# A nonselective automatic method for kinetic simulations of gas mixtures under ionizing radiation: case study of a nuclear-to-chemical concept

Antoine Dion, Marie Géléoc, Jean-philippe Renault

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Antoine Dion, Marie Géléoc, Jean-philippe Renault. A nonselective automatic method for kinetic simulations of gas mixtures under ionizing radiation: case study of a nuclear-to-chemical concept. Chemistry-Methods, 2025, 2025, pp.e202500086. 10.1002/cmtd.202500086. hal-05311032

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# A Nonselective Automatic Method for Kinetic Simulations of Gas Mixtures under Ionizing Radiation: Case Study of a Nuclear-to-Chemical Concept

Antoine Dion,* Marie Géléoc, and Jean-Philippe Renault*

Kinetic simulations are efficient tools for supporting the development of technologies. However, in radiation-based technologies, as many intermediates are involved in the chemistry, simulations can be challenging to implement. To address these challenges, a versatile, nonselective automated method for the implementation of radiolysis kinetic simulations is developed. The approach uses curated various open-access databases and the FACSIMILE software and is accompanied by diagnostic tools. For validation, the simulation results are compared to experimental data from the literature for a CO₂/O₂/CO mixture and comparable results are found. This method is then used to evaluate a more complex system: an original nuclear-to-chemical concept for flue gas

(N₂/CO₂/H₂O/O₂/CO/NO₂/SO₂) valorization. A parametric study that includes varying the initial pressure, temperature, and composition to identify regimes of interest is performed. The conversion of CO₂ is found to improve by a factor of five with the addition of 90(vol.%) NH₃, and the production of energetic molecules is evidenced with the addition of H₂S, with some promising yield maxima like an H₂ production > 900 molecules·100 eV⁻¹. This shows the potential of the developed method for kinetic studies and identification of regimes of interest. Overall, this study could open the path toward rapid and rigorous concept testing for various chemistry applications.

## 1. Introduction

Recent years have witnessed significant advancements in nuclear power technology, particularly through the development of small modular reactors (SMRs). Many concepts are under design,[1] as they appear as candidates of choice to provide low-carbon electricity. This type of energy is essential to support the energy transition through an electrification strategy, which affects many sectors, from the transport industry[2] to the process industry.[3] In the process industry, this switch from fossil fuel-based processes to electrical ones can be seen with the development of electrocatalysis (e.g., syngas production from H₂O/CO₂,[4] urea from flue gas[5]) or of plasmalysis (H₂ and solid carbon production from CH₄[6]). In the conventional approach, nuclear energy is converted to heat, then heat to electricity, and finally electricity to chemical energy (Nuc-to-Heat-to-Elec-to-Chem). Conversions of energy always come with

losses: ≈30% efficiency for Heat-to-Elec[7] and ≈35% efficiency for Elec-to-Chem (at a system scale).[8] An alternative understudy is the direct use of the heat produced in industrial processes (Nuc-to-Heat-to-Chem).[1]

However, there is an alternative paradigm: the direct conversion of nuclear energy into chemical energy (Nuc-to-Chem). In this strategy, first explored in the mid-XX century, the full power of nuclear energy is used.[9] The particles produced by the nuclear reactions (i.e., gamma, photons, and neutrons) trigger radiation chemical processes instead of or in addition to the heat and/or electricity production.[9,10] These types of reactors were named chemonuclear reactors.[11]

This strategy ultimately yields productions of interest (e.g., energetic molecules) and/or conversions of interest (e.g., pollutants) that have been envisioned in various patents. For example, there are the works of Teichman and Gomberg et al. for the production of H₂ from H₂O,[12,13] or that of Leffert et al. for the production of CO from CO₂ via the reverse Boudouard reaction (C + CO₂ -> CO + CO).[14] More complex systems had also been envisioned, like the multistep conversion of H₂O to H₂ with CO intermediate,[15] or the production of CO from CO₂ with the aid of inert gases[16] to quench catalytic cycles, limit recombinations, and capture energy more efficiently.[10] More recently, Ramirez-Corredorez et al. reviewed the use of ionizing radiation for CO₂ conversion[17] and investigated the use of radiation from nuclear reactors,[18] highlighting how an optimal synergy between heat, electricity, and ionizing radiation can fully unlock nuclear energy.

Indeed, different concepts of Nuc-to-Chem exist. One can think of fully dedicating a reactor for chemistry purposes, while another strategy is the use of the so-called *wasted radiation* as

A. Dion, M. Géléoc, J.-P. Renault

NIMBE

LIONS

Université Paris-Saclay, CEA, CNRS

91191 Gif-sur-Yvette, France

E-mail: antoine.dion@cea.fr

jean-philippe.renault@cea.fr

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Supporting information for this article is available on the WWW under https://doi.org/10.1002/cmtd.202500086

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© 2025 The Author(s). Chemistry - Methods published by Chemistry Europe and Wiley-VCH GmbH. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
discussed by Schmeda-Lopez,[19] also designed as residual radiation.[20] In the present article, the term loss radiation is chosen.

Loss of radiation is a well-known phenomenon, occurring even in conventional nuclear reactors. A part of the radiation (≈3% of the thermal power in some of the current ones[21]) produced by reactors is not converted to usable heat and is lost in the reactor shielding.[19] So its potential use would not compete with heat/electricity production.

For SMRs, as the reactor size decreases due to higher surface area to volume ratios (S/V ratios), the loss amount will be much higher and is estimated to be more than 7%.[21] which imposes a larger shielding for radiation confinement.[22] This makes SMRs interesting candidates for the use of loss radiation to induce chemical reactions.

An advantage of such ionizing radiation technology is its robustness: robustness to initial gas mixture composition (e.g., no risk of catalyst deactivation by impurities) and operating conditions (pressure, temperature). Hence, there is no need for high gas purity, which is usually achieved at a high energy cost,[23,24] and this robustness releases engineering and operational constraints.

A limitation of the development of such technologies is the lack of predictive tools, which are a major necessity for the evaluation of concepts.[17] To investigate such concepts, modeling tools are efficient, particularly kinetic simulation, which allows for the estimation of valuable product yields.

However, as stated by Fritsch et al. and De Salvo et al.,[25,26] the fundamental problem in radiolysis kinetic modeling is to be able to model such complex mixtures (e.g., in a nonpurified gas stream) to evaluate the efficiency of such processes. This is a cumbersome problem, as complex mixtures involve many atoms, which exponentially increases the number of equations to collect for simulation.[27]

As a consequence, in research papers, the radiolytic reaction systems for simulations are usually limited to pure gas streams or traces of impurities, such as the one known as reference for CO₂ decomposition by Kummler et al. in 1977.[28] Ad hoc systems were sometimes developed for specific purposes (e.g., SOx and NOx abatement[29–32] or the evaluation of risks of nuclear fireball phenomena in the troposphere and stratosphere[33]). But, there is currently no general method for rapid prototyping of such gas processing.

In the present article, we focus on developing a versatile method for simulation implementation. Rather than relying on purely theoretical descriptions of the graph network, we focus on curated databases and develop an automated nonselective approach. Additionally, we suggest visualization and diagnostic tools to guide system analysis, and we introduce a new parameter, the radiolytic stage ratio, to further analyze large kinetics systems in radiation chemistry.

The final case study here is the radiolysis of flue gas, which is a substrate of interest in the energy transition context, especially if a process allows for the transformation of CO₂ without further purification.[34]

# 2. Model and Methods

## 2.1. Numerical Kinetics

In this study, we performed zero-dimension (0D) microkinetic simulations at constant pressure and temperature to evaluate the species' concentrations under radiation.

Sets of chemical reactions representing a chemical reaction system were built based on data from the literature. Ordinary differential equations (ODE) were derived from those systems and their kinetic parameters. Equation (1) summarizes this procedure

$$ \frac{\partial c_i}{\partial t} = \sum_j \left( (\alpha_{i(P)} - \alpha_{i(R)}) \times k_j \times \prod_{i(R)} (c_{i(R)} - \alpha_{i(R)}) \right) \quad (1) $$

where c is the concentration, $\frac{\partial c}{\partial t}$ the concentration variation rate, α the stoichiometric coefficient, i the chemical species index, i(R) index of the reactants side, i(P) index of the products side, j the reaction index, and k the kinetic constant.

The equations were solved to determine the evolution of each species over time. This was done via the FACSIMILE (MCPA Software Ltd.).[35] This software is based on Gear's implicit method,[36] particularly adapted to stiff systems, such as radiation-induced ones. Also, FACSIMILE (MCPA Software Ltd.)[35] has a proven track record on radiolysis 0D kinetic simulations (e.g., the IODAIR-IRSN model[37,38] that was adapted for more complex mixtures in our study).

In the context of our study, the simulation time does not exceed 60 s, on a standard computer, even for the largest systems (S4, ≈5000 reactions).

