y Many theoretical and experimental results show that anomalous diffusion/dispersion occurs in porous media. To exactly solve anomalously fast dispersion, we introduce a structural derivative diffusion model to present superfast diffusion via a logarithmic structural function in space. The fundamental solution of the diffusion model is a form of log-normal distribution, and the corresponding analytical mean squared displacement grows like e(t/beta 2), 0 < beta < 1. Compared with the existing models, the proposed model is more effective and accurate in fitting experimental data. (C) 2019 Elsevier Ltd. All rights reserved.