## 2 Modeling  
### Basis Model  
The complexity of the gasification process leads to many studies in model development to give a better understanding of the gasification process [15]. The stoichiometric models of biomass gasification usually consist of three influencing factors, namely: (1) the type of biomass, (2) the gasification agent, and (3) the syngas composition to be modeled. This study used a global stoichiometric model with an air gasification agent (Equation (1)) as the basis for developing new models. \[\mathrm{CH_{x}O_{y}N_{2}}+w\mathrm{H_{2}O}+m(\mathrm{O_{2}}+3.76\mathrm{N_{2} })\Leftrightarrow n_{1}\mathrm{CO}+n_{2}\mathrm{CO_{2}}+n_{3}\mathrm{CH_{4}}+ n_{4}\mathrm{H_{2}}+n_{5}\mathrm{H_{2}O}+n_{6}\mathrm{N_{2}}+n_{7}\mathrm{C}+n_{8} \mathrm{C_{6}H_{6}} \tag{1}\]  
All inputs on the left side of Equation (1) were assumed to be at a temperature of 25 \({}^{\circ}\)C and a pressure of 1 bar. The total amount of gas on the right side of Equation (1) can be defined as follows. \[n_{t}\ =\ \sum n_{i}\ =\ \ \ n_{1}+n_{2}+n_{3}+n_{4}+n_{5}+n_{6}+n_{8} \tag{2}\]  
where \(n_{i}\) is the unknown number of moles of the \(i\)th type of gas. Tar (C\({}_{6}\)H\({}_{6}\)) formation is included in Equation (1), which can be in the form of C\({}_{2}\)H\({}_{2}\), C\({}_{2}\)H\({}_{4}\), C\({}_{2}\)H\({}_{6}\), C\({}_{3}\)H\({}_{8}\), C\({}_{6}\)H\({}_{6}\), and C\({}_{7}\)H\({}_{8}\)[17], but mostly, the tar is in the form of benzene (C\({}_{6}\)H\({}_{6}\)) [20]. The number of moles \"\(w\)\" in Equation (1) indicates the amount of moisture (H\({}_{2}\)O) per kmol of biomass and it is calculated using Equation (3) [5; 11]. \[w\ =\ \frac{m_{bio}\times\mathrm{MC}}{m_{\mathrm{H_{2}O}}(1-\mathrm{MC})} \tag{3}\]where \(m_{bio}\) denotes the mass of biomass and \(m_{\rm H_{2}O}\) represents the mass of water. Equation (1) includes the number of oxygen atoms per kmol of biomass denoted as \"\(m\)\", which can be determined using Equation (4) [21]. \[m\ =\ \Big{(}1+\frac{x}{4}-\frac{y}{2}+\frac{z}{2}\Big{)}ER \tag{4}\]  
The number of moles of gasification products, including the carbon, (\(n_{1}\)-\(n_{8}\)) is unknown, therefore, the following mass balances are utilized to further determine \(n_{\rm i}\). Carbon mass balance:  
\[F_{1}\ =\ n_{1}+n_{2}+n_{3}+n_{7}+6n_{8}-1\ =\ 0 \tag{5}\]  
Hydrogen mass balance:  
\[F_{2}\ =\ 4n_{3}+2n_{4}+2n_{5}+6n_{8}-x-2w\ =\ 0 \tag{6}\]  
Oxygen mass balance:  
\[F_{3}\ =\ n_{1}+2n_{2}+n_{5}-y-w-2m\ =\ 0 \tag{7}\]  
Nitrogen mass balance:  
\[F_{4}\ =\ n_{6}-z-3.76m\ =\ 0 \tag{8}\]  
where \(F_{1}\) denotes the mass balance of carbon, hydrogen, oxygen, and nitrogen. At least eight equations are required to solve \(n_{1}\)-\(n_{8}\). Therefore, four of the six equations for the reaction equilibrium constants [22] below were employed to indirectly solve \(n_{1}\)-\(n_{8}\). Boudouard reaction (R1):  
\[\rm C+CO_{2}\stackrel{{ K_{1}}}{{\leftrightarrow}}2 CO \tag{9}\]  
Heterogeneous water gas shift reaction (R2):  
\[\rm C+H_{2}O\stackrel{{ K_{3}}}{{\leftrightarrow}}CO+H_{2} \tag{10}\]  
Hydrogasification reaction (methane formation) (R3):  
\[n_{t}\ =\ \sum n_{i}\ =\ \ \ n_{1}+n_{2}+n_{3}+n_{4}+n_{5}+n_{6}+n_{8} \tag{2}\]0  
Water gas shift reaction (R4):  
\[n_{t}\ =\ \sum n_{i}\ =\ \ \ n_{1}+n_{2}+n_{3}+n_{4}+n_{5}+n_{6}+n_{8} \tag{2}\]1  
Methane decomposition reactions (R5):  
\[n_{t}\ =\ \sum n_{i}\ =\ \ \ n_{1}+n_{2}+n_{3}+n_{4}+n_{5}+n_{6}+n_{8} \tag{2}\]2  
Steam reforming reaction (R6):  
\[n_{t}\ =\ \sum n_{i}\ =\ \ \ n_{1}+n_{2}+n_{3}+n_{4}+n_{5}+n_{6}+n_{8} \tag{2}\]3  
The equilibrium reaction constant (\(K_{1}\))-(\(K_{6}\)) of Equations (9)-(14) is defined as follow.