Using Green Energy Sources in Trigeneration Systems to Reduce Environmental Pollutants: Thermodynamic and Environmental Evaluation

Abstract

With rising electricity demand and environmental concerns, renewable energy is increasingly important. Geothermal power plants offer an opportunity to utilize natural energy sources advantageously. These systems can be coupled with other power cycles, like gas Brayton cycles, to maximize their potential output. Biogas is considered a viable replacement for fossil fuels such as natural gas to further mitigate pollutant gas emissions. In this paper, a biogas-fueled gas turbine coupled with a double-expansion geothermal cycle is proposed that uses, for heat recovery, combustion product gases to run a Kalina cycle. After heating the geothermal fluid twice for double expansion, the product hot gases also heat water in a domestic water heater. Also, three thermoelectric generators are utilized to increase the overall output. Using the geothermal cycle’s waste heat, a humidifier–dehumidifier desalination unit is considered for freshwater production. Green energy, freshwater, and heat are the system’s products, all of which are useful. The proposed system is examined from a thermodynamic perspective using EES V.10.561 (Engineering Equation Solver) software. For the considered input parameters, energy and exergy efficiencies of 36% and 44% are achieved.

1. Introduction

As environmental problems and the world’s energy usage grow, many have been inspired to create more beneficial energy conversion technologies. While many industrial sectors transform the available energy into more usable forms, the conversion of energy in power plants is extremely important in today’s industrialized society [1]. As a well-known fuel for several industrial and home applications, biogas has allowed businesses to create liquid biofuels as a viable alternative to petroleum fuels. This fuel has the potential to be used in various power generation cycles, such as gas turbines. Small-scale gas turbines can also benefit from biomass gasification as a similar fuel to biogas [2,3]. Due to its renewable nature, CH4-rich biogas is frequently utilized to replace fossil fuels (like natural gas) [4]. A further way to exploit renewable energy sources is by utilizing geothermal energy, i.e., heat extracted from underground resources [5]. In addition to producing electricity, geothermal energy is utilized for practical purposes such as space heating and cooling, industrial processes, and greenhouse heating. Geothermal resources with temperatures over 150 °C are often exploited to produce electricity [6,7,8].

Another significant issue is the significant growth in potable water needs as a result of the rising global population and living standards. Social and economic growth in many countries is hampered by freshwater scarcity. This problem can be addressed by desalination units, which can be thermally or electrically driven [9,10]. Thermoelectric devices exploit a temperature difference to generate electricity directly. A thermoelectric module produces an electric potential difference if the temperatures of its two ends differ or the opposite if a voltage is applied to both ends [11].

Various studies have been reported on these topics. Aliahmadi et al. [12] proposed three organic Rankine cycle (ORC) systems based on geothermal energy to increase efficiency and maximize waste heat recovery. The systems’ exergy efficiencies were found to be 59%, 58%, and 60% for their respective baseline layouts. Liu et al. [13] studied four geothermal systems for electricity and freshwater production. Thermodynamic and exergoeconomic assessments showed that the system with a double-flash geothermal cycle, a humidification–dehumidification (HDH) desalination system, and two thermoelectric generator (TEG) units was the most promising. The examined metrics were net generated power output, energy and exergy efficiencies, and the total unit cost of products, which were found to be 4.5 USD/GJ, 107 kW, 46%, and 52%, respectively. Ghaebi et al. [14] examined thermodynamically a new hybrid system powered by a solid oxide fuel cell (SOFC) and assessed its viability. The results show that the trigeneration system produces heating, net power output rates of 370 kW and 1605 kW, and 346 kg/h of distilled water.

Abbasi et al. [15] presented an exergoeconomic analysis of a novel integrated geothermal system that generates both hydrogen and freshwater, similar to the system considered in the present article. Hydrogen and freshwater generation are carried out by a humidifier–dehumidifier (HDH) and a proton exchange membrane electrolyzer (PEME), respectively. According to optimization studies, the best operating mode has values of 22%, 2.9 USD/m³, and 7.4 USD/kg for energy efficiency, freshwater cost, and hydrogen cost, respectively. Musharavati et al. [16] investigated a geothermal-based combined cooling, heat, and power (CCHP) system connected to a TEG using thermodynamic and exergoeconomic analyses and multi-objective optimization. The values of the net output power and useable energy products are 140 kW and 807 kW, respectively. Additionally, the system under consideration exhibits an energy efficiency of 56% and an exergy efficiency of 23%.

Zhang et al. [17] suggested a novel hybridization of the waste heat recovery idea with the flash-binary geothermal cycle, the gas turbine cycle, the organic flash cycle, and the multi-effect desalination subsystem to achieve effective cogeneration of electricity and fresh water. The effectiveness of the suggested system is examined from the perspectives of energy, efficiency, the environment, and economics. The suggested system offers 8016 kW net power, 15.99 kg/s freshwater with 35.43% exergetic efficiency, 110.9 t/kW levelized total emission, and a payback period of 3.42 years under base circumstances. Feili et al. [18] proposed a cogeneration system to supply electricity and freshwater while also recovering waste heat from a marine diesel engine. The system consists of a humidification–dehumidification desalination unit and an absorption power cycle. The sum unit cost of the product of the system, as well as the first- and second-law efficiencies, are calculated to be 193 USD/GJ, 92%, and 24%, respectively. Gholizadeh et al. [19] investigated a new trigeneration system powered by biogas for the generation of electric power, refrigeration, and potable freshwater. The proposed system consists of a gas turbine cycle, an organic Rankine cycle, an ejector cooling cycle-based novel cooling/electricity cogeneration system, and a humidification–dehumidification unit. In this system, five working fluids are examined. The unit cost of trigeneration is reduced by 6.71%, while the net electricity, refrigeration load, total grain output ratio, and energy efficiency increase by around 2.6%, 23%, 14%, and 13%, respectively, when toluene is used as the working fluid compared to the second best one. Javaherian et al. [20] studied a dual-source multigeneration energy system consisting of a reverse osmosis desalination unit, an absorption refrigeration system, a supercritical carbon dioxide recompression Brayton cycle, a gas turbine, and an organic Rankine cycle, from thermodynamic, environmental, and economic standpoints. The energy and exergy efficiencies were found to be 45% and 54%, respectively, for the base circumstances and a system total input energy rate of 699 MW.

