Issue 
EPJ Nuclear Sci. Technol.
Volume 3, 2017



Article Number  1  
Number of page(s)  16  
DOI  https://doi.org/10.1051/epjn/2016037  
Published online  30 January 2017 
https://doi.org/10.1051/epjn/2016037
Regular Article
Energetic and economic cost of nuclear heat − impact on the cost of desalination
^{1}
Commissariat à l'Énergie Atomique et aux Énergies Alternatives,
13108
SaintPaullezDurance Cedex, France
^{2}
DEN/DER/SESI, CEA Cadarache, Bât. 1222,
13108
SaintPaullezDurance Cedex, France
^{3}
International Institute of Nuclear Energy,
91191
GifsurYvette Cedex, France
^{⁎} email: saied.dardour@cea.fr
Received:
5
April
2016
Received in final form:
8
November
2016
Accepted:
8
November
2016
Published online: 30 January 2017
An exploratory study has been carried out to evaluate the cost of heat supplied by a pressurized water reactor type of nuclear reactors to thermal desalination processes. In the context of this work, simplified models have been developed to describe the thermodynamics of power conversion, the energetics of multieffect evaporation (MED), and the costs of electricity and heat cogenerated by the dualpurpose power plant. Application of these models show that, contrary to widespread belief, (nuclearpowered) MED and seawater reverse osmosis are comparable in terms of energy effectiveness. Process heat can be produced, in fact, by a relatively small increase in the core power. As fuel represents just a fraction of the cost of nuclear electricity, the increase in fuelrelated expenses is expected to have limited impact on power generation economics.
© S. Dardour and H. Safa, published by EDP Sciences, 2017
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
1 Introduction
With almost 75 million cubic meter per day of worldwide installed capacity [1], desalination is the main technology used to meet water scarcity. About two third of this capacity is produced by reverse osmosis (RO) (Fig. 1). The remaining one third is produced mainly by thermal desalination plants – multieffect evaporation (MED) and multistage flash (MSF), mostly in the Middle East.
Seawater desalination is an energyintensive process.^{1} According to [2], the lowest energy consumption – and the closest to the minimum set by thermodynamics (1.06 kWh m^{−3}) [3] – is achieved by RO processes equipped with energy recovery devices. Seawater RO (SWRO) electricity utilization ranges, in fact, between 4 and 7 kW_{e}h m^{−3} [4]. Some plants, producing large amount of desalinated water, claim even lower energy consumption; 3.5 kW_{e}h m^{−3} for Ashkelon, Israel [4]; and 2.7–3.1 kW_{e}h m^{−3} (depending on temperature and membrane ageing) for Perth, Australia [5].
Thermal desalination processes consume heat,^{2} in addition to electricity. Heat consumption varies between 40 and 65 kWh_{th} m^{−3} for MED, and 55–80 kWh_{th} m^{−3} for MSF [2]. MSF's electric power consumption is higher than MED's because of pressure drops in flashing chambers and the possible presence of brine recirculation loops [6]. MSF's pumping power varies between 2.5 and 5 kWh_{e} m^{−3} [7]. MED manufacturers claim specific electricity consumptions lower than 2.5 kWh_{e} m^{−3}.
Fig. 1 Total worldwide installed capacity by technology. 
1.1 Power consumption: thermal desalination systems vs. membranebased processes
Thermal desalination systems are often coupled to power generation units to form “integrated water and power plants” (IWPPs) in which steam is supplied to the desalination unit by the power plant.
The cost of process heat provided by such plants is traditionally evaluated based on the “missed electricity production” – steam diverted to the process is no longer used for electricity production – leading, systematically, to higher energy costs for the thermal desalination processes compared to RO. MED's steam supply costs between 4 and 7 kWh_{e} m^{−3} of “missed electricity production” according to [2]. If we add 1.2–2.5 kWh_{e} m^{−3} of pumping energy, we end up with an equivalent electric power consumption in the range [5.2–9.5] kWh_{e} m^{−3}.
