Open Access
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

© S. Dardour and H. Safa, published by EDP Sciences, 2017

Licence Creative Commons
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 – multi-effect evaporation (MED) and multi-stage flash (MSF), mostly in the Middle East.

Seawater desalination is an energy-intensive 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 kWeh m−3 [4]. Some plants, producing large amount of desalinated water, claim even lower energy consumption; 3.5 kWeh m−3 for Ashkelon, Israel [4]; and 2.7–3.1 kWeh 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 kWhth m−3 for MED, and 55–80 kWhth 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 kWhe m−3 [7]. MED manufacturers claim specific electricity consumptions lower than 2.5 kWhe m−3.

thumbnail Fig. 1

Total worldwide installed capacity by technology.

1.1 Power consumption: thermal desalination systems vs. membrane-based 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 kWhe m−3 of “missed electricity production” according to [2]. If we add 1.2–2.5 kWhe m−3 of pumping energy, we end up with an equivalent electric power consumption in the range [5.2–9.5] kWhe 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 MWth 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 cost-effective than SWRO. The authors provided two-calculation examples – MED processes fueled by coal-fired power plants in India – for which the cost of desalinated water is 50% lower than SWRO's.

1.2 “Nuclear steamcost

The cost of process heat depends on the contribution, to the total cost of electricity, of fuel-related expenses – a contribution widely considered to be lower for nuclear-powered 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 (MED3) and membrane-based (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 dual-purpose 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 high-pressure body of the turbine (HPT1 and HPT2). The fluid is then dried-up and superheated before supplying the low-pressure stages (LPT1, LPT2 and LPT3). Liquid water extracted from the condenser (Condenser2) is finally preheated and readmitted back to SG.

A steam extraction point was positioned between the outlet of LPT2 and the inlet of LPT3. This location allows for a variable quantity (y = 0–100%) of steam (the steam normally flowing through LPT3) to be diverted to an external process. The pressure at the steam extraction point (PSteamEx) may vary between 0.05 bar (pressure at the condenser) and 2.685 bar (pressure at LPT2 outlet), and the temperature (TSteamEx) 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 Condenser1, the latent heat of condensation is transferred to the external process. Condenser2 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.

thumbnail 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 in-house 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 (WElec) and process heat (QPro) 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 (QSG);

  • the temperature at the steam extraction point (TSteamEx);

  • the fraction of steam (normally expending through LPT3) 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); v2/2, 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 constant-entropy 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 losses7 are not taken into account (the calculated “net” power and heat outputs are actually “gross” power and heat outputs).

Table 1

Assumed pressure distribution.

2.3 Energetic performance of the PCS

Tables 2 and 3 show the characteristics of a 2748 MWth single-purpose plant (SPP) generating 1000 MWe of electricity.

The contribution of steam turbines to SPP's electricity output is shown in Figure 3. LPT3 delivers 213 MWe 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 (TSteamEx = 80 °C), the plant would generate 787 MWe of electricity and 1730 MWth 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 MWe of electricity and 1000 MWth of heat. The characteristics of configuration – we will call it DPP1 (dual-purpose plant) – are listed in Tables 4 and 5.

The differences between SPP and DPP1 are highlighted (underlined) in Tables 25. The two Rankine cycles have identical characteristics except for points 10–12. In DPP1, turbine LPT3 is partly bypassed – the exergy of the rerouted steam is later “destructed” in Condenser1 – resulting in a 123 MWe decrease in power generation compared to SPP.

The number of MWe of electricity production lost for each MWth supplied to the external process (123 kWe per MWth in the case of DPP1) is a traditional measure of the energetic cost of process heat. This measure will be referred to as the “W-cost 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 MWe – and the heat production level at 1000 MWth – SG have to deliver an additional 338 MWth. The portion of diverted steam has also to be adjusted (51.5%). This configuration – we will call it DPP2 (Tabs. 6 and 7) – not only offers higher power conversion efficiency (32.40%) compared to DPP1 (31.91%), but also results in lower heat cost, as we will see in Section 2.

