A biogas-fired cogeneration (cooling and power) system combined with biomethane facilities: 3E evaluation, sensitivity analyses and optimization

Abstract

The increasing demand for power and cooling generation presents a dual challenge: an unavoidable increase in carbon emissions from fossil fuel combustion and the associated difficulties in meeting the escalating investment requirements for power plant generation. As a result, there is an urgent call for the advancement of innovative cycles that not only improve performance, but also play a role in mitigating carbon emissions. This study presents a novel approach to biogas-powered cogeneration with the objective of concurrently producing electricity and cooling while utilizing heat from liquefied natural gas. The primary objective is to achieve a reduction in carbon emissions compared to similar existing work. The innovative system combines an open-loop Brayton cycle (gas turbine cycle) powered by biogas, a closed-loop Brayton cycle, a liquefied natural gas open power generation cycle, and a dual-stage combined cooling and power unit consisting of an organic Rankine cycle integrated with an ejector refrigeration cycle. A thermodynamic and economic analysis was conducted to assess the performance of the current study in comparison to previous models. To achieve optimum conditions, a comprehensive multi-objective optimization has been used, taking into account crucial decision variables, energy and exergy indicators, the carbon emission per energy ratio of the product, and the overall cost of the unit product. The results obtained underscore the environmental superiority of this system over other proposals. In the most optimal state, this system demonstrates a remarkable 48% reduction in carbon emissions. Optimization reveals that the developed unit can generate 1860 kW of net electricity and 427.3 kW of cooling. Achieving an energetic efficiency of 80.79%, an exergetic efficiency of 41.5%, a carbon emission per energy ratio of product of 9.902 kg/kW per day, and a unit cost of products of 9.816 $/GJ. In particular, the energy efficiency of the integrated gas turbine closed-loop Brayton cycle system experiences a remarkable 71.17% improvement under optimal conditions. Among the various components of the developed cogeneration system, the combustion chamber contributes the most to the overall exergy destruction rate, closely followed by the condenser, the first heat exchanger of the liquefied natural gas power system. Proposed CCP system fueled by biogas and LNG.

Graphical abstract

1 Introduction

The imperative for power generation and cooling is essential for survival, gaining increasing importance with the increasing global population. The proliferation of fossil power plants is correlated with a surge in greenhouse gas emissions. Currently, power generation accounts for more than 30% of anthropogenic carbon dioxide emissions (Towhid Gholizadeh et al., 2024). The escalation in carbon dioxide emissions contradicts the objectives established by the Intergovernmental Panel on Climate Change (IPCC), specifically the goal of limiting the temperature increase to two degrees by the end of the century compared to the preindustrial era. Hence, scientists are currently confronted with a fundamental challenge: escalating power and cooling production in alignment with environmental constraints and concurrently mitigating the emission of greenhouse gases. The growing focus on integrating renewable energy into energy systems is a result of Global initiatives aimed at reducing fossil fuel consumption. In this context, the waste heat produced by biogas-powered energy systems presents an opportunity to improve the performance of these systems and mitigate their greenhouse gas emissions. Waste heat emanating from diverse power generation systems, typically characterized by elevated temperatures and exergy, is normally released into the environment, causing significant deleterious effects. Although efforts have been made to harness waste energy, the results have been varied, with some initiatives achieving notable success, while others exhibited suboptimal performance or lacked economic viability. Therefore, the design of an optimal system to mitigate wasted energy, offering economic and environmental advantages along with optimal efficiency, is of particular importance.

In this regard, numerous efforts have been made in recent years; Ghaebi et al. (Ghaebi et al.) Utilized waste heat from a biogas steam reforming (BSR) system to generate electricity. They achieved this using an organic Rankine cycle (ORC) with R600 as the working medium. Through optimization efforts, it was determined that critical parameters such as the steam-to-carbon ratio and the carbon dioxide (CO₂) to methane (CH₄) ratio should be set at 2.99 and 0.502, respectively, to achieve the optimal operating mode. Zareh et al. (Zareh et al.-a) conducted an investigation on a combined heat and power (CHP) system, exploring its exergoeconomic and thermodynamic relationships when using natural gas (NG) and biogas as input fuels. The study revealed that the combustion chamber and anaerobic processes were the main contributors to the overall irreversibility of the biogas-based scenario. In particular, their findings demonstrated an improvement in the energetic performance factor from 46.94 to 50.64%, accompanied by a reduction in the total product cost (OPC) from 98.71 to 66.7 $/MWh when transitioning from biogas to natural gas utilization. Although their innovation led to a 32% improvement in economic criteria, there was a lack of investigation into potential environmental penalties. Amiri et al. (Amiri et al.) formulated a robust optimization model for a biogas-driven combined heat and power (CHP) system in Sweden. Their study demonstrated a significant annual reduction of 21,000 tons in CO₂ emissions compared to a conventional coal-fired power plant. On the other hand, their invented system yields a significant annual cost benefit of 22 MSEK. Zeng et al. (Zeng et al., 2017) integrated a porous media burner into the combustion chamber of a combined heat and power (CHP) system, utilizing non-catalytic fuel. This approach was aimed at ensuring consistent, high-temperature reformed syngas suitable for a biogas-fueled solid oxide fuel cell (SOFC), thereby extending the system’s startup time. The experimental results underscored the achievement of a reforming efficiency of 42.3%. Jabari et al. (Jabari et al.) developed a combined cooling and power (CCP) system based on a biogas-driven gas turbine (GT) cycle for a hotel located in Iran. The authors employed a mixed integer nonlinear program to minimize the calculated total product cost (OPC) by optimizing power consumption within the setup. Although they asserted that the innovative system could potentially reduce carbon emissions, no specific environmental impact metrics were provided. In a groundbreaking study, Leonzio (Engineering and 2018) developed and examined a biogas-powered trigeneration system that integrated two heat pumps, a Rankine cycle power plant, and a heat recovery unit. This configuration generated 925 kW of electricity, a cooling load of 473 kW and a thermal load of 2523 kW, using a biogas input of 3280 kW. The reported primary energy rate (PER) was 1.04. The simulation results indicated a 40% reduction in CO2 emissions and a 28% increase in electricity production through this designed unit. Sevinchan et al. (Sevinchan et al.) employed a Brayton cycle, an ORC, a two-stage biomass digester, a water separator, a single-effect absorption cooling system (ACS) and a heat recovery unit for multigeneration. The devised unit produced a cooling load of 87.54 kW, electricity of 1078 kW, fresh water of 40 kg/day, and a heating load of 198 kW. Furthermore, the overall first- and second-law efficiencies were found to be 72.5% and 30.44%, respectively. Based on a BSR foundation, Rostamzadeh et al. (Rostamzadeh et al., 2018, 2019) recommended the use of a geothermal hybridized biogas for polygeneration purposes. They showcased the viability of this configuration from economic, thermodynamic, and environmental perspectives. They demonstrated that reducing the CO2 / CH4 molar ratio or increasing the steam per carbon ratio increased the energetic performance of the entire set-up. Su et al. (Su et al., 2018) employed a reforming reaction to convert biogas into syngas and subsequently integrated solar energy to initiate a combined cooling, heating, and power (CCHP) system. Their findings highlighted a 5.41% increase in efficiency for the hybrid solar-biogas CCHP system compared to a reference system. Although their findings highlighted superior operational performance, the lack of attention to environmental and economic concerns has raised doubts about the viability of using this system. In a recent investigation, Liang et al. (Liang et al., 2020) optimized a novel solar-driven supercritical Brayton cycle (SBC) focusing on thermodynamic aspects and excluding economic and environmental considerations from their optimization process. In a separate investigation conducted by Ochoa et al. (Ochoa et al., 2017), the performance of an SBC coupled with an ORC was enhanced solely in terms of thermodynamics through optimization. This optimization process excluded considerations of environmental impact (environment index, EI) and unit cost. In another similar work, Yang et al. (Yang et al.) included an economic metric in the optimization of a CCHP system based on SBC, but they also excluded EI from their multi-objective optimization scheme.

In recent years, there has been a growing body of research focused on integrated energy systems powered by biogas, with the overarching goal of improving the efficiency of primary systems, such as the gas turbine cycle, while simultaneously generating various energy products and mitigating their environmental impact. In fact, the quest for higher efficiency and reduced carbon emissions is a common goal among scientists exploring integrated energy systems. The considerable potential of large-scale biogas processes for versatile energy production, coupled with their ability to significantly reduce carbon emissions compared to fossil fuel-based power plants, underscores the enormous opportunities for their application. As scientists strive to improve the efficiency of integrated systems and minimize their environmental footprint, the continued exploration and development of biogas-driven solutions promise to yield even greater benefits for sustainable energy production.

