We define an effective Lagrangian statistical model in phase space ($x$, $t$, $v$) for describing transport in highly heterogeneous velocity fields with complex spatial organizations. The spatial Markovian nature (and temporal non-Markovian nature) of Lagrangian velocities leads to an effective transport description that turns out to be a correlated continuous time random walk. This model correctly captures the Lagrangian velocity correlation properties and is demonstrated to represent a forward model for predicting transport in highly heterogeneous porous media for different types of velocity organizations.

• Received 27 May 2008

DOI:https://doi.org/10.1103/PhysRevLett.101.090601