The number of MWth added to core power, per MWth supplied to the external process (338 kWth per MWth in the case of DPP2) provides an alternative measure of the energetic cost of steam – we will call it the “Q-cost 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 TSteamEx. At 75 °C, each MWthh of thermal power supplied to the process costs 111 kWeh of electricity. At 100 °C, the cost increases to 169 kWeh MWthh−1 (×1.5), and at 125 °C it reaches 223 kWeh MWthh−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)

Table 2

SPP (PWR 2748 MWth → 1000 MWe): thermodynamic points.

Table 3

SPP (PWR 2748 MWth → 1000 MWe): mechanical and thermal powers.

thumbnail Fig. 3

Contribution of steam turbines to SPP's electricity output.

thumbnail 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).

Table 4

DPP1 (PWR 2748 MWth → 877 MWe + 1000 MWth at 80 °C): thermodynamic points.

Table 5

DPP1 (PWR 2748 MWth → 877 MWe + 1000 MWth at 80 °C): mechanical and thermal powers.

Table 6

DPP2 (PWR 3086 MWth → 1000 MWe + 1000 MWth at 80 °C): thermodynamic points.

Table 7

DPP2 (PWR 3086 MWth → 1000 MWe + 1000 MWth at 80 °C): mechanical and thermal powers.

thumbnail Fig. 5

WCH and QCH vs. temperature at the steam extraction point.

3 Economic cost of heat

3.1 Single-purpose plant

To evaluate the cost of electricity relative a single-purpose 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) cocst, annual cash out, construction period, ($); npv (1$, cst), NPV of a fixed expense of 1$ per year, spent during the construction period, ($); ci, annual revenue generated from the sale of electricity, ($); coopr, 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; codcm, 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 periods8: (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 expenses10 (construction, fuel, O&M and decommissioning) are evaluated on the basis of specific costs:

  • The specific cost of construction11: in $ per (installed) kWe.

  • The specific cost of fuel: in $ per (produced) MWeh.

  • The specific cost of O&M: in $ per (produced) MWeh.

  • The specific cost of decommissioning: in $ per (installed) kWe.

Once minimal annual cash in (ci) is evaluated, the cost of electricity is deduced by dividing ci by the annual electricity production volume12 (PElec,1Y): (10) , cost of electricity; PElec,1Y, annual electricity production volume (kWeh). ($ per kWeh).

A numerical example of electricity cost calculation for a 1000 MWe PWR is provided in Table 8. The results show good agreement with the evaluation reported in OECD' 2010 Projected Costs of Generating Electricity [9].

Table 8

SPP (PWR 2748 MWth → 1000 MWe): electricity cost.

3.2 Dual-purpose 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 MWe PWR example of Table 8. According to the thermodynamic model described in the previous section, the reactor can produce up to 1730 MWth of process heat at 80 °C. Each MWthh supplied to the external process at this temperature will cause the reactor's net power output to decrease by 123 kWeh (W-cost of heat). With a cost of electricity of 5.82 cents per kWeh, the cost of heat would be equal to 7.15 $ per MWthh (0.715 cents per kWthh).

An alternative method of evaluating the cost of heat (Method 2) consists of considering a modified reactor design (DPP2, 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 MWe) while meeting the demand of the external process in terms of thermal power (1000 MWth at 80 °C).

At 80 °C, the Q-cost of heat is equal to 338 kWhth per MWth. This means that, in order to produce 1000 MWth of process heat at 80 °C, without affecting the electric power generation capacity, the core power has to be raised from 2748 to 3086 MWth (+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 scaled-up applying a capital scaling function13 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 Single-Purpose 1000 MWe PWR example of Table 8 costs 4.102 billion $ to construct. Adding 338 MWth 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 distribution15 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 DPP2 have the same power generation capacity, the annual electricity production volume can differ between the two plants depending on the availability of DPP2 vs. SPP. If we assume a 1% decrease in availability for DPP2 compared to SPP (84% for DPP2 vs. 85% for SPP), the increase in fuel costs would be equal to 12.31%. (12) PElec,1Y,SPP, annual electricity production volume, SPP (kWeh); PElec,1Y,DPP, annual electricity production volume, DPP (kWeh); PCore,1Y,SPP, annual production volume, thermal power, SG, SPP (kWthh); PCore,1Y,DPP, annual production volume, thermal power, SG, DPP (kWthh).

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 DPP2 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 – (ciDPP) is calculated for DPP2.