In this study, we propose a novel dual-source trigeneration cycle based on a biogas-fueled gas turbine and geothermal cycles and clean water production. For effective heat recovery, a Kalina cycle and three TEGs are utilized in conjunction with an HDH unit for water desalination. Biogas is considered a renewable energy source for power cycles, and the combination of biogas-fueled systems with other sustainable energy sources, such as geothermal sources, can provide environmental advantages. To enhance the system’s viability, a domestic water heater (DWH) is considered to utilize the remaining energy of exhaust gases. The HDH unit utilizes the waste heat from the geothermal cycle to provide freshwater. This system produces green energy and freshwater; it also provides heating and cooling via a DWH and evaporator at a Kalina cycle, which functions as a cooler for injected water. Condensers can be replaced by TEG units for extra power generation, which raises the system’s overall power generation capacity. These systems convert temperature differences directly to energy. Energy and exergy analyses are carried out to improve understanding of the system and quantify its advantages.

The novel trigeneration system considered here is shown schematically in Figure 1.

2. System Description

The considered trigeneration system is shown in Figure 1. The system is comprised of four cycles: gas turbine, double-expansion geothermal, Kalina, and HDH desalination. An air preheater (AP) is utilized in the Brayton cycle to increase heat recovery. Air, after being heated in the AP, is input with biogas to the combustion chamber. After expansion through the gas turbine and heating the compressed air at the AP, product gases heat extracted geothermal fluid (which is treated as water) at two energy recovery units (ERUs) (points 7–9) to allow steam turbines (STs) to generate more power.

Product gases also heat water–ammonia at the Kalina cycle for power generation before entering a DWH. The Kalina cycle is a regenerative double-separation cycle that has an evaporator for absorbing heat from injected water for cooling purposes. Separated steam in the geothermal cycle at flash chamber 1 (FC) is heated before expansion and is mixed with the separated steam at FC2. It is then heated at ERU2 and expanded at ST2 once more. Water after FC2 is cooled at the heat exchanger by an HDH desalination unit before expansion in expansion valve 3 (EV).

In the HDH unit, the air stream cycles in a closed circuit while the seawater with a particular amount of salinity is routed to an open loop. Air is humidified by the humidifier while seawater is evaporated with the help of air, and the leftovers are rejected from the humidifier as brine. As air exits the humidifier, enters the dehumidifier, and then returns to the humidifier with cold air, distilled water is ultimately generated. Three TEGs are used to produce electricity directly from temperature differences in the geothermal and Kalina cycles.

3. Materials and Methods

The modeling and analysis of the proposed system are described from the perspectives of energy and exergy, and basic equations governing each of the components of the proposed system are given.

3.1. Combustion Chamber

The chemical reaction in the gas turbine combustion chamber, which is the main part of the proposed system, can be expressed based on the fuel–air ratio as follows [2,20]:

$$\begin{gathered} \overline{\lambda } \left(0.6 {CH}_4+0.4 {CO}_2\right)+[0.2059 O_2+0.7748 N_2+0.0003 {CO}_2+ \\ 0.019{ H}_{2}O]\to \left(1+\overline{\lambda }\right) \left[Y_{{CO}_2}{CO}_2+Y_{H_{2}O}{H}_{2}O+Y_{O_2}{O}_2+Y_{N_2}{N}_2\right] \end{gathered}$$

(1)

Here, $\overline{\lambda }$ is the molar flow rate ratio of fuel to air, which is as follows:

$$\overline{\lambda }=\frac{{\dot{n}}_f}{{\dot{n}}_a}$$

(2)

The molar flow rate of combustion products exiting the combustion chamber can be obtained based on the quantity $\overline{\lambda }$ and the molar flow rate of air, where

$$\frac{{\dot{n}}_p}{{\dot{n}}_a}=1+\overline{\lambda }$$

(3)

Here, ${\dot{n}}_p$ is the molar flow rate of combustion products exiting the combustion chamber. The molar percentages of the products present in the chemical reaction, based on the molar balance of these products, can be obtained from the following relationships:

$$Y_{{CO}_2}=\frac{0.0003+\overline{\lambda }}{1+\overline{\lambda }}$$

(4a)

$$Y_{H_{2}O}=\frac{0.019+1.2 \overline{\lambda }}{1+\overline{\lambda }}$$

(4b)

$$Y_{O_2}=\frac{0.2059-1.2 \overline{\lambda }}{1+\overline{\lambda }}$$

(4c)

$$Y_{N_2}=\frac{0.7748}{1+\overline{\lambda }}$$

(4d)

An energy rate balance in the combustion chamber for steady-state conditions can be written as follows:

$${\dot{Q}}_{CC}+{\dot{n}}_f{\overline{h}}_f-{\dot{n}}_p{\overline{h}}_p+{\dot{n}}_a{\overline{h}}_a=0$$