## 2.2. Network Visualization

A visualization approach was developed to improve the comprehension of large chemical reaction systems. This approach is based on multidirectioned graphs and adjacency matrices from the Python library networkX.[39]

# 3. Results and Discussion

## 3.1. Defining Irradiation Conditions

We evaluate our automated nonselective approach for complex gas mixture kinetic modeling through a proposed nuclear-to-chemical concept. This concept consists of using the lost radiation from an SMR to induce the chemical reactions of interest. Figure 1 provides a schematic representation of the proposed concept. First, the input gas to be treated goes into a mixing chamber where the injection or withdrawal of gases is permitted. After the potential heating and/or compression steps, it flows into a mesh-filled double-wall shell. It should be noted that the proper choice of the mesh material and geometry (distances between layers) may improve radiation scavenging by enhancing the wall effect, increasing the dose at interfaces[40] and limiting the
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<figure><img src="image_7.png" /><figcaption>**Figure 1.** The proposed nuclear-to-chemical concept: a doubled wall vessel structure for the use of loss radiation, combined with the optimization of the neutron conversion through a boronated meshed Hastelloy.</figcaption></figure>

neutron activation issue. A boronated mesh, for example, favors neutron conversion to alpha and gamma.[41] While in the double wall reactor, the gas is exposed to a mix of radiation, thus inducing chemical reactions. Finally, an output gas is obtained. We explore a dual benefit from the technology: the reduction of CO₂ emissions as part of the impurified flue gas and the production of products of interest. Note that these products will need to be separated from the output gas. This double-wall vessel permits the benefit of radiation loss and, if required, the reactor's waste heat without modifying the core geometry, thus easing the integration into the SMRs' designs under development.

The modeling of such a system requires information on the chemistry and operating conditions (pressure, temperature, absorbed dose rate, irradiation time). The chemistry is detailed later (see Section 3.2). **Table 1** summarizes some operating conditions from the literature.

Information on SMRs that we found (see Table 1) is mainly restricted to the temperature and pressure of the core or a coolant loop. Broad temperature and pressure ranges are covered depending on the technologies, from 110 to 900 °C and atmospheric pressure to more than 100 bar. Another consideration is that the radiation mix produced by a reactor also depends on the technology. This mix mainly comprises neutrons and gamma, from which the absorbed dose rate can be calculated from their fluxes.[42,43] For the scope of this study, we use the already calculated local dose rate values, which we extend to a global dose rate. As these values are not yet available on SMRs, we also focus on research nuclear reactors for which operating conditions can be found in the second part of Table 1. It can be seen that dose rate values vary from 0.1 to 12 kGy s⁻¹, all types of radiation included. For the simulations, we selected 10 kGy s⁻¹ and an irradiation time (i.e., the residence time of the gas in the reactor) of 400 s. This time is approximate based on the dose rate chosen and the radiolytic yields (reactions 1–5) with the constraint of limiting the total radiolytic conversion to

10–20% set to minimize secondary reactions that would consume the targeted products.[44] Contrary to the radiation field, temperature and pressure can more easily be adjusted. The temperature and pressure in the double wall mesh depend on the core temperature, the input gas conditions, and potential preheating/cooling and compression steps. We defined the base case of our simulation based on a typical output gas from a cement plant: at 300 °C, 1.5 bar, and a gas composition consisting of 20 (vol.%) CO₂, 20 (vol.%) H₂O, 8 (vol.%) O₂, 50 (vol.ppm) SO₂, 50 (vol.ppm) NO₂, 50 (vol.ppm) CO, the rest ≈52 (vol.%) being N₂.[45] However, different temperatures, pressures, and gas compositions were evaluated in a parametric study.

In these conditions, assuming a typical SMR of thermal power 100 MWth, 7% leaks (thermal), and a total absorbance of the leaks by the volume of the gas, we can roughly estimate the potential irradiated gas mass flow rate to 1.75 kg s⁻¹ ≈ 150 tonne day⁻¹.

## 3.2. Defining a Robust and Automated Nonselective Simulation Approach

To conduct kinetic simulations, sets of chemical reactions are required. In most of the literature, the compilation of the chemical reactions is done manually.[28,30,33,46–48] This manual approach raises some limitations. First, as the system's complexity increases regarding the chemical species involved, it can be time-consuming and difficult to have sufficient completeness. Then, doing it manually also often ascribed the procedure to the author's appreciation, which limits simulation comparison. In that sense, we replace the manual approach with an automated nonselective one. The latter is based on big data and curated open-access databases (Scheme 1). Doing so opens a path toward more straightforward complex mixture kinetic modeling. It is also of particular interest as it limits bias and benefits from the work done by open-access database providers on data checking.
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<table><caption>**Table 1.** Comparison of different nuclear reactors' operating conditions, with Wth for the thermal capacity.</caption><thead><tr><th>Reactor</th><th>Reference</th><th>Temperature core<br>OR inlet-outlet<br>coolant [°C]</th><th>Pressure core<br>[bar]</th><th>Dose rate<br>[kGy·s<sup>-1</sup>]</th><th>Remarks</th></tr></thead><tbody><tr><td colspan="6"><strong>Small modular reactor</strong></td></tr><tr><td>ACP100 (385 Wth)</td><td>IAEA<sup>[1]</sup></td><td>286-319</td><td>a)</td><td>a)</td><td>Integral PWR, water-cooled SMR</td></tr><tr><td>GE BWRX-300 (870 MWth)</td><td>IAEA<sup>[1]</sup></td><td>270-288</td><td>72</td><td>a)</td><td>Direct cycle BWR</td></tr><tr><td>CALOGENA (30 MWth)</td><td>IAEA<sup>[1]</sup></td><td>110</td><td>6</td><td>a)</td><td>Pool type SMR</td></tr><tr><td>NUWARD (2 × 540 Wth)</td><td>IAEA<sup>[1]</sup></td><td>280-307</td><td>150 (primary)</td><td>a)</td><td>Integral PWR water-cooled SMR</td></tr><tr><td>GTHTR300 (600 Wth)</td><td>IAEA<sup>[1]</sup></td><td>600-900</td><td>7 (primary)</td><td>a)</td><td>High-temperature gas-cooled SMR</td></tr><tr><td>LFR-AS-200 (480 Wth)</td><td>IAEA<sup>[1]</sup></td><td>420-540</td><td>Low atmospheric</td><td>a)</td><td>Lead cooled fast SMR</td></tr><tr><td>THORIZON (250 Wth)</td><td>IAEA<sup>[1]</sup></td><td>500-800</td><td>Low atmospheric</td><td>a)</td><td>Molten salt SMR</td></tr><tr><td>WAMR (80 M Wth)</td><td>IAEA<sup>[1]</sup></td><td>a)</td><td>Low atmospheric</td><td>a)</td><td>Molten salt SMR</td></tr><tr><td>MoveluX (10 M Wth)</td><td>IAEA<sup>[1]</sup></td><td>500-600</td><td>Low atmospheric</td><td>a)</td><td>Hat pipe cooled and<br>calcium hybrid SMR</td></tr><tr><td colspan="6"><strong>Research reactor</strong></td></tr><tr><td>PWR</td><td>Macdonald et<br>Engelhardt<sup>[84]</sup></td><td>295-300</td><td>150</td><td>12</td><td>Data in the main loop of the<br>primary coolant circuit</td></tr><tr><td>PUR-1 reactor</td><td>Jiang et al.<sup>[85]</sup></td><td>50</td><td>3</td><td>1.8</td><td>Pool-type reactor</td></tr><tr><td>INCA</td><td>Takiguchi et al.<sup>[86]</sup></td><td>290</td><td>a)</td><td>8.3</td><td>Data in-pile loop</td></tr><tr><td>Tsugura-2</td><td>Takiguchi et al.<sup>[86]</sup></td><td>305</td><td>a)</td><td>6.5</td><td>Data in-core region</td></tr><tr><td>TRIGA (105 kW)</td><td>Plant et al.<sup>[87]</sup></td><td>a)</td><td>a)</td><td>0.1</td><td>Light-water-cooled, pool-type reactor</td></tr><tr><td>Melusine (40 MW)</td><td>IAEA report<sup>[42]</sup></td><td>a)</td><td>a)</td><td>1.5</td><td>Light-water-cooled, pool-type reactor</td></tr><tr><td>FRJ-2</td><td>IAEA report<sup>[88]</sup></td><td>30-100</td><td>a)</td><td>1.3</td><td>Gamma irradiation plant</td></tr><tr><td>SMIRNOF irradiation rig</td><td>Cheymol et al.<sup>[89]</sup></td><td>200</td><td>a)</td><td>2</td><td>Material Testing Reactors</td></tr></tbody><tfoot><tr><td colspan="6"><sup>a</sup>Data not available.</td></tr></tfoot></table>

<figure><img src="image_9.png" /><figcaption>**Scheme 1.** Methods used to derive the evolution of the chemical concentration.</figcaption></figure>

Then, these systems of reactions were evaluated via visualization and diagnostic tools, converted to systems of differential equations via (Equation 1), solved via FACSIMILE (MCPA Software Ltd.),[35] and finally, postprocessed (see Scheme 1). In FACSIMILE (MCPA Software Ltd.),[35] two engine types are available: Compaq and Salford. We found that Compaq performed better than Salford; the latter raised more underflow errors. Restarting the solver parameters at the point of discontinuities is also particularly efficient in limiting underflow errors. Note that when the number of outputs is too high, we implemented a divide-

and-conquer approach to simplify the output file generation. Indeed, FACSIMILE (MCPA Software Ltd.)[35] shows some limitations in filing large output files. We used two simulation files corresponding to the same chemical system: the first one generates the concentrations for half of the chemical species, while the second generates the concentrations for the other half.

