupling of SRC and SEAC contributes to further improving the energy utilization efficiency. Based on recent studies [15,18], some of the researchers have already conducted the thermodynamic and exergoeconomic analyses of a biomass-integrated co-fired combined cycle (BICFCC), in which the waste heat of the DFGT cycle is only converted into power by the SRC or ORC.

To the best of the authors’ knowledge, there have been few studies on BICFCC to date. The novelty of this work lies in expanding the application of BICFCC to power and cooling cogeneration systems through the integration of high-efficiency subsystems, including an SRC, an SEAC, and an ORC. These subsystems are not typically utilized in BICFCC configurations, highlighting the unique contribution of this research. The exhaust gas flows into the SRC and ORC in sequence for power, while the condensation heat of the SRC is converted into the cooling capacity by the SEAC. Compared with the BICFCC, the cogeneration system in this work could exploit the waste heat sufficiently to achieve the higher energy utilization efficiency and satisfy different kinds of energy demands. The primary purposes of this work can be considered as follows:

(1)

A novel DFGT-based cogeneration system is proposed, and detailed thermodynamic and economic models are developed for simulating the system’s performance.

(2)

In-depth parametric analysis is carried out to assess the impact of crucial operation parameters on the performance criteria.

(3)

Multi-objective optimization is performed to ascertain the most favorable operating conditions for the proposed system.

2. System Description

Figure 1 illustrates the schematic diagram of the cogeneration system. As is indicated, the topping cycle is a DFGT fed by natural gas and biomass. The bottoming cycles include an SRC, an SEAC, and an ORC. The waste heat produced by the DFGT is employed sequentially to drive both the SRC and ORC systems, facilitating power generation. Furthermore, the SEAC system is powered by the condensation heat released from the SRC to facilitate cooling production. The working principles of these subsystems can be described as follows.

In the DFGT cycle, ambient air (stream 1) undergoes compression in an air compressor (AC), leading to its entry into the air preheater (AP) where it is heated by the flue gas (stream 10). Subsequently, the heated air (stream 3) reacts with the injected natural gas (stream 4) within the combustion chamber (CC), resulting in the production of high-temperature combustion products (stream 5) that are then expanded in the gas turbine (GT) to generate power. Additionally, the syngas (stream 9) derived from the biomass gasifier (Ga) is conveyed into the post-combustion chamber (PCC), where it undergoes a reaction with the oxygen present in the exhaust gas (stream 6) from the GT. This process leads to an elevation in both the mass flow rate and temperature of the flue gas. Subsequent to the release of heat to the compressed air within the AP, the high-temperature exhaust gas (stream 11) serves as the heat source for the bottoming heat recovery cycles.

In the bottoming cycles, the exhaust gas firstly flows through a heat recovery steam generator (HRSG), where the pressurized water (stream 14) absorbs heat to be converted into superheated vapor (stream 15). Then, it is expanded in the steam turbine (ST) to generate electricity. After that, the low-pressure vapor (stream 16) at the exit of the ST is condensed into saturated liquid (stream 17) in the generator (Gen) to supply the heat required for the SEAC. In the SEAC, the lithium bromide-water (LiBr-H₂O) is employed as working pairs. The weak solution (stream 23) absorbs heat in the generator where it is separated into a strong solution (stream 18) and water vapor (stream 24). The strong solution passes through the solution heat exchanger (SHE) to preheat the weak solution (stream 22), and then, the low-temperature strong solution (stream 19) flows into the absorber (Abs) through an expansion valve (EV1). Meanwhile, the refrigerant vapor is condensed in the condenser (Con). The saturated liquid (stream 25) is throttled by an expansion valve (EV2) and flows into the evaporator (Eva), where it is evaporated to produce the cooling capacity. After that, the refrigerant vapor (stream 27) is absorbed by the strong solution (stream 20) in the absorber. Finally, the weak solution (stream 21) is pumped back to the generator.

The residual thermal energy of the exhaust gas is utilized by an ORC. In consideration of environmental impact and safety concerns, it is advisable to use working fluids that exhibit low global warming potential (GWP) and minimal ozone depletion potential (ODP) and are non-corrosive and non-flammable. Moreover, there is a risk associated with organic working fluids undergoing decomposition at elevated temperatures during direct heat exchange with exhaust gases, which could lead to component damage and safety hazards. In the context of the ORC loop, a working fluid that enhances cycle efficiency is selected. Research has demonstrated that R600a (isobutane) serves as an effective working fluid for low- to medium-temperature waste heat recovery, offering high power generation capacity and efficiency [31]. The decomposition temperature of R600a is relatively elevated, at approximately 300–320 °C [32], thereby eliminating the risk of decomposition when employing exhaust gas (stream 12) as the heat source. In addition to its operational advantages, R600a is also environmentally favorable, characterized by an ODP of 0 and a GWP of roughly 20 [33], making it a sustainable choice in line with environmental and safety standards.

In the ORC, the liquid working fluid (stream 34) undergoes a heating process in the vapor generator (VG) to reach its saturated vapor state (stream 35). Subsequently, it is expanded in the vapor turbine (VT) to generate power. After that, the exhaust vapor (stream 36) is subjected to condensation, transforming it into saturated liquid (stream 37) through the transfer of heat to the cooling water in the vapor condenser (VC). Ultimately, this saturated liquid is pressurized using pump (Pu2) before being returned to the vapor generator (VG).

3. System Modeling

In this section, mathematical models for the system are formulated by leveraging the principles of thermodynamics and economics. To facilitate the modeling process, the following assumptions are considered [34,35,36]:

• The processes operate under steady-state conditions;
• Changes in kinetic and potential energies and exergies are not taken into account;
• Heat losses from the components into the environment are negligible;
• Pressure drops in pipelines are excluded from consideration;
• The composition of ambient air is 21% oxygen and 79% nitrogen by volume;
• Ideal gas behavior is assumed for all gas mixtures;
• In the SEAC, the refrigerant leaving the evaporator or condenser is taken to be saturated, and the solutions at the outlet of the generator and absorber are in an equilibrium state corresponding to their temperatures and pressures;
• In the ORC, the working fluids leaving the vapor generator and condenser are treated as saturated vapor and liquid, respectively;
• Constant isentropic efficiencies are applied to pumps, turbines, and the compressor.

3.1. Energy Analysis

3.1.1. Combustion Chamber

In the combustion chamber, the natural gas reacts with the air. The chemical equation for a complete combustion is presented as follows [18]:

$${\mathrm{CH}}_4+{\mathrm{n}}_{\mathrm{air},1}\left({\mathrm{O}}_2+3.76{\mathrm{N}}_2\right)\to {\mathrm{n}}_1{\mathrm{N}}_2+{\mathrm{n}}_2{\mathrm{O}}_2+{\mathrm{n}}_3{\mathrm{CO}}_2+{\mathrm{n}}_4{\mathrm{H}}_2\mathrm{O}$$

(1)

The energy balance equation for an adiabatic combustion is expressed as follows:

$${\overline{h}}_{f-{\mathrm{CH}}_4}^0+n_{\mathrm{air},1}{\overline{h}}_{\mathrm{air},1}=n_1({\overline{h}}_{f-N_2}^0+\mathsf{\Delta }{\overline{h}}_{N_2})+n_2\left({\overline{h}}_{f-O_2}^0+\mathsf{\Delta }{\overline{h}}_{O_2}\right)+n_3\left({\overline{h}}_{f-{\mathrm{CO}}_2}^0+\mathsf{\Delta }{\overline{h}}_{{\mathrm{CO}}_2}\right)+n_4({\overline{h}}_{f-H_{2}O}^0+\mathsf{\Delta }{\overline{h}}_{H_{2}O})$$

(2)

where ${\overline{h}}_{f-j}^0$ and $\mathsf{\Delta }{\overline{h}}_j$ are the enthalpy of formation and the difference in specific enthalpy for the jth component, respectively. The coefficients $n_1$ to $n_4$ refer to the kilomoles of the constituents.

3.1.2. Biomass Gasifier

To forecast the composition of the producer gas, the equilibrium model is utilized, predicated on the assumption that all chemical reactions attain thermodynamic equilibrium and that the pyrolysis products reach a state of balance in the reduction zone prior to their departure from the gasifier. The overarching reaction of gasification for biomass fuel is formulated as follows: [18,37]:

$$\mathrm{C}{\mathrm{H}}_{\mathrm{a}}{\mathrm{O}}_{\mathrm{b}}{\mathrm{N}}_{\mathrm{c}}+{w\mathrm{H}}_2\mathrm{O}+n_{\mathrm{air},2}\left({\mathrm{O}}_2+3.76{\mathrm{N}}_2\right)\to n_5{\mathrm{H}}_2+n_6\mathrm{CO}+n_7{\mathrm{CO}}_2+n_8{\mathrm{H}}_2\mathrm{O}+n_9{\mathrm{CH}}_4+n_{10}{\mathrm{N}}_2$$

(3)

where CH_aO_bN_c stands for the chemical formula of the biomass, w is the moisture content of biomass, and $n_{\mathrm{air},2}$ is the kilomoles of oxygen in the air participating in the reaction.