(5)

where ${\dot{Q}}_{CC}$ is the rate of heat transfer to the environment, which is considered to be 2% of the lower calorific value of the fuel per unit mole of air consumed in the combustion chamber [21]. That is,

$${\dot{Q}}_{CC}=-0.02 \overline{\lambda } {\overline{LHV}}_{fuel}$$

(6)

By inserting Equation (6) in Equation (5), we can write the following:

$$\overline{\lambda }{\overline{ h}}_f-\left(1+\overline{\lambda }\right){\overline{ h}}_p+{\overline{h}}_a=0.02 \overline{\lambda } {\overline{LHV}}_{fuel}$$

(7)

3.2. Thermoelectric Generator (TEG)

The trigeneration system considered here uses several TEG units, whose governing equations can be expressed as follows [12,22]:

$${\eta }_{TEG}={\eta }_C\frac{\sqrt{1+{ZT}_m}-1}{\sqrt{1+{ZT}_m}+\frac{T_L}{T_H}}$$

(8)

Here, ${ZT}_m$ is the figure of merit, $T_L$ and $T_H$ are the temperatures of the TEG cold and hot sides, respectively, and ${\eta }_C$ is the Carnot efficiency, which can be expressed as follows:

$${\eta }_C=1-\frac{T_L}{T_H}$$

(9)

The efficiency of the TEG can also be expressed as follows:

$${\eta }_{TEG}=\frac{{\dot{W}}_{TEG}}{{\dot{Q}}_{ELEGENT}}$$

(10)

Here, ${\dot{W}}_{TEG}$ is the electrical power produced by the TEG, and ${\dot{Q}}_{ELEGENT}$ is the thermoelectric heat transfer rate. That is,

$${\dot{Q}}_{ELEGENT}={\dot{m}}_{cooling}(h_{cold,in}-h_{cold,out})$$

(11)

3.3. Modeling Assumptions

• All processes of the proposed system are considered to be at steady state;
• Pressure drops in connecting pipes can be ignored;
• Biogas fuel contains 60% methane and 40% carbon dioxide [20,23];
• All gases in the proposed system are assumed to be ideal [2];
• Geofluid temperature and pressure losses in the separation and condensation processes are negligible [6];
• During the processes, the effects of variations in kinetic energy and potential can be disregarded [24];
• The average dew point temperature of the incoming air and the dry bubble temperature of the departing air from the dehumidifier are equal to the temperature of distilled water [18,25].

Table 1. Input data and parameters.

Parameter	Value	Unit	Reference(s)
Air compressor pressure ratio	10	-	[20,21]
Air compressor isentropic efficiency	86	%	[20,21]
Combustion chamber inlet air temperature	700	K	[20,21]
Gas turbine inlet temperature	1250	K	[20,21]
Gas turbine net power output	1	MW	[2]
Geothermal mass flow rate	6	Kg/s
Geothermal temperature	230	K	[6]
FC1 inlet pressure	500	kPa
FC2 inlet pressure	70	kPa
Pressure of TEG1	10	kPa
DWH efficiency	85	%
Ammonia mass fraction of basic solution	28	%	[11]
P37	7	bar	[11]
Humidifier and dehumidifier efficiency	85	%	[18]
Desalination top temperature	345	K
Seawater salinity	35	g/kg	[18]
Figure of merit of TEG	0.8	kPa	[13]

provides some of the input data used to simulate the proposed system.

3.4. Thermodynamic Modeling

System modeling is now described from the point of view of the first and second laws of thermodynamics. Then, for each part of the trigeneration system, energy and exergy balances and other equations are shown in

Table 2. Energy and exergy rate balances and other relations for system components.

