# Dynamic simulation of a solar-based iron producing plant using hydrogen as reductant

Damien Jaffré, Sylvain Rodat, Stéphane Abanades

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Damien Jaffré, Sylvain Rodat, Stéphane Abanades. Dynamic simulation of a solar-based iron producing plant using hydrogen as reductant. Chemical Engineering Science, 2025, 320, pp.122429. 10.1016/j.ces.2025.122429. hal-05221499

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# Dynamic simulation of a solar-based iron producing plant using hydrogen as reductant

Damien Jaffré, Sylvain Rodat, Stéphane Abanades

CNRS, Processes, Materials and Solar Energy Laboratory (PROMES), 7 rue du Four Solaire, 66120 Odeillo Font-Romeu, France

## ARTICLE INFO

### Keywords:

Solar metallurgy

Direct reduced iron

Iron/steel making

Solar reactor

Hydrogen

Thermochemical iron ore reduction

Dynamic modelling

## ABSTRACT

Steel metallurgy is a high consumer of fossil energy and a major emitter of CO₂. The process of direct reduction of iron oxide using concentrated solar power and H₂ as reductant is a promising path for carbon-neutral steel making. This study aims to evaluate for the first time the potential of large-scale solar iron-producing plant through dynamic modelling to predict annual process performance under real fluctuating solar irradiation. The model, based on unsteady mass and energy balance equations, was first validated for a lab-scale reactor. An upscaled 10 MW solar reactor operating continuously was then designed and simulated with a loaded mass of 4.5 tons of iron oxide, reaching an equilibrium temperature around 1000 °C. The equilibrium temperature decreased (1530–680 °C) when increasing the quantity of loaded iron oxide (1–22.5 tons), while iron production still increased (0.8–1.8 kg/kWh of solar energy). The effect of decreasing the direct normal irradiation (DNI) (1000 to 500 W/m²) on the decrease of the equilibrium temperature (1016 to 840 °C) and thus on the decrease of the reaction rate and production was emphasized. Dynamic simulation yielded an annual Fe production capacity of almost 30,000 tons in design conditions using representative solar meteorological data. Step-by-step steady-state simulations were compared to dynamic simulations, giving equivalent results for long term process yield assessment. Annually, 20 % of the solar energy was dedicated to the reaction and 70 % to reactants heating, with less than 10 % of heat losses. The instantaneous iron production was chiefly proportional to the DNI. The developed dynamic model successfully predicted the global production capacity and annual performance of large-scale solar metallurgical plants.

## 1. Introduction

In the context of climate change and fossil fuel depletion, the decarbonation of economy is a critical international route to ensure sustainability of society. The International Energy Agency (IEA) defined 50 key components of the energy systems that are critical for clean energy transitions. Steel industry and thus iron making is one of these 50 components, as iron and steel production processes account for around 34 % of the total world coal consumption with a carbon footprint of iron of 1.4 tons of CO₂ per ton of iron (Birol, 2021). 92 % of the iron manufacturing uses unabated blast furnace as reducing process (IEA, 2023). This process involves coke for both supplying the energy and the carbon reductant needed for the reduction of iron oxide. The remaining 8 % of iron is manufactured by fossil-based DRI (direct reduced iron) without carbon capture and storage. The Net Zero Emissions (NZE) by 2050 scenario targets a decrease of blast furnace to 83 % with an increasing use of recycled scrap metallic input in the meantime. In

addition, using low-carbon reductants is a targeted path to reduce the carbon intensity of DRI (IEA, 2023).

Iron oxide reduction can be achieved using several reductants (C, CO, CH₄, H₂). Their comparative performance and behavior have been investigated (Chuayboon and Abanades, 2024; Heidari et al., 2021). In order to decarbonize the steel industry, the roadmap encourages that DRI using H₂ as a reductant should reach 5 % of the steel production (IEA, 2024). However, H₂ does not exist in native form in industrial quantity on Earth. Hence, H₂ needs to be produced from renewable and carbon-free resources.

Above 570 °C, the direct reduction of iron oxide with H₂ is a three-step reaction ((1) to (3)), with iron(III) oxide (hematite, Fe₂O₃) successively reduced to magnetite (Fe₃O₄), then to wüstite (FeO), and finally to iron (Fe):

$$3\text{Fe}_2\text{O}_3 + \text{H}_2 \rightarrow 2\text{Fe}_3\text{O}_4 + \text{H}_2\text{O} \quad (1)$$

$$2\text{Fe}_3\text{O}_4 + 2\text{H}_2 \rightarrow 6\text{FeO} + 2\text{H}_2\text{O} \quad (2)$$

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: stephane.abanades@promes.cnrs.fr (S. Abanades).</footnote>
Nomenclature

$A_{aper}$ Area of the reactor aperture (m²)

$COP$ Coefficient of performance of the plant (g/kWh)

$Cp_j(T)$ Specific heat capacity at constant pressure of the compound j at reactor temperature (J/mol.K)

$CR$ Concentration ratio (–)

$DNI$ Direct Normal Irradiation (W/m²)

$E_a$ Activation energy (J/mol)

$f(\alpha)$ Function of the solid-gas reaction model depending on the extent of reaction (–)

$F_j^{inlet}$ Inlet molar flowrate of compound j (mol/s)

$F_j^{outlet}$ Outlet molar flowrate of compound j (mol/s)

$h_j$ Molar enthalpy of compound j

$k(T)$ Kinetic rate of the reaction at reactor temperature (1/s)

$k_0$ Pre-exponential factor (1/s)

$m$ Reaction order with respect to H₂ (–)

$n_0$ Initial quantity of solid reactant (mol)

$n_f$ Final quantity of solid reactant (mol)

$n_j$ Quantity of the compound j (mol)

$P_{reac}$ Pressure in the reactor (Pa)

$Q_{cond}$ Conduction losses (W)

$Q_{rad}$ Radiation losses (W)

$Q_{sun}$ Incoming solar power (W)

$R$ Ideal gas constant (J/mol.K)

$R_{th}$ Thermal resistance of the apparatus (K/W)

$T_{ext}$ Ambient temperature (K)

$T_{reac}$ Temperature of the reactor (K)

$U$ Internal energy of the reactor (J)

$V_{reac}$ Volume of the reactor (m³)

$y_j$ Molar fraction

Greek letters

$\alpha$ Extent of reaction (–)

$v_j$ Stoichiometric coefficient of the species j in the reduction reaction

$\Delta H$ Reaction enthalpy (J/mol)

$\Delta t$ Time step (s)

$$6\text{FeO} + 6\text{H}_2 \rightarrow 6\text{Fe} + 6\text{H}_2\text{O} \quad (3)$$

Those three successive steps lead to the global reaction of direct reduced iron (4):

$$\text{Fe}_2\text{O}_3 + 3\text{H}_2 \rightarrow 2\text{Fe} + 3\text{H}_2\text{O}(\text{g}) \quad \Delta H' = 97.5 \text{ kJ/mol} \quad (4)$$

For a complete reduction of iron oxide, temperature from 500 °C to 1000 °C is needed with an adjusted residence time in the reactor (Abanades and Rodat, 2024). Hydrogen was used as a reducing agent to convert iron oxide into iron by the recovery of valuable elements from iron tailings (Meng et al., 2025), or to process iron minerals (Tang et al., 2025; Tian et al., 2025), using natural gas or electricity as the process heating source. However, these processes still used carbon-based energy sources to reach the required temperature. To achieve the temperature target with a renewable source, a pertinent route is the use of concentrated solar thermal (CST) energy. The principle of CST is to concentrate with the help of mirrors the solar energy at a focal point or line to reach high flux density and high temperature.