We based our modeling approach on the common three-stage radiolysis description: the physical stage, the physicochemical stage, and the chemical stage. The first stage corresponds to the interactions between the ionizing radiation
<figure><img src="image_10.png" /></figure>

and the sample, producing chemical species called primary species.[49] Following this stage, the chemical equilibrium is disturbed, and relaxation follows. Various reactions occur between the new species. Ion reactions dominate the physicochemical stage, and radical reactions the chemical one.

During the physical stage, the production of the primary species and consumption of the parent species were considered in the 0D kinetic model by means of primary radiolytic yields. Radiolytic yields express the number of molecules and atoms produced or consumed per energy absorbed, and primary radiolytic yield expresses the number of molecules and atoms produced or consumed per energy absorbed following the primary events occurring during the physical stage. These yields are broadly adopted by the radiation science community. In the present study, we follow the notation proposed by Elliot et al. "g" for primary yields and "G" for other yields,[50] and we express these yields in molecule·100 eV⁻¹. Several studies of reference provide such yields.[51] Hence, Equation (2) describes the physical stage of the decomposition of CO₂ under radiation (rad.)

$$6.97 \text{CO}_2 \xrightarrow{100\text{eV rad.}} 3.94 \text{CO}_2^+ + 3.03 \text{E}^- + 2.24 \text{CO}_2^+ + 0.07 \text{C}^+ + 0.51 \text{CO}^+ + 0.21 \text{O}^+ + 0.21 \text{CO} + 0.65 \text{O} \quad (2)$$

where CO₂ is consumed, and CO₂*, E⁻, CO₂+, C+, CO+, O⁺, CO and O are produced. The reaction is for 100 eV radiation (rad.) absorbed, so the stoichiometric constants give access to the primary yields with the chosen unit (i.e., molecule·100 eV⁻¹). The physical stage leads to many intermediates, including positive ions, radicals, and excited species (electronically, vibrationally, and rotationally). For the framework of that study, only primary "hot" atoms were considered and designed with *. They represent atoms and molecules with an excess of energy.[52]

Regarding kinetics, these processes can be described as either zero-order consumptions/productions or first-order ones. Hence, if we note A, the gas irradiated, and B, the produced primary species, two possibilities exist: see Equation (3) and (4)

$$0\text{-order: } k_{\text{B(A)}}(t) = \alpha \times (\text{DOSERATE}(t) \times \rho_{\text{A}}(t)) \times g_{\text{B(A)}} \times \beta_{\text{A}}(t) \quad (3)$$

$$1\text{-order: } k_{\text{B(A)}}(t) = \alpha \times \left( \text{DOSERATE}(t) \times \frac{M_{\text{A}}}{Na} \right) \times g_{\text{B(A)}} \times \beta_{\text{A}}(t) \quad (4)$$

with α = −1 to account for the consumption and α = 1 for the production.

It is worth noting that variations in the dose rate were implemented using step functions. While this approach is not optimal for the solver, it did not cause any noticeable issues in FACSIMILE (MCPA Software Ltd.)[35]

We assumed the perfect gas law and constant pressure and temperature over the irradiation time. Hence, the density is determined through Equation (5)

$$\rho_{\text{A}}(t) = \frac{(\text{Fracvol}_{\text{A}}(t) \times P) \times M_{\text{A}}}{R \times T} \quad (5)$$

The assumption of the ideal gas law establishes an equivalence between molar and volumetric ratios and between molar

and volumetric concentrations. We arbitrarily chose volume units for this study, indicated as (vol.).

In (Equation 4), Fracvol is the volumetric fraction and β a coefficient used to split the radiation between the different initial gases. This split was done based on the electronic density (Ne) as suggested by Willis et al.[53] in their work on nitrogen-oxygen mixtures and the mass of each species via Equation (6)

$$\beta_{\text{A}}(t) = \frac{m_{\text{A}}(t) \times Ne_{\text{A}}}{\sum_{j} m_{j}(t) \times Ne_{j}} \quad (6)$$

Ne is calculated in Equation (7) as per Manohara et al.[54]

$$Ne_{\text{A}} = \frac{\left(\frac{\mu}{\rho}\right)_{\text{A}}}{\sigma_{\text{eA}}} \quad (7)$$

where (μ/ρ) is the mass attenuation and σe the average cross section per electron. The average cross section is obtained from Equation (8)

$$\sigma_{eA} = \frac{1}{n} \times \sum_{k} \frac{n_{k}}{Z_{k}} \times \sigma_{k} \quad (8)$$

with k the index of the atoms of the molecule A, n the number of atoms in A, Z the associated atomic number, and σ the atomic cross section. Finally, the atomic cross section is described by Equation (9)

$$\sigma_k = \frac{Am_k}{Na} \times \left(\frac{\mu}{\rho}\right)_k \quad (9)$$

where Am is the atomic mass, and Na is the Avogadro number.

The mass attenuation coefficients were obtained from the X-COM database provided by the NIST[55] at an energy of 2 MeV. This value is a reasonable estimation of a nuclear reactor's average gamma spectrum energy.[43]

To assess the impact of assuming either zero-order or first-order kinetics for the production/consumption processes in the physical stage, we conducted a preliminary simulation focusing on Reaction 1, using either Equation (2) or (3). This was done at an arbitrary temperature of 300 K, pressure of 1 atm, dose rate of 5 × 10⁵ kGy h⁻¹, and irradiation time of 500 s. Figure 3 plots the CO production and CO₂ consumption for these two simulations.

The limitations of both strategies are immediately apparent in Figure 2. The zero-order approach fails to represent the decrease in CO production rate as the CO₂ proportion in the mixtures decreases. In contrast, the first-order fails to describe the destruction of CO as its proportion in the mixtures increases. Indeed, representing the radiolysis of radiation products would require knowing each intermediate's radiolytic yields (g), which is not feasible in a generalized strategy with the current literature.

In the following, we place our simulations in the low conversion regime, where the variation of the proportion of CO₂ and CO in the mixtures will be low enough for these issues to be negligible. Indeed, as shown in Figure 3, both zero-order and first-order simulations give similar results at a low conversion level (<20%). We selected arbitrary zero-order kinetic laws.
<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /><figcaption>Figure 2. Evolution of the concentrations of CO₂ and CO under radiation at T = 26.85 °C, p = 1.013 bar, dose rate = 5 × 10⁵ kGy h⁻¹, irradiation time = 500 s.</figcaption></figure>

Such conversion levels are common in the process industry, with, for example, CO₂ conversions near 20–50% in the reverse water gas shift reaction-based process.[56] Low conversions also ease the withdrawal of the products, which is known to improve the yields.

To study complex mixtures of gases, besides Equation (2), more radiolytic decomposition reactions shall be introduced. The selection of the radiolytic primary yields is of main importance in our radiolysis simulations. To our knowledge, no curated database of primary yields currently exists. In the literature, authors often rely on their interpretation from a few reference studies. A crucial point is to ensure mass and charge balances in those primary events, as well as to ensure all primary species are part of the species of the systems.

For CO₂ radiolysis, the selected yields are those from Kummler et al.[28] completed with the original study of Willis and Boyd[51] to confirm the mechanism associated with the formation of C⁺.

$$6.97 \text{CO}_2 \xrightarrow{100 \text{ eV rad}} 3.94 \text{CO}_2^+ + 3.03 \text{E}^- + 2.24 \text{CO}_2^+ \\ + 0.07 \text{C}^+ + 0.51 \text{CO}^+ + 0.21 \text{O}^+ + 0.21 \text{CO} + 0.65 \text{O} \quad (10)$$

For O₂ radiolysis, the yields selected are those from Willis and Boyd,[51] interpreting all neutral excited species as O₂⁺.

$$5.27 \text{O}_2 \xrightarrow{100 \text{ eV rad}} 1.99 \text{O}_2^+ + 3.28 \text{E}^- + 2.05 \text{O}_2^+ \\ + 1.23 \text{O}^+ + 1.23 \text{O} \quad (11)$$

The yields obtained are in the same order as the ones introduced by Kummler et al.[28] (e.g., g(O₂) = −5.15 molecules·100 eV⁻¹) and Mätzing et al.[29] (e.g., g(O₂) = −5.38 molecules·100 eV⁻¹).