Component	Mass and Energy Balance and Other Relations	Exergy Balance
Gas turbine subsystem
Air compressor	${\dot{W}}_{AC}={\dot{m}}_1\left(h_2-h_1\right)$ ${\eta }_{AC}=\frac{h_1-h_{2S}}{h_1-h_2}$	${\dot{E}}_1+{\dot{W}}_{AC}={\dot{E}}_2+{\dot{E}}_{D,AC}$
Gas turbine	${\dot{W}}_{GT}={\dot{m}}_5\left(h_5-h_6\right)$ ${\eta }_{GT}=\frac{h_5-h_6}{h_5-h_{6S}}$	${\dot{E}}_5={\dot{E}}_6+{\dot{W}}_{GT}+{\dot{E}}_{D,GT}$
Preheater	${\overline{h}}_2-{\overline{h}}_3=(1+\lambda )({\overline{h}}_7-{\overline{h}}_6)$	${\dot{E}}_2+{\dot{E}}_6={\dot{E}}_3+{\dot{E}}_7+{\dot{E}}_{D,APH}$
Combustion chamber	−$0.02 \mathsf{\lambda } \overline{LHV}+{\overline{h}}_a+\mathsf{\lambda } {\overline{h}}_f-\left(1+\lambda \right) {\overline{h}}_p=0$ ${\eta }_{th,GT}=\frac{{\dot{W}}_{net,GT}}{{\dot{Q}}_{tot,in,GT}}, {\eta }_{ex,GT}=\frac{{\dot{W}}_{net,GT}}{{\dot{EX}}_{tot,in,GT}}$	${\dot{E}}_3+{\dot{E}}_4={\dot{E}}_5+{\dot{E}}_{D,CC}$
Geothermal subsystem
EV1	$h_{11}=h_{12}$	${\dot{E}}_{11}={\dot{E}}_{12}={\dot{E}}_{D,\mathrm{E}\mathrm{V}1}$
EV2	$h_{14}=h_{17}$ $h_{24}=h_{25}$	${\dot{E}}_{14}={\dot{E}}_{17}={\dot{E}}_{D,\mathrm{E}\mathrm{V}2}$ ${\dot{E}}_{24}={\dot{E}}_{25}={\dot{E}}_{D,\mathrm{E}\mathrm{V}3}$
EV3
FC1	${\dot{m}}_{12}{h}_{12}={\dot{m}}_{14}{h}_{14}+{\dot{m}}_{15}{h}_{15}$ ${\dot{m}}_{12}={\dot{m}}_{14}+{\dot{m}}_{15}$	${\dot{E}}_{12}={\dot{E}}_{14}+{\dot{E}}_{15}+{\dot{E}}_{D,\mathrm{F}\mathrm{C}1}$
FC2	${\dot{m}}_{17}{h}_{17}={\dot{m}}_{18}{h}_{18}+{\dot{m}}_{19}{h}_{19}$ ${\dot{m}}_{17}={\dot{m}}_{18}+{\dot{m}}_{19}$	${\dot{E}}_{17}={\dot{E}}_{18}+{\dot{E}}_{19}+{\dot{E}}_{D,\mathrm{F}\mathrm{C}2}$
ERU1	${\dot{Q}}_{ERU1}={\dot{m}}_7\left(h_7-h_8\right)$ ${\dot{Q}}_{ERU1}={\dot{m}}_{13}\left(h_{15}-h_{13}\right)$	${\dot{E}}_7+{\dot{E}}_{13}={\dot{E}}_8+{\dot{E}}_{15}+{\dot{E}}_{D,ERU1}$
ERU2	${\dot{Q}}_{ERU2}={\dot{m}}_8\left(h_8-h_9\right)$ ${\dot{Q}}_{ERU2}={\dot{m}}_{16}\left(h_{20}-h_{16}\right)$	${\dot{E}}_8+{\dot{E}}_{16}={\dot{E}}_9+{\dot{E}}_{20}+{\dot{E}}_{D,ERU2}$
ST1	${\dot{W}}_{st1}={\dot{m}}_{15}\left(h_{15}-h_{16}\right)$	${\dot{E}}_{15}={\dot{E}}_{16}+{\dot{E}}_{st1}+{\dot{E}}_{D,\mathrm{s}\mathrm{t}1}$
ST2	${\dot{W}}_{st2}={\dot{m}}_{21}\left(h_{21}-h_{22}\right)$	${\dot{E}}_{21}={\dot{E}}_{22}+{\dot{E}}_{st2}+{\dot{E}}_{D,\mathrm{s}\mathrm{t}2}$
TEG 1	${\dot{Q}}_{TEG1}={\dot{m}}_{22}\left(h_{22}-h_{23}\right)$ ${\dot{Q}}_{TEG1}={\dot{m}}_{56}\left(h_{57}-h_{56}\right)$	${\dot{E}}_{22}+{\dot{E}}_{56}={\dot{E}}_{23}+{\dot{E}}_{57}+{\dot{W}}_{TEG1}+{\dot{E}}_{D,TEG1}$
${\eta }_{th,Geothermal}=\frac{{\dot{W}}_{net,Geo}}{{\dot{m}}_1(h_1-h_{26})}, {\eta }_{ex,Geothermal}=\frac{{\dot{W}}_{net,Geo}}{{\dot{E}}_1-{\dot{E}}_{26}}$
Kalina subsystem
Vapor generator	${\dot{Q}}_{VG}={\dot{m}}_9(h_9-h_{10})$ ${\dot{Q}}_{VG}={\dot{m}}_{50}(h_{34}-h_{50})$	${\dot{E}}_9+{\dot{E}}_{50}={\dot{E}}_{10}+{\dot{E}}_{34}+{\dot{E}}_{D,VG}$
Separator 1	${\dot{m}}_{34}={\dot{m}}_{35}+{\dot{m}}_{36}$ ${\dot{m}}_{34}{x}_{34}={\dot{m}}_{35}{x}_{35}+{\dot{m}}_{36}{x}_{36}$	${\dot{E}}_{34}={\dot{E}}_{35}+{\dot{E}}_{36}+{\dot{E}}_{D,sep1}$