Rognoni et al. [8] suggested an alternative way to evaluating the cost of heat “duly considering the benefits of cogeneration”. The approach no longer views process heat as a “missed electricity production”, but, rather, as “a result of a (limited) raise in the primary power” – the power released from combustion. According to this approach, the energetic cost of process heat is equal to the number of MW_{th} added to the boiler thermal power output. Since fuel represents just a fraction of the cost of electricity, process heat is expected to be cheaper than predictions based on the traditional cost evaluation method. As a result, thermal desalination processes – precisely MED – can be potentially more costeffective than SWRO. The authors provided twocalculation examples – MED processes fueled by coalfired power plants in India – for which the cost of desalinated water is 50% lower than SWRO's.
1.2 “Nuclear steam” cost
The cost of process heat depends on the contribution, to the total cost of electricity, of fuelrelated expenses – a contribution widely considered to be lower for nuclearpowered electricity generators compared to fossil power plants [9]. Past studies show, in fact, that heat recovery from light water reactors is economically competitive for a number of low temperature applications, including district heating [10] and seawater desalination [11].
The study described in this paper aims at evaluating the – energetic and economic – cost of process heat, supplied by pressurized water reactor (PWR) to a thermal desalination process. The objective is to provide a basis for comparing thermal (MED^{3}) and membranebased (SWRO) desalination processes in terms of energy costs. Simplified models, describing the thermodynamics of a generic PWR power conversion system, the energetics the MED process, and the costs of electricity and process heat produced by the dualpurpose plant (DPP), support this study. These models, and the results of their application, are presented and discussed in the next sections.
2 Energetic cost of heat
The energetic cost of heat was evaluated based on the power conversion system (PCS) architecture described in the next paragraph.
2.1 Power conversion system architecture
Figure 2 illustrates the workflow of the PCS being modeled.
The system is basically a Rankine cycle representative of the technologies commonly applied is PWRs. Steam leaving steam generators (SG) undergoes two expansions in the highpressure body of the turbine (HPT_{1} and HPT_{2}). The fluid is then driedup and superheated before supplying the lowpressure stages (LPT_{1}, LPT_{2} and LPT_{3}). Liquid water extracted from the condenser (Condenser_{2}) is finally preheated and readmitted back to SG.
A steam extraction point was positioned between the outlet of LPT_{2} and the inlet of LPT_{3}. This location allows for a variable quantity (y = 0–100%) of steam (the steam normally flowing through LPT_{3}) to be diverted to an external process. The pressure at the steam extraction point (P_{SteamEx}) may vary between 0.05 bar (pressure at the condenser) and 2.685 bar (pressure at LPT_{2} outlet), and the temperature (T_{SteamEx}) between 33 and 129 °C. The range of temperatures generally required by thermal desalination systems generally falls within these limits.
The power plant condenser was (virtually) split in two. In Condenser_{1}, the latent heat of condensation is transferred to the external process. Condenser_{2} cools the condensates down to 33 °C. The heat duty of each of the two condensers strongly depends on the quantity of steam diverted to the process.
Fig. 2 Power conversion system architecture. 
2.2 Thermodynamic model
A thermodynamic model, evaluating the energetic performance of the PCS described in the previous paragraph, was developed using CEA's inhouse tool ICV.^{4}
The model calculates the characteristics of the 23 points of the flowsheet – temperature, pressure, steam quality,^{5} enthalpy, exergy and flowrate – the power of the major components of the PCS, as well as the amounts of electricity (W_{Elec}) and process heat (Q_{Pro}) cogenerated by the system.
Model inputs include:

an assumed pressure distribution within the PCS (Tab. 1);

SG outlet temperature (290 °C) and thermal power output (Q_{SG});

the temperature at the steam extraction point (T_{SteamEx});

the fraction of steam (normally expending through LPT_{3}) diverted to the external process (y).
The calculation of the Rankine cycle is performed sequentially, component by component, applying the mass and energy balance equations (Eqs. (1) and (2)^{6}) to different control volumes. (1) (2) , mass flowrate (kg/s); , thermal power (W); , mechanical power (W); , specific enthalpy (J/kg); v^{2}/2, specific kinetic energy (J/kg); g × z, specific potential energy (J/kg).
The state of the fluid at the outlet of steam turbines and water pumps is determined applying an isentropic efficiency (88% for turbines and 87% for pumps): (3) (4) ε, isentropic efficiency; , specific enthalpy at inlet (J/kg); , specific entropy at inlet (J/kg/K); , specific enthalpy at outlet (J/kg); , specific entropy at outlet (J/kg/K); , specific enthalpy at outlet for a constantentropy transformation.
The following assumptions were also made:

Steam admitted to different heat exchangers is assumed to leave all its latent heat to the fluid flowing on the secondary side of the exchanger.

A fixed pinch point temperature difference of 15 °C was systematically applied to determine the outlet fluid temperature on the secondary side.

Energy losses^{7} are not taken into account (the calculated “net” power and heat outputs are actually “gross” power and heat outputs).
Assumed pressure distribution.
2.3 Energetic performance of the PCS
Tables 2 and 3 show the characteristics of a 2748 MW_{th} singlepurpose plant (SPP) generating 1000 MW_{e} of electricity.
The contribution of steam turbines to SPP's electricity output is shown in Figure 3. LPT_{3} delivers 213 MW_{e} of mechanical power, which represents 21% of the total electricity output.
If all the steam normally flowing towards this turbine is redirected to the external process (T_{SteamEx} = 80 °C), the plant would generate 787 MW_{e} of electricity and 1730 MW_{th} of process heat. The reactor's process heat generation capacity depends, in fact, on the core power, and on the temperature at the steam extraction point, as shown in Figure 4.
Now, if only a portion of this steam – exactly 57.8% – is diverted, the plant would produce 877 MW_{e} of electricity and 1000 MW_{th} of heat. The characteristics of configuration – we will call it DPP_{1} (dualpurpose plant) – are listed in Tables 4 and 5.
The differences between SPP and DPP_{1} are highlighted (underlined) in Tables 2–5. The two Rankine cycles have identical characteristics except for points 10–12. In DPP_{1}, turbine LPT_{3} is partly bypassed – the exergy of the rerouted steam is later “destructed” in Condenser_{1} – resulting in a 123 MW_{e} decrease in power generation compared to SPP.
The number of MW_{e} of electricity production lost for each MW_{th} supplied to the external process (123 kW_{e} per MW_{th} in the case of DPP_{1}) is a traditional measure of the energetic cost of process heat. This measure will be referred to as the “Wcost of heat” or WCH: (5)
This “loss” in electricity production can be avoided by increasing the thermal power of the core. To keep the electricity generation capacity at 1000 MW_{e} – and the heat production level at 1000 MW_{th} – SG have to deliver an additional 338 MW_{th}. The portion of diverted steam has also to be adjusted (51.5%). This configuration – we will call it DPP_{2} (Tabs. 6 and 7) – not only offers higher power conversion efficiency (32.40%) compared to DPP_{1} (31.91%), but also results in lower heat cost, as we will see in Section 2.
The number of MW_{th} added to core power, per MW_{th} supplied to the external process (338 kW_{th} per MW_{th} in the case of DPP_{2}) provides an alternative measure of the energetic cost of steam – we will call it the “Qcost of heat” or QCH: (6) QCH is simply obtained dividing WCH by SPP's power conversion efficiency.
The increase in core power considered in this study is purely conceptual.^{8} Adopting QCH as a measure of the energetic cost of steam makes it possible, in fact, to take into account the advantages cogeneration offers.
Figure 5 shows how WCS and QCH vary with T_{SteamEx}. At 75 °C, each MW_{th}h of thermal power supplied to the process costs 111 kW_{e}h of electricity. At 100 °C, the cost increases to 169 kW_{e}h MW_{th}h^{−1} (×1.5), and at 125 °C it reaches 223 kW_{e}h MW_{th}h^{−1} (×2).
The energetic cost of heat depends, actually, on the enthalpy at the steam extraction point, which is a function of the level of temperature required by the external process (Eq. (7)). (7)
SPP (PWR 2748 MW_{th} → 1000 MW_{e}): thermodynamic points.
SPP (PWR 2748 MW_{th} → 1000 MW_{e}): mechanical and thermal powers.
Fig. 3 Contribution of steam turbines to SPP's electricity output. 
Fig. 4 Available heat for the external process vs. temperature at the steam extraction point. Blue bar: PWR 1000 MWe (2748 MWth); orange bar: PWR 1650 MWe (4534 MWth). 
DPP_{1} (PWR 2748 MW_{th} → 877 MW_{e} + 1000 MW_{th} at 80 °C): thermodynamic points.
DPP_{1} (PWR 2748 MW_{th} → 877 MW_{e} + 1000 MW_{th} at 80 °C): mechanical and thermal powers.
DPP_{2} (PWR 3086 MW_{th} → 1000 MW_{e} + 1000 MW_{th} at 80 °C): thermodynamic points.
DPP_{2} (PWR 3086 MW_{th} → 1000 MW_{e} + 1000 MW_{th} at 80 °C): mechanical and thermal powers.
Fig. 5 WCH and QCH vs. temperature at the steam extraction point. 
3 Economic cost of heat
3.1 Singlepurpose plant
To evaluate the cost of electricity relative a singlepurpose plant, we first calculate the minimal annual cash in – generated from the sale of electricity – required to have a positive NPV. NPV refers here to the net present value of future free cash flows:

annual expenses related to, construction, purchase of nuclear fuel, operation and maintenance (O&M), and decommissioning, on one hand;

annual revenue generated from the sale of electricity, on the other hand.
The minimal annual cash in (ci) is related to cash outflows by equation (8): (8) co_{cst}, annual cash out, construction period, ($); npv (1$, cst), NPV of a fixed expense of 1$ per year, spent during the construction period, ($); ci, annual revenue generated from the sale of electricity, ($); co_{opr}, annual expenses related to fuel and O&M, economic lifetime of the plant, ($); npv (1$, opr), NPV of a fixed expense of 1$ per year, spent over the economic lifetime of the plant; co_{dcm}, annual cash out, decommissioning period, ($); npv (1$, dcm), NPV of a fixed expense of 1$ per year, spent during the decommissioning period.
NPV terms of equation (8) are estimated based on a fixed discount rate (r) applicable for the three periods^{8}: (9)
Equation (8) assumes fixed values of future inflows and outflows over the three key phases of the lifetime of the plant: construction (cst), operation (opr) and decommissioning (dcm).
Annual expenses^{10} (construction, fuel, O&M and decommissioning) are evaluated on the basis of specific costs:

The specific cost of construction^{11}: in $ per (installed) kW_{e}.

The specific cost of fuel: in $ per (produced) MW_{e}h.

The specific cost of O&M: in $ per (produced) MW_{e}h.

The specific cost of decommissioning: in $ per (installed) kW_{e}.
Once minimal annual cash in (ci) is evaluated, the cost of electricity is deduced by dividing ci by the annual electricity production volume^{12} (P_{Elec,1Y}): (10) , cost of electricity; P_{Elec,1Y}, annual electricity production volume (kW_{e}h). ($ per kW_{e}h).
A numerical example of electricity cost calculation for a 1000 MW_{e} PWR is provided in Table 8. The results show good agreement with the evaluation reported in OECD' 2010 Projected Costs of Generating Electricity [9].
SPP (PWR 2748 MW_{th} → 1000 MW_{e}): electricity cost.
3.2 Dualpurpose plant
The traditional method (Method 1) for evaluating the cost of process heat consists in multiplying the cost of electricity, as calculated for SPP, by the expected decrease in electricity production.
Consider the 1000 MW_{e} PWR example of Table 8. According to the thermodynamic model described in the previous section, the reactor can produce up to 1730 MW_{th} of process heat at 80 °C. Each MW_{th}h supplied to the external process at this temperature will cause the reactor's net power output to decrease by 123 kW_{e}h (Wcost of heat). With a cost of electricity of 5.82 cents per kW_{e}h, the cost of heat would be equal to 7.15 $ per MW_{th}h (0.715 cents per kW_{th}h).
An alternative method of evaluating the cost of heat (Method 2) consists of considering a modified reactor design (DPP_{2}, cf. Tabs. 6 and 7) offering higher core power output compared to SPP. Such plant would generate the same amount of electricity as SPP (1000 MW_{e}) while meeting the demand of the external process in terms of thermal power (1000 MW_{th} at 80 °C).
At 80 °C, the Qcost of heat is equal to 338 kWh_{th} per MW_{th}. This means that, in order to produce 1000 MW_{th} of process heat at 80 °C, without affecting the electric power generation capacity, the core power has to be raised from 2748 to 3086 MW_{th} (+12.3%).
The effect of increasing core power on construction costs can be estimated based on the formula: (11)
Equation (11) assumes that:

–
Nuclear Island represents roughly x = 25% of the costs.

