# Thermal coupling between a Small Modular Nuclear Reactor and a High-Temperature Steam Electrolysis process: Energy performance mapping of key design options

Nicolas Tauveron, David Haubensack, Pierre Dumoulin, Nicolas Alpy

## ► To cite this version:

Nicolas Tauveron, David Haubensack, Pierre Dumoulin, Nicolas Alpy. Thermal coupling between a Small Modular Nuclear Reactor and a High-Temperature Steam Electrolysis process: Energy performance mapping of key design options. Sustainable Energy Technologies and Assessments, 2026, 85, pp.104780. 10.1016/j.seta.2025.104780. cea-05458892

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https://cea.hal.science/cea-05458892v1

Submitted on 14 Jan 2026

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# Thermal coupling between a small modular nuclear reactor and a high-temperature steam electrolysis process: energy performance mapping of key design options☆

Nicolas Tauveron<sup>a,*</sup>, David Haubensack<sup>b</sup>, Pierre Dumoulin<sup>a</sup>, Nicolas Alpy<sup>b,†</sup>

## ARTICLE INFO

### Keywords:

Nuclear hydrogen production

Small modular reactor

High temperature steam electrolysis

Thermal coupling

Electric coupling

## ABSTRACT

This article presents the main results of a three-year R&D program on the coupling of a Small Modular Reactor (SMR) nuclear unit to a hydrogen production process using High-Temperature Steam Electrolysis (HTSE). Different coupling architectures are investigated and their energetic evaluation is performed in comparison with a reference configuration. The separate effects that are considered are comprehensive and include: thermal coupling (with or without, unidirectional or bidirectional – modulo internal heat recovery effort in the HTSE process itself), direct or indirect steam supply, location of the Rankine cycle extraction point, pressurization of the HTSE (with or without mechanical energy recovery through gas expansion) and oxygen content (impact of the swept gas). Remarkably, the simulation results obtained on the reference configuration show a gain of over 13% in hydrogen production compared with the solution involving no thermal coupling between the SMR and the HTSE process (when HTSE heat is provided through electrical heaters), with a deviation as low as 3 % from an idealized configuration with freely available heat. It even outperforms the heat-pump solution by more than 4 %. These key energetic results were supplemented by other technical criteria, such as those relating to safety and technological maturity.

## Introduction

Taking advantage of new plant designs, Small Modular nuclear Reactors (SMRs) can be used to produce not only electricity, but also heat through nuclear cogeneration systems typically to produce hydrogen. Inline, nuclear systems are expected to contribute to the decarbonization of transportation, industrial processes and district heating. Concerning hydrogen production, around 100Mt are produced and consumed each year [1], mainly for industrial applications: chemistry (ammonia production) and refining. Even without considering new uses of hydrogen, the needs should grow in refineries to process heavy hydrocarbons or in

the steel industry for advanced processes ore reduction, up to 115Mt in 2030 [1]. Currently, demand for hydrogen is mainly achieved by production from unabated fossil fuels [1], steam methane reforming without carbon capture accounting for 62 %. The associated CO₂ emissions were estimated at over 900Mt for the year 2021 [1]. However, low-carbon emission technologies exist, such as water electrolysis technologies, which mainly rely on electricity as an energy source. One can distinguish:

- Alkaline electrolysis: a proven technology used on an industrial scale;

Abbreviations: B, Blower; C, Cooler; CD, ConDenser; COP, Coefficient Of Performance; CPR, H₂ ComPressor; EH, Electric Heater; FWT, FeedWater Tank; GT, Gas Turbine; HP, High-Pressure; HPP, High-Pressure Pump; HPT, High-Pressure Turbine; HRS, Turbine Heat Recovery System; HT, High Temperature; HT-COCIR, High Temperature COupling CIRcuit; HTSE, High Temperature Steam Electrolysis; HX, Heat Exchanger; IC, InterCooler; LP, Low-Pressure; LPP, Low-Pressure Pump; LPT, Low-Pressure Turbine; LT-COCIR, Low Temperature COupling CIRcuit; ND, Non Dimensional; PHH, High Pressure preHeater; PHL, Low Pressure preHeater; PU, Pumping Unit; PWR, Pressurized Water Reactor; RH, ReHeater; RU, Refrigeration Unit; SEP, liquid-steam SEParator; SG, Steam Generator; SMR, Small Modular Reactor; SOEC, Solid Oxide Electrolyzer Cell; WD, Water Drain.

<footnote><sup>a</sup> Université Grenoble Alpes, CEA, LITEN, DTCH, LCST, F-38000 Grenoble, France</footnote>

<footnote><sup>b</sup> CEA, DES, IRESNE, DER, SESI, LEMS, F-13108 Saint Paul Lez Durance, France</footnote>

<footnote>* This article is part of a special issue entitled: 'Net-zero emissions' published in Sustainable Energy Technologies and Assessments.</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: nicolas.tauveron@cea.fr (N. Tauveron).</footnote>
<figure><img src="image_3.png" /><figcaption>Fig. 1. SMR and HTSE architectures featuring the typical temperatures levels of the main components.</figcaption></figure>

- Proton exchange membrane electrolysis: a newer technology, in commercial use for several years;

- High Temperature Steam Electrolysis (HTSE), used for this study because it has the potential to produce hydrogen using less electricity than the low-temperature technologies mentioned above [2,3].

Although various techniques have emerged [4] based on thermo-chemical cycle concepts (sulfur-based [5] or copper-chlorine-based [6] cycles) using High-Temperature (HT) heat from fourth-generation reactors, the focus here is therefore on HTSE technology compatible with Pressurized Water Reactor (PWR) – type SMR developments. In the last years, practical architectures to couple a nuclear power plant and a HTSE to massively produce sustainable hydrogen, have been studied, sometimes to increase the revenue by offering hybrid operation opportunities in case of load-following constraints [3,4] or even to produce peak electricity using hydrogen as a storage medium [7,8].

