Design-based system performance assessment of a combined power and freshwater cogeneration system

1 Introduction

Nowadays, optimizing the performance of energy systems, reducing costs, and decreasing the pollutant of production is a serious trouble for designers and engineers, for which many solutions have been proposed. One of the best solutions is simultaneous production systems which are widely used in many industrial factories due to their higher efficiency (Baniassadi et al., 2016). In these systems, heat and electricity are produced simultaneously in one process, which can be used for domestic hot water, space heating, swimming pool heating, laundry processes, and absorption cooling (Rosen, 2021). Providing water and energy for the growing population of the world is a big challenge for human beings. Furthermore, due to the large amount of salt water worldwide, desalination is a suitable solution for the production of freshwater (Pugsley et al., 2016; Wang et al., 2019). Recently, the integration of water desalination systems with power generation systems has been taken into consideration by many researchers (Bai et al., 2023). Michael et al. evaluated the efficiency of combining the evaporative desalination system with the power and heat generation plant. In this article, a multi-effect evaporative desalination-thermal vapor compression (MED-TVC) desalination plant with a capacity of 36,000 m³/day was studied. Based on the development model found in EES software, sensitivity analysis was performed on it. The effect of several design and operation parameters on the fraction of the energy output evaluated as “efficient cogeneration” was investigated. The results showed that this fraction increases almost linearly with the number of MED units which were supplied with steam (Tamburini et al., 2016). Baniassadi et al. (2016) investigated the potential of exhaust waste heat recovery of a microturbine for seawater desalination by using an organic Rankine cycle (ORC). The heat obtained from the microturbines was used by operating the ORC, and the generated power was transferred to the reverse osmosis (RO) desalination water plant. Furthermore, the biological absorption of CO₂ through microalgae cultivation by exploiting microturbine exhaust gases was considered (Tajik Mansouri et al., 2020). Cardona et al. integrated a small thermal desalination system MEE with small size (2000 m³/day) with one system SWRO single-stage seawater reverse osmosis. The heat and electricity needed for the system was provided by a gas engine. The results of 30% and 8% reduction in carbon dioxide emissions showed the carbon and unit cost of freshwater (Demir and Dincer, 2022). Salimi and Amidpour contributed toward modeling, simulation, parametric study, and economic evaluation of the internal combustion engine with desalination (Salimi and Amidpour, 2017). A multipurpose water desalination system, with the MED-TVC thermal steam concentrator, was simulated and optimized for economic analysis with a new approach in MATLAB software using the extra heat. A steam generator, with HRSG heat recovery, was used to provide the required heat for steam production (Harandi et al., 2021). The multiobjective optimization was done by using genetic algorithms based on the NSGA II non-major sorting. Finally, it is evident that the heating steam temperature is more influenced by GOR than by other decision variables.

Jamshidian et al. (2022) developed a solar hybrid desalination system that is independent of any fossil-based power source. They found that compared to a single multieffect desalination plant, the hybrid system could increase the total recovery by 15%. Moreover, an approximately 8% drop in the final cost of 1 m³ of produced freshwater was observed. Ghiasirad et al. (2021) proposed a multigeneration system fueled by a geothermal source integrated with a humidification–dehumidification desalination cycle. They reported that the overall system performance in winter was better than that in summer. Furthermore, the system had considerably high heating, cooling, and freshwater capacities. Moreover, thermoeconomic indexes were notably lower than those of similar systems. Zuo et al. (2020) investigated the numerical simulations for the wind supercharging solar chimney power plant integrated with a seawater desalination unit and a gas waste heat cycle. They considered the effect of the flue gas jet on the flow field in the chimney and the influence of rotational speed on the power output and freshwater yield. The power generation and hourly freshwater rate for that plant were approximately 0.38 MW and 20.3 ton/h, respectively. Shahsavari et al. (2022) developed the optimum sizing of a hybrid CHP and desalination unit as a polygeneration plant for supplying rural demands. As observed from the results, that system had a ∼58.5% lower carbon dioxide emission than conventional natural gas-driven plants and less than 27 km of grid breakeven distance. Moreover, the CHP reduced the annual fuel consumption by almost 225 m³/yr. Catrini et al. (2017) developed a CHP plant coupled with the MED unit considering the exergetic and exergoeconomic costs for all the material streams. In the aforementioned plant, the concentrated brine was alternatively considered a residue to be disposed or a resource to be exploited. Moreover, reverse electrodialysis was adopted for exergy recovery from the concentrated brine. They reported that the high unit costs were determined for the material streams and energy flows. You et al. (2020) developed a combined cooling, heating, and power system integrated with an MED system, a fuel cell, and a microgas turbine. They reported that the most exergy degradation of components is mainly due to endogenous components with gas turbines, inverters, and air compressors. Tawalbeh et al. (2023) reported that the desalination integrated with salinity gradient solar ponds was reported to exceed 50% exergy efficiency. Furthermore, those plants could show enhanced overall efficiency (approximately 30%) in hybrid power systems. However, the environmental concerns and large-scale requirements are still among the main challenges.

Mario Gorta et al. evaluated the production of power and freshwater with a gas turbine, S-CO₂ supercritical cycle, and ORC with a water unit. An RO desalination unit was added to the power generation cycle to produce freshwater at a low cost. The results showed that the proposed combined system with excess heat recovery leads to high efficiency with a low cost of energy and freshwater (Manesh et al., 2021). Benalcazar determined the optimal size of thermal energy storage systems for CHP plants according to specific investment costs. The results showed that the integration of TES leads to a significant reduction in the use of steam boilers and reduces fuel costs and environmental impact (Benalcazar, 2021). Lepixar et al. improved the CHP system by integrating TES technology into the heat and power generation energy system. The investigated solutions included the connection of CHP with electric boilers and TES which helps balance heat and electricity loads and provides the possibility of creating an RES in the system (Lepiksaar et al., 2021). Haj Abdullahi evaluated the use of cooling and heating energy storage tanks in the optimization of the multiple production system. The optimization of the heating, cooling, and CCHP generation system by using a gas engine as the main driver is presented in this work. It was determined that using TES + CES tanks improved the optimal TAP by 9.48%, 5.19%, and 2.23%, respectively, compared to not using storage tanks (Hajabdollahi, 2015a).

