Desalinated Water Costs from Steam, Combined, and Nuclear Cogeneration Plants Using Power and Heat Allocation Methods

: This work presents a detailed thermo-economic analysis of unit water costs from dual-purpose cogeneration plants. The power levelized cost was ﬁrst calculated for stand-alone steam, nuclear, and combined-cycle power plants. The cost of energy needed to operate the desalination systems connected to power plants was evaluated based on two different approaches: power-and heat-allocated methods. Numerical models based on the heat and mass balances of the power and desalination plants’ components were developed and validated. Comprehensive and updated data generated using Desaldata libraries were correlated to estimate the capital, labor, overhead, and maintenance costs for different desalination systems. The levelized water cost produced by multi-effect distillation, multi-effect distillation with vapor compression, multi-stage ﬂash, and reverse osmosis systems connected to different power plants was estimated. The impact of various controlling parameters, including the price of natural gas, nuclear power plant installation cost, and the desalination capacity on water cost, was investigated. For all simulated cases, the levelized water cost evaluated using the heat-allocated method was found to be lower by 25–30% compared to that estimated using the power-allocated method. The cost of water produced using reverse osmosis remains below that produced by other desalination technologies. However, using the heat-allocated method to estimate the levelized water cost narrows the gap between the costs of water produced by multi-effect distillation and that produced by seawater reverse osmosis. The results also show that the use of the multi-effect distillation process in a cogeneration conﬁguration rather than multi-effect distillation with vapor compression can result in a lower water cost. The proﬁt analysis shows slight differences between the proﬁt of a power plant connected to a reverse osmosis system and the proﬁt of a power plant connected to a plain multi-effect distillation system.


