Suitable particle size range of sand filter layers based on fractal dimension characteristics

Abstract: This study aims to evaluate the filtration performance of sand filters using fractal dimensions. Three kinds of sand filters were also selected with particle size in the range of 1.0-1.18, >1.18-1.4, and >1.4-1.7 mm. The Yellow River sediment in the people's Victory Canal was collected as impurity particles in the raw water. The distribution of particle size in the Yellow River sediment was measured using a laser diffraction particle size analyzer (Mastersizer 3000, Dandong Baite Instrument Co., Ltd). It was found that the calculated mean values of skewness and kurtosis were 0.12 and -0.01, respectively, for the samples from the Yellow River sediment, indicating an outstanding normal distribution. Additionally, the samples were also collected from the Yellow River sediment in Lankao County, thereby verifying the distribution of particle size. It was found that the skewness and kurtosis values of the sediment sample in Lankao County were -0.11 and -0.23, respectively, where the frequency distribution of particle size also conformed to the normal distribution. An industrial CT scanner (C16M3201, Luoyang Tengda Testing Service Co., Ltd) was used to map the filter layer. The image processing and pixel coverage were utilized to calculate the porosity of cross section, the box-counting fractal dimension, and the ratio of the minimum to the maximum aperture (aperture ratio) in the three kinds of sand filter layers. The results showed that the porosities were 0.421, 0.431, and 0.439, respectively, while the box-counting fractal dimensions were 1.695, 1.709 and 1.726, respectively, and the aperture ratio was 1/17, 1/18, and 1/21, respectively, for the three types of layers. Then, the applicability of fractal theory was also evaluated for the quartz sand filters. Subsequently, a fractal model of filtration probability was established for the sand filters. The ranges of pore diameter in the three kinds of sand filters were 59.5-1 002, 66.9-1 220, and 72.9-1 503 μm, respectively. In the sediment of the Yellow River from the people's Victory Canal, the probabilities of impurity particles above 100 um passing through the sand filter were 0.67%, 0.81%, and 0.93%, respectively. In the Yellow River Sediment from Lankao County, the probabilities of impurity particles above 100 μm passing through the sand filter were 0.62%, 0.80%, and 0.91%, respectively. It inferred that the presence of surface filtration was proved theoretically. A systematic investigation was also made on the influence of surface filtration on Backwash frequency. Consequently, an optimal filter layer was achieved to reduce the surface filtration, particularly with the particle size in the range of >1.4-1.7 mm suitable for sand filters. The finding can provide strong support to explore the internal structure of sand filters and the selection of filter material.