Solar energy is an efficient power supplier for thermochemical reactions, especially involving iron ore processing (Purohit et al., 2021; Rahbari et al., 2025) or redox pairs (Abanades and Villafan-Vidales, 2013; Abanades, 2023). Additionally, reduction of iron oxide was considered as part of a two-step cycle for producing hydrogen/syngas from H₂O and CO₂ (Steinfeld et al., 1999; Abanades and Villafan-Vidales, 2011). Iron oxide redox cycling process using solar energy was identified as a promising route for hydrogen storage (Brinkman et al., 2021). Iron and syngas were produced by reducing Fe₂O₃ and Fe₃O₄ with methane in high-temperature solar thermochemical processes (Steinfeld, 1998; Chuayboon et al., 2020). The continuous solar-driven iron oxide (Fe₂O₃) or zinc oxide (ZnO) reduction combined with gasification of agricultural biomass to produce carbon-neutral syngas and metal in a single process was also studied (Chuayboon and Abanades, 2023; Chuayboon and Abanades, 2024).

Several types of solar chemical reactors for the thermal reduction of metal oxides were investigated. A thermogravimetric reactor located at the focal point of a concentrating parabola was used to reduce tungsten trioxide. The carboreduction reaction was complete upon heating to 1280 °C. A high specific surface area of carbon favored the solid-gas reaction mechanism (Villafán-Vidales et al., 2017). A packed-bed solar reactor was dedicated to the reduction of iron oxide mixed with a sand bed irradiated by concentrated solar energy and swept by a gas mixture

of argon and hydrogen. The reduction process was demonstrated up to 1000 °C. Importance of temperature, particle size, and H₂ mole fraction was unraveled (Abanades and Rodat, 2024). Solar reactors using screw-feeders to bring the metal oxide in the reacting zone instead of a settled packed-bed allowed a continuous feeding of the reactor and thus a continuous production of metal (Abanades et al., 2007; Charvin et al., 2008).

Rotary kilns are usually selected for high temperature solar processes with moving particle bed as they are able to reach higher thermal efficiencies than other reactor types (Alonso et al., 2017). Rotating-cavities associated with conical-shape receiver or vortex receiver were designed for the solar production of hydrogen (Steinfeld, 2005). Limestone calcination producing 95 % to 98 % purity lime was processed in a 10-kW solar rotary kiln. Residence time, decomposition temperature and feed rate were identified as key parameters, and thermochemical efficiency (defined as the ratio between the reaction enthalpy and the incoming solar power) reached 20 % to 35 % (Meier et al., 2004; Meier et al., 2006). Laboratory zinc oxide reduction was carried out. The cavity reached 2000 K, leading to a purity of Zn of 95 %, with 14 % of thermochemical efficiency (Müller et al., 2006). A temperature of 900 °C was reached in a solar-heated rotary kiln for batch-wise redox cycles of cobalt as a mean of energy storage (Neises et al., 2012).

The different motions and mixing mechanisms of solid particles within a rotary kiln were studied to maximize heat transfer, depending on the Froude number and the filling degree. Rolling mode was identified as the best mode to ease heat transfer (Mellmann, 2001; Mungyeko Bisulandu and Huchet, 221 (2023)), leading to a 90 % thermochemical reactor efficiency for the biomass pyrolysis process (Amjed et al., 2024). However, solar rotary kilns are limited to less than 100 MWth for geometrical and optical considerations. A thermal efficiency of 83 % was reached for the heating of solid particles (Gallo et al., 2016). Specifically, a novel rotary-cavity reactor was designed, constructed and tested for a lab-scale experimental study of solar direct iron ore reduction with H₂ as reductant (Abanades et al., 2025).

Upscaling those technologies and evaluating them in industrial conditions requires to model the processes and to analyze the dynamic operation of the solar process on a yearly basis. The main issue for the modelling of thermochemical processes is to well understand and characterize the kinetic mechanisms ruling the reaction. Specific kinetic models of iron ore reduction by H₂ simulating the successive reactions, were developed and applied to a shaft furnace. An optimal temperature of 800 °C for the DRI with H₂ as reductant was identified (Wagner,
2008).

The main reaction mechanism leading the process is strongly dependent on the experimental conditions. Temperature, H₂/CO ratio, H₂ flow rate, mineralogy, particle size, and impurities are depicted as key parameters of the kinetics of iron ore reduction by hydrogen (Heidari et al., 2021), as well as surface area of oxide particles and concentration of H₂ (Hou et al., 2012). Using simulated light flux, reduction experiments by hydrogen were carried out in batch mode on iron ore pellets or disks, reaching 96 % reduction yield (Sanglard et al., 2024). Gas flow rate is a key parameter for optimizing the process. An over stoichiometric ratio of H₂ is necessary with various values depending on the reactor geometry (Wagner, 2008; Jabbour and El Hassan, 2022; Abanades and Rodat, 2024). In Fe₂O₃ reduction process, the reaction rate increased with both temperature and H₂ content in inlet gas (Piotrowski et al., 2005) and was proportional to the molar concentration of H₂, with a reaction order of 1 (Barde et al., 2016). Based on TGA measurements, single-step kinetic rates of the reduction of Fe₂O₃ by H₂ were proposed (Monazam et al., 2014; Abanades and Rodat, 2024).

Previous dynamic and steady-state modeling tools have been developed to simulate solar-based thermochemical processes. Dynamic modelling of a solar thermochemical reactor devoted to ZnO reduction operating continuously was performed to simulate its behavior during transient periods (Charvin et al., 2008). Simulations showed that radiative losses through the aperture become predominant at 50 MW scale and a minimum concentration ratio of 2500 was necessary to reach a temperature above 2000 K. Dynamic simulation coupling solar/combustion heating and steam biomass gasification using real solar irradiation data was developed to estimate the annual performance of large-scale solar gasification plants (Boujjat et al., 2020; Curcio et al., 2023; Curcio et al., 2025). Solar processes involving high temperature air generator (above 1000 °C) were investigated. Useful thermal efficiency above 70 % was identified, as well as global thermochemical efficiencies between 20 % and 40 % (Rafique et al., 2022; Ingenhoven et al., 2023; Rahbari et al., 2025). In addition, dynamic modelling of DRI in shaft-furnace with hydrogen and syngas as reductant and methane as heat source was studied, helping to understand the plant behavior during transient periods (Immonen and Powell, 2024).

However, dynamic modelling of solar-based iron-making plants using hydrogen as reductant was never investigated. This study addresses the dynamic simulation and upscaling of the reduction of iron ore with hydrogen and solar energy. To predict the production yield of an industrial iron-making solar plant, new dedicated dynamic modelling tools are needed. The goal of this work is to evaluate the production capacity of an industrial scale solar iron-making plant of 10 MW of incoming solar thermal power under real solar irradiation conditions and to predict the transient behavior of the solar metallurgical process, without a precise design of such an industrial-scale plant. A dynamic simulation was performed to predict the reactor performance in transient conditions under variable solar power input using representative solar irradiation data. To validate the quality of the model, simulation of a lab-scale reactor representative of the installation at CNRS-PROMES in Odeillo, France, was first performed and compared with experimental data. Then, simulations were carried out for a large-scale facility representative of future industrial solar-based iron producing plants. To date, such dynamic modelling to simulate DRI reactor operation under fluctuating solar power input has never been proposed to our knowledge. Its potential to predict the global production capacity and annual performance of large-scale solar metallurgical plants was demonstrated.

## 2. Description of the solar reactors

The studied thermochemical reactors are powered by a concentrated solar energy system using high-intensity solar radiation to drive the iron ore reduction reaction. The solar concentration system typically consists of mirrors that focus sunlight onto the receiver aperture, which then

transfers the concentrated energy to the reactor. This heat is used to initiate and sustain the thermochemical process.

