Table 5.

Result of reaction kinetic model test of transesterification reaction at hybrid catalytic-plasma reactor.

No.	Prediction of Reaction Mechanism	Reaction Kinetic Model (mole/gcat.min)	Value of Reaction Rate Constant	R2 Value Fischer F-Value (ANOVA)
I	The reaction of TG with adsorbed M gives ME and G $\text{TG}+3\text{Ms}\underset{{\text{k}}_{\text{s}}^{\prime }}{\overset{{\text{k}}_{\text{s}}}{\rightleftarrows }}3\text{ME}+\text{G}+3\text{s}$ The reaction mechanism is as follows: 1)$3\text{M}+3\text{s}\rightleftharpoons 3\text{Ms}$ 2)$\text{TG}+3\text{Ms}\rightleftharpoons 3\text{ME}+\text{G}+3\text{s}$	$\left(r_s\right)=\frac{k_s\left(C_{TG}{K}_M{C}_M^3-\frac{C_{ME}^3{C}_G}{K_s}\right)}{{\left(K_M^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}{C}_M+1\right)}^3}$	ks = 0.0147 KM = 0.0026 Ks = 0.0101	R2 = 0.8816 F-value = 14.6785
II	The reaction of TG with adsorbed M gives desorbed ME and G $\text{TG}+3\text{Ms}\underset{{\text{k}}_{\text{s}}^{\prime }}{\overset{{\text{k}}_{\text{s}}}{\rightleftarrows }}3\text{MEs}+\text{G}$ The reaction mechanism is as follows: 1)$3\text{M}+3\text{s}\rightleftharpoons 3\text{Ms}$ 2)$\text{TG}+3\text{Ms}\rightleftharpoons 3\text{MEs}+\text{G}$ 3)$3\text{MEs}\rightleftharpoons 3\text{ME}+3\text{s}$	$\left(r_s\right)=\frac{k_s\left(C_{TG}{K}_M{C}_M^3-\frac{K_{ME}}{K_s}{C}_{ME}^3{C}_G\right)}{{\left(K_M^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}{C}_M+K_{ME}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}{C}_{ME}+1\right)}^3}$	ks = 0.0078 KM = 0.0061 KME = 2.942 × 10−6 Ks = 0.9709	R2 = 0.9267 F-value = 22.8575
III	The reaction of TG with adsorbed M gives ME and G desorbed $\text{TG}+3\text{Ms}\underset{{\text{k}}_{\text{s}}^{\prime }}{\overset{{\text{k}}_{\text{s}}}{\rightleftarrows }}3\text{ME}+\text{Gs}+2\text{s}$ The reaction mechanism is as follows: 1)$3\text{M}+3\text{s}\rightleftharpoons 3\text{Ms}$ 2)$\text{TG}+3\text{Ms}\rightleftharpoons 3\text{ME}+\text{Gs}+2\text{s}$ 3)$\text{Gs}\rightleftharpoons \text{G}+\text{s}$	$\left(r_s\right)=\frac{k_s\left(C_{TG}{K}_M{C}_M^3-\frac{K_G}{K_s}{C}_{ME}^3{C}_G\right)}{{\left(K_M^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}{C}_M+K_G{C}_G+1\right)}^3}$	ks = 0.0035 KM = 0.0418 KG = 0.4189 Ks = 1.1009	R2 = 0.5912 F-value = 2.1336
IV	The reaction of TG with adsorbed M gives desorbed ME and desorbed G $\text{TG}+3\text{Ms}+\text{s}\underset{{\text{k}}_{\text{s}}^{\prime }}{\overset{{\text{k}}_{\text{s}}}{\rightleftarrows }}3\text{MEs}+\text{Gs}$ The reaction mechanism is as follows: 1)$3\text{M}+3\text{s}\rightleftharpoons 3\text{Ms}$ 2)$\text{TG}+3\text{Ms}+\text{s}\rightleftharpoons 3\text{MEs}+\text{Gs}$ 3)$3\text{MEs}\rightleftharpoons 3\text{ME}+3\text{s}$ 4)$\text{Gs}\rightleftharpoons \text{G}+\text{s}$	$\left(r_s\right)=\frac{k_s\left(C_{TG}{K}_M{C}_M^3-\frac{K_{ME}{K}_G}{K_s}{C}_{ME}^3{C}_G\right)}{{\left(K_M^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}{C}_M+K_{ME}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}{C}_{ME}+K_G{C}_G+1\right)}^4}$	Result: Divergence	-

Annotation: TG = triglyceride; M = methanol; ME = methyl ester; G = glycerol; TGs = adsorbed triglyceride; Ms = adsorbed methanol; MEs = adsorbed methyl ester; Gs = adsorbed glycerol; C_TG = concentration of triglyceride (gmol/L); C_M = concentration of methanol (gmol/L); C_ME = concentration of methyl ester (gmol/L); C_G = concentration of glycerol (gmol/L); k_s = constant of reaction rate for surface reaction, (min⁻¹); k_M = constant of reaction rate for M component (methanol), (min⁻¹); k_ME = constant of reaction rate for ME component (methyl ester), (min⁻¹); k_G = constant of reaction rate for G component (glycerol), (min⁻¹); K_s = equilibrium constant for surface reaction; K_M = equilibrium constant for M component (methanol); K_ME = equilibrium constant for ME component (methyl ester); K_G = equilibrium constant for G component (glycerol).