The moisture level in the biomass is quantifiable based on the mass-based moisture content (MC), which is defined as follows: [18]:

$$w=\frac{\mathit{MC}\times {\mathit{MW}}_{\mathrm{biomass}}}{(1-\mathit{MC})\times {\mathit{MW}}_{{\mathrm{H}}_2\mathrm{O}}}$$

(4)

where ${\mathit{MW}}_{\mathrm{biomass}}$ and ${\mathit{MW}}_{{\mathrm{H}}_2\mathrm{O}}$ are the molecular weights of the biomass and water, respectively. In this study, the type of biomass is wood (CH_1.44O_0.66, MC = 20%) [15,18,37].

In the gasification process, the main chemical reactions are shown as follows [18]:

$$\mathrm{C}+{\mathrm{CO}}_2\rightleftharpoons 2\mathrm{CO}$$

(5)

$$\mathrm{C}+{\mathrm{H}}_2\mathrm{O}\rightleftharpoons \mathrm{CO}+{\mathrm{H}}_2$$

(6)

$$\mathrm{C}+{2\mathrm{H}}_2\rightleftharpoons {\mathrm{CH}}_4$$

(7)

Equations (5) and (6) can be combined to give the water-gas shift reaction [18]:

$$\mathrm{CO}+{\mathrm{H}}_2\mathrm{O}\rightleftharpoons {\mathrm{CO}}_2+{\mathrm{H}}_2$$

(8)

The equilibrium constants for Equations (7) and (8) are defined as follows [35]:

$$K_1=\frac{n_9}{{n_5}^2}{\left(\frac{P_{\mathrm{Ga}}/P_{\mathrm{ref}}}{n_{\mathrm{tot}}}\right)}^{-1}$$

(9)

$$K_2=\frac{n_5{n}_7}{n_6{n}_8}{\left(\frac{P_{\mathrm{Ga}}/P_{\mathrm{ref}}}{n_{\mathrm{tot}}}\right)}^0$$

(10)

where P_Ga is the gasification pressure. K₁ and K₂ are related to the change in the Gibbs functions for the corresponding reactions, shown as follows [18]:

$$\mathrm{In}{K}_1=-\frac{\mathsf{\Delta }{G}_1^0}{\overline{R}{T}_{\mathrm{Ga}}}$$

(11)

$$\mathrm{In}{K}_2=-\frac{\mathsf{\Delta }{G}_2^0}{\overline{R}{T}_{\mathrm{Ga}}}$$

(12)

where $\overline{R}$ is the universal gas constant, and $T_{\mathrm{Ga}}$ is the gasifier temperature. $\mathsf{\Delta }{G}_1^0$ and $\mathsf{\Delta }{G}_2^0$ can be calculated based on the following [18]:

$$\mathsf{\Delta }{G}_1^0=\left({\overline{h}}_{{\mathrm{CH}}_4}-T_{\mathrm{Ga}}{\overline{s}}_{{\mathrm{CH}}_4}^0\right)-2\left({\overline{h}}_{{\mathrm{H}}_2}-T_{\mathrm{Ga}}{\overline{s}}_{{\mathrm{H}}_2}^0\right)$$

(13)

$$\mathsf{\Delta }{G}_2^0=\left({\overline{h}}_{{\mathrm{CO}}_2}-T_{\mathrm{Ga}}{\overline{s}}_{{\mathrm{CO}}_2}^0\right)+\left({\overline{h}}_{{\mathrm{H}}_2}-T_{\mathrm{Ga}}{\overline{s}}_{{\mathrm{H}}_2}^0\right)-\left({\overline{h}}_{\mathrm{CO}}-T_{\mathrm{Ga}}{\overline{s}}_{\mathrm{CO}}^0\right)-\left({\overline{h}}_{{\mathrm{H}}_2\mathrm{O}}-T_{\mathrm{Ga}}{\overline{s}}_{{\mathrm{H}}_2\mathrm{O}}^0\right)$$

(14)

For an adiabatic process in the biomass gasifier, the energy balance equation at a given temperature can be expressed as follows [18]:

$$\begin{gathered} {\overline{h}}_{f-\mathrm{biomass}}^0+w{\overline{h}}_{f-{\mathrm{H}}_2\mathrm{O}}^0+n_{\mathrm{air},2}{\overline{h}}_{\mathrm{air},2}=n_5\left({\overline{h}}_{f-{\mathrm{H}}_2}^0+\mathsf{\Delta }{\overline{h}}_{{\mathrm{H}}_2}\right)+n_6\left({\overline{h}}_{f-\mathrm{CO}}^0+\mathsf{\Delta }{\overline{h}}_{\mathrm{CO}}\right)+n_7\left({\overline{h}}_{f-{\mathrm{CO}}_2}^0+\mathsf{\Delta }{\overline{h}}_{{\mathrm{CO}}_2}\right) \\ +n_8({\overline{h}}_{f-{\mathrm{H}}_{2\mathrm{O}}}^0+\mathsf{\Delta }{\overline{h}}_{{\mathrm{H}}_2\mathrm{O}})+n_9({\overline{h}}_{f-{\mathrm{CH}}_4}^0+\mathsf{\Delta }{\overline{h}}_{{\mathrm{CH}}_4})+n_{10}({\overline{h}}_{f-{\mathrm{N}}_2}^0+\mathsf{\Delta }{\overline{h}}_{{\mathrm{N}}_2}) \end{gathered}$$

(15)

3.1.3. Post-Combustion Chamber

In the post-combustion chamber, the produced syngas reacts with the oxygen content of the exhaust gas at the outlet of the gas turbine. The following equation can be applied for a complete combustion reaction [18]:

$$\begin{gathered} n_1{\mathrm{N}}_2+n_2{\mathrm{O}}_2+n_3{\mathrm{CO}}_2+n_4{\mathrm{H}}_2\mathrm{O}+n_{\mathrm{biomass}}\left(n_5{\mathrm{H}}_2+n_6\mathrm{CO}+n_7{\mathrm{CO}}_2+n_8{\mathrm{H}}_2\mathrm{O}+n_9{\mathrm{CH}}_4+n_{10}{\mathrm{N}}_2\right)\to \\ {n}_{11}{\mathrm{N}}_2+n_{12}{\mathrm{O}}_2+n_{13}{\mathrm{CO}}_2+n_{14}{\mathrm{H}}_2\mathrm{O} \end{gathered}$$

(16)

where $n_{\mathrm{biomass}}$ is the kilomoles of the biomass entering the gasifier.

Assuming an adiabatic combustion process, the energy balance for the reaction is given by the following:

$$\sum _j{n_j\left({\overline{h}}_{f-j}^0+\mathsf{\Delta }\overline{h}\right)}_{\mathrm{syngas}}+\sum _j{n_j\left({\overline{h}}_{f-j}^0+\mathsf{\Delta }\overline{h}\right)}_{\mathrm{exh},\mathrm{CC}}=\sum _j{n_j\left({\overline{h}}_{f-j}^0+\mathsf{\Delta }\overline{h}\right)}_{\mathrm{exh},\mathrm{PCC}}$$

(17)

where $n_j$ is the kilomoles of the jth component in the syngas, exhaust gas from the combustion chamber, or exhaust gas from post-combustion chamber.

3.1.4. Other System Components

The general form of the steady-state governing equations of the mass balance, energy balance, and concentration balance for each component of the system can be written as follows [35]:

$$\sum {\dot{m}}_{\mathit{in}}=\sum {\dot{m}}_{\mathit{out}}$$

(18)

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

(19)

$$\sum {\dot{m}}_{\mathit{in}}{X}_{\mathit{in}}=\sum {\dot{m}}_{\mathit{out}}{X}_{\mathit{out}}$$

(20)

where X denotes the mass concentration of LiBr in the solution.

The mass and energy balance equations for the components of the proposed system are presented in

Table 1. Mass and energy balance equations for the system components.