The lab-scale reactor installed at CNRS-PROMES is placed at the focal point of a 2 m diameter concentrating parabola. A heliostat tracks the sun and reflects the solar radiation toward the parabola parallel to its focal axis. Rays are then concentrated at the front face of the thermochemical reactor. The irradiation pattern at the focal point of a parabola is a Gaussian profile. The peak concentration ratio (CR) is 10,500 and the integrated flux in the 18 mm wide focal zone is 1.4 kW, resulting in a mean concentration ratio of 5500.

The cavity receiver of the reactor is made of stainless steel and presents a truncated conical shape (Fig. 1a) (length: 97 mm; inner diameter: 60 mm at the back, 80 mm at the front; outer diameter: 92 mm). The conical shape of the receiver induces an inclination of the internal wall of 5.9° with the horizontal. A diaphragm made of alumino-silicate is placed at the front face of the cavity to allow the concentrated solar power to enter through the aperture while reducing the radiation losses. Alumino-silicate insulation is also placed around the cavity receiver to limit the conduction losses (outer diameter: 260 mm, length: 200 mm, thermal conductivity: 0.2 W/m.K). The global thermal resistance of the system is estimated to be 1.1 K/W. Reactants (iron oxides and hydrogen) are fed by a feeding screw at the back of the cavity. Argon is injected through the diaphragm aperture and from the bottom inlet to ensure the sweep of the produced H₂O. Solid particles exit the cavity by gravity and are collected through the bottom tank. The gas mixture is evacuated through the top outlet.

The simulated large-scale reactor is upscaled at 10 MW (Fig. 1b). In order to reach a suitable range of temperature for DRI (500 to 1000 °C), solar tower can be a suitable concentrating technology at this power range. A large field of heliostats tracks the sun and concentrates the solar rays at the front of the reactor placed at the top of the tower. A typical concentration ratio (CR) for such a field is 600. A secondary concentrator with a CR of 4 is supposed to be placed in front of the aperture to reach a total CR of 2400. This secondary concentrator could either be a beam-down reflector or CPC at the aperture (Agrafiotis et al., 2015). However, the concentrating device is not specifically studied in this work. Similar to the lab-scale reactor, a stainless-steel receiver is placed in the reactor to absorb the incoming solar power. The cylindrical reactor cavity, designed to maintain a 1000 °C temperature at nominal conditions is 3.9 m long with a diameter of 3.9 m and an aperture of 2.3 m (for 10 MW power input). The cavity is insulated by two layers of insulation, a first layer dedicated to high temperature directly around the steel cavity with a thermal conductivity of 0.2 W/(m.K) and a second dedicated to lower temperature at the outside with a thermal conductivity of 0.05 W/(m.K). A sensitivity study showed the impact of insulation thickness on the behavior of the reactor (Supplementary Materials, section 2.3). A 5 cm thickness for both layers was selected to be representative of the conduction losses, leading to an estimated thermal resistance of 9x10⁻³ K/W. Reactants are fed from the cavity back through a screw-feeder in the same way as in the lab-scale reactor. Table 1 presents the geometrical characteristics of both reactors.

In industrial conditions, no argon is needed anymore, thus enabling to maximize the H₂ concentration, which is a kinetic factor of the reaction. The potential water vapor condensation is mitigated through the injection of pure H₂ in excess (instead of Ar) which also acts as the carrier gas. Then, the transported H₂O can be separated by condensation and unreacted H₂ can be recycled back into the reactor. Moreover, as only H₂ and H₂O are present in the gas mix, recirculation of the heated excess H₂ is feasible after H₂O separation, for example by condensation and recovering steam enthalpy with preheating of the incoming reactants. Thus, only the reacting H₂ needs to be supplied and heated in the reactor, drastically reducing the amount of energy to preheat H₂.
<figure><img src="image_3.png" /><figcaption>Fig. 1. Scheme of the directly-irradiated cavity-type lab-scale reactor (a) and the large-scale reactor (b).</figcaption></figure>

## 3. Description of the dynamic model

### 3.1. Global model principles

The aim of the dynamic model is to predict the production of iron within the solar reactor under fluctuating solar power input. To achieve this goal, a 0D model was developed using unsteady mass and energy balance equations to determine the variation of the reactor temperature and of the quantity of each species under real-sun conditions. A perfectly stirred isothermal reactor is supposed with the temperature of the receiver, the gas mixture, and the solid particles being equal. The set of equations ruling the temperature evolution in the reactor is strongly non-linear. Thus, a discrete numerical scheme is built to solve the set of equations at each time step. An explicit first order Euler scheme is used to solve the model. The complete numerical scheme is available in the Supplementary Materials (section 1).

The annual production of the plant is investigated for various initial or functioning conditions (quantity of iron oxide in the reactor, temperature, size of the reactor) in order to evaluate the performance variations of the plant. The thermochemical efficiency, i.e., the ratio between the reaction power and the incoming solar power, is evaluated and compared in different scenarios. To evaluate the performance of the reactor, the coefficient of performance (COP) is introduced and defined as the ratio between the mass of produced Fe and the incoming solar energy.

To run the dynamic simulations, meteorological data files with a 2-

minute time step are used. This time step was chosen as a compromise to ensure the stability of the model with a reduced calculation time and data (more details provided in Supplementary Materials, section 2.1). The 2-minute meteorological data file is a typical meteorological year data (TMY) set from Odeillo, France, extracted from Meteonorm 7.2.1. TMY is a format of data set of values of solar radiation and meteorological elements (Kalogirou, 2012) generated out of long-term (20 years) of observational data.

### 3.2. Mass balance of each species

The mass balance equation gives the general formulation for the evolution of the quantity n of a given compound j:

$$ \frac{dn_j}{dt} = F_{j,inlet}^{inlet} - F_{j,outlet}^{outlet} + v_j \cdot k_{T_{reac}} \cdot n_{Fe_2O_3,0} \quad (5) $$

Where $F_{j,inlet}^{inlet}$ is the inlet mass flowrate, $F_{j,outlet}^{outlet}$ is the outlet mass flowrate, $v_j$ is the stoichiometric coefficient of the compound j, k is the kinetic rate of the reaction, T is the temperature of the reactor (assumed isothermal), and $n_{Fe_2O_3,0}$ is the quantity of iron oxide in the reactor and at the start of the reaction. A zero-order kinetic rate is assumed based on previous experiments (Abanades and Rodat, 2024).

As the global DRI reaction (4) involves four different species, four mass balance equations are derived from (5):
<table><caption>**Table 1**

Characteristics of the two reactors.</caption><thead><tr><th></th><th>Lab-scale (Abanades et al., 2025)</th><th>Large scale</th></tr></thead><tbody><tr><td>Design power</td><td>1.4 kW</td><td>10 MW</td></tr><tr><td>Concentration ratio</td><td>5500</td><td>2400</td></tr><tr><td>Design temperature</td><td>1000 °C</td><td>1000 °C</td></tr><tr><td>Design fill ratio</td><td>1.7 %</td><td>1.9 %</td></tr><tr><td>Inner diameter</td><td>60 to 80 mm (conical shape)</td><td>3.9 m</td></tr><tr><td>Aperture diameter</td><td>18 mm</td><td>2.3 m</td></tr><tr><td>Aperture area</td><td>2.5 cm<sup>2</sup></td><td>4.2 m<sup>2</sup></td></tr><tr><td>Inner volume</td><td>440 cm<sup>3</sup></td><td>46.6 m<sup>3</sup></td></tr><tr><td>Receiver mass</td><td>2.1 kg</td><td>24 tons</td></tr><tr><td>Thermal resistance</td><td>1.1 K/W</td><td>9x10<sup>-3</sup> K/W</td></tr></tbody></table>

$$ \frac{dn_{Fe_2O_3}}{dt} = F_{Fe_2O_3}^{inlet} - k_{T_{reac}} \cdot n_{Fe_2O_3,0} \quad (6) $$

$$ \frac{dn_{Fe}}{dt} = 2 \cdot k_{T_{reac}} \cdot n_{Fe_2O_3,0} - F_{Fe_1}^{outlet} \quad (7) $$

$$ \frac{dn_{H_2}}{dt} = F_{H_2}^{inlet} - 3 \cdot k_{T_{reac}} \cdot n_{Fe_2O_3,0} - y_{H_2} \cdot F_{outlet} \quad (8) $$

$$ \frac{dn_{H_2O}}{dt} = 3 \cdot k_{T_{reac}} \cdot n_{Fe_2O_3,0} - y_{H_2O} \cdot F_{outlet} \quad (9) $$