A large number of configurations, design options, market scenario have emerged for SMR-HTSE coupling. Concerning heat supply to the HTSE, several architectural choices have been imagined: heat from the SMR Steam Generator (SG) outlet has been mainly considered [9–13], or from a specific boiler [14]. Some works consider other locations within the Rankine cycle, mainly at a Lower Pressure (LP) from Low Pressure Turbine (LPT) [13,15,16] or from deaerator [17]. Indirect use of steam from the Rankine cycle is generally considered, but some authors have studied direct use [18] or use in a combined cycle [19]. Possibility to include additional heat from external sources is also analyzed: for example, solar heat [20], heat-pump [16], electrical heaters [21] or gas-

fired units [21]. There are also various stack design choices, for example concerning its pressure level or oxygen content. A positive effect of pressurization, is generally suggested [22] although certain connected challenges for the HTSE have still to be overcome [23]. Thus, some authors consider SMR-HTSE coupling with atmospheric [24] or pressurized [9] configurations. Concerning the anode line, different schemes are developed: some authors consider the production of pure oxygen [7,12,20] whereas others prefer to keep a swept gas [9,14,17]. In summary, many architectural configurations and design parameters may be relevant for electrically and thermally coupling an SMR to an HTSE. Remarkably, to authors knowledge, configurations considering the return of heat from HTSE to SMR have not been reported in the literature. A main purpose of this article is therefore to study various configurations considering this heat return possibility and to compare them with each other and with certain other relevant configurations such as heat supplied to the HTSE process by heat pumps or corresponding to freely available heat (the latter hypothetical case constitutes the most advantageous reference in terms of thermodynamics).

One difficulty that arises when trying to determine the best technical choices is that assumptions considered in the provided references are not consistent with each other. The methodology applied in this work addresses this deficiency by comparing solutions with relevant reference hypotheses. A central point of the study carried out is to examine a case whose established performance is decoupled from forecasts of the price of electricity and hydrogen: the nuclear reactor is entirely dedicated to the production of hydrogen (which is a realistic economic configuration according to [25]). In section 2, the considered coupled systems (SMR &
<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Numerical coupling flowchart.</figcaption></figure>

HTSE) are presented. Section 3 describes and reports simulation results for the reference coupling configuration. Sections 4 and 5 present the 15 alternative configurations and compare them to the reference configuration.

## Materials and methods

This section provides a brief description, for the sake of conciseness, of the two entities considered for coupling. Temperature levels are also highlighted here. Finally, numerical scheme for the coupling is addressed.

### SMR Rankine cycle

The Rankine cycle considered is the power conversion cycle of an SMR of PWR type, with a 540 MW thermal power. Fig. 1 (top) shows the layout composed as follows: the SG producing superheated steam at 4.5 MPa / 300 °C, a High Pressure Turbine (HPT) and a LPT connected by a shaft to the alternator (ALT), a separator (SEP) to remove liquid droplets and a reheater (RH), using a fraction of the SG output to reheat the vapor at the LPT inlet, a condenser (CD) acting as a heat sink of the Rankine cycle, Low and High pressure Pumps (respectively, LPP and HPP) to restore the cycle pressure ratio and circulate water returning to the SG, Low and High Pressure preHeaters (respectively, PHL and PHH), using a fraction of each turbine flow to preheat this cold water, and in between a
<figure><img src="image_5.png" /><figcaption>Fig. 3. SMR-HTSE reference coupling architecture (featuring simulation results for main thermal exchanges and electrical production / consumptions).</figcaption></figure>

FeedWater Tank (FWT) gathering the outputs of the reheater, the HPT preheater extraction line, and the liquid drained from the separator. The condenser temperature is set to 32 °C corresponding to sea water cooling system conditions.

CYCLOP software, which has been validated against French nuclear Rankine cycles [26], is used to compute the optimal working point of the cycle, applying simplex algorithm. The maximal gross electrical output for pure electricity generation is 186 MW and the corresponding net efficiency rates 33.7 % [27]. Assumptions used for component efficiencies are reported in Appendix 1 (Table 3).

## HTSE

The HTSE is an electrochemical splitting of steam into hydrogen and oxygen gases. The whole mechanism is endothermic and as the operating temperature rises, the free enthalpy diagram of reaction is known to indicate a large decrease for work (electricity) requirement and a noticeable increase in the heat demand. The HTSE technology takes advantage of this thermodynamic law by operating at HT, typically in the range of 700 to 850 °C. Very importantly since the point explains the possibility of coupling with a PWR-type reactor, at the process level, thanks to efficient heat recovery from the product stream (superheated

gas or steam), inlet temperatures can be reduced to the saturation value corresponding to the stack operating pressure, with an operational superheat margin. Thus, in the case of an atmospheric Solid Oxide Electrolyzer Cells (SOEC) unit, the required inlet steam temperature is 115 °C, as shown in Fig. 1 (bottom), which presents a conceptual view of the different process engineering steps of the HTSE model developed (note that multiple modules and parallel branches should be actually involved).

In Fig. 1 (bottom), SOEC stacks represent the core element of the system. Multiple cells are stacked together, made of ceramic materials, where hydrogen and oxygen are produced at 700 °C. Electric heaters (EH) are used at anode and cathode inlets. Water drains (WD) are used in the cathode outlet lines. Hydrogen Compressors (CPR) pressurize hydrogen up to a final pressure; for technological reasons, maximal pressure ratio between inlet and outlet is limited. Air blower (B) is designed to fill the specified amount of swept gas (air) at the anode inlet. Hydrogen blower (B) is used to fill the appropriate amount of hydrogen at the cathode inlet to prevent from oxidation issue. Intercoolers (IC) are heat exchangers and condensing units which cool and condense the H₂-steam mixture at cathode outlet lines. Heat recovery systems (HRS) are high temperature heat exchangers. Refrigeration unit (RU) condenses the steam in the H₂-steam mixture. Cooler (C) cools the air-oxygen
mixture at the anode outlet. Heat exchanger (HX) denotes the heat exchanger which cools the H₂-steam mixture down to -15 °C. Each cooler (intercoolers IC1, IC2, IC3, IC4 and cooler C5) can be divided into three steps of cooling as will be better discussed in section 3. Numerical simulations of the whole process are performed with EES software [28]. Appendix 1 reports main assumptions (Table 4) and equations. Hydrogen pressure delivery has been set to 3 MPa; an additional compression stage may be used to meet any other precise hydrogen delivery [29].