Introduction
Freshwater shortages in many regions are steadily increasing, leading to a significant expansion in the desalination sector.Broadly speaking, the technologies of desalination are divided into two main groups: evaporation/condensation (also called thermal) and membrane-based methods.The main sub-methods of thermal desalination systems are multi-stage flash distillation (MSF) and multi-effect distillation (MED).Both technologies require thermal and electrical forms of energy for their operation.Reverse osmosis (RO), the major membrane process, is the leading pressure-driven membrane process that has gained acceptance in the desalination industry worldwide.Unlike thermal processes, this technology requires only electrical energy.Currently, RO plants account for nearly 60% of the world's total freshwater production [1].Published statistics indicate that new Energies 2023, 16, 2752 2 of 28 desalination plants in almost all RO-based technologies have been installed primarily in "hot spots", including the Middle East and North Africa (MENA) regions [2].
A power plant, an industrial facility, generates electrical energy using a variety of technologies and working fluids.The most employed power facilities at the industrial scale are steam power plants (SPP), gas turbine plants (GTP), and combined-cycle power plants (CPP).Many of the power plants in the world use fossil fuels, such as coal, oil, and natural gas, to generate electricity.Others use nuclear energy, but there are also cleaner renewable energy sources such as solar, wind, geothermal, and hydroelectric sources [3][4][5].About 80% of the world's energy is generated by fossil fuels; the remaining part is generated by other energy sources, such as nuclear energy or renewable energy sources [6,7].Coupled power desalination powered by solar energy has been identified by the US Department of Energy (DOE) as an important potential step to solve the water-energy nexus [8].
Combining power generation and desalination technologies has important merits, including better utilization of the primary supplied heat, sharing the infrastructure and costs of both facilities, and answering appropriately to the variation in the water and power demands.In addition, it has reduced environmental impacts such as CO 2 emissions and brine rejected concentration.In fact, the discharged brine leaving the desalination plant becomes diluted when mixed with the rejected cooling water from the power plant.Most of the operating dual-purpose power and desalination plants are driven by fossil fuels, contributing to CO 2 emission rates and greenhouse gas effects.Nuclear power, which is a mature technology, is identified as an attractive solution to drive high-capacity desalination plants [9].
Usually, thermal power plants are evaluated on the basis of their energetic performance, which is derived from the first law of thermodynamics.Another criterion for evaluating energy systems is exergetic performance, which is based on the second law of thermodynamics [10][11][12][13][14][15].Aljundi [16] evaluated a steam power plant and provided component-by-component modeling and a detailed breakdown of energy and exergy losses.Zubair and Habib [17] evaluated regenerative-heat Rankine power plants using second-law thermodynamic analysis.Butcher and Reddy [18] performed a second-law thermodynamic analysis to investigate a waste heat recovery-based power generation system.Dong et al. [19] carried out dynamic modeling and simulation analysis of a nuclear power plant connected to the MED-TVC system.Khan et al. [20] conducted a techno-economic analysis of KANUPP for different desalination technologies.The results show that the cost of water for each coupled technology has different trends.Haya et al. [21] provided an overview of recent advances and technical features of nuclear desalination plants (NDP).It was concluded that hybrid nuclear systems are promising alternatives for future energy and water challenges.In 2020, Sadeghi et al. [22] conducted an economic evaluation of the possible desalination processes for the first unit of the Bushehr NPP.According to this study, the proposed process is RO + MED with a thermal/RO ratio of 0.7 and a total capacity of 150,000 m 3 /day.A Polish case study [23] of a techno-economic analysis for operation in partial cogeneration and its application examined cost variation.A major limitation of these studies consists of the use of the program DEEP (Desalination Economic Evaluation Program, developed by the International Atomic Energy Agency [24]), in which there is no provision for modeling the various hybrid desalination plant systems.
Performance assessments of dual-purpose cogeneration plants where two types of energy, namely electric and thermal, are involved are not easy to perform.It has been established that comparing the economics and energetics of desalination processes driven by different energy sources, such as electrically driven reverse osmosis (RO) and thermally driven MED and MSF plants, is not straightforward [25][26][27][28].Altman et al. [25] pointed out that "A direct comparison of the energy used by these two systems (RO and thermal desalination systems) would have no meaning".In addition, evaluating the unit cost of electric power and that of desalinated water produced using cogeneration dual-purpose plants is not based on a common or universally adopted approach [25,29].Therefore, water cost estimation by allocation between power and water for a cogeneration configuration remains a controversial issue.ElNashar [27] pointed out that the multiplicity of methods used for cost allocation for water and power cogeneration plants contributes to such an issue.ElNashar [27] considered an existing dual-purpose power and desalination cogeneration plant located in Abu Dhabi to conduct a detailed cost analysis.He compared the unit cost of water and electricity employing five different methods using either energy or exergy as the basis for pricing.Hamed [29] performed a comprehensive techno-economic study using the exergy accounting method to estimate the unit costs of water and electric power from a combined-cycle plant integrated with a hybrid MSF and RO desalination system.This cogeneration plant, which refers to the operating Ras Alkhair plant, has a power capacity of 2645.5 MW and a total water production of about 1 Mm 3 /day.The results show in particular that the unit cost of water ranges from USD 0.826/m 3 to USD 2.26/m 3 while the per unit electricity generation cost varies from USD 0.0227/kWh to USD 0.097/kWh, as the oil price rises from USD 6/bbl to USD 72/bbl, respectively.