Separator 2	${\dot{m}}_{37}={\dot{m}}_{38}+{\dot{m}}_{39}$ ${\dot{m}}_{37}{x}_{37}={\dot{m}}_{38}{x}_{38}+{\dot{m}}_{39}{x}_{39}$	${\dot{E}}_{37}={\dot{E}}_{38}+{\dot{E}}_{39}+{\dot{E}}_{D,sep2}$
Kalina turbine	${\dot{W}}_{kt}={\dot{m}}_{35}\left(h_{35}-h_{37}\right)$	${\dot{E}}_{35}={\dot{E}}_{37}+{\dot{W}}_{kt}+{\dot{E}}_{D,KT}$
TEG 2	${\dot{Q}}_{TEG2}={\dot{m}}_{52}\left(h_{52}-h_{51}\right)$ ${\dot{Q}}_{TEG2}={\dot{m}}_{38}\left(h_{38}-h_{40}\right)$	${\dot{E}}_{35}+{\dot{E}}_{51}={\dot{E}}_{37}+{\dot{E}}_{52}+{\dot{W}}_{TEG2}+{\dot{E}}_{D,TEG2}$
EV4	$h_{40}=h_{41}$	${\dot{E}}_{40}={\dot{E}}_{41}+{\dot{E}}_{D,\mathrm{E}\mathrm{V}4}$
EV5	$h_{39}=h_{43}$	${\dot{E}}_{39}={\dot{E}}_{43}+{\dot{E}}_{D,EV4}$
EV6	$h_{45}=h_{46}$	${\dot{E}}_{45}={\dot{E}}_{46}+{\dot{E}}_{D,\mathrm{E}\mathrm{V}6}$
Evaporator	${\dot{Q}}_{vap}={\dot{m}}_{41}\left(h_{42}-h_{41}\right)$ ${\dot{Q}}_{evap}={\dot{m}}_{54}\left(h_{54}-h_{55}\right)$	${\dot{E}}_{41}+{\dot{E}}_{54}={\dot{E}}_{42}+{\dot{E}}_{55}+{\dot{E}}_{D,evap}$
TEG 3	${\dot{Q}}_{TEG3}={\dot{m}}_{47}\left(h_{47}-h_{48}\right)$ ${\dot{Q}}_{TEG3}={\dot{m}}_{52}\left(h_{53}-h_{52}\right)$	${\dot{E}}_{47}+{\dot{E}}_{52}={\dot{E}}_{48}+{\dot{E}}_{53}+{\dot{W}}_{TEG3}+{\dot{E}}_{D,TEG3}$
Pump	${\dot{W}}_{pump}={\dot{m}}_{48}\left(h_{49}-h_{48}\right)$	${\dot{E}}_{48}+{\dot{W}}_{pump}={\dot{E}}_{49}+{\dot{E}}_{D,pump}$
Regenerator	${\dot{Q}}_{RG}={\dot{m}}_{49}\left(h_{50}-h_{49}\right)$ ${\dot{Q}}_{RG}={\dot{m}}_{36}\left(h_{36}-h_{45}\right)$ ${\eta }_{th,Kalina}=\frac{{\dot{W}}_{net,Kalina}}{{\dot{m}}_9(h_9-h_{10})}, {\eta }_{ex,ORC}=\frac{{\dot{W}}_{net,Kalina}}{{\dot{E}}_9-{\dot{E}}_{10}}$	${\dot{E}}_{36}+{\dot{E}}_{49}={\dot{E}}_{45}+{\dot{E}}_{50}+{\dot{E}}_{D,\mathrm{R}\mathrm{G}}$
HDH desalination subsystem
Heat exchanger	${\dot{Q}}_{Heat exchanger}={\dot{m}}_{19}\left(h_{19}-h_{24}\right)$ ${\dot{Q}}_{Heat exchanger}={\dot{m}}_{28}\left(h_{29}-h_{28}\right)$	${\dot{E}}_{19}+{\dot{E}}_{28}={\dot{E}}_{24}+{\dot{E}}_{29}+{\dot{E}}_{D,\mathrm{H}\mathrm{e}\mathrm{a}\mathrm{t} \mathrm{e}\mathrm{x}\mathrm{c}\mathrm{h}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{e}\mathrm{r}}$
Humidifier	${\dot{m}}_{31}{h}_{31}+{\dot{m}}_{29}{h}_{29}={\dot{m}}_{30}{h}_{30}+{\dot{m}}_{32}{h}_{32}$ ${\dot{m}}_{31}+{\dot{m}}_{29}={\dot{m}}_{30}+{\dot{m}}_{32}$	${\dot{E}}_{31}+{\dot{E}}_{29}={\dot{E}}_{30}+{\dot{E}}_{32}+{\dot{E}}_{D,\mathrm{H}\mathrm{u}\mathrm{m}}$
Dehumidifier	${\dot{m}}_{32}{h}_{32}+{\dot{m}}_{27}{h}_{27}={\dot{m}}_{28}{h}_{28}+{\dot{m}}_{33}{h}_{33}$ ${\dot{m}}_{33}={\dot{m}}_{32}({\mathsf{ɷ}}_2-{\mathsf{ɷ}}_1)$ ${\eta }_{th,HDH}=\frac{{\dot{m}}_{33}{h}_{33}}{{\dot{m}}_{19}(h_{19}-h_{24})}, {\eta }_{ex,HDH}=\frac{{\dot{W}}_{net,Kalina}}{{\dot{E}}_{19}-{\dot{E}}_{24}}$	${\dot{E}}_{57}={\dot{E}}_{58}+{\dot{E}}_{59}+{\dot{E}}_{D,RO}$ ${\dot{E}}_{32}+{\dot{E}}_{27}={\dot{E}}_{33}+{\dot{E}}_{28}+{\dot{E}}_{D,\mathrm{D}\mathrm{h}\mathrm{u}\mathrm{m}}$
Domestic water generator
DWH	${\dot{Q}}_{DWH}={\dot{m}}_{10}\left(h_{10}-h_{10\mathrm{a}}\right)$ ${\dot{Q}}_{DWH}={\dot{m}}_{58}\left(h_{59}-h_{58}\right)$	${\dot{E}}_{10}+{\dot{E}}_{58}={\dot{E}}_{10\mathrm{a}}+{\dot{E}}_{59}+{\dot{E}}_{D,DWH}$