## Numerical coupling methodology

The numerical coupling procedure consists in two optimization processes operated in a serial manner and described in Fig. 2: HTSE system is optimized for hydrogen production and SMR Rankine system is optimized for co-generation. Thermal and electrical powers as well as temperature levels are exchanged, in a bidirectional manner since heat recovery from HTSE process to SMR Rankine cycle is also considered as mentioned in the introduction.

To authors knowledge, the coupling concept considered here has not been reported in the literature: there are simpler configurations, based on different assumptions and the information shared is not detailed enough to allow even partial validation. Nevertheless, a verification effort through code-to-code benchmarks has been performed. Two exercises were accomplished on the reference configuration described in section 3: a first using DYMOLA software and a second against a CYCLOP-PROSIM coupled simulation (PROSIM is a commercial software, with some HTSE applications available [30]). These last models are reported in [25,31]. The two cross-comparisons showed very good accuracy (differences of less than 0.01 % and 0.1 % respectively, explained for the last case by the implementation of fluid properties).

## Results of the reference configuration

### Coupling concept

In this configuration, electric and thermal couplings are considered. Electric coupling relies on the use of AC/DC converter for SOEC (no electric loss is considered). The thermal coupling is based on two separate circuits (Fig. 3 – Top), HT-COCIR and LT-COCIR, whose temperatures are moderate and lengths are short (the distance between the SMR and the HTSE is assumed to be on the order of 1000 m in [3]) so that heat losses are neglected. As reported in Fig. 3-Top:

- Heat from the SMR is removed by heat exchanger HX1, which connects the Rankine cycle to the HT-COCIR circuit, an intermediate pressurized water loop designed to transport heat. Steam is drawn from the outlet of the HPT, so that component HX1 is effectively parallel to the Rankine PHH. Heat is removed from the HT-COCIR circuit by an HX2 SG, which produces superheated steam at 115 °C from liquid water at 25 °C to meet the demand of the HTSE. It is supplemented by a SG (S1 circuit) that uses some of the recovered heat from the HTSE.

- Heat recovery from the HTSE unit to the SMR: this system includes several heat exchangers (S2) that return waste heat to the SMR via an intermediate pressurized water loop (LT-COCIR). This loop transfers its heat to the SMR through a heat exchanger (HX3) mounted in parallel with the Rankine PHL. Preliminary optimization studies concluded that this circuit should operate between 40 °C and 90 °C.

Fig. 3 (bottom) allows understanding where the heat fluxes S1 and S2 come from. Indeed, each cooler (IC1, IC2, IC3, IC4 and C5) can be divided into three steps of cooling (S1, S2, S3) giving access to 3 temperature ranges. The use of S1 and S2 has been explained above and heat from this last stage S3 is not recovered, as it is too low.

<table><caption>**Table 1**
Reference configuration results.</caption><thead><tr><th></th><th></th><th>SMR designed for HTSE coupling (configuration 1)</th><th>SMR designed for pure electric production</th><th>Design modification requirements</th></tr></thead><tbody><tr><td rowspan="7">SMR</td><td>SG thermal power (MWth)</td><td>540</td><td rowspan="7">540</td><td rowspan="7">New heat exchangers and pipes</td></tr><tr><td>HX1 heat extraction from Rankine to HTSE (MWth)</td><td>35</td></tr><tr><td>HX3 heat recovery from HTSE to the Rankine (MWth)</td><td>20</td></tr><tr><td>Gross Generator Production (MWe)</td><td>180</td><td>186</td></tr><tr><td>SG mass flow (kg/s)</td><td>234</td><td>234</td><td>No change</td></tr><tr><td>Condenser mass flow (kg/s)</td><td>166.5</td><td>178.5</td><td>-6.7 %</td></tr><tr><td>HTSE</td><td>SOEC consumption (MWe)</td><td>148.5</td><td></td><td></td></tr><tr><td></td><td>Hydrogen Compressor consumptions (MWe)</td><td>10</td><td></td><td></td></tr><tr><td></td><td>Total Electrical consumption (MWe)</td><td>176</td><td></td><td></td></tr><tr><td></td><td>HRS1 Duty (MWth)</td><td>18.5</td><td></td><td></td></tr><tr><td></td><td>HRS2 Duty (MWth)</td><td>20</td><td></td><td></td></tr><tr><td></td><td>Hydrogen production (kg/s)</td><td>1.2</td><td></td><td></td></tr></tbody></table>

### Results of the reference configuration (configuration 1)

Table 1 reports the main thermodynamic results for the SMR-HTSE coupling reference case and allows for comparison with an SMR designed for electricity generation. It highlights that the 540 MWth nuclear heat source leads to an H₂ production of 1.2 kg/s, with thermal power extracted and reinjected into the SMR of 35 and 20 MWth, respectively. The HTSE system is primarily powered by electrical consumption (176 MWe versus a thermal consumption of 35 MWth). Among the various electrical consumption points, the fuel cell (SOEC) is the main consumer (148.5 MWe), while the hydrogen compressors represent a significant secondary consumption, justifying the next study of the pressurized SOEC. Another important point is the crucial role of the heat recovery systems (HRS1 and HRS2) in enabling the fluid streams to reach a temperature close to that at the fuel cell inlet. Nevertheless, HT electrical resistors are necessary to reach the required temperature. The last column provides additional comments and data regarding the design modifications required between the two cases. It highlights that the low heat flux values exchanged between the SMR and the HTSE, compared to the SG thermal output (20 and 35 MWth, compared to 540 MWth), induce slight changes in mass flow rates and power outputs, with differences of less than 7 %. These changes primarily affect the low-pressure components (LPT and condenser).

