A Preliminary Exergy Analysis of the EU DEMO Fusion Reactor

The Energy Storage System (ESS) is part of the Intermediate Heat Transfer System (IHTS) designed to feed the PCS releasing steady-state electric power to the electricity grid. The current design of the ESS is constituted by two different tanks filled in with molten salt and connected by a pipeline in which molten salt flows in two directions depending on the operating phase of the reactor [4]. During the pulse phase, the molten salt is moved from the cold tank to the hot tank after heat exchange with the cooling water conveyed from the FW PHTS. The hot tank stores the high temperature molten salt heated through two intermediate water-salt heat exchangers. The cold tank recovers the low temperature molten salt cooled during the dwell phase to produce the superheated steam conveyed to turbines of the PCS. This configuration requires the pumping of molten salt from the cold tank to the hot tank during dwell mode and vice versa during the opposite mode.

As far as the molten salt is concerned, HITEC is the commercial product of a ternary salt characterized by chemical, physical and thermodynamic properties suitable for process conditions requested by the ESS plant. HITEC is a eutectic mixture of water-soluble and inorganic salts of potassium nitrate KNO₃, sodium nitrate NaNO₃ and sodium nitrite NaNO₂ [5] with the following composition: 7 % of NaNO₃, molecular weight 84.995 g/mol; 40 % of NaNO₂ molecular weight 69.0 g/mol; 53 % of KNO₃ molecular weight 101.103 g/mol; the molecular weight of the mixture equal to 87.134 g/mol.

The design of the ESS relies on the following parameters characterizing the physical properties and the behaviour of molten salt during heating and cooling phases: liquid phase specific heat, melting-solidification latent heat, maximum allowable temperature, solidification temperature, viscosity v/s temperature, salt mass used in ESS system.

HITEC molten salt specific heat at constant pressure is c_p = 1.56 kJ/(kg K) and it is suggested to be considered as constant value with temperature independence. However, expressions are available in the literature [6] to calculate enthalpy and entropy for ESS design.

During the pulse (2 h) the BZ PHTS thermal power (1483 MW_th) is delivered to the PCS. The FW PHTS delivers a thermal power of 439.8 MW_th to the ESS: a fraction of this power is transferred to the PCS, 265.9 MW_th, and 173.9 MW_th are stored during the pulse phase corresponding to a stored energy of 1.25×10⁶ MJ that will be delivered to the PCS during the dwell time. The thermal power during the pulse period is transferred from the ESS to the PCS through one Helical Coil Steam Generator (HCSG). The hot molten salt flows in shell side and transfers thermal energy to water flowing in the tube side. The molten salt temperature cycle is 280-320 ℃. The feedwater enters in the HCSG with an inlet temperature of 238 ℃ and exits with an outlet temperature of 299 ℃ at 6.41 MPa. The HCSG mass flow rate of HITEC is 4375.4 kg/s, and the feedwater mass flow rate, calculated with the enthalpy balance, is 284.1 kg/s.

During the dwell time (600 s), the mass flow of molten salt from hot to cold tanks is 33436 kg/s. The ESS tank contains 20062 t of molten salt at the beginning of dwell, thus about 11000 m³ are needed to store this mass. In this phase, the ESS delivers power to PCS through four HCSGs. The average power available in dwell mode is approximately 2086 MW_th, thus the power of each HCSG is 521.5 MW_th. It is noteworthy that, one out of the four HCSGs is the one operating during pulse time to transfer 265.9 MW_th, as described. The thermal power recovered from Divertor Cassette, Divertor Plasma Facing Components (PFC) and Vacuum Vessel (VV), is used in the feedwater regenerative preheating through specifically designed heat exchangers. Figure 1 shows the PHTS boundary conditions accounted for in the design of the PCS carried out by means of GateCycle^TM application. The output data and information have been gathered in a spreadsheet here adopted for further calculations of interest.

The objective of the present study is to provide a Second Law analysis of all components based on the exergy method to adopt a rigorous and complete approach to assess dissipation phenomena having an impact in the efficiency of the plant.