Component	Mass and Energy Balance Equations
Air compressor	${\dot{W}}_{\mathrm{AC}}={\dot{m}}_1\left(h_2-h_1\right)$
	${\dot{m}}_1={\dot{m}}_2$
Air preheater	${\dot{m}}_2\left(h_3-h_2\right)={\dot{m}}_{10}\left(h_{10}-h_{11}\right)$
	${\dot{m}}_2={\dot{m}}_3$, ${\dot{m}}_{10}={\dot{m}}_{11}$
Gas turbine	${\dot{W}}_{\mathrm{GT}}={\dot{m}}_5\left(h_5-h_6\right)$
	${\dot{m}}_5={\dot{m}}_6$
HRSG	${\dot{Q}}_{\mathrm{HRSG}}={\dot{m}}_{11}\left(h_{11}-h_{12}\right)={\dot{m}}_{14}\left(h_{15}-h_{14}\right)$
	${\dot{m}}_{11}={\dot{m}}_{12}$, ${\dot{m}}_{14}={\dot{m}}_{15}$
Steam turbine	${\dot{W}}_{\mathrm{ST}}={\dot{m}}_{15}\left(h_{15}-h_{16}\right)$
	${\dot{m}}_{15}={\dot{m}}_{16}$
Pump 1	${\dot{W}}_{\mathrm{pu}1}={\dot{m}}_{14}\left(h_{14}-h_{17}\right)$
	${\dot{m}}_{14}={\dot{m}}_{17}$
Generator	${\dot{Q}}_{\mathrm{gen}}={\dot{m}}_{16}\left(h_{16}-h_{17}\right)={\dot{m}}_{18}{h}_{18}+{\dot{m}}_{24}{h}_{24}-{\dot{m}}_{23}{h}_{23}$
	${\dot{m}}_{16}={\dot{m}}_{17}$, ${\dot{m}}_{23}={\dot{m}}_{18}+{\dot{m}}_{24}$
SHE	${\dot{Q}}_{\mathrm{SHE}}={\dot{m}}_{18}\left(h_{18}-h_{19}\right)={\dot{m}}_{22}\left(h_{23}-h_{22}\right)$
	${\dot{m}}_{18}={\dot{m}}_{19}$, ${\dot{m}}_{22}={\dot{m}}_{23}$
Absorber	${\dot{Q}}_{\mathrm{abs}}={\dot{m}}_{28}\left(h_{29}-h_{28}\right)={\dot{m}}_{20}{h}_{20}+{\dot{m}}_{27}{h}_{27}-{\dot{m}}_{21}{h}_{21}$
	${\dot{m}}_{28}={\dot{m}}_{29}$, ${\dot{m}}_{21}={\dot{m}}_{20}+{\dot{m}}_{27}$
Solution pump	${\dot{W}}_{\mathrm{SP}}={\dot{m}}_{21}\left(h_{22}-h_{21}\right)$
	${\dot{m}}_{21}={\dot{m}}_{22}$
Condenser	${\dot{Q}}_{\mathrm{con}}={\dot{m}}_{24}\left(h_{24}-h_{25}\right)={\dot{m}}_{30}\left(h_{31}-h_{30}\right)$
	${\dot{m}}_{24}={\dot{m}}_{25}$, ${\dot{m}}_{30}={\dot{m}}_{31}$
Evaporator	${\dot{Q}}_{\mathrm{eva}}={\dot{m}}_{20}\left(h_{27}-h_{26}\right)={\dot{m}}_{30}\left(h_{32}-h_{33}\right)$
	${\dot{m}}_{26}={\dot{m}}_{27}$, ${\dot{m}}_{32}={\dot{m}}_{33}$
Vapor generator	${\dot{Q}}_{\mathrm{VG}}={\dot{m}}_{12}\left(h_{12}-h_{13}\right)={\dot{m}}_{35}\left(h_{35}-h_{34}\right)$
	${\dot{m}}_{12}={\dot{m}}_{13}$, ${\dot{m}}_{34}={\dot{m}}_{35}$
Vapor turbine	${\dot{W}}_{\mathrm{VT}}={\dot{m}}_{35}\left(h_{35}-h_{36}\right)$
	${\dot{m}}_{35}={\dot{m}}_{36}$
Vapor condenser	${\dot{Q}}_{\mathrm{VC}}={\dot{m}}_{36}\left(h_{36}-h_{37}\right)={\dot{m}}_{38}\left(h_{39}-h_{38}\right)$
	${\dot{m}}_{36}={\dot{m}}_{37}$, ${\dot{m}}_{38}={\dot{m}}_{39}$
Pump 2	${\dot{W}}_{\mathrm{pu}2}={\dot{m}}_{34}\left(h_{34}-h_{37}\right)$
	${\dot{m}}_{34}={\dot{m}}_{37}$

.

3.2. Exergy Analysis

The exergy balance equation for each component can be written as follows [38]:

$${\dot{\mathit{Ex}}}_F={\dot{\mathit{Ex}}}_P+{\dot{\mathit{Ex}}}_D+{\dot{\mathit{Ex}}}_L$$

(21)

where ${\dot{\mathit{Ex}}}_F$, ${\dot{\mathit{Ex}}}_P$, ${\dot{\mathit{Ex}}}_D$, and ${\dot{\mathit{Ex}}}_L$ are the rates of supplied fuel, generated product, exergy destruction and exergy loss, respectively. The exergy balance equations for the system components are presented in

Table 2. Exergy balance equations for the system components.

Component	$\mathbf{Exergy} \mathbf{of} \mathbf{Fuel} \left({\dot{\mathit{Ex}}}_{\mathbf{F}}\right)$	$\mathbf{Exergy} \mathbf{of} \mathbf{Product} ({\dot{\mathit{Ex}}}_{\mathit{P}})$	$\mathbf{Exergy} \mathbf{Destruction} \left({\dot{\mathit{Ex}}}_{\mathbf{D}}\right)$
Air compressor	${\dot{\mathit{Ex}}}_{40}$	${\dot{\mathit{Ex}}}_2-{\dot{\mathit{Ex}}}_1$	${\dot{\mathit{Ex}}}_{F,\mathit{AC}}-{\dot{\mathit{Ex}}}_{P,\mathit{AC}}$
Air preheater	${\dot{\mathit{Ex}}}_{10}-{\dot{\mathit{Ex}}}_{11}$	${\dot{\mathit{Ex}}}_3-{\dot{\mathit{Ex}}}_2$	${\dot{\mathit{Ex}}}_{F,\mathit{AP}}-{\dot{\mathit{Ex}}}_{P,\mathit{AP}}$
Combustion chamber	${\dot{\mathit{Ex}}}_3+{\dot{\mathit{Ex}}}_4$	${\dot{\mathit{Ex}}}_5$	${\dot{\mathit{Ex}}}_{F,\mathit{CC}}-{\dot{\mathit{Ex}}}_{P,\mathit{CC}}$
Gas turbine	${\dot{\mathit{Ex}}}_5-{\dot{\mathit{Ex}}}_6$	${\dot{\mathit{Ex}}}_{41}+{\dot{\mathit{Ex}}}_{40}$	${\dot{\mathit{Ex}}}_{F,\mathit{GT}}-{\dot{\mathit{Ex}}}_{P,\mathit{GT}}$
PCC	${\dot{\mathit{Ex}}}_6+{\dot{\mathit{Ex}}}_9$	${\dot{\mathit{Ex}}}_{10}$	${\dot{\mathit{Ex}}}_{F,P\mathrm{CC}}-{\dot{\mathit{Ex}}}_{P,P\mathit{CC}}$
Biomass gasifier	${\dot{\mathit{Ex}}}_7+{\dot{\mathit{Ex}}}_8$	${\dot{\mathit{Ex}}}_9$	${\dot{\mathit{Ex}}}_{F,\mathit{Ga}}-{\dot{\mathit{Ex}}}_{P,\mathit{Ga}}$
HRSG	${\dot{\mathit{Ex}}}_{11}-{\dot{\mathit{Ex}}}_{12}$	${\dot{\mathit{Ex}}}_{15}-{\dot{\mathit{Ex}}}_{14}$	${\dot{\mathit{Ex}}}_{F,\mathit{HRSG}}-{\dot{\mathit{Ex}}}_{P,\mathit{HRSG}}$
Steam turbine	${\dot{\mathit{Ex}}}_{15}-{\dot{\mathit{Ex}}}_{16}$	${\dot{\mathit{Ex}}}_{42}$	${\dot{\mathit{Ex}}}_{F,\mathit{ST}}-{\dot{\mathit{Ex}}}_{P,\mathit{ST}}$
Pump 1	${\dot{\mathit{Ex}}}_{43}$	${\dot{\mathit{Ex}}}_{14}-{\dot{\mathit{Ex}}}_{17}$	${\dot{\mathit{Ex}}}_{F,\mathit{Pu}1}-{\dot{\mathit{Ex}}}_{P,\mathit{Pu}1}$
Generator	${\dot{\mathit{Ex}}}_{16}-{\dot{\mathit{Ex}}}_{17}$	${\dot{\mathit{Ex}}}_{18}+{\dot{\mathit{Ex}}}_{24}-{\dot{\mathit{Ex}}}_{23}$	${\dot{\mathit{Ex}}}_{F,\mathit{gen}}-{\dot{\mathit{Ex}}}_{P,\mathit{gen}}$
SHE	${\dot{\mathit{Ex}}}_{18}-{\dot{\mathit{Ex}}}_{19}$	${\dot{\mathit{Ex}}}_{23}-{\dot{\mathit{Ex}}}_{22}$	${\dot{\mathit{Ex}}}_{F,\mathit{SHE}}-{\dot{\mathit{Ex}}}_{P,\mathit{SHE}}$
Absorber	${\dot{\mathit{Ex}}}_{20}+{\dot{\mathit{Ex}}}_{27}-{\dot{\mathit{Ex}}}_{21}$	${\dot{\mathit{Ex}}}_{29}-{\dot{\mathit{Ex}}}_{28}$	${\dot{\mathit{Ex}}}_{F,\mathit{abs}}-{\dot{\mathit{Ex}}}_{P,\mathit{abs}}$
Solution pump	${\dot{\mathit{Ex}}}_{44}$	${\dot{\mathit{Ex}}}_{22}-{\dot{\mathit{Ex}}}_{21}$	${\dot{\mathit{Ex}}}_{F,\mathit{SP}}-{\dot{\mathit{Ex}}}_{P,\mathit{SP}}$
Condenser	${\dot{\mathit{Ex}}}_{24}-{\dot{\mathit{Ex}}}_{25}$	${\dot{\mathit{Ex}}}_{31}-{\dot{\mathit{Ex}}}_{30}$	${\dot{\mathit{Ex}}}_{F,\mathit{con}}-{\dot{\mathit{Ex}}}_{P,\mathit{con}}$
Evaporator	${\dot{\mathit{Ex}}}_{26}-{\dot{\mathit{Ex}}}_{27}$	${\dot{\mathit{Ex}}}_{33}-{\dot{\mathit{Ex}}}_{32}$	${\dot{\mathit{Ex}}}_{F,\mathit{eva}}-{\dot{\mathit{Ex}}}_{P,\mathit{eva}}$
Vapor generator	${\dot{\mathit{Ex}}}_{12}-{\dot{\mathit{Ex}}}_{13}$	${\dot{\mathit{Ex}}}_{35}-{\dot{\mathit{Ex}}}_{34}$	${\dot{\mathit{Ex}}}_{F,\mathit{VG}}-{\dot{\mathit{Ex}}}_{P,\mathit{VG}}$
Vapor turbine	${\dot{\mathit{Ex}}}_{35}-{\dot{\mathit{Ex}}}_{36}$	${\dot{\mathit{Ex}}}_{45}$	${\dot{\mathit{Ex}}}_{F,\mathit{VT}}-{\dot{\mathit{Ex}}}_{P,\mathit{VT}}$
Vapor condenser	${\dot{\mathit{Ex}}}_{36}-{\dot{\mathit{Ex}}}_{37}$	${\dot{\mathit{Ex}}}_{39}-{\dot{\mathit{Ex}}}_{38}$	${\dot{\mathit{Ex}}}_{F,\mathit{VC}}-{\dot{\mathit{Ex}}}_{P,\mathit{VC}}$
Pump 2	${\dot{\mathit{Ex}}}_{46}$	${\dot{\mathit{Ex}}}_{34}-{\dot{\mathit{Ex}}}_{37}$	${\dot{\mathit{Ex}}}_{F,\mathit{Pu}2}-{\dot{\mathit{Ex}}}_{P,\mathit{Pu}2}$

