Fluid flow through porous media is important in several applications, such as the flow of water in aquifers, the spread of injected chemicals or surfactants in hydrocarbon reservoirs, and the movement of chemicals in catalytic reactors. In these processes, the local fluid velocities need to be predicted, not only the average velocities in the porous medium. For example, in tissue engineering perfusion bioreactors, cells are seeded on the scaffold surfaces in order to receive nutrients from the surrounding fluid and grow in size. However, the cells may be washed away by very high fluid velocities or might not be able to obtain sufficient amount of nutrients due to very low velocities and mass transfer of the nutrients to the cells. In addition, the very high or very low velocities of chemical in catalytic packed bed reactors may lead to hot spots, thereby reducing the efficiency of the catalyst. Hence, a-priori knowledge of the velocity distribution enables the prediction on the percentage of dead cells in bioreactors or the deactivated catalyst in packed bed reactors as well as their efficiency. The goal of this work is to present a method to estimate the fluid velocity distribution in various types of porous media within statistical accuracy. The flow of water through twelve different types of porous media with a range of porosity between 0.13 and 0.85, including five samples of sandstone, one sample of carbonate, one sample of synthetic silica, three samples of sphere packings and two samples of fiber scaffolds was simulated by the Lattice Boltzmann method (LBM), which has been validated previously against analytical solutions[1],[2],[3]. Moreover, the local fluid velocities were normalized by the mean velocity magnitude and then the dimensionless velocity distribution of the flow through randomly packed spheres was validated against experimental results[4]. The two-sample Kolgomorov-Smirnov (KS) goodness-of-fit test was utilized to examine whether the normalized velocity magnitude distributions followed the pore-volume distributions, which were calculated by a maximal ball algorithm[5]. It was found that the velocity distribution and pore-volume distribution in each porous medium were statistically similar. This finding has a significant impact on the prediction of the velocity distribution; one can determine the velocity distribution of a complex porous medium by examining its pore structure and measuring its average pore velocity. More importantly, the velocity distribution can be tuned by adjusting the pore structure of a porous medium.
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