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\begin{document}

\title{Upscaling of solute plumes in periodic porous media through a trajectory
based spatial Markov model}



\author[1]{Emanuela Bianchi Janetti}%
\author[2]{Thomas Sherman}%
\author[3]{Gael Raymond Guedon}%
\author[2]{Diogo Bolster}%
\author[3]{Giovanni Michele Porta}%
\affil[1]{Politecnico di Milano, Italy}%
\affil[2]{University of Notre Dame}%
\affil[3]{Politecnico di Milano}%


\vspace{-1em}



  
  \date{May 21, 2024}


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\begin{abstract}
We propose an approach to upscale solute transport in spatially periodic
porous media. Our methodology relies on pore scale information to
predict large scale transport features, including explicit
reconstruction of the solute plume, breakthrough curves at fixed
distances, and spatial spreading transverse to the main flow direction.
The proposed approach is grounded on the recently proposed
trajectory-based Spatial Markov model (tSMM), which upscales transport
based on information collected from advective-diffusive particle
trajectories across one periodic element. In previous works, this model
has been applied solely to one-dimensional transport in a single
periodic pore geometry. In this work we extend the tSMM to the
prediction of multi-dimensional solute plumes. This is obtained by
analyzing the joint space-time probability distribution associated with
discrete particles, as yielded by the tSMM. By comparing numerical
results from fully resolved simulations and predictions obtained with
the tSMM over a wide range of P\selectlanguage{ngerman}éclet numbers, we demonstrate that the
proposed approach is suitable for modeling transport of conservative and
linearly decaying solute species in a realistic pore space and showcase
the applicability of the model to predict steady state solute plumes.
Additionally, we evaluate the model performance as a function of
numerical parameters employed in the tSMM parameterization.%
\end{abstract}\selectlanguage{ngerman}%



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