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吸附质在球形颗粒的内扩散可用固相内扩散偏微分方程描述，当使用吸附剂球心的浓度为零时，可得到解析解模型；当使用在球心的浓度梯度为零时，只能得到数值解。本文分析了在这两种不同的边界条件下导出的分析解和数值解模型之间的差别，当分别用两种模型计算颗粒内瞬时溶质浓度分布和吸附剂颗粒体积平均吸附量的结果表明：在吸附发生的初期(如τ= 0.0001)，二者的相对误差为24%，当吸附持续较长时间时，二者的数值基本相同。若以固相内扩散方程的数值解为基准，在吸附发生初期，二次方推动吸附速率近似模型的误差为29%，LDF模型的相对误差高达95%。二次推动力吸附速率模型是有效的，而只有当τ>0.05时，LDF模型才是有效的。作为吸附速率的近似模型，前者比后者有更高的精度。
The internal diffusion of adsorbate in spherical particles can be described by the partial differential equation in solid phase diffusion. When the concentration of adsorbent spherical center is zero, the analytical solution model can be obtained. When the concentration gradient in spherical center is zero, Get numerical solution. This paper analyzes the differences between analytical solutions and numerical solution models derived under these two different boundary conditions. When two models are used to calculate the instantaneous solute concentration distribution within the particles and the average volume loading of the adsorbent particles, respectively, In the initial stage of adsorption (such as τ = 0.0001), the relative error between the two is 24%. When the adsorption lasts longer, the values of the two are basically the same. Based on the numerical solution of the diffusion equation in the solid phase, the error of the approximate model of the second-order adsorption rate was 29% and the relative error of the LDF model was 95% at the initial stage of adsorption. The second-pass adsorption rate model is valid, whereas the LDF model is valid only for τ> 0.05. As an approximate model of adsorption rate, the former has higher accuracy than the latter.