.

The exergy content in a fluid stream is composed of four components: physical exergy, chemical exergy, kinetic exergy, and potential exergy. If the kinetic and potential aspects are disregarded, the stream’s specific exergy can be represented as follows [38]:

$${\mathit{ex}}_i={\mathit{ex}}_i^{\mathit{ph}}+{\mathit{ex}}_i^{\mathit{ch}}$$

(22)

where ${\mathit{ex}}_i^{\mathit{ph}}$ and ${\mathit{ex}}_i^{\mathit{ch}}$ are the specific chemical exergy and specific physical exergy respectively, defined as follows [38]:

$${\mathit{ex}}_i^{\mathit{ph}}=h_i-h_0-T_0\left(s_i-s_0\right)$$

(23)

$${\mathit{ex}}_i^{\mathit{ch}}=\sum _i{x}_i{\mathit{ex}}_{0,i}^{\mathit{ch}}+\stackrel{-}{R}{T}_0\sum _i{x}_i\mathrm{In}{x}_i$$

(24)

where $x_i$ and ${\mathit{ex}}_{0,i}^{\mathit{ch}}$ denote the mole fraction and standard chemical of ith component, respectively.

The specific chemical exergy of a solid biomass fuel is determined based on the following [18]:

$$e_{\mathrm{biomass}}^{\mathit{ch}}={\psi \mathrm{LHV}}_{\mathrm{biomass}}$$

(25)

where $\psi$ represents the proportion of chemical exergy to the lower heating value (LHV) of the biomass’s organic fraction, calculated as follows [18]:

$$\psi =\frac{1.044+0.016\frac{M_{\mathrm{H}}}{M_{\mathrm{C}}}-0.34493\frac{M_{\mathrm{O}}}{M_{\mathrm{C}}}\left(1+0.0531\frac{M_{\mathrm{H}}}{M_{\mathrm{C}}}\right)}{1-0.4124\frac{M_{\mathrm{O}}}{M_{\mathrm{C}}}}$$

(26)

where M_O, M_C, and M_H are the mass fractions of oxygen, carbon, and hydrogen, respectively. The LHVs of dry biomass and natural gas are 18,732 kJ/kg and 50,020 kJ/kg, respectively [15].

The exergy efficiency of kth component is characterized based on the following [38]:

$${\eta }_{\mathit{ex},k}=\frac{{\dot{\mathit{Ex}}}_{P,k}}{{\dot{\mathit{Ex}}}_{F,k}}$$

(27)

The exergy destruction ratio is characterized as the proportion of exergy destruction in the kth component relative to the system’s overall exergy destruction [38]:

$$y_{D,k}=\frac{{\dot{\mathit{Ex}}}_{D,k}}{{\dot{\mathit{Ex}}}_{D,\mathit{tot}}}$$

(28)

3.3. Exergoeconomic Analysis

An exergoeconomic analysis combines an exergy analysis with economic principles to reveal the cost formation process and calculate the cost per exergy unit of the product. For each component, the cost balance equation can be expressed as follows [38]:

$$\sum {\dot{C}}_{\mathit{in},k}+\sum {\dot{C}}_{q,k}+{\dot{Z}}_k=\sum {\dot{C}}_{\mathit{out},k}+{\dot{C}}_{w,k}$$

(29)

In which,

$${\dot{C}}_j=c_j{\dot{\mathit{Ex}}}_j$$

(30)

where ${\dot{C}}_j$ represents the cost rate ($/h), and $c_j$ stands for the cost per unit of exergy ($/GJ). ${\dot{Z}}_k$ denotes the aggregate cost rate for the kth component, encompassing capital investment, operating, and maintenance expenses, and is computed as detailed below [39]:

$${\dot{Z}}_k=\frac{\mathit{CRF}\times {\varphi }_r\times Z_k}{N}$$

(31)

where $Z_k$ is the capital cost of the kth component, and ${\varphi }_r$ and N are the maintenance factor (1.06) and annual operating hours (8000). CRF indicates the capital recovery factor, which is computed based on the following [39]:

$$\mathit{CRF}=\frac{i_r{(1+i_r)}^{n_t}}{{(1+i_r)}^{n_t}-1}$$

(32)

where i_r is the annual interest rate (5%), and n_t is the lifetime of the system (20 years).

The average unit cost of the fuel ($c_{F,k}$), unit cost of the product ($c_{P,k}$), and cost rate of exergy destruction (${\dot{C}}_{D,k}$) for the kth component are respectively given as follows [38]:

$$c_{F,k}=\frac{{\dot{C}}_{F,k}}{{\dot{\mathit{Ex}}}_{F,k}}$$

(33)

$$c_{P,k}=\frac{{\dot{C}}_{P,k}}{{\dot{\mathit{Ex}}}_{P,k}}$$

(34)

$${\dot{C}}_{D,k}=c_{F,k}{\dot{\mathit{Ex}}}_{D,k}$$

(35)

The relative cost difference (r_k) and exergoeconomic factor (f_k) for the kth component are respectively defined as follows [38]:

$$r_k=\frac{c_{P,k}-c_{F,k}}{c_{F,k}}$$

(36)

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

(37)

The total cost rate (TCR) of the system is calculated as follows [23,39]:

$$\mathrm{TCR}=\sum {\dot{Z}}_k+{\dot{C}}_{D,k}+{\dot{C}}_{\mathrm{NG}}+{\dot{C}}_{\mathrm{Biomass}}$$

(38)

In order to evaluate the component costs of the heat exchangers, the heat transfer areas (A_k) should be determined first, which is calculated based on the following [19]:

$$A_k=\frac{{\dot{Q}}_k}{U_k∆T_{\mathit{lm},k}}$$

(39)

where $∆T_{\mathit{lm},k}$ represents the logarithmic mean temperature difference, and U_k denotes the heat transfer coefficient. The equations used to calculate the heat transfer coefficients of heat exchangers are listed in Appendix A.

The cost balance and auxiliary equations for the system components are presented in

Table 3. Cost balance and auxiliary equations for the system components.

