Thermoeconomic analysis and multi-objective optimization of a novel trigeneration system consisting

Abstract

Keywords: Trigeneration; Kalina cycle; Humidification-dehumidification; Desalination; Optimization

Introduction

The supply of freshwater has become a serious challenge in many regions, mainly due to industrialization and rapid population growth [1]. Desalination technologies powered by various renewable energy sources can play a key role in meeting this challenge while mitigating environmental impacts. Among the various types of thermal desalination systems, the humidification-dehumidification (HDH) process exhibits distinct advantages over commonly used technologies, including simple design, low capital, and maintenance costs and capability of being powered by low-temperature heat sources [2, 3]. Due to these positive features, a comprehensive review was conducted on HDHbased refrigeration, power generation, and desalination cycles [4]. Multi-generation technologies, including cogeneration and trigeneration, not only are beneficial for mitigating freshwater and energy demands, but also have higher efficiencies and lower operating costs than single product systems [5, 6]. Combined HDH-power systems have received increasing attention due to their important role in supplying freshwater and electricity using low-temperature heat sources, including waste heat and various renewable energies. Heretofore, the combination of an organic Rankine cycle (ORC) with various configurations of HDH systems has received more attention than other power generation technologies, mainly because of the maturity, flexibility, and reliability of ORCs [7]. Various configurations of HDHORC technologies with different working fluids have been studied [8, 9]. Moreover, researchers have investigated the integration of a regenerative ORC [10] and a single-extraction ORC [11] with an HDH desalination process. Another technology suitable for power generation from low-temperature heat sources such as waste heat and some renewable energy sources is the Kalina cycle [12]. Rodríguez et al. [13] compared the thermoeconomic performance of

an ORC and a Kalina cycle for power generation using lowtemperature geothermal water. The Kalina cycle generated 18% more net power and had a 17.8% lower levelized electricity cost than the ORC. The Kalina cycle has been widely integrated with multi-generation cycles, mainly due to the advantages of ammonia-water over organic working fluids. Despite the advantages of the Kalina cycle, such as having a variable temperature over the boiling process and environmentally favorable characteristics, the integration of the Kalina cycle with HDH technology has not yet been investigated [4]. The common characteristic of the previous combined HDH-power systems is the existence of three main components, namely humidifier, heater, and condenser. A potential method to reduce the complexity is the use of evaporative condensers instead of conventional condensers. Evaporative condensers are widely utilized in the ammonia-water based refrigeration industry because they permit lower condensing temperatures and power consumption [14]. In this regard, the evaporative condenser not only acts as the condenser of the power cycle but also functions as the humidifier and heater of the HDH cycle, reducing the complexity of combined power-HDH technologies. Recently, the application of the evaporative condenser in an HDH desalination system was investigated by Xu et al. [15]. In this enhanced HDH system, the humidifier and dehumidifier of the HDH cycle were substituted by an evaporative condenser. It was shown that the gained output ratio of the proposed HDH cycle is significantly higher than that of conventional HDH systems, highlighting the positive effect of using an evaporative condenser for humidification and condensation processes. As mentioned before, proposing novel combined cycles driven by low-temperature heat sources can effectively mitigate the freshwater and energy demands. This study aims to introduce a novel trigeneration cycle which is powered

by low-temperature geothermal heat sources. This novel trigeneration cycle is comprised of Kalina and HDH cycles for the generation of electricity, freshwater, and hot water. To the best of authors’ knowledge, the combination of Kalina and HDH desalination cycles has not been investigated yet, and previous studies were mainly focused on combined ORC-HDH systems. Moreover, in this study, the application of the evaporative condenser in the Kalina cycle is investigated. The utilization of the evaporative condenser, which acts as humidifier and heater of the HDH desalination system, not only reduces the system complexity but also lowers the water consumption in the condensation process of the ammonia-water solution. First, the thermoeconomic performance of the system is comprehensively investigated, and the effects of key design parameters on thermoeconomic criteria are analyzed using the Engineering Equation Solver (EES) software. Finally, a multi-objective optimization based on the genetic algorithm is performed with a computer code developed in MATLAB to maximize the thermodynamic performance of the system and minimize the relevant cost. A Pareto curve is also obtained from the optimization, which shows the variation of both objective functions.