This research suggests using a thermal energy storage tank to store excess heat and use it during necessary hours, reducing system costs and pollutants. The system includes a gas turbine for power generation and a backup boiler for heat supply if needed.

2 Materials and methods

2.1 Gas turbine—multieffect evaporative distillation hybrid system

Figure 1 shows a general schematic of the simultaneous production system of heat, electricity, and desalinated water CHP + MED. In this system, the required electricity is supplied from the main driver, which is the gas turbine, and in case of shortage, it is purchased from the network. The produced heat, which is discharged to the external environment through the exhaust, is recovered by using a heat exchanger with 90% efficiency and is used to provide the required heat for desalination and building. This heat exchanger is usually part of the drive system (Sanaye and Hajabdollahi, 2016). If the heat produced by the driver is less than the total requirement, the backup boiler will supply it.

FIGURE 1

FIGURE 1. Gas turbine multieffect evaporative distillation hybrid system.

Figure 2 shows the general schematic of the heat, electricity, and desalination system using the thermal energy storage tank CHP + MED + TES. If there is excess heat in the system, it would use it and would not waste on the environment like the previous system (Ma Y. et al., 2023; Gu et al., 2023; Tian et al., 2023). The working method of the energy storage tank is such that the excess heat of the stimulus is stored and used in the next timesteps according to the considered strategy, if necessary. The existence of this energy storage tank not only prevents the backup boiler from working more but also leads to the production of fewer pollutants.

FIGURE 2

FIGURE 2. Novel gas turbine multieffect evaporative distillation hybrid system with an energy storage tank.

Figure 3 shows a typical example of an MED-TVC desalination plant. Its main components consist of N number of evaporators, a condenser, and a thermal vapor compressor (ejector). Their most common arrangement is parallel feeding (He et al., 2022; Wu et al., 2022; Han et al., 2023). In the parallel feeding arrangement, the flow direction of water vapor and liquid is similar to each other and is simpler than that of the other two arrangements. In general, the structure of this type of desalination is such that the steam produced in each effect is used as a driving fluid in the next effect. As shown in Figure 3, after the feed water enters the condenser, it exchanges heat with the steam coming out of the last heat exchanger and then exits at the temperature $T_f$ (Huang S. et al., 2021; Lu C. et al., 2022; Lv et al., 2023). A part of the water entering the condenser is returned to the sea to convert the steam exiting from the last heat exchanger that entered the condenser into a liquid, and the rest of the feed water F is equally divided between all effects. The purpose of cooling water is to remove the excess heat from the driving steam. In a parallel flow system, steam flows from left to right in the direction of the pressure drop, whereas the feeding water enters each effect in a vertical direction. The driving steam, which is supplied from an external source, is compressed, with some steam drawn from the last heat exchanger by the thermal steam compressor (ejector) and enters the first heat exchanger from the desalination water. Then, the feed water is sprayed on the evaporator tubes and heated up to the boiling temperature of the first heat exchanger and evaporates. It should be noted that the temperature of the first exchanger is also known as the high temperature of saltwater. The amount of feed water that evaporates forms the amount of $D_1$ in the first converter, which is used as a heat source at a lower temperature and pressure in the next converter (Wang et al., 2023a; Wang et al., 2023b). The temperature of the steam produced in the first converter $T_v$ is lower than the boiling temperature in this converter by the amount of BPE (increase in the boiling temperature of water at a certain pressure), which is due to the presence of salts dissolved in water. The vapors formed in each exchanger are passed through a drip catcher to remove the water droplets. The temperature of the steam passing through the dropper decreases due to friction loss. To use the energy of the brine in the first converter, the brine is sent to the next converter. In addition to the mentioned equipment, there are 2 to N other equipment called flash chambers (Ma X. et al., 2023; Liu and Xu, 2023). The condensed heating steam in the second evaporator tubes enters the flash chamber of the same converter, and because the working pressure of the flash chamber is lower than the pressure of the converter, some of that steam enters the next converter, and this process continues until the N converter. It should be mentioned that the produced steam $D_n$ in the last converter is divided into two parts: one part $D_{ev}$ is drawn by the thermal steam compressor and the other part $D_c$ is sent to the condenser.

FIGURE 3

FIGURE 3. Multieffect thermal vapor-compression desalination systems.

2.2 Thermodynamic modeling of the CHP + MED + TES system equipment

The freshwater system has gained a lot of importance recently and is expected to increase in the future, so its thermodynamic modeling is presented with more complete details. The CHP system energy modeling is done based on existing relationships for efficiency and performance of equipment including the gas turbine and backup boiler at different partial loads. The energy storage tank is also modeled in terms of energy by considering it as a control volume whose enthalpy is checked at its input and output (Ashour, 2003; Al-Mutaz and Wazeer, 2014; Sanaye and Hajabdollahi, 2016; Esrafilian and Ahmadi, 2019; Xu et al., 2021; Zhao et al., 2022; Zhu et al., 2022; Luo et al., 2023).

2.3 Desalination modeling (MED-TVC)

In this section, the equations governing multieffect evaporative desalination with a thermal steam condenser have been described. Modeling is done by applying energy and mass conservation equations in evaporators, condensers, thermal vapor compressors (ejectors), and flash chambers. The design variables include the number of effects (n), driving steam pressure ($P_s$), feedwater flow rate $\left(F\right)$, and driving steam flow rate $D_m$. The rest of the parameters are considered constant.