Component	Cost Balance Equation	Auxiliary Equation
Air compressor	${\dot{C}}_1+{\dot{C}}_{40}+{\dot{Z}}_{\mathrm{AC}}={\dot{C}}_2$	$c_1=0$
Air preheater	${\dot{C}}_2+{\dot{C}}_{10}+{\dot{Z}}_{\mathrm{AP}}={\dot{C}}_3+{\dot{C}}_{11}$	$\frac{{\dot{C}}_{10}}{{\dot{\mathit{Ex}}}_{10}}=\frac{{\dot{C}}_{11}}{{\dot{\mathit{Ex}}}_{11}}$
Combustion chamber	${\dot{C}}_3+{\dot{C}}_4+{\dot{Z}}_{\mathrm{CC}}={\dot{C}}_5$
Gas turbine	${\dot{C}}_5+{\dot{Z}}_{\mathrm{GT}}={\dot{C}}_6+{\dot{C}}_{40}+{\dot{C}}_{41}$	$\frac{{\dot{C}}_5}{{\dot{\mathit{Ex}}}_5}=\frac{{\dot{C}}_6}{{\dot{\mathit{Ex}}}_6},\frac{{\dot{C}}_{40}}{{\dot{\mathit{Ex}}}_{40}}=\frac{{\dot{C}}_{41}}{{\dot{\mathit{Ex}}}_{41}}$
PCC	${\dot{C}}_6+{\dot{C}}_9+{\dot{Z}}_{\mathrm{PCC}}={\dot{C}}_{10}$
Biomass gasifier	${\dot{C}}_7+{\dot{C}}_8+{\dot{Z}}_{\mathrm{Ga}}={\dot{C}}_9$	$c_8=0$
HRSG	${\dot{C}}_{11}+{\dot{C}}_{14}+{\dot{Z}}_{\mathrm{HRSG}}={\dot{C}}_{12}+{\dot{C}}_{15}$	$\frac{{\dot{C}}_{11}}{{\dot{\mathit{Ex}}}_{11}}=\frac{{\dot{C}}_{12}}{{\dot{\mathit{Ex}}}_{12}}$
Steam turbine	${\dot{C}}_{15}+{\dot{Z}}_{\mathrm{ST}}={\dot{C}}_{16}+{\dot{C}}_{42}$	$\frac{{\dot{C}}_{15}}{{\dot{\mathit{Ex}}}_{15}}=\frac{{\dot{C}}_{16}}{{\dot{\mathit{Ex}}}_{16}}$
Pump 1	${\dot{C}}_{17}+{\dot{C}}_{43}+{\dot{Z}}_{\mathrm{pu}1}={\dot{C}}_{14}$	$\frac{{\dot{C}}_{42}}{{\dot{\mathit{Ex}}}_{42}}=\frac{{\dot{C}}_{43}}{{\dot{\mathit{Ex}}}_{43}}$
Generator	${\dot{C}}_{16}+{\dot{C}}_{23}+{\dot{Z}}_{\mathrm{gen}}={\dot{C}}_{17}+{\dot{C}}_{18}+{\dot{C}}_{24}$	$\frac{{\dot{C}}_{16}}{{\dot{\mathit{Ex}}}_{16}}=\frac{{\dot{C}}_{17}}{{\dot{\mathit{Ex}}}_{17}}$
		$\frac{{\dot{C}}_{18}-{\dot{C}}_{23}}{{\dot{\mathit{Ex}}}_{18}-{\dot{\mathit{Ex}}}_{23}}=\frac{{\dot{C}}_{24}-{\dot{C}}_{23}}{{\dot{\mathit{Ex}}}_{24}-{\dot{\mathit{Ex}}}_{23}}$
SHE	${\dot{C}}_{18}+{\dot{C}}_{22}+{\dot{Z}}_{\mathrm{SHE}}={\dot{C}}_{19}+{\dot{C}}_{23}$	$\frac{{\dot{C}}_{18}}{{\dot{\mathit{Ex}}}_{18}}=\frac{{\dot{C}}_{19}}{{\dot{\mathit{Ex}}}_{19}}$
Absorber	${\dot{C}}_{20}+{\dot{C}}_{27}+{\dot{C}}_{28}+{\dot{Z}}_{\mathrm{abs}}={\dot{C}}_{21}+{\dot{C}}_{29}$	$\frac{{\dot{C}}_{21}}{{\dot{\mathit{Ex}}}_{21}}=\frac{{\dot{C}}_{20}+{\dot{C}}_{27}}{{\dot{\mathit{Ex}}}_{20}+{\dot{\mathit{Ex}}}_{27}}, c_{28}=0$
Solution pump	${\dot{C}}_{21}+{\dot{C}}_{44}+{\dot{Z}}_{\mathrm{SP}}={\dot{C}}_{22}$	$\frac{{\dot{C}}_{43}}{{\dot{\mathit{Ex}}}_{43}}=\frac{{\dot{C}}_{44}}{{\dot{\mathit{Ex}}}_{44}}$
Condenser	${\dot{C}}_{24}+{\dot{C}}_{30}+{\dot{Z}}_{\mathrm{con}}={\dot{C}}_{25}+{\dot{C}}_{31}$	$\frac{{\dot{C}}_{24}}{{\dot{\mathit{Ex}}}_{24}}=\frac{{\dot{C}}_{25}}{{\dot{\mathit{Ex}}}_{25}},c_{30}=0$
Evaporator	${\dot{C}}_{26}+{\dot{C}}_{32}+{\dot{Z}}_{\mathrm{eva}}={\dot{C}}_{27}+{\dot{C}}_{33}$	$\frac{{\dot{C}}_{26}}{{\dot{\mathit{Ex}}}_{27}}=\frac{{\dot{C}}_{27}}{{\dot{\mathit{Ex}}}_{27}},c_{32}=0$
Vapor generator	${\dot{C}}_{12}+{\dot{C}}_{34}+{\dot{Z}}_{\mathrm{VG}}={\dot{C}}_{13}+{\dot{C}}_{35}$	$\frac{{\dot{C}}_{12}}{{\dot{\mathit{Ex}}}_{12}}=\frac{{\dot{C}}_{13}}{{\dot{\mathit{Ex}}}_{13}}$
Vapor turbine	${\dot{C}}_{35}+{\dot{Z}}_{\mathrm{VT}}={\dot{C}}_{36}+{\dot{C}}_{45}$	$\frac{{\dot{C}}_{35}}{{\dot{\mathit{Ex}}}_{35}}=\frac{{\dot{C}}_{36}}{{\dot{\mathit{Ex}}}_{36}}$
Vapor condenser	${\dot{C}}_{36}+{\dot{C}}_{38}+{\dot{Z}}_{\mathrm{VC}}={\dot{C}}_{37}+{\dot{C}}_{39}$	$\frac{{\dot{C}}_{36}}{{\dot{\mathit{Ex}}}_{36}}=\frac{{\dot{C}}_{37}}{{\dot{\mathit{Ex}}}_{37}},c_{38}=0$
Pump 2	${\dot{C}}_{37}+{\dot{C}}_{46}+{\dot{Z}}_{\mathrm{pu}2}={\dot{C}}_{34}$	$\frac{{\dot{C}}_{45}}{{\dot{\mathit{Ex}}}_{45}}=\frac{{\dot{C}}_{46}}{{\dot{\mathit{Ex}}}_{46}}$

. The cost functions applied to estimate the capital costs of the system components are listed in Appendix B. All the cost values are calculated at their reference years ($Z_{\mathrm{ref}}$), and they should be updated to the values at the present year ($Z_{\mathrm{PY}}$) using the chemical engineering plant cost index (CEPCI) based on the following relation [19]:

$$Z_{\mathrm{PY}}=Z_{\mathrm{ref}}\times \frac{{\mathit{CEPCI}}_{\mathrm{PY}}}{{\mathit{CEPCI}}_{\mathrm{ref}}}$$

(40)

3.4. Overall Performance Assessment

The thermal efficiency of the cogeneration system is defined as follows:

$${\eta }_{\mathrm{th}}=\frac{{\dot{W}}_{\mathrm{GT}}+{\dot{W}}_{\mathrm{ST}}+{\dot{W}}_{\mathrm{VT}}-{\dot{W}}_{\mathrm{AC}}-{\dot{W}}_{\mathrm{pu}1}-{\dot{W}}_{\mathrm{pu}2}+{\dot{Q}}_{\mathrm{eva}}}{{\dot{m}}_4{\mathrm{LHV}}_{\mathrm{NG}}+{\dot{m}}_{\mathrm{biomass}}{\mathrm{LHV}}_{\mathrm{biomass}}}$$

(41)

The exergy efficiency of the cogeneration system is computed based on the following:

$${\eta }_{\mathrm{ex}}=\frac{{\dot{W}}_{\mathrm{GT}}+{\dot{W}}_{\mathrm{ST}}+{\dot{W}}_{\mathrm{VT}}-{\dot{W}}_{\mathrm{AC}}-{\dot{W}}_{\mathrm{pu}1}-{\dot{W}}_{\mathrm{pu}2}+\left({\dot{\mathit{Ex}}}_{33}-{\dot{\mathit{Ex}}}_{32}\right)}{{\dot{\mathit{Ex}}}_1+{\dot{\mathit{Ex}}}_4+{\dot{\mathit{Ex}}}_7+{\dot{\mathit{Ex}}}_8}$$

(42)

The sum unit cost of the product (SUCP) of the cogeneration system is given by the following:

$${\mathit{SUCP}}_{\mathrm{sys}}=\frac{{\dot{C}}_{41}+{\dot{C}}_{42}+{\dot{C}}_{45}-{\dot{C}}_{43}-{\dot{C}}_{44}-{\dot{C}}_{46}+{\dot{C}}_{33}}{{\dot{W}}_{\mathrm{GT}}+{\dot{W}}_{\mathrm{ST}}+{\dot{W}}_{\mathrm{VT}}-{\dot{W}}_{\mathrm{AC}}-{\dot{W}}_{\mathrm{pu}1}-{\dot{W}}_{\mathrm{pu}2}+{\dot{\mathit{Ex}}}_{33}}$$

(43)

3.5. Multi-Objective Optimization

Optimization is widely recognized as a prevalent method in energy system design. Within the scope of an actual engineering project, it is essential to holistically consider all evaluation criteria, thereby capturing the system’s performance across various dimensions. The multi-objective optimization technique is particularly beneficial for addressing problems with two or more, potentially conflicting, objective functions simultaneously. The optimization procedure is initiated with the definition of objective functions, followed by the identification of decision variables and their respective boundaries, which can be formulated as follows [40]:

$$\min F\left(X\right)={\left[f_1\left(X), f_2\right(X),\dots , f_k\left(X\right)\right]}^T$$

(44)

subject to

$$g_i(X) \le 0, i =1,\dots , m$$

(45)

$$h_j(X)=0, j =1,\dots , n$$

(46)

$$X_{k,\mathit{min} }\le X_k \le X_{k,\mathit{max}}$$

(47)

where X, F(X), and f(X) are the vectors of decision variables, the multi-objective function, and the single-objective function, respectively; $g_i\left(X\right)$ and $h_j\left(X\right)$ are the inequality and equality constraints, respectively; and $X_{k,\mathit{min} }$ and $X_{k,\mathit{max}}$ are the bottom and top bounds of the kth decision variables, respectively.