System Description And Assumption

A schematic diagram of the proposed trigeneration cycle is shown in Figure 1. The system is based on a Kalina power generation cycle and an HDH desalination cycle and produces freshwater, electricity, and heating from a low-temperature geothermal heat source. To reduce the complexity, an evaporative condenser is utilized, which integrates the Kalina cycle condenser, the humidifier, and the heater of the HDH cycle in a single unit. In this regard, a two-phase ammonia-water solution enters the evaporative condenser (state 1) and, after transferring its heat to the entering air (state 11) and saline water streams, exits as a saturated liquid (state 2). The sprayed saline water in the evaporative condenser turns the entering air (state 11) into a saturated air stream (state 12) and the saline water is then pumped back to the evaporative condenser using a circulating pump. A make-up stream of saline water (state 14) enters the evaporative condenser to compensate for the amount of water absorbed by the air stream. By rejection of heat from the saturated air to the ammonia-water solution inside the dehumidifier, freshwater is produced (state 15) and dehumidified air leaves the dehumidifier as

Figure 1. Schematic diagram of the proposed trigeneration system.

a saturated stream (state 13). In the vapor generator, the entering geothermal water from production well (state 18) increases the temperature of the inlet ammonia-water solution (state 4). Consequently, lower temperature geothermal water (state 19) and higher temperature two-phase ammonia-water solution (state 5) exit the vapor generator to the reinjection well and separator, respectively. The twophase ammonia-water solution (state 5) is split into two streams: a saturated vapor (state 6) and a saturated liquid (state 7). Electricity is generated by the expansion of the saturated vapor through the turbine. Meanwhile, heating is provided in the domestic water heater, in which the inlet low-temperature domestic water (state 16) absorbs the heat removed from the incoming saturated liquid ammonia-water solution (state 7) to reach the desired domestic hot water (state 17). Finally, the liquid ammonia-water solution (state 8) exiting the domestic water heater passes through an expansion valve (state 9) and is mixed with the turbine outlet ammonia-water solution (state 10) to continue the cycle (state 1). The following assumptions are invoked in the investigation of the proposed trigeneration system: • The system operates under steady-state conditions. • Pressure losses and variations in kinetic and potential energies are neglected. • The flow passing through the expansion valve experiences an isenthalpic process. • The ammonia-water leaving the evaporative condenser is saturated liquid [16]. • The pump and turbine both have an isenthalpic efficiency of 0.85 [17]. • Geothermal water having a mass flow rate and pressure of 3 kg/s and four bar is the heat source [10]. • In the vapor generator, the terminal temperature difference is 10°C and the pinch temperature 3°C [13]. • The vapor and liquid streams leaving the separator are saturated. • Water at a pressure and temperature of 3 bar and 15°C enters the domestic water heater and, after being warmed, leaves this component at 60°C. Moreover, the terminal temperature difference is 5°C [18, 19]. • The air leaving the evaporative condenser and dehumidifier is saturated. • The effectiveness of the dehumidifier is 0.8 [20]. • The ambient air temperature, pressure, and relative humidity are 25°C, 100 kPa, and 50%, respectively.

Methodology

Using a code developed in EES (Engineering Equation Solver), the effects of key design parameters on thermoeconomic criteria are investigated. Also, a multi-objective optimization is performed by coupling EES and MATLAB software to achieve the best performance of the trigeneration system.

Energy, Exergy and Economic Analyses Considering each component of the proposed trigeneration system as a control volume, mass and energy balances are applied at the component level. A computer simulation code using EES software is developed to calculate the thermophysical properties of each stream so as to investigate the thermoeconomic performance of the system. For a control volume under steady-state conditions with kinetic and potential energies neglected, mass and energy rate balance equations, as well as the exergy destruction, can be written as follows:

An exergy analysis is carried out to investigate the performance of the trigeneration system from the perspective of the second law of thermodynamics. To calculate the total exergy of each stream, both thermophysical and chemical exergy rates are considered:  = Ex  Ph + Ex  Ch Ex

where the physical exergy rate is calculated as:  Ph = m  (h − h 0 ) − T0 (s − s0 ) Ex