The literature reports definitions and applications relating to properties underpinning the exergy method and the Second Law analysis [7-8]. The ESS is essentially characterized by the contribution of thermal energy transfer by means of heat interactions occurring in different types of exchangers. In addition, the mechanical exergy balance is accounted for. Calculation of exergy are based on the process conditions and properties deriving from the IHTS design and optimization; all data and information relating to stream interested in the present verification analysis of IHTS are those reported in the literature [1] as the result of a design project. Hence, dimensions and materials of plant components are not directly involved in this exergy analysis and, therefore, are not addressed to along calculations. Finally, the exergy balance is obtained from the algebraic sum of contributions pertaining to all components constituting the ESS. As far as the dissipation processes are concerned, the heat and mass interaction flows internally to water and molten salt are neglected. Two options are considered for the PCS supply during dwell phase: (1) ESS with molten salt hot and cold tanks; (2) methane fuelled fired boiler for steam production. As far as the reference system R is concerned, the environment conventional conditions corresponding to 298 K and 1 bar is assumed. Therefore, water is in sub-cooled liquid state and its reference thermodynamic properties to calculate exergy are the specific enthalpy h_R=104.877 kJ⁄kg and the specific entropy s_R=0.367 kJ⁄((kg K) ). Among those thermodynamic properties of molten salt in the liquid state implied in the exergy analysis, the following expressions are here adopted for enthalpy and entropy [6]:

$h-{{h}_{R}}=\int_{298.15}^{{{T}_{MELT}}}{{{c}_{p}}dT}+\Delta {{h}_{MELT}}+\int_{{{T}_{MELT}}}^{T}{{{c}_{p}}dT}=0.8\times {{10}^{-1}}{{T}^{2}}+27.75T-14568.9J/mol$  (4)

$s-{{s}_{R}}=\int_{298.15}^{{{T}_{MELT}}}{\frac{{{c}_{P}}}{T}dT}+\frac{\Delta {{h}_{MELT}}}{{{T}_{MELT}}}+\int_{{{T}_{MELT}}}^{T}{\frac{{{c}_{P}}}{T}dT}=1.6\cdot {{10}^{-1}}T+27.75\ln T-202.83J/(mol.K)$  (5)

These properties are calculated with respect to the reference environment condition and are specially defined to calculate the thermal exergy variations along the ESS process. In order to ensure the uniformity with the unit of measure system here adopted, the numerical results of above functions are divided by the molecular weight of the molten salt to obtain kJ⁄kg and kJ⁄(kgK) respectively. Calculations have been carried out on the basis of GateCycle^TM program output resulting from the design of plant configuration as described in the process flow diagram [10].

4.1 Thermal exergy

The canonical definition of specific thermal exergy for open bulk flow systems, through the control volume defining the contributing streams to the plant, is the following [7-8]:

$ex^T=(h-h_R )-T_R (s-s_R )$ (6)

in which h and s are the specific enthalpy and specific entropy at the generic thermodynamic condition of the system and h_R and s_R are the same properties at the reference state conditions of the reservoir represented by the environment. the above expression is used to evaluate the exergy balance of all heat exchangers operating in the plant. As far as the thermal exergy rates, the following expression is adopted that accounts for mass flowrates:

$\dot{EX}^T=\dot{m}⋅(h-h_R )-T_R (s-s_R )$ (7)

1.png

Figure 1. Process flow diagram of EU DEMO with ESS configuration

4.2 Chemical exergy

The comparison of performances provided by the two plant configuration options under discussion needs to evaluate the chemical exergy of the methane combustion process in the auxiliary boiler. To do so, the canonical definition of specific molar chemical exergy for open systems is adopted. The special case of hydrocarbons can be handled considering the following typical combustion reaction:

$aCO_2+\frac{b}{2}H_2 O↔C_a H_b+(a+\frac{b}{4}) O_2$ (8)

