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\begin{document}

\title{Experimental support for a simplified approach to CTRW transport models
and exploration of parameter interpretation}



\author[1]{Scott K. Hansen}%
\affil[1]{Ben-Gurion University of the Negev}%


\vspace{-1em}



  
  \date{May 21, 2024}


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\begin{abstract}
We empirically test our earlier theoretical arguments about
simplification of continuous-time random walk (CTRW) solute transport
models, namely that without loss of generality the velocity-like term
may be set to mean groundwater velocity, the dispersion-like term
defined by a classical, velocity-independent dispersivity, and the
so-called time constant, \selectlanguage{greek}τ, \selectlanguage{english}set to unity. We also argue that for
small-scale heterogeneous advection (HA) and mobile-immobile mass
transfer (MIMT) CTRW transition time distributions, \selectlanguage{greek}Ψ\selectlanguage{english}(t), are unaffected
by mean flow velocity. To experimentally test these claims, we
re-analyze two bench-scale transport experiments---one for HA, one for
MIMT---each performed at multiple flow rates in otherwise identical
conditions, and show it is possible to simultaneously explain all
breakthrough curves in each, subject to the above constraints. We
compare our calibrations with earlier efforts for the same data sets. In
the HA calibration we identify a \selectlanguage{greek}Ψ\selectlanguage{english}(t) of the same functional form as
previous authors, and which yielded breakthrough predictions essentially
identical to theirs, but with greatly differing parameters. This
illustrates how values of individual CTRW parameters may not map
one-to-one onto underlying physics. We recommend reporting complete
model descriptions, discuss how the simplified approach assists in this
and other theoretical considerations.%
\end{abstract}%



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