The chemical exergy rate is the work rate obtainable in bringing a stream of matter from the restricted dead state to the dead state reversibly, and can be written as:  x  o   1− x  o  Ch = m   Ex  e Ch,NH3 +   e Ch,H2 O   M H2 O   M NH3  

Here, e°Ch,NH and e°Ch,H O denote the standard chemical 3 2 exergies of ammonia and water, respectively [19, 21]. The equations used for the calculation of energy and exergy rates in each component are listed in the Table 1. Moreover, energy and exergy efficiencies are considered as thermodynamic performance criteria and are defined for the system as follows:

For analyzing the performance from freshwater productivity viewpoint, the gained-output-ratio (GOR) is defined as [4]: GOR =

ṁ18 (h18 – h19) = ṁ4(h5 – h4) İvapor generator = (Ėx18 + Ėx4) – (Ėx19 + Ėx5)

ṁ7 (h7 – h8) = ṁ16(h17 – h16) İwater heater = (Ėx7 + Ėx16) – (Ėx8 + Ėx17)

ṁ1h1 + ṁ11h11 + ṁ14h14 = ṁ2h2 + ṁ12h12 ṁ14 = ṁ11(ω12 – ω11)

İevaporative condenser = (Ėx1 + Ėx11 + Ėx14) – (Ėx2 + Ėx12) Dehumidifier ε = max

 h12 -h13 h 4 -h 3  ,  h -h   12 13,ideal h 4,ideal -h 3 

h13,ideal = h(AirH2O, T3, RH13, P13) ṁ3h3 + ṁ12h12 = ṁ4h4 + ṁ13h13 + ṁ15h15 İdehumidifier = (Ėx3 + Ėx12) – (Ėx4 + Ėx13 + Ėx15) ẇ pump = v2(P3 – P2)/ηpump İpump = (Ẇpump + Ėx2) – Ėx3 Ẇturbine = ṁ6(h6 – h10) İturbine = Ex6 – (Ẇturbine + Ėx10) ṁ5h5 = ṁ6h6 + ṁ7h7 İseparator = Ėx5 – (Ėx6 + Ėx7) Expansion valve

ṁ9h9 + ṁ10h10 = ṁ1h1 İmixing chamber = (Ėx9 + Ėx10) – Ėx1

Here, Żk denotes the capital investment cost rate, calculated as [24]:

and where ech,w in Eq. (14) denotes the specific chemical exergy of freshwater [22].

Where, ṁfw and hfg represent the freshwater production rate and evaporation latent heat of desalinated water, respectively. To investigate the proposed system from an economic viewpoint, the total cost rate is considered as the economic index and is expressed as follows [23]:

where Zk is the capital investment cost, φ is the maintenance factor which is set to 1.06, τ is annual operating hours which is set to 8000, and CRF is capital recovery factor, which is defined as [25]: CRF =

Here, i and N correspond respectively to the interest rate and the system lifetime, and are selected to be 12% and 20 years [25]. The capital investment cost (Zk) is calculated for each component according to the expressions in Table 2, and the heat transfer area of each heat exchanger is calculated based on the LMTD (logarithmic mean temperature difference) method. The heat transfer rate for component k can be expressed as:    = U A  (Th1 − Tc2 ) − (Th2 − Tc1 )  Q k k k  Ln ((Th1 − Tc2 ) / (Th2 − Tc1 )) 

Approximate values of the overall heat transfer coefficients of each heat exchanger in the system are listed in Table 3.

