The diffusion regime (sub-diffusive, standard, or super-diffusive) is defined by the order of the derivative in the corresponding transport equation. We develop an accurate computational method for the direct estimation of the diffusion regime. The method is based on the derivative order estimation using the asymptotic analytic solutions of the diffusion equation with the integer order and the time-fractional derivatives. The robustness and the computational cheapness of the proposed method are verified using the experimental methane and methyl alcohol transport kinetics through the catalyst pellet.

中文翻译：

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扩散状态验证的一种精确计算方法

扩散方式（亚扩散，标准扩散或超扩散）由相应输运方程中导数的阶数定义。我们开发了一种直接计算扩散状态的精确计算方法。该方法基于使用具有整数阶和时间分数导数的扩散方程的渐近解析解的导数阶估计。使用实验性甲烷和甲醇通过催化剂颗粒的传输动力学，验证了所提出方法的鲁棒性和计算便宜性。