Assuming that the temperature difference is constant in all effects, so the following equation is used to calculate it (Al-Mutaz and Wazeer, 2014):

$\Delta T=\frac{T_1-T_n}{n-1}.(1)$

The compressed steam temperature $T_s$ is obtained from the following equation:

$T_s=T_1-\Delta T.(2)$

The steam temperature in the last heat exchanger is obtained from the following equation (Al-Mutaz and Wazeer, 2014):

$T_{{\nu }_n}=T_n-BPE.(3)$

The specific heat capacity of water, which is a function of water temperature and salinity, is obtained from the following equation (Al-Mutaz and Wazeer, 2014):

$C_p=\left[a+\left(b.T_1\right)+\left(c.{\left(T_1\right)}^2\right)+\left(d.{\left(T_1\right)}^3\right)\right].{\left(10\right)}^{-3}.(4)$

The pressure of condensed steam $P_s$ and expanded steam $P_{ev}$ by the ejector is obtained from the following equations (El-Dessouky and Ettouney, 2002):

$P_s=1000\ast \exp \left(\frac{-3892.7}{T_s+273.15-42.6776}+9.5\right),(5)$

$P_{ev}=1000\ast \exp \left(\frac{-3892.7}{T_{vn}+273.15-42.6776}+9.5\right).(6)$

Pressure is in kilopascals and temperature is in degree Celsius (Gao et al., 2021; Lin et al., 2022a; Lin et al., 2022b; Lu L. et al., 2022). The expansion ratio in the ejector can be obtained with Equation 7, and the compression ratio in the ejector can be obtained with Equation (8) (Al-Mutaz and Wazeer, 2014):

$ER=\frac{P_m}{P_{ev}},(7)$

$CR=\frac{P_s}{P_{ev}}.(8)$

If the driving flow and the suction fluid is water vapor, the model equation for calculating the suction ratio $R_a$ is as follows:

$R_a=0.234\frac{{\left(P_s\right)}^{1.19}}{{\left(P_{ev}\right)}^{1.04}}\ast {\left(ER\right)}^{0.015}.(9)$

The amount of steam drawn is determined by the following equation:

$D_{ev}=\frac{D_m}{R_a}.(10)$

The brine temperature in each heat exchanger is lower than the previous effect by $∆T$. Therefore, by assuming that the temperature of the saltwater in the heat exchanger $i$ is $T_i$, the temperature of the saltwater in the next converter i+1 can be obtained using the following equation (Al-Mutaz and Wazeer, 2014; Li R. et al., 2022; Du et al., 2022; Li et al., 2023; Liu, 2023):

$T_{i+1}=T_i-\Delta T,i=\mathrm{1,2,3},\dots ,n.(11)$

The steam temperature in each heat exchanger is calculated as follows:

$T_{vi=}{T}_i-BPE.(12)$

The feedwater flow rate for each heat exchanger is obtained from the following equation:

$F_i=\frac{F}{n},i=\mathrm{1,2,3},\dots ,n.(13)$

The steam condensation temperature ${Tc}_i$ is compared to the boiling temperature $T_i$ by the value of BPE, losses due to pressure drop in the droplet $∆T_P$, and the frictional pressure drop in the connection line $∆T_T$ of the condensation process $∆T_C$ is lower, and its relationship is as follows (Al-Mutaz and Wazeer, 2014):

$T_{ci}=T_i-BPE-{\Delta T}_p-{\Delta T}_t-{\Delta T}_c.(14)$

The latent heat of driving steam, steam in the evaporator, and condenser are obtained from the following relationships:

$\lambda =2589.583+0.9156\ast T-4.834\ast {10}^{-2}\ast T^2.(15)$

In the aforementioned equations, the temperature is given in degree Celsius (Chen et al., 2022; Zhang et al., 2022; Li et al., 2023; Xia et al., 2023) and the latent heat is given in kJ/kg. The steam produced in the first effect is obtained by using the law of conservation of energy as follows (Al-Mutaz and Wazeer, 2014):

$D_1=\frac{\left(D_m+D_{ev}\right).{\lambda }_s-F_1.C_p.\left(T_1-T_f\right)}{{\lambda }_1}.(16)$

The saltwater concentration balance is estimated from the following equation:

$X_{b1}=\frac{F_1}{\left(F_1-D_1\right)}.X_f.(17)$

The steam produced in the second heat exchanger is estimated from the following equation (Al-Mutaz and Wazeer, 2014):

$D_2=\frac{D_1.{\lambda }_{1-}{F}_2.C_p\left(T_2-T_f\right)+B_1.C_p\left(T_1-T_2\right)}{{\lambda }_2}.(18)$

The temperature and salinity of the heat exchanger output brine are calculated from the following equations, (Al-Mutaz and Wazeer, 2014):

$B_2=F_2+B_1-D_2,(19)$

$X_{b2}=\frac{{X_{f.}f}_1+X_{b1}.B_1}{\left(F_1-D_1\right)}.(20)$

The flash efficiency for 2 to n heat exchangers is obtained from the following equation (Sanaye and Hajabdollahi, 2016):

$NE{A}_i=\frac{33.{\left(T_{i-1}-T_i\right)}^{0.55}}{T_{vi}},i=\mathrm{2,3},\dots ,n.(21)$

The cooling air temperature when entering into the heat exchanger can be calculated using the following equation (Al-Mutaz and Wazeer, 2014):

$T^{\prime }=T_i+NE{A}_i,i=\mathrm{2,3},\dots ,n.(22)$

Equation 15 is used for the latent heat of vaporization at $T_i^{\prime }$ temperature (Liu and Liu, 2021a; Liu and Liu, 2021b; Wang et al., 2022a). The flashed steam from brine from converter 2 to $n$ is obtained from the following equation:

$d_i=\frac{B_{i-1}.C_p\left(T_{i-1}-{T_i}^{\prime }\right)}{T_{vi}}i=\mathrm{2,3},\dots ,n.(23)$

In order to calculate the ${{NEA}_i}^{\prime }$ value for the flash chamber, the following relationship can be used (Al-Mutaz and Wazeer, 2014):

${{NEA}_i}^{\prime }=\frac{33.{\left(T_{ci-1}-T_{vi}\right)}^{0.55}}{T_{vi}},i=\mathrm{2,3},\dots ,n.(24)$

The condensation temperature of the vapors entering the flash chambers can be estimate using the following equation:

$T^{″}=T_{vi}+{{NEA}_i}^{\prime }i=\mathrm{2,3},\dots ,n.(25)$

The flashed steam in flash chambers is estimated as follows (Al-Mutaz and Wazeer, 2014):

${d_i}^{\prime }=D_{i-1}.C_p\left(\frac{T_{ci-1}-{T_i}^{″}}{{{\lambda }_i}^{″}}\right).(26)$

The amount of steam created from the effect of 3 to $n$ can be estimated from the following equation (Al-Mutaz and Wazeer, 2014):

$D_i=\frac{\left(D_{i-1}.{\lambda }_{i-1+}{d}_{i-1}.{\lambda }_{i-1+}{d_{i-1}}^{\prime }.{{\lambda }_{i-1}}^{\prime }\right)-F_i.C_p\left(T_i-T_f\right)+B_{i-1}.C_p(T_{i-1}-T_i)}{{\lambda }_i},i=\mathrm{3,4},\dots ,n.(27)$

The total amount of condensation is obtained by the following equation (Al-Mutaz and Wazeer, 2014):

$D_t=D_1+D_2+D_3+\dots D_n={\displaystyle \sum _{i=1}^n}{D}_{i}i=\mathrm{1,2},\dots ,n.(28)$

The output brine and salinity of converter 3 to n are calculated from the following equations, respectively (Al-Mutaz and Wazeer, 2014):

$B_i=F_i+B_{i-1}-D_{i}i=\mathrm{3,4},\dots ,n,(29)$

$X_{b2}=\frac{{X_{f.}f}_i+X_{bi-1}.B_{i-1}}{B_i}.(30)$

The vapors created in the last heat exchanger are divided into two parts: one part enters the $D_c$ condenser and the other is drawn by the thermal vapor compressor $D_{ev}$ (Li et al., 2021; Wang et al., 2022b; Liao et al., 2022). The amount of steam entering the condenser is calculated with the following equation:

$D_c=D_n-D_{ev}.(31)$

The overall heat transfer coefficient is estimated from the following equation (Al-Mutaz and Wazeer, 2014):

$U_i=\frac{1939.4+1.40562\ast T_i-0.0207525\ast {\left(T_i\right)}^2+0.0023486\ast {\left(T_i\right)}^3}{1000}.(32)$

The heat transfer level for the first exchanger is estimated from the following equation:

$A_1=\frac{\left(D_s+D_{ev}\right).{\lambda }_2}{U_1.\left(T_s-T_1\right)}.(33)$

The heat transfer level for the 2 to $n$ converter is estimated from the following equation (Al-Mutaz and Wazeer, 2014):

$A_i=\frac{D_i.{\lambda }_i}{U_1.\left(T_{ci}-T_i\right)}i=\mathrm{2,3,4},\dots ,n.(34)$

The total surface heat transfer effects are estimated using the following equation:

$A_t=A_1+A_2+A_3+\dots A_n={\displaystyle \sum _{i=1}^n}{A}_i,i=\mathrm{1,2,3},\dots ,n.(35)$

The average logarithmic temperature difference and the overall heat transfer coefficient of the condenser can be calculated from the following two equations (Al-Mutaz and Wazeer, 2014):

$LMT{D}_c=\frac{T_f-T_{cw}}{\ln \left(\frac{T_{vn}-T_{cw}}{T_{cn}-T_f}\right)},(36)$

$U_c=1.7194+3.2063\ast {10}^{-2}\ast T_{vn}-1.5971\ast {10}^{-5}\ast {\left(T_{vn}\right)}^2+1.9918\ast {10}^{-7}\ast {\left(T_{vn}\right)}^3.(37)$

The heat transfer level of the condenser is estimated from the following equation:

$A_c=\frac{D_c.{\lambda }_n}{U_c\left(LMT{D}_c\right)}.(38)$

The flow rate of cooling water is obtained from the law of conservation of energy as follows (Al-Mutaz and Wazeer, 2014):

$A_c=\frac{A_e+A_c}{C_p\left(T_f-T_{cw}\right)}.(39)$

The specific heat transfer level is calculated as the sum of the heat transfer level of the exchangers and the condenser over the total produced water as follows (Li P. et al., 2022; Duan et al., 2023):

$A_d=\frac{A_e+A_c}{D_t}.(40)$

The performance of the MED-TVC system under the title of GOR is defined as follows (Al-Mutaz and Wazeer, 2014):

$GOR=\frac{D_t}{D_m}.(41)$

One of the most important features of thermal freshwater is specific heat consumption, which is defined as the amount of thermal energy consumed by the system to produce 1 l of freshwater (Deng et al., 2023). This relationship is calculated from the first law of thermodynamics as follows:

$Q=\frac{D_m{.\lambda }_m}{D_t}.(42)$

2.4 CHP system modeling

The total heating demand (building heating and desalination) is estimated from the following relationship (Hajabdollahi et al., 2015):

$\dot{H_{dmn,tot}=}{D}_m{.\lambda }_m+\dot{H_{dmn}.}(43)$

The first term of the equation is related to the required energy consumption for evaporative desalination. $D_m$ and ${\lambda }_m$ are the driving steam flow rate, and latent heat is the first effect of desalination. The total heat demand ($\dot{H_{dmn}}$) is provided through the heat recovered from the main drive and, if necessary, from the storage tank and backup boiler (Hajabdollahi et al., 2015; Huang N. et al., 2021; Lin et al., 2023a; Lin et al., 2023b).

