Optimizing the energy recovery section in thermal desalination systems for improved thermodynamic, economic, and environmental performance

Integration of energy recovery section with thermal desalination systems improves their performance from thermodynamics, economics, and environmental viewpoints. This is because it significantly reduces input energy, heat transfer area, and capital cost requirements. Above all, the system outlet streams can achieve thermal equilibrium with the environment by supplying heat for useful preheating purposes thus reducing the environmental impacts. The plate heat exchangers are generally employed for this purpose as preheaters. The current paper presents a comprehensive investigation and optimization of these heat exchangers for thermal desalination systems applications. An experimentally validated numerical model employing Normalized Sensitivity Analysis and Genetic Algorithm based cost optimization is developed to investigate their performance at assorted operating conditions. The analysis showed that the heat transfer coefficient, pressure drop, and outlet water cost were improved by an increase in feed flow rate. However, with an increased flow rate, the comprehensive output parameter (h/ΔP) decreased due to the high degree increase in pressure drop. Moreover, an increase in the chevron angle reduced the heat transfer coefficient, pressure drop, and water cost. Finally, the optimization lowered the heat transfer area by ~79.5%, capital investment by ~62%, and the outlet cost of the cold stream by ~15.7%. The operational cost is increased due to the increased pressure drop but the overall impact is beneficial as Ctotal of equipment is reduced by ~52.7%.

However, these systems operate at high top brine temperature (i.e., ≥ 55°C), and are regarded as energy and cost-intensive systems [13]. Therefore, substantial research has been conducted to improve their performance from thermodynamic and economic viewpoints [14][15][16]. One important development in this regard is the energy recovery i.e., preheating of intake by heat recovery from the distillate and brine streams [17]. This approach offers many advantages from thermodynamic, monetary, and environmental perspectives as it recovers heat that would be wasted otherwise resulting in higher thermal losses and increased risk for the aquatic life in the vicinity [18,19]. Moreover, it also reduces the sensible heating loads in the evaporators which lowers the area and investments [20].
The most commonly used preheaters for this purpose are the corrugated plate heat exchangers (PHXs) [21]. The salient features that make PHXs the most suitable for this job include narrow temperature control, easy maintenance, high operating reliability, and flexibility to accommodate varying loads [22,23]. However, it is important to mention that despite considerable importance, a cost-optimized design and analysis of PHXs as preheaters has seldom been conducted in desalination system studies [24][25][26]. Rather, the heat exchanger design is either missing [27] or restricted to preliminary sizing [28]. The heat transfer area in these studies is estimated using conventional heat transfer coefficient correlations that are only a function of temperature proposed by Dessouky et al. [29][30][31]. Though the methods give a quick estimate of the heat transfer area, the reliability of such calculations is suspected. This is because the heat transfer coefficients in heat exchangers are the functions of temperature, pressure, thermophysical properties, geometric constraints, and flow characteristics [32][33][34]. For instance, many studies reported the plate chevron angle (ß) as the most important geometric parameter governing the thermodynamic performance of PHXs [35][36][37][38][39]. Similarly, flow rate, fluid properties, and heat duty also have a remarkable effect on thermohydraulic performance [40][41][42]. The optimization studies have also reported multiple geometric and process parameters that control the PHX performance [43][44][45][46]. The most influencing parameters have been identified as, number of plates/channels, plate type (pattern), dimensions of chevron corrugation, number of passes, type of channel flow [47][48][49].
The literature review suggests that there is a significant need for a rigorous cost-effective design and analysis of the energy recovery section for thermal desalination systems. One of the recent works partially addressing this issue is conducted by Jamil et al. [50]. However, the study presented the design and analysis of preheating section from a thermohydraulic viewpoint only and lacks economic analysis and optimization. The current paper is focused to add value by optimizing the thermal-hydraulic model (presented in [50]) for minimum cost. For this purpose, a very useful and reliable tool "Exergoeconomic Analysis" is employed as a simultaneous application of thermodynamics and monetary analyses. The study is designed to achieve the following objectives: (a) a detailed thermal-hydraulic design and analysis using experimentally validated numerical model, (b) Second Law analysis, (c) economic analysis for capital and operational cost, (d) sensitivity analysis for Normalized Sensitivity Coefficients (NSC) and Relative Contribution (RC) of sensitive parameters, (e) parametric analysis using a one-factor-ata-time approach, and (f) optimization for minimum cost using Genetic Algorithm.