Table 2. The capital investment cost function of each component Component

Multi-Objective Optimization

Multi-objective optimization is a robust tool for attaining the best design parameters in energy systems exhibiting conflicting objective functions that need to be addressed simultaneously [31, 32]. In multi-objective optimization, there exists a set of optimum solutions known as the Pareto frontier, instead of the unique solution obtained from the single-objective optimization process [33]. Multi-objective optimization assists decision-makers in selecting the best design point among the set of optimal solutions according to preferences in an industrial project. In this study, a genetic algorithm is utilized in the optimization process, and exergy efficiency, as well as total cost rate, are considered as the two objective functions in the multi-objective optimization. The overall exergy efficiency considers the energy quality as well as deviations of the system from its idealized working condition. Therefore, overall exergy efficiency was preferred to energy efficiency and chosen as the objective function. Figure 2 presents the flow chart for the multi-objective optimization methodology. As can be seen, multi-objective optimization starts with the definition of design parameters and their boundaries (Table 4). By choosing the genetic algorithm properties according to Table 5, the multi-objective optimization algorithm generates the initial random population. In an iterative process, the generated population in MATLAB is evaluated based on objective functions imported from EES. More details on Table 4. Base case condition and variation boundaries for each of the design parameters in parametric study. Design parameter

Results And Discussion

Parametric Analysis In the parametric analysis, five key design parameters are considered: turbine inlet pressure, condenser temperature, basic solution ammonia concentration, air mass flow

rate, and heat source temperature. To investigate the effects of each design parameter on the thermoeconomic performance of the system, when a parameter is changed, the others are held constant (at the base case condition). The base case condition and its corresponding thermo-physical properties for each state of the trigeneration system are given in Table 6. For the base case condition, the energy efficiency, exergy efficiency, and total cost rate of the proposed cycle are 44.2%, 32.1%, and 1.55 $/h, respectively. Also, the proposed cycle produces 21.22 kW of electricity, 163.8 kW heating, and 37.51 kg/h freshwater. The developed thermodynamic

Table 6. Thermodynamic properties of each state for the base case condition* State

*P6 = 17 bar, T2 = 313.15 K, X2 = 0.65, 15 T18 = 373. K, ṁ a = 1.5 kg/s

Figure 3. Variation in power output of the Kalina cycle versus turbine inlet pressure. model is verified using the data obtained from Rodríguez et al. [13] for a Kalina cycle driven by low-temperature geothermal water. The variation in power output with different turbine inlet pressures for two heat source temperatures (100°C and 110°C) is shown in Figure 3 There is an optimum value for inlet turbine pressure to generate the maximum power output for each heat source temperature. It can be seen that under similar working conditions (ṁ18 =

1 s , X2 = 0.84, T2 = 37°C), there was a favorable agreement between the obtained results from this study and those from Rodríguez et al. [13]. The exergy destruction of each component is illustrated in Figure 4.It can be seen that the evaporative condenser and water heater components had the highest

Figure 5. Variations in various thermoeconomic criteria with turbine inlet pressure.

Figure 6. Variations in various thermoeconomic criteria with condenser temperature.

Figure 8. Variations in various thermoeconomic criteria with air mass flow rate.

Figure 7. Variations in various thermoeconomic criteria with basic ammonia concentration. irreversibilities, constituting of 31.77% and 23.35% of total exergy destruction, respectively. This highlights the need for better designing of the evaporative condenser, which can lead to enhanced exergetic performance of the cycle. It is worth mentioning that the condenser in previous combined ammonia-water cycles also had the highest share of exergy destruction [16, 38]. The effects of varying the turbine inlet pressure on energy efficiency, exergy efficiency, and total cost rate are shown in Figure 5. It is seen that the energy efficiency increases steadily with increasing turbine inlet pressure. The main reason for this is that, by increasing the turbine inlet pressure, the required input energy to the vapor generator decreases significantly. Moreover, the effect of heating load augmentation as a direct result of increasing the turbine inlet pressure is more significant than the associated

decline in the generation rate of electricity and freshwater. It can be also observed that both exergy efficiency and total cost rate exhibit similar behavior as the turbine inlet pressure increases. As the turbine inlet pressure increases, the exergy efficiency and total cost rate reach a peak and then experience a downward trend. This is due to the fact that an increase in the turbine inlet pressure has an opposite effect on the exergies of heating and freshwater. That is, a rise in turbine inlet pressure leads to a decrease in freshwater exergy and an increase in heating exergy. Furthermore, the cost rates of the turbine and domestic water heater rise while those of the evaporative condenser and vapor generator decrease, leading to an optimum value for the total cost rate. As illustrated in Figure 6, the higher is the condenser temperature; the lower are the energy and exergy efficiencies. With an increase in condenser temperature, the capacity of the evaporative condenser drops significantly, thereby lowering the production rate of freshwater. Furthermore, the total cost rate decreases considerably at higher condenser temperatures, mainly due to the decline in the cost rates of the evaporative condenser and turbine.