By using the following relationship, the fuel consumption of the backup boiler is obtained as follows (Hajabdollahi et al., 2015):

$\dot{m_{f,b}=}\frac{\dot{H}}{\eta .LH{V}_f},(44)$

where$\dot{H}$ is the heat load of the backup boiler. Power changes in terms of partial load for gas turbines are obtained from the following function (Hajabdollahi et al., 2015):

$\frac{\dot{E_{GT,PL}}}{\dot{m_{f,PL}.}LH{V}_f}=\frac{-0.2255{\left(PL\right)}^2+1.135\left(PL\right)+11.71}{100}.{\eta }_{GT,nom}.(45)$

The heat changes that can be recovered from the gas turbine exhaust in terms of partial load are calculated from the following function (Hajabdollahi, 2015b):

$\frac{\dot{H_{GT,PL}}}{\dot{m_{f,PL}.}LH{V}_f}=1.598{\left(PL\right)}^{-0.6553}+0.3903,(46)$

in which $\eta$, $\dot{m_r},\text{and\hspace{0.17em}}LH{V}_r$ are nominal efficiency, fuel consumption, and low calorific value of fuel, respectively. The gas turbine fuel consumption function at partial load is as follows (Hajabdollahi, 2015b):

$\frac{\dot{m_{f,PL}}}{\dot{m_{f,nom}}}=0.4772\exp \left(0.007565\left(PL\right)\right)-0.2123\exp \left(+0.02677\left(PL\right)\right).(47)$

The nominal fuel consumption $\dot{m_{f,nom}}$ is obtained from the following equation (Sanaye and Hajabdollahi, 2016):

$\dot{m_{f,nom}=}\frac{\dot{W}}{{\eta }_{nom}.LH{V}_f}.(48)$

The thermal efficiency of the boiler is assumed to be a function of the partial load as follows (Hajabdollahi et al., 2015):

$\frac{\dot{m_{th,PL}}}{\dot{m_{th,nom}}}=0.0951+1.525\left(PL\right)+0.624{\left(PL\right)}^2.(49)$

The efficiency of the gas turbine is estimated according to the nominal capacity of the following function (Sanaye and Hajabdollahi, 2016):

${\eta }_{nom,GT}=\frac{1.22\left(-9.2\ast {10}^{-8}{E_{nom}}^2+0.001724E_{nom}+18.1\right)}{100}.(50)$

The modeling of the energy storage tank by choosing it as a volume to control the input and output enthalpies in it is checked as follows (Hajabdollahi et al., 2015):

$\dot{H_{stor}}\left(t+1\right)={\eta }_{stor}.\dot{H_{stor}}\left(t\right)+\dot{H_{GT}}\left(t\right)-\dot{H_{dmn,tot}}\left(t\right),$

$when:\dot{H_{GT}}\left(t\right)˂\dot{H_{dmn,tot}}\left(t\right)and\dot{H_{stor}}\left(t\right)\ge \dot{H_{dmn,tot}}\left(t\right)and\dot{H_{GT}}\left(t\right)+\dot{H_{stor}}\left(t\right)\ge \dot{H_{dmn,tot}}\left(t\right).(51)$

Here, ${\eta }_{stor}$ and $t$ are related to the efficiency of the energy storage tank equal to 90% and the time step, respectively (Xiao et al., 2023). On the other hand, when the total heat demand is greater than the heat (stimulator + storage tank), the energy storage tank is completely discharged and supplied with an auxiliary boiler (Hajabdollahi et al., 2015).

$\dot{H_{stor}}\left(t+1\right)=0when\dot{H_{GT}}\left(t\right)˂\dot{H_{dmn,tot}}\left(t\right)and\dot{H_{GT}}\left(t\right)+\dot{H_{stor}}\left(t\right)˂\dot{H_{dmn,tot}}\left(t\right).(52)$

When the drive heat recovery is greater than the total heating load, the excess heat is stored in the energy storage tank (Hajabdollahi et al., 2015):

$\dot{H_{stor}}\left(t+1\right)={\eta }_{stor}.\dot{H_{stor}}\left(t\right)+\dot{H_{GT}}\left(t\right)-\dot{H_{dmn,tot}}\left(t\right),(53)$

$when\dot{H_{GT}}\left(t\right)\ge \dot{H_{dmn,tot}}\left(t\right).$

2.5 Optimization

In this study, the minimization of the total annual cost is as follows (Hajabdollahi et al., 2015):

$TAC\left(\frac{\$}{year}\right)={\displaystyle \sum _{j=1}^4}{\left(a\mathrm{ɸ}{C}_{in}\right)}_j+{\displaystyle \sum _{i=1}^N}\left[{\dot{E}}_{b,1}*{\phi }_{e,b,i}+{\dot{m}}_{fi}*LH{V}_f*{\phi }_{f,i}+3600*{\dot{m}}_{co2}*{\psi }_{em}\right]*{\tau }_i,(54)$

where $\mathrm{j}$ and $C_{in}$ in the aforementioned relationship are the number and investment of system equipment, respectively, including the gas turbine, boiler, evaporative water softener, and energy storage tank (Jiang et al., 2022; Yu et al., 2023). The annualizing coefficient a is obtained from the following equation (Hajabdollahi et al., 2015):