### Description of alternative coupling configurations

A methodology enabling the systematic study of the distinct effects of different possible technical alternatives is implemented, resulting in 15 additional configurations (each of them being optimized): with or without thermal coupling, direct or indirect steam supply, location of
<figure><img src="image_6.png" /><figcaption>Fig. 4. Cross-comparison results of 6 key indicators for the 16 configurations.</figcaption></figure>

the extracting point in the Rankine cycle, one way or two-way thermal coupling, internal heat recovery in the HTSE, pressurized SOEC and oxygen content. Three purely electrical coupling configurations are also being studied. The coupling architectures of the 15 configurations are detailed in Appendix 2 (Table 5), a fairly complex matrix to which the reader is invited to refer for the following description.

### Standard SOEC configurations with thermal and electrical SMR coupling

The objective is to study the impact of modulating thermal and

electrical couplings and the choice of heat extraction point along the expansion line. The corresponding configurations are numbers 2 to 8 in Appendix 2, the justification for which is as follows:

- The first point concerns the optimal use of the heat recovered from the HTSE: should priority be given to returning heat to the SMR or, conversely, maximizing its use for HTSE steam production? To study this possibility, configuration 2 merges the heat from S1 with S2 and returns the balance to the SMR via the LT-COCIR (i.e., S1 does not supplement the SMR to produce steam). In contrast, in configuration
3, most of the recovery heat from the HTSE is used to boil water, while a small portion is managed by a single recovery system and returned to the SMR via the LT-COCIR. This point is taken further with configuration 4 which is a one-way thermal coupling: heat is transferred from the SMR to the HTSE, but no heat is sent back from the HTSE to the SMR (i.e., there is no LT-COCIR). In configuration 5, the steam used in the HTSE is supplied directly by the SMR, without any intermediate circuit but still extracted from the HPT outlet, as was the case for the reference and 2-4 configurations (for a fair comparison, a throttle valve is used in configuration 5 to meet the pressure requirement). Although this configuration is hardly realistic (e.g., questionable regarding chemical compatibility of water quality or safety), it serves as a reference for estimating the “energy cost” of configurations with an intermediate pressurized water loop. Configuration 5 applies the same HTSE recovery heat scheme than the one applied in the reference configuration and this is also the case for configurations 6-8 below.

- Finally, the origin of the heat in the Rankine cycle is considered. In configurations 6&7, heat is transferred to the HTSE from the SG outlet, whereas in configuration 8, heat is extracted at the optimal exergetic point within the LPT. The difference between configurations 6&7 lies in the degree of superheating at the SG outlet.

### Advanced SOEC configurations with thermal and electrical SMR coupling

Configurations 9 to 13 (reminder, see Appendix 2) allow the performance of SOECs under pressure to be studied, bearing in mind that these configurations are more complex to design and control [23]. Recent numerical and experimental studies have shown limited or non-monotonic variations in cell performance [33–35]: as a first approximation, it is assumed that there is no change in SOEC performance, so that the main expected benefits of pressurization are a reduction in the pressurization requirements of the hydrogen produced [35] and a reduction in the diameter of the pressure pipes. The expected counter-effects include increased pressurization requirements for the air inlet and mechanical stresses related to pressure. Configuration 9 serves as a reference: it replicates the choice made for the reference configuration, except for the HTSE pressure, which is set at 10 bar. This configuration is further studied, taking into account other possible improvements:

- Configuration 10 considers a near-zero air intake at the anode aimed at mitigating the aforementioned disadvantages of anode pressurization. Oxy-fuel applications can be considered a relevant and coherent industrial framework.

- Performance of pressurized SOECs can be further enhanced by reducing electricity consumption through the inclusion of an expander in the anode circuit between HRS2 and C5 (configurations 11 to 13). The HP air-enriched flow expands through a turbogenerator to produce electricity. A gas turbine configuration is used, with the turbogenerator and air compressor mounted on the same shaft. An isentropic efficiency of 0.9 is assumed, which approximately corresponds to the performance of modern turbines [36] and is close to the value of 0.89 reported in [9]. Configuration 11 considers the same conditions as configuration 9, while configuration 12 combines the expansion option and pure oxygen. Configuration 13 is identical to configuration 12, but with an increase in pressure to 20 bar.

All these configurations (9 to 13) share the same heat source in the Rankine cycle as configuration 6, since higher SOEC pressures result in steam being produced at a higher temperature: heat is thus extracted from the steam generator.

### Electric – only SMR coupling configurations

Configurations without thermal coupling between the SMR and HTSE units are considered (i.e., without HT-COCIR and LT-COCIR

circuits). In this case, the heat for the HTSE unit can come either from its own waste heat recovery or from an auxiliary system. An ideal initial configuration (configuration 14) assumes that a tertiary plant can directly supply steam or heat to the HTSE unit. Although very hypothetical, this configuration represents a technically and economically ideal case and provides a useful point of comparison. A more realistic scenario (configuration 15) involves supplying heat to the HTSE unit via electric resistance heaters. More specifically, this configuration is similar to configuration 4, except that the heat is supplied by a LT direct electric heating device with an efficiency of 95 %. A less technologically mature architecture uses a heat pump. This heat pump is designed with cyclopentane as the refrigerant, a compressor efficiency of 85 %, and pinch points set at 10 °C. Its compression ratio has been optimized, resulting in a Coefficient Of Performance (COP) of 3.3, a typical value for heat pumps with a temperature difference of 40 °C [32]. In this architecture, in addition to the heat from system S1, the heat production process for vaporizing water using a heat pump is optimized in two stages:

- The recovery heat at low temperature (circuit S2) is raised to a temperature of 130 °C by the HT heat pump;

- Additional heat is supplied by an electric heating element at the boiler outlet.

### Cross-Comparison results and Analysis

To ease the comparison between the different configurations, the system performance is considered through non-dimensional parameters, with the reference configuration as the scaling factor. Thus, the dimensionless “ND” hydrogen production of a given configuration X, which encodes its coupling performance and is therefore a key indicator, simply reads:

$$ \frac{\text{HydrogenProductionofconfigurationX}_{\text{ND}}}{\text{HydrogenProductionofconfigurationX}} = \frac{\text{HydrogenProductionofconfigurationX}}{\text{HydrogenProductionofconfiguration1}} $$

The results of the 16 configurations are presented in Fig. 4, in terms of the 6 following indicators: hydrogen production, total and SOEC electricity consumptions, Rankine cycle condenser mass flow rate and bidirectional thermal powers between the SMR and HTSE.