The multi-objective optimization problems can be solved using a genetic algorithm (GA). This method is inspired by evolutionary biology, which adopts a stochastic and global comprehensive search strategy to locate optimal solutions [41].

This procedure begins with the generation of a random initial population, which subsequently undergoes evolutionary operations, such as selection, mutation, crossover, and inheritance. Through successive generations, this population gravitates towards optimal solutions [42]. GA identifies a set of optimal solutions, constituting a Pareto frontier, where each solution is a balanced compromise among different objectives, with none being dominant as the simultaneous improvement of objectives is not feasible.

For the selection of the final optimal solution, the TOPSIS (Technique for Order Preference by Similarity to Ideal Situation) decision-making approach is employed [43]. This technique aims to identify alternatives that are closest to the positive ideal solution (optimal value for each objective function) and farthest from the negative ideal solution (worst value for each objective function). The decision matrix formation and the calculation methods for determining the distance from both ideal and non-ideal solutions are formulated as follows [44]:

$$f_{\mathit{ij}}=\frac{x_{\mathit{ij}}}{\sqrt{\sum _{i=1}^m{x}_{\mathit{ij}}^2}}$$

(48)

$${\mathit{ED}}_{i+}=\sqrt{\sum _{j=1}^n{\left(f_{\mathit{ij}}-f_{\mathit{ij}}^{\mathrm{ideal}}\right)}^2}$$

(49)

$${\mathit{ED}}_{i-}=\sqrt{\sum _{j=1}^n{\left(f_{\mathit{ij}}-f_{\mathit{ij}}^{\mathrm{non}-\mathrm{ideal}}\right)}^2}$$

(50)

$${\mathit{Cl}}_i=\frac{{\mathit{ED}}_{i-}}{{\mathit{ED}}_{i+}+{\mathit{ED}}_{i-}}$$

(51)

Finally, the solution exhibiting the highest value of Cl_i is chosen as the preferred final solution.

4. Results and Discussion

In this section, four sub-sections are arranged to display the results of the thermodynamic and exergoeconomic evaluation of the proposed system, including model validation, base case results, a parametric study, and multi-objective optimization. For the simulation, MATLAB R2018b software is utilized, and the properties of the working fluids are sourced from the REFPROP 9.0 database.

4.1. Model Validation

To corroborate the accuracy of the models developed in this study, the results from key subsystems, like the GT cycle, biomass gasifier, ORC, and SEAC, are contrasted with findings from prior research. The data in

Table 4. Comparison of the simulation results of the GT cycle in this work with those reported by Khaljani et al. [39].

Point	Substance	P (kPa)		T (K)		$\dot{\mathit{m}}$ (kg/s)		${\dot{\mathit{Ex}}}_{\mathit{ph}}$ (MW)		${\dot{\mathit{Ex}}}_{\mathit{ch}}$ (MW)		$\dot{\mathit{Ex}}$ (MW)
		Ref. [39]	This Work	Ref. [39]	This Work	Ref. [39]	This Work	Ref. [39]	This Work	Ref. [39]	This Work	Ref. [39]	This Work
1	Air	101.3	1.013	298.15	298.15	94.75	94.80	0	0	0	0	0	0
2	Air	1013	1013	603.5	603.7	94.75	94.80	28.577	28.602	0	0	28.577	28.602
3	Air	962.4	962.4	850	850	94.75	94.80	43.54	43.56	0	0	43.54	43.56
4	Methane	1200	1200	298.15	298.15	1.704	1.705	0.654	0.651	87.579	87.628	88.234	88.280
5	Comb. gas	914.2	914.2	1520	1520	96.454	96.508	105.761	104.989	0.3805	0.3807	106.142	105.370
6	Comb. gas	115.7	115.7	1006	1006.1	96.454	92.508	41.947	41.148	0.3805	0.3807	42.328	41.528

,

Table 5. Comparison of the component percentages of the syngas obtained from this work and those reported in the literature (wood-CH_1.44O_0.66, MC = 20%, T_Ga = 1073.15 K).

Constituent	Cao et al. [36]	Roy et al. [45]	This Work
H2 (%)	21.66	21.63	21.50
CO (%)	20.25	20.25	20.21
CH4 (%)	1.011	0.98	0.95
CO2 (%)	12.36	12.48	12.50
N2 (%)	44.72	44.94	44.84

,

Table 6. Comparison of the results obtained from this work with those reported by Saleh et al. [46] for the ORC cycle using R600a as the working fluid.

Parameter	Teva (K)	Tcon (K)	Pcon (kPa)	Peva (kPa)	$\dot{\mathit{m}}$ (kg/s)	ηth (%)
Ref. [46]	373.15	303.15	403.8	1998	20.423	12.12
This work	373.15	303.15	404.7	1987	20.568	12.12

and

Table 7. Comparison of the simulation results of the LiBr-H₂O SEAC in this work with those reported by Nondy et al. [30] under the same operating conditions (${\dot{Q}}_{\mathrm{eva}}$ = 3.51 kW, T_gen = 363.15 K, T_eva = 280.15 K, T_abs = 313.15 K, T_con = 313.15 K, ${\mathsf{\epsilon }}_{\mathrm{SHE}}$ = 0.8).

Parameter	Ref. [30]	This Work
Heat capacity of generator (kW)	4.5999	4.6000
Heat capacity of condenser (kW)	3.7432	3.7420
Heat capacity of absorber (kW)	4.368	4.368
Evaporator pressure (kPa)	1.0021	1.0021
Condenser pressure (kPa)	7.3844	7.3849
Weak solution concentration (%)	62.33	62.15
Strong solution concentration (%)	56.72	56.66
Refrigerant mass flow rate (kg/s)	0.0015	0.0015
Weak solution mass flow rate (kg/s)	0.0151	0.0154
Strong solution mass flow rate (kg/s)	0.0166	0.0169
Coefficient of performance	0.763	0.763

show considerable concordance between the outcomes of this study and those documented in existing literature. This consistency underscores the reliability of the developed model in accurately predicting the performance of the proposed system.

4.2. Base Case Results

Table 8. Input parameters for the proposed system.

Parameter	Value	Unit
DFGT [15,18]
Air compressor isentropic efficiency (${\eta }_{\mathrm{is},\mathrm{AC}}$)	87	%
Air compressor pressure ratio (${\mathit{PR}}_{\mathrm{AC}}$)	9	-
Gas turbine isentropic efficiency (${\eta }_{\mathrm{is},\mathrm{GT}}$)	89	%
Inlet temperature of combustion chamber (T3)	850	K
Gas turbine inlet temperature (T5)	1400	K
Exhaust gas temperature at the outlet of air preheater (T11)	1000	K
Pressure drop of gas in the CC	1	%
Pressure drop of air in the AP	5	%
Pressure drop of flue gas in the AP	3	%
Pressure drop of flue gas in the PCC	1	%
Pressure drop of flue gas in the HRSG	5	%
Pressure drop of flue gas in the VG	5	%
Net power output of DFGT (${\dot{W}}_{\mathrm{DFGT}}$)	5000	kW
SRC [44]
Turbine inlet pressure (P15)	12,000	kPa
Pinch point temperature difference of HRSG (ΔTPP,HRSG)	30	K
Condenser temperature (T17)	363.15	K
Steam turbine isentropic efficiency (${\eta }_{\mathrm{is},\mathrm{ST}}$)	85	%
Pump isentropic efficiency (${\eta }_{\mathrm{is},\mathrm{pu}1}$)	80	%
SEAC [47]
Generator temperature (T18)	358.15	K
Absorber temperature (T21)	308.15	K
Condenser temperature (T25)	308.15	K
Evaporator temperature (T27)	278.15	K
Effectiveness of solution heat exchanger	70	%
Cooling water inlet/outlet temperature in absorber (T28/T29)	298.15/303.15	K
Cooling water inlet/outlet temperature in condenser (T30/T31)	298.15/303.15	K
Cooling water inlet/outlet temperature in evaporator (T32/T33)	285.15/280.15	K
ORC [40]
Turbine inlet pressure (P35)	2200	kPa
Condenser temperature (T37)	308.15	K
Turbine isentropic efficiency (${\eta }_{\mathrm{is},\mathrm{VT}}$)	80	%
Pump isentropic efficiency (${\eta }_{\mathrm{is},\mathrm{pu}2}$)	80	%
Cooling water inlet/outlet temperature in condenser (T38/T39)	298.15/303.15	K

details the input parameters for the four subsystems. Utilizing these values and resolving the associated mathematical equations yields the simulation outcomes. The thermodynamic and economic characteristics of each stream are catalogued in

Table 9. Thermodynamic properties and costs of the streams for the system.