.

Mass and energy rate balances for the proposed system, which operates at steady state, are as follows:

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

(12)

$${\dot{Q}}_{cv}+\sum {\dot{m}}_i{h}_i=\sum {\dot{m}}_e{ h}_e+{\dot{W}}_{cv}$$

(13)

Here, $\dot{m}$, ${\dot{Q}}_{cv}$, and ${\dot{W}}_{cv}$ are the mass flow rate, heat transfer rate, and power, respectively, for the corresponding control volume.

The second law of thermodynamics is used to determine the input and output exergy flow rates and component exergy destruction rates for the trigeneration system. A rate balance of exergy for a steady-state process in a control volume is expressible as follows:

$${\sum }_{inlets}{\dot{E}}_i+\sum {\dot{Q}}_j(1-\frac{T_0}{T_j})={\sum }_{outlets}{\dot{E}}_e+{\dot{W}}_{cv}+{\dot{E}}_{D,k}$$

(14)

Here, $\sum {\dot{Q}}_j(1-\frac{T_0}{T_j})$ denotes the exergy transfer rate related to the heat difference; ${\dot{E}}_D$ is the exergy destruction rate. Also, $\dot{E}$ is the total exergy rate, which is equal to the sum of physical and chemical exergy rates:

$$\dot{E}={\dot{E}}_{ph}+{\dot{E}}_{ch}$$

(15)

where ${\dot{E}}_{ph}$ is physical exergy and ${\dot{E}}_{ch}$ chemical exergy. These can be expressed as follows:

$${\dot{E}}_{ph}=\sum {\dot{m}}_i\left[\left(h_i-h_0\right)-T_0\left(s_i-s_0\right)\right]$$

(16)

$${\dot{E}}_{ch}=\dot{n }(\sum y_i{\overline{e}}_i^{ch,0}+\overline{R}{T}_0\sum y_i\ln \left(y_i\right))$$

(17)

Here, ${\overline{e}}_i^{ch,0}$ is the standard chemical exergy of an ideal gas, and $\overline{R}$ is the universal gas constant.

3.5. Overall Performance Evaluation

Energy and exergy efficiencies, as well as the carbon dioxide emission index, can be expressed, respectively, as follows [20,21]:

$${\mathsf{ղ}}_{I,tot}=\frac{{\dot{W}}_{net,tot}+{\dot{m}}_{41}(h_{41}-h_{42})+{\dot{m}}_{58}(h_{59}-h_{58})+{\dot{m}}_{33}{h}_{33}}{{\dot{n}}_{f }{\overline{LHV}}_{fuel}+{\dot{m}}_{11}(h_{11}-h_{26})}$$

(18)

$${\mathsf{ղ}}_{II,tot}=\frac{{\dot{W}}_{net,tot}+\left({\dot{E}}_{42}-{\dot{E}}_{41}\right)+\left({\dot{E}}_{59}-{\dot{E}}_{58}\right)+{\dot{E}}_{33}}{{\dot{n}}_f {\overline{e^0}}_{ch,fuel}+({\dot{E}}_{11}-{\dot{E}}_{26})}$$

(19)

$$\zeta =\frac{{\dot{m}}_{{CO}_2,product}}{{\dot{W}}_{net,total}}$$

(20)

4. Results and Discussion

4.1. Modelling Validation

To validate the modeling results for the trigeneration system, the gas turbine and geothermal cycles are validated separately using different articles.

4.1.1. Gas Turbine

The variation of energy efficiency with the inlet temperature of the gas turbine in the present study is compared with data from Gholizadehet et al. [2] in Figure 2. It can be seen that, for the same functional conditions, the results from the gas turbine system simulation are in good agreement, supporting the accuracy and correctness of the system modeling.

According to this diagram, the highest percentage of error is equal to 0.068%, and the lowest percentage of error is equal to 0.094.

4.1.2. Geothermal Cycle

The main parameters of the geothermal cycle for the present study, which include net generated power, first-law efficiency, second-law efficiency, and exergy destruction rate, are compared with those of Yari [6] in Figure 3. The results are observed to be in good agreement, with a maximum deviation of around 3.3% (for exergy destruction rate).

4.2. System Analysis

The important performance values for the proposed trigeneration system are given in

Table 3. Important performance values of the trigeneration cycle.

Parameter	Value
Energy efficiency (%)	36.2
Exergy efficiency (%)	44.2
Net generated power (kW)	2068
Cooling load (kW)	182
Heating load (kW)	407.5
Freshwater rate (kg/s)	0.134
CO2 emission index (kg/kWh)	0.539
Total exergy destruction (kW)	2937

, including energy efficiency, exergy efficiency, net output power, carbon dioxide emission rate, produced freshwater flow rate, heating and cooling rate, and exergy destruction rate of the overall system.

In Figure 4, the exergy destruction rate for the trigeneration system is broken down by subsystems. The gas turbine cycle is seen to have the highest rate and percentage of exergy destruction (around 52%). Also, the DWH has the lowest rate of exergy destruction in the system.

Table 4. Energy efficiency, exergy efficiency, and net power produced for each system.

System	Energy Efficiency (%)	Exergy Efficiency (%)	Net Power Output (kW)
Gas turbine	29.71	28.31	1000
Geothermal	24.92	21.7	1035.86
Kalina	4.679	12.01	31.84
HDH	35.53	21.07	-

lists values of energy efficiency, exergy efficiency, and net output power of the proposed system, broken down by subsystems. According to this table, the energy efficiencies of the gas turbine cycle, geothermal cycle, Kalina cycle, and HDH desalination cycle are 29.71%, 24.92%, 4.68%, and 35.53%, respectively. Also, the highest exergy efficiency among all constituent systems is seen to be associated with the gas turbine cycle, at 28.31%.