Although certain objectives have been achieved through prior research, there remains a need for further studies to enhance and extend the performance achievements reported so far. Recently, we introduced an innovative system (Gholizadeh et al. 2019a) propelled by a biogas-fueled gas turbine (GT) cycle. The system’s performance is optimized through the incorporation of a modified organic Rankine Cycle (ORC), demonstrating superior thermodynamic and thermoeconomic characteristics. Although an ORC has a simpler structure, enhancing reliability, it is essential to recognize that the use of organic refrigerants remains a challenge because of concerns related to flammability and toxicity. Furthermore, when operating at elevated exhaust gas temperatures, a notable temperature discrepancy arises between the exhaust gases and the organic fluid in the ORC. This discrepancy can be effectively addressed by implementing a closed-loop Brayton cycle (CLBC) between the GT cycle and the envisioned combined cooling and power (CCP) system. The integration of a CLBC offers a solution to temperature differentials, enhancing the overall efficiency and reliability of the system. In other studies, we have used waste thermal energy from the GT cycle through a single vapor generator for an ORC-based CCP system (Gholizadeh et al. 2019b) or for the trigeneration of cooling, power, and fresh water (Gholizadeh et al. 2020). However, in this investigation, a pioneering strategy is adopted by integrating a dual stage cooling and power cogeneration configuration that combines the incorporation of a CLBC with an organic Rankine Cycle (ORC) and an ejector refrigeration cycle (ERC). This study illustrates the advantages of using a high-temperature power system such as the CLBC to recover waste heat from a gas turbine (GT), as opposed to directly integrating an ORC-based system after the GT cycle. Unlike previous proposed designs (references (Gholizadeh et al., 2019a, 2019b, 2020)), which faced substantial exergy losses due to the low efficiency in converting GT cycle exergy into the underlying ORC system, our approach addresses this concern. It should be noted that in our previous work, the environmental and economic implications of the proposed system were not emphasized extensively. Despite the improvement in performance, there has been ambiguity regarding their environmental effects. The novel approach introduced here incorporates a closed-loop Brayton Cycle (CLBC) between the bottoming and topping cycles, effectively mitigating thermal mismatch and enhancing power conversion efficiency. Consequently, the operational efficacy of the system exceeds previous designs, particularly in terms of power conversion efficiency. Furthermore, this study introduces the integration of an open source LNG power generation cycle, using a preheater to capture exhaust gas heat from the gas turbine (GT) cycle. This integration not only elevates the overall power conversion efficiency, but also facilitates the conversion of liquefied natural gas to its gaseous form. The comparative analysis within this study’s subsection quantitatively illustrates the superiority of our developed system over previously proposed configurations. Thus, beyond the practical application of such a system, our primary goal is to theoretically improve the system from a thermodynamic perspective, minimize energy wastage, and, most importantly, increase efficiency while reducing carbon emissions to reach a sustainable integrated system. In particular, our system has a distinct advantage over references (T Gholizadeh, Vajdi, and, and 2019-b), (Al-Rashed et al.), and (Zareh et al.-b).

Therefore, this study introduces a pioneering approach to waste heat recovery within a biogas-based gas turbine (GT) cycle. The innovative strategy adopts an advanced operating mode characterized by exceptional efficiency. The envisioned system architecture includes a closed-loop Brayton Cycle (CLBC), a dual-stage combined cooling and power (CCP) unit integrating an organic rankine cycle (ORC) employing R245fa as the working fluid, synergistically combined with an ejector refrigeration cycle (ERC), along with a power generation module using liquefied natural gas (LNG). The primary objectives of this investigation can be succinctly delineated as follows.

• (1) The novel waste heat recovery solution for the biogas-propelled GT cycle enhances overall power generation through a tripartite approach that involves a closed-loop Brayton Cycle (CLBC), an organic Rankine cycle (ORC), and a power generation cycle powered by liquefied natural gas (LNG).

• (2) A thorough investigation has been conducted to assess the environmental and economic aspects of the proposed systems. This study introduces key metrics such as net present value (NPV) and carbon emission per energy rate of Products (CDE) for a comprehensive evaluation.

• (3) Integration of an ejector refrigeration cycle (ERC) with the ORC allows cooling generation as an enhancing mechanism.

• (4) The hierarchical waste management strategy introduced in this investigation improves operational efficiency in terms of thermodynamics and economics, surpassing similar approaches.

• (5) An analysis of sensitivity factors is conducted.

• (6) A comprehensive exploration encompassing thermodynamic and economic parameters is performed, along with a multiobjective optimization utilizing a genetic algorithm.

2 System description

Figure 1 illustrates the innovative biogas-powered cogeneration system, strategically engineered to meet demand for both electricity generation and cooling. The setup consists of four discrete components: a biogas-driven gas turbine (GT) cycle, a dual stage combined cooling and Power (CCP) system merging an organic Rankine Cycle (ORC) with an ejector refrigeration cycle (ERC), a closed-loop Brayton cycle (CLBC), and a power generation module exploiting liquefied natural gas (LNG).

Fig. 1

Proposed CCP system fueled by biogas and LNG

In the gas turbine (GT) cycle, the process begins with the intake of ambient air, which is compressed by the compressor. The compressed air is then directed to the combustion chamber, where the biogas supplied undergoes combustion. The resulting high-energy gas is used in the gas turbine (GT) to generate electricity. The exhaust gases, which carry high temperatures, flow into the gas heater (GH) to drive the closed-loop Brayton Cycle (CLBC). Subsequently, the exhaust gases proceed to the preheater (PH), where they transfer heat to the natural gas (NG). In the closed-loop Brayton Cycle (CLBC) phase, supercritical CO2 functions as the circulating working fluid. Through gas turbine 2, supercritical CO2 undergoes expansion, transferring its thermal energy to the dual-stage combined cooling and power (CCP) system via vapor generator 1 (VG 1). Subsequently, CO2 undergoes compression and cooling, transitioning to the saturated vapor state through VG2. Subsequently, the vapor is recompressed to supercritical CO2 using compressor 1. The dual-stage combined cooling and power (CCP) cycle harnesses the heat energy from the closed-loop Brayton Cycle (CLBC) in two steps. Initially, saturated vapor is guided into the first turbine, acting as the primary flow for the ejector. When the secondary flow occurs, the combined mixture is expelled from the ejector and subsequently entered the condenser. In this phase, the mixture is condensed and divided into two separate streams. One stream undergoes expansion to reach the evaporator pressure before entering the ejector. Meanwhile, the second flow is directed to vapor generator 2 (VG2) using mechanical power for pumping. The VG2 effluent is then divided into two streams. One stream enters turbine 1, while the second stream is pumped back to VG2 pressure with the aid of pump 2, thus completing the two-stage CCP process. Within the section dedicated to open LNG (LNG) power generation, the stored LNG undergoes pressurization within a storage tank, attaining the necessary pressure level through an isentropic procedure. Subsequently, the energy contained in LNG is extracted through a dual-stage approach comprising a condenser and a pre-cooler. LNG then undergoes expansion through the second turbine and is utilized as natural gas (NG).

In the realm of thermodynamics, where energy transformations govern the behavior of substances, the temperature-entropy (T-S) diagram emerges as a vital tool. Therefore, in Fig. 2, the T-S diagrams of the cycle are presented.

Fig. 2

T-S diagrams of the proposed cycle for a carbon dioxide and b R245fa

3 Materials and methods

3.1 Assumptions

The thermal modeling of the developed cogeneration system is based on the following assumptions.

• 1. The simulation and corresponding analysis are conducted under the assumption of steady-state conditions (Hamed Ghiasirad & Skorek-Osikowska, 2023).

• 2. The gas mixture is treated according to the ideal gas assumption (Ghiasirad, et al. 2023).

• 3. 2% of the LHV of the fuel is presumed as thermal loss of combustion (Javanfam et al., 2022).

• 4. A pressure drop of approximately 4% is considered for the combustion chamber (T Gholizadeh, Vajdi, and, and 2020).

• 5. According to experimental data considering wastewater sludge as biomass, the molar share of CH4, CO₂ and H₂O in biogas is approximately 62.26%, 36.09%, and 1.65%, respectively (Mirmasoumi et al., 2018).

• 6. Air is constituted from 77.48% of ${N}_{2}$, 20.59% of ${O}_{2}$, 0.03% of ${CO}_{2}$, and 1.9% of ${H}_{2}O$ $(\text{Hamed Ghiasirad et al}.\boldsymbol{ }2022)$.

Furthermore, the necessary quantitative data and assumptions are presented in detail in Table 1.

Table 1 Input parameters for similutaion

3.2 Thermodynamic analysis

Using mass and energy conservation equations in general form, the mass and enthalpy required for a specific state can be computed as Mass balance relation:

$$\sum\limits_{i} {\mathop m\limits^{ \cdot } _{{in}} } = \sum\limits_{O} {\mathop m\limits^{ \cdot } _{{out}} }$$

(1)

where $\dot{m}$ is the mass flow rate.

Energy balance relation (Gholizadeh Baris et al., 2023):

$$\dot{Q}_{c.v.} - \dot{W}_{c.v.} = \sum \left( {\dot{m}h} \right)_{out} - \sum (\dot{m}h)_{in}$$

(2)

where $\dot{Q}_{c.v.}$ and $\dot{W}_{c.v.}$ refer to the heat transfer rate and work of the control volume, while any variations in kinetic and potential energies are disregarded.

The equilibrium equation grounded in second-law analysis for the k-th element of a system is expressed as (Towhid Gholizadeh et al., 2024):

$$\mathop {Ex}\limits^{ \cdot }_{D,k} + \mathop {Ex}\limits^{ \cdot }_{{\dot{W}_{k} }} - \mathop {Ex}\limits^{ \cdot }_{{\dot{Q}_{k} }} = \mathop \sum \limits_{i = 1}^{n} \mathop {Ex}\limits^{ \cdot }_{in,k,i} - \mathop \sum \limits_{i = 1}^{n} \mathop {Ex}\limits^{ \cdot }_{out,k,i}$$

(3)

$\dot{E}x_{D,k}$ denotes the exergy destruction rate, $\mathop {Ex}\limits^{ \cdot }_{{\dot{W}_{k} }}$ work rate, $\mathop {Ex}\limits^{ \cdot }_{{\dot{Q}_{k} }}$ heat loss, $\mathop {Ex}\limits^{ \cdot }_{in,k}$ the input stream exergy rate, and $\mathop {Ex}\limits^{ \cdot }_{out,k}$ the output stream exergy rate (Hamed Ghiasirad et al., 2020b).

$$\mathop {Ex}\limits^{ \cdot }_{{\dot{W}_{k} }} = \dot{W}_{k}$$

(4)

$$\mathop {Ex}\limits^{ \cdot }_{{\dot{Q}_{k} }} = \mathop \sum \limits_{j} \left( {1 - \frac{{T_{0} }}{{T_{j,k} }}} \right)\dot{Q}_{k}$$

(5)

The exergy rate of the input and output streams is dependent on the physical ($\mathop {Ex}\limits^{ \cdot }_{ph,k,i}$) and chemical ($\mathop {Ex}\limits^{ \cdot }_{ch,k,i}$) exergy rates (Hamed Ghiasirad et al., 2020b).

$$\mathop {Ex}\limits^{ \cdot }_{ph,k,i} = \dot{m}_{i} \left[ {\left( {h_{i} - h_{0,i} } \right) - T_{0} \left( {s_{i} - s_{0,i} } \right)} \right]$$

(6)

$$\mathop {Ex}\limits^{ \cdot }_{ch,k,i} = \dot{n}_{i} \left( {\sum Y_{m} \overline{ex}_{m}^{ch,o} + RT_{0} \sum Y_{m} ln\left( {Y_{m} } \right)} \right)$$

(7)

$Y_{m}$ represents the molar fraction of the ${\text{compound}} m$ in ${\text{stream}} i$, and $\overline{ex}_{m}^{ch,o}$ represent the chemical molar standard exergy.

