Two-phase Lattice Boltzmann Simulation Study on Flow Pattern in a Silty Sand Model

The spilled oil can be trapped in porous media, such as beach sand, wetland soils and marine sediments, over decades after the disaster of oil spill, which is dependent on the type of the sediments. Silty sand is a prototype of the sediments, where the pore space between sand grains (~100 microns) can be filled by silt grains (a few microns to tens of microns). Here, we have studied the drainage of oil into a silty sand model initially saturated with water by using lattice Boltzmann simulations. The simulation study has been compared with micro-capillary video microscopy experiments. The aim of this study is to understand the oil spill pattern and the flow dynamics inside the sedimentary media, which is so opaque that the flow pattern (inside it) is invisible. Lattice Boltzmann, which is one of the computational fluid dynamics methods, is adopted as a tool of computing two-phase immiscible fluid flow in this study. This method has several strong points: above all, complicated fluid-solid boundary can be easily applied. In this study, the capillary number is varied not only by changing fluid velocity, but by changing interfacial tension. As a porous media, granular model, which is made by packing of a lot of same-sized spherical elements (silt grains), is adopted. The discontinuous oil front migration is observed in the case of low capillary number, whereas, the relationship between oil-traveled distance and simulation time was close to linear in the case of high capillary number. The breakthrough time and capillary number has a linear relation in log-log scale, when changing only fluid velocity. Additionally, the relationship is also linear when changing interfacial tension. However, the slopes of the two lines are different and the line slope in changing fluid velocity is steeper. While the simulation is generally consistent with experimental result, it further enables us understand the flow dynamics in detail. Further study is undergoing towards the underlining mechanism of the observed linear relationship.