It relies on the molar fractions of constituents of substances and is expressed in the form here reported [7-8] based on the difference of hydrocarbon chemical potential μ before and after the reaction at the reference system represented by the environmental reservoir R:

$\overline{ex}_{{{C}_{a}}{{H}_{b}}}^{C}={{\mu }_{{{C}_{a}}{{H}_{b}}}}-\mu _{{{C}_{a}}{{H}_{b}}}^{R}={{\left[ {{{\bar{g}}}_{{{C}_{a}}{{H}_{b}}}}+\left( a+\frac{b}{4} \right){{{\bar{g}}}_{{{O}_{2}}}}-a{{{\bar{g}}}_{C{{O}_{2}}}}-\frac{b}{2}{{{\bar{g}}}_{{{H}_{2}}O}} \right]}_{{{T}_{R}},{{p}_{R}}}}+\bar{R}{{T}_{R}}\ln \left[ \frac{{{\left( x_{{{O}_{2}}}^{R} \right)}^{a+b/4}}}{{{\left( x_{C{{O}_{2}}}^{R} \right)}^{a}}{{\left( x_{{{H}_{2}}O}^{R} \right)}^{b/2}}} \right]$ (9)

where x_i is the molar fraction of each i-th constituent appearing in the equation and $\overline{g_i}$ is the molar Gibbs chemical potential at standard conditions of T_R=298.15 K and p_R=101.325 kPa.

4.3 Mechanical exergy

The use of mechanical exergy is specially devised and here adopted to evaluate the second law performance of steam turbines [9-10]. The mechanical exergy does not account for the operating fluid mass kinetic energy and gravitational or electro-magnetic potential energy of the whole mass referred to its center of gravity. These components, termed as kinetic exergy and potential exergy respectively, are neglected when considering the balance of a plant. Then, mechanical exergy accounts for internal mechanical energy $u^M=u^M(p)=-pV$ that depends on pressure and volume entering and exiting the control volume identifying the elemental machine stage operating along an adiabatic process of a steam turbine. An adiabatic reversible process is defined as isoentropic since no heat interactions occur along the expansion (or compression) process. Then, the thermal exergy, defined in terms of maximum net useful work, with null variation of entropy in the expression $ex^T=(h-h_R )^T-T_R (s^T-s_R^T )$, should be coincident with the enthalpy change between input and output states, $Δex^T=W=h_{OUT}-h_{IN}$. Though, this definition is pertaining to thermal exergy associated to the thermal internal energy $u^T=u^T (T)=Ts$ while the adiabatic expansion releasing internal work is associated to the mechanical component of internal energy. Instead, the mechanical exergy, should be defined as the maximum net useful heat depending on the difference of mechanical internal energy between inlet and outlet operating fluid states. The definition $ex^M=(h-h_R )^M+p_R v_R (s^M-s_R^M )$ is suitable to evaluate this capability associated to pressure and the volume with respect to pressure and specific volume of the reference state of the reservoir. The term $p_R v(s^M-s_R^M )$ represents the mechanical exergy loss, or the non-useful work released to the reservoir at $p_R v_R$. Indeed, this term accounts for the fact that, although the variation of enthalpy equals the work interaction released to the external system, the capability in terms of work-to-heat conversion through and ideal cycle is not the same due to the different pressure-to-volume relationship that determines a different available mechanical internal energy. The energy loss in terms of non-useful work interaction released to the reservoir has to be accounted for in the exergy balance of steam turbines. Hence, for a steam turbine stage the following equations apply:

Input: ${ex}_{IN}^M=h_{IN}+p_R v_R (s_{IN}^M-s_R^M )$ (10)

Output: $W_{OUT}^{EXT}⇔{ex}_{OUT}^M={Q_{IN-OUT}^{AR→} }_{WORK}^{MAX} {ex}_{OUT}^M=h_{OUT}+p_R v_R {s_{OUT}^M-s_R^M }$

$ex_{DES}^M=p_R v_R {s^{IRR} }^M$ (11)

The steam turbine mechanical exergy balance along a real process is the following:

$Δex^M=Δex_REV^M+Δex_IRR^M$ $= (h_{OUT}-h_{IN} )+p_R v_R (s_OUT^REV-s_IN^REV )^M+p_R v_R (s^IRR )^M$ (12)

where the term $p_R v_R (s^IRR )^M$ represents the mechanical exergy destruction.