Further, the exergy efficiency ($\eta_{ex,k}$) and the exergy destruction ratio ($y_{D,k}$) of ${\text{control volume }}k$ are obtained by:

$$\eta_{ex,k} = \frac{{\dot{E}x_{P,k} }}{{\dot{E}x_{F,k} }} \times 100$$

(8)

where $\dot{E}x_{P,k}$ refers to the product’s exergy and $\dot{E}x_{F,k}$ refers to the fuel’s exergy.

The energy and exergy relations for the simulated unit are listed in Table 8.

3.3 Economic analysis

Within this investigation, the specific exergy costing method (SPECO) was used to determine costs by integrating the exergy concept into each state of the system’s configuration. This approach, also called exergoeconomic analysis, is based on the cost balance equation depicted below (Adrian Bejan et al., 1996)

$$\dot{Z}_{k,PY} + \dot{C}_{{\dot{Q},k}} - \dot{C}_{{\dot{W}_{k} }} = \mathop \sum \limits_{i = 1}^{n} \dot{C}_{out,k,i} - \mathop \sum \limits_{i = 1}^{n} \dot{C}_{in,k,i}$$

(9)

where,

$$\dot{C}_{{\dot{Q},k}} = c_{{\dot{Q},k}} \left( {1 - \frac{{T_{0} }}{{T_{j} }}} \right)\dot{Q}_{k}$$

(10)

$$\dot{C}_{{\dot{W}_{k} }} = c_{{\dot{w},k}} \dot{W}_{k}$$

(11)

$$\mathop C\limits^{ \cdot }_{in,k,i} = c_{in,k,i} \mathop {Ex}\limits^{ \cdot }_{in,k,i}$$

(12)

$$\mathop C\limits^{ \cdot }_{out,k,i} = c_{out,k,i} \mathop {Ex}\limits^{ \cdot }_{out,k,i}$$

(13)

c refers to the unit cost per exergy. The investment cost rate of ${\text{control volume }}k$ ($\dot{Z}_{k}$) can be computed by (Adrian Bejan et al., 1996):

$$\dot{Z}_{k} = PEC_{k} \frac{ \varphi CRF }{N}$$

(14)

where $PEC_{k}$ is the equipment purchased for the purchased equipment cost of the ${\text{control volume }}k$. Furthermore, $\varphi$ is the maintenance factor, $N$ is the total number of hours that correspond to the operation throughout the year, and $CRF$ represents the capital recovery factor.

$$CRF = \frac{{i_{r} \left( {1 + i_{r} } \right)^{n} }}{{\left( {1 + i_{r} } \right)^{n} - 1}}$$

(15)

According to this equation, $CRF$ is a function of annual interest rate ($i_{r}$) and lifetime of the system ($n$).

Table 9 lists the related equations for the cost balance, the auxiliary equations, and $the PEC$ formulations for each control volume in Fig. 1. The $PEC$ of the heat exchangers depends on the active heat transfer area given by Eq. (16) (Kalan et al., 2021).

$$A_{k} = \frac{{\mathop Q\limits^{ \cdot }_{k} }}{{U_{k} \Delta T_{LMTD,k} }}$$

(16)

where $U_{k}$ represents the overall heat transfer coefficient of the ${\text{heat exchanger}} k$ and $\Delta T_{LMTD,k}$ is its logarithmic average temperature difference.

Furthermore, the measures of the economic capacity of ${\text{control volume }}k {\text{that}}\;{\text{ include}}$ the exergoeconomic factor ($f_{k}$), exergy destruction cost rate ($\dot{C}_{D,k}$), and relative cost difference ($r_{k}$) are formulated as the following (T Gholizadeh, Vajdi, and, and 2020).

$$\dot{C}_{D,k} = c_{F,k} \dot{E}x_{D,k}$$

(17)

3.4 Environmental impact analysis

The widespread use of fossil fuels as feed for powering numerous multigenerational plants inherently leads to a significant emission of CO₂. Recognizing the imperative need to address carbon emissions and align with decarbonization goals, this research has been oriented toward the utilization of biogas. The primary motivation is to actively contribute to the reduction of carbon emissions. In this study, the evaluation of carbon dioxide emissions (measured in kilograms) per unit of energy production was performed using the following equation, reflecting a conscientious effort to assess and minimize the environmental impact of the multigeneration system (Javaherian et al., 2023).

$$CDE = \frac{{\dot{m}_{{CO_{2} }} }}{{\dot{W}_{net,total} + \dot{Q}_{Eva} }}$$

(18)

3.5 Major performance of the multigeneration cycle

The efficiency of the gas turbine (GT) cycle in terms of energy is expressed as (T Gholizadeh, Vajdi, and, and 2019-b):

$$\eta_{en,GT} = \frac{{\dot{W}_{GT1} - \dot{W}_{AC} }}{{\dot{n}_{Biogas} \cdot \overline{LHV}_{Biogas} }}$$

(19)

The energy efficiency of the combined gas turbine closed-loop Brayton Cycle (GT-CLBC) unit is defined as follows (T Gholizadeh, Vajdi, and, and 2019-b):

$$\eta_{en,GT - CLBC} = \frac{{\dot{W}_{net,GT - CLBC} }}{{\dot{n}_{Biogas} \cdot \overline{LHV}_{Biogas} }}$$

(20)

where

$$\dot{W}_{net,GT - CLBC} = \dot{W}_{GT1} + \dot{W}_{GT2} - \dot{W}_{AC} - \dot{W}_{Com1} - \dot{W}_{Com2}$$

(21)

The energy utilization factor (EUF) is defined for the overall integrated system and can be stated as follows (T Gholizadeh, Vajdi, and, and 2019-b):

$${\text{EUF}} = \frac{{\dot{W}_{net,total} + \dot{Q}_{Eva} }}{{\dot{n}_{Biogas} .\overline{LHV}_{Biogas} }}$$

(22)

where

$$\dot{W}_{net,total} = \dot{W}_{GT1} + \dot{W}_{GT2} - \dot{W}_{AC} - \dot{W}_{Comp1} - \dot{W}_{Comp2} + \dot{W}_{Tur1} + \dot{W}_{Tur2} - \dot{W}_{Pu1} - \dot{W}_{Pu2} - \dot{W}_{Pu3}$$

(23)

The exergy efficiency of the gas turbine (GT) cycle is formulated as (T Gholizadeh, Vajdi, and, and 2019-b):

$$\eta_{ex,GT} = \frac{{\dot{W}_{GT} - \dot{W}_{AC} }}{{\dot{n}_{Biogas} \cdot \overline{ex}_{ch,Biogas}^{0} }}$$

(24)

The exergy efficiency of the gas turbine closed-loop Brayton cycle unit (GT-CLBC) is as (T Gholizadeh, Vajdi, and, and 2019-b):

$$\eta_{en,GT - CLBC} = \frac{{\dot{W}_{net,GT - CLBC} }}{{\dot{n}_{Biogas} \cdot \overline{ex}_{ch,Biogas}^{0} }}$$

(25)

The exergy efficiency of the overall integrated cogeneration unit is (T Gholizadeh, Vajdi, and, and 2019-b):

$$\eta_{en,cog} = \frac{{\dot{W}_{net,cog} + \left( {\mathop {Ex}\limits^{ \cdot }_{32} - \mathop {Ex}\limits^{ \cdot }_{31} } \right)}}{{\dot{n}_{Biogas} \cdot \overline{ex}_{ch,Biogas}^{0} + \left( {\mathop {Ex}\limits^{ \cdot }_{30} - \mathop {Ex}\limits^{ \cdot }_{26} } \right)}}$$

(26)

The formula for calculating the UOPC (unit cost of the overall product) of the gas turbine cycle is given by (T Gholizadeh, Vajdi, and, and 2020)

$$UOPC_{GT} = \frac{{\dot{C}_{w,GT1} - \dot{C}_{w,AC} }}{{\dot{W}_{GT1} - \dot{W}_{AC} }}$$

(27)

The UOPC (unit overall product cost) for the combined gas turbine closed-loop Brayton Cycle system can be expressed as (T Gholizadeh, Vajdi, and, and 2020):

$$UOPC_{GT - CLBC} = \frac{{\dot{C}_{w,GT - CLBC} }}{{\dot{W}_{net,GT - CLBC} }}$$

(28)

where

$$\dot{C}_{w,GT - CLBC} = \dot{C}_{w,GT1} + \dot{C}_{w,GT2} - \dot{C}_{w,AC} - \dot{C}_{w,Comp1} - \dot{C}_{w,Comp2}$$

(29)

The expression to determine the unit total product cost (UOPC) of the entire integrated cogeneration system can be written as follows.

$$UOPC_{cog} = \frac{{\dot{C}_{w,cog} + \dot{C}_{32} }}{{\dot{W}_{net,cog} + \mathop {Ex}\limits^{ \cdot }_{32} }}$$

(30)

where $\dot{C}_{32}$ is the cost rate of the released cold exergy of the evaporator and $\dot{C}_{w,cog}$ is the cost rate of the the the net electricity of cogeneration system.

$$\dot{C}_{w,cog} = \dot{C}_{w,GT1} + \dot{C}_{w,GT2} + \dot{C}_{w,Tur1} + \dot{C}_{w,Tur2} - \dot{C}_{w,AC} - \dot{C}_{w,Comp1} - \dot{C}_{w,Comp2} - \dot{C}_{w,Pum1} - \dot{C}_{w,Pum2} - \dot{C}_{w,Pum3}$$

(31)

To assess the economic viability of the existing multigeneration system, evaluation of the net present value (NPV) is imperative. NPV serves as a crucial metric in determining the profitability of the system throughout the project’s lifetime. By considering the present value of future cash flows and accounting for the time value of money, NPV provides valuable insight into the economic feasibility and financial sustainability of the multigeneration system (Ebrahimi-Moghadam et al.; Javaherian et al., 2023).

$$NPV = - FC + \mathop \sum \limits_{i = 1}^{n} \left( {ANS \times IF_{i} \times RDF_{i} } \right)$$

(32)

The relationships pertaining to FC, ANS, IF, and RDF, along with the utilized parameters, are detailed in Appendix C. This supplementary section provides a comprehensive reference for readers to delve into the specific equations and factors relevant to the mentioned variables, enhancing the transparency and clarity of the presented information.