$a=\frac{ir}{1-{\left(1+ir\right)}^{-k}},(55)$

where $ir$ is the inflation rate and k is the life of the equipment which is 15 years, $\mathrm{ɸ}$ is the system maintenance coefficient that is equal to 1.05, N is the number of the desired strategy matrices and is equal to 24, $2{\tau }_i$ is equal to the number of days of both seasons (182.5) (Cai et al., 2022; Jiang et al., 2022; Yu et al., 2023), ${\phi }_{e,b,i}$ is the price of buying electricity from the network, ${\phi }_{f,i}$ is the price of diesel, and ${\psi }_{em}$ is the price of pollutant emissions. By adding the last term in the bracket, the environmental effect is considered in the optimal selection of the (CHP + MED) system equipment. The considered variables are as follows:

$P{L}_{b,,,,i}\le 1⩝i=\mathrm{1,2,3},\dots ,n,(56)$

$x_b\le 70000ppm,(57)$

${PL}_{desalination,i}\le 1⩝i=\mathrm{1,2,3},\dots ,n.(58)$

In this research, selling electricity to the grid is not allowed, and the excess electricity in each stage must be 0 or negative

$\dot{E_{exc,i}}\le 0⩝i=\mathrm{1,2,3},\dots ,n,(59)$

Buying electricity is equivalent to a negative amount of electricity. In order to ensure that the temperature of the smoke is maintained above the dew point temperature and to prevent the formation of sulfuric acid and corrosion of the chimney, the following condition is considered:

$T_{stack}-148.8>0⩝i=\mathrm{1,2,3},\dots ,n.(60)$

The cost of gas fuel is 0.01054 $/kWh, purchase of electricity from the grid is 0.071667 $/kWh, and the emission penalty is 0.02086 $/kg of carbon dioxide (Sanaye and Hajabdollahi, 2016). The genetic algorithm is one of the oldest and most powerful optimization algorithms. According to the literature, acceptable optimal results can be achieved by using this algorithm to optimize energy conversion systems (Miao et al., 2021; Yuan and Yang, 2022; Zhang Z. et al., 2023).

2.6 Case studies

The study case is the proposed method of adding a thermal energy storage tank to the CHP + MED system for a commercial building in Ahvaz city to supply heat, electricity, and freshwater simultaneously (Lu et al., 2017). This building has 250 rooms, with an average area of 40 m² for each room. It is to be noted that for simulation and mathematical modeling of the studied system, MATLAB and EES software were used.

In general, any study based on numerical evaluation and simulation has limitations compared to experimental and practical work. In this regard, the following assumptions were considered to simplify the simulation (Kaheal et al., 2023; Mousavi Rabeti et al., 2023; Yi et al., 2023):

1. The hybrid energy system works under steady-state conditions.

2. The temperature difference is the same in all converters.

3. Distilled water is free of salt.

4. Boiling point increase for all effects is 0.8.

5. Thermodynamic losses are negligible.

6. The temperature difference in all effects of the desalination unit is constant.

7. The flow rate of all effects of the desalination unit is the same.

8. The thermal efficiency of the boiler is assumed to be a function of partial load.

9. Components under constant isentropic efficiency are considered.

10. The system can work without any restrictions in the considered studied region and can be implemented.

11. The cost of replacing spare parts and insurance are considered 1.5% and 0.05% of the total direct cost, respectively.

12. The owner’s cost rate is 10% of the direct material and labor costs.

3 Results

3.1 Validation

The investment cost of system equipment is shown in Table 1. To validate the code developed in MATLAB software, in the multieffect evaporative desalination model with a thermal steam condenser, reference input parameters (You et al., 2020) in Table 2 have been used. The output results from the computational code with the modeling available in reference (You et al., 2020) compared the allowable error in an engineering range, which was than 2%, as shown in Table 3.

TABLE 1

TABLE 1. Initial price of the equipment.

TABLE 2

TABLE 2. Working conditions of desalination in the reference (You et al., 2020) and this research.

TABLE 3

TABLE 3. Validation of the evaporative desalination model.

The energy required for desalination is provided from the heat recovered from the gas turbine and the storage tank in case of excess heat and finally from the backup boiler in case of shortage. For this purpose, first, the calculation code governing on the problem is developed in MATLAB software, and then it is optimized with a genetic algorithm. The number of design variables for combining the CHP + MED-TVC + TES system is 31 items, including gas turbine capacity, backup boiler capacity, energy storage tank capacity, and engine partial load every 2 hours out of every 24 h. Furthermore, a total of 24 items, the number of desalination effects, driving steam pressure in the first effect, flow rate feed water, and driving steam flow rate are selected to reduce the annual cost. In the combination of the CHP + MED-TVC system, all the mentioned variables, except the capacity of the energy storage tank, a total of 30 cases have been selected. The strategy used in the system is that for every 24 h of the two seasons of the year, the demand for heat, electricity, and freshwater for the whole year should be satiated, according to Figure 4.

FIGURE 4

FIGURE 4. Energy and freshwater demand for year.

The new strategy presented by many cases can be examined, which is also evaluated with a specific case study. The number of chromosomes of the genetic optimization algorithm, 300 mutation probability, 0.02 integration probability (Meng and Suzuki, 2016; Wang J. et al., 2022; Sun et al., 2023; Yang et al., 2023), and 1,000 generations were considered. Step design variables and their range in Table 4, as well as the optimal design variables for CHP + MED system composition in both cases, are given in Table 5:

TABLE 4

TABLE 4. Design variables, their steps, and ranges.

TABLE 5

TABLE 5. Optimal design variables.

3.2 CHP + MED + TES system results

As can be seen in Figure 5, the heat required for heating the building and desalination water throughout day and night is equal to the total heat produced by the driver, backup boiler, and storage tank, in which the heat produced by the driver is more than the total requirement. This excess heat is stored in the energy storage tank, and it is used when necessary and prevents the boiler from working or working more in the following hours. Figure 4 shows that in spring and summer, the heat demand is lower than the electricity demand throughout day and night.

