Lattice Boltzmann method for solute transport in dual-permeability media

Abstract

Dual-permeability models are currently under active investigation for predicting the flow and transport of pollutant concentration in porous media. The basic idea of these models is usually to separate the medium into two distinct flow regions with separate hydraulic and solute movement properties. Most of the dual-permeability approaches presented to date assume the reaction terms to be independent of space. For local reaction processes in soils, however, the depth effects are important and should be incorporated into the dual-permeability models. To reveal the transport phenomenon in such case, the best way is to obtain an exact solution with a suitable analytical approach, but it may be hard or even impossible for this general scenario. As such, this paper seeks an alternative method, and propose a lattice Boltzmann method for solute transport in dual-permeability media. The Chapman–Enskog analysis shows that the present model can recover the governing equations correctly. The capability and accuracy of this model is first verified by two problems: the non-reactive mass transfer in dual-permeability porous media, and the solute transport in a depth-dependent soil. With this model, we further studied the contaminant transport in dual-permeability soil with depth-dependent reaction rates. The numerical results show that when the exchange coefficient is relatively smaller, there are usually two peaks for the breakthrough curves (BTCs), whereas it degenerates to a single peak as the exchange coefficient increases. In addition, we note that the distributions of the concentration in different domains are nearly the same for a larger exchange coefficient. As for the pore water velocity, it is found that when the difference in the pore water velocity in the two domains is significant, the BTC exhibits a bimodal distribution. However, there is only one peak for the BTCs when the above difference is insignificant. Further, as compared with the constant-reaction rate cases, we observe that the BTCs obtained for the media with depth-dependent rates lie in the intermediate zone defined by the above two extremes. Finally, we adopt the current approach to simulate the solute transport in an Andisol and observe that the difference between the numerical and experimental results is insignificant, indicating our approach is capable in modeling solute transport in porous media.