For dual power and desalination systems, many cost estimation procedures were investigated [27,[30][31][32][33][34][35] to determine the energy cost of water production.These procedures include exergy-and energy-allocated methods.The energy-allocated method can be divided into power-allocated [30][31][32][33] and heat-allocated methods [34,35].In the powerallocated method, PAM, the loss in power generation is considered the energy needed to operate the desalination systems.An alternative approach, known as the heat-allocated method (HAM), consists of not focusing on "the missed or lost electric power" and considering that the increase in the heat added to the power plant is the energy needed to operate the thermal desalination systems [34,35].
Several studies on electricity and water production cogeneration plants have been conducted using the equivalent power consumed approach [36,37].This method is based on the fact that the adequate value of steam supplied to the thermal desalination units lies in its ability to produce work.Therefore, the energy used to thermally desalinate seawater by supplying steam to desalination units is considered a power loss that would be better expanded to a condenser.Darwish et al. [37] concluded, using this approach applied to a case study from Kuwait, that the specific energy consumption of desalinated water using MSF technology was 25 kWh/m 3 , which is much higher than that corresponding to other conventional processes, namely RO (5 kWh/m 3 ) or MED (12 kWh/m 3 ), when steam is extracted at low pressures from steam turbines.The high energy cost of MSF-desalinated water in dual purpose cogeneration structures led Darwish to strongly recommend stopping the construction of new MSF desalination plants to the benefit of RO, essentially [38].It was reported that both power loss and exergy methods lead to the same results in terms of the unit cost of water in a cogeneration mode [36].
[25] established a frame for the theoretical studies on the energy consumption of desalination systems connected or not to power generation plants.The main idea on which they centered their comprehensive analysis is to track back the heat and power inputs to their common primary energy source, such as the fuel supplied to power and water cogeneration plants.The results of this study pointed out that when the energy consumption associated with water production is evaluated on a primary energy basis, the gap between power and thermal desalination technologies is reduced.The RO desalination process, however, still has the lowest specific energy consumption.Similarly, Ng et al. [39] pointed out that the conventional methods of energy consumption and efficiency have been defined based on the derived energy consumption, such as steam or electricity.They proposed a unified universal performance ratio (UPR) using exergy efficiency based on primary energy.This UPR takes into account the conversion factors required to convert the derived electric power and thermal input at a given temperature to primary energy.These conversion factors were obtained from the analysis of more than 20 published works on combined-cycle power and desalination plants.The main findings drawn from this study are that the performance of all conventional and widely used desalination technologies is far from the thermodynamic limit.In addition, the actual performance values of these technologies based on the UPR are not dispersed but are close regardless of the process type.This conclusion aligns with what was reported by [26].
It is also worth considering the important work of Ihm et al. [26], in which two operating power and desalination cogeneration plants located on the east coast of Saudi Arabia were used as reference cases.The first plant was a simple oil-fired power plant while the second was a combined-cycle power plant.The focus of the analysis was also on considering the fuel energy needed for desalination, which was found to be lower by about 49% when combined-cycle technology was used.This reduction was attributed to the higher efficiency of the combined cycle.The authors recommended that when natural gas is used at a reasonable cost, high-performance MED-TVC thermal desalination technology coupled with a combined-cycle power plant can be a feasible option for Gulf countries as compared to a RO option.
The economic viability of integrating power and desalination structures can be assessed by evaluating the final cost of produced water.Specifically, this work focuses on evaluating the cost of desalinated water using the power-allocated method (PAM) as well as the heat-allocated method (HAM) from cogeneration plants based on the most reliable power and desalination systems.The study is based on updated and reliable technical specifications and cost details of the various systems and components as well as on reliable and validated numerical models.The obtained results aim to contribute to the clarification, via the first law of thermodynamics only, of the above-mentioned controversial issues on unit water costs by considering two different assessment methods.
The investigation procedure consisted of the following steps: we analyzed the standalone power plant performance to determine full power and the levelized power cost for given heat added; then, we analyzed the performance of a power plant connected to a desalination system to determine the loss of power generation for the same heat added; and lastly, we analyzed the performance of a power plant connected to a desalination system to determine the increase in the heat added to maintain the full power and determine the cost of water production based on power-and heat-allocated methods.

