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考虑非线性吸附平衡关系、吸附剂内外传质阻力以及表面扩散系数为固相浓度的函数的基础上,建立间歇搅拌吸附槽中大孔吸附树脂吸附DMF的表面扩散模型,由于该模型为高度非线性的偏微分方程,只能采用数值方法求解。因此,对MATLAB中pdepe函数进行适当修改,并针对吸附表面扩散模型边界条件的特点建立边界条件函数,使其可应用于具有Robin边界条件的吸附数学模型的求解。当间歇搅拌吸附槽的搅拌速度为100rpm,温度为298K条件下,应用修改后的pdepe函数结合优化工具箱求解吸附表面扩散模型,获得有效表面扩散系数D0=1.04×10-10m2/s和液相传质系数KF=9.60×10-6m/s;模型计算得到的吸附速率与实验测定结果的均方根误差为ε=0.008。结果表明:DMF在NKA-Ⅱ树脂上吸附动力学过程与吸附表面扩散模型吻合良好,应用修改后的pdepe函数可方便地求解具有Robin边界条件的表面吸附模型,结果准确可靠。
Considering the nonlinear adsorption equilibrium relationship, the mass transfer resistance inside and outside the adsorbent and the diffusion coefficient as a function of solid phase concentration, the surface diffusion model of DMF adsorbed by the macroporous adsorption resin in intermittent stirred tank is established. Since the model is highly non- Linear partial differential equations can only be solved numerically. Therefore, the pdepe function in MATLAB is modified appropriately, and the boundary condition function is established according to the characteristics of the boundary conditions of the adsorption surface diffusion model so that it can be applied to solve the adsorption mathematical model with Robin boundary conditions. When the stirring speed of intermittent stirring adsorption tank is 100rpm and the temperature is 298K, the modified surface pdepe function and optimization toolbox are used to solve the adsorption surface diffusion model, and the effective surface diffusion coefficient D0 = 1.04 × 10-10m2 / s and liquid phase The mass transfer coefficient KF = 9.60 × 10-6m / s. The root mean square error of the adsorption rate calculated by the model and experimental results is ε = 0.008. The results show that the adsorption kinetics of DMF on NKA-Ⅱ resin is in good agreement with the adsorption surface diffusion model, and the surface adsorption model with Robin boundary condition can be easily solved by the modified pdepe function. The results are accurate and reliable.