### Configurations with standard SOEC: Comparison of thermal and electrical SMR coupling options

This section addresses a comparison of the standard SOEC configurations described in section 4.1, which corresponds to the 8 first configurations of Fig. 4.

The results of configurations 1 to 3 show that the HTSE waste heat recovery method actually has a minor effect on HTSE performance (hydrogen production is fairly similar for these three cases, Fig. 4 – top), although notable differences do apply to the bidirectional SMR-HTSE coupling, as shown by the balance of thermal powers to be exchanged (Fig. 4 – bottom). The comparison with unidirectional thermal coupling (configuration 4) deserves particular attention, as it is the simplest thermal coupling architecture. The results indicate that it has two drawbacks: it induces the most significant, albeit limited, modification of the Rankine cycle (as indicated by the variation in the condenser mass flow rate, Fig. 4 – top) and lower performance than the bidirectional thermal coupling configurations (configurations 1 to 3).

The “energy cost” of indirect coupling (effect of the intermediate pressurized water loop) is also addressed: it is shown that the direct coupling solution (configuration 5) results in only a slight increase in hydrogen production. Another key aspect is the location of heat extraction (configurations 6 to 8). Heat extraction from the steam generator outlet (configurations 6 and 7) is less efficient (reminder:
hydrogen production being the key performance indicator) because the temperature of this stream (approximately 300 °C) is much higher than the average temperature required (approximately 115 °C), resulting in a greater exergetic loss than necessary and therefore less work delivered, reducing overall performance. Conversely, heat extraction within the LPT (configuration 8) is the most efficient option, although installing a new extraction line inside the LPT may present a technical constraint and, in any case, reduces the design flexibility with respect to the actual operation of the installation, compared to extraction from the HPT outlet as in the reference configuration. Finally, the degree of superheating is found to have no significant impact (configuration 7).

### Cross-comparison between standard and advanced SOEC with thermal and electrical SMR coupling

The second comparison examines the advantages of using advanced SOECs compared to standard SOECs. First, it is observed that all the 6 indicators reported (Fig. 4, top and bottom) for each optimized advanced SOEC configuration (configurations 9 to 13) deviate more significantly from those of the reference configuration than the options in section 5.1, although the variation in hydrogen production performance remains limited (< 10 %). Nevertheless, as with the 8 configurations using standard SOECs, none of these configurations requires major modifications to the Rankine cycle, as the variation in condenser flow rate remains limited (Fig. 4 – Bottom).

One specific aspect studied is the effect of pressurization. It is interesting to note that pressurization alone has little impact on hydrogen production: the pressurized SOEC (configuration 9) achieves a similar production to the atmospheric SOEC with the same heat source (configuration 6). This is explained by the fact that the increased air pressurization requirements compensate for the reduced hydrogen pressurization requirements. This point is confirmed by configuration 10, where the oxygen content has a significant influence (up to a 6.5 % increase in hydrogen production compared to configuration 6, see Fig. 4 – top), mainly due to the elimination of swept gas pressurization and electrical heating prior to stack entrance.

The study of improving the performance of advanced SOECs is continued in configuration 11 by introducing a turbine into the anode circuit. To further optimize, it is combined with the swept gas suppression system as for configuration 10. The combined configurations 12 and 13 offer the highest hydrogen production: configuration 12 shows a 9 % gain in hydrogen production compare to configuration 6 while doubling of the SOEC pressure from 10 to 20 bar (configuration 13) has a secondary impact.

### Cross-comparison between thermal and electrical SMR coupling configurations and electrical-only coupling configurations

The third comparison addresses difference with thermally uncoupled (14 to 16) configurations. Among the electric-only coupling configurations, the idealized case with freely available heat and no utilization constraint (configuration 14) represents an upper limit of efficiency relative to standard SOEC configurations. It is noteworthy that this configuration only improves efficiency by 3 % compared to the reference configuration. In contrast, when considering a more realistic scenario where HTSE heat is supplied via electrical heaters (configuration 15), the reference configuration achieves a 13 % gain in hydrogen production. Use of a thermally decoupled approach that is less mature in terms of technology, such as a heat pump solution, (configuration 16), reduces the reference configuration gain to 4 %.

### Additional engineering criteria

Complementary to purely energetical evaluations, other criteria should be taken in consideration:

<table><caption>**Table 2**

Steam constraints, preliminary safety and maturity considerations.</caption><thead><tr><th>Configurations</th><th>Steam constraints</th><th>Safety, compare to the reference</th><th>Maturity of coupling technologies and comparison with the reference</th></tr></thead><tbody><tr><td>Reference (config 1.)<br>HTSE waste heat integrated in the Rankine cycle (config. 2.)<br>HTSE waste heat management (config. 3.)<br>One-way thermal coupling (config. 4.)</td><td>Favorable (*)</td><td>Similar</td><td>Thermal coupling is considered as a mature technology (TRL 9), based on the extensively used district heating technology [37].</td></tr><tr><td>Direct coupling (config. 5.)<br>Heat from the steam generator (config. 6. & 7.)</td><td>Highly unfavorable: steam is common to both units<br>Favorable (*)</td><td>A bit more favorable as LT-COCIR is suppressed<br>Highly unfavorable as physical barriers between SMR and HTSE are suppressed<br>Less favorable due to proximity with SMR nuclear core (**).<br>Similar</td><td>Similar (except that a specific internal steam extraction is required).<br>Unfavorable as oxygen enriched environments have very specific constraints. A TRL 4 pilot is studied in the frame of direct reduced iron plant development [38].</td></tr><tr><td>Pure oxygen configurations (config. 10., 12. & 13.)</td><td></td><td>Unfavorable due to chemical reactivity.</td><td>Less favorable due to higher temperatures and pressures of coupling medium. 200 °C seems to be an upper state-of-the-art option (TRL 9) [37].<br>Nevertheless, a recent very high temperature industrial coupling has been accomplished [39].<br>TRL 9 for the electric boiler [40].</td></tr><tr><td>Pressurized SOEC config. 9-13.<br>Pressurized SOEC with expansion (config. 11. &13.)</td><td></td><td>Risks associated with Pressurization</td><td>Less favorable due to higher temperatures and pressures of coupling medium. 200 °C seems to be an upper state-of-the-art option (TRL 9) [37].<br>Nevertheless, a recent very high temperature industrial coupling has been accomplished [39].<br>TRL 9 for the electric boiler [40].</td></tr><tr><td>Electrical heating device (config. 15.)</td><td></td><td>More favorable as HT-COCIR LT-COCIR are suppressed.</td><td>TRL 5-7 for large high temperature heat-pump [37,41].</td></tr><tr><td>Heat-pump (config. 16.)</td><td></td><td>Seems less favorable due to pressure and flammability of the heat-pump refrigerant. Must be reconsidered in case a new product would be suitable [41].</td><td>TRL 5-7 for large high temperature heat-pump [37,41].</td></tr></tbody></table>