Power Plants Description
Three types of power plants were investigated: steam power plant (SPP), nuclear power plant (NPP), and combined power plant (CPP).These power plants are connected to three types of desalination plants: MED, MED-TVC, and MSF-OT, as shown in Figures 1-3 and in Appendix A.
The objective of the power plant analysis was to estimate the levelized power cost for the standalone power plants under full load conditions.In the first case, a steam power plant, SPP, was coupled to a plain MED system, as shown in Figure 1.The boiler supplies steam to a three-stage turbine.The steam is reheated before entering the intermediate pressure turbine.There are seven feed-water heaters; one of them is an open type.The pressures of the feed-water heaters are distributed based on the optimum condition, where the temperature differences between the saturation temperatures of the feed-water heaters are equal [40].The conditions and parameters used for the simulation of the steam power plant are listed in Table 1.The thermodynamic analysis of the steam power plant without desalination was performed using EES software [41].For the three types of power plants (SPP, NPP, and CPP), the following information and data are given: - The heat available from natural gas or nuclear fuel to operate the power plant is fixed at Q H = 3000 MW. - The condenser temperature is assumed to be 10 • C above the seawater temperature.- The efficiency of each component of each plant is given in Table 1.
For each case (SPP, NPP, and CPP), a numerical model based on conservation equations of mass and energy of each component and on reliable technical specifications and data (see, for example, Table 1) was developed and validated.The mass and energy balances for each power plant were checked for several conditions.In addition, several comparison tests with basic power cycles were conducted.All these verifications and tests confirmed the reliability and accuracy of the developed models for the SPP, NPP, and CPP options.
In addition, for the steam power plant, the boiler outlet conditions were fixed at 100 bar and 550 • C in the present study.The pressures of the reheater and feedwater heaters are shown in Table 1.The steam was reheated to 550 • C before entering the intermediate pressure turbine.
The same procedure was used to analyze the thermodynamics of a stand-alone nuclear power plant, i.e., without desalination, as shown in Figure 2. The outlet condition of the nuclear power plant steam generator was fixed at 280 • C for dry, saturated steam in the current investigation.The steam was reheated to 270 • C before entering the low-pressure turbine.The feedwater heaters' pressures are specified in Table 1.For the combined power plant without desalination, Figure 3 depicts a cycle diagram with the various components.Gas turbine inlet conditions were maintained at 14 bars and 1227 • C (TIT = 1500 K).The HRSG pressure was maintained at 20 bars.The steam at the HRSG outlet was superheated and was assumed to be 20 • C below the gas turbine exhaust temperature (TET).The HRSG pinch point was assumed to be 10 • C. The steam loop has six feedwater heaters (Figure 3), whose pressures are listed in Table 1.The steam was reheated before entering the low-pressure steam turbine and was 30  The estimated full load of the power plants, the overall efficiency, and the overall heat rate are shown in Table 1.For example, the calculated thermal efficiencies of the standalone SPP, NPP, and CPP are 39.5%, 35.6%, and 51.4%, respectively.