–
The cost relative to Nuclear Island:

Depends on core power exclusively.

Can be scaledup applying a capital scaling function^{13} with a scaling exponent equal to n = 0.6.^{14}


–
The remaining 75% of the costs depend solely on the plant power generation capacity (which is the same for both SPP and DPP).
The SinglePurpose 1000 MW_{e} PWR example of Table 8 costs 4.102 billion $ to construct. Adding 338 MW_{th} to core power would increase this cost by i = 1.8%. If x and n – which are rather uncertain – are uniformly distributed, in [15–35] (%) for x, and in [0.4–0.8] for n, i would have the distribution^{15} shown in Figure 6 (mean value for cost increase: 1.8%, standard deviation: 0.56%). A cost increase of 3.5% appears to be an upper limit.
Increasing core power has also an impact on fuel costs. A simple way to take it into account is to apply a correction factor (f) to SPP's specific fuel cost (Eq. (12)). Although SPP and DPP_{2} have the same power generation capacity, the annual electricity production volume can differ between the two plants depending on the availability of DPP_{2} vs. SPP. If we assume a 1% decrease in availability for DPP_{2} compared to SPP (84% for DPP_{2} vs. 85% for SPP), the increase in fuel costs would be equal to 12.31%. (12) P_{Elec,1Y,SPP}, annual electricity production volume, SPP (kW_{e}h); P_{Elec,1Y,DPP}, annual electricity production volume, DPP (kW_{e}h); P_{Core,1Y,SPP}, annual production volume, thermal power, SG, SPP (kW_{th}h); P_{Core,1Y,DPP}, annual production volume, thermal power, SG, DPP (kW_{th}h).
The rise in O&M expenses is expected to be less sensitive to the increase in core power compared to fuel costs. The correction factor (f′), applicable to SPP's specific O&M cost, is assumed to be the following: (13) Table 9 provides a preliminary economic evaluation of DPP_{2} vs. SPP. The cost of heat reported in this table is calculated following the steps listed below:

The – minimal annual cash in required to have a positive NPV – (ci_{DPP}) is calculated for DPP_{2}.

We assume that all electricity generated by DPP_{2} is sold at 5.82 cents per kW_{e}h – i.e. the cost of electricity as produced by SPP (c_{kWeh,SPP}).

We use the difference between, the – minimal annual cash in required to have a positive NPV – and, the – annual revenue generated from the sale of electricity – as a basis for evaluating the cost of heat (Eq. (14)).
The cost of heat, as calculated by this method (Method 2), is equal to 0.308 cent per kW_{th}h (80 °C), which represents 5.30% of the cost of electricity produced by SPP. This cost is 57% percent lower than the cost calculated by Method 1. Figure 7 shows how the cost varies with the level of temperature required by the external process.
At 75 °C, each kW_{th}h of thermal power supplied to the process costs 0.282 c$. At 100 °C, the cost rises to 0.408 c$ kW_{th}h^{−1} (×1.45), and at 125 °C it reaches 0.525 c$ kW_{th}h^{−1} (×1.86). These costs, estimated based on Method 2, represent 4.9–9.0% of the cost of electricity, depending on the steam extraction temperature (Fig. 8).
The ratio – cost of heat to cost of electricity – will be referred to as the Ecost of heat (ECH). ECH is subject to the size effect (Fig. 9). It is also sensitive to availability of the cogeneration plant, as shown in Figure 10.
Method 2 provides an alternative approach to converting MW_{th} to MW_{e}, considering the benefits of cogeneration – it allocates CAPEX and OPEX to the two byproducts – but also, the constraints introduced by the integrated system – higher expenses, extended construction period, lower availability, etc.
In the next section, we will use this method to compare two nuclearpowered integrated water and power plants, based on either, multieffect distillation, or, seawater RO.
Fig. 6 Number of entries (vertical axis) for which i equals a certain value (horizontal axis). 
DPP_{2} (PWR 3086 MW_{th} → 1000 MW_{e} + 1000 MW_{th} at 80 °C): electricity and heat costs.
Fig. 7 Cost of heat vs. temperature at the steam extraction point. 
Fig. 8 Cost of heat to cost of electricity vs. temperature at the steam extraction point. 
Fig. 9 Cost of heat to cost of electricity vs. temperature at the steam extraction point (Method 2) for different values of process thermal power (MW_{th}). 
Fig. 10 Cost of heat to cost of electricity vs. temperature at the steam extraction point (Method 2) for different values of (DPP_{2}) availability. 
4 Impact on the cost of desalination
4.1 MED process performance model
The MED process performance model aims at evaluating its specific thermal power consumption, in kW_{th}h m^{−3} for fresh water produced by the plant. Based on the simplified approach already implemented in the DEEP Code [16], the model follows the three steps described below:

–
First, the number of MED stages is determined (Eq. (15)) based on:

The temperatures at the first stage (top brine temperature) and the final condenser.

The average temperature drop between stages.


The gain output ratio (GOR) (kilograms of fresh water produced per kilogram of steam supplied to the process) is then estimated based on an average effect efficiency of 0.8:

The specific power consumption (kW_{th}h m^{−3}) is finally deduced:
A numerical example of MED process performance calculation is provided in Table 10.
The specific thermal power consumption evaluated by this model is sensitive to both, the temperature difference between MED effects, and, the stage average efficiency, as illustrated by Figures 11 and 12 .
Example of MED process performance calculation (1).
Fig. 11 MED specific thermal power consumption vs. top brine temperature. 1.5, 1.75, 2.0, 2.25, 2.5: average temperature drop between stages (°C). 
Fig. 12 MED specific thermal power consumption vs. top brine temperature. 0.7, 0.75, 0.8, 0.85, 0.9: GOR to number of stages. 
4.2 MED equivalent specific electric power consumption
The calculations, reported in this paragraph, are based on the following assumptions:

–
MED model inputs are basically those listed in Table 10. Only the top brine – and steam supply – temperatures vary.

–
A (pinch point temperature) difference of 5 °C between MED's steam supply temperature and the temperature at the steam extraction point (T_{SteamEx}, power conversion system).

–
Conversion of MED specific power thermal consumption to an electric equivalent is performed based on either:
Figure 13 shows how MED's equivalent electric power consumption^{16} varies with the top brine temperature (TBT). Conversion from W_{th} to W_{e} is based, in this case, on the Wcost of heat (WCH).
The power required to produce a cubic meter of fresh water, as calculated by Method 1, is higher for MED than for SWRO, except for processes operating at a TBT higher than 60, with a specific electric consumption lower than 1 kW_{e} m^{−3}, for which the equivalent electric power consumption is in the range 6–7 kW_{e} m^{−3}.
If the – cost of heat to cost of electricity – ratio (ECH), as calculated by Method 2, is used as a basis for converting W_{th} to W_{e}, MED's efficiency, in terms of energy utilization, is globally improved, as illustrated by Figure 14.
Figure 14 shows that, for specific consumptions in the range [1–4] kW_{e} m^{−3}, MED's equivalent electric power consumption varies between 3 and 6 kW_{e} m^{−3}, matching the range of the RO specific electric consumption as reported in literature.
MED's equivalent electric power consumption can be further reduced by, raising the TBT,^{17} decreasing the average temperature drop between MED stages,^{18} or, increasing MED effects' efficiency^{19} (GOR to number of stages), as illustrated by the example provided in Table 11.
Fig. 13 MED energy cost vs. top brine temperature. Based on Method 1. 1, 2, 3, 4: MED specific electric consumption equal to 1, 2, 3 and 4 kW_{e} m^{−3} respectively. min, mid, and max: minimal, medium and maximal specific electric consumption of the SWRO process as reported in literature. 
Fig. 14 MED energy cost vs. top brine temperature. Based on Method 2. 1, 2, 3, 4: MED specific electric consumption equal to 1, 2, 3 and 4 kW_{e} m^{−3} respectively. min, mid, and max: minimal, medium and maximal specific electric consumption of the SWRO process as reported in literature. 
Example of MED process performance calculation (2).
5 Conclusion
Process heat has an energetic and an economic cost that affects the cost of desalination. The exploratory study, described in this paper, attempted to evaluate these costs based on simplified models.
The power conversion system model provided a basis for assessing the “Wcost of heat” (WCH) – number of kW_{e} of “missed electricity production” per MW_{th} of process power – and the “Qcost of heat” (QCH) – number of kW_{th} of additional core power (required to keep a constant level of electricity production) per MW_{th}.
The economic model helped evaluate the “Ecost of heat” (ECH), defined as the ratio – cost of heat to cost of electricity – taking into account cogeneration's benefits and constraints.
The three costs – WCH, QCH, and ECH – depend primarily on the level of temperature required by the process. ECH also depends on the economic model's inputs.
This work confirms two conclusions from an earlier study by Rognoni et al. [8]:

Evaluating the heat cost on the basis of WCH (and the cost of electricity generated by a singlepurpose power plant) leads to higher energy costs for MED compared to SWRO.

A rigorous technoeconomic approach, duly considering the benefits of cogeneration, results in lower heat costs, and comparable equivalent electric power consumptions between MED and SWRO.
Energy is an important contributor to the cost of desalted water – a contributor among many others: construction, O&M, chemicals, insurance, labor… –. Evaluating the cost of desalted water should take into account all the expenses related to the project, including the investments needed to construct (or extend) water transfer and supply networks (IWPPs are generally located far from urban and industrial areas).
Water desalination plants produce huge amounts of reject brine. This brine can be turned into salt [17] or used to convert CO_{2} into useful and reusable products such as sodium bicarbonate [18]. These processes – still under development – can potentially improve the economics of seawater desalination while minimizing the impact of brine discharge on the environment.
To identify the most appropriate reactorprocess combination for a given site, casespecific evaluations have to be performed, considering the precise characteristics of the power generation system, the reactor to process heat transfer loop, the seawater desalination unit, and the water transport system. Other important factors have also to be considered such as the final use of the product, the quality of the feed, the – intake, pretreatment, posttreatment and brine reject – structures, and the variability of the demand for power and water.
Abbreviations
DEEP: desalination economic evaluation program (Software)
IAEA: international atomic energy agency
ICV: interconnected control volumes (software)
IWPP: integrated water and power plant
O&M: operation and maintenance
PWR: pressurized water reactor
SteamEx: steam extraction point
SWRO: seawater reverse osmosis
Appendix
Cost of heat vs. temperature at the extraction point.
T  WCH  QCH  ECH  T  WCH  QCH  ECH 

