## 3 Modeling Methodology
### Influence of Excess Air Ratios in the Main Combustion Zone  
The excess air ratio in primary combustion zone has significant impacts on the boiler operation performance. For the convenience of expression, the excess air ratio in primary combustion zone is defined as \(\alpha_{1}\). Figure 10 illustrates the average temperature distribution within furnace in the cases that the \(\alpha_{1}\) varies among 0.65, 0.75, and 0.85 under three blending methods with the semi-coke blending ratio of 45%. The average temperature distribution within the furnace exhibited relative good symmetry. The average temperature within furnace increased first and then decreased with the enhancement in \(\alpha_{1}\). The overall temperature within the furnace in the \"out-furnace\" case was higher than that in the \"in-furnace\" cases. The pulverized coal can be combusted well and the temperature within furnace was enhanced with more air injected. Since the temperature of the air injected was much lower than the temperature within furnace, too much air brought about a decrease of the temperature within the furnace. As shown in Figure 11, the mole fraction of NO had an increase and the trend flattened out with the increase of \(\alpha_{1}\). The change trend of the NO mole fraction in the \"in-furnace- up\" case was similar to that in the \"out-furnace\" case, while the mole fraction of NO in the \"in-furnace down\" case established a clear increase tendency with the injection of OFA. Figure 12 displays several essential indices under various \(\alpha_{1}\). With the increase in \(\alpha_{1}\), the NO\({}_{x}\) concentration at the furnace outlet showed an increasing trend and various blending methods shared the same trend. As the \(\alpha_{1}\) rose, more air was injected in the primary combustion zone, since the total air remained constant. The unburned carbon could be consumed and release more heat, which led to the increase of the NO\({}_{x}\) production. In addition, the high concentration of oxygen resulted in the abatement of reducing atmosphere. Hence, the reduction of NO\({}_{x}\) declined, which is consistent with the tendency of NO\({}_{x}\) concentration as shown in Figure 11. When the \(\alpha_{1}\) rises, the change trend of the carbon content in fly ash and burnout ratio was opposite. Compared with the case where the \(\alpha_{1}\) is 0.65, the air injected into the furnace became less when the \(\alpha_{1}\) became 0.65, leading to the anoxic combustion phenomenon. When the \(\alpha_{1}\) increased to 0.85, large quantities of air in low temperature were sprayed into the primary combustion zone, resulting in the decline of the temperature within furnace and the delay of ignition. Hence, the degree of incomplete combustion of pulverized coal increased. The average temperature at the furnace outlet dropped with the increasing \(\alpha_{1}\). When the \(\alpha_{1}\) is 0.85, a drop of the outlet temperature in the \"out-furnace\" case was dramatic, larger than those in the \"in-furnace\" cases. The NO\({}_{x}\) concentration increased by nearly 100 mg/m\({}^{3}\), while the burnout ratio increased significantly and the carbon content in fly ash went down to 1/5 when the \(\alpha_{1}\) was changed from 0.65 to 0.75. When the \(\alpha_{1}\) increased to 0.85, the NO\({}_{x}\) concentration increased by nearly 50 mg/m\({}^{3}\) and the carbon content in fly ash increased more than three times, while the burnout ratio only showed a slight difference. The research of [PERSON] et al. [35] illustrated that when the ratio of OFA was increased, the boiler combustion efficiency was reduced, while NO\({}_{x}\) concentration was also reduced due to the enhanced the effects of the air staged combustion. Hence, a balance must be found between the NO\({}_{x}\) concentration and the boiler efficiency. When the semi-coke blending ratio is 45%, the optimal \(\alpha_{1}\) in this study is 0.75 to achieve low NO\({}_{x}\) concentration based on good operation performance of wall-fired boiler.