Levelized Cost of Electricity (LPC) Evaluation
The levelized cost of electricity (LPC) was estimated for the individual power plants based on the DEEP model [24].The economic analysis of power generation was based on the parameters listed in Table 2.The effect of the natural gas price [42] on LPC for SPP and CPP is shown in Figure 4.For NPP, the LPC was estimated for two installation costs (Table 2), and their effect on the LPC is also shown in Figure 4.The two installation costs considered were 2157 USD/kW (referred to as NPP1) and 4250 USD/kW (referred to as NPP2).These two values can delimit the range of the installation costs of NPP worldwide.Figure 4 shows that the LPC of the CPP is lower than that of the SPP because of the high efficiency of the CPP.For the NPP plant, the LPC is mainly a function of the installation cost.

Water Cost
In the current investigations, the desalination models presented by Zeitoun et al. [46] and Zeitoun et al. [47] were integrated with the models of the power plants described above to simulate different power and desalination cogeneration scenarios.The details of the design and analysis of the plain MED and MED-TVC desalination systems were presented in [46].The details of the design and the analysis of the MSF-OT system can be found in [47].
It is of interest to clarify that the developed numerical models, based on rigorous theoretical formulations of the desalination systems, were systematically checked and compared to data from previous works.For example, the MED-TVC model was validated using field data from existing MED-TVC desalination plants and previous models' results.Table 3 compares the main output parameters of the MED-TVC plant, as calculated with the results of Bin Amer [48] and field data from the Al-Taweelah plant [48].Table 4 compares the model results with those of previous authors and field data.These various validation tests demonstrate the capability of the developed models to accurately predict the performance of different plants under different design and operation conditions.The levelized water cost, USD/m 3 , was estimated using the following equation [51]: Capex, labor, overhead, chemical, and parts costs for different desalination plants were calculated from correlations generated using data obtained from Desaldata [51], listed in Table 5, and are presented in Figures 5-7.It is worth mentioning that the generated data from Desaldata [51] are based on a large number of data corresponding to updated and real information from plants constructed and planned worldwide.Therefore, we consider that these correlations represent, with a high level of confidence and accuracy, the operating and capital costs related to MED, MSF, and SWRO technologies.Figure 5 illustrates that the impact of the plant capacity is restricted to capacities lower than 0.5 Mm 3 /day.The MSF capex cost is almost double the unit capital cost of RO.The labor and overhead costs are simply independent of the employed desalination technology.They approach a high plant capacity of 0.03 USD/m 3 and 0.02 USD/m 3 , respectively (Figures 6 and 7).The operating energy cost, OPEcost, was estimated using two procedures: the powerallocated and heat-added allocated methods (PAM and HAM), as described below.

Power-Allocated Method
The power-allocated method, PAM, has been presented in many investigations including [28,37,38].In this method, the operating energy cost is estimated based on the loss of the power plant output due to the steam extracted and supplied for desalination.In this section, the supplied fuel energy (Q H ) was maintained at a fixed rate of 3000 MW, and the power plants and the connected desalination system were simulated together to estimate the power loss.The loss in power output W D includes the power loss due to the steam bleeding needed to operate the thermal desalination plant and the power needed to operate the pumps of the water production plant: where ∆W is the loss in the power output after connecting the desalination system and W pump is the power needed by desalination system pumps [33,35]; where W full is the standalone plant's full power corresponding to full power heat-added Q H , and W p is the power output of the steam power plant after steam bleeding to the desalination system.W pump is estimated based on the power needed by the pumps to circulate the seawater into the system and withdraw the fresh water and brine from the system.The unit energy cost to operate the desalination systems, in USD/m 3 , was calculated based on It is worth also reminding that, for a desalination unit, the GOR should be maximized for better utilization of the supplied steam, while the total area of the heat exchangers (evaporators, condenser, and preheaters), A e , should be minimized.The specific area to the GOR ratio (A e /GOR) (or the area to the specific energy consumption (SEC) product) is an important quantity to investigate.For lower total cost purposes, this ratio should be minimized.This approach, which is based on minimizing energy consumption and the heat exchanger's area, was adopted in the present investigation.The MED, MED-TVC, and MSF information that was used for the coupling with the power plants corresponds to the optimum conditions for these desalination processes (i.e., minimum A e /GOR).Thus, for example, the optimum case for the MED-TVC structure corresponds to the option with ten effects, and TVC is connected to the seventh effect.Details are given in [46,47].
For the plain MED connected to an SPP (Figure 1), the heating steam was extracted at the seventh FWH level (see Table 1).The simulation of SPP connected to plain MED was carried out for different desalination daily capacities to determine the loss of power allocated to desalination.Table 6 depicts a sample of the obtained data for a plain MED system of eight effects connected to an SPP.Table 6 also shows the power developed by the power plants connected to the eight effects of the plain MED system for different desalination daily capacities.One can see for each power technology (SPP, NPP, or CPP), the power developed (W p ), the power needed to drive the MED pumps (W pump ), and the power required by the MED desalination unit (W D ) are given for each desalination capacity.The above procedure was conducted for nuclear and combined power plans connected to plain MED systems.Samples of the obtained data for these cases are also shown in Table 6.As shown in Table 6, the SPP, NPP, and CPP can operate a plain MED system up to 300,000, 400,000, and 150,000 m 3 /day, respectively.
For MED-TVC and MSF-OT systems connected to SPP, NPP, and CPP, samples of simulation data are presented in Tables 7 and 8.