Where the molar fraction $y_j$ is defined by:

$$ y_j = \frac{n_j}{\sum n_j} \quad (10) $$

The feeding rate of $Fe_2O_3$, $F_{Fe_2O_3}^{inlet}$, is chosen according to the controlling strategy of the installation. A continuous operating mode is selected by simulating a process where production of Fe is carried out with a regulated constant quantity of oxide in the reactor. In this logic, $F_{Fe_2O_3}^{inlet}$ is continuously equal to the instant consumption of $Fe_2O_3$. $F_{Fe_1}^{outlet}$ is the outlet flowrate of solid iron and is supposed to be equal to the instantaneous iron production. The quantity of pure iron in the reactor is thus always equal to 0.

### 3.3. Reaction kinetic rates

The extent of reaction $\alpha$ is defined as the ratio between the quantity of reactant already consumed and the maximal quantity of reactant able to react:

$$ \alpha = \frac{n_0 - n}{n_0 - n_f} \quad (11) $$

Where $n_0$ is the initial quantity of solid reactant, $n_f$ is the theoretical final quantity of solid reactant, and $n$ is the current quantity of solid reactant. The reaction rate is generally derived from the Arrhenius law:

$$ \frac{d\alpha}{dt} = k_0 \cdot \exp\left(-\frac{E_a}{R \cdot T_{reac}}\right) f(\alpha) \quad (12) $$

To simulate the reaction occurring in the real-sun PROMES lab-scale reactor, the kinetic parameters were derived from experimental data previously generated. In the data analysis of this experimental campaign, a power function of the $H_2$ mole fraction was identified as a good fit for the reaction rate while the activation energy was directly

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

Parameters values of the kinetic model (Abanades and Rodat, 2024).</caption><thead><tr><th>Parameter</th><th>Value</th><th>Unit</th></tr></thead><tbody><tr><td>k<sub>0</sub> (lab scale)</td><td>0.0074</td><td>1/s</td></tr><tr><td>k<sub>0</sub> (large scale)</td><td>0.0456</td><td>1/s</td></tr><tr><td>E<sub>a</sub></td><td>38,500</td><td>J/mol</td></tr><tr><td>m</td><td>1.213</td><td>–</td></tr></tbody></table>

derived from experimental data (Abanades and Rodat, 2024). A sensitivity analysis unraveled the impact of the activation energy on the behavior of the reactor (increasing the activation energy by 20 % decreased the global performance of the reactor by 16 %, whereas decreasing $E_a$ by 20 % led to an increase of the global iron production by 20.8 %, as detailed in Supplementary Materials, section 2.4). $k_0$ was set to obtain a particle reaction time of 60 min at lab-scale according to the same study and 15 min in design conditions for the large-scale reactor. The iron reduction process was supposed to be complete with no by-product formation, according to thermodynamic and kinetic analysis (Abanades and Rodat, 2024; Abanades et al., 2025). Then, based on equation (12), the reaction rate is defined as (13) with the parameters values of Table 2.

$$ \frac{d\alpha}{dt} = k_0 \cdot \exp\left(-\frac{E_a}{R \cdot T_{reac}}\right) \cdot [y_{H_2}]^m \quad (13) $$

The perfect gas law defines the total quantity of gas $n_{gas}$ in the reactor (14). Then, the total excess of gas flowing out of the reactor during the time step $\Delta t$ can be determined (15).

$$ n_{gas} = \frac{P_{reac} \cdot V_{reac}}{R \cdot T_{reac}} \quad (14) $$

$$ F_{outlet} = \frac{\sum_j n_j \cdot gas - n_{gas}}{\Delta t} \quad (15) $$

The outlet molar flowrate of each gaseous species $F_j^{outlet}$ is proportional to their molar fraction $y_j$ in the reactor (16):

$$ F_j^{outlet} = y_j \cdot F_{outlet} \quad (16) $$

### 3.4. Energy balance

The reaction rate is mainly driven by the reactor temperature. This temperature was calculated by solving the energy balance equation including the solar incoming power, the variation of enthalpy of the reactants from input to reactor temperature, the enthalpy of reaction at the reactor temperature, and the conduction and radiation losses (17). The concentrated solar energy $Q_{sun}$ depends on the Direct Normal Irradiation (DNI), which is the power density coming from the sun direction on a surface normal to the sun rays, the aperture area, and the concentration ratio (CR) (18). Conduction losses $Q_{cond}$ through the reactor walls are simulated by the thermal resistance $R_{th}$ of the reactor (19). The receiver is supposed to be a blackbody cavity emitting through the front aperture of area $A_{aper}$, leading to the expression of the radiation losses $Q_{rad}$ (20). All the other external walls are supposed to be at low temperature and thus their radiation losses can be neglected.

$$ \frac{dU}{dt} = Q_{sun} - \sum_j F_j^{inlet} (h_{j,T_{reac}} - h_j^{inlet}) - \Delta H_{T_{reac}} - Q_{cond} - Q_{rad} \quad (17) $$

$$ Q_{sun} = \text{DNI} \cdot CR \cdot A_{aper} \quad (18) $$

$$ Q_{cond} = \frac{T_{reac} - T_{ext}}{R_{th}} \quad (19) $$

$$ Q_{rad} = \sigma \cdot A_{aper} (T_{reac}^4 - T_{ext}^4) \quad (20) $$

The reactor mass to be heated includes the mass of the steel receiver, of the iron oxide, and of the insulation. The temperature of the reactor is supposed to be uniform both in the steel receiver and in the gas and solid zone. Thus, a unique temperature is set for both receiver and gas mixture. Hence, the energy balance (17) gives an expression of the internal energy variation of the reactor (21) and then the temperature variation of the reactor (22). The impact of the thermal inertia on the model stability is studied in Supplementary Materials (section 2.2). A 5 cm thick receiver provided representative performance results with
<table><caption>**Table 3**
Description of simulation runs at equilibrium points.</caption><thead><tr><th rowspan="2"></th><th rowspan="2">Run#</th><th colspan="4">Simulation inputs</th><th colspan="4">Simulation results</th><th colspan="8">Power breakdown</th></tr><tr><th>Iron oxide mass [g]</th><th>H<sub>2</sub> Flow rate (NL/min)</th><th>Ar flow rate (NL/min)</th><th>DNI (W/m<sup>2</sup>)</th><th>Reaction rate (%/min)</th><th>Temperature (°C)</th><th>Iron production (g/min)</th><th>Reaction power (W)</th><th>Thermochemical efficiency (Wrec/Wsun)</th><th>COP (g/kWh sun)</th><th>Conduction loss</th><th>Excess H<sub>2</sub> heating</th><th>Reactant H<sub>2</sub> heating</th><th>Ar heating</th><th>Radiation loss</th><th>Fe<sub>2</sub>O<sub>3</sub> preheat</th><th>Reaction power</th><th>Total power</th></tr></thead><tbody><tr><td rowspan="3">LAB-SCALE</td><td>1</td><td>40</td><td>1</td><td>1.5</td><td>1000</td><td>0.0162</td><td>1168 °C</td><td>0.45</td><td>3.83</td><td>0.27 %</td><td>19.4</td><td>74.8 %</td><td>1.3 %</td><td>0.5 %</td><td>1.9 %</td><td>20.4 %</td><td>0.8 %</td><td>0.3 %</td><td>1400 W</td></tr><tr><td>2</td><td>30</td><td>1</td><td>1.5</td><td>1000</td><td>0.0162</td><td>1170 °C</td><td>0.34</td><td>2.88</td><td>0.21 %</td><td>14.6</td><td>74.9 %</td><td>1.5 %</td><td>0.4 %</td><td>1.9 %</td><td>20.5 %</td><td>0.6 %</td><td>0.2 %</td><td>1400 W</td></tr><tr><td>3</td><td>30</td><td>0.5</td><td>2</td><td>1000</td><td>0.0163</td><td>1172 °C</td><td>0.34</td><td>2.90</td><td>0.21 %</td><td>14.7</td><td>75.1 %</td><td>0.5 %</td><td>0.4 %</td><td>2.6 %</td><td>20.7 %</td><td>0.6 %</td><td>0.2 %</td><td>1400 W</td></tr><tr><td rowspan="5">LARGE-SCALE</td><td>4</td><td>0</td><td>1</td><td>1</td><td>1000</td><td>0.0166</td><td>1182 °C</td><td>0.00</td><td>0.00</td><td>0.00 %</td><td>0</td><td>75.7 %</td><td>1.9 %</td><td>0.0 %</td><td>1.3 %</td><td>21.2 %</td><td>0.0 %</td><td>0.0 %</td><td>1400 W</td></tr><tr><td>5</td><td>1,000,000</td><td>750,000</td><td>0</td><td>1000</td><td>0.1893</td><td>1529 °C</td><td>132,400</td><td>1,001,000</td><td>10.0 %</td><td>797</td><td>1.9 %</td><td>0.0 %</td><td>27.6 %</td><td>0.0 %</td><td>17.4 %</td><td>42.9 %</td><td>10.0 %</td><td>10 MW</td></tr><tr><td>6</td><td>2,250,000</td><td>750,000</td><td>0</td><td>1000</td><td>0.1130</td><td>1227 °C</td><td>178,000</td><td>1,474,000</td><td>14.8 %</td><td>1070</td><td>1.6 %</td><td>0.0 %</td><td>29.2 %</td><td>0.0 %</td><td>8.4 %</td><td>46.1 %</td><td>14.8 %</td><td>10 MW</td></tr><tr><td>7</td><td>4,500,000</td><td>750,000</td><td>0</td><td>1000</td><td>0.0682</td><td>1016 °C</td><td>215,000</td><td>1,936,000</td><td>19.4 %</td><td>1292</td><td>1.3 %</td><td>0.0 %</td><td>28.8 %</td><td>0.0 %</td><td>4.6 %</td><td>45.9 %</td><td>19.4 %</td><td>10 MW</td></tr><tr><td>8</td><td>9,000,000</td><td>750,000</td><td>0</td><td>1000</td><td>0.0398</td><td>848 °C</td><td>251,000</td><td>2,394,000</td><td>24.00 %</td><td>1508</td><td>1.1 %</td><td>0.0 %</td><td>27.7 %</td><td>0.0 %</td><td>2.6 %</td><td>44.6 %</td><td>24.0 %</td><td>10 MW</td></tr><tr><td rowspan="3">LAB-SCALE</td><td>9</td><td>22,500,000</td><td>750,000</td><td>0</td><td>1000</td><td>0.0191</td><td>678 °C</td><td>300,000</td><td>2,913,000</td><td>29.21 %</td><td>1807</td><td>0.8 %</td><td>0.0 %</td><td>26.3 %</td><td>0.0 %</td><td>1.3 %</td><td>42.3 %</td><td>29.2 %</td><td>10 MW</td></tr><tr><td>10</td><td>40</td><td>1</td><td>1.5</td><td>900</td><td>0.0133</td><td>1087 °C</td><td>0.37</td><td>3.27</td><td>0.26 %</td><td>17.8</td><td>77.2 %</td><td>1.5 %</td><td>0.4 %</td><td>2.0 %</td><td>18.0 %</td><td>0.7 %</td><td>0.3 %</td><td>1260 W</td></tr><tr><td>11</td><td>40</td><td>1</td><td>1.5</td><td>800</td><td>0.0105</td><td>999 °C</td><td>00.29</td><td>2.68</td><td>0.24 %</td><td>15.8</td><td>79.8 %</td><td>1.6 %</td><td>0.3 %</td><td>2.0 %</td><td>15.5 %</td><td>0.6 %</td><td>0.2 %</td><td>1120 W</td></tr><tr><td rowspan="6">LARGE-SCALE</td><td>12</td><td>40</td><td>1</td><td>1.5</td><td>700</td><td>0.0079</td><td>904 °C</td><td>0.22</td><td>2.07</td><td>0.21 %</td><td>13.5</td><td>82.3 %</td><td>1.7 %</td><td>0.3 %</td><td>2.1 %</td><td>12.9 %</td><td>0.4 %</td><td>0.2 %</td><td>980 W</td></tr><tr><td>13</td><td>40</td><td>1</td><td>1.5</td><td>600</td><td>0.0054</td><td>801 °C</td><td>0.15</td><td>1.46</td><td>0.17 %</td><td>10.8</td><td>84.9 %</td><td>1.9 %</td><td>0.2 %</td><td>2.2 %</td><td>10.4 %</td><td>0.3 %</td><td>0.2 %</td><td>840 W</td></tr><tr><td>14</td><td>40</td><td>1</td><td>1.5</td><td>500</td><td>0.0033</td><td>689 °C</td><td>0.09</td><td>0.88</td><td>0.13 %</td><td>7.83</td><td>87.3 %</td><td>2.0 %</td><td>0.1 %</td><td>2.2 %</td><td>8.0 %</td><td>0.2 %</td><td>0.1 %</td><td>700 W</td></tr><tr><td>15</td><td>4,500,000</td><td>750,000</td><td>0</td><td>900</td><td>0.0627</td><td>986 °C</td><td>197,000</td><td>1,799,000</td><td>20.05 %</td><td>1319</td><td>1.4 %</td><td>0.0 %</td><td>28.5 %</td><td>0.0 %</td><td>4.6 %</td><td>45.5 %</td><td>20.0 %</td><td>9 MW</td></tr><tr><td>16</td><td>4,500,000</td><td>750,000</td><td>0</td><td>800</td><td>0.0570</td><td>955 °C</td><td>180,000</td><td>1,656,000</td><td>20.76 %</td><td>1348</td><td>1.5 %</td><td>0.0 %</td><td>28.1 %</td><td>0.0 %</td><td>4.7 %</td><td>45.0 %</td><td>20.8 %</td><td>8 MW</td></tr><tr><td>17</td><td>4,500,000</td><td>750,000</td><td>0</td><td>700</td><td>0.0510</td><td>920 °C</td><td>161,000</td><td>1,501,000</td><td>21.50 %</td><td>1380</td><td>1.7 %</td><td>0.0 %</td><td>27.7 %</td><td>0.0 %</td><td>4.8 %</td><td>44.4 %</td><td>21.5 %</td><td>7 MW</td></tr><tr><td rowspan="2">18</td><td>4,500,000</td><td>750,000</td><td>0</td><td>600</td><td>0.0449</td><td>882 °C</td><td>141,000</td><td>1,337,000</td><td>22.35 %</td><td>1418</td><td>1.9 %</td><td>0.0 %</td><td>27.2 %</td><td>0.0 %</td><td>4.9 %</td><td>43.7 %</td><td>22.4 %</td><td>6 MW</td></tr><tr><td>19</td><td>4,500,000</td><td>750,000</td><td>0</td><td>500</td><td>0.0386</td><td>840 °C</td><td>121,000</td><td>1,163,000</td><td>23.33 %</td><td>1462</td><td>2.1 %</td><td>0.0 %</td><td>26.6 %</td><td>0.0 %</td><td>5.1 %</td><td>42.9 %</td><td>23.3 %</td><td>5 MW</td></tr></tbody></table>
<figure><img src="image_4.png" /><figcaption>Fig. 2. Power repartition in a lab-scale reactor during heating in Run #1 (40 g of Fe₂O₃, 1 NL/min of H₂, 1.5 NL/min of Ar, 1000 W/m² of DNI).</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 3. Power repartition in a large-scale industrial reactor during heating for Run #7 (4.5 tons of Fe₂O₃, 750 Nm³/min of H₂, 1000 W/m² of DNI).</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>Fig. 4. Effect of the amount of Fe₂O₃ in the reactor on the temperature and the COP for the large-scale reactor under a constant DNI of 1000 W/m².</figcaption></figure>

proper stability of the numerical scheme.

$$ \sum_{j} n_j C p_{j,T_{reac}} \frac{dT_{reac}}{dt} = \frac{dU}{dt} \qquad (21) $$

$$ \frac{dT_{reac}}{dt} = \frac{1}{\sum_{j} n_j C p_{j,T_{reac}}} \left[ Q_{sun} - \sum_{j} P_{j,inlet} (h_{j,T_{reac}} - h_{j,inlet}) - \Delta H_{T_{reac}} - Q_{cond} - Q_{rad} \right] \qquad (22) $$

# 4. Results and discussion

## 4.1. Impact of variations of design conditions on performance

In this section, the dynamic model is used to investigate the

instantaneous power repartition depending on the temperature. The incoming solar power can be consumed by conduction and radiation losses, by the heating of iron oxide, hydrogen and argon if present, and by the endothermic reduction reaction. If losses are lower than the incoming power, the remaining power is consumed by the reactor heating. The reactor is cooling if losses are higher than the incoming power. Equilibrium temperature is reached when the incoming power is equal to losses.

Different simulations were carried out to evaluate the reactor performance and to investigate the influence of the mass of iron oxide, the flowrate of H₂ and Ar, and the DNI. The equilibrium temperature was estimated as well as the iron production, the reaction rate, the thermochemical efficiency, and the power breakdown. Table 3 summarizes the inputs and the main results at steady state for each simulation run.

<figure><img src="image_7.png" /><figcaption>Fig. 5. Power breakdown as a function of the mass of Fe₂O₃ for Runs #5 to #9 (Large scale reactor; DNI = 1000 W/m²; mass of Fe₂O₃ = 1 ton to 22.5 tons).</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>**Fig. 6.** Impact of the DNI on (a) the equilibrium temperature, (b) the COP, (c) the reaction rate, and (d) the iron production for both large and lab-scale reactors (40 g of Fe₂O₃, 1 NL/min of H₂, 1.5 NL/min of Ar for lab-scale; 4.5 tons of Fe₂O₃, 750 Nm³/min of H₂ for large scale).</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>**Fig. 7.** Solar power repartition for different DNI at equilibrium for a large-scale reactor (4.5 tons of Fe₂O₃).</figcaption></figure>

### 4.1.1. Simulations at constant DNI in lab-scale reactor

In Runs #1 to #3, operational conditions for the lab-scale reactor were the ones used in real sun experiments (Abanades et al., 2025). Fig. 2 illustrates the power repartition in Run #1, showing the conduction losses, the heating of the H₂ in excess, the heating of the actually reacting H₂, the heating of Ar, the radiation losses, the Fe₂O₃ heating, the reaction power, and the reactor heating. The reactor reaches a steady-state temperature when the reactor heating power is equal to 0.

For the three runs, the equilibrium temperature of the reactor

calculated by the model was around 1170 °C. At this temperature, the power dedicated to the reaction was 0.2 % to 0.3 %. 75 % of the incoming power was lost by conduction, and 20 % was lost by radiation. The total heating of H₂ represented less than 2 %, as well as Ar heating, in Runs #1 and 2. In Run #3, H₂ heating counted for less than 1 % and Ar heating for 2.6 %, accordingly to the flow rate differences between Run #3 and the previous two. Iron oxide heating counted for less than 1 % of the incoming power for the three runs. The goal of the lab-scale reactor is not to reach high conversion rate but to validate the concept of solar-
<figure><img src="image_10.png" /><figcaption>Fig. 8. Temperature evolution during the reactor heating without reaction.</figcaption></figure>

aided DRI using hydrogen, so those low efficiency values are not an issue.

The calculated COP from simulations was compared with an experimental COP estimated from real sun experiments on the lab-scale reactor (Abanades et al., 2025), using the mass of recovered iron product, the total reaction duration, and the incoming power. The experimental COP (22.7, 14.6, and 16.5 g/kWh in Runs #1–3, respectively) was consistent with the calculated COP (19.4, 14.6, and 14.7 g/kWh in Runs #1–3, respectively), which validates the dynamic model predictions based on experimental data of iron production at lab-scale.

Run #4 simulated a run without iron oxide and with 1 NL/min of H₂ and Ar. These conditions corresponded to those used in CFD simulation (Abanades et al., 2025). This CFD calculation indicated that the gas mixture in the cavity presented a temperature distribution in the range 1000–1150 °C, while the steel receiver reached a maximum temperature of 1260 °C, i.e., 100 °C more than the maximal gas temperature. In the current investigation, the simulated temperature of the reactor is 1182 °C. This temperature is thus consistent with previous CFD simulation. The power breakdown was chiefly the same than for Runs #1 and #2, except for the reactant heating and the reaction power as no reactant was considered in this run.

### 4.1.2. Simulation at constant DNI in large scale reactor

The large-scale reactor was simulated with constant DNI from Runs #5 to #9. The design quantity of iron oxide in the reactor was set in order to reach an equilibrium temperature around 1000 °C and a reaction time of 15 min. According to the reactor geometry already defined,

this design quantity of iron oxide present in the reactor was thus set at 4.5 tons (Run #7 with equilibrium temperature of 1016 °C). This results in a nominal production of around 215 kg/min of pure iron and thus a nominal feeding of iron oxide of 307 kg/min. According to thermodynamics, an over-stoichiometric ratio of 18 between H₂ and Fe₂O₃ was recommended to allow the total completion of the DRI reaction (Abanades and Rodat, 2024). To reach this over-stoichiometric ratio at the design point, the design flowrate of H₂ was set to 750 Nm³/min.

Design conditions were simulated in Run #7. The power repartition over the temperature is illustrated in Fig. 3. The calculated equilibrium temperature was just above 1015 °C. By upscaling the reactor, the conduction losses were widely decreased in comparison with the lab scale, representing around 1 % of the incoming power. This result is consistent with previous studies reporting conduction losses below 1 % (Rafique et al., 2022) or neglecting the conduction losses in highly concentrated solar technologies (Gentile et al., 2024; Li and Bai, 2025). The thermochemical efficiency reached 19.4 % of the total power balance, the Fe₂O₃ preheating counted for ~ 46 %, and the H₂ preheating for ~ 29 %. Less than 5 % of the incoming power was lost by radiation. In this run, 94 % of the incoming power was dedicated to the heating of the reactants and to the reaction itself. For each kWh of incoming solar power, 1.29 kg of Fe was produced.

For Runs #5 to #9, a parametric study highlights the impact of the quantity of iron oxide (from 1 to 22.5 tons) on the performance of the reactor. Fig. 4 illustrates the evolution of the equilibrium temperature and the COP for the five runs. Temperature dropped with an increasing quantity of iron oxide in the reactor, by around 200 °C when iron oxide quantity was multiplied by 2, as more energy was dedicated to the reaction than to the heating of the reactor. In the meantime, the COP increased by ~ 220 g/kWh when the quantity was increased two-fold. It means that, in the studied range, the reaction rate decreased more slowly than the iron oxide quantity rose, leading to the rise of production in absolute value.

For the integrity of the steel receiver, its temperature should not reach 1600 °C, which is its melting temperature. Moreover, the reactor temperature needs to be higher than 570 °C for the DRI. Hence, the quantity of iron oxide should not be out of the range 1–22.5 tons for the given geometry.

The power breakdown of Runs #5 to #9 is presented in Fig. 5. The more iron oxide was present in the reactor, the more energy was dedicated to the reaction. Thus, the thermochemical efficiency was 10 % with 1 ton in Run #5 and reached almost 30 % with 22.5 tons in Run #9.

With more iron oxide in the reactor and more iron production, the reacting H₂ mass flowrate was increased to follow the increase of iron production. However, as the temperature was lowered with more iron oxide, the power dedicated to the heating of H₂ remained stable in the five runs (from 29 % to 26 %). In the same manner, the heating of Fe₂O₃ remained almost stable in the five runs (from 46 % to 42 %). With the

<figure><img src="image_11.png" /><figcaption>Fig. 9. (a) Evolution of DNI, temperature and iron production and (b) Quantity of H₂ and H₂O in the cavity during two consecutive days in January in a typical annual simulation of a large-scale plant in Odeillo (4.5 tons of iron oxide in the reactor).</figcaption></figure>
<table><caption>**Table 4**
Monthly and yearly cumulated DNI, iron production and maximal temperature (4.5 tons of iron oxide).</caption><thead><tr><th></th><th>Jan.</th><th>Feb.</th><th>Mar.</th><th>Apr.</th><th>May.</th><th>Jun.</th><th>Jul.</th><th>Aug.</th><th>Sept.</th><th>Oct.</th><th>Nov.</th><th>Dec.</th><th>Total</th></tr></thead><tbody><tr><td>Cumulated DNI (kWh/m²)</td><td>143</td><td>150</td><td>194</td><td>187</td><td>178</td><td>205</td><td>259</td><td>226</td><td>215</td><td>167</td><td>141</td><td>144</td><td>2209</td></tr><tr><td>Iron production (tons)</td><td>1944</td><td>2026</td><td>2595</td><td>2506</td><td>2463</td><td>2842</td><td>3476</td><td>3071</td><td>2882</td><td>2273</td><td>1930</td><td>1968</td><td>29,976</td></tr><tr><td>Max T<sub>reac</sub> (°C)</td><td>1037</td><td>1052</td><td>1059</td><td>1059</td><td>1059</td><td>1058</td><td>1057</td><td>1055</td><td>1054</td><td>1051</td><td>1041</td><td>1022</td><td>1256</td></tr></tbody></table>

<figure><img src="image_12.png" /><figcaption>**Fig. 10.** Typical monthly energy repartition, iron production and solar insolation (cumulated DNI) in Odeillo (4.5 tons of iron oxide).</figcaption></figure>

temperature variation from 1530 °C in Run #5 to 680 °C in Run #9, the conduction losses remained at a low level from 1.9 % to 0.8 %.

### 4.1.3. Simulations with varying DNI for both lab-scale and large-scale reactors

In Runs #10 to #19, the mass of iron oxide and gas inlet flowrate were constant (40 g of $Fe_2O_3$, 1 NL/min of $H_2$, 1.5 NL/min of Ar for lab-scale; 4.5 tons of $Fe_2O_3$, 750 $Nm^3$/min of $H_2$ for large scale) and the DNI was varying from 1000 $W/m^2$ to 500 $W/m^2$. Fig. 6 illustrates the impact of the DNI on the equilibrium temperature, COP, reaction rate, and iron production.

For the lab-scale reactor, a decrease of the DNI from 1000 to 500 $W/m^2$ resulted in a sharp decrease of the reactor steady-state temperature (from 1168 °C in Run #1 to 689 °C in Run #14, Fig. 6a). This temperature decrease had a major impact on the performance of the reactor. As this temperature was decreased by 480 °C, the reaction rate was divided by 5 (Fig. 6c), resulting in a Fe production divided by 5 (Fig. 6d) and a COP divided by 2.5 (Fig. 6b).

In contrast, due to lower thermal losses, the temperature of the large-scale reactor only decreased by 176 °C, a DNI of 500 $W/m^2$ generating a steady-state temperature of 840 °C (Run #19). At such a temperature, the reaction rate, and by extension the iron production, was divided by 1.8. Thus, as thermal losses are low, the iron production was also divided by 1.8 (215 kg/min at 1000 $W/m^2$ versus 121 kg/min at 500 $W/m^2$). Since the iron production is chiefly proportional to the DNI, the COP remained stable between 1.29 (Run #7) and 1.46 kg/kWh (Run #19).

A consequence is that a large-scale reactor with characteristics equivalent to the ones described in this work might maintain good performance outputs under low DNI, with a production almost proportional to the solar irradiation. In addition, the intermittence of the direct irradiation might be well tolerated by such an installation as the temperature variations remain smooth and the production is not sharply

decreased.

The power repartition for the large-scale reactor at DNI from 1000 to 500 $W/m^2$ (Runs #7 and #15–19) is illustrated in Fig. 7. The absolute power was proportional to the DNI (Fig. 7a) and the relative proportion of each power consumer or loss remained stable independently of the DNI (Fig. 7b).

### 4.2. Dynamic simulation

The model was used in dynamic mode to predict the performance of a solar-based iron making plant under transient conditions. First, the behavior of reactors was investigated without any chemical reaction and under constant solar irradiation. Second, annual simulations were carried out to evaluate the iron production of such a plant and to investigate its variation during the year using fluctuating meteorological data.

#### 4.2.1. Thermal behavior without reaction

For both lab-scale and large-scale reactors, the thermal behavior was studied without any presence of iron oxide, nor $H_2$ or inert gas. A constant DNI was applied and the temperature of the reactor was evaluated over time. The heating progression of the reactors for two different DNI (500 and 1000 $W/m^2$) is illustrated in Fig. 8. For the lab-scale reactor, an equilibrium temperature of 1200 °C was reached for a DNI of 1000 $W/m^2$, after a heating time of ~ 40 min. This result is consistent with previous experimental measurements and CFD simulation results (Abanades et al., 2025) where the maximum temperature of the receiver wall with no reaction was 1260 °C. With a lower DNI, the maximum temperature reached 700 °C. The heating time was the same, around 40 min. For the large-scale industrial reactor, with a DNI of 1000 $W/m^2$, the calculated temperature reached 2500 °C in ~ 100 min. With a lower DNI of 500 $W/m^2$, the equilibrium temperature was slightly lower than 2000 °C, only reached after 120 min.
<figure><img src="image_13.png" /><figcaption>**Fig. 11.** (a) Monthly iron production vs. incoming energy for different quantities of iron oxides, (b) Comparison of the COP in annual dynamic simulation, annual step-by-step steady-state simulation, and at 1000 W/m², (c) Annual production of iron depending on the quantity of iron oxide in the reactor (dynamic conditions, 10 MW plant in Odeillo).</figcaption></figure>
### 4.2.2. Annual production yield

The dynamic simulation aimed to evaluate the global performance and the iron production yield of a large-scale solar reactor. Dynamic modelling of direct reduction by hydrogen in real sun conditions has not been considered before. Simulations were run to evaluate the typical annual production yield of an industrial solar-aided iron producing plant with characteristics as described in Table 1.

The DNI, temperature, iron production profiles along with the evolution of H₂ and H₂O quantities in the reactor for two consecutive days are presented in Fig. 9. During these days, the maximal DNI was slightly over 900 W/m², temperature reached slightly above 1000 °C, and up to almost 200 kg/min of iron was produced. These values were similar to results in Run #10 with a constant DNI of 900 W/m². During the second day, the DNI was very inconstant. When the DNI was low for a short duration, the temperature still remained at a sufficient level to allow iron production. Hence, fast DNI variability is not detrimental for the production of iron. During this period, 10% to 15% of the H₂ present in the cavity was consumed by the DRI reaction. This result was consistent with the fact that a H₂:Fe₂O₃ molar ratio of 18 was targeted, which was 6 times the stoichiometric ratio of the DRI reaction. The daily variations of the iron production rate were then integrated to calculate the cumulated iron produced over a given period.

Iron production and cumulated DNI, representing the total incoming energy, are presented month by month in Table 4 and Fig. 10. The annual yield of the plant was almost 30,000 tons of iron for an annual insolation of 2209 kWh/m². During the highest insulated month (July), almost twice as much energy was harvested than during the lowest insulated month (November). Furthermore, the iron production in July was also almost twice as important as the iron production in November. A production of 13.6 ± 0.2 tons per (kWh/m²) was calculated, independently of the month, showing that the production is proportional to the incoming solar power.

Additionally, Fig. 10 shows the energy repartition over the year. Each bar height represents the total solar energy entering the reactor during the month, derived from the integration of the dynamic calculated data (with 2-min time step). Each month, 20 % of the incoming energy was dedicated to the reaction enthalpy itself. 40 % of the incoming energy was consumed by the preheating of the iron oxide. The H₂ preheating absorbed 25 % to 30 % of the incoming solar energy. Conduction and radiation losses counted for less than 10 % of the total energy balance. These proportions are almost constant along the year.

### 4.2.3. Impact of the mass of iron ore on the monthly and annual performances

A parametric study was carried out to evaluate the impact of the iron oxide quantity in the reactor on the global performance of the plant. For five different iron oxide quantities in the reactor (from 1 to 22.5 tons), the monthly iron production was projected versus the monthly cumulated solar energy at the front face of the reactor in Fig. 11(a). Each point represents the monthly iron production vs. the monthly cumulated DNI. Twelve points are thus represented for each iron oxide mass. Hence, the twelve points of the 4.5-tons curve represent the same data as presented in Fig. 10. A linear trend curve is calculated for each mass and all the R² values are above 0.998. For each of these curves, the slope of the linear regression is the COP of the plant in tons/MWh. The iron production increased with an increasing quantity of oxide in the reactor, even if it also led to a higher power consumption and thus a lower temperature and a lower reaction rate, in agreement with Fig. 4.

Step-by-step steady-state simulations were also carried out in which, at each time step, the equilibrium was supposed to be instantaneously reached, without transients and thermal inertia. The equilibrium temperature was calculated according to the DNI with no energy variation term in equation (17). COP values were then compared between annual dynamic simulations, dynamic simulation at constant DNI of 1000 W/m², and step-by-step steady-state simulations in Fig. 11(b). It appeared that there was no major difference between the COP in dynamic

simulations and in step-by-step steady-state simulation. The energy consumed by the reactor heating at the beginning of the days was compensated by the energy stored by the reactor (thermal inertia) at the end of the day when temperature decreased at low DNI. In dynamic simulations, various DNI occurred during the year. In the weather data file used, the mean DNI value when sun was above horizon was 580 W/m² and the maximal value was 1023 W/m². It was previously established (section 4.1.3) that the COP increased when the DNI decreased. Thus, the COP in dynamic simulations was higher than the COP at a constant DNI of 1000 W/m².

The annual production yield in dynamic simulations depending on the quantity of iron oxide present in the reactor is shown in Fig. 11(c). A logarithmic regression of the iron production as a function of the mass of iron oxide is given for the dynamic simulation.

With an iron quantity increasing from 1 to 22.5 tons in the reactor, the annual iron production yield increased from 20,000 to 41,000 tons per year. Considering that the production of 1 ton of iron emits 1.4 tons of CO₂ in the conventional iron-making process, this solar-aided iron production process could lead to a decrease in CO₂ emissions from 28,000 to 58,000 tons per year, paving the way toward decarbonation of the iron and steel metallurgical industry based on renewable H₂ and concentrated solar energy.

## 5. Conclusion

Solar-aided DRI with H₂ is a promising path for the decarbonation of the steel industry. The purpose of this work was to evaluate the performance of a large-scale solar iron-making plant using H₂ as reductant. A new dynamic model was developed to predict the performance of such a plant and evaluate the annual iron production yield. The reactor model including unsteady mass and energy balance equations was used to calculate the evolution of temperature of the reactor and mass flow rates of the different produced species.

The performance of a lab-scale reactor was first simulated for model results validation. The calculated reactor temperature was similar to both the temperature obtained from CFD simulations and the experimentally measured temperature (in the range of 1000–1260 °C).

For the large-scale reactor at steady-state (under design conditions: 1000 W/m², 4.5 tons of loaded Fe₂O₃), about 20 % of the incoming solar power was dedicated to the reaction and ~ 46 % to the iron oxide heating. Conduction and radiation losses represented less than 6 % of the incoming solar power, while ~ 29 % was dedicated to the heating of the reacting H₂. An iron production of 1.29 kg per kWh of incoming solar energy was obtained. When the amount of loaded iron oxide increased, more power was dedicated to the reaction, leading to a decrease of the equilibrium temperature (about −200 °C when doubling the quantity), but still increasing the iron production per kWh of incoming solar power. With the increase of iron oxide quantity loaded in the cavity (1 to 22.5 tons), the thermochemical efficiency increased (10 to 29 %). The Fe production was chiefly proportional to the DNI, ranging between 1.3 and 1.5 kg/kWh of solar energy.

Dynamic simulations of the 10 MW solar reactor using real solar irradiation data led to an annual Fe production of ~ 30,000 tons, which corresponded to a cut down of 42,000 tons of CO₂ emissions. The power repartition between reaction, reactants heating, and losses was the same than in design conditions. Moreover, this power breakdown was constant over the year. The results of dynamic simulations were compared with step-by-step steady-state simulation. Annual production was almost identical, meaning that inertia during transients did not affect the annual energy balance and iron production. A logarithmic trend was identified between the annual production and the quantity of Fe₂O₃ loaded in the reactor. Dynamic modelling was relevant to predict the performance of large-scale solar iron producing plants.

Future work will be devoted to the development of reactor design and suitable management strategies to optimize the iron production and to overcome the transient and intermittent aspects of solar energy,
including system heat recovery, through thermal energy storage, and hybridization for continuous processing during night-time and cloudy conditions. Developing continuous solar industrial processes will pave the way toward carbon neutral steel metallurgy.

### CRediT authorship contribution statement

**Damien Jaffré:** Writing – original draft, Visualization, Validation, Software, Investigation, Formal analysis, Data curation. **Sylvain Rodat:** Writing – review & editing, Validation, Supervision, Investigation, Formal analysis. **Stéphane Abanades:** Writing – review & editing, Visualization, Validation, Supervision, Software, Resources, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Acknowledgement

This work was funded by the French National Agency for Research (ANR, METASOL project, contract N°ANR-20-CE05-0008-02).

### Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.ces.2025.122429.

### Data availability

Data will be made available on request.

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