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.

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.