<footnote>*: Each subsystem has its own constraints.</footnote>

<footnote>**: In case of a break event occurring in the pipe connected to HX1, break mass flow would not be limited by turbine admission, as in configuration 1.</footnote>
- Steam chemistry constraints, as requirements are very different in the SMR and the HTSE;

- Safety, as nuclear power and hydrogen plants have their own safety and security issues that could possibly interact;

- Maturity, as both SMR and HTSE are emerging technologies.

A preliminary assessment of these qualitative criteria is reported in Table 2 that highlights that the reference configuration performs favorably, despite being more complex than purely electrical or one-way configurations.

## Conclusions

This paper addresses a clean and massive hydrogen production through the coupling of a SMR to a HTSE. Different possible coupling architectures and their energetic performance were investigated: with or without thermal coupling, direct or indirect steam supply, location of the sampling point in the Rankine cycle, one-way or two-way thermal coupling, internal heat recovery in the HTSE, pressurized SOEC and oxygen content. Overall, 16 coupling configurations were evaluated, each of them being optimized through steady state simulations.

The results obtained on the reference simulation configuration show a gain of over 13 % in hydrogen production compared with the solution involving no thermal coupling between the SMR and the HTSE (heat being provided through electrical heaters), and only 3 % less than a very idealized configuration of freely available heat. It even outperforms the heat-pump solution by more than 4 %. From a purely energetic point of view, each optimized configuration with an atmospheric SOEC deviates rather slightly from the reference simulation configuration. Possible ways to increase performance could be to extract heat exactly where needed in the turbine, and to use advanced SOEC technologies which enable to pressurize SOEC and/or to reduce swept gas flow.

We underline that all simulations were performed with a set of hypotheses which can be debatable due to the level of technological development and complexity of the system. The aim was instead to

carefully compare different configurations between each other – based on clear and given performance hypotheses – and not to provide final absolute results. An initial methodology for developing a grid of qualitative and quantitative criteria such as those relating to safety and technological maturity has been deployed and is intended to be enriched over the coming years. Economic considerations will obviously be integrated. This global methodology based on cross-comparisons of thermal coupling between SMR and molecule production is to be extended to more complex configurations of molecule productions (kerosene, methanol, etc.).

## CRediT authorship contribution statement

**Nicolas Tauveron:** Writing – review & editing, Methodology, Formal analysis, Conceptualization. **David Haubensack:** Writing – review & editing, Methodology, Formal analysis, Conceptualization. **Pierre Dumoulin:** Writing – review & editing, Methodology, Formal analysis, Conceptualization. **Nicolas Alpy:** Writing – review & editing, Methodology, Formal analysis, Conceptualization.

## Declaration of competing interest

Tauveron has patent pending to CEA. Haubensack has patent pending to CEA. Dumoulin has patent pending to CEA. Alpy has patent pending to CEA. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgments

This work was supported by the CEA (French Atomic and Alternative Energy Commission), IDNES project (Innovative Decarbonized Nuclear Energy Systems) from the SMR (Small Modular Reactors) Program. We would like to thank Coralie Quadri and Guillaume Montzieux from CEA/LITEN for their useful help in the verification process.

# Appendix 1

SMR Rankine and HTSE process performance hypothesis.

The steam generator (heat source of the Rankine cycle) generates a superheated steam at 4.5 MPa (absolute) / 300 °C. The condenser (heat sink of the Rankine cycle) is set to 5 kPa (absolute) / 32 °C.

Table 3 reports hypotheses that are used to specify the characteristics of the Rankine components, as representative of a modern PWR.

<caption>**Table 3**</caption>

Rankine cycle components hypothesis.

<table><tr><td>Isentropic efficiency of the HP turbine, [%]</td><td>91.5</td></tr><tr><td>Isentropic efficiency of the LP turbine, [%]</td><td>90</td></tr><tr><td>Isentropic efficiency of LP and HP pumps, [%]</td><td>88</td></tr><tr><td>Mechanical efficiency of pump motors, [%]</td><td>99</td></tr><tr><td>Mechanical efficiency of alternator, [%]</td><td>99</td></tr><tr><td>Auxiliaries consumption, [%] of electrical output</td><td>2</td></tr><tr><td>Maximal internal pinch point of reheater, [°C]</td><td>5</td></tr><tr><td>Maximal pinch points of HP and LP preheaters, [°C]</td><td>5</td></tr><tr><td>Pressure drop in steam generator, [kPa]</td><td>500</td></tr><tr><td>Pressure drop in reheater and preheaters, [kPa]</td><td>40</td></tr></table>

