DOI: 10.5061/dryad.2z34tmprt
title: Improved dual-permeability model for characterizing the mass transfer process inside matrix blocks

description: The dual-permeability model (DPM) is highly
 efficient for describing bimodal transport in
 heterogeneous porous media. However, it uses only one domain to
 describe the matrix blocks, and it
 therefore ignores the impact of the mass
 transfer process inside the matrix blocks at the
 microscale. Therefore, in this study, to investigate the effect
 of the mass transfer process in dual-permeability media
 and the computational accuracy when considering it, the
 dual-permeability model with a transition domain (DPMTD) is
 proposed based on the DPM. Comparison
 of the DPMTD with the DPM by applying them to a sand column
 experiment with the same concept as the
 model reveals that the DPMTD captures the
 bimodal transport (especially the first peak) more effectively because it
 calculates the rapid exchange of solute in the early
 stage more accurately. Subsequently, the same conclusion is
 reached when both models are applied to a reported solute
 displacement experiment for an Andisol. In short, we suggest that
 the mass transfer process inside matrix blocks
 needs to be characterized in the model to achieve higher
 accuracy and provides a new approach for modeling the solute
 transport of preferential flow.
description: To verify the rationality of the new model and compare the DPMTD
 with the DPM, an experiment is designed. It is similar to the experiment
 of Köhne and Mohanty (2005), which used a cylindrical macropore filled
 with coarse sand crossing through a sand column. Although the
 experimental sand column is artificially filled, it is not meaningless. It
 can reflect the microscopic idea of the DPM at the macroscopic level. In
 essence, this experiment is designed based on the concept of the DPM, and
 this approach has been widely used by researchers. In this way, a
 macropore filled with coarse sand can be considered to represent the
 preferential flow path, and some parameters in the conceptual model can be
 obtained directly from the experimental conditions to prevent the fitting
 parameters from being inconsistent with actual values in the numerical
 simulation. In this experiment, two kinds of sand (fine
 sand and coarse sand) are used as filling materials. A cylindrical
 container made of acrylic with a diameter of 26 cm and height of 65 cm is
 used (the bottom is densely drilled with round holes with a diameter
 of 1 mm). A layer of metal mesh is laid on the porous plate to prevent the
 loss of particles from the sand column. The main part of the sand
 column above the mesh comprises fine sand 52 cm high with a core of coarse
 sand 3 cm in diameter as the macropore in the center. There is a water
 separator with a height of 5 cm and a diameter of 3 cm at the bottom of
 the macropore to prevent exit effects. The percolate in different zones is
 designed to flow out from different outlets (the percolate of the
 macropore flows out from outlet 1, and the percolate of the matrix flows
 out from outlets 2 to 5). The radii of the annular percolate collection at
 the bottom are 1.5 cm, 3.5 cm, 6.5 cm, 11 cm and 13 cm. The ion
 concentration of the percolate is measured with a conductivity meter. The
 macropore is filled with coarse sand to prevent the collapse of the
 macropore during the experiment and obtain the parameters of the model
 directly from the experimental conditions. In addition, the physical
 parameters of the matrix and macropores are measured as a reference for
 the subsequent numerical simulation. The
 experiment above is numerically simulated to verify the rationality of the
 DPMTD and compare it with the DPM. Both models use the same parameter
 values for simulation to make them comparable. Of course, there are also
 many studies that use the optimal fitting parameters in simulations and
 then investigate the differences between each model. However, since the
 physical parameters of the sand column in this study can be directly
 obtained from the experimental conditions, it is more reasonable to use
 the same parameters in the simulations and then examine the differences
 between the DPM and DPMTD. The above numerical
 simulation is carried out under the premise that the model parameters are
 known, which demonstrates that the novel model is closer to reality.
 However, it has not yet been demonstrated whether the DPMTD shows the
 advantage when the model parameters are unknown. Therefore, the DPMTD is
 applied to a solute displacement experiment conducted for an Andisol from
 an upland field at the National Institute of Vegetable and Tea Science in
 Mie, Japan. Although the DPMTD can capture bimodal
 transport more efficiently than the DPM, it has a shortcoming, similar
 to many other models: the fitting parameters are uncertain. Compared with
 the DPM, the new model has one more parameter, η. Therefore, the data of
 the sand column experiment in this study are taken as a reference to study
 how η affects the DPMTD and estimate an empirical range of η.