FIGURE 5

FIGURE 5. Heat produced or consumed by the CHP + MED + TES system equipment throughout the year.

In these two seasons, according to Figure 5, from 2 to 10 o’clock, the heat produced by the driver is more than the total heat requirement of the building and the desalination water requirement, and in this way, the excess heat is stored in the storage tank. Again, from 12:00 to 14:00, the production heat of the stimulator increases and reaches full load by 24:00, and the desalination energy consumption also increases (Min et al., 2023). From 12:00 p.m. to 6:00 p.m., the total heat required for desalination and heating is greater than the heat produced by the driver, so the storage tank starts to discharge.

During the autumn and winter seasons, according to Figure 4, the need for electricity decreases from 02:00 to 10:00 AM and increases from 12:00 to 18:00, and its peak continues until 24:00. It is clear that the actuator produces more heat at a higher partial load and less heat at a lower partial load. According to Figure 5, from 4:00 to 4:00 p.m., not only the generator works at partial load but also the heat demand is almost high in the early hours of this time, as a result of which the heat in the generator is not excessive and the back-up boiler is used to provide all the heat needs (Zhang X. et al., 2023). The boiler is turned off from 14:00 to 24:00, and additional heat is stored again from 16:00 to 24:00.

The heat produced by the engine is 87.226 MWh for the whole year, and the fuel consumed by the engine and boiler is 4,815,669 and 336,064 kg/year, respectively. The optimal parameters include the rated capacity of the gas turbine 2,500, backup boiler 2,600, and heat storage tank 2.3 Mw/hr. Furthermore, for desalination, the number of stages is 11, and the driving steam pressure is 1,000 kPa, the flow rate of seawater feed is 200, and the flow rate of driving steam is 1 kg/s.

Figure 6 shows that the electricity produced by the gas turbine provides an optimal part of the total electricity requirement. The shortage of this electricity is purchased from the network. After optimizing the desalination parameters, including the suction ratio in the ejector of 0.94, the performance coefficient of 12.26, and the specific heat consumption of 200.82 kJ/kg, the total purchase of electricity from the network is 13.527 MWh and the electricity produced by the generator is 49.772 MWh for the whole year (Chen et al., 2023a). The total electricity required in the whole year is 633 MWh. The generator provides 78.62% of the total electricity requirement, and the rest is purchased from the network. The penalty for pollutant emissions produced by the booster and backup boiler is 2.40292*10⁵ $/year.

FIGURE 6

FIGURE 6. Electricity produced or consumed by the CHP + MED + TES system equipment throughout the year.

Figure 7 shows the freshwater production and demand by desalination throughout the year. Because in the CHP+MED system combination mode with and without the thermal energy storage tank, the freshwater is assed in (Chen et al., 2023b; Yin et al., 2023).

FIGURE 7

FIGURE 7. Freshwater production and demand by desalination throughout the year.

3.3 The results of the CHP + MED system

In this section, the results related to the modeling and optimization of the combination of the CHP + MED system without a storage tank are presented. In this system, the total heat required at all hours of the day and night for the building, and desalination is supplied from the generator and in case of shortage from the backup boiler because the heat required in autumn and winter is more than that in spring and summer (especially from 4:00 to 12:00 p.m.).

According to Figure 4, the electricity demand is low in winter and autumn from 8:00 a.m. to 2:00 p.m., 12 is almost uniform. Figure 8 shows that the actuator is on partial load and produces relatively lower heat. Therefore, the backup boiler produces more heat during these hours than during other hours. For the spring and summer seasons, the backup boiler provides the shortage of heat to meet the total heating and desalination needs at all hours. In this system, the heat produced by the driver is 81.022 Mwh/year, the fuel consumed by the driver is 4,506.129, and for the backup boiler, 1,075 tons has been obtained for the whole year.

FIGURE 8

FIGURE 8. Heat produced or consumed by the CHP + MED system equipment throughout the year.

After optimizing the rated driving capacity of 2.2 MWh, the rated capacity of the backup boiler is 2.8 MWh, also for desalination, the number of stages, driving steam pressure of 4 MPa, seawater flow rate of 300, and driving steam flow rate of 1 kg/s have been achieved.

As can be seen in Figure 9, after optimization, a part of the electricity demand is purchased by the supply driver, and the remaining power purchased from the grid. The total electricity requirement is 633 MWh/year, in which 47.416 MWh or 76.3% is purchased by the generator and the remaining 15,884 kWh is purchased from the grid.

FIGURE 9

FIGURE 9. Electricity produced by the CHP + MED system.

The optimal capacity of the driver is 300 kW or 13.5% compared to the CHP + MED + TES system, and its fuel consumption is reduced by 7.1%. The fine for pollutant emissions produced by the booster and backup boiler 2.6032*105 $/yr has been obtained.

The reason for making the system cheaper by using a storage tank is the choice of a driver with a higher nominal capacity, which leads to more electricity production and a 4.01% reduction in electricity purchase. On the other hand, the heat produced by the drive in the CHP + MED + TES system is 8.02% more than that in the CHP + MED system, which makes the fuel consumption of the backup boiler decrease by 70.35% throughout year. The surcharge of pollutant emission for this system has increased by 8.58% compared to the CHP + MED + TES system.

Figure 10 shows the effect of fuel price changes, electricity purchase from the grid, and pollutant emission fines on the total annual cost. With the help of the following figure, considering the different prices in different cities, the total annual cost is obtained.

FIGURE 10

FIGURE 10. Effect of changing fuel prices on the total annual cost.