Table 4 reports hypotheses for the HTSE process that were mainly taken from bibliographic references [27].
<table><caption>**Table 4**
HTSE process performance hypothesis.</caption><tr><td>Cathode stream temperature at the SOEC stack inlet and outlet, [°C]</td><td>700</td></tr><tr><td>Anode stream temperature at the SOEC stack inlet and outlet, [°C]</td><td>700</td></tr><tr><td>Cathode stream H<sub>2</sub> mole fraction at the SOEC stack inlet, [%]</td><td>10</td></tr><tr><td>Steam utilization factor SG, [%]</td><td>60</td></tr><tr><td>Electricity consumption per kg of H<sub>2</sub> w<sub>H2.elec</sub>, [kWh/kg]</td><td>36</td></tr><tr><td>SOEC stack operating pressure at the cathode side (absolute), [kPa]</td><td>1.45 (unless another value is mentioned)</td></tr><tr><td>SOEC stack operating pressure at the anode side (absolute), [kPa]</td><td>1.45 (unless another value is mentioned)</td></tr><tr><td>Maximal pressure ratio of H<sub>2</sub> compressors</td><td>3.3</td></tr><tr><td>Isentropic efficiency of H<sub>2</sub> compressors / blowers, [%]</td><td>80</td></tr><tr><td>Isentropic efficiency of air compressors / blowers, [%]</td><td>85</td></tr><tr><td>Mechanical efficiency of H<sub>2</sub> or air compressors / blowers, [%]</td><td>95</td></tr><tr><td>Electrical efficiency of H<sub>2</sub> or air compressor / blower drivers, [%]</td><td>92</td></tr><tr><td>Low temperature heat exchanger efficiency, [%]</td><td>35</td></tr><tr><td>Refrigeration unit Coefficient Of Performance, [-]</td><td>2.5</td></tr><tr><td>Heat exchanger pressure losses, [kPa]</td><td>20</td></tr><tr><td>Heat recovery system efficiencies, [%]</td><td>90</td></tr><tr><td>Heat recovery system pressure losses, [kPa]</td><td>20</td></tr><tr><td>Cooler and intercooler efficiencies, [%]</td><td>90</td></tr><tr><td>Cooler and intercooler pressure losses, [kPa]</td><td>20</td></tr><tr><td>H<sub>2</sub> pressure delivery (absolute), [MPa]</td><td>3</td></tr><tr><td>H<sub>2</sub> temperature delivery, [°C]</td><td>33</td></tr><tr><td>Aerocondensing unit Coefficient Of Performance, [-]</td><td>20</td></tr><tr><td>Oxygen content in air-oxygen mixture, [%]</td><td>40 (unless another value is mentioned)</td></tr><tr><td>Electric heater efficiency, [%]</td><td>95</td></tr><tr><td>AC/DC converter efficiency, [%]</td><td>95</td></tr></table>

## Thermodynamic Modelling

The simulations are performed through a 0D, steady-state approach. Here are the main components equations:

- Heat Exchangers (HX) with phase change (Evaporator, Steam generator, Condenser, Preheaters, Intercoolers): in these phase-changing HX, there is a heat transfer between two fluids, where one of them changes phase. The energy balance between the secondary fluid (sf) and the working fluid (wf) in the condenser, preheaters and intercoolers is described in Equation (1). In the evaporator and in the steam generator, the same equation applies in the reverse way.

$$ \dot{Q}_{cd} = \dot{m}_{wf} \cdot (h_{wf.su.cd} - h_{wf.ex.cd}) \quad (1) $$

$$ \dot{Q}_{cd} = \dot{m}_{sf} \cdot (h_{sf.ex.cd} - h_{sf.su.cd}) $$

Equations (2) & (3) present the application of pinch point (pp) temperature difference in the condenser, with x0 and x1 being the saturation temperatures at qualities equal to 0 and 1, respectively.

$$ \dot{Q}_{pp.cd} = \dot{m}_{sf} \cdot (h_{sf.pp.cd} - h_{sf.su.cd}), \quad (2) $$

$$ \dot{Q}_{pp.cd} = \dot{m}_{wf} \cdot (h_{wf.x1.cd} - h_{wf.ex.cd}) $$

$$ \Delta T_{pp.cd} = T_{wf.x1.cd} - T_{sf.pp.cd} \quad (3) $$

- Sensible HX (Cooler, Heat Recovery Unit and Coupling HX): in these HX, two fluids are exchanging heat without any phase change. HX are considered to be counterflow. The energy balance taking place in the HX is the same than in a phase change HX, adding the heat transfer equation which depends on an assumed HX effectiveness (Equation (4)).

$$ \dot{Q}_{HX} = \dot{C}_{min,HX} \cdot \varepsilon_{HX} \cdot (T_{hot,HX} - T_{cold,HX}) \quad (4) $$

- Turbines: the turbines are used to convert the fluid internal energy in electricity. For both approaches of this paper, the turbines are calculated through a constant isentropic efficiency. The energy balance used to compute the turbine production corresponds to Equation (5):

$$ \dot{W}_{turb} = \dot{m}_{wf} \cdot \eta_{is.turb} \cdot (h_{wf.su.turb} - h_{wf.is.ex.turb}) \quad (5) $$

The corresponding electrical production on the shaft is given by:

$$ \dot{W}_{prod.elec} = (\sum \dot{W}_{turb}) \cdot (\eta_{mech.turb} \cdot \eta_{elec.alt}) \quad (6) $$

- Pumps, blowers, compressors: These compression machines are calculated thanks to a constant isentropic efficiency. Equation (7) is a generic equation which can be applied to all the cited machines.
$$ \dot{W}_{comp} = \dot{m}_{wf} \cdot (h_{wf,su,comp} - h_{wf,is,ex,comp}) / \eta_{is,comp} \quad (7) $$

The corresponding electrical consumption of the driving motor is given by:

$$ \dot{W}_{mot,elec} = \dot{W}_{comp} / (\eta_{mech,comp} \cdot \eta_{elec,mot}) \quad (8) $$

- Aerocondenser, Refrigeration unit: Equation (9) presents the coefficient of performance (COP), linking the electric consumption and the cooling duty.

$$ COP = \frac{\dot{Q}_{cooling}}{\dot{W}_{elec}} \quad (9) $$

- SOEC behaviour: a thermo-neutral behaviour is assumed. The SOEC behaviour is described through lumped-component model. Hence:

Notes:

* Inlet and outlet temperatures of all energetic fluxes are fixed at a constant temperature of 700 °C.

* A fixed ratio of steam conversion is imposed (equation (10)).

* The electrical consumption is given by equation (11).

$$ SC = \frac{\dot{m}_{H2,produced}}{\dot{m}_{H2O,in}} \quad (10) $$

$$ \dot{W}_{SOEC,elec} = \dot{m}_{H2,produced} w_{H2,elec} \quad (11) $$

Nomenclature

<table><tr><td>˙C</td><td>Heat capacity rate, W/K</td></tr><tr><td>h</td><td>Specific enthalpy, J/kg</td></tr><tr><td>ṁ</td><td>Mass flow rate, kg/s</td></tr><tr><td>n</td><td>Molar flow rate, mol/s</td></tr><tr><td>Q</td><td>Heat duty, W</td></tr><tr><td>SC</td><td>Steam conversion Ratio, -</td></tr><tr><td>T</td><td>Temperature, °C</td></tr><tr><td>w</td><td>Energy, J/kg or kWh/kg</td></tr><tr><td>Ẇ</td><td>Work, W</td></tr><tr><td colspan="2">Subscripts</td></tr><tr><td>alt</td><td>Alternator</td></tr><tr><td>cd</td><td>Condenser</td></tr><tr><td>cold</td><td>Cold side of a HX</td></tr><tr><td>comp</td><td>Compression machine</td></tr><tr><td>elec</td><td>Electrical</td></tr><tr><td>ex</td><td>Exhaust</td></tr><tr><td>hot</td><td>Hot side of a HX</td></tr><tr><td>in</td><td>Inlet</td></tr><tr><td>is</td><td>Isentropic</td></tr><tr><td>mech</td><td>Mechanical</td></tr><tr><td>min</td><td>Minimal</td></tr><tr><td>mot</td><td>Motor</td></tr><tr><td>out</td><td>Outlet</td></tr><tr><td>pp</td><td>Pinch Point</td></tr><tr><td>sf</td><td>Secondary fluid</td></tr><tr><td>su</td><td>Supply</td></tr><tr><td>th</td><td>Thermal</td></tr><tr><td>turb</td><td>Turbine</td></tr><tr><td>wf</td><td>Working Fluid</td></tr></table>

Appendix 2

Fig. 5 presents architecture coupling details for configurations 4, 5, 6 & 7, 8. The other thermal coupling configurations contain the same circuits and arrangements as in configuration 1 (given in Fig. 3).
<figure><img src="image_7.png" /><figcaption>Fig. 5. Thermal coupling architectures for alternative configurations (Top, from left to right: configurations 4, 5. Bottom, from left to right: configurations 6 & 7, 8)</figcaption></figure>

Table 5 reports the characteristics of the 16 simulated configurations.

<table><caption>**Table 5**

SMR-HTSE configurations (Heat origin and heat recovery purpose).</caption><thead><tr><th>Configurations</th><th>Heat origin in the Rankine cycle and transferred to the HT-COCIR</th><th>Heat recovery circuits IC1, C5<br>Purpose of the transfer: steam production for the HTSE (S1, S2 to boiler preheating, S2 to Heat-Pump) or preheating the water feedback line of the Rankine cycle (S2 to LT-COCIR)</th><th>Heat recovery circuits IC2, IC3, IC4</th></tr></thead><tbody><tr><td>Reference (config. 1.)<br>HTSE waste heat integrated in the Rankine cycle (config. 2.)<br>HTSE waste heat management (config. 3.)<br>One-way thermal coupling (config. 4.)<br>Direct coupling (config. 5.)<br>Heat from the Steam Generator (config. 6.)<br>Heat from Steam Generator with a high superheating degree (config. 7.)</td><td>HP Turbine Outlet<br>Direct steam<br>Steam Generator</td><td>(S1) (S2) to LT-COCIR<br>(S2) to LT-COCIR<br>(S1) (S2) to LT-COCIR<br>(S1)<br>(S1) (S2) to LT-COCIR</td><td>(S2) to LT-COCIR<br>(S1) (S2) to LT-COCIR<br>(S1)<br>(S2) to LT-COCIR</td></tr></tbody></table>

(continued on next page)
<table><caption>Table 5 (continued)</caption><thead><tr><th>Configurations</th><th>Heat origin in the Rankine cycle and transferred to the HT-COCIR</th><th>Heat recovery circuits IC1, C5<br>Purpose of the transfer: steam production for the HTSE (S1, S2 to boiler preheating, S2 to Heat-Pump) or preheating the water feedback line of the Rankine cycle (S2 to LT-COCIR)</th><th>Heat recovery circuits IC2, IC3, IC4</th></tr></thead><tbody><tr><td>Heat from the LP Turbine (config. 8.)</td><td>LP Turbine</td><td></td><td></td></tr><tr><td>Pressurized SOEC (config. 9.)</td><td rowspan="6">Steam Generator</td><td></td><td></td></tr><tr><td>Pressurized SOEC with pure oxygen (config. 10.)</td><td></td><td></td></tr><tr><td>Pressurized SOEC with expansion (config. 11.)</td><td></td><td></td></tr><tr><td>Pressurized SOEC with expansion and pure oxygen (config. 12.)</td><td></td><td></td></tr><tr><td>Pressurized SOEC with expansion and pure oxygen (config. 13.) (20 bar)</td><td></td><td></td></tr><tr><td>Ideal waste heat (config. 14.)</td><td>–</td><td>(S1)</td><td>(S1)</td></tr><tr><td>Electrical heating device (config. 15.)</td><td></td><td>(S1) (S2) to boiler preheating</td><td>(S2) to boiler preheating</td></tr><tr><td>Heat-pump (config. 16.)</td><td></td><td>(S1) (S2) to Heat-Pump<br>Evaporator</td><td>(S2) to Heat-Pump<br>Evaporator</td></tr></tbody></table>

## Data availability

The authors do not have permission to share data.

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