3.6 Sensitivity index

The sensitivity index is a measure that indicates the impact of variations in individual decision parameters on objective functions. It is obtained by dividing the discrepancy between the maximum and minimum values of an objective function by the cumulative changes caused by all decision variables within their specified range. This guarantees that the sum of the sensitivity indices for an objective function is equal to unity. The sensitivity index for each function is derived using the method described in the following.

$$\Delta EUF^{k} = EUF_{\max }^{k} - EUF_{\min }^{k}$$

(33)

$$\Delta \eta_{ex}^{k} = \eta_{\max }^{k} - \eta_{\min }^{k}$$

(34)

$$\Delta UOPC^{k} = UOPC_{\max }^{k} - UOPC_{\min }^{k}$$

(35)

$$SI_{EUF}^{k} = \frac{{\Delta EUF^{k} }}{{\sum \Delta EUF^{k} }}$$

(36)

$$SI_{{\eta_{en} }}^{k} = \frac{{\Delta \eta_{en}^{k} }}{{\sum \Delta \eta_{en}^{k} }}$$

(37)

$$SI_{UOPC}^{k} = \frac{{\Delta UOPC^{k} }}{{\sum \Delta UOPC^{k} }}$$

(38)

3.7 Multi-objective optimization

The optimization process aims to identify the optimal operational conditions and enhance the system’s performance, particularly in scenarios involving multigeneration frameworks. To achieve this, this study proposes and implements multiobjective optimization techniques for the examined system. In particular, a genetic algorithm is chosen and used, leveraging its intelligent search capabilities in an evolutionary algorithm to identify the optimal solution. The effectiveness of the genetic algorithm in energy system contexts has been demonstrated in previous research (T Gholizadeh, Vajdi, and, and 2020). Consequently, this study adopts the genetic algorithm, focusing on three objective functions (${\eta }_{en}$, ${\eta }_{ex}$, and ${UOPC}_{sys}$). The configuration settings for this algorithm in the EES software are detailed in Table 2. Initially, the optimization process focuses on the optimization of individual functions. Subsequently, the multi-objective function (MOO) is expressed in Eq. (40) is used for multi-objective optimization (Gholizadeh, Vajdi, and, and 2020).

Table 2 Inputs for the genetic algorithm (Gholizadeh et al. 2020)

Three design parameters of the energy and exergy efficiencies and UOPC are considered objective functions. The selected decision variables are as follows:

$$8 \le r_{AC} \le 15$$

$$115 \le P_{cond} \left( {kPa} \right) \le 124$$

$$20,000 \le P_{8} \left( {kPa} \right) \le 60,000$$

$$2,000 \le P_{9} \left( {kPa} \right) \le 5,000$$

$$320 \le P_{15} \left( {kPa} \right) \le 820$$

$$500 \le P_{23} \left( {kPa} \right) \le 1,800$$

$$1,200 \le T_{3} \left( K \right) \le 1,550$$

$$250 \le T_{eva} \left( K \right) \le 265$$

$$680 \le T_{8} \left( K \right) \le 780$$

$$410 \le T_{14} \left( K \right) \le 420$$

(39)

The concurrent objective of optimizing thermal and exergy efficiencies while minimizing the unit overall product cost (UOPC) is achieved through the introduction of a multi-objective operator (MOO) defined as follows (T Gholizadeh, Vajdi, and, and 2020):

$$Max\left( {MOO = w_{1} \times \eta_{en} + w_{2} \times \eta_{ex} + w_{3} \times CDE + w_{4} \times \left( {1 - UOPC_{sys} /c_{7} } \right)} \right)$$

(40)

$$w_{1} + w_{2} + w_{3} + w_{4} = 1 , 0 \le w_{1} ,w_{2} ,w_{3} ,w_{4} \le 1$$

(41)

while ${c}_{7}$ represents the unit cost of biogas.

4 Results and discussion

4.1 Model validation

In this section, the validation process for the main components and subsystems of the developed model is carried out. The accuracy of the Brayton cycle is demonstrated in Fig. 3, while Table 3 and Fig. 4 provide evidence of the validated ejector mode.

Fig. 3

Validation of the Brayton cycle with somehsaraei et al. (Somehsaraei et al.) study

Table 3 Validation of the ejector simulation with the study by Huang et al. (“A 1-D analysis of ejector performance”) study

Fig. 4

Validation of the simulation of the ejector with the study of Sadeghi et al. (Sadeghi et al.) study

According to Fig. 3, the result of the study by Somehsaraei et al. (Somehsaraei et al.) is used to validate the result of the Brayton cycle in the present work. In this regard, the power consumed by the air compressor, the power produced by the gas turbine, and the mass flow rate of the input fuel are obtained and compared with the variation in the methane fraction. Here, the difference margin is below 3%.

Using different pressures and temperatures for the input terminals of the ejector and different operating temperatures based on numerical and experimental studies by Huang et al. (“A 1-D analysis of ejector performance”) and Sadeghi et al. (Sadeghi et al.), the ejector entrainment ratio of the ejector is calculated and compared with Ref. (“A 1-D analysis of ejector performance”) (see Table 3).

In Fig. 4, the production cooling capacity was determined by modifying the temperature of the second fluid entry into the ejector (evaporator temperature). The results obtained from this modification were compared with a Ref. (Sadeghi et al.), and Fig. 4 shows that the study by results aligns well with the study by Sadeghi et al. (Sadeghi et al.) study.

Validation of the model for the anaerobic digestion process was performed using input data from Ogorure et al. (Ogorure et al.). The mass results and the percentage by mass of animal waste, as presented in Table 4, demonstrate the precision of the model used in this study.

Table 4 Validation of anaerobic digestion for Animal wast

4.2 Model comparison

In this section, we embark on a comprehensive evaluation of the strengths and limitations inherent in our innovative biogas-driven cogeneration system that are indicated in Table 5. To facilitate this assessment, we undertake a comparative analysis by aligning the key performance metrics of our design with those documented in a relevant literature source, specifically Ref. (Gholizadeh et al. 2019b) Our primary objective in this investigation is to improve the operational efficiency of the previous biogas-driven cogeneration system. Our emphasis is on optimizing electricity generation through improved waste management strategies. The main distinguishing factor between our current cogeneration system and the systems discussed in Ref. (T Gholizadeh, Vajdi, and, and 2019-b) lies in the arrangement, where our implementation integrates a closed-loop Brayton cycle between the gas turbine cycle and the ORC-based unit. This configuration change aims to achieve increased efficiency in electricity generation through a well-designed configuration. Another difference is inclusion of the LNG power generation set-up to recover exhaust gas energy released from the CLBC gas heater of the CLBC for regasification purposes. There are also some minor differences in layouts of both systems, including employment of two-stage ORC in the combined ORC-ERC system to capture more energy from the CLBC, which also improves overall performance of the unit. The previous developed model was applicable for two cooling temperature levels, which are not considered here, although it can be extended based on the given data in the previous model.

Table 5 Comparison results between the current developed cogeneration system and those reported in Ref. (Gholizadeh et al. 2019b), (Al-Rashed et al.), and (Zareh et al.-b)

In order to have a real comparison, it is imperative to set the same input condition for both systems. For this purpose, the air compressor ratio is fixed at 10, the gas turbine input temperature is given 1300 K, the evaporator temperature is set at 258 K, and the net power of the GT cycle is fixed at 1000 kW to investigate the effects of the bottoming cycles included in both studies. The ambient temperature and pressure are assumed to be 293.2 K and 101.3 kPa, respectively. The results indicate that the value of net power production has increased from 1189 to 1927 kW, indicating a greater improvement of more than 62%. However, the cooling production is decreased by 24.58%, which is mainly reflected by the fact that the previous model has two evaporators, which leads to more cooling production. Another disadvantage of the present model is given in Ref. (T Gholizadeh, Vajdi, and, and 2019-b) is its high exergy destruction rate, which is mainly due to the use of the CLBC. However, the energy and exergy efficiencies are improved by 36.5% and 4%, respectively. To substantiate the reduced environmental impact of our system, we performed a comprehensive comparison of the CDE parameters. The results revealed that our system exhibits an 18.7% lower CDE, underscoring its environmental efficiency.

