Title: Temporal Markov Processes for Transport in Porous Media: Random Lattice Networks,
Abstract: Monte Carlo (MC) simulations of transport in random porous networks indicate
that for high variances of the log-normal permeability distribution, the
transport of a passive tracer is non-Fickian. Here we model this non-Fickian
dispersion in random porous networks using discrete temporal Markov models. We
show that such temporal models capture the spreading behavior accurately. This
is true despite the fact that the slow velocities are strongly correlated in
time, and some studies have suggested that the persistence of low velocities
would render the temporal Markovian model inapplicable. Compared to previously
proposed temporal stochastic differential equations with case specific drift
and diffusion terms, the models presented here require fewer modeling
assumptions. Moreover, we show that discrete temporal Markov models can be used
to represent dispersion in unstructured networks, which are widely used to
model porous media. A new method is proposed to extend the state space of
temporal Markov models to improve the model predictions in the presence of
extremely low velocities in particle trajectories and extend the applicability
of the model to higher temporal resolutions. Finally, it is shown that by
combining multiple transitions, temporal models are more efficient for
computing particle evolution compared to correlated CTRW with spatial
increments that are equal to the lengths of the links in the network.