4.3. Parametric Study

To investigate the performance of the proposed system for different working conditions, a comprehensive parametric study is carried out. Note that the considered parameters and their ranges are chosen based on other sources and according to the working conditions of the system.

4.3.1. Effect of Air Compressor Pressure Ratio

Figure 5 illustrates how varying the pressure ratio of the air compressor affects the main system parameters. As the pressure ratio increases, a reduction in energy efficiency is seen at first, followed by an increase. The primary cause of this process is a drop in the mass flow rate of air caused by the rise in the pressure ratio. Since the ratio of fuel to air in this state is constant, this process also results in a decline in the mass flow rate of combustion products. Since the gas turbine’s combustion gases provide thermal energy to other subsystems, a reduction in the combustion product flow rate lowers the net power output for the entire system and lowers the cooling and heating outputs. On the other hand, as the air compressor pressure ratio rises, the fuel flow rate likewise falls, which results in less energy entering the combustion chamber. But, since the decreasing trend of cooling and heating outputs prevails over the increasing trend of the net power of the system, there ultimately is a decrease in the amount of useful energy produced by the system. As the produced useful energy decreases, the energy efficiency of the overall system decreases to a point. This decreasing trend stops at a pressure ratio of around 9.7. The minimum value of energy efficiency occurs at a pressure ratio of around 9.65 and is 36.2%.

The variation of exergy efficiency with pressure ratio is also shown in Figure 5. As stated in the previous section, as the pressure ratio increases, the fuel mass flow rate decreases. This reduction causes a decrease in the rate of exergy input to the combustion chamber. By reducing the input exergy rate, the exergy efficiency increases for the overall system. The exergy efficiency reaches a peak of 44.2% at a pressure ratio of 10.5. After the pressure ratio of 10, the amount of exergy input to the gas turbine system is increased, which ultimately causes a decrease in the exergy efficiency. The lowest value of exergy efficiency at a pressure ratio of 16 is 43.62%.

In Figure 5, it is seen that the net power produced is minimum at a pressure ratio of 10.21; after that, it exhibits an increasing trend. The value of the net power at this pressure ratio is 2067 kW. Above the pressure ratio of 10.21, the power output of the overall system increases, and its value reaches 2101 kW at the pressure ratio of 16. The reason for the increase in the net output power is the increase in the power produced by steam turbines 1 and 2, as well as the increase in power related to the Kalina cycle and thermoelectrics.

The variation in the carbon dioxide emission index with air compressor pressure ratio is also displayed in Figure 5. As the air compressor pressure ratio increases, the index first drops and subsequently rises, because carbon dioxide’s mass flow rate (like net power output) decreases as the pressure ratio rises. Note, however, that the decreasing trend of the carbon dioxide mass flow rate is overcome by the decreasing trend of production power, which causes a reduction in the carbon dioxide emission rate. This decreasing trend stops at a pressure ratio of 10.48, after which it takes on an upward trend. The minimum value of the carbon dioxide emission index is 0.5392 kg/kWh.

4.3.2. Effect of Gas Turbine Inlet Temperature

The variation of system parameters with gas turbine inlet temperature is depicted in Figure 6. This figure shows that the mass flow rate of the combustion products declines as the gas turbine’s inlet temperature increases. As a result, the system’s net power, cooling, and thermal outputs, as well as the amount of freshwater produced, all decrease. According to the energy balance equation for the combustion chamber, the mass flow rate of the fuel consumed (biogas) also drops as a result of the reduction in the mass flow rate of gaseous products, which lowers the energy input to the combustion chamber. It should be noted that the decreasing trend of the rate of useful energy produced by the system, including net power, thermal, and cooling outputs, is more pronounced than the decreasing trend of the input energy rate to the system, which causes a decrease in the energy efficiency and exergy efficiency. Note also that the energy input rate to the system is the sum of the heating value of biogas in the gas turbine and the input energy from the geothermal system. The lowest values of energy efficiency, exergy efficiency, and net generated power at 1600 K are 34.49%, 44.03%, and 1997 kW, respectively.

As the mass flow rate of the combustion products declines with increasing gas turbine inlet temperature, the net power produced by the overall system also continuously decreases and changes from 2090 (at 1200 K) to 1997 (at 1600 K). Changes in the environmental pollution index of the system with gas turbine inlet temperature are also shown in Figure 6. The fuel flow rate declines as the gas turbine’s input temperature rises. Also, since the system consumes less fuel, the emission index is reduced. This index varies from 0.5423 kg/kWh at 1200 K to 0.5335 kg/kWh at 1600 K.

4.3.3. Effect of Geothermal Inlet Temperature

Figure 7 illustrates how varying geothermal input temperature (T11) affects the energy and exergy efficiencies, net production power, and the environmental pollution index for the trigeneration system. It is observed that energy efficiency continuously rises as the geothermal inlet temperature drops, and the exergy efficiency becomes a maximum at a geothermal inlet temperature of around 470 K. The reason for this trend is as follows. The rate of the freshwater flow declines while the net power produced by the system increases with the geothermal input temperature, but the increase in net power is greater than the drop in the freshwater flow rate. Since the thermal and cooling output rates are constant at this state, the useful energy production rates for the system increase.

Given that the gas turbine net power output of the set is constant, the power of ST1 and ST2 increasing with the geothermal input temperature is the primary cause of the rise in the net power output of the overall system. The rise in mass flow rate and the difference in specific enthalpy between the input and output of these turbines are the primary drivers of their increased power. It is noteworthy that the output power of the thermoelectric generator 1 decreases with increasing geothermal input temperature, but this decrease is insignificant compared to the increase in the power of steam turbines 1 and 2.