In the second comparison. To compare the present work with Ref. (Al-Rashed et al.), the flow rate of biogas entering the system in the present work was considered 1 kg/s, and the molar percentage of methane in methane was 58% and the molar percentage of carbon dioxide in biogas was considered 42%, and also the cost of biogas is considered 2.749 GJ/s. Based on the results presented, the exergy efficiency of Ref (Al-Rashed et al.), is a little higher than that of the present work. A notable advantage of our system is its ability to generate cooling, a feature absent from Ref. (Al-Rashed et al.), thus enhancing its overall functionality and appeal. From an environmental perspective, there are no notable differences between the two systems. However, it is important to note that the unit cost of the product of our system is 30% lower than that of Ref. (Al-Rashed et al.), emphasizing a cost-effective advantage. In the third comparison. The current study considers an input fuel flow rate of 4.2 kg/s for comparison with Ref. (Zareh et al.-b). The results obtained from the present work indicate that the exergy efficiency of (Zareh et al.-b) is reported as 46.94%, while the system studied in the present work demonstrates an exergy efficiency of approximately 38%. Despite its lower exergy efficiency, the system under investigation demonstrates a significant 60% reduction in the unit cost of the product, thus improving the overall energy efficiency. Beyond the energetic and economic advantages mentioned, our proposed system has a distinct environmental benefit, as evidenced by a notable decrease in CDE from 19.35 to 11.85 kg/kW day.

4.3 Sensitivity analysis

To identify the parameter with the most pronounced impact on the system, both from a thermodynamic and economic point of view, a sensitivity analysis was performed and the corresponding sensitivity index is depicted in Fig. 5. According to Fig. 5, the energy utilization factor exhibits the highest sensitivity index for the evaporator temperature (Teva) at 0.246, while the inlet temperature of GT 1 closely follows with a value of 0.243. Regarding exergy efficiency, among the variables examined, the most significant sensitivity index of 0.534 is associated with the GT 1 input temperature (T3), followed by the GT 2 inlet pressure (P8) with a sensitivity index of 0.116. Regarding economic considerations, the unit total product cost (UOPC) exhibits the highest sensitivity index, mainly influenced by the GT 2 outlet pressure (P9) at 0.223. Furthermore, the GT 1 input temperature (T3) holds the second highest sensitivity index of 0.173. In summary, the GT 1 inlet temperature stands out as the most influential parameter, as it ranks highest in the sensitivity index for the energy utilization factor and second highest for both exergy efficiency and UOPC.

Fig. 5

Impact of decision variables on the sensitivities to the objective function

4.4 Results of the simulation

Figure 6 and Table 6 present the optimization in four different scenarios. Energy Utilization Factor Optimization Design (EUFOD) mode, Energy Efficiency Optimization Design (EEOD) mode, Unit Overall Product Cost Optimization Design (UPCOD) mode, CDE Optimization Design (CDEOD) and Multi-Objective Optimization Design (MOOD) mode.

Fig. 6

Outcomes for the base mode and optimal results

Table 6 Outcomes for the base mode and optimal results

Comparing the results between the EUFOD (Energy Utilization Factor Optimization Design) mode and the base mode reveals notable differences. The refrigeration load, energy utilization factor (EUF), and exergy efficiency experience increase by 102%, 23%, and 1.3%, respectively. However, net electricity, CDE, and unit overall product cost (UOPC) demonstrate a decrease of 4.5%, 18.77%, and 7.3%, respectively. Specifically, net electricity, refrigeration load, energy utilization factor, exergy efficiency, CDE, and UOPC in the EUFOD mode are calculated as 1836 kW, 488.4 kW, 82.34, 39.35%, 9.629 kg / kW.day, and 10.09 $/GJ, respectively. To achieve this optimized scenario, the following parameter settings are used: air compressor pressure ratio of 15, gas turbine 1 inlet temperature of 1550 K, evaporator temperature of 265 K, gas turbine 2 inlet temperature of 780 K, gas turbine 2 inlet pressure of 20,000 kPa, gas turbine 2 outlet pressure of 4946 kPa, vapor generator 1 temperature of 420 K, vapor generator 2 pressure of 1800 kPa, condenser pressure of 115 kPa, and turbine 1 outlet pressure of 820 kPa.

When the results between the EEOD (Exergy Efficiency Optimization Design) mode and the base mode, discernible variations emerge. The energy utilization factor (EUF), the energy efficiency, and the unit overall product cost (UOPC) exhibit increments of 3%, 16%, and 2%, respectively. On the contrary, the net electricity and refrigeration load experience reductions of 4% and 60%, respectively. It is important to note that in this scenario, the CDE value experienced a 7.2% improvement, although this improvement is less pronounced compared to the EUFOD scenario. In concrete terms, net electricity, refrigeration load, energy utilization factor, exergy efficiency, CDE, and UOPC in EEOD mode are calculated as 1851 kW, 96 kW, 68.9, 45%, 10.98 kg/kW.day and 11.13 $/GJ, respectively. To achieve this optimized configuration, the following parameter settings are implemented: air compressor pressure ratio of 15, gas turbine 1 inlet temperature of 1550 K, evaporator temperature of 250 K, gas turbine 2 inlet temperature of 780 K, gas turbine 2 inlet pressure of 60,000 kPa, gas turbine 2 outlet pressure of 5000 kPa, vapor generator 1 temperature of 420 K, vapor generator 2 pressure of 1683 kPa, condenser pressure of 124 kPa and turbine 1 outlet pressure of 320 kPa.

In reviewing the results between the overall unit product cost optimization design mode and the base mode, different differences come to light. The net energy, refrigeration load, and energy utilization factor (EUF) show increments of 5.7%, 158%, and 20.6%, respectively. In exergy efficiency, CDE and unit overall product cost (UOPC) experience reductions of 6.7%. 15.8% and 14%, respectively. Specifically, net electricity, refrigeration load, energy utilization factor, exergy efficiency, CDE, and UOPC in the UOPCOD mode are calculated as 2037 kW, 622.3 kW, 80.77, 36.24%, 9.98 kg/kW day and 9.37 $/GJ, respectively. To achieve this optimized scenario, the following parameter settings are employed: air compressor pressure ratio of 8, gas turbine 1 inlet temperature of 1486 K, evaporator temperature of 265 K, gas turbine 2 inlet temperature of 752.3 K, gas turbine 2 inlet pressure of 20,000 kPa, gas turbine 2 outlet pressure of 5000 kPa, vapor generator 1 temperature of 410 K, vapor generator 2 pressure of 500 kPa, condenser pressure of 115 kPa, and turbine 1 outlet pressure of 820 kPa.

Upon examination of the disparities between the CDEOD mode and the base mode, notable distinctions emerge. It is imperative to improve all metrics, resulting in a notable increase of 102% in refrigeration load, 23% in EUF, and 0.5% in anergy efficiency. On the contrary, CDE and UOPC register reductions of 18.7% and 7.3%, respectively. Specifically, in the CDEOD mode, the calculated values for net electricity, refrigeration load, energy utilization factor, exergy efficiency, CDE and UOPC are 1836 kW, 488.4 kW, 82.34, 39.35%, 9.629 kg/kW day and 10.09 $/GJ, respectively. Achieving this optimized scenario involves employing the following parameter settings: air compressor pressure ratio of 15, gas turbine 1 inlet temperature of 1550 K, evaporator temperature of 265 K, gas turbine 2 inlet temperature of 780 K, gas turbine 2 inlet pressure of 20,000 kPa, gas turbine 2 outlet pressure of 4946 kPa, vapor generator 1 temperature of 420 K, vapor generator 2 pressure of 1800 kPa, condenser pressure of 115 kPa and turbine 1 outlet pressure of 820 kPa.

Upon comparing the results between the MOOD mode (Multi-Objective Optimization Design) and the base mode, several significant findings emerge. Energy Utilization Factor (EUF) and exergy efficiencies witness enhancements of 20.6% and 2.65%, respectively. Furthermore, the CDE and UOPC decrease by 17.2% and 9.07%, respectively, rendering the MOOD mode the preferable configuration. It is worth noting that the optimization conducted results in a substantial increase in cooling capacity by 77.04%, accompanied by a marginal reduction in net electricity by 3.21%. Despite a slight decrease in the generated power, this optimization is recommended to increase the cooling capacity.

In conclusion, integration of the CLBC system with the GT cycle yields improvements in energy and exergy efficiencies of 32.93% and 32.92% in the base mode, and 33.66% and 33.68% in the MOOD mode, respectively. Taking into account the economic aspect, the UOPC of the CLBC system compared to the GT cycle shows a rise of 13.51% in the base mode and a decline of 9.42% in the optimal mode.

Analogously to the integration of the entire new combined cooling and power (CCP) system with the GT-CLBC cycle, the energy efficiency experiences a substantial enhancement of 63.06% in the base mode. However, there is a negligible decline in exergy efficiency. In the MOOD mode, the energy efficiency further improves by 71.17%, while the exergy efficiency experiences a modest decline of 7.38%. Economically, the UOPC of the combined CCP system, in contrast to the GT-CLBC cycle, undergoes a decrease of 19.45% in the base mode and 20.45% in the MOOD mode.

Table 7 presents the role of each element in the overall energetic and economic evaluation of the developed design. The results showed that the high value of overall exergy destruction is due to the combustion chamber by exergy destruction of 1058 kW (for the base mode) and 759.4 kW (for the MOOD mode), since these elements transfer a high heat rate between the cold and hot streams. Among all components, gas turbines and gas heaters have the highest investment cost in the base mode. Gas turbine 1 demonstrates exceptional exergy efficiency, achieving 94.66% in its base mode and even higher 95.28% in the optimum mode. The total cost rate related to the exergy destruction in the base and optimum modes was reached at 70.16 $/h and 50.89 $/h, respectively. For a better understanding, the share of each element in exergy destruction is shown in Fig. 6. As illustrated in Fig. 7, exergy destruction in certain components increases in the optimum mode compared to the base mode. However, this does not significantly affect total exergy destruction. In particular, exergy destruction in crucial components, such as the combustion chamber, experiences a notable decrease when optimum conditions are employed. Consequently, the overall exergy destruction decreases from 2890 kW in the base mode to 2496 kW in the optimum mode.

