2. Literature overview on modeling for plasma-based CO2 conversion

Describing a detailed plasma chemistry in 2D or 3D models, with 100s of species and chemical reactions, is not yet feasible, due to excessive calculation times. Therefore, a detailed plasma chemistry is typically described by 0D chemical kinetic models or sometimes by 1D fluid models. The first papers on CO2 plasma chemistry modeling were published back in 1987–1995 but were applied to CO2 lasers [22–24]. Some papers also studied the vibrational kinetics of CO2 for gas flow applications [25, 26]. Rusanov et al. [27] were the first to develop a model for CO2 conversion in a MW plasma, based on particle and energy conservation equations for the neutral species, and an analytical description of the vibrational distribution function.

In the last decade, the research on plasma-based CO2 conversion experienced a clear revival, and quite some plasma chemistry models have been developed in literature, for either pure CO2 splitting [7, 28–48] or CH4 (of interest for hydrocarbon reforming) [49–52], as well as in various mixtures, that is, CO2/CH4 [53–66], CH4/O2 [66–72], CO2/H2O [73], and CO2/H2 [74, 75], of interest for producing value-added chemicals, or in mixtures of CO2/N2 [76, 77] or CH4/N2 [78–83], more closely mimicking reality, as N2 is a major component in effluent gases. Recently, we gave an overview of such 0D models for plasma-based CO2 and CH4 conversion [84], and we also presented a very comprehensive plasma chemistry model for CO2 and CH4 conversion in mixtures with N2, O2, and H2O [85]. These plasma chemistry models can provide detailed information on the underlying chemical reaction pathways for the conversion or product formation.

Furthermore, to investigate which reactor designs can lead to improved CO2 conversion, 2D or even 3D fluid models can be used; they offer a good compromise between level of detail and calculation time. To our knowledge, the number of 2D models for describing CO2 conversion is very limited [86, 87], and there exist no 3D models yet for this purpose. Most of the 2D/3D fluid models developed up to now in the literature for the typical plasma reactors used for CO2 conversion are developed in argon or helium, or sometimes air, with limited chemistry, to reduce the calculation time.

For packed bed DBD reactors, different types of modeling approaches have been developed. Chang [88] presented a 0D plasma chemistry model, simply predicting the enhancement factor of the electric field in the voids between the packing pellets from the ratio of the dielectric constant of the pellets and the gas phase. Takaki et al. [89] applied a simplified time-averaged 1D model in N2, based on solving the transport equations and Poisson's equation. Zhang et al. [90] performed 2D particlein-cell/Monte Carlo collision (PIC/MCC) simulations for the filamentary discharge behavior in a parallel-plate packed bed DBD reactor in air. Kang et al. [91] developed a 2D fluid model for a DBD with two stacked ferroelectric beads and studied the propagation of the microdischarges, but no plasma species were explicitly considered. Russ et al. [92] applied a 2D fluid model for studying transient microdischarges in a packed bed DBD operating in dry exhaust gas. Based on a 2D fluid model for a packed bed reactor with dielectric rods, Kruszelnicki et al. [93] presented a very interesting and detailed study on the mechanism of discharge

### Modeling for a Better Understanding of Plasma-Based CO2 Conversion DOI: http://dx.doi.org/10.5772/intechopen.80436

propagation in humid air, reporting that the discharges can generally be classified in three modalities: positive restrikes, filamentary microdischarges, and surface ionization waves. They observed that the type of discharge dominating the production of reactive species depends on the dielectric facilitated electric field enhancement, which is determined by the topography and orientation of the dielectric lattice. Finally, they demonstrated that photoionization plays an important role in discharge propagation through the dielectric lattice, because it seeds initial charge in regions of high electric field, which are difficult to access for electrons from the main streamer [93]. Van Laer et al. [94–96] developed two complementary 2D fluid models to describe a packed bed DBD in helium, to elucidate the electric field enhancement between the packing beads, and the effect of the dielectric constant of the packing beads, as well as the gap size and bead size. Wang et al. [97] applied a 2D fluid model to a packed bed DBD in air, studying the behavior of positive restrikes, filamentary microdischarges, and surface discharges, as well as the transition in discharge modes upon changing the dielectric constant of the packing beads. Finally, Kang et al. [98] also presented a 2D fluid model to study surface streamer propagation in a simplified packed bed reactor, in comparison with experimental data, obtained from time-resolved ICCD imaging.

For MW plasmas, a large number of models were presented in the literature, and we refer to [99] for a recent overview. Van der Mullen et al. [100–102] as well as Graves et al. [103] developed self-consistent 2D fluid models, based on Maxwell's equations for the electromagnetic field and plasma fluid equations, assuming ambipolar diffusion. Some of these models were applied to intermediate pressure coaxial microwave discharges [102], while others describe atmospheric pressure cylindrical (surfaguide or surfatron) MW plasmas [101, 103]. Although being very valuable, these models did not apply to the application of CO2 conversion. Recently, Georgieva et al. [99] performed a comparison between two fluid models, based on the coupled solution of the species conservation equations and Poisson's equation (i.e., so-called non-quasi-neutral approach) on the one hand and on a quasi-neutral approach on the other hand, but again these models were developed for argon.