For CO radiolysis, the yields selected are those from Kummler et al.[28] with the addition of CO⁺ dissociation to C and O coming from Willis and Boyd[51] study.

$$3.16 \text{CO} \xrightarrow{100 \text{ eV rad}} 0.05 \text{CO}^+ + 3.11 \text{E}^- + 2.36 \text{CO}^+ \\ + 0.55 \text{C}^+ + 0.55 \text{O} + 0.20 \text{O}^+ + 0.20 \text{C} \quad (12)$$

For H₂O, the yields are those from Willis and Boyd.[51]

$$7.25 \text{H}_2 \text{O} \xrightarrow{100 \text{ eV rad}} 3.95 \text{H}_2^+ + 3.30 \text{E}^- + 1.99 \text{H}_2 \text{O}^+ \\ + 0.57 \text{OH}^+ + 0.67 \text{H}^+ + 0.06 \text{O}^+ + 0.01 \text{H}_2^+ \\ + 0.57 \text{H} + 0.01 \text{O} + 0.06 \text{H}_2 + 0.67 \text{OH} \quad (13)$$

For N₂ radiolysis, the yields are from Willis and Boyd[51] with g(N2*) chosen from excitation cross-section data.

$$5.47 \text{N}_2 \xrightarrow{100 \text{ eV rad}} 2.51 \text{N}_2^+ + 2.96 \text{E}^- + 2.27 \text{N}_2^+ \\ + 0.69 \text{N}^+ + 0.69 \text{N} \quad (14)$$

For CH₄ radiolysis, the yields are coming from the work of Okazaki et al.,[57] excluding the species produced by the Auger effect.

$$7.33 \text{CH}_4 \xrightarrow{100 \text{ eV rad}} 3.96 \text{CH}_4^+ + 3.48 \text{E}^- + 1.63 \text{CH}_4^+ \\ + 1.42 \text{CH}_3^+ + 0.32 \text{CH}_2^+ + 0.11 \text{H}^+ + 1.41 \text{H} + 0.27 \text{H}_2 \quad (15)$$

H₂ yields are coming from Armstrong and Willis, regrouping all singlet excitation giving H + H as H₂⁺.[58]

$$6.14 \text{H}_2 \xrightarrow{100 \text{ eV rad}} 3.39 \text{H}_2^+ + 2.75 \text{E}^- + 2.58 \text{H}_2^+ \\ + 0.17 \text{H}^+ + 0.17 \text{H} \quad (16)$$

For NH₃ and H₂S, the yields are those from Willis and Boyd.[51]

$$9.87 \text{NH}_3 \xrightarrow{100 \text{ eV rad}} 6.10 \text{NH}_3^+ + 3.77 \text{E}^- + 2.00 \text{NH}_3^+ \\ + 1.6 \text{NH}_2^+ + 0.17 \text{NH}^+ + 1.94 \text{H} \quad (17)$$

$$7.79 \text{H}_2 \text{S} \xrightarrow{100 \text{ eV radiation}} 3.80 \text{H}_2 \text{S}^+ + 3.99 \text{E}^- + 1.74 \text{H}_2 \text{S}^+ \\ + 1.32 \text{SH}^+ + 2.94 \text{H} + 0.81 \text{S}^+ + 0.12 \text{H}^+ + 0.12 \text{SH} \quad (18)$$

The physico-chemical and chemical stages were treated in the same equation block, with the following limitations: only “hot” atoms/molecules were considered as excitation, and this is only from the molecular species initially present in the mixture. In these steps, the primary species of initial gases react with each other through ion-neutralization, ion-scavenging, electron attachment, germination, recombination, etc.[59] As previously mentioned, these reactions were emulated through chemical reaction systems, built through our automated approach. The algorithm flowchart (Figure 3) summarizes this automated method. Several filters and checks were performed to ensure a robust approach. Sections 1 and 5 of the Supporting Information complement this flowchart with a detailed description of the method.

We then defined the dissociative pathways of excited molecules formed in Equations (2) and (10) – (18) by (Equation 19) – (33).[51,57,58] If different reactions exist from the same “hot” atom/molecule, such as H₂O, NH₃, CH₄, and H₂S, they were modulated via reaction yields (GR). These equations are added to the block named COMBINE in Figure 3.

$$\text{CO}_2^* \xrightarrow{k_{19}} \text{CO} + \text{O} \quad (19)$$
<figure><img src="image_13.png" /></figure>

<figure><img src="image_14.png" /><figcaption>**Figure 3.** The algorithm's flowchart of the automated nonselective approach proposed to develop a system of elementary reactions for radiation-induced kinetic simulations. Red squares indicate a user's required actions.</figcaption></figure>

$$O_2^+ \xrightarrow{k20} O + O \qquad (20) \qquad H_2O^+ \xrightarrow{k22} H + OH \ (\text{GR22} = 3.50 \text{ molecule}.100 \text{ eV}^{-1}) \qquad (22)$$

$$CO^+ \xrightarrow{k21} C + O \qquad (21) \qquad H_2O^+ \xrightarrow{k23} H_2 + O \ (\text{GR23} = 0.45 \text{ molecule}.100 \text{ eV}^{-1}) \qquad (23)$$
<figure><img src="image_15.png" /></figure>

$$N_2^+ \xrightarrow{k24} N + N \quad (24)$$

$$H_2^+ \xrightarrow{k25} H + H \quad (25)$$

$$CH_4^+ \xrightarrow{k26} CH_2 + H_2 \ (GR26 = 1.27 \text{ molecule}.100 \text{ eV}^{-1}) \quad (26)$$

$$CH_4^+ \xrightarrow{k27} CH + H + H_2 \ (GR26 = 0.48 \text{ molecule}.100 \text{ eV}^{-1}) \quad (27)$$

$$CH_4^+ \xrightarrow{k28} C + H_2 + H_2 \ (GR28 = 0.16 \text{ molecule}.100 \text{ eV}^{-1}) \quad (28)$$

$$CH_4^+ \xrightarrow{k29} CH_3 + H \ (GR29 = 2.05 \text{ molecule}.100 \text{ eV}^{-1}) \quad (29)$$

$$NH_3^+ \xrightarrow{k30} NH_2 + H \ (GR30 = 5.40 \text{ molecule}.100 \text{ eV}^{-1}) \quad (30)$$

$$NH_3^+ \xrightarrow{k31} NH + H_2 \ (GR31 = 0.70 \text{ molecule}.100 \text{ eV}^{-1}) \quad (31)$$

$$H_2S^+ \xrightarrow{k32} H + SH \ (GR32 = 3.30 \text{ molecule}.100 \text{ eV}^{-1}) \quad (32)$$

$$H_2S^+ \xrightarrow{k33} H_2 + S \ (GR33 = 0.50 \text{ molecule}.100 \text{ eV}^{-1}) \quad (33)$$

$k19$ was estimated by Kummler et al. ($k19 = 1 \times 10^9 \text{ s}^{-1}$).[28] Then, the same kinetic was assumed for other gases: $k19 = k20 = k21 = k22 = k23 = k24 = k25 = k26 = k27 = k28 = k29 = k30 = k31 = k32 = k33 = 1 \times 10^9 \text{ s}^{-1}$. These kinetics constants are considerably higher orders of magnitude than other reactions, which highly participate to the system's stiffness.

For the rest of this study, the databases used for input of the automatic approach detailed in Figure 3 are the three open-access curated kinetic databases: KIDA (version 2024),[60] UMIST (version 2022),[61] and GRIMECH (version 3.0).[62]

The evolution of the chemical composition is analyzed over time with particular interest in the radiolytic yield G(t), the sum of the products' G-values $\sum GPROD(t)$, the process selectivity S(t), and the conversion Conv(t). Radiolytic yields give information on the efficiency of the production/consumption of a species. It is worth highlighting that we chose the total energy absorbed by the mixture as the reference in the radiolytic yield calculation. The process selectivity expresses a product's proportion relative to the others. Conversions are the number of consumed molecules regarding the initial composition.

Finally, we introduce the radiolytic stages ratio -Rad. Stages Ratio-. This ratio provides information on the relative importance of the physico-chemical and chemical stages relative to the physical one in the conversion process. This ratio is found insightful, especially in the analysis of complex mixtures.

Formulas for each of these parameters of interest are detailed in the Supporting Information Section 2, Equations (S1) to (S9). For information, some of these values are plotted in a cumulative form (see Supporting Information Section 2 for more details).

### 3.3. Limitation of the Model

The model detailed previously has some limitations, which are essential to bear in mind while pursuing simulations. First, it relies on the knowledge of the primary radiolytic yield (g) of the molecule present in the initial composition. Finding primary radiolytic yield values can be challenging. There is no curated radiolytic yield values database, and different values could be found in different studies, in the same order of magnitude, though. Such a database would greatly benefit the community. Secondly, OD kinetics implies some hypotheses, such as the homogeneity of the chemical reactions. We also made the hypothesis of a homogeneous energy deposition. Homogeneity is an acceptable hypothesis in the gas phase, especially after $\approx 10^{-12}$ s after the first collisions.[59] At a shorter time scale, some heterogeneous phenomena excluded from this model (primary species diffusion,[59] droplet reaction,[63] aerosol formation,[30] clustering effect,[52] etc.) explain finer observations, such as the slight change in g-values regarding different irradiation. The results of the kinetic simulations also rely heavily on the precision of the kinetic constants. Indeed, some databases, especially in radiation chemistry, can include assumed reactions and reasonable rate constants that were never systematically measured. However, our previous tests showed these databases compared well with systematically remeasured experimental data.[64]

The quality of the results of the kinetic simulations also depends on the compliance with the principle of detail balancing,[65] which we limit by the use of curated databases. Methodology, as the one introduced by Standbury and Harshman,[66] could be applied to check compliance with the principle of detail balancing, but this appears challenging, especially for large-scale radiolysis models, as it would require the knowledge of the equilibrium constants.