The variation of the carbon dioxide emission index with the geothermal input temperature is also shown in Figure 7. The main parameter influencing the trend is the net power production of the overall system because the mass flow rate of carbon dioxide is constant at this stage. Additionally, the pollution index declines as the geothermal input temperature increases since power production rises continually as the geothermal fluid (water) temperature rises. At a temperature of 520 K, the carbon dioxide emission index is 0.5199 kg/kWh.

Generally, raising the geothermal inlet temperature has a favorable impact on the overall system on both the net power output and the carbon dioxide emission index.

4.3.4. Effect of Flash Chamber 1 Inlet Pressure

Figure 8 shows the variation of selected system parameters with the pressure of flash chamber 1. The behaviors of both energy and energy efficiency as FC1’s input pressure rises are similar. Starting at 200 kPa, the energy and exergy efficiencies of the system increase and reach their maximum at around 500 kPa. Increasing the inlet pressure of FC1 decreases the mass flow rate of ST1. Despite the fact that the mass flow rate to ST1 decreases, the overall generated power increases until it is maximized at 500 kPa, because ST1 works in a greater pressure span and produces more power with the extra pressure. Note that the generated power in steam turbine 2 decreases with the increase in the flash chamber 1 pressure, but the increase in the output power of steam turbine 1 is greater than the decrease in steam turbine 2, which ultimately leads to an increase in the net production power of the entire system. It should also be noted that the power produced by the gas turbine unit is constant. On the other hand, when increasing the pressure of FC1, the rate of heat exchange in ERU2 decreases, which raises the output temperature of the combustion products from this heat exchanger (point 9). With the increase in temperature, the amount of energy in the vapor generator increases, which ultimately leads to an increase in refrigeration. Note that the flow rate of freshwater produced rises with increasing FC1 pressure.

The variation in carbon dioxide emission rate with FC1 pressure is also shown in Figure 8. According to the points mentioned in the previous section, an increase in the inlet pressure of FC1 leads to an increase in the total power production of the system, which ultimately reduces the carbon dioxide emission rate. It can be observed that increasing the pressure to 500 kPa is useful in all aspects.

4.3.5. Effect of Temperature Difference of Heat Exchanger of HDH Unit

The influence of the temperature difference in the desalination unit heat exchanger $({\Delta T}_{Heat exchanger}=T_{19}-T_{24})$ on the flow rate of the produced freshwater is shown in Figure 9. It is seen that increasing the heat exchanger’s temperature difference in this unit has a direct and noticeable impact on raising the mass flow rate of freshwater products. For example, when the heat exchanger’s temperature difference is raised from 10 K to 100 K, the freshwater flow rate increases from 0.13 kg/s to 2.18 kg/s.

5. Overall Performance Results

The main findings and the conclusions drawn from them are as follows:

• Energy and exergy efficiencies and the carbon dioxide emission index are 36.20%, 44.22%, and 0.5394 kg/kWh, respectively;
• For the overall system, the generated power, heating rate, cooling rate, and freshwater flow rate are 2068 kW, 407.5 kW, 182 kW, and 0.1337 kg/s, respectively;
• The power produced by TEG1, TEG2, and TEG3 is 95.9 kW, 2.92 kW, and 9.31 kW, respectively;
• Of the total exergy destruction rate of the trigeneration system, the gas turbine with 52.15% and the DWH with 2.4% exhibit the highest and lowest values, respectively;
• With increasing pressure ratios for the gas turbine units, the energy efficiency, net power production, and carbon dioxide emission index first decrease and then increase, while the exergy efficiency decreases first and then increases;
• As the gas turbine pressure ratio rises, the energy efficiency, net production power, and carbon dioxide emission index all initially decrease and then increase. The energy efficiency decreases at first and then increases.

6. Conclusions

In the present study, a trigeneration system with two heat sources (biogas and geothermal energy) that produces green energy, clean water, and cooling and heating production is simulated and analyzed from the perspectives of energy, exergy, and the environment. To investigate the performance of the system at various conditions, a comprehensive parametric analysis is performed from the thermodynamic and environmental perspectives.

Table 5. Comparison of energy and exergy efficiencies from the literature with the present system.

Reference	Heat Source	Energy Efficiency (%)	Exergy Efficiency (%)	Product Output
Musharavati et al. [16]	Geothermal	55.81	22.63	Power, heating, and cooling
Azariyan et al. [26]	Geothermal	22.28	21.37	Power, cooling, and hydrogen production
Feili et al. [27]	Geothermal	20.37	20.95	Power and hydrogen production
Wang et al. [28]	Gas turbine	52.95	40.2	Power, heating, and cooling
Present study	Gas turbine and geothermal	36.2	44.22	Power, cooling, heating, and freshwater production

compares the energy efficiency and exergy efficiencies of relevant previous studies and those of the current study. The heat source used in this study is a combination of gas turbine cycles and geothermal sources. In fact, the combination of these two sources, on the one hand, reduces the amount of environmental pollution and, on the other hand, increases exergy efficiency. According to this table, the exergy efficiency of the present study is significantly greater compared to previous studies, which demonstrates the efficiency benefits and novelty of this work compared to previous works.

Several topics merit further investigation, and the authors plan on carrying out these studies in the future. They include the following:

• A technoeconomic analysis and calculation of net present value and return on investment;
• A risk and system reliability analysis;
• A comprehensive environmental impact assessment. This includes a Life Cycle Assessment to offer alternatives to comprehensively evaluate the environmental impact and sustainability of the proposed system.