Table 7 Results of exergy and cost features of the commponets in base and MOOD mode

Fig. 7

Contribution of components to the exergy destruction rate at the base and in the MOOD mode

To perform a comprehensive assessment of the current system, the Net Present Value (NPV) is shown in Fig. 8. To explore various scenarios, three different electricity cost scenarios were examined: 0.08$/kWh, 0.09$/kWh, and 0.1$/kWh. The results reveal that in the optimistic scenario, where the electricity cost is 0.1$/kWh, the NPV turns positive, indicating that the investment is anticipated to generate more cash inflows than outflows, starting from the sixth year. On the contrary, for scenarios with electricity costs of 0.08$/kWh and 0.09$/kWh, the NPV becomes positive in the eighth and eleventh years, respectively. This analysis provides insights into financial performance under different electricity cost scenarios, helping to make strategic decision making for potential investors or stakeholders.

Fig. 8

Impact of the electricity price on the net present value in all years during the lifetime of the system

4.5 Parametric study

This section involves a detailed analysis that focuses on the impact of three key thermodynamic parameters: gas turbine 1 input temperature, methane molar fraction, and air compressor pressure ratio. The investigation explores their influence on different performance metrics within the context of the study.

4.5.1 Influence of gas turbine 1 inlet temperature

The impact of varying the gas turbine 1 inlet temperature (GT1-IT) on the cooling load, electricity generation, the energy utilization factor (EUF), the CDE, the energetic efficiency, the exergetic efficiency, and the total unit cost of the product (UOPC) across the GT cycle, the CLBC cycle, and the overall CCP system is shown in Fig. 9. As GT1-IT fluctuates within the defined range of 1200–1600 K, a notable occurrence emerges, a minimum point in the CLBC mass flow rate, leading to a reduced heat supply through vapor generators. This, in turn, results in the combined GT-CLBC system experiencing its lowest values for both net produced power and cooling load, notably transpiring around ${T}_{GT1,in}=\text{1,325} K$. Similarly, the net electricity output of the entire CCP system reaches its nadir, hovering around 1,913.8 kW, coinciding with ${T}_{GT1,in}=\text{1,540} K$. This observation underscores the sensitivity of system performance to variations in GT1-IT, emphasizing the importance of optimal operating conditions for enhanced efficiency. In particular, the thermal load of the combustion chamber and its exergy rate exhibit more pronounced reductions than the net electricity and cooling, leading to an increase in EUF, exergetic efficiency, and energetic efficiency for the GT cycle, CLBC cycle, and the entire CCP system as GT1-IT increases. Meanwhile, the UOPC of the system decreases as GT1-IT increases until it reaches ${T}_{GT1,in}=\text{1,475} K.$ However, beyond this temperature, there is a notable and sharp ascent in the UOPC, indicating a shift in the system dynamics. As GT1-IT increases from 1200 to 1600 K, there is a notable impact on CDE, resulting in a reduction of 8.5% in its value. This observation underscores the sensitivity of CDE to changes in the gas turbine input temperature. Importantly, the findings highlight that the newly developed cogeneration unit consistently outperforms both the standalone GT and CLBC systems throughout the GT1-IT range, showcasing superior performance and cost-effectiveness.

Fig. 9

Impact of GT1-IT on: a net electricity, cooling load, CDE, b EUF, exergy and energy efficiency, and UOPC of GT, GT-CLBC, and overall CCP systems

4.5.2 Influence of methane molecule fraction

The impact of changes in the methane molar fraction (MMF) from 0.5 to 1.0 on cooling load, electricity generation, energy utilization factor (EUF), CDE, exergy, and energy efficiency within the newly developed CCP system, as well as the basic GT cycle, is illustrated in Fig. 10. With constant electricity generation by the gas turbine cycle, the net power output demonstrates an increase from 1917 to 1946 kW in the cogeneration system. Similarly, in the GT-CLBC system, the net power output increases from 1326 to 1336 kW as the MMF increases. This suggests that a higher MMF is positively correlated with enhanced power output in both systems, highlighting the impact of the mass flow rate on overall performance. This increase is attributed to the elevated amount of thermal energy transferred to the ORC-based CCP system and CLBC through vapor generators and gas heaters. The cooling capacity shows an increase of 3.13% with the doubling of the MMF. This enhancement is attributed to the larger volume of vapor being directed to the ejector, resulting in an increase in the cooling capacity of the unit in tandem with the increase in MMF. This observation highlights the direct relationship between MMF and cooling capacity, emphasizing the influence of MMF on the system’s cooling performance. Simultaneously, the increase in MMF positively influences the net power of electricity and cooling load, while exerting a negative impact on the energy efficiency and EUF of the system. Specifically, with an increase in MMF from 0.5 to 1.0, the EUF decreases from 67.1 to 66.6, indicating a reduction in overall efficiency. Furthermore, the rise in MMF intensifies UOPC. In light of this, the UOPC values for GT, GT-CLBC, and CCP systems experience an increase of 4.2%, 3.7%, and 3.7%, respectively. This highlights the complex interplay of factors that affect system performance as the MMF varies, necessitating a balanced consideration for optimal operational outcomes. In fact, the positive effects of the increase in MMF extend beyond the increase in net electricity and cooling load. The alteration of MMF contributes to a small but notable increase in exergy efficiency. Moreover, CDE experiences a significant improvement with the increase in MMF. The results underscore that carbon emissions are halved with the doubling of MMF, reflecting a positive environmental impact. These findings highlight the multifaceted influence of MMF on system performance, including efficiency gains and environmental benefits. In conclusion, the presented cogeneration unit consistently outperforms the basic topping system in all MMF ranges, firmly establishing itself as the preferred choice. The superior performance is evident in various aspects, including increased net energy and cooling load, improved exergy efficiency, and improved CDE. These findings underscore the effectiveness and general advantages of the proposed cogeneration unit compared to the basic evaporation system.

Fig. 10

Impact of MMF on a net electricity, cooling load, CDE, b EUF, and exergy and energy efficiency of the GT, GT-CLBC, and overall CCP systems

4.5.3 Impact of air compressor pressure ratio

Figure 11 shows the influence of variations in ACPR (air compressor pressure ratio) on various performance parameters, including cooling load, net electricity generation, Energy Utilization Factor (EUF), exergy and energy efficiency, CDE and unit overall product cost (UOPC) for both individual core systems and integrated cogeneration unit. As the ACPR increases, the heat supplied to both the CLBC and the Organic Rankine Cycle (ORC)-based combined cooling and power (CCP) systems undergoes a reduction. This results in a decrease in the mass flow rate of the refrigerant through these systems, serving as the primary factor behind the observed decrease in cooling load and net electricity. Specifically, with the increase of ACPR from 8 to 15, the cooling load decreases from 265 to 214 kW, and the net electricity output of the cogeneration system decreases from 2010 to 1830 kW. This correlation highlights the sensitivity of the cooling load and net electricity to variations in ACPR within the system. The energy efficiency of both the GT and GT-CLBC cycles shows improvement with the increase of the ACPR. However, the EUF trend presents a more nuanced pattern. As the ACPR increases, the EUF initially increases, reaching its maximum value of 66.96 at an ACPR of 11. Subsequently, the EUF starts to decline with further increases in ACPR. This observed trend can be attributed to a significant decrease in net electricity resulting from the integration of LNG power generation and the Organic Rankine Cycle (ORC)-based Combined Cooling and Power (CCP) systems with the GT-CLBC system. The intricate relationship between ACPR, EUF, and net electricity highlights the complex dynamics at play in the system. Simultaneously, the increase in ACPR exerts a positive effect on exergy efficiency, enhancing it. This improvement is attributed to the more significant reduction in the heat supplied by combustion compared to the decrease in the output commodities. The impact on UOPC is complex. With an increase in ACPR, the UOPC of the GT increases linearly from 11.7 to 12.5 $/GJ. On the contrary, the UOPC of the GT-CLBC initially decreases until it reaches its minimum of 13.5 $/GJ, after which it starts to increase with further increases in ACPR. In contrast, the UOPC of the CCP system is linearly with the rise of ACPR. In particular, the UOPC of the integrated CCP system remains consistently lower than that of the standalone GT and CLBC systems. From an environmental point of view, the impact of ACPR variations on the environmental metric, the CDE, is relatively minor. At an ACPR of 8, the CDE value is 11.88. As the ACPR increases, the CDE value begins to decrease, reaching its minimum (although this reduction is marginal, approximately 0.25%) at an ACPR of 10.8. Subsequently, the CDE value starts to increase again, reaching 11.91 at an ACPR of 15. Although alterations in ACPR have a discernible influence on CDE, the overall impact on this environmental metric remains within a relatively narrow range. This suggests that from an environmental perspective, the system’s performance is relatively stable across the considered ACPR range.

Fig. 11

Impact of ACPR on a net electricity, cooling load, CDE, b EUF, exergy and energy efficiencies, and UOPC of the GT, GT-CLBC, and overall CCP systems

5 Conclusions

The escalating demand for power and cooling generation poses a dual challenge: an inevitable surge in carbon emissions resulting from the combustion of fossil fuels and the associated hurdles in meeting the growing need for increased investment in power plant generation. Consequently, there is a pressing need for the development of innovative cycles that not only improve performance but also contribute to a reduction in carbon emissions. The primary objective of this research was to propose an innovative method for recovering waste heat from a biogas-powered gas turbine (GT) cycle. This approach involves the integration of a closed-loop Brayton cycle (CLBC), a liquefied natural gas (LNG) open power generation cycle, and a dual-stage combined cooling and power (CCP) unit that combines an organic Rankine cycle (ORC) with an ejector refrigeration cycle (ERC). The study encompassed thermodynamic and economic analyses, accompanied by a multi-objective optimization utilizing a genetic algorithm. The main findings of the study can be summarized as follows:

• The analysis identifies the combustion chamber as the main contributor to irreversibility within the system, marked by the highest exergy destruction rate. The following is the condenser, responsible for the initial heat recovery from liquefied natural gas. To prevent resource degradation, it is imperative to prioritize the development of both the combustion chamber and a novel condenser. Focusing on advances in these key components is crucial to improving overall system efficiency and sustainability.

