Mathematical Modelling of the Impact of IR Laser Radiation on an Oncoming Flow of Nanoparticles with Methane

   Introduction. The study is devoted to the numerical investigation of laser radiation’s effect on an oncoming two-phase flow of nanoparticles and multicomponent hydrocarbon gases. Under such exposure, the hydrogen content in the products increases, and methane is bound into more complex hydrocarbons on the surface of catalytic nanoparticles and in the gas phase. The hot walls of the tube serve as the primary source of heat for the reactive two-phase medium containing catalytic nanoparticles.

   Materials and Methods. The main method used is mathematical modelling, which includes the numerical solution of a system of equations for a viscous gas-dust two-phase medium, taking into account chemical reactions and laser radiation. The model accounts for the two-phase gas-dust medium’s multicomponent and multi-temperature nature, ordinary differential equations (ODEs) for the temperature of catalytic nanoparticles, ODEs of chemical kinetics, endothermic effects of radical chain reactions, diffusion of light methyl radicals CH₃ and hydrogen atoms H, which initiate methane
conversion, as well as absorption of laser radiation by ethylene and particles.

   Results. The distributions of parameters characterizing laminar subsonic flows of the gas-dust medium in an axisymmetric tube with chemical reactions have been obtained. It is shown that the absorption of laser radiation by ethylene in the oncoming flow leads to a sharp increase in methane conversion and a predominance of aromatic compounds in the product output.

   Discussion and Conclusion. Numerical modelling of the dynamics of reactive two-phase media is of interest for the development of theoretical foundations for the processing of methane into valuable products. The results obtained confirm the need for joint use of mathematical modelling and laboratory experiments in the development of new resource-saving and economically viable technologies for natural gas processing.

1. Snytnikov V.N., Peskova E.E., Stoyanovskaya O.P. Mathematical Model of a Two-Temperature Medium of Gas–Solid Nanoparticles with Laser Methane Pyrolysis. Mathematical Models and Computer Simulations. 2023;15:877–893. doi: 10.1134/S2070048223050095

2. Peskova E.E. Mathematical Modeling of Nonstationary Problems Related to Laser Thermochemistry of Methane in the Presence of Catalytic Nanoparticles. Doklady Mathematics. 2024;109(3):256–261. doi: 10.1134/S1064562424702107

3. Pinaeva L.G., Noskov A.S., Parmon V.N. Potentialities of the Direct Catalytic Processing of Methane into in-Demand Chemicals. Review. Kataliz v promyshlennosti. 2017;17(3):184–200. (In Russ.) doi: 10.18412/1816-0387-2017-3-184-200

4. Guo X., Fang G., Li G. et al. Direct, Nonoxidative Conversion of Methane to Ethylene, Aromatics, and Hydrogen. Science. 2014;344(6184):616–619. doi: 10.1126/science.1253150

5. Frank-Kamenetskii D.A. Diffusion and Heat Transfer in Chemical Kinetics. Plenum Press, New York; 1969. (In Russ.)

6. Day M.S., Bell J.B. Numerical simulation of laminar reacting flows with complex chemistry. Combustion Theory and Modelling. 2000;4(4):535–556.

7. Borisov V.E., Yakush S.E., Sysoeva E.Y. Numerical Simulation of Cellular Flame Propagation in Narrow Gaps. Mathematical Models and Computer Simulations. 2022;14:755–770. doi: 10.1134/S2070048222050039

8. Lashina E.A., Peskova E.E., Snytnikov V.N. Mathematical modeling of the homogeneous-heterogeneous non-oxidative CH₄ conversion: the role of gas-phase H or CH₃. Reaction Kinetics, Mechanisms and Catalysis. 2023;136:1775–1789. doi: 10.1007/s11144-023-02442-8

9. Hairer E., Wanner G. Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems. Springer-Verlag, Berlin; 1996.