For low-current nonthermal GA discharges (typically near 1 A or below), some simple 1D analytical or semi-analytical models have been developed [104–109], including the plasma string model [104] and the Elenbaas-Heller model, assuming an equilibrium plasma, with the radius of the plasma channel being constant [105– 107] or with a correction based on an analytical relation between the electric field and the electron and gas temperatures for non-equilibrium plasma [108] or focusing on the discharge electrical parameters [109]. These simple models cannot describe the complex behavior of the GA, such as the unsteady behavior in time and space, arc restrike, non-equilibrium effects, effects of flow patterns, etc., and they did not include a detailed chemistry. Gutsol and Gangoli [110] presented a simple 2D model of a GA, in a plane parallel to the gas flow and perpendicular to the discharge current, which provided very useful information about the gas-discharge interaction. Within our group, we developed a 2D non-quasi-neutral fluid model for the arc gliding process in an argon GA [111], and we compared the glow and arc mode in this setup [112]. We also presented a 2D quasi-neutral model [113], which was also applied in 3D modeling for a classical (diverging electrode) GA [114] and a reverse vortex flow (RVF) GA (also called GA plasmatron; GAP) [115]. These models were developed for argon, but we also developed a 1D fluid model [44] and two different 2D models [86, 87] for a (classical or RVF) GA in CO2, considering the detailed plasma chemistry of CO2 conversion. An overview of both 0D chemical kinetic models and 2D/3D fluid models for plasma reactors of interest for CO2 conversion was presented in [116].

(typically based on 2D, or even 3D, fluid models), and we will show some characteristic examples from our own research, to illustrate how such models can give more insight in the underlying mechanisms. First, however, we will present a brief overview of the different models relevant to CO2 conversion that have been

2. Literature overview on modeling for plasma-based CO2 conversion

and chemical reactions, is not yet feasible, due to excessive calculation times. Therefore, a detailed plasma chemistry is typically described by 0D chemical kinetic models or sometimes by 1D fluid models. The first papers on CO2 plasma chemistry modeling were published back in 1987–1995 but were applied to CO2 lasers [22–24]. Some papers also studied the vibrational kinetics of CO2 for gas flow applications [25, 26]. Rusanov et al. [27] were the first to develop a model for CO2 conversion in a MW plasma, based on particle and energy conservation equations for the neutral species, and an analytical description of the vibrational distribution function.

Describing a detailed plasma chemistry in 2D or 3D models, with 100s of species

In the last decade, the research on plasma-based CO2 conversion experienced a clear revival, and quite some plasma chemistry models have been developed in literature, for either pure CO2 splitting [7, 28–48] or CH4 (of interest for hydrocarbon reforming) [49–52], as well as in various mixtures, that is, CO2/CH4 [53–66], CH4/O2 [66–72], CO2/H2O [73], and CO2/H2 [74, 75], of interest for producing value-added chemicals, or in mixtures of CO2/N2 [76, 77] or CH4/N2 [78–83], more closely mimicking reality, as N2 is a major component in effluent gases. Recently, we gave an overview of such 0D models for plasma-based CO2 and CH4 conversion [84], and we also presented a very comprehensive plasma chemistry model for CO2 and CH4 conversion in mixtures with N2, O2, and H2O [85]. These plasma chemistry models can provide detailed information on the underlying chemical reaction path-

Furthermore, to investigate which reactor designs can lead to improved CO2 conversion, 2D or even 3D fluid models can be used; they offer a good compromise between level of detail and calculation time. To our knowledge, the number of 2D models for describing CO2 conversion is very limited [86, 87], and there exist no 3D models yet for this purpose. Most of the 2D/3D fluid models developed up to now in the literature for the typical plasma reactors used for CO2 conversion are developed in argon or helium, or sometimes air, with limited chemistry, to reduce the calcula-

For packed bed DBD reactors, different types of modeling approaches have been developed. Chang [88] presented a 0D plasma chemistry model, simply predicting the enhancement factor of the electric field in the voids between the packing pellets from the ratio of the dielectric constant of the pellets and the gas phase. Takaki et al. [89] applied a simplified time-averaged 1D model in N2, based on solving the transport equations and Poisson's equation. Zhang et al. [90] performed 2D particlein-cell/Monte Carlo collision (PIC/MCC) simulations for the filamentary discharge behavior in a parallel-plate packed bed DBD reactor in air. Kang et al. [91] developed a 2D fluid model for a DBD with two stacked ferroelectric beads and studied the propagation of the microdischarges, but no plasma species were explicitly con-

sidered. Russ et al. [92] applied a 2D fluid model for studying transient

microdischarges in a packed bed DBD operating in dry exhaust gas. Based on a 2D fluid model for a packed bed reactor with dielectric rods, Kruszelnicki et al. [93] presented a very interesting and detailed study on the mechanism of discharge

ways for the conversion or product formation.

tion time.

8

reported in literature.

Plasma Chemistry and Gas Conversion