Then, we also limit excitation by the use of "hot" atoms. A consideration of the vibrational, rotational, and/or electronically excited states would give a finer description, but it complicates the set of equations and often restricts simulations to pure systems.[67,68] Potential impacts of the photons emitted on the chemistry were excluded, as were the potential variations of temperature and pressure during irradiation.

When doing a simulation, there is always a tradeoff between precision and complexity. It shall be made regarding the simulation's objectives. Considering the scope of this study (time scales > $10^{-12}$ s and estimation of stable products' yields), the approximations made appear suitable.

### 3.4. Validation of the Method

Regarding previous limitations, to evaluate the proposed approach's benefit and validity, we compared three systems (S1, S2, and S3): first with each other and then with experimental data from the literature. S1 is a chemical reaction network from the literature with some minor equilibrium adjustments, S2 was built manually based on the latest kinetic data, and S3 is derived via the approach detailed in Figure 3. We focused on the
<figure><img src="image_16.png" /></figure>

simulation of a mixture of CO₂, CO, and O₂, for which extensive experimental data and a kinetic reaction network known as a reference exist in the literature. This system was set up by Kummler et al. in 1977 and was used as a base for S1.[28] Importantly, as mentioned by these authors, a lack of kinetic data led them to fill most of the reaction kinetic constants by analogy and estimation, so S2 was created from the latest found kinetic data.

S1 is composed of 21 chemical species (19 from the original[28] with the addition of O₂* and CO*) and 77 reactions (75 out of the 76 from the original[28] with the addition of Equations (19) and (20)). One equation from the original[28] was not considered because it appeared redundant. S2 has 28 chemical species and 136 reactions, and S3 has 61 chemical species and 230 reactions. Mind that for S3, a temperature of 26.85 °C was input to construct the system. This temperature impacts the selection of the kinetic constants and the reactions (see Figure 3). The systems S1, S2, and S3, along with their kinetic data, are part of the Supporting Information Section 3.

Graphs are efficient tools for complex network visualization. Previous studies propose different graph-based approaches with different focuses, purposes.[69,70] Our visualization approach consists of the use of graphs and matrices. The following figures provide for S1 (Figure 4), S2 (Figure 5), and S3, (Figure 6), the Reactants-Products graphs and the Reactants-Reactants matrices. The graphs and matrices associate the physico-chemical and chemical stages that follow the primary reactions (Equation (2), Equation (10), and Equation (11) for CO₂/O₂/CO radiolysis). In the matrices, a yellow square indicates that a reaction exists. In the graphs, each node is a chemical species, and edges are from a reactant to a product if they are in the same chemical reaction. In our graph approach, the node sizes are linearly related to the degree of the node and the edge thicknesses are related to the number of reactions relating a reactant and a product.

The graphs show an increase in the system's complexity from S1 to S3. S1 is based on the Kummler et al.'s model.[28] The authors obtained this model by simplifying a larger model. Consequently, the S1 graph has few peripheral species, suggesting that the intermediates weakly involved in the system were excluded. This is not the case for S3, for which the automated nonselective approach leads to a denser and more spatially extended graph. S2 was manually defined to have a complete model. However, the graph still shows poor completeness, which shows the difficulty of manually achieving a complete system, even for a system involving only C—O chemistry. The matrices indicate the potential missing reactions. It mainly concerns reactions between complex ions, short-lifetime species that are difficult to study experimentally. The species are sorted from left to right and top to bottom by the initial gases and their primary species. Then, follow the species produced as a combination of previous species. This means that the more a species is on the right (or the bottom), the more steps are required to form that species, starting from the initial and primary species. The systems show identical neutral, stable products except for O₃, which is only considered in S2, in agreement with Meaburn et al.,[71] which attests to this production of O₃. Photons that can be seen in the list of species of S3 come from chemiluminescent reactions. Their potential interactions via photochemistry are not included, so they show no interaction in the matrix.

For the three systems, the densities can be calculated from their graph to evaluate their completeness. This is done by excluding the “hot” atoms from the calculation. “Hot” atoms are excluded as they do not react with others, which can significantly impact the density in systems with a low number of nodes and limit the comparison between systems. We calculated 0.36, 0.38, and 0.10 for S1, S2, and S3, respectively. It shows that it is challenging to have a complete system of reactions. The lower density of S3 could come from the fact that it

<figure><img src="image_17.png" /><figcaption>**Figure 4.** System 1 (S1): CO₂/O₂/CO radiolysis, left: Reactants-Reactants matrix, right: Reactants-Products graph.</figcaption></figure>
<figure><img src="image_18.png" /></figure>

<figure><img src="image_19.png" /><figcaption>**Figure 5.** System 2 (S2): CO₂/O₂/CO radiolysis, left: Reactants–Reactants matrix, right: Reactants–Products graph. M is a chemical species: the third body in a third-body reaction. Edges from M to M are hidden for visualization concerns.</figcaption></figure>

<figure><img src="image_20.png" /><figcaption>**Figure 6.** System 3 (S3): CO₂/O₂/CO radiolysis, left: Reactants–Reactants matrix, right: Reactants–Products graph. M is a chemical species: the third body in a third-body reaction. Edges from M to M are hidden for visualization concerns.</figcaption></figure>

includes more complex species, which do not interact with each other.

For each system, a simulation was performed for a single shot of Febetron (pulse duration = 1 × 10⁻⁹ s, dose rate = 1 × 10²⁸ eV g⁻¹ s⁻¹). This single pulse fulfilled our conversion limitation of <20%. The comparison of the three systems in terms of G(CO) is plotted versus time in **Figure 7**.

As S1 is mainly derived from the Kummler et al. system,[28] the slight corrections done on S1 to equilibrate equations have a minimal impact on G(CO). S1 and S3, achieve the same CO production at the end of the irradiation step (≈7.8 molecules·100 eV⁻¹), whereas S2 reaches a G(CO) of 5 molecules·100 eV⁻¹. This lower yield is probably due to more favored recombinations of intermediate species. The
<figure><img src="image_21.png" /></figure>

<figure><img src="image_22.png" /><figcaption>**Figure 7.** Evolution with time of radiolytic yield of CO induced by a single pulse of Febetron (pulse duration = $1 \times 10^{-9}$ s, dose rate = $1 \times 10^{28}$ eV g$^{-1}$ s$^{-1}$), *p* = 1.013 bar, T = 26.85 °C, CO₂ with traces of CO 1(vol.ppm) and O₂ 1(vol.ppm); reference: Kummler et al.[28] We chose the total energy absorbed by the mixture as the reference in the radiolytic yield calculation. Radiolytic yields are from Equation (S1), Supporting Information.</figcaption></figure>

<figure><img src="image_23.png" /><figcaption>**Figure 9.** Evolution of the steady-state radiolytic yield of CO with the dose rate at constant irradiation time (single pulse radiolysis of pure CO₂, *p* = 1.013 bar, T = 26.85 °C, pulse duration = $1 \times 10^{-9}$ s); references: Anderson et al.[82](Van der Graaf proton radiolysis, *p* = 0.4 atm), Meaburn et al.[71] (single pulse electron radiolysis, *p* = 0.6 atm, Tpulse = $130 \times 10^{-9}$ s), Willis et al.[83] (single pulse electron radiolysis from 705 Febetron *p* = 0.6 atm). Note that the measurement from Meaburn et al.[71] was then corrected by Willis et al.[83] for dosimetry concerns. The value shown in the figure is the corrected value. We chose the total energy absorbed by the mixture as the reference in the radiolytic yield calculation. Radiolytic yields are from Equation (S1), Supporting Information.</figcaption></figure>

automatic method performs as well as S1 regarding the produc-
tion of CO.

To better evaluate our model regarding potential optimization levers, a validation step consisting of a parametric study of the three systems, as regards the literature data, was performed. The parameters of interest are the initial volumetric ratio of CO, O₂, the dose rate, the temperature, and the pressure. The results obtained are shown in **Figures 8, 9, 10, and 11**.

From Figure 8, the three systems show the same tendencies: a decrease in the CO radiolytic yield with the addition of CO or O₂. Regarding the evolution with CO, system S1 performed slightly better than S3, while with O₂, they both show good performances. The system S2 is not adapted in either case.

For the evolution of the dose rates (see Figure 9), S2 performs better at low dose rates and S1 and S3 at high dose rates. We do not observe significant dependence on the dose rate for all systems regarding the steady-state CO radiolytic yield.

For the temperature dependence in Figure 10, it is worth mentioning that all kinetic constants introduced in systems S2 and S3 are defined for a recommended temperature range. S1 was defined without any recommended temperature. Therefore, a rigorous temperature dependence study would

require reconstructing a new system at each temperature, which would be too demanding for practical purposes. Furthermore, the expected corrections are usually lower than the intrinsic uncertainties of the kinetic constants. A second limit in this dependence study is the definition of a steady-state. Indeed, at high temperature, the thermodynamic equilibration dynamic can superimpose to the irradiation one. Therefore, the simulations and experimental results were compared for different end points (i.e., endpoint 1 (Figure 10, left), endpoint 2 (Figure 10, right)), showing that the steady-state, due to thermodynamic equilibration, is only achieved at a longer time at high temperature via the CO₂ combustion reaction. This effect is not captured by S1.