Heat-Added Allocated Method
The heat-added allocated method, HAM, was discussed in [34,35].In this method, the full power, W full , estimated for the standalone power plants is maintained at a fixed rate (Table 1), while the heat added to the power plant is increased by ∆Q to substitute the thermal energy of the steam extracted for the desalination system.In the heat-added allocated method, the operating energy cost in USD/m 3 was estimated based on the cost of the increase in the head-added ∆Q and the power needed to operate the pumps of the desalination systems: In the HAM method, it is assumed that the boiler of the SPP and the steam generator of the NPP are capable of producing an additional 10% to 15% of the full-load steam.This assumption means no change in their CAPEX is needed to estimate PLC and WLC.For the combined power plant, to increase the heat supplied to the combustion, it may be required to replace the compressor with a larger one or increase the turbine inlet temperature.The first solution would result in the replacement of the gas turbine and operating it at partial load, which means that the heat-added allocation is not suitable for the combined power plant as increasing the turbine inlet temperature may overheat the turbine.However, CPP plant simulation was carried out in the current investigation for comparison purposes.
In the current analysis, SPP, NPP, and CPP, connected to MED, MED-TVC, and MSF-OT, were simulated for different daily desalination capacities to estimate the increase in heat added.Tables 9-11 include the allocated heat to the desalination systems and the pumping power needed to operate the desalination systems.

