# Pentane Depletion by a Surface DBD and Catalysis Processing
## 3 Experimental Results
### Intermediate Reaction Species  
As shown in Figure 4, the plasma (acting for \(t>0\)) shrinks the area of the pentane chromatogram peak, while other peaks appear. The water trace also changes as it depends on both the depletion processing, generated as by-products of VOC abatement species, and on the humidity transported by the chromatograph carrier gas (Helium). We could identify the acetylene and the propane peaks with the use of a calibration cylinder. We were not able to identify the peaks classified as \"Other\" in Figure 4, which are suspected to be C4 species, nor were we able to perform a CO2 calibration. Thus, we will just concentrate on acetylene and propane here. In order to fit the measured concentrations of the acetylene and propane species, denoted generically by x, we assume that the latter is regulated by a simple phenomenological differential equation consisting of a source term, proportional to \(\rho_{5}(t)\), minus a loss term describing its extinction. The time evolution of the concentration \(\rho_{\rm x}(t)\) of species \(x\) is then given by the following equation:  
\[\frac{d\rho_{\rm x}(t)}{dt}=\frac{1}{\tau_{\rm x5}}\rho_{5}(t)-\frac{1}{\tau_ {\rm x}}\rho_{\rm x}(t), \tag{3}\]  
where \(\rho_{5}(t)=\rho_{5}(0)\exp(-t/\tau_{5})\) (cf. Equation (1)), and x stands for acetylene or propane. Here, \(\tau_{\rm x5}\) represents the time scale for the generation of species x as a result of pentane decomposition, and \(\tau_{\rm x}\) is the time scale for the decomposition of the species x itself during the treatment. Thus, \(\tau_{\rm x5}\) and \(\tau_{\rm x}\) are the two parameters in the model. The differential equation (Equation (3)) admits an exact solution, given by the equation below:  
\[\frac{\rho_{\rm x}(t)}{\rho_{5}(0)}=\frac{\tau_{\rm x}\tau_{5}}{\tau_{5}-\tau_ {\rm x}}\frac{1}{\tau_{\rm x5}}\left(e^{-t/\tau_{5}}-e^{-t/\tau_{\rm x}}\right). \tag{4}\]  
Figure 6: Pentane decomposition efficiency (g/kWh) after 1 min of plasma treatment according to the initial pentane concentration. The lines serve as visual guides. The error bars were obtained by calculating the error propagation in the estimation of the efficiency. In the case of an initial pentane concentration of \(\rho_{5}(0)=1200\) ppm, for the two plasma powers, with and without a catalyst, we obtain the \(\tau_{\text{x5,x}}\) parameters by fitting the experimental data, as reported in Figure 7. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Specie**} & **Power (W)** & \multirow{2}{*}{**Catalyst**} & \(\tau_{\text{S}}\) & \(\tau_{\text{x5}}\) & \(\tau_{\text{x}}\) \\ \cline{3-6}  & **(W)** & & **(min)** & **(min)** & **(min)** \\ \hline \multirow{4}{*}{Acetylene} & \multirow{2}{*}{16.9} & No & 5.3 \(\pm\) 0.8 & 32.1 \(\pm\) 3.0 & 27.4 \(\pm\) 8.0 \\ \cline{3-6}  & & Yes & 5.3 \(\pm\) 0.8 & 31.8 \(\pm\) 2.0 & 6.5 \(\pm\) 1.0 \\ \cline{3-6}  & & No & 1.7 \(\pm\) 0.2 & 8.4 \(\pm\) 0.7 & 1.7 \(\pm\) 0.2 \\ \cline{3-6}  & & Yes & 1.7 \(\pm\) 0.2 & 7.1 \(\pm\) 1.0 & 1.1 \(\pm\) 0.1 \\ \hline \multirow{4}{*}{Propane} & \multirow{2}{*}{16.9} & No & 5.3 \(\pm\) 0.8 & 8.3 \(\pm\) 2.0 & 3.7 \(\pm\) 1.0 \\ \cline{3-6}  & & Yes & 5.3 \(\pm\) 0.8 & 5.2 \(\pm\) 2.0 & 0.8 \(\pm\) 0.3 \\ \cline{3-6}  & & No & 1.7 \(\pm\) 0.2 & 4.6 \(\pm\) 1.0 & 2.2 \(\pm\) 0.8 \\ \cline{3-6}  & & Yes & 1.7 \(\pm\) 0.2 & 5.7 \(\pm\) 2.0 & 2.6 \(\pm\) 1.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Acetylene and propane characteristic times for different plasma treatments. The initial pentane concentration for this table corresponds to 1200 ppm. The errors for \(\tau_{\text{x}}\) and \(\tau_{\text{x5}}\) were obtained as discussed in Figure 7.  
Figure 7: Normalized concentrations of intermediate products, acetylene, and propane, according to treatment time T (min), at 1200 ppm initial pentane concentration. (**a,c**) Acetylene at \(P=16.9\) W and \(P=44.2\) W, respectively. (**b,d**) Propane at \(P=16.9\) W and \(P=44.2\) W, respectively.