The pressure dependence data were difficult to find in the literature. The work from Kalashnikov et al. suggests a substantial increase in CO yield around 100 bar, due to a change in the track structure.[72] As such an effect modifies the primary yields (Figure 11), it cannot be captured by S1, S2, or S3, where these parameters are kept constant.

<figure><img src="image_24.png" /><figcaption>**Figure 8.** Evolution of the steady-state radiolytic yield of CO with the initial volumetric ratio of CO and O₂, the rest being CO₂ (*p* = 1.013 bar, T = 26.85 °C, pulse duration = $1 \times 10^{-9}$ s, dose rate = $1 \times 10^{28}$ eV g$^{-1}$ s$^{-1}$); reference: Lee.[81] We chose the total energy absorbed by the mixture as the reference in the radiolytic yield calculation. Radiolytic yields are from Equation (S1), Supporting Information.</figcaption></figure>
<figure><img src="image_25.png" /></figure>

<figure><img src="image_26.png" /><figcaption>**Figure 10.** Evolution of the steady-state radiolytic yield of CO with temperature (single pulse radiolysis of pure CO₂, *p* = 1.013 bar, *T* = 26.85 °C, pulse duration = 1 × 10⁻⁹ s, dose rate = 5 × 10¹⁶ eV cm⁻³ s⁻¹), left: endpoint 1 right: endpoint 2; reference: Kalashnikov et al.[⁷²] We chose the total energy absorbed by the mixture as the reference in the radiolytic yield calculation. Radiolytic yields are from Equation (S1), Supporting Information.</figcaption></figure>

<figure><img src="image_27.png" /><figcaption>**Figure 11.** Evolution of the steady state radiolytic yield of CO with pressure (pure CO₂, *T* = 26.85 °C), reference: Kalashnikov et al.[⁷²] Note that in the reference, there is no indication of the value of the dose rate; it only indicates ²³S U fission radiolysis. Simulations are done at 1 × 10²⁸ eV g⁻¹ s⁻¹ and pulse duration 1 × 10⁻⁹ s. We chose the total energy absorbed by the mixture as the reference in the radiolytic yield calculation. Radiolytic yields are from Equation (S1), Supporting Information.</figcaption></figure>

Thus, through this validation, the automated nonselective approach for modeling gas mixtures radiolysis gives good agreement with experimental data from the literature and usually performs better than the manual conventional way of constructing reaction systems. One identified limit is high-pressure effects that would require considering track structure and diffusion effects. This could be done, for example, through Monte Carlo simulations, Independent Reaction Time (IRT)[⁷³] approaches, or with lighter analytical models as the one proposed by Kummler et al.[²⁸]

### 3.5. Case Study: SMR Coupling to Flue Gas (S4)

Then, from this approach, we modeled complex gas mixtures, such as flue gases. As a reminder, the base case of the simulation consists of a flue gas composition of 20(vol.%) CO₂, 20(vol.%) H₂O, 8(vol.%) O₂, 50 (vol.ppm) SO₂, 50 (vol.ppm) NO₂, 50 (vol.ppm) CO and the rest ≈52(vol.%) N₂, temperature 300 °C, pressure 1.5 bar, and a dose rate of 10 kGy s⁻¹ for an irradiation time of 400 s. As CO, NO₂, and SO₂ are in minor quantities, we did not

incorporate their negligible decomposition under radiation during the physical stage, following the criteria of dilution reported by Fritsch et al.[⁷⁰]

This new chemical network (S4) was derived from the proposed big data approach and the three databases mentioned previously: KIDA (version 2024),[⁶⁰] UMIST (version 2022),[⁶¹] and GRIMECH (version 3.0).[⁶²] This system comprises 448 chemical species and 4780 reactions. The system S4, along with its kinetic data, is part of the Supporting Information Section 3.

Network visualizations through graphs and matrices are plotted in **Figure 12**, and graph diagnostics in **Figure 13**.

The density of Reactants–Reactants is 0.03 (“hot” atom excluded). It is an order of magnitude below what was obtained from the previous systems. This is due to the more complex species involved in the system, which are more difficult to study experimentally and thus are less represented in the databases. For further analysis of the system, we create five chemical categories: C, H, N, O, and S. A chemical species is part of a category if it comprises the category element, and we plot in Figure 13 the number of nodes in each category and the matrix of connections.

From Figure 13, left, C and H are predominant. N and O come after, followed by S. This suggests information is lacking in the N, O, and S chemistry. The matrix of the connections (Figure 13, right) gives more details on potential lack of reactions. Categories C and H have the best connection with the rest of the system, and S has the lowest. If we look at category O, we see good connections with categories C and H, and low ones with S and N. The lack of information is thus ascribed to the O and N categories and the O and S categories. It is worth noticing that even for such a complex system, it is not limited by the computational cost. Typically, such a simulation is performed in ≈1 min on a standard computer.

If not specified, values of interest (i.e., G-value, ΣGPROD(*t*), process selectivity, conversion, and radiolytic stages ratio) are indicated at 500 s. This time corresponds to an irradiation time of 400 s plus a typical order of magnitude found in the literature to estimate the completion of radical chemistry.[⁵⁹]

**Table 2** gives the results of the base case simulation for the main components.
<figure><img src="image_28.png" /></figure>

<figure><img src="image_29.png" /><figcaption>**Figure 12.** System 4 (S4): N₂/H₂O/CO₂/O₂/CO/NO₂/SO₂ radiolysis, left: Reactants-Reactants matrix, right: Reactants-Products graph. M is a chemical species, the third body in a third-body reaction. Edges from M to M are hidden, and the node sizes are fixed at a constant value for visualization concerns.</figcaption></figure>

<figure><img src="image_30.png" /><figcaption>**Figure 13.** Graph diagnostic of the system S4, left: number of nodes per category (average shown as a red dotted line), right: matrix of chemical category connections (sum of each column added at the top).</figcaption></figure>

Converted gases, N₂, CO₂, H₂O and NO₂, have negative G-values. CO₂ is the most converted gas (2.69%). Conversely, N₂, whereas dominant in the mixture, has a conversion close to 0%. This stability with respect to irradiation comes from i) a low primary g-value (see reaction 5) and ii) chemistry potentially favoring back reactions. O₂, even if present in the initial mixture, has a positive G-value. It can be produced by CO₂ and H₂O radiolysis. We also observed good consumption of the initial traces of NO₂. However, SO₂ conversion is negligible. Literature reports many studies on SO₂ abatement in flue gas via electron beam, and even industrial pilot plants have shown good results of 80–100% conversion of NOx and SO₂ at temperatures 90–150 °C for NOx and SO₂ initial concentrations of 50–1000 ppm and dose 10–50 kGy.[⁵⁹] From further investigation,

according to results from a pilot plant reported by Chmielewski,[⁷⁴] there is a dose dependence for NOx conversion: 50% conversion at 4 kGy and 74% at 12 kGy, which could support the difference from our simulations. Then, by analyzing the species involved, we observe that the databases used for (S4) do not incorporate nitric and sulfuric acid liquid products and some of their intermediates.

Looking at the product of the process, interestingly, we see ≈75% of the products as energy vectors (CO, H₂, H₂O₂), with approximately $\sum \text{GPROD} = 0.8 \text{ molecule} \cdot 100 \text{ eV}^{-1}$. But, it is worth noticing that the G-values, process selectivities and conversions might experience maxima of interest before converging to a steady-state. In this way, we note, G(CO)(t = 2.0 × 10⁻⁴ s) = 1.31 molecule·100 eV⁻¹, G(H₂)(t = 1.1 × 10⁻² s) = 0.14 molecule·100 eV⁻¹,
<figure><img src="image_31.png" /></figure>

<table><caption>**Table 2.** S4 base case simulation results regarding main G-value, process selectivity and conversion, values given for convenience at 500 s for all chemical species. Conversions are only applicable to species part of the initial composition. We chose the total energy absorbed by the mixture as the reference in the radiolytic yield calculation. Radiolytic yields are from Equation (S1), Supporting Information, process selectivity from Equation (S5), Supporting Information, and conversion from Equation (S7), Supporting Information.</caption><thead><tr><th>t = 500 s</th><th>N<sub>2</sub></th><th>CO<sub>2</sub></th><th>H<sub>2</sub>O</th><th>O<sub>2</sub></th><th>NO<sub>2</sub></th><th>SO<sub>2</sub></th><th>CO</th><th>H<sub>2</sub></th><th>H<sub>2</sub>O<sub>2</sub></th><th>NO</th><th>N<sub>2</sub>O</th></tr></thead><tbody><tr><td>G (molecule.100 eV<sup>-1</sup>)</td><td>-0.02</td><td>-0.44</td><td>-0.16</td><td>0.18</td><td>-0.002</td><td>0</td><td>0.44</td><td>0.05</td><td>0.11</td><td>0.01</td><td>0.01</td></tr><tr><td>Process selectivity [%]</td><td>0</td><td>0</td><td>0</td><td>23.4</td><td>0</td><td>0</td><td>55.2</td><td>5.8</td><td>13.6</td><td>1.5</td><td>1.6</td></tr><tr><td>Conversion [%]</td><td>0.01</td><td>2.69</td><td>0.95</td><td>&lt;0</td><td>52.7</td><td>0</td><td>&lt;0</td><td>a)</td><td>a)</td><td>a)</td><td>a)</td></tr></tbody></table>