Figure 9. Variations in various thermoeconomic criteria with heat source temperature.

Figure 10. Distribution of optimized points and the Pareto optimal solutions for objective functions.

Table 7. Parameter values for base case and optimized conditions for points A-D. Parameter

Figure 7 indicates the variations in energy and exergy efficiencies and total cost rate with basic ammonia concentration. Higher basic ammonia concentrations result in lower energy efficiencies. This stems from the fact that, for fixed temperature and pressure of the two-phase ammoniawater solution entering the separator (state 5), the vapor quality increases (Q5) by increasing the basic ammonia concentration. Therefore, the required input heat to the vapor generator rises, while the generated heating load provided by the domestic water heater decreases. An optimum value of the exergy efficiency can be attained by altering the basic ammonia concentration due to its opposite effect on the exergy of the produced freshwater and heating load. With an increase in the basic ammonia concentration, the capacity of the evaporative condenser and freshwater productivity rises. Also, increasing the basic ammonia concentration

leads to larger values of the vapor generator and evaporative condenser costs, thus increasing the total cost rate. As depicted in Figure 8, the energy and exergy efficiencies experience a downward trend with an increase in the air mass flow rate. The main reason for this is that, by increasing the air mass flow rate entering the evaporative condenser, a decrease occurs in the absolute humidity of the air entering the dehumidifier, resulting in lower freshwater productivity. Moreover, the total cost rate decreases at higher air mass flow rates due to the lower evaporative condenser cost. Figure 9 indicates the influence of heat source temperature on several thermoeconomic criteria. As can be seen, higher heat source temperatures lead to a lower energy efficiency due to the increased input energy to the cycle. However, there exists an optimum value for heat source

Figure 11. Scatter distributions of various design parameters with population in Pareto frontier: turbine inlet pressure (a), condenser temperature (b), basic ammonia concentration (c), air mass flow rate (d) and heat source temperature (e).

temperature that maximizes the exergy efficiency. By increasing the heat source temperature, the flow cost rates of the vapor generator and turbine rise, resulting in a significant increase in the total cost rate. Optimization Results As can be inferred from the parametric analysis of the proposed cycle, variations in the design parameters exhibit conflicting effects on objective functions. This highlights the importance of multi-objective optimization for achieving the best design point aligned with the priority of objective functions. Figure 10 presents all genetic points optimized in terms of exergy efficiency and total cost rate over 1000 generations. The red curve in Figure 10 represents the Pareto frontier, where a set of optimum solutions are available to design the system. As can be seen, higher values for total cost rate are required at higher exergy efficiencies. While the highest exergy efficiency occurs at point D, the total cost rate is at its maximum. This indicates that point D is the best of the optimal design points in terms of exergy efficiency. But, point A has the minimum total cost rate and exergy efficiency, providing the best optimal solution in terms of total cost rate. In multi-objective optimization, it is desirable for decision makers to reach a hypothetical ideal point where the exergy efficiency is maximized, and the total cost rate is minimized. Since it is impossible to optimize both objective functions simultaneously, the final optimal design point (for example point B or C in Figure 10), should be chosen from the Pareto frontier considering the degree of importance of both objective functions. In this study, selecting the point C as the design point seems rational, providing acceptable values of exergy efficiency and total cost rate. Table 7, shows the design parameters and thermoeconomic criteria for the base case and optimum points A-D. Points A and D are single-objective optimum solutions in terms of total cost rate and exergy efficiency, respectively. The lowest total cost rate of 1.14 $/h and the highest exergy efficiency of 41.57% are considered as the solutions of single-objective optimization at points A and D, respectively. Point B, with an exergy efficiency of 25.45% and a total cost rate of 1.31 $/h can be selected as the optimal design point. Also, the system could be designed at optimum point C, with a total cost rate of 1.47 $/h, as well as a higher exergy efficiency (32.47%) compared to point B. To achieve a relationship between exergy efficiency and total cost rate, a curve is fitted on the optimum solution Pareto frontier as: Z total =

