A mathematical model was developed for a diffusion–reaction process in a spherical catalyst pellet contained in a heterogeneous packed bed reactor. The model developed was solved to predict the effectiveness factor and also to perform sensitivity analysis for steam reforming of methanol on Cu/ZnO/Al₂O₃ catalyst a source of hydrogen fuel. The method of orthogonal collocation was used to solve the resulting differential equation. At temperature below 473 K the effect on intra-particle diffusion limitation is reduced to the minimum indicated by the effectiveness factor being almost equal to one but as the temperature increases above 473 K there is considerable increase in the diffusion limitation effect. The effects of thermal conductivity, diffusion coefficient, catalyst size and surface temperature on effectiveness factor for the reaction process were also considered. Result indicates that catalyst size of \(1.623\,\, \times \,\,10^{ - 4}\) m eliminates the effect of intra-particle diffusion resistance in the pellet. The variation of effectiveness factor with Thiele modulus, showing the asymptotic values, using power law and Langmuir–Hinshelwood–Hougen–Watson (LHHW) kinetics, was predicted. The two reaction kinetics had almost the same magnitude of effectiveness factor at different Thiele modulus which indicates that they can adequately predict the reaction process.

中文翻译：

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Cu / ZnO / Al 2 O 3催化剂颗粒上甲醇水蒸气重整效果因子的计算

建立了一个数学模型，用于非均相填充床反应器中球形催化剂颗粒中的扩散反应过程。解决了建立的模型的问题，以预测效率因素，并对甲醇在Cu / ZnO / Al ₂ O ₃上进行蒸汽重整进行灵敏度分析催化剂是氢燃料的来源。使用正交配置的方法来求解所得的微分方程。在低于473 K的温度下，对粒子内扩散限制的影响减小到最低程度，由有效性因子几乎等于1表示，但是当温度升高到473 K以上时，扩散限制效果会显着增加。还考虑了热导率，扩散系数，催化剂尺寸和表面温度对反应过程效率因子的影响。结果表明催化剂大小为\（1.623 \，\，\ times \，\，10 ^ {-4} \） m消除了颗粒中颗粒内扩散阻力的影响。使用幂律和Langmuir-Hinshelwood-Hougen-Watson（LHHW）动力学预测了效率因子随Thiele模量的变化，显示了渐近值。两种反应动力学在不同的Thiele模量下具有几乎相同的有效因子幅度，这表明它们可以充分预测反应过程。