Abstract
Anomalous transport is found to be ubiquitous in complex geological formations and it has a paramount impact on petroleum engineering and groundwater sciences. This process can be well described by the continuous time random walk (CTRW) model, in which the probability density function $w(t)$ of a particle's transition time $t$ follows a power law for large $t$: $w(t)\ensuremath{\sim}{t}^{\ensuremath{-}1\ensuremath{-}\ensuremath{\alpha}}$ ($0<\ensuremath{\alpha}<2$). In this work, based on the CTRW theory, a semifractional advection-diffusion equation is proposed to model the anomalous transport for $1<\ensuremath{\alpha}<2$, which is, as evidenced by field and numerical experiments, possibly the typical situation for many complex geological porous media with weakly heterogeneous microstructures.
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