Results and Discussion
The levelized water cost for SWRO was estimated for comparison reasons.For a reverse osmosis system, the water cost can be estimated based on the allocated power procedure.The correlations given in Table 5 and the estimated levelized power cost (Figure 4) for different power generation scenarios and natural gas prices were used in this analysis.The energy operating cost of SWRO was estimated based on 3.5 kWh/m 3 , as reported by Desaldata [51].
The natural gas price has fluctuated considerably in the last two years.Figure 8 illustrates the effect of the power generation technology, the natural gas price fluctuation, and the desalination capacity on the SWRO levelized water cost.For SPP and CPP, the LWC mainly depends on the natural gas price.The LWC for SPP and CPP is very closed at NGP = 2.5 USD/Mbtu.The LWC for a nuclear power plant of low capital cost NPP1 competes with SPP and CPP with low-price natural gas.The water cost of SWRO operated by CPP is lower than SWRO operated by SPP because of the higher efficiency of the CPP.The SWRO of NPP1 has a low unit cost of water, mainly because of its low LPC (low installation cost).The lowest unit water cost by SWRO is around 0.7 USD/m 3 .This value is very close to what has been reported by several authors.
The unit water cost estimation becomes less straightforward when dealing with thermal desalination in cogeneration structures.Levelized water costs based on the powerand heat-allocated methods of the investigated power and desalination scenarios are presented in Figures 9-14.The effect of natural gas prices and desalination capacities are also shown in these figures.For the nuclear power plant, the effect of the installation cost is also included.Figure 9 shows the LWC using the power-allocated method (PAM) and heat-allocated method (HAM) for a plain MED plant connected to an SPP for four values of natural gas price.The LWC estimated based on the HAM is lower by about 25-30% than the LWC estimated based on the PAM.During the SPP design, oversizing the boiler to maintain the full power, which is inexpensive, Editedwill lead to a low LWC. Figure 9 shows that, for the natural gas price values considered, the unit water cost ranges from 0.80 to 1.46 USD/m 3 and from 1.02 to 2.06 USD/m 3 when using HAM and PAM, respectively.
A comparison of water costs using different desalination technologies connected to SPP is illustrated in Figure 10.The heat-added allocated method, HAM, competes with the PAM for plain MED, MED-TVC, and MSF-OT desalination systems.However, for the two cost estimation procedures, PAM and HAM, the LWC for plain MED is slightly lower than that of MED-TVC.This is an interesting finding.The reason can be attributed to the fact that the loss of power to drive the TVC is higher than the gain associated with the increase in GOR of the MED-TVC system.The water cost from SWRO remains below that of other desalination methods.However, using the HAM procedure narrows the gap between plain MED and SWRO.The HAM procedure makes MED promising for a large system and also reduces the cost of MSF-OT by 25-30%.
The effects of nuclear power plant installation cost and LWC estimation methods are shown in Figure 11 for a plain MED system connected to an NPP.The LWC estimated based on the PAM depends mainly on the levelized cost of power (LPC).This is the reason for the lower cost of NPP1 compared to NPP2.For the HAM, the LWC does not depend on the NPP installation cost, as the latter affects only the LPC.In addition, since the MED pumps' power is not significant compared to NPP full power, the LWC estimated using the HAM is very close for both NPP1 and NPP2.
Figure 12 depicts the impact of using HAM and PAM on the water cost (LWC) for different desalination systems connected to NPP1.Again, the plain MED competes with MED-TVC for both PAM and HAM.The LWC for SWRO is still lower, about 5% below MED, estimated using HAM.
The combined-cycle power plant (CPP) data shown in Figure 13 reveal that this powerful technology cannot be connected to a large plain MED desalination system due to the limited steam produced by the HRSG. Figure 14 indicates again that the LWC from SWRO remains the lowest, but it is very close to the LWC of plain MED estimated using the HAM approach.On the other hand, Figure 14 highlights the notable difference between the unit cost of water associated with the MSF process using PAM and that of the RO process.This agrees with what was reported previously, such as in [37], for example.
The effect of power generation technology on LWC when adopting the HAM procedure is depicted in Figure 15 for both the MED and RO processes.The natural gas price is fixed at 2.5 USD/Mbtu.The presented data reveal that the LWC of SWRO is very close for the different power sources.It is worth reminding that the power levelized cost (LPC) was found to be close for SPP and CPP technologies at low natural gas prices and comparable with that of NPP1 (Figure 4).The comparison indicates also that the LWC of SWRO is slightly below that of the plain MED connected to CPP or NPP (Figure 15).Another criterion associated with the cost of water is proposed and used in the following section.The profit percentage of the dual-purpose plant can be another criterion in addition to the LWC to determine the cogeneration plant viability.The profit percentage can be calculated from: Pro f it% = (AEP + AWP)/(PPIC + WPIC) (6) where AEP and AWP are the annual profits from the sale of electricity and water, respectively, and PPIC and WPIC are the total power and desalination plants installation costs.Data in Tables 2 and 3 were used to estimate the installation costs.The profit depends on the difference between the sale price and the levelized cost.The annual profit from the electricity sale can be estimated from: where ESP is the electricity sale price and W s is the salable electric power: The annual profit from water sales can be estimated from: where WSP is the water sale price.Data from the heat allocation method (HAM) were used in the following comparison.For comparison purposes, we assume that the sale prices of electricity and water were 0.06 USD/kWh and 1.5 USD/m 3 respectively.Figure 16 shows comparisons between percentage profit for SPP, CPP, and NPP coupled with plain MED or SWRO.These comparisons were conducted for the natural gas price (NGP) of 2.5 USD/Mbtu and low installation cost NPP.The difference in profit percentage between MED and SWRO connected to a certain power plant is not significant.This small difference resulted mainly from the low installation cost of SWRO.The percentage profit of the CPP is high due to its high efficiency.The percentage profit of the NPP is low compared to other power plants because of its high installation cost.This exercise depends on many parameters.The change in fuel cost, power, and desalination performance will affect these results.However, the current data indicate that desalinating water using SWRO has a cost that is not substantially superior to that of plain MED.