Impact of the energy recovery section
The layout of a traditional desalination system integrated with the energy recovery (ER) section is shown in Figure 1. The ER section consists of two plate heat exchangers i.e., feed and brine preheaters based on the hot fluid stream. A recent study by Abid et al. [51,52] on the impacts of incorporating energy recovery section with a forward feed MED system conforms its benefits from thermodynamics, economic, and environmental perspectives. The analysis reported that for a 4effect forward feed MED system, the ER section increased the feed temperature up to 35%.
Consequently, the Gain Output Ratio (GOR) improved by 17.9%, the Specific Energy Consumption (SEC) decreased by 15% (refer Figure 2 (a)) and the heat transfer area by reduced by 0.42%. The total exergy destruction and the water production cost are reduced by 5.5% and 10.5% (see Figure 2 (b)) due to the reduction in heat transfer area and energy consumption. In addition, the temperatures of the distillate and brine streams are lowered by 45 percent and 50 percent, which is an added advantage from the environmental point of view (refer to Figure 4). Therefore, critical analysis and cost-optimized design of the energy recovery section are essential to achieve the goals of minimum water production cost.

Heat exchanger configuration
The system under consideration consists of a corrugated plate heat exchanger and two pumps to manage the desired flow rates and pressures as shown in Figure 4. The system preheats the intake seawater using a hot brine stream coming from a Single Effect Mechanical Vapor Compression (MVC) based thermal desalination system [53]. The operating parameters i.e., temperatures, mass flows, and salinity of cold and hot streams are taken from recent studies for a practical design and analysis purpose as summarized in Table 1 [53].
The hydraulic design involves the calculation of total pressure drop which is the sum of the pressure drop in channels, ports, and manifolds as given [39,56].
The pumping power, which is the main parameter governing the operational cost of the heat exchanger is calculated as.
A detailed discussion regarding the selection and implementation of these correlations is presented in the referred study [50].

Exergy analysis
It is an important tool for heat exchanger optimization because it involves the calculation of lost work (exergy destruction) [57]. This is because the desirable high heat transfer coefficients in HXs are accompanied by corresponding high-pressure drops. The exergy analysis accounts for the variations in temperature and pressure simultaneously thus measuring overall performance. The performance index for this analysis is exergy destruction [58,59]. To conduct this analysis, the flow exergy is calculated at each terminal point (i.e., inlets and outlets of the pumps and HX) based on the mass flow rate salinity, temperature, and pressure as given in Eq. 5. After that, a standard exergy balance equation is solved for all the component to get XD as given in Eq. 6. In the current study, the specific flow exergy ex is calculated using the seawater library [60,61].

Economic analysis
For standalone heat exchangers, the economic analysis is generally restricted to the calculation of capital and operational expenses i.e., CAPEX and OPEX, respectively [62][63][64].
However, for a system analysis with multiple components e.g., desalination systems consisting of heat exchangers, evaporators, pumps, compressors, etc. the stream cost is far more important than merely CAPEX and OPEX [65]. This is because, in these systems, the heat exchanger performance depends upon the plant operating parameters, and thus the HX is designed to fulfill the plant requirements rather than simply optimum local performance [53,66]. The details regarding the different components of economic analysis are presented below.
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Capital expenses
These capital expenses (CAPEX) measure the money expended in equipment purchasing at the time and location of the study. The best approach for the calculation of CAPEX is the use of empirical correlations developed by researchers after an extensive survey. This is because for a flexible and rigorous design and analysis the parameter-dependent cost can only accommodate the variations in process and design parameters conveniently [67]. Therefore, in the current study, the CAPEX for pumps and heat exchanger is calculated using reliable correlation [68]. In this regard, all the correlations reported in the literature and their applicability ranges for heat exchangers are summarized in Table 2. It can be observed that the capital cost for a pump is given in terms of flow rate, pressure differential, and efficiency. While for heat exchanger the capital cost correlations are based on the heat transfer area. An installation factor of 1.5-2.0 is also used to accurately predict the expenses required to make the heat exchanger functional at the point of utility. Moreover, the constants in the correlations vary with changing materials, however the general form for all the correlations is almost same.
It is important to mention that the use of the above-discussed correlations requires a reasonable adjustment to adapt to the monetary variation in the equipment purchasing costs over the years due to fiscal policy changes [69]. In this aspect, the most systematic approach is the use of the cost index factor (Cindex) [70,71]. The Cindex is computed using CEPCI index of the original/reference year and the present year as given below [72,73].
Cindex 1.7 is determined in the current analysis based on CEPCI1990 390 [74] and CEPCI2020 650 [75]. Nevertheless, the influence of Cindex is, however, studied for a wide variety of values for detailed design and analysis purposes.
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Exergoeconomic analysis and cost flow
The hot water outlet cost is estimated by applying the general cost approach [53]. In this regard, the CAPEX calculated above is transformed into the yearly rate of capital cost Z ($/y) through capital recovery factor (CRF) which is given as [66].
( ) ( ) Then the cost flow rate in seconds i.e.
Thereafter, the cost balance takes the form [82]. The cost balance for pump and HX are given as: , The intake cost of cold water is taken from reference [83]. Meanwhile, it is worth mentioning that the components with multiple outputs (i.e., HXs, evaporation effects, flashing stages, and RO trains, etc.,) need supplementary equations for the solution. For a system with "k" outputs, a "k-1" number of supplementary equations are needed [84]. The equality of the average cost of inlet and outlet streams is based on these equations [85]. The auxiliary equation to solve the cost balance of PHX is given as: , , Page 11 of 35

Sensitivity analysis
The sensitivity analysis also used as uncertainty propagation analysis (in experiments) is a powerful tool to assess the response of the output parameter to the perturbations in input parameters [86,87]. Besides measuring the "goodness" of results, this analysis can also satisfactorily conduct malfunction diagnosis and design improvements by highlighting the most responsive parameters for subsequent research [88,89]. In this regard, partial derivative-based sensitivity analysis is one of the most useful methods [90]. In this technique, all independent variables are simulated as a sum of their nominal values and the disturbances/perturbations as below [91].
where X denotes the nominal value and  X U the uncertainty about the nominal value.
The respective uncertainty in the output parameter Y(X) due to uncertainty in X is given as [92].
For a multi-variate response variable, the total uncertainty is given as [93].
Where each partial derivative term in the above equation represents the sensitivity coefficient (SC) of the respective variable [93]. These coefficients are further refined by normalizing the perturbations in the outlet parameter Y and input parameter X by their corresponding nominal values and are known as Normalized Sensitivity Coefficients (NSC) [94]. This normalization allows a comparison of parameters with a significantly different magnitude on a common platform [95]. These coefficients are given mathematically as [96].
Where NSC is the normalized sensitivity coefficient and the NU is the normalized uncertainty.
Page 12 of 35 In the current analysis, the heat transfer coefficient, pressure drop, operational cost, and stream cost are taken as response parameters. The input variables involve process parameters like mass flow rate, fluid temperature, and monetary parameters i.e., interest rate, energy cost, and cost index factor.
The relative contribution (RC) of the input parameter is another key factor that is used to classify the leading responders to uncertainty by merging the sensitivity coefficients with the actual uncertainties [95]. It is calculated as a square of the product of SC and U, normalized by U 2 of the output parameter [96].

Numerical solution strategy
The above presented mathematical model is numerically solved on Engineering Equation Solver (EES) software. First, the process parameters (i.e., T, P, m, etc.) are provided as input known data (refer to Table 1). Then the thermophysical properties are calculated at inlets and outlets of the pumps and heat exchanger using the seawater library [61]. This is followed by a detailed exergoeconomic analysis. Then the normalized sensitivity analysis is conducted to estimate the NSC and RC of important input parameters. This is followed by the parametric analysis of sensitive input parameters on the comprehensive HX performance. Finally, the Genetic Algorithm is employed for optimization of the geometric parameters for the minimum total cost (Ctotal). The solution flow chart for the numerical code is presented in Figure 5.
The simulation is based on the following standard assumptions: (a) steady flow process,

Model validation
The numerical model developed is validated with the experimental data from a laboratoryscale PHX (Model: edibon-TIPL-0083/16) shown in Figure 6. The geometric parameters of the experimental setup are presented in the referred study [50]. The experiments are conducted for three different operating scenarios as summarized in Figure 7. For each case, the setup is operated for 35 minutes and the data is recorded after the system stabilized. For numerical validation, the recorded data (from the data acquisition system i.e., edibon-SCADA) is imported in EES software using the Look-up table command. Figure 6

Preliminary design
It involves thermohydraulic design and analysis from an exergy and economic viewpoint as presented in Table 3 also reported by Jamil and Zubair [53]. The initial design reports that an area of 245 m 2 is required to increase the intake seawater temperature from 21°C to 57°C by recovering heat from the brine stream entering the HX at 63°C and leaving at 23°C. The other thermalhydraulic performance parameters are calculated as hh = 12.2 kW/m 2 K, hc = 12.5 kW/m 2 K,

Sensitivity analysis
The study is carried out to determine the most influential parameters influencing the output parameters, i.e. the coefficient of heat transfer, pressure drop, operating cost, and stream cost. The results are presented in terms of NSC and RC as shown in Figure 8. It is seen that (refer to Figure   8 (a)) The most influential parameters in terms of NSC for the heat transfer coefficient (hc) are the Likewise, from the economic viewpoint (refer to Figure 8  and ~1.65%, respectively as illustrated in Figure 8 (d).
Overall, the exergoeconomic performance of PHX is sensitive to several processes and fiscal parameters. Therefore, an equivalent apportionment should be given to sensitive parameters while designing/analyzing the heat exchanger.

Thermal hydraulic and economic
The most influential parameters affecting the heat transfer coefficient (h) and pressure drop (ΔP) of PHXs are mass flow rate and plate chevron angle [50]. The h and ΔP increased with increasing flow rate. However, the pressure drop observed a higher-order increase compared to h.
Therefore, the h/ΔP factor reduced with increasing flow rate as shown in Figure 9. Similarly, for chevron angle, the h/ΔP followed the order as β = 65° > 60° > 50° > 45° with the lowest for β = 30° due to very high-pressure drop.
Similarly, the operational cost (OPEX) and outlet cost of the cold stream ( , co C ) increased because the pressure drop is increasing at high order which consumes more pumping power and ultimately the cost of electricity increased as illustrated in Figures 9 and 10. Thus, for the chevron angle, the OPEX and , co C followed the order as β = 30° > 45° > 50° > 60° with the lowest for β = 65° due to low-pressure drop at high chevron angle which consumes low pumping power.

Effect of economic parameters
The conventional studies are primarily targeted at analyzing the effect of the flow and geometric parameters. However, the investigation of the combinatory effect of process and fiscal parameters on the thermo-economics performance gained significant importance in recent studies [23,65]. This is because the system operating with a different inflation rate, the unit cost of electricity, the chemical cost would certainly have different operating costs (OPEX) with similar thermal-hydraulic efficiency [53,66]. As the sensitivity analysis emphasizes in the above section, the importance of influencing economic parameters on the monetary output of PHXThe investigation of the fiscal parameters of PHX's economic output has therefore yielded accurate results for different regions and/or different economic policies over time.
The total cost ( total C ) and product cost of the cold stream ( , co C ) are increasing as the cost index factor, inflation rate and cost of electricity are increasing as shown in Figure 10. For instance, for index C = 1.7, total C and , co C (refer to Figure 11 (a) and (b)) increased ~62% and ~13.85% for β = 30° over 30 years due to market inflation. Similarly, for β = 30°, the , co C (refer to Figure 11 (c) and (d)) increased ~17.7% and ~3.80% when the inflate rate and electricity cost varies from 1-14% and 0.01-0.15 $/kWh respectively. Therefore, for chevron angle, total C and , co C followed the order as β = 30° > 45° > 50° > 60° with the lowest for β = 65° for the fiscal parameters.

Optimization
After a detailed normalized sensitivity and parametric analyses, the cost optimization of PHX as a brine preheater of a conventional single effect MVC system as shown in Figure 12 is conducted. For this purpose, the Genetic Algorithm ie employed such that the total cost (Ctotal) of equipment is taken as an objective function that must be minimized meanwhile maintaining the thermal performance of PHX. The decision parameters against the objective function (Ctotal) are port diameter, the horizontal distance between opening, pitch, tube thickness, enlargement factor, and a number of plates. The ranges of constrains variables are selected carefully from the literature [49,97] as summarized in Table 4. It is important to mention that the chevron angle (β) is taken as constant for optimization because the chevron angle is the most influential geometric parameters which affect the thermal performance of the heat exchanger [35][36][37][38][39]. Therefore, it's taken as constant to maintain or improve the thermal performance of the heat exchanger [97,98]. The values of Page 23 of 35 algorithm-specific parameters i.e., generations = 400, population size = 150, and mutation probability = 0.035 are taken as reported by Hajabdollahi et al. [49]. The convergence of the genetic algorithm is illustrated in Figure 14. The perfect convergence has occurred almost within 201 generations (30,475 iterations). However, the Ctotal is reduced by ~52.5% at 50 generations (7677 iterations). Table 4.

Parameters
Guess Values  The detailed results of the optimization for PHX via a genetic algorithm (GA) is represented in Table 5. It can be observed that the optimization altered the thermal, hydraulic, and economic performance of PHX. The thermal performance of PHX is improved as the heat transfer of hot and cold streams is increased by ~58.74% and ~58.73 respectively which increased the overall heat transfer coefficient by ~65.4%. However, the pressure is high as compared to standard values but within the permissible range of plate heat exchanger i.e., 0.1-1.5 MPa [56]. The comprehensive parameter h/ΔP is reduced by ~46.6% because of pressure drops. The pumping power is also increased by 2.97 folds to overcome the pressure drop across the heat exchanger.
Meanwhile, due to the modification in the design parameters, the number of plates and tube thickness is reduced while the port diameter and tube pitch are increased. The heat transfer area is reduced significantly by~79.5% which reduced the capital investment (CAPEX) by ~62%. Also, the operational cost (OPEX) increased from 6.02 k$ to 17.91 k$ due to pumping power. However, the overall impact is beneficial as the total cost ( total C ) of the equipment is reduced by ~52.7%.
Similarly, the outlet cost of the feed water stream is reduced by ~15.7%.
Overall, the sensitivity analysis and optimization of traditional PHX have greatly enhanced the design and analysis process. Therefore, modern system analysis should be extended to normalized sensitivity analysis and optimization rather than relying exclusively on classical parametric analysis.

Concluding remarks
A liquid phase water-to-water plate heat exchanger is investigated as a preheater that uses hot brine coming from a single effect mechanical vapor compression (SEE-MVC) based thermal desalination system. The system is analyzed from thermo-hydraulic, and economic viewpoints.
The EES based numerical code is validated against the experimental setup. Sensitivity and parametric analyses are used to investigate the most important parameters. The exergy-and-cost flow-based exergoeconomic analysis is also conducted to calculate the exergies and outlet cost of streams at each component of the system. Finally, the multi-objective optimization of PHX is performed using the Genetic Algorithm. The major findings of the study are as follows.
• The normalized sensitivity analysis shows that the most influential parameters in terms of NSC • The parametric analysis shows that an increase in the feed mass flow rate decreases h/ΔP because of high order rise in pressure drop but increases the operational cost and outlet cost of the cold stream due to high consumption of pumping power to overcome pressure drop.
Therefore, for the chevron angle, the OPEX and , co C followed the order as β = 30° > 45° > 50° > 60° with the lowest for β = 65° due to low-pressure drop at a high angle which required low power.
• The fiscal parameters such as unit cost of electricity, inflation rate, and cost index factor have an equivalent effect on the operational cost and outlet cost of PHX compared to the process and design parameters. An increase in ele C , index C , and i increased the operational and outlet cost of the cold stream.
• The GA optimization improved the performance of PHX by modifying the design parameters.
The optimum heat exchanger area is reduced by ~79.5%, capital investment by ~62%, and the outlet cost of the cold stream by ~15.7%. The operational cost is increased from 6.02 k$ to Page 27 of 35 17.91 k$ due to increased pressure drop. However, the overall impact is beneficial as total C is reduced by ~52.7%.

Acknowledgment
The authors acknowledge the support provided by Northumbria University, UK under reference # RDF20/EE/MCE/SHAHZAD and MCE QR funds 2020/21. Ben Xu would like to thank the support from EPSRC grants EP/N007921/1.

Nomenclature
Ch constant for Nusselt number calculation in