State	Fluid	$\dot{\mathit{m}}$ (kg/s)	P (kPa)	T (K)	h (kJ/kg)	s (kJ·kg−1·K−1)	$\dot{\mathit{Ex}}$ (kW)	$\dot{\mathit{C}}$ ($/h)	c ($/GJ)
1	Air	17.65	101.3	298.15	0	6.888	78.61	0	0
2	Air	17.65	911.70	583.84	299.94	6.957	5010.0	283.38	15.71
3	Air	17.65	866.12	850	595.16	7.388	7953.10	404.32	14.12
4	Natural gas	0.247	866.12	298.15	−4666.96	10.497	12,895.01	401.91	8.66
5	Comb. gas	17.90	857.45	1400	522.49	8.147	17,027.69	810.20	13.22
6	Comb. gas	17.90	116.88	924.59	−52.67	8.227	6309.26	300.20	13.22
7	Biomass	0.570	101.3	298.15	−7104.72	-	9940.34	61.54	1.72
8	Air	0.924	101.3	298.15	0	6.888	4.12	0	0
9	Biogas	1.494	101.3	1073.15	−2710.35	10.099	8439.52	67.26	2.21
10	Comb. gas	19.39	115.72	1218.70	−257.48	8.608	12,230.98	370.59	8.42
11	Comb. gas	19.39	112.24	1000	−526.19	8.374	8373.34	253.71	8.42
12	Comb. gas	19.39	106.63	438.98	−1181.43	7.434	1105.16	33.49	8.42
13	Comb. gas	19.39	101.3	378.15	−1247.79	7.286	672.52	20.38	8.42
14	Water	3.77	12,000	364.63	392.45	1.201	146.43	7.44	14.11
15	Water	3.77	12,000	934.61	3762.28	6.975	6361.88	238.80	10.43
16	Water	3.77	70.18	368.15	2669.70	7.506	1645.41	61.76	10.43
17	Water	3.77	70.18	363.15	377.04	1.193	97.84	3.67	10.43
18	LiBr/H2O	21.33	5.63	358.15	217.14	0.463	1786.19	80.89	12.58
19	LiBr/H2O	21.33	5.63	323.15	152.58	0.273	1616.21	73.20	12.58
20	LiBr/H2O	21.33	0.87	323.15	152.58	0.273	1616.21	73.20	12.58
21	LiBr/H2O	24.13	0.87	308.15	85.37	0.211	649.27	27.35	11.70
22	LiBr/H2O	24.13	5.63	308.15	85.37	0.211	649.27	27.36	11.70
23	LiBr/H2O	24.13	5.63	336.17	142.44	0.389	751.37	35.23	13.03
24	Water	2.80	5.63	358.15	2659.54	8.637	248.94	13.06	14.58
25	Water	2.80	5.63	308.15	146.63	0.505	1.65	0.09	14.58
26	Water	2.80	0.87	278.15	146.63	0.528	−17.33	−0.91	14.58
27	Water	2.80	0.87	278.15	2510.06	9.025	−493.41	−25.89	14.58
28	Water	393.56	101.3	298.15	104.92	0.367	0	0	0
29	Water	393.56	101.3	303.15	125.82	0.437	68.21	20.97	85.38
30	Water	336.79	101.3	298.15	104.92	0.367	0	0	0
31	Water	336.79	101.3	303.15	125.82	0.437	58.37	13.12	62.45
32	Water	315.58	101.3	285.15	50.51	0.181	385.78	0	0
33	Water	315.58	101.3	280.15	29.53	0.106	749.07	26.17	9.70
34	R600a	3.27	2200	309.45	287.69	1.289	176.46	15.65	24.64
35	R600a	3.27	2200	378.71	681.08	2.379	400.36	33.23	23.05
36	R600a	3.27	464.77	324.79	632.72	2.416	205.50	17.06	23.05
37	R600a	3.27	464.77	308.15	283.67	1.286	165.83	13.76	23.05
38	Water	54.63	101.3	298.15	104.92	0.367	0	0	0
39	Water	54.63	101.3	303.15	125.82	0.437	9.47	6.09	178.71

, while

Table 10. Exergy and exergoeconomic factors for the system.

Component	${\dot{\mathit{Ex}}}_{\mathit{F},\mathit{k}}$ (kW)	${\dot{\mathit{Ex}}}_{\mathit{P},\mathit{k}}$ (kW)	${\dot{\mathit{Ex}}}_{\mathit{D},\mathit{k}}$ (kW)	${\mathit{\eta }}_{\mathit{ex},\mathit{k}}$ (%)	${\dot{\mathit{Z}}}_{\mathit{k}}$ ($/h)	${\dot{\mathit{C}}}_{\mathit{D},\mathit{k}}$ ($/h)	fk	rk
Air compressor	5294.15	4931.39	362.76	93.15	15.50	18.36	0.458	0.136
Air preheater	3857.64	2943.11	914.54	76.29	4.06	27.71	0.128	0.356
Combustion chamber	20,848.12	17,027.69	3820.43	81.67	3.97	147.74	0.026	0.230
Gas turbine	10,718.43	10,294.15	424.28	96.04	10.87	20.19	0.350	0.063
PCC	14,748.78	12,230.98	2517.80	82.93	3.13	62.73	0.047	0.216
Biomass gasifier	9944.45	8439.52	1504.93	84.87	5.71	9.31	0.380	0.288
HRSG	7268.17	6215.45	1052.72	85.52	11.15	31.90	0.259	0.229
Steam turbine	4716.47	4119.79	596.68	87.35	8.59	22.40	0.277	0.200
Pump 1	58.10	48.59	9.51	83.63	1.15	0.43	0.728	0.720
Generator	1547.57	1283.77	263.81	82.95	0.63	9.90	0.060	0.219
SHE	169.98	102.10	67.89	60.06	0.18	3.07	0.055	0.703
Absorber	473.53	68.21	405.32	14.41	1.02	17.08	0.056	6.296
Condenser	247.29	58.37	188.92	23.61	0.15	9.91	0.014	3.284
Evaporator	476.07	363.29	112.79	76.31	1.18	5.92	0.167	0.373
Vapor generator	432.65	223.90	208.74	51.75	4.47	6.32	0.414	1.591
Vapor turbine	194.86	158.19	36.66	81.18	2.28	3.04	0.428	0.405
Vapor condenser	39.67	9.47	30.20	23.87	2.80	2.51	0.528	6.752
Pump 2	13.16	10.62	2.54	80.72	0.35	0.30	0.545	0.524

displays the distribution of exergy and exergoeconomic parameters across the cogeneration system’s components. The findings highlight that the air compressor incurs the highest investment cost rate at 15.50 $/h, with the HRSG and gas turbine following at 11.15 $/h and 10.87 $/h, respectively. From an exergy perspective, the gas turbine and air compressor exhibit superior performance, both exceeding 90% in exergy efficiency, whereas the SEAC’s absorber demonstrates the lowest exergy efficiency at 14.41%.

Figure 2 and Figure 3 illustrate the contributions to the exergy destruction rate and the cost associated with exergy destruction across the system components, respectively. As can be seen, the combustion chamber leads in the exergy destruction rate, contributing to 30.51% of the system’s total exergy destruction, followed closely by the post-combustion chamber. This high rate of exergy destruction, coupled with the significant fuel cost rate, also makes the combustion chamber the highest cost of exergy destruction.

Table 11. Thermodynamic and exergoeconomic evaluation results of the base case.

Performance Parameters	Unit	Value
SRC turbine work (${\dot{W}}_{\mathrm{ST}}$)	kW	4119.79
SRC pump consumed power (${\dot{W}}_{\mathrm{pu}1}$)	kW	58.10
ORC turbine work (${\dot{W}}_{\mathrm{VT}}$)	kW	158.19
ORC pump consumed power (${\dot{W}}_{\mathrm{pu}2}$)	kW	13.16
Net power output (${\dot{W}}_{\mathrm{net}}$)	kW	9206.7
Cooling output (${\dot{Q}}_{\mathrm{eva}}$)	kW	6621
Annual net power output	MW·h	73,653.8
Annual cooling output	GJ	190,685.0
Thermal efficiency (${\eta }_{\mathrm{th}}$)	%	75.69
Exergy efficiency (${\eta }_{\mathit{ex}}$)	%	41.76
Unit cost of the GT produced power ($c_{\mathrm{GT}}$)	$/GJ	14.06
Unit cost of the SRC produced power ($c_{\mathrm{SRC}}$)	$/GJ	12.52
Unit cost of the ORC produced power ($c_{\mathrm{ORC}}$)	$/GJ	32.39
Unit cost of exergy production for cooling ($c_{\mathrm{eva}}$)	$/GJ	9.70
SUCP of the system (${\mathit{SUCP}}_{\mathrm{sys}}$)	$/GJ	13.37

presents the thermodynamic and exergoeconomic evaluation results of the cogeneration system in the base case. The results suggest that the system can produce a net power of 9206.7 kW and a cooling capacity of 6621 kW. Taking into account the operating hours per year, the annual power and cooling production are estimated to be 73,653.8 MW·h and 190,685.0 GJ, respectively. The overall energy efficiency, exergy efficiency, and SUCP stand at 75.69%, 41.76%, and 13.37 $/GJ, respectively. Moreover, the unit cost of power generated by the ORC turbine (32.39 $/GJ) significantly surpasses that of the gas turbine (14.06 $/GJ) and the SRC turbine (12.52 $/GJ), while the unit cost of the cooling product is comparatively lower, at 9.70 $/GJ.

