Equivalent permeability model of dual-porosity and bi-dispersed porous media based on the intermingled fractal units

Dual-porosity and bi-dispersed porous media (DBPM) widely exist in geotechnical engineering, material engineering, soil science, and groundwater exploitation. Therefore, it is significant to quantify the relationship between permeability and matrix–fracture structure parameters for mastering fluid's seepage and transport characteristics. Hence, this paper derives an analytical solution of equivalent permeability for DBPM based on the intermingled fractal units (IFU). The developed model considers the capillary pressure of fractures and capillaries and the tortuosity of fractures and capillaries. Specifically, the number of porous matrix fractal units in IFU is quantified, and then, the dimensionless permeability is calculated, defined as the ratio of the permeability of np matrix fractal units to a single fracture fractal unit. The results reveal that equivalent permeability is mainly contributed by fracture permeability. Next, the second dimensionless permeability is defined to compare further and quantify the permeable ability of fracture and porous matrix. The results highlight that the permeability difference between a single fracture fractal unit and a single porous matrix fractal unit is approximately 7–11 orders of magnitude. Overall, through this paper, the preferential flow mechanism of DBPM can be better described and understood by introducing the above two dimensionless permeabilities and analyzing the influence of structural parameters on them.