One of the influencing parameters on the amount of freshwater produced is the fuel flow rate fed to the energy system. Figure 11 shows the effect of the fuel flow rate fed to the energy system on the amount of freshwater produced and total annual cost. By increasing the flow rate of fuel fed to the process, more thermal energy can be available for the cycle, which consequently improves the thermal energy administered into the desalination unit. Therefore, the rate of freshwater produced can increase. However, due to the increase in cost related to the increase in fuel consumption, the total annual cost of the energy system will relatively increase. Figure 11 confirms that by increasing the rate of fuel input into the system from 1 to 5 kg/s, the rate of freshwater produced and the total annual cost will increase by 33.2% and 4.6%, respectively.

FIGURE 11

FIGURE 11. Effect of the fuel flow rate fed to the energy system on the amount of freshwater produced and the total annual cost.

Another parameter that affects the performance of the energy system is the pressure of the input flow to the gas turbine. Figure 12 shows the effect of gas turbine inlet flow pressure on the amount of freshwater produced and the total annual cost. Although increasing the pressure of the gas turbine inlet flow can increase the production power rate of the turbine, it is due to the reduction of the enthalpy of the turbine output flow (in fact, the reduction of the waste heat of the gas turbine), which results in less heat being available to the desalination unit. As a result, the amount of freshwater produced decreases. In addition, increasing the pressure of the input flow to the turbine requires spending additional costs for the compression process, which causes the growth of the overall annual cost of the energy system. Figure 12 exhibits that by increasing the pressure of the input flow to the turbine from 1 to 5 MPa, the rate of freshwater produced and the total annual cost will decrease and increase by 16.9% and 8.18%, respectively.

FIGURE 12

FIGURE 12. Effect of gas turbine inlet flow pressure on the amount of freshwater produced and the total annual cost.

Increasing the effect number of the MED unit is another critical parameter that can affect the total annual cost of the energy system. Increasing the effect number of the MED unit can increase the rate of freshwater production due to increasing the number of desalination stages. However, this can increase the total annual cost of the energy system. However, it is expected that the unit cost of freshwater production will decrease with the increase in the production rate of freshwater. This requires further analysis in future research. The influence of effect number of the MED unit on the amount of freshwater produced and the total annual cost of the energy system is displayed in Figure 13. As seen, by increasing the effect number of the MED unit from 4 to 7, the rate of freshwater produced and the total annual cost will increase by 58.3% and 2.1%, respectively.

FIGURE 13

FIGURE 13. Influence of effect number of the MED unit on the amount of freshwater produced and the total annual cost of the energy system.

3.4 Comparative analysis

In order to verify the obtained results and also highlight the advantages of the proposed energy system, the overall result of the research has been compared with the results reported in similar studies in the form of a comparative evaluation. Table 6 summarizes the comparative analysis. As can be seen, the hybrid energy system can achieve a lower total annual cost (and in some cases, competitive results) than other similar technologies for producing power and freshwater. However, it is recommended that in future studies, the experimental and environmental behaviors of the proposed energy system should be studied and analyzed carefully so that an eco-friendly and efficient system can be addressed.

TABLE 6

TABLE 6. Summary of comparative analysis.

4 Conclusion

Nowadays, optimizing the performance of energy systems, reducing costs, and decreasing pollutant of production is a serious trouble for designers and engineers for which many solutions have been proposed. One of the ways to reduce the cost of energy systems, which is proportional to the increase in efficiency, is the use of combined heat and power production systems. In this research, the modeling and investigation of the combined gas turbine and desalination system for the production of heat, electricity, and freshwater has been done.

In this study, some of them used the excess heat of the drive system for the required heat of the desalination water, and the others used it to feed the Rankine organic power generation cycle, which seems necessary to check the energy storage tank to use this heat for the CHP and freshwater system. To increase the efficiency and evaluate the reliability of the studied system, the effect of the thermal storage tank on the overall efficiency of the system has been evaluated.

In order to reduce the operating costs of the CHP and water desalination system, the studied system has been optimized using the intelligent algorithm. The results showed that the use of the thermal storage tank has a direct relationship with the amount of fuel consumption in the gas turbine, and this parameter will have a direct effect on the emission of pollutants so that the use of the thermal tank will increase the efficiency of the system and reduce the fuel consumption in the gas turbine and reduce the costs of the system.

The optimal technical results in these systems showed that in the combined heat, power, and water desalination system, the gas turbine with a nominal capacity of 14% is larger, the heat production is 8.2% higher, and its fuel consumption is increased by 7.1.

Suggestions for future work include the following (Liao et al., 2023):

Performance evaluation of the three latent heat storage designs.

Performance analysis of a co-generation system using solar energy.

Thermo-economic analysis of a combined based power and freshwater cogeneration system.

Data availability statement

The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding authors.

Author contributions

EE: conceptualization, formal analysis, and writing–original draft. JN: data curation, investigation, project administration, software, and writing–original draft. AC: methodology, project administration, resources, software, and writing–original draft. IA-K: resources, software, validation, and writing–review and editing. MJ: investigation, methodology, supervision, conceptualization, formal analysis, and writing–original draft. PY-M: data curation, validation, visualization, and writing–original draft. RA: conceptualization, data curation, methodology, project administration, and writing–review and editing. IK: methodology, project administration, software, supervision, and writing–review and editing. DM: formal analysis, funding acquisition, investigation, methodology, project administration, resources, supervision, software, and writing–review and editing.

Funding

The author(s) declare that the financial support was received for the research, authorship, and/or publication of this article. This research was financially supported by the Ministry of Small and Medium-sized Enterprises (SMEs) and Startups (MSS), Korea, under the “Regional Specialized Industry Development Plus Program (R&D, S3246057)” supervised by the Korea Technology and Information Promotion Agency for SMEs (TIPA). This work was also financially supported by the Ministry of Trade, Industry, and Energy (MOTIE) through the fostering project of the establishment project of industry–university fusion district.

Conflict of interest

The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors, and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

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