4.4 Irreversible processes and exergy destruction

Real processes imply irreversible phenomena determining an amount of entropy production. The Gouy-Stodola theorem ensures the direct relationship between entropy production and exergy destruction as expressed by the following relation [8]:

${ex}_{DES}^T=T_R s_{IRR}^T$ (13)

A formulation extended to all type of irreversible processes should account for chemical exergy destruction and mechanical exergy destruction, according to the following generalized version of Gouy-Stodola theorem:

${ex}_{DES}^G={ex}_{DES}^T+{ex}_{DES}^C+{ex}_{DES}^M=T_R s_{IRR}^T+μ_R s_{IRR}^C+p_R v_R s_{IRR}^M$ (14)

That considers the generalized reservoir conditions at T_R, μ_R and p_R ensuring the equality of all thermodynamic potentials and the stable equilibrium state.

4.5 Exergy balance and exergy efficiency

The calculation of exergy balance of a component is obtained considering the difference of exergy content of entering and exiting mass of the same stream through the control volume. However, in case of a single stream entering without exiting or, vice versa, exiting without entering, the exergy property has to be calculated based on the canonical definition with respect to the external reference system or environment.

The exergy balance is calculated in terms of exergy rate to account for the total exergy associated to the amount of mass contributing to the balance of any plant component. Therefore, for each component the balance is expressed in terms of exergy flows.

As far as the overall efficiency is concerned, the fuel and product streams are used in the literature to define the exergetic efficiency as follows:

$\eta _{OV}^{EX}=\prod\nolimits_{j=1}^{n}{\eta _{j}^{EX}=}\prod\nolimits_{j=1}^{n}{1-\frac{E{{{\dot{X}}}_{D}}}{E{{{\dot{X}}}_{{{F}_{1}}}}}=1-\frac{E{{{\dot{X}}}_{D}}}{\sum\nolimits_{j=1}^{m}{E{{{\dot{X}}}_{{{F}_{1}}}}}}}$ (15)

where the symbols D and F stand for destruction and fuel respectively. Anyway, for sake of clarity and uniformity, the term input (or inlet) denoted by the symbol IN will be here used in lieu of fuel.

Exergy Input:

${\dot{EX}}_{\begin{matrix}   PLS \\   FUEL  \\\end{matrix}}$=$\dot{EX}_{IN}^{BZ,OTSG,HOT}+\dot{EX}_{IN}^{FW,IHX,HOT}+\dot{EX}_{IN}^{DIV,CAS}+\dot{EX}_{IN}^{DIV,PFC}+\dot{EX}_{IN}^{VV}$ (16)

$\dot{EX}_{\begin{matrix}   DW \\   FUEL  \\\end{matrix}}$=$\dot{EX}_{IN}^{BZ,OTSG,HOT}+\dot{EX}_{IN}^{HCSG,HOT}+\dot{EX}_{IN}^{DIV,CAS}+\dot{EX}_{IN}^{DIV,PFC}+\dot{EX}_{IN}^{VV}$ (17)

Exergy Destruction:

$\dot{EX}_{\begin{matrix}   PLS  \\   DES  \\\end{matrix}}$=$\Delta \dot{E}X_{PLS}$ and $\dot{EX}_{\begin{matrix}   DW  \\   DES  \\\end{matrix}}=\Delta \dot{E}X_{DW}$ (18)

