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\begin{document}

\title{Relating Darcy-scale chemical reaction order to pore-scale spatial
heterogeneity}



\author[1]{Po-Wei Huang}%
\author[2]{Bernd Flemisch}%
\author[3]{Chaozhong Qin}%
\author[1]{Martin Oliver Saar}%
\author[4]{Anozie Ebigbo}%
\affil[1]{ETH Zurich}%
\affil[2]{University of Stuttgart}%
\affil[3]{Chongqing University}%
\affil[4]{Helmut Schmidt University}%


\vspace{-1em}



  
  \date{May 27, 2024}


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\begin{abstract}
Due to spatial scaling effects, there is a discrepancy in mineral
dissolution rates in porous media measured at different spatial scales.
Many reasons for this spatial scaling effect can be given. We
investigate one such reason, i.e. how pore-scale spatial heterogeneity
in porous media affects overall mineral dissolution rates. Using the
bundle-of-tubes model as an analogy for porous media, we show that the
Darcy-scale reaction order increases as the statistical similarity
between the pore sizes and the effective-surface-area ratio of the
porous sample decreases. The analytical results quantify mineral spatial
heterogeneity using the Darcy-scale reaction order and give a
mechanistic explanation to the usage of reaction order in Darcy-scale
modeling. The relation is used as a constitutive relation of reactive
transport at the Darcy scale. We test the constitutive relation by
simulating flow-through experiments. The proposed constitutive relation
is able to model the solute breakthrough curve of the simulations. In
addition, our results imply that we can infer mineral spatial
heterogeneity of a porous medium using measured solute concentration
over time in a flow-through dissolution experiment.%
\end{abstract}%



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