  • We assume that all electricity generated by DPP2 is sold at 5.82 cents per kWeh – i.e. the cost of electricity as produced by SPP (ckWeh,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)).

(14)

The cost of heat, as calculated by this method (Method 2), is equal to 0.308 cent per kWthh (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 kWthh of thermal power supplied to the process costs 0.282 c$. At 100 °C, the cost rises to 0.408 c$ kWthh−1 (×1.45), and at 125 °C it reaches 0.525 c$ kWthh−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 E-cost 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 MWth to MWe, 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 nuclear-powered integrated water and power plants, based on either, multi-effect distillation, or, seawater RO.

thumbnail Fig. 6

Number of entries (vertical axis) for which i equals a certain value (horizontal axis).

Table 9

DPP2 (PWR 3086 MWth → 1000 MWe + 1000 MWth at 80 °C): electricity and heat costs.

thumbnail Fig. 7

Cost of heat vs. temperature at the steam extraction point.

thumbnail Fig. 8

Cost of heat to cost of electricity vs. temperature at the steam extraction point.

thumbnail 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 (MWth).

thumbnail Fig. 10

Cost of heat to cost of electricity vs. temperature at the steam extraction point (Method 2) for different values of (DPP2) 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 kWthh 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.

(15) NStages, number of stages; int (function), round down real numbers to the nearest integer; Tmax, top brine temperature, (°C); Tmin, temperature at the final condenser, (°C); ΔTStages, average temperature drop between stages, (°C).
  • 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:

(16)
  • The specific power consumption (kWthh m−3) is finally deduced:

(17) L, latent heat at steam supply temperature, (kJ kg−1).

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 .

Table 10

Example of MED process performance calculation (1).

thumbnail 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).

thumbnail 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 (TSteamEx, power conversion system).

  • Conversion of MED specific power thermal consumption to an electric equivalent is performed based on either:

    • the W-cost of heat (cf. Sect. 2.3) (Method 1), or,

    • the – cost of heat to cost of electricity – ratio (ECH) as calculated by Method 2 (cf. Sect. 3.2).

Figure 13 shows how MED's equivalent electric power consumption16 varies with the top brine temperature (TBT). Conversion from Wth to We is based, in this case, on the W-cost 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 kWe m−3, for which the equivalent electric power consumption is in the range 6–7 kWe 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 Wth to We, 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] kWe m−3, MED's equivalent electric power consumption varies between 3 and 6 kWe 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' efficiency19 (GOR to number of stages), as illustrated by the example provided in Table 11.

thumbnail 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 kWe m−3 respectively. min, mid, and max: minimal, medium and maximal specific electric consumption of the SWRO process as reported in literature.

thumbnail 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 kWe m−3 respectively. min, mid, and max: minimal, medium and maximal specific electric consumption of the SWRO process as reported in literature.

Table 11

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 “W-cost of heat” (WCH) – number of kWe of “missed electricity production” per MWth of process power – and the “Q-cost of heat” (QCH) – number of kWth of additional core power (required to keep a constant level of electricity production) per MWth.

The economic model helped evaluate the “E-cost 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 single-purpose power plant) leads to higher energy costs for MED compared to SWRO.

  • A rigorous techno-economic 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 CO2 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 reactor-process combination for a given site, case-specific 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, post-treatment and brine reject – structures, and the variability of the demand for power and water.

Abbreviations

CAPEX: capital expenditures

DEEP: desalination economic evaluation program (Software)

DPP: dual-purpose plant

ECH: E-cost of heat

ED: electrodialysis

GOR: gain output ratio

HPT: high pressure turbine

IAEA: international atomic energy agency

ICV: interconnected control volumes (software)

IWPP: integrated water and power plant

LPT: low pressure turbine

MED: multi-effect evaporation

MSF: multi-stage flash

NPV: net present value

O&M: operation and maintenance

OPEX: operating expenditures

PCS: power conversion system

PWR: pressurized water reactor

QCH: Q-cost of heat

RO: reverse osmosis

SG: steam generator

SPP: single-purpose plant

SteamEx: steam extraction point

SWRO: seawater reverse osmosis

TBT: top brine temperature

WCH: W-cost of heat

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, W-cost of heat (kWe of “missed electricity production” per MWth supplied to the process); QCH, Q-cost of heat (kWth of additional core thermal power per MWth supplied to the process); ECH, E-cost of heat (kWe of electricity per MWth supplied to the process).

