4.1 0D chemical kinetic modeling

function of the electron energy. A more detailed description of the free electron kinetics in CO2 plasma is provided in [32–37], where a state-to-state vibrational kinetic model was self-consistently coupled with the time-dependent electron

efficiency (η) can be obtained with the following formulas:

ηð Þ¼ %

lation time, in contrast to, for instance, PIC-MCC simulations.

and the electron and ion diffusion coefficients and mobilities.

SEI kJ l 

0D models allow to predict the gas conversion, the product yields, and selectivities, based on the calculated plasma species densities at the beginning and the end of the simulations, corresponding to the inlet and outlet of the plasma reactor. Furthermore, based on the power introduced in the plasma and the gas flow rate, the specific energy input (SEI) can be computed, and from the latter, the energy

> <sup>¼</sup> Plasmapower kWð Þ Flowrate <sup>l</sup>

> > ΔHR kJ mol

SEI kJ l 

for CO2 splitting) and XCO<sup>2</sup> is the CO2 conversion. Note that this formula is only applicable to pure CO2 splitting, but a similar formula can be applied to the other gas mixtures, using another reaction enthalpy and accounting not only for the CO2 conversion but also for the conversion of the other gases in the mixture.

where ΔHR is the reaction enthalpy of the reaction under study (e.g., 279.8 kJ/mol

Even though some spatial dependences of the plasma reactors can be taken into

These fluid models solve a number of conservation equations for the densities of the various plasma species and for the average electron energy. The energy of the other plasma species can be assumed in thermal equilibrium with the gas. The conservation equations for the species densities are again based on source and loss terms, defined by the chemical reactions, like in the 0D models. The source of the electron energy is due to heating by the electric field, and the energy loss is again dictated by collisions. In addition, transport is now included in the conservation equations, defined by diffusion and by migration in the electric field (for the charged species) and (in some cases) by convection due to the gas velocity. Furthermore, the conservation equations are coupled with Poisson's equation for a selfconsistent calculation of the electric field distribution from the charged species densities, although more simplified quasi-neutral (QN) models have also been used [113], to further reduce the calculation time. Such a QN model neglects the nearelectrode regions and treats only the quasi-neutral bulk plasma. It does not solve the Poisson equation, but calculates the ambipolar electric field from the ion densities

Finally, in many cases, the gas temperature and gas flow behavior are calculated with a heat transfer equation and the Navier-Stokes equations, respectively, while in GA models, the cathode heat balance can also be accounted for, to properly describe the electron emission processes. The fluid (plasma) model and the models

account in 0D chemical kinetic models, as explained above, they are not really suitable for describing detailed plasma reactor configuration or predict how modifications to the reactor geometry would give rise to better CO2 conversion and energy efficiency. For this purpose, 2D or even 3D models are required, and fluid models are then the most logical choice, because they still allow a reasonable calcu-

min

<sup>∗</sup><sup>60</sup> <sup>s</sup>

∗XCO<sup>2</sup> ð Þ %

∗22:4 <sup>l</sup> mol 

min 

(2)

(3)

Boltzmann equation.

Plasma Chemistry and Gas Conversion

3.2 2D or 3D fluid modeling

12

0D chemical kinetic models typically provide information about the calculated gas conversion, energy efficiency, and product formation, as a function of specific operating conditions, as well as about the underlying chemistry explaining these results. The latter will be illustrated here, based on the modeling work performed within our group PLASMANT, for pure CO2 splitting, as well as CO2/CH4, CH4/O2, CO2/H2, and CO2/H2O mixtures. For more details about the modeling results in these mixtures, and more specifically the calculated conversions, product yields and energy efficiencies, and comparison with experiments, we refer to the original research papers mentioned below, as well as two recent review papers [84, 116].