• In the base case, net output electricity and cooling were measured at 1926 kW and 241.4 kW, respectively. Furthermore, key performance indicators were calculated, including energy efficiency (66.94%), exergy efficiency (38.85%), carbon emissions per energy rate of products (CDE—11.854 kg / kW.day) and unit total product cost (UOPC—10.89 $ / GJ). Unit cost and carbon emission data indicate that optimization of the cycle is essential to address both financial and environmental challenges.

• The implementation of multi-objective optimization resulted in notable enhancements across various metrics. The energy utilization factor experienced an improvement of 20.6%, the exergy efficiency increased by 2.65%, the CDE decreased by 19.2% and the unit total cost of the product cost (UOPC) was reduced by 9%. Consequently, there was a substantial 77% increase in cooling load, while the net electricity production marginally decreased by 3.4%. The optimized values for the cooling load, net electricity generation, exergy and energy efficiencies, CDE, and UOPC within the proposed system were determined as 427.3 kW, 1,860 kW, 41.5%, 80.79%, 9.816 kg / kW.day and 9.902 $/GJ, respectively.

• An optimization design mode targeting carbon emissions per energy rate of products (CDE) was implemented, revealing a significant reduction in carbon emissions. The CDE decreased significantly to 9.629 kg / kW. Day, demonstrating a substantial benefit in terms of environmental impact. This scenario has the potential to accelerate the achievement of sustainability goals, underlining the positive impact of optimization strategies on reducing carbon emissions in the system.

• The implementation of MOOD mode resulted in significant improvements in the energy utilization factor and exergy efficiencies of the GT cycle, with increases of 11.7% and 11.8%, respectively, attributed to the integration of the CLBC cycle.

• Our analysis of the net present value (NPV) under varying electricity cost scenarios reveals positive returns. The optimistic scenario at 0.1$/kWh shows a positive NPV from the sixth year, while at 0.08 $/kWh and 0.09 $/kWh, a positive NPV is achieved in the eighth and eleventh years, respectively. These insights assist potential investors and stakeholders in making strategic decisions based on the system’s financial performance.

• In the MOOD scenario, the current system unexpectedly achieves a substantial reduction in carbon emissions compared to other references. In the optimal case examined in this investigation, the amount of carbon is 9.902 kg/kW.day, whereas references 15, 32, and 33 report values of 14.58 kg/kW.day, 11.68 kg/kW.day, and 19.35 kg/kW.day, respectively, which signifies a reduction of 32%, 15.22%, and 48%. These findings underscore the notable environmental friendliness of the proposed system compared to its predecessors.

• Economically, the unit overall product cost (UOPC) of the integrated CCP system showed a decrease of 26.7% in the base mode and 22.09% in the optimal mode compared to the standalone GT-CLBC system standalone. Furthermore, under optimal conditions, the total investment cost rate and the exergy destruction cost rate were calculated as 13.1 $/h and 53.03 $/h, resulting in an overall exergoeconomic factor and a relative cost difference of approximately 19.82% and approximately 65.4%, respectively. These improvements surpassed the base case by approximately 5.88% and around 1.71%.

• In a wider context, the main influencer that impacts overall system performance was found to be the input temperature of the gas turbine 1. Specifically, it had the highest sensitivity index for exergy efficiency at 0.534, the second highest for the energy utilization factor at 0.243, and the second highest for UOPC at 0.173. Furthermore, the highest sensitivity index for both the energy utilization factor and the UOPC was associated with the evaporator temperature and the gas turbine 2 outlet pressure, registering values of 0.246 and 0.223, respectively.

Appendices

Appendix A: Mass, Energy, and Exergy Balance Equations

The table below delineates the integral mass, energy, and exergy equations of the proposed system. This comprehensive representation aims to elucidate the intricate relationships and dynamics within the system, providing a basis for a detailed analysis of its operational principles.

Appendix B: Cost-balance equations

The following table elucidates the cost-balance equations associated with each component of the proposed system. This tabulated presentation aims to provide a clear understanding of the financial considerations and the distribution between the various elements of the system, facilitating a comprehensive analysis of the cost dynamics involved.

Appendix C: NPV equations and parameters

To assess the economic feasibility of the existing multigenerational system, key financial metrics are used: Net present value (NPV). These parameters serve as crucial indicators for evaluating the profitability of the system over the project’s lifetime (Tables 8 and 9). By evaluating NPV, this analysis provides valuable insights into the economic viability of the multigeneration system throughout its operational lifespan (Bejan et al., 1995).

Table 8 Mass, energy, and exergy balance equations used for components

Table 9 displays equations dependent on the costs used to evaluate the components

$$NPV = - FC + \mathop \sum \limits_{i = 1}^{n} \left( {ANS \times IF_{i} \times RDF_{i} } \right)$$

(c-1)

$$IF_{i} = \left( {1 + \frac{R}{100}} \right)^{ - i}$$

(c-2)

$$RDF_{i} = \left( {1 + \frac{RIR}{{100}}} \right)^{ - i}$$

(c-3)

In the preceding equations, R represents the rate of inflation, set at 5%, while $RIR$ denotes the real interest rate, calculated as the difference between the discount rate $DR$ and the inflation rate $R$. Here, $the DR$ is specified as 8%. Furthermore, the variable $i$ signifies the year within the operational lifetime (Ebrahimi-Moghadam et al.). The fixed cost $FC$ is defined as the aggregate of direct costs $DC$ and indirect costs $IR$, with a detailed breakdown provided in Table 10.

Table 10 Investment costs of the multigeneration system (Bejan et al., 1995)

Additionally, the annual net savings $of the ANS$ can be determined using the following equation (A Bejan et al., 1995):

$$ANS = AI - OC$$

(c-4)

The calculation of annual income (AI), maintenance cost ($C^{O\& M}$), and fuel consumption cost ($C_{f}$) contributing to operational costs (OC) is derived using the following formulas (Ebrahimi-Moghadam et al.):

$$AI = AI_{elec} + AI_{C}$$

(c-5)

$$AI_{elec} = c_{elec} \times N \times \dot{W}_{net}$$

(c-6)

$$AI_{C} = c_{cooling} \times N \times \dot{Q}_{cooling}$$

(c-7)

$${\text{C}}^{{{\text{O}}\& {\text{M}}}} = 0.06 \times {\text{PEC}}$$

(c-8)

$$C_{env} = \left( {z_{co2} \times \dot{m}_{co2} } \right) \times 3600 \times NB\;\;z_{co2} = 0.024\$ /kg_{CO2}$$

(c-9)

$$C_{f} = FP \times LHV_{fuel} \times \dot{m}_{fuel} \times 3600 \times N$$

(c-10)

$$OC = C^{{O\& M}} + C_{f} + C_{{env}}$$

(c-11)

The economic viability of the proposed system is bolstered by the sale of products, namely power and cold. The assumed unit cost of these products, along with other pertinent economic assumptions, is detailed in Table 10. This comprehensive table provides a foundation for understanding the financial parameters and assumptions crucial to evaluating the economic benefits derived from the system’s product sales.

The total cost of the components comprising the multigeneration plant is denoted as PEC. Additional parameters essential for economic calculations are given in Table 11. This table serves as a reference point and provides a detailed overview of the specific parameters utilized in the economic evaluation of the multigenerational system.

Table 11 Input parameters related to economic calculations (Towhid Gholizadeh et al., 2019a, b, c)

Appendix D: results of the parametric study

In this appendix, a detailed presentation of supplementary results has been illustrated to provide comprehensive insights into the findings of this study. This additional information aims to improve the clarity and transparency of the research results.

4.1 D-1: Impact of the gas turbine 2 input temperature

The influence of GT2-IT (gas turbine 2 inlet temperature) on cooling, electricity, EUF, exergy and energy efficiency and UOPC of the basic and developed CCP unit is shown in Fig.

Fig. 12

Impact of GT2-IT on the: electricity, cooling load, EUF, exergy and energy efficiencies, and UOPC of the GT-CLBC and overall CCP systems

12. As GT2-IT increases, gas turbine 2 extracted electricity, as well as compressors 1 and 2 utilized power decrease. However, since the rate of the electricity of compressors is significant compared to the electricity extracted from GT 2, the electricity of the CLBC and the overall CCP system will increase. Increasing GT2-IT also leads to an increase in the heat of vapor generator 1 directed into the ORC-based CCP system, which will result in a greater reduction in the heat received from vapor generator 2. Consequently, the mass flow rate of the saturated vapor with intermediate pressure will decrease, leading to a smaller extraction of the vapor from turbine 1. Thus, the flow rate of the motive vapor mass will decrease, drawing less secondary flow into the ejector. Therefore, increasing the gas turbine 2 inlet temperature reduces the generated cooling load. Since the increase rate of net electricity outweighs the decrease rate of cooling load in terms of first and second laws of thermodynamics, the EUF, exergy, and energy efficiencies of both CLBC and overall systems will augment. From an economic perspective, the UOPC of the CLBC system decreases as GT2-IT increases, as the rate of generated electricity is considerable. However, in terms of UOPC of the overall CCP system, the rate of generated electricity is only substantial until around 746 K, while its cost rate will become more significant onward. Therefore, a nadir point is observed for the UOPC of the overall CCP system versus GT2-IT. Furthermore, based on Fig. 8 it can be deduced that the overall CCP system surpasses the basic electricity generation systems (GT and GT-CLBC systems) through all GT2-IT ranges in terms of cost and first-law efficiency.

4.2 D-2: Impact of the gas turbine 2 inlet pressure

The effect of GT2-IP (gas turbine 2 inlet pressure) on cooling load, EUF, electricity, exergy and energy efficiencies, and the UOPC of the GT-CLBC and overall CCP unit is sketched in Fig.

Fig. 13

Impact of GT2-IP on net electricity, cooling load, EUF, exergy and energy efficiency, and UOPC of the GT-CLBC and general CCP systems

13. As GT2-IP increases, the power of gas turbine 2 and the used electricity of the compressors increase. Through a precise inspection, it is discovered that the GT 2 output electricity is substantial compared to that of the compressors utilized electricity up to $P_{GT2,in} = 42,857 kPa$, while the trend is reversed. The same is also true with regard to net general net electricity, where the maximum net overall electricity is observed at $P_{GT2,in} = 28,571 \;kPa$. The maximum combined GT-CLBC and overall CCP systems are calculated at 1,329.57 kW and 1,934.94 kW, respectively. Due to the same reason as pinpointed in the previous subsection, the cooling load declines as GT2-IP increases. From a thermodynamics point of view, the trend of energetic efficiency of the GT-CLBC system is similar to its net electricity, since generated net electricity has a dominant impact on thermal performance. In the trend of the overall CCP system, the variation of energetic efficiency of the overall CCP system is nearly similar to its net electricity, except that the peak value is not observed in the examined range. In terms of exergy, a maximum value is seen for the exergetic efficiencies of the combined GT-CLBC and overall CCP systems at approximately $P_{GT2,in} = 42,857\; kPa$ and $P_{GT2,in} = 48,571 \;kPa$, respectively. Under this condition, the maximum exergetic efficiencies of the combined GT-CLBC and the overall CCP systems are calculated at 38.92% and 38.94%, respectively. From an economic point of view, the UOPC of the GT-CLBC and the overall CCP systems increases as the cost rate of the electricity generated by the turbines continuously increases.

4.3 D-3: impact of gas turbine 2 outlet pressure

The impact of GT2-OP (gas turbine 2 outlet pressure) on the cooling load, electricity, EUF, exergy, and energy efficiency and UOPC of the GT-CLBC and overall CCP systems is sketched in Fig.

Fig. 14

Impact of GT2-OP on net electricity, cooling load, EUF, exergy and energy efficiency, and UOPC of the GT-CLBC and general CCP systems

14. As GT2-OP increases, the electricity extracted from gas turbine 2 decreases, as well as compressors 1 and 2. However, since the rate of the electricity of compressors is significant compared to the electricity extracted from GT 2, the electricity of the CLBC and the overall CCP system will increase. Increasing GT2-OP also leads to an increase in the heat of vapor generator 1 directed into the ORC-based CCP system, which will result in a reduction in the heat received by vapor generator 2. Consequently, the mass flow rate of the saturated vapor with intermediate pressure will decrease, leading to a smaller extraction of the vapor from turbine 1. Thus, the flow rate of the motive vapor mass will decrease, drawing less secondary flow into the ejector. Therefore, increasing the gas turbine 2 outlet pressure has the same effect as the gas turbine 2 inlet temperature and will decrease the generated cooling load. Since the increase rate of net electricity outweighs decrement outweighs the decrease rate of the cooling load in terms of first and second laws of thermodynamics, the EUF, energetic and exergetic efficiencies of both CLBC and overall systems will augment. From an economic perspective, the UOPC of the CLBC system has a maximum value of 13.52 $ / GJ in GT2-OP of 2,857 kPa. Meantime, the UOPC of the overall CCP system reduces as the GT2-OP increases due to a large value of net overall electricity and its dominant impact.

4.4 D-4: impact of the temperature of the vapor generator 1

Figure

Fig. 15

Impact of VG1 temperature on: electricity, cooling load, EUF exergy and energy efficiency, and UOPC of the GT-CLBC and overall CCP systems

15 shows the impact of VG1-T (vapor generator 1 temperature) on electricity, cooling load, EUF, exergy and energy efficiencies, and UOPC of GT-CLBC and general CCP systems. As VG1-T increases, the electricity generated by the GT-CLBC system decreases quite a bit, since the inlet energy of compressor 1 increases slightly and compressor 1 increases. On the other side, the generation of electricity via turbine 1 increases as the temperature of vapor generator 1 increases, and hence the net electricity of the overall CCP system will increase. This variation also increases the suction power of the ejector through the throat nozzle, and hence the cooling load will increase as well. The variation of the energetic and exergetic efficiencies of both the combined GT-CLBC and the overall CCP systems with vapor generator 1 temperature resembles the variation of electricity as expounded earlier, since the energetic efficiency is only affected by the output commodities and the input heat via the combustion process is unvarying. As the vapor generator 1 temperature increases, the net electricity and cooling load also increased, too; which leads to an increase in the cost rate associated with these commodities in the same order. Therefore, an exact inspection reveals that the UOPC of both the combined GT-CLBC and the overall CCP system will remain almost fixed with any alteration of the vapor generator 1 temperature.

4.5 D-5: impact of the 2 pressure of the vapor generator

Figure

Fig. 16

Impact of VG2 pressure on: electricity, cooling load, EUF, exergy and energy efficiencies, and UOPC of GT-CLBC and overall CCP systems

16 shows the impact of the vapor generator 2 (VG2-P) on the cooling load, EUF, electricity, exergy and energy efficiencies, and UOPC of the GT-CLBC and general CCP systems. As VG2-P increases, the electricity generated by the GT-CLBC system decreases as the inlet and outlet energies of compressor 2 increase and more utilized will be used by the compressors. Although other expansion/compression components influence the electricity variation of the GT-CLBC system, their impacts are negligible versus the compressor 1 consumption electricity increment. Additionally, as the pressure of vapor generator 2 increases, more electricity will be generated via turbine 1 and hence the net electricity of the overall CCP system will increase. This variation also increases the suction power of the ejector through the throat nozzle at high pressures of the vapor generator 2 (only at > 790 kPa), while it will decrease the suction power at low pressures. Therefore, the cooling load will have a minimum point compared to VG2-P. The variation of exergy and energy efficiencies of both combined GT-CLBC and the overall CCP systems with vapor generator 2 pressure resembles the variation of electricity (similar to the temperature of vapor generator (1). As the output commodities solely influence the energetic and exergetic efficiencies, the combined GT-CLBC system experiences a decrease in these efficiencies as the pressure of the vapor generator 2 increases. In terms of the energy utilization factor (EUF), energetic efficiency, and exergetic efficiency of the overall CCP system improve with this change. A detailed examination reveals that the unit overall product cost (UOPC) decreases for both the combined GT-CLBC and the overall CCP systems as the pressure of the vapor generator 2 increases.

4.6 D-6: impact of condenser pressure

Figure

Fig. 17

Impact of condenser pressure on: electricity, cooling load, EUF, exergy, and energy efficiencies, and UOPC of the GT-CLBC and overall CCP systems

17 shows the variation of the cooling load, EUF, electricity, exergy and energy efficiencies, and UOPC of the combined GT-CLBC and overall CCP systems with disparate condenser pressures. With an increase in condenser pressure, no changes occur in the top subcycle and hence the changes are observed in the bottoming subcycle (ORC-based CCP system). According to this sketch, increasing the condenser pressure decreases the cooling load (since the inlet energy of the evaporator increases) while increasing the electricity extracted from the combined GT-CLBC and overall CCP systems. The central reasons are as follows. As the condenser pressure increases, the electricity of turbine 1 increases, whilst utilized by compressor 1 declines. Although the capacities of other expansion/compression equipment vary, these two components play a significant role in the evaluation. From a second law of thermodynamics perspective, the net electricity of each examined system will influence the exergetic efficiency of the systems as the condenser pressure varies. Accordingly, increasing the condenser temperature increases the exergetic efficiency of both combined systems as a result of the increase rate in net power. In terms of the 1st law of thermodynamics, the energetic efficiency of the combined GT-CLBC system increases as the condenser pressure increases, since its net electricity increases. However, the energy utilization factor system has a minimum decrease at low condenser pressures, whereas it increases at high condenser pressures. This is critical because, at low condensation pressures, the decrease in the cooling load is substantial compared to the increase in electricity, while the trend reverses at high condenser pressures. In terms of economic evaluation of systems, the UOPC of the combined GT-CLBC system goes up so slightly (since the generated electricity in this system and the cost rate associated with it increase with a same dominance), while the UOPC of the overall CCP system is decreased (since the generated electricity in this system rises appreciably).

4.7 D-7: Impact of the evaporator temperature

Figure

Fig. 18

Impact of evaporator temperature on the electricity, cooling load, EUF, exergy, and energy efficiencies, and UOPC of the GT-CLBC and overall CCP systems

18 shows the variance of cooling load, EUF, electricity, exergy, and energy efficiencies, and UOPC of the combined GT-CLBC and overall CCP systems with disparate evaporator temperatures. The net electricity and cooling load of the overall CCP system increase as the evaporator temperature increases, while the electricity of the combined GT-CLBC system remains constant. As a result, the energetic and exergetic efficiencies and UOPC of the combined GT-CLBC system will remain unvarying. However, the energy utilization factor of the overall CCP system increases as the evaporation temperature increases (since the cooling load and net electricity increase), while its exergetic efficiency decreases as the exergy of LNG supplied to the overall system increases substantially. The UOPC of the overall CCP system also reduces as the evaporator temperature increases, mainly because of the considerable increase in net electricity compared with its cost rate.

4.8 D-8: Impact of turbine 1 outlet pressure

Figure

Fig. 19

Impact of turbine 1 outlet pressure on: electricity, cooling load, EUF, exergy and energy efficiencies, and UOPC of the GT-CLBC and overall CCP systems

19 represents the variance of the electricity, cooling load, EUF, exergy and energy efficiencies, and UOPC of the combined GT-CLBC and overall CCP systems with disparate turbine 1 outlet pressures (T1-OP). The cooling load of the overall CCP system increases as the turbine 1 outlet pressure increases, whilst its net electricity decreases as the turbine 1 expansion ration decreases. Since the rate of increase of the cooling load is appreciable compared to the rate of decrease of the net electricity, the energy utilization factor of the overall system will increase. In contrast, since the rate of exergy of cooling is insignificant compared to the decrement rate of net electricity, the exergetic efficiency and UOPC of the overall CCP system will be lessened. However, the electricity of the combined GT-CLBC system remains constant, and consequently the energetic and exergetic efficiencies and UOPC of the combined GT-CLBC system will remain unchanged.