4.3. Parametric Study

4.3.1. Effect of Air Compressor Pressure Ratio on the System Performance

Figure 4 presents the effect of the air compressor pressure ratio (PR_AC) on the system performance. With the increase in the PR_AC, the thermal and exergy efficiencies reach their peak values at a higher value of the PR_AC of about 14 and decrease subsequently. On the contrary, the SUCP reaches its nadir when the value of PR_AC is around 9 and then increases. The trends can be explained by the fact that the system performance depends on the performance of DFGT because the efficiencies of the bottoming cycles are kept unchanged due to fixed operating parameters. According to the DFGT, the thermal heat supplied by natural gas and biomass is minimal at a specific PR_AC under the constant output power. At this point, the DFGT exhibits the highest thermal and exergy efficiencies, while the mass flow rate of exhaust gas is at its lowest. Consequently, the net power output and cooling capacity, as well as exergy destruction, have minimum values.

4.3.2. Effect of Preheated Air Temperature on the System Performance

Figure 5 demonstrates the effect of the preheated air temperature (PAT) on the system performance. From Figure 5a, the negative correlations between PAT and thermal efficiency, exergy efficiency, and SUCP are observed. Meanwhile, as depicted in Figure 5b, the net power and cooling capacity, as well as exergy destruction of the system, present upward trends with an increase in the PAT. This is mainly due to the syngas consumption increasing as the PAT rises, leading to reduced system efficiency and an increased exhaust gas mass flow rate. Thus, the net power and cooling capacity increase because more thermal energy of exhaust gas could be utilized in the bottoming cycles.

4.3.3. Effect of Gas Turbine Inlet Temperature on the System Performance

The impact of the gas turbine inlet temperature (GTIT) on the system performance is sketched in Figure 6. Observations from Figure 6a,b indicate that the thermal and exergy efficiencies are augmented with an increasing GTIT, while the net power and cooling capacity, as well as exergy destruction, decrease. This might be explained by the fact that, as the GTIT rises, the mass flow rate of the flue gas declines significantly due to the enthalpy difference through the gas turbine increasing when the power capacity of the DFGT is kept constant. As a consequence, the syngas consumption in the post-combustion chamber decreases dramatically as the GTIT is augmented, even though the natural gas consumption increases slightly, resulting in the reduction in total fuel consumption; thus, the energy and exergy efficiencies will increase. In addition, the net power and cooling capacity of the system decrease because less thermal heat is available for the bottoming cycles. The increase in the SUCP is mainly attributed to the increased investment cost of the gas turbine, which is very sensitive to the higher GTIT.

4.3.4. Effect of Steam Turbine Inlet Pressure on the System Performance

The effect of the steam turbine inlet pressure (STIP) on the system performance is presented in Figure 7. As shown in Figure 7a, the exergy efficiency improves as the STIP rises, while the energy efficiency drops at first and then increases. According to Figure 7b, an elevation in the STIP results in an increase in net power owing to the improvement in the SRC efficiency. However, the reduction in SRC condensation heat leads to the decrease in cooling capacity. Consequently, the exergy efficiency improves, reflecting the higher quality of electricity production compared to cooling capacity.

4.3.5. Effect of SRC Condensation Temperature on the System Performance

Figure 8 illustrates the influence of the SRC condensation temperature on the system performance. As shown in Figure 8a, an increase in the SRC condensation temperature results in an increase in the SUCP and a decrease in exergy efficiency, while the thermal efficiency will be maximized. According to Figure 8b, the net power declines as the SRC condenser temperature rises owing to the decrease in SRC efficiency, while the cooling capacity of the SEAC is augmented due to its COP and the input heat increase. System thermal efficiency is contingent on the combined output of the power and cooling capacity. Meanwhile, the output exergy declines as the net power drops because the quality of electricity is higher than that of the cooling capacity, which causes the exergy efficiency to decrease. Moreover, the SUCP and TCR increase slightly because the investment costs of SEAC components become higher.

4.3.6. Effect of ORC Turbine Inlet Pressure on the System Performance

The effect of the ORC turbine inlet pressure on the system performance is presented in Figure 9. Obviously, changes in the ORC turbine inlet pressure do not affect the topping cycles, with variations only observed in the bottoming ORC cycle. According to Figure 9, slight increases in thermal and exergy efficiencies, as well as SUCP, are noted with the rise in the ORC turbine inlet pressure. In general, the ORC turbine inlet pressure has little influence on the system performance because the power produced by the ORC constitutes a small fraction of the total output power.

4.4. Optimization Results

This section outlines the findings from a multi-objective optimization process, aimed at identifying the best operating parameters for the system under consideration. The primary goals of this optimization are to enhance exergy efficiency and minimize the specific SUCP, addressing both thermodynamic and economic factors. Key operating parameters and their respective limits, ascertained through a parametric study, are detailed in

Table 12. Selected decision variables of the proposed system and their limits.

Parameter	Unit	Range
PRAC	-	$6\le {\mathit{PR}}_{\mathrm{AC}} \le 16$
$T_3$	K	${650\le T}_3\le 950$
$T_5$	K	${1100\le T}_5\le 1500$
$P_{15}$	kPa	${\mathrm{10,000}\le P}_{15}\le \mathrm{18,000}$
$T_{17}$	K	${358.15\le T}_{17}\le 368.15$
$P_{35}$	kPa	${1500\le P}_{35}\le 3500$

. A Genetic Algorithm (GA) process, formulated in MATLAB, is employed for this dual-objective optimization task. Figure 10 presents the Pareto frontier derived from these optimization results, where each point signifies an optimal solution. Notably, an increase in exergy efficiency corresponds to an increase in the SUCP, revealing a distinct compromise between these two objectives. The peak exergy efficiency is achieved at point A, whereas the lowest SUCP is found at point B. To pinpoint the most suitable final optimal solution, the TOPSIS method is applied, resulting in the selection of point C as the ultimate choice.

Table 13. The values of decision variables and objective functions at points A, B, and C.

Parameter	A	B	C
PRAC	13.76	9.03	9.50
T3 (K)	788.37	857.93	858.70
T5 (K)	1499.94	1301.68	1373.42
P15 (kPa)	14,739.51	14,239.23	14,215.99
T17 (K)	358.41	358.88	358.33
P35 (kPa)	2990.84	3045.45	3026.29
${\dot{W}}_{\mathrm{net}}$(kW)	8517.86	10,315.28	9612.41
${\dot{Q}}_{\mathrm{eva}}$ (kW)	5039.52	7710.96	6657.44
ηth (%)	77.31	74.31	75.19
ηex (%)	46.52	39.92	41.90
${\mathit{SUCP}}_{\mathrm{sys}}$ ($/GJ)	15.03	12.42	12.99

displays the values for the objective functions and decision variables at points A, B, and C on the Pareto frontier.

5. Conclusions

In this study, the combination of the SRC, SEAC, and ORC as a cogeneration system is suggested for the waste heat recovery of a DFGT cycle fed by natural gas and biomass. A detailed thermodynamic and exergoeconomic evaluation, parametric analysis, and two-objective optimization of the system have been carried out. The main conclusions are summarized as follows:

(1)

In the baseline scenario, the system achieves the overall energy efficiency, exergy efficiency, and SUCP of the system of 75.69%, 41.76%, and 13.37 $/GJ respectively. Concurrently, it generates net power and cooling capacities of 9206.7 kW and 6621 kW.

(2)

Within the system, the combustion chamber is the primary contributor to the exergy destruction rate, followed closely by the post-combustion chamber. These two components also significantly contribute to the cost of exergy destruction.

(3)

Optimal thermal and exergy efficiencies are achieved at a higher air compressor pressure ratio of approximately 14, while the lowest SUCP is observed at a pressure ratio near 9.

(4)

Improvements in thermal and exergy efficiencies can be achieved by increasing the gas turbine inlet temperature or decreasing the preheated air temperature at the expense of economic performance deterioration.

(5)

The system performs better regarding exergy efficiency and SUCP at a higher SRC inlet pressure or lower SRC condensation temperature.

(6)

Under the optimal operating conditions, the system achieves an enhancement in exergy efficiency by 0.3% and a decrease in the SUCP by 2.8%, relative to the baseline scenario.

The primary challenge of DFGT-based cogeneration systems lies in their complexity, which poses significant issues for maintaining reliability and stability. Addressing this requires advanced control strategies and expert management, as complexity tends to increase maintenance demands and operational costs, thereby impacting the economic feasibility of the system. Future research could focus on developing dynamic simulation models to thoroughly analyze the system’s behavior under varying operational conditions. Such studies would be crucial in assessing the system’s stability and adaptability, thus providing deeper insight into its practical effectiveness and long-term sustainability. Additionally, incorporating real-time operational data in future research could significantly enhance the precision and validity of these dynamic models.