To calculate the exergy rates efficiency, exergy fuel flows considered are thermal power withdrawn from the Breeding Zone, First Wall, Divertor Cassette, Divertor PFCs, and Vacuum Vessel. The pulse-dwell sequence can be considered as a series of exergy contributions. The exergy efficiency pertaining to both modes can be calculated in terms of exergy rates. However, the expression of the overall exergy efficiency relating to the whole pulse-dwell sequence has to be obtained in terms of amount of exergy calculated along pulse and dwell time periods. The overall exergy efficiency accounts for the sum of exergy input and the sum of exergy destruction contributions during pulse and dwell modes. The expression of overall exergy efficiency characterizing ESS and auxiliary boiler configurations become the following:

$\eta _{PLS+DW}^{EX}=1-\frac{E{{{\dot{X}}}_{\begin{matrix}   DES  \\   PLS+DW  \\\end{matrix}}}}{E{{{\dot{X}}}_{\begin{matrix}   IN  \\   PLS+DW  \\\end{matrix}}}}=1-\frac{E{{{\dot{X}}}_{\begin{matrix}   DES  \\   PLS  \\\end{matrix}}}+E{{{\dot{X}}}_{\begin{matrix}   DES  \\   DW  \\\end{matrix}}}}{E{{{\dot{X}}}_{\begin{matrix}   IN  \\   PLS  \\\end{matrix}}}+E{{{\dot{X}}}_{\begin{matrix}   IN  \\   DW  \\\end{matrix}}}}=1-\frac{{{\overset{\centerdot }{\mathop{EX}}\,}_{\begin{matrix}   DES  \\   PLS  \\\end{matrix}}}\cdot {{\tau }_{PLS}}+{{\overset{\centerdot }{\mathop{EX}}\,}_{\begin{matrix}   DES  \\   DW  \\\end{matrix}}}\cdot {{\tau }_{DW}}}{{{\overset{\centerdot }{\mathop{EX}}\,}_{\begin{matrix}   IN  \\   PLS  \\\end{matrix}}}\cdot {{\tau }_{PLS}}+{{\overset{\centerdot }{\mathop{EX}}\,}_{\begin{matrix}   IN  \\   DW  \\\end{matrix}}}\cdot {{\tau }_{DW}}}$ (19)

where $τ_{PLS}$ and $τ_{DW}$ are the time duration of pulse and dwell modes.

A viable alternative solution to reduce plant layout complexity and due to molten salt tanks and connection piping is to replace the ESS with an auxiliary boiler. This fired steam generator is evaluated being fuelled by natural gas (100% methane CH_4) and provides thermal power production during the dwell phase. The design thermal duty of this steam generator is about 254 MW as it is foreseen that, during dwell phase, 10% of the mass flow rate, and hence thermal power released with respect to pulse phase, is considered for plant operation. Moreover, to avoid thermal fluctuations and consequent thermal fatigue, the auxiliary steam generator is operated in continuous mode during both pulse and dwell phases to ensure a constant duty. This implies that the thermal power released by the auxiliary boiler has to be considered during pulse mode in addition to that thermal power not used for molten salt heating. Therefore, the entire thermal power produced by the reactor during pulse mode is available for the PCS and provided by four OTSG operating in parallel to use the thermal power generated in both breeding zone and first wall. The combustions reaction can be written as follows:

$αCH_4+x(O_2+3.76N_2 )→aCO_2+bH_2 O+cN_2+dO_2$

The standard specific molar chemical exergy of methane, with respect to the reference reservoir R represented by the environment at T_R=298.15 K and p_R=101.325 kPa is [12]:

$\overline{ex}_{CH_4}^C=μ_{CH_4} (T_R,p_R )-μ_{CH_4}^R (T_R,p_R )=831.2 kJ/mol$

Considering the molar weight of methane equal to 16.04g/mol, then the specific chemical exergy is:

$\overline{ex}_{CH_4}^C=\frac{831.2kJ/mol}{16.04g/mol}\cong 51.82 J⁄kg$

The Lower Heating Value (LHV) of the methane is 802.3 kJ/mol=50147.5 kJ⁄kg, then the mass flowrate expressed in mol/s of methane needed to produce 254MW of thermal power is obtained considering an auxiliary boiler with no economizer as pre-heating is no needed; then its design implies a lower thermal efficiency equal to η_BOILER=0.86. Thus, the methane mass flowrate is:

$\frac{\dot{Q}}{η_{BOILER⋅LHV}}\cong 368.14\frac{mol}{s} =5.905 \frac{kg}{s}$

This is the mass flowrate that is to be accounted for exergy balance with the option of auxiliary boiler to producing 254 MW of thermal power.