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1

Energy is, in many cases, the largest contributor to the desalted water cost, varying from one-third to more than one-half of the cost of produced water.

2

MED's top brine temperature (TBT) generally varies between 60 and 75 °C. MSF's TBT is higher, 90–110 °C.

3

MSF is out of scope in this paper, as it consumes higher amounts of energy compared to MED.

4

ICV simulates the steady-state 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 build-in library providing the properties of steam and water [12], including saline-water [13].

5

Mass of vapor to total mass in a saturated liquid–vapor mixture. Values lower than 0 or higher than 1 indicate that the fluid is either subcooled (−100) or superheated (200).

6

In practice, the “kinetic + potential energies” term of equation (2) is neglected, leading to a simpler formulation of the energy conservation principle.

7

Thermal losses at heat exchangers. Mechanical losses at pumps, turbines and generators. Electrical power consumption, internal to the power plant and the external process.

8

Increasing the fission power of the core is not always technologically feasible, especially for plants that are already “big”.

9

Traditionally, the rate used in discounted cash flow analysis is adjusted for risk, period by period. This is not the case for this exercise.

10

All expenses are considered “overnight”, i.e. interest free. Inflation (fuel cost escalation in particular) is not taken into account.

11

Owner's, construction and contingency costs.

12

The annual electricity production volume is evaluated from the reference electric power generation capacity assuming a constant average availability of the plant.

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].

14

When n is unknown, a value of 0.6 is generally assumed (rule of six-tenths).

15

Figure 6 was obtained after (Latin Hypercube) sampling of two inputs, carried out using CEA's open source software URANIE [15].

16

Electric equivalent of the thermal power supplied by the nuclear reactor, plus, electric power consumption internal to the process.

17

Raising the TBT exposes the plant to severe corrosion and scaling problems. In recent years, many of these problems have been solved thanks to improvements in materials and anti-scalants.

18

Reducing the temperature difference requires larger heat transfer surfaces.

19

Effect efficiency can be improved by reducing thermal losses.

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

Table 1

Assumed pressure distribution.

Table 2

SPP (PWR 2748 MWth → 1000 MWe): thermodynamic points.

Table 3

SPP (PWR 2748 MWth → 1000 MWe): mechanical and thermal powers.

Table 4

DPP1 (PWR 2748 MWth → 877 MWe + 1000 MWth at 80 °C): thermodynamic points.

Table 5

DPP1 (PWR 2748 MWth → 877 MWe + 1000 MWth at 80 °C): mechanical and thermal powers.

Table 6

DPP2 (PWR 3086 MWth → 1000 MWe + 1000 MWth at 80 °C): thermodynamic points.

Table 7

DPP2 (PWR 3086 MWth → 1000 MWe + 1000 MWth at 80 °C): mechanical and thermal powers.

Table 8

SPP (PWR 2748 MWth → 1000 MWe): electricity cost.

Table 9

DPP2 (PWR 3086 MWth → 1000 MWe + 1000 MWth at 80 °C): electricity and heat costs.

Table 10

Example of MED process performance calculation (1).

Table 11

Example of MED process performance calculation (2).

All Figures

thumbnail Fig. 1

Total worldwide installed capacity by technology.

In the text
thumbnail Fig. 2

Power conversion system architecture.

In the text
thumbnail Fig. 3

Contribution of steam turbines to SPP's electricity output.

In the text
thumbnail 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
thumbnail Fig. 5

WCH and QCH vs. temperature at the steam extraction point.

In the text
thumbnail Fig. 6

Number of entries (vertical axis) for which i equals a certain value (horizontal axis).

In the text
thumbnail Fig. 7

Cost of heat vs. temperature at the steam extraction point.

In the text
thumbnail Fig. 8

Cost of heat to cost of electricity vs. temperature at the steam extraction point.

In the text
thumbnail 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 (MWth).

In the text
thumbnail Fig. 10

Cost of heat to cost of electricity vs. temperature at the steam extraction point (Method 2) for different values of (DPP2) availability.

In the text
thumbnail 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
thumbnail 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
thumbnail 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 kWe 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
thumbnail 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 kWe 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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