−121.6ηex2 + 6518ηex + 1239 η − 189.8ηex2 + 6882ηex − 417.2 3 ex

It is worth mentioning that according to Table 7, the amount of heating load is more than the power generation in the present cycle. In the case of more need for power generation, there is a possibility for the further studies on

the replacement of the water heater with an ORC cycle for more generation of power. As can be seen from Table 7, design parameters at optimum points experience a scattered distribution within their boundaries. To better highlight the variations of design parameters during the optimization process, scattered distribution diagrams are shown in Figure 11. It can be inferred from Figure 11 (a-d) that the turbine inlet pressure (P6), condenser temperature (T2), basic ammonia concentration (X2) and air mass flow rate (ṁa) each have a scattered distribution among their examined boundaries. This illustrates that these design parameters have conflicting effects on improving the exergy efficiency and total cost rate. However, as depicted in Figure 11 (e), heat source temperature (T18) exhibits a different behavior and tends to be as low as possible at the optimum points. Furthermore, decreasing the heat source temperature enhances both of the objective functions. It is worth mentioning that the ranges in Figure 11 are considered with a margin of 10–15% to cover the all possible operation points of the system [23, 39].

Conclusion

A novel trigeneration system comprised of Kalina and humidification-dehumidification desalination cycle is investigated from thermoeconomic a viewpoint. The proposed cycle benefits from an evaporative condenser, which not only cools the temperature of the ammonia-water solution in the Kalina cycle, but also acts as the humidifier and heater of the humidification-dehumidification desalination cycle. Therefore, system complexity decreases by substituting the three mentioned components with an evaporative condenser. A thermoeconomic analysis and multi-objective optimization are performed, and the effects of design parameters on system performance are studied. The following conclusions can be drawn from the results: • Increasing the turbine inlet pressure causes the energy efficiency to rise continuously, while exergy efficiency and total cost rate take on optimum values. • Energy and exergy efficiencies and total cost rate decrease as air mass flow rates and condenser temperatures rise. • A higher basic ammonia concentration results in lower energy efficiency and higher total cost rate. Moreover, the exergy efficiency reaches a peak and then experiences a downward trend as the basic ammonia concentration rises. • With an increase in heat source temperature, energy efficiency declines, but exergy efficiency and total cost rate rise. • In the multi-objective optimization, a curve is fitted on the optimal solution Pareto frontier, indicating the relationship between exergy efficiency and total cost rate. It can be seen from the Pareto frontier that an

increase of 118% in exergy efficiency can be attained only by a 30% rise in total cost rate. • The optimization results show that the turbine inlet pressure, condenser temperature, basic ammonia concentration, and air mass flow rate each exhibit a scattered distribution within their examined boundaries, indicating that they have a significant impact on the trade-off between objective functions. However, declining heat source temperatures tend to increase the exergy efficiency and decrease the total cost rate.

Nomenclature

A CRF e Ė x GOR h HDH I İ LMTD M ṁ N ORC P Q̇ s T U v Ẇ X Z Ż

area (m2) capital recovery factor standard chemical exergy (kJ/kg) exergy flow rate (kW) gained-output-ratio specific enthalpy (kJ/kg) humidification-dehumidification interest rate (%) Exergy destruction (kW) logarithmic mean temperature difference (K) molar mass (g/mol) mass flow rate (kg/s) system lifetime (year) organic Rankine cycle pressure (bar) heat transfer rate (kW) specific entropy (kJ/kg, K) temperature (K) overall heat transfer coefficient (kW/m2, K) Specific volume (m3/kg) Work rate (kW) ammonia mass fraction capital investment cost ($) total cost rate ($/h)

Greek letter η efficiency τ annual operating hours φ maintenance factor Subscripts 0 Dead state A air C cold stream Ch chemical fw freshwater H2O water In inlet NH3 ammonia out outlet Ph physical

Data Availability Statement

The authors confirm that the data that supports the findings of this study are available within the article. Raw data that support the finding of this study are available from the corresponding author, upon reasonable request.

Conflict Of Interest

The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Ethics

There are no ethical issues with the publication of this manuscript.

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