The air mass flowrate, considering air excess of 10%, is equal to 117.32 kg⁄s.

The temperature at the center of the burning flame in the combustion chamber can be assumed at 2000°C=2273K.

The rate of exergy destruction is calculated as follows:

$\Delta \dot{EX}_{DES}=\Delta \dot{EX}_{DES}^T+\Delta \dot{EX}_{DES}^C=\Delta \dot{EX}_{IN}-\Delta \dot{EX}_{OUT}$ (27)

where $\dot{EX}_IN = heat losses to environment + thermal exergy input + chemical exergy input$

$\dot{EX}_IN = 0.02∙5.905∙50147.5∙\left(1-\frac{298}{2273}\right)+117.32∙∙281.7+5.905∙1.06∙50147.5 \approx 352083 kJ⁄s$

$\Delta \dot{EX}_{OUT}=(5.905+117.32)∙957.42=117978 kJ⁄s$

$\Delta \dot{EX}_{DES}=352083-117978=234105 kJ⁄s≈234 MW$

Tables 3 and 4 include all calculated values pertaining to pulse and dwell mode respectively, of the configuration with auxiliary boiler.

Table 3. DEMO exergy input and exergy destruction with auxiliary boiler in pulse mode

Similarly to the configuration with ESS, also in the case with the auxiliary boiler the exergy efficiency is calculated based on the exergy amount during each reactor operating mode time duration.

Pulse Mode

$\eta_{PLS}^{EX}$=$1-\frac{\Delta \dot{EX}_{PLS}}{\dot{EX}_{\begin{matrix}   PLS  \\   FUEL  \\\end{matrix}}} $=$1-\frac{\Delta \dot{EX}_{PLS}}{\dot{EX}_{\begin{matrix}  OTSG,SH  \\   IN  \\\end{matrix}}}$ (28)

Dwell Mode

$\eta_{DW}^{EX}$=$1-\frac{\Delta \dot{EX}_{DW}}{\dot{EX}_{\begin{matrix}   DW  \\   FUEL  \\\end{matrix}} }$=$1-\frac{\Delta \dot{EX}_{DW}}{\dot{EX}_{\begin{matrix}   OTSG,SH  \\   IN  \\\end{matrix}}}$ (29)

Main result of the present research is a performance evaluation based on exergy method adopted to calculate balances and efficiencies of components and systems constituting the overall plant. The second Law, underpinning the exergy method, focuses on dissipative phenomena implying entropy production and exergy destruction representing performance indicator to detect solution for the design enhancement. The PHTS, IHTS, ESS and PCS of DEMO fusion reactor and balance of plant assessed by means of the exergy method reveals that the efficiency of the system designed with molten salts remains higher with respect to the alternative solution with an auxiliary boiler replacing the ESS. The difference of exergy efficiency between the solutions here considered could suggest the suitability of both configurations. Nevertheless, on the one side, the strong exergo-dissipative combustion reaction that would lower the performance with the auxiliary boiler is mitigated by the thermal power reduction to 10% during dwell mode. Though, this solution determines a higher stress level and fatigue in steam turbine components. On the other side, the ESS with molten salt ensures the continuity of full power release; moreover, this configuration could undergo design improvements based on optimized shapes of intermediate heat exchangers derived from the entropy generation minimization underpinning the Constructal Law and Constructal Thermodynamics approach [13] specifically applied to heat interactions phenomena and heat exchangers design [14]. Anyway, the selection of the most suitable option requires a more accurate evaluation of the balance of plant in terms of reliability and economics considering the location of the plant and the need of additional infrastructures.