Water seepage characteristics in porous media with various conduits: Insights from a multi-scale Darcy-Brinkman-Stokes approach

Conduits are widely distributed in porous media, such as natural rocks and soils, which could be the dominant water discharge channels. Investigations regarding the seepage process in such porous media with conduits are rather significant and have attracted many researchers' attention. However, the conventional method to describe this type of seepage could not consider that in both the porous zone and fracture zone simultaneously. In this study, the multi-phase Darcy-Brinkman-Stokes (DBS) method is selected to simulate the seepage in porous rock with various conduits. The DBS method includes the Darcy method in the porous region and the Navier-Stokes method in the solid-free region. Accordingly, non-conduit porous rock, solid free pure conduit region, and porous rock with conduits are simulated respectively, using the approach accompanied by an open-source solver in OpenFoam. Comparing the experimental results and the results using Navier-Stokes (N-S) simulation, the applicability of the DBS method to describe the seepage in a rock mass with conduits is verified. Using the DBS approach, three aspects of the investigations are then conducted, namely, flux variations with the aperture of the conduit, influence factors of the transition layer, and various situations of rectangular conduit. The simulation results show that the flow rate of rock mass with circular conduit and the maximum velocity of conduit are positively correlated with the circular aperture. And the width of the transition layer is positively correlated with aperture and permeability but independent of the pressure gradient. In addition, the law for the square conduit is similar to that of circular conduit, while the results of rectangular conduit show some different features.