## 4 Results and Discussion
### Empirical Correlation between Independent and Dependent Variables in Biomass Gasification  
Tables 11 and 12 show predicted compositions of CO, CO\({}_{2}\), CH\({}_{4}\), H\({}_{2}\), N\({}_{2}\), and tar-(C\({}_{6}\)H\({}_{6}\)) by the models M1A-M6D. However, the models cannot be used to establish sensitivity correlations between independent and dependent variables in biomass gasification. Therefore, an empirical correlation derived from the models needs to be established to evaluate how changes in input variables affect compositions of CO, CO\({}_{2}\), CH\({}_{4}\), H\({}_{2}\), N\({}_{2}\), and tar-(C\({}_{6}\)H\({}_{6}\)) gas. [PERSON] et al. (2015) developed a second-order polynomial equation to correlate volatile matter (VM) and fixed carbon (FC) with the composition of CO, H\({}_{2}\), and CH\({}_{4}\). [PERSON] et al. (2016) established multiple linear correlations with ER and temperature (T) as independent variables to estimate the composition of CO, CH\({}_{4}\), and H\({}_{2}\) gas. [PERSON] et al. (2016) established a correlation between T, air flow ratio (AR), hydrogen-to-carbon (H/C), and oxygen-to-carbon (O/C) ratio with LHV, yield, and composition of syngas. [PERSON] et al. (2016) applied the response surface method to develop a second-order polynomial correlation between ER, T, and time as the independent variables with the composition of syngas, whereas [PERSON] et al. (2018) used multiple linear regression to predict CO, CO\({}_{2}\), H\({}_{2}\), and N\({}_{2}\) gas. The results of this study indicated that models M1D, M2C, and M3C have good validity and accuracy in simulating producer gas composition from biomass gasification. Further, one of these models was used to establish an empirical correlation between O/C, H/C, N/C, ER, and T as the independent variables and CO, CO\({}_{2}\), CH\({}_{4}\), H\({}_{2}\), N\({}_{2}\), C\({}_{6}\)H\({}_{6}\) content, LHV-gas, and CGE as the dependent variables. The M2C model was selected for this establishment because the multivariable regression coefficient of determination for each response variable is the largest compared with the M1D and M3C models. Based on M2C model, the following empirical correlation between the independent and dependent variables in biomass gasification is set up. \[X\ =\ a_{0}\bigg{(}\frac{H}{C}\bigg{)}^{a_{1}}\bigg{(}\frac{O}{C}\bigg{)}^{a_{2}} \bigg{(}\frac{N}{C}\bigg{)}^{a_{3}}(ER)^{a_{4}}T^{a_{5}} \tag{47}\]  
Unlike the correlation established by [PERSON] et al. (2016), the correlation in Equation (47) uses ER instead of AR and includes the ratio of H/C, O/C, and N/C. The \(X\) variable is the dependent variable that includes CO, CO\({}_{2}\), CH\({}_{4}\), H\({}_{2}\), N\({}_{2}\) in % mol, C\({}_{6}\)H\({}_{6}\) (g/Nm\({}^{3}\)), LHV-gas (MJ/Nm\({}^{3}\)), and CGE (%). Further, Equations (48)-(52) were established based on Equation (47) and the predicted data by the M2C model. The empirical correlations described by Equations (48)-(53) were further used to investigate the impact of independent variables on the dependent variables. \[\text{CO}\ =\ 0.0020\bigg{(}\frac{H}{C}\bigg{)}^{-0.2908}\bigg{(}\frac{O }{C}\bigg{)}^{0.1062}\bigg{(}\frac{N}{C}\bigg{)}^{-0.0108}ER^{-0.1760}T^{1.286 9};R^{2}\text{adj}\ =\ 0.9815 \tag{48}\]  
\[\text{CO}_{2}\ =\ 1.1650\times 10^{6}\bigg{(}\frac{H}{C}\bigg{)}^{-0.4372} \bigg{(}\frac{O}{C}\bigg{)}^{0.7438}\bigg{(}\frac{N}{C}\bigg{)}^{0.0005}ER^{-0. 1184}T^{-1.5803};R^{2}\text{adj}\ =\ 0.9931 \tag{49}\]