Implications and Prospects
The present study concerns the evaluation of unit water costs using power and heat allocation methods for power and desalination cogeneration plants.One important finding is that using the power allocation method results in an overestimation of the water cost of the thermal desalination processes.In this work, we focused on the unit water cost and did not focus specifically on the energy cost of water for each case.A detailed analysis of the specific energy consumption for each desalination process, both standalone and in cogeneration mode, will be undertaken in future work.Different allocations and evaluation methods including exergy will be employed.In addition, a concise and rigorous comparison between the projected results of future studies and those from the open literature will be conducted.This extensive future work, in addition to the present results, will contribute to understanding and explaining the discrepancies between different previous investigations on the computed levelized water cost, which will help to clarify the LWC situation to the industrial and scientific communities.Moreover, the current investigation has shown that the simple MED connected to different power plants leads to lower unit water costs as compared to the MED-TVC process.This point also needs extensive investigation.Therefore, the current work can be extended to include MED with/without preheaters connected to subcritical/supercritical steam, nuclear, and combined power plants.Finally, the integration of renewable energy sources into desalination processes using various allocation approaches is an attractive research topic.

Conclusions
Detailed thermo-economic analysis was performed for three types of power plants (steam, nuclear, and combined cycle) connected to four types of conventional desalination technologies (MED, MED-TVC, and MSF, RO).Numerical models based on heat and mass balances for the components of the power and desalination systems were built and validated.The levelized power cost of standalone power plants was estimated based on the DEEP model.Libraries of Desaldata were used to generate correlations to estimate the capital, labor, overhead, and maintenance costs of different desalination technologies.The cost of energy needed to operate the desalination plants was estimated based on the power-and heat-allocated methods.The levelized water cost for MED, MED-TVC, MSF-OT, and SWRO connected to different power plants was estimated.In addition, the effect of natural gas prices on LWC was investigated.The LWC estimated using the heat-allocated method was found to be lower by about 25-30% compared to the LWC estimated using the power-allocated method.This result makes the thermal methods, particularly the MED process, comparable to the RO method when the heat allocation method is adopted.One interesting finding is related to the use of the simple MED in a cogeneration mode compared to the MED-TVC.It was found that the LWC of the plain MED was lower than that of MED-TVC.This finding needs further analysis in future work.The profit analysis of cogeneration plants indicated an insignificant difference between using the SWRO and the plain MED.Moreover, the percentage profit of cogeneration SPP and CPP was found to be much higher than that of the cogeneration nuclear power plant.

Figure 4 .
Figure 4. Effect of natural gas price on levelized power cost (LPC) for different power plants.

Table 7 .
Allocated power to operate MED-TVC plant.

Figure 16 .
Figure 16.Percentage profit expected for plain MED and SWRO connected to different power plants.

Figure A1 .
Figure A1.Steam power plant connected to MED-TVC.

Figure A4 .
Figure A4.Nuclear power plant connected to MSF-OT.

Figure A5 .
Figure A5.Combined power plant connected to MED-TVC.

Figure A6 .
Figure A6.Combined power plant connected to MSF-OT.Figure A6.Combined power plant connected to MSF-OT.

Figure A6 .
Figure A6.Combined power plant connected to MSF-OT.Figure A6.Combined power plant connected to MSF-OT.
S Figure 2. Nuclear power plant (NPP) connected to plain MED.
• C below the gas turbine exhaust TET temperature.

Table 2 .
Economic parameters used in levelized cost of electricity (PLC) calculation.
Note: Al-Taweelah MED Plant data obtained from Bin Amer.

Table 6 .
Allocated power to operate plain MED (8 effects) plants.

Table 9 .
Allocated heat added to operate plain MED (8 effects).

Table 10 .
Allocated heat added to operate MED-TVC.