33  0  1  7  81  125  345  54 
34  3  9  8  82  128  351  55 
35  6  17  9  83  130  358  56 
36  9  25  10  84  133  364  57 
37  12  32  11  85  135  371  57 
38  15  40  12  86  137  377  58 
39  17  48  14  87  140  384  59 
40  20  56  15  88  142  390  60 
41  23  63  16  89  144  396  61 
42  26  71  17  90  147  403  62 
43  28  78  18  91  149  409  63 
44  31  86  19  92  151  415  63 
45  34  93  20  93  153  422  64 
46  37  101  21  94  156  428  65 
47  39  108  22  95  158  434  66 
48  42  116  23  96  160  440  67 
49  45  123  24  97  162  447  68 
50  47  131  25  98  165  453  68 
51  50  138  26  99  167  459  69 
52  53  145  27  100  169  465  70 
53  55  152  28  101  171  471  71 
54  58  160  29  102  174  478  72 
55  61  167  30  103  176  484  73 
56  63  174  31  104  178  490  73 
57  66  181  32  105  180  496  74 
58  68  188  33  106  183  502  75 
59  71  195  34  107  185  508  76 
60  74  202  35  108  187  514  77 
61  76  209  36  109  189  520  78 
62  79  216  36  110  191  526  78 
63  81  223  37  111  193  532  79 
64  84  230  38  112  196  538  80 
65  86  237  39  113  198  544  81 
66  89  244  40  114  200  550  82 
67  91  251  41  115  202  556  82 
68  94  258  42  116  204  562  83 
69  96  265  43  117  206  568  84 
70  99  271  44  118  208  574  85 
71  101  278  45  119  211  580  85 
72  104  285  46  120  213  586  86 
73  106  292  47  121  215  592  87 
74  109  298  48  122  217  598  88 
75  111  305  49  123  219  603  89 
76  113  312  49  124  221  609  89 
77  116  318  50  125  223  615  90 
78  118  325  51  126  225  621  91 
79  121  332  52  127  227  627  92 
80  123  338  53  128  230  633  92 
T, temperature at the extraction point (°C); WCH, Wcost of heat (kW_{e} of “missed electricity production” per MW_{th} supplied to the process); QCH, Qcost of heat (kW_{th} of additional core thermal power per MW_{th} supplied to the process); ECH, Ecost of heat (kW_{e} of electricity per MW_{th} supplied to the process).
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ICV simulates the steadystate behavior of components such as boilers, heat exchangers, pumps, compressors and turbines, as well as workflows – typically heat transfer loops and power conversion cycles – based on these components. ICV has a buildin library providing the properties of steam and water [12], including salinewater [13].
Capital cost scaling functions are often used to account for economies of scale (as the nuclear island gets larger in size, it gets progressively cheaper to add additional capacity). Examples from the power generation industry are provided in [14].
Cite this article as: Saied Dardour, Henri Safa, Energetic and economic cost of nuclear heat − impact on the cost of desalination, EPJ Nuclear Sci. Technol. 3, 1 (2017)
All Tables
DPP_{1} (PWR 2748 MW_{th} → 877 MW_{e} + 1000 MW_{th} at 80 °C): thermodynamic points.
DPP_{1} (PWR 2748 MW_{th} → 877 MW_{e} + 1000 MW_{th} at 80 °C): mechanical and thermal powers.
DPP_{2} (PWR 3086 MW_{th} → 1000 MW_{e} + 1000 MW_{th} at 80 °C): thermodynamic points.
DPP_{2} (PWR 3086 MW_{th} → 1000 MW_{e} + 1000 MW_{th} at 80 °C): mechanical and thermal powers.
DPP_{2} (PWR 3086 MW_{th} → 1000 MW_{e} + 1000 MW_{th} at 80 °C): electricity and heat costs.
All Figures
Fig. 1 Total worldwide installed capacity by technology. 

In the text 
Fig. 2 Power conversion system architecture. 

In the text 
Fig. 3 Contribution of steam turbines to SPP's electricity output. 

In the text 
Fig. 4 Available heat for the external process vs. temperature at the steam extraction point. Blue bar: PWR 1000 MWe (2748 MWth); orange bar: PWR 1650 MWe (4534 MWth). 

In the text 
Fig. 5 WCH and QCH vs. temperature at the steam extraction point. 

In the text 
Fig. 6 Number of entries (vertical axis) for which i equals a certain value (horizontal axis). 

In the text 
Fig. 7 Cost of heat vs. temperature at the steam extraction point. 

In the text 
Fig. 8 Cost of heat to cost of electricity vs. temperature at the steam extraction point. 

In the text 
Fig. 9 Cost of heat to cost of electricity vs. temperature at the steam extraction point (Method 2) for different values of process thermal power (MW_{th}). 

In the text 
Fig. 10 Cost of heat to cost of electricity vs. temperature at the steam extraction point (Method 2) for different values of (DPP_{2}) availability. 

In the text 
Fig. 11 MED specific thermal power consumption vs. top brine temperature. 1.5, 1.75, 2.0, 2.25, 2.5: average temperature drop between stages (°C). 

In the text 
Fig. 12 MED specific thermal power consumption vs. top brine temperature. 0.7, 0.75, 0.8, 0.85, 0.9: GOR to number of stages. 

In the text 
Fig. 13 MED energy cost vs. top brine temperature. Based on Method 1. 1, 2, 3, 4: MED specific electric consumption equal to 1, 2, 3 and 4 kW_{e} m^{−3} respectively. min, mid, and max: minimal, medium and maximal specific electric consumption of the SWRO process as reported in literature. 

In the text 
Fig. 14 MED energy cost vs. top brine temperature. Based on Method 2. 1, 2, 3, 4: MED specific electric consumption equal to 1, 2, 3 and 4 kW_{e} m^{−3} respectively. min, mid, and max: minimal, medium and maximal specific electric consumption of the SWRO process as reported in literature. 

In the text 
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