$G(H_2O_2)$ ($t = 1.0 \times 10^{-1}$ s) = 0.39 molecule·100 eV⁻¹, and $G(CO_2)$ ($t = 2.0 \times 10^{-2}$ s) = -6.62 molecule·100 eV⁻¹. Maxima were also noticed by some authors as Prelas et al.[75] These maxima suggest potential process optimizations via product withdrawal during the irradiation. Indeed, the withdrawal of the products limits the back recombinations, which are known to drastically decrease the radiolysis efficiency.[17]

We then conducted a parametric study regarding pressure, temperature, and initial composition to further explore the concept's potential. We considered the addition of: H₂O, H₂, NH₃, CH₄, and H₂S via the mixer. Concerning the withdrawal of gases, we only focused on H₂O withdrawal, for which it is easily applicable via a drying step. This study only required the addition of Equations (15) – (18) and (25) – (33) to system (S4, Supporting Information). The composition ranges of the added gases are between 0(vol.%) and 90(vol.%), the rest being the flue gas defined previously. Detailed values of pressures, temperature, and volumetric fractions of each simulation are indicated in Table S4–S10, Supporting Information Section 4.

The temperature, pressure, and initial composition are managed via a potential heater, chiller, mixer, and dryer (Figure 1). We can also benefit from the core temperature if heating is required, and/or choose reactor technologies more prone to such a temperature. Figures 14 and 15 give the results of the simulations in terms of the parameters of interest: G-values, process selectivity (here plotted in a cumulative way), and conversion. Only significant chemical species are plotted. We note {NOx} for nitrogen oxides, which includes NO, N₂O, and N₂O; {SOx} for sulfur oxides: SO and SO₂; {RSC} for reduced sulfur compounds: S₂, HS₂, and OCS; and {C2+} for C2+ products including C₂H₄, CH₂CCH₂, C₄H₄, C₅H₅, C₅H₆, CH₃C₄H, C₆H₂, C₆H₆, and C₅H₅CCH.

As for the base case simulation from the parametric study depicted in Figures 14 and 15, we see the production of molecules of interest (CO, H₂) and the conversion of interest (CO₂, NO₂). To ease the analysis, we introduced the sum of the products' G-values noted in $\sum GPROD(t)$. $\sum GPROD(t)$ is indicated on the top of each radiolytic yield plots in Figures 14 and 15 and better detailed in the Supporting Information (see Section 4, Figure S2, Supporting Information). As an example, in Figure 14 h, at 90(vol.%) of H₂O, we observe a high H₂ process selectivity (≈40%). Still, looking at the $\sum GPROD(t)$, we see that products are negligible, so this regime is of low interest in a context of the development of a process ($\sum GPROD(t) \approx 0$ molecules·100 eV⁻¹).

$\sum GPROD(t)$ allows the identification of two groups in the varied parameters: those degrading the radiolysis process and those improving it. Figure 14 depicts the result for the first group (pressure, temperature, and H₂O composition) and Figure 15 the second group (H₂, CH₄, and NH₃ composition). This is a simple split between the parameters, as the impact on radiolysis can be more subtle.

### 3.5.1. Pressure Variation (Figure 14a-c)

With the evolution of pressure, we denote a slight increase from 1.5 bar to 10 bar in the radiolytic effect seen in a rise in the G-values and conversions, followed by a decrease at higher pressure (keeping in mind the limitation in the pressure effect of the model). The reduction in NO₂ conversion is also significant, from 52.7% at the base case to 0% at 100 bar. From the scope of that study, there is no benefit of pressure in such a technology.

### 3.5.2. Temperature Variation (Figure 14d-f)

Increasing temperature shows considerable decreases in the conversions of interest. Above 600 °C, we even see a production of CO₂ by CO oxidation. The cumulative process selectivity shows a substantial rise in NOx, particularly in NO, coming from the oxidation of N₂. It is associated with a total consumption of the residual O₂. This conversion of N₂ is the main new mechanism activated in the high temperature regime, but it is limited to 0.4% at 1000 °C.

Lowering the temperature from 300 °C, on the other hand, improves the radiolytic conversions, as shown by the increases in the G-values. We see a maximum conversion for CO₂ at 100 °C of 4.1%. NO₂ and N₂ conversions also increase as the temperature goes down.

### 3.5.3. H₂O Composition Variation (Figure 14g-i)

The CO₂ conversion is also degraded with an increase in the H₂O initial content in the mixture. This is in accordance with experimental data in a CO₂/H₂O mixture and ascribed to an acceleration of the back reaction of CO toward CO₂.[76,77] The impact on NO₂ conversion is less severe. Consequently, drying the mixture shows great interest; CO₂ conversion increases to ≈10% with $G(CO_2) = -1.9$ molecule·100 eV⁻¹, and a high G(CO) of

<footnote>a)Not applicable.</footnote>
<figure><img src="image_32.png" /></figure>

<figure><img src="image_33.png" /><figcaption>**Figure 14.** a,d,g) Parametric study for the radiolysis of the gas mixture in terms of radiolyti yield, b,e,h) cumulative process selectivity, and c,f,i) conversion with the (a–c) evolution of pressure, (d–f) temperature, and (g–i) the initial composition in H₂O, the base case being at 300 °C, 1.5 bar, H₂O 20(vol.%). Σ GPROD is indicated on the top of each radiolytic yield plots and from Equation (S4), Supporting Information. The process selectivity is plotted in a cumulative way, which explains that 100% is reached. Some curves overlap each other. In (e), NO is specified for indication. We chose the total energy absorbed by the mixture as the reference in the radiolytic yield calculation. Radiolytic yields are from Equation (S1), Supporting Information, process selectivity from Equation (S5), Supporting Information, and conversion from Equation (S7), Supporting Information.</figcaption></figure>

1.9 molecule·100 eV⁻¹ and a process selectivity of 70%, idem for NO₂ conversion, which shows an increase from 52 to 75% with H₂O withdrawal.

### 3.5.4. H₂ Composition Variation (Figure 15a–c)

The addition of H₂ implies that the medium is more reductive. From Figure 15, adding H₂ improves the conversion of CO₂ to CO, and we see close to 30(vol.%) of H₂, a doubling of the conversion of CO₂ and production of CO with a conversion close to 5.7% and G(CO) close to 1 molecule·100 eV⁻¹. The O₂ from the radiolytic decomposition of CO₂ is trapped by H₂, which limits the back reaction toward CO₂. H₂O is formed, a product of minor interest, but which can be easily separated. This chemical trapping was evidenced in the literature up to 5% H₂ addition.[78]

### 3.5.5. NH₃ Composition Variation (Figure 15d–f)

NH₃ was used as an alternative source of reducing species. Adding NH₃ up to 10(vol.%) increases the conversion of CO₂ by a factor of 2.

Up to 80(vol.%) of NH₃, the main reactions involve the decomposition of NH₃ and the formation of H₂O and N₂, as shown by the increase in H₂O, and the decreases in O₂ and N₂ G-values. Above 80(vol.%), a regime favoring the production of H₂ is reached, with the same order of magnitude observed for CH₄ but at a relatively lower selectivity. At 90(vol.%) NH₃, we observe a maximum of 15.1% CO₂ conversion. This peak in CO₂ conversion can be explained by comparing the evolution of the main neutral species with time at 90(vol.%) and 70(vol.%) NH₃. Results are shown in Section 4, Figure S5, Supporting Information.
<figure><img src="image_34.png" /></figure>

<figure><img src="image_35.png" /><figcaption>**Figure 15.** a,d,g,j) Parametric study for the radiolysis of the gas mixture in terms of radiolytic yield, b,e,h,k) cumulative process selectivity, and c,f,i,l) conversion with the evolution of the initial composition in (a–c) H₂, (d–f) NH₃, (g–i) CH₄, and (j–l) H₂S; the base case being at 0(vol.%) for those. ΣGPROD is indicated on the top of each radiolytic yield plots and from Equation (S4), Supporting Information. The process selectivity is plotted in a cumulative way, which explains that 100% is reached. Some curves overlap each other. We chose the total energy absorbed by the mixture as the reference in the radiolytic yield calculation. Radiolytic yields are from Equation (S1), Supporting Information, process selectivity from Equation (S5), Supporting Information, and conversion from Equation (S7), Supporting Information.</figcaption></figure>

Information. We see that at 90(vol.%) NH₃ a total consumption of O₂ is reached near 1 × 10² s, consumption accompanied by the production of oxygen-based species: NO, H₂O, and CO. This suggests we can find an optimal O₂/NH₃ ratio to optimize CO₂ conversion.

