Supplementary Materials Modeling and Optimization for Gas Distribution Patterns on Biomass Gasification Performance of a Bubbling Spout Fluidized Bed Panxing Kang, †, ⊥ Xiayi(Eric) Hu, †,‡, ⊥ Yujian Lu, † Kuang Wang, † Rui Zhang, † Luchang Han, † Haizhuan Yuan, *,§ Hongbo Chen, † Xiao Luo, ∥ Yefeng(Jeffrey) Zhou *,†,‡ † National & Local United Engineering Research Centre for Chemical Process Simulation and Intensification, Chemical Process Simulation and Optimization Engineering Research Center of the Chinese Ministry of Education, Xiangtan University, Xiangtan 411105, P. R. China ‡ Hunan Provincial Engineering Research Center of Sepiolite Resource for Efficient Utilization, P. R. China § Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Hunan 411105, PR China ∥ College of Chemistry and Chemical Engineering, Hunan University, Changsha 410082, P. R. China ⊥ These authors contribute equally to this paper. * Corresponding Author: Haizhuan Yuan E-mail: yhz@xtu.edu.cn * Corresponding Author: Yefeng Zhou E-mail: zhouyf@xtu.edu.cn Governing equations Table S1. Governing equations of gas and multi-component particle phase flow. 1. The continuity equations of gas phase and multi-component particle phases (g = gas phase; gas species i = 1,2,…,ng; m = particle phase; m = 1,2,…,ns): 1 1 ( ) ( ) g s n n g g g g g im i m u S t          (S1-1) 1 ( ) ( ) g n m m m m m im i u S t         (S1-2) 2. The momentum conversation equations of gas phase and multi-component particle phases: 1 1 1 ( ) ( ) ( ) s g s g g g g g g g n n n g g g g g gm g m im i m i m u uu t P g u u Su                         (S1-3)