### 3.5.6. CH₄ Composition Variation (Figure 15g-i)

The addition of CH₄ aims to favor the production of {C2+} products. Their production starts at ≈40(vol.%) of CH₄ with values between 0.01 and 1.1 molecule·100 eV⁻¹. We see an increase
<figure><img src="image_36.png" /></figure>

in the production of the {C2+} products up to a process selectivity of 11% at 90(vol.%) CH₄ with molecules up to {C5+} being formed (see Section 4, Figure S3, Supporting Information, for more details). Below 40(vol.%) of CH₄, the dominant processes are O₂, CO₂, and NO₂ consumption. Parallel to {C2+} products, H₂ is formed with yields from ≈1 molecule·100 eV⁻¹ at 40(vol.%) to 14 molecule·100 eV⁻¹ at 90(vol.%). N₂ conversion also shows a slightly favorable regime close to 75(vol.%) CH₄. We also note that in this range, there are good NOx and SOx conversions. However, CO₂ conversion is no longer possible. This shows that, at these irradiation conditions (i.e., dose rate and irradiation time), carbon from {C2+} products shall mostly come from CH₄ decomposition. One can also think it comes from both CO₂ and CH₄, but with total back reactions toward CO₂. But as we see only a low concentration of {C2+} products containing O, the latter explanation is less probable.

Then, as for the base case simulation, we observe interesting maxima with the addition of CH₄ that give insight into potential

improvement in the process. We note: G(CO)(t = 1.2 × 10⁻³ s) = 21.0 molecules·100 eV⁻¹ with 70(vol.%) CH₄ which suggests a radio-catalyzed process.

### 3.5.7. H₂S Composition Variation (Figure 15j–l)

Adding H₂S is similar to adding CH₄ with {RSC} productions instead of {C2+} production. Conversions of CO₂ are improved by approximately a factor of 2 with a small amount of H₂S, then stabilize up to 60(vol.%) H₂S. From that point, a regime that favors the back reaction of CO to CO₂ is reached. The production of {RSC} and H₂ is near 6 and 12 molecules·100 eV⁻¹ respectively. See Section 4, Figure S4, Supporting Information, for more details on {RSC}. Going to the zone of high {RSC} productions is interesting as it is accompanied by high H₂ production, and conversions of O₂ and NO₂. However, CO₂ and NO₂ conversions are degraded.

On the low H₂S additional regime, we found the advantage of high H₂S conversion up to 70% with 10(vol.%) added. This point of

<figure><img src="image_37.png" /><figcaption>**Figure 16.** a) CO₂ radiolytic stages ratio with the evolution of pressure, b) temperature, and initial composition in c) H₂O, d) H₂, e) CH₄, f) NH₃, and g) H₂S. The base case is at 300 °C, 1.5 bar, H₂O 20(vol.%), and H₂, NH₃, CH₄, and H₂S at 0(vol.%). Radiolytic stages ratios are from Equation (S8), Supporting Information.</figcaption></figure>
<figure><img src="image_38.png" /></figure>

$H_2S$ addition is interesting as it combined conversions of $CO_2$ (5.7%), $O_2$ (100%), and $NO_2$ (85%). There is an interest in converting $H_2S$, which is a pollutant from industrial streams. Furthermore, conversion of $H_2S$ is better if mixed with the flue gas than alone. This improvement is up to a factor of 2.3 at 10(vol.%) $H_2S$. However, the improvement is obtained at the expense of increased SOx concentration with a net production of 5 molecules·100eV⁻¹, selectivity of around 20%.

These findings are in coherence with Rustamov et al. who experimentally identified in a mixture of $H_2S/CO_2$, at temperatures greater than 200 °C, a regime that favors syngas ($H_2 + CO$) production with radiolytic yields in the order of 9.2–14.4 molecules·100 eV⁻¹.[⁷⁹]

Similarly to the addition of $CH_4$, the addition of $H_2S$ also shows interesting maxima with $G(H_2)(t = 0.4 s) = 973.4$ molecules·100 eV⁻¹ with 80(vol.%) $H_2S$.

Finally, some general comments from Figures 14 and 15: first $\{C2+\}$ products are only produced in quantities with additional $CH_4$, not with other H-based molecules ($H_2O$, $H_2$, and $NH_3$). This can be explained by the fact that the mechanism from $CH_4$ is more straightforward than with $H_2O$, $H_2$, and $NH_3$. Then, in general, except for the addition of $H_2O$, the addition of gas improves the production/consumption of species of interest. Except for the production of $H_2$ or $\{C2+\}$, these benefits are fully achieved with low gas addition (≈10 vol.% or lower). However, these conclusions must be interpreted in light of the irradiation conditions (i.e., dose rate and irradiation time). Similar findings were observed on plasma chemistry simulations.[⁷⁸]

To better understand the catalytic regimes, we plot the radiolytic stages ratio in **Figure 16**. This is done for the molecule of main concern: $CO_2$.

A ratio greater than 1 indicates that during the physicochemical and chemical stages, the decomposition of $CO_2$ occurs radio-catalytically, in addition to the physical stage decomposition through Equation (2). From Figure 16, radio-catalytical regime are achieved with specific temperature (≈100 °C), low $H_2O$ content (<10 vol.%) or from small addition (10 vol.%) of $H_2$, $NH_3$, and $H_2S$.

If the ratio equals 1, the conversion is equal to the conversion from the physical stages, so there is no impact of the physicochemical and chemical stages, or the back reactions following primary events compensate for the primary decomposition. A ratio between 0 and 1, as with pressure variations, indicates significant back reactions from the physico-chemical and chemical stages, which inhibit decomposition from the physical stages. If the ratio is negative, back reactions are significant, and the chemistry occurring during the physico-chemical and chemical stages favors the formation of $CO_2$ from the initial components. This effect is particularly pronounced when carbon-containing species, such as $CH_4$, are added. Adding $CH_4$ even at low ratios favors the $CO_2$ production and degrades its decomposition.

Figures 14, 15 and 16 provide numerous information, some of which have been presented in this article. Depending on industrial and/or legislation constraints, it can help to identify other optimal regimes.

# 4. Conclusion

## 4.1. Key Findings

In summary, starting from the potential use of ionizing radiation in treating complex gas mixtures, and the need for simulation tools to quickly assess their potential, we proposed an automated nonselective approach for OD kinetic simulation based on kinetic curated databases and the knowledge of radiolytic primary yields. We also introduce diagnostic tools to support the evaluation of the validity of the simulations.

We found good agreements with experimental data from the literature for a simple mixture of $CO_2/O_2/CO$ with variation of initial temperature and composition. Pressure variation is limited with this OD kinetic modeling and would require other tools (e.g., Monte-Carlo simulation). Still, regarding the validation steps, the proposed method is appropriate to give guidance for experimental work and appears to be an efficient tool for optimization exploration.

This method was applied to a new Nuc-To-Chem concept, which uses the radiation losses from SMRs to induce chemical reactions in a complex mixture of gases, with limited geometry modification and neutron activation. We think this strategy provides a promising coupling with nuclear energy and opens new pathways for the synthesis and conversion of chemicals. The assessment of the potential of this concept in terms of conversion of interest and production of interest was quickly implemented through the automated developed approach. We performed simulations with varying pressure and temperature. We also investigated the addition of $H_2O$, $H_2$, $CH_4$, $NH_3$, and $H_2S$ and a preirradiation drying step. This parametric study shows how our method helps identify interesting regimes even for complex impurified mixtures.

Via these simulations, we also evidenced some radiolytic yield maxima of great interest for the optimization of gas treatments. We introduced also a new parameter, the radiolytic stages ratio, which helps identify radio-catalyzed regimes. We think this ratio can be easily adapted to a time-dependent ratio for better analysis of the radiolytic mechanism.

## 4.2. Perspectives

In this model, we limit the radiolysis conversion to 10–20% to avoid the radiolysis of the products of radiolysis. Extending the model to a higher conversion may open to the formation of more complex molecules. However, going to such irradiation regimes would require the knowledge of the primary radiolytic yield (g) of all chemical species involved, for which no database is currently available. The formation of such a database would be of great interest to the community.

We believe this method could guide future optimization by notably helping in the exploration of new additive-based strategies, as was done, for example, for SOx and NOx abatement radiation-induced technologies with the addition of $H_2O_2$, hydrated lime ($Ca(OH)_2$), or $N_2H_4$.[⁸⁰]
<figure><img src="image_39.png" /></figure>

We hope this work helps identify industrial cases of interest and benefit, more broadly, the environmental transition. Such a methodology can also be developed for any kinetic case study outside the radiation chemistry perimeter and be used as a way to explore the coupling of different activation pathways.

## Acknowledgements

This work has benefited from French State aid managed by the Agence Nationale de la Recherche under France 2030 plan, bearing the reference code ANR-22-PESP-0010: Projet ciblé "POWERCO2" within the PEPR project SPLEEN.

## Conflict of Interest

The authors declare no conflict of interest.

## Data Availability Statement

The data that support the findings of this study are available in the supplementary material of this article.

**Keywords:** chemonuclear reactors • computational chemistry • decarbonation • gas-phase reactions • kinetics • radiation chemistry

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Manuscript received: June 20, 2025

Revised manuscript received: August 22, 2025

Version of record online: