Fractal Characteristic Of The Granular Sludge In The Start-up Anaerobic Baffled Reactor(ABR)

Abstract: The physical properties and fractal dimensions within different topological spaces of the granular sludge in anaerobic baffled reactor (ABR) were investigated. During the process of ABR start-up, diameters of granules measured at horizontal projected view were 1.02～2.49 mm, and were 1.59～3.02 mm at vertical projected view; the results of effective density calculated by Allen equation and Logan-Allen equation were different, the front one showed the range were between 0.76 kg·m-3 and 77.58 kg·m-3 when the latter showed 0.96～91.08 kg·m-3; ree setting rates were 1.96～45.27mm·s-1. After complete the ABR start-up, the black and granules with distinct boundary were found in all five compartments of ABR, their SVI values were between 25 ml·g -1 and 35 ml·g -1; their diameters measured at horizontal projected view were 1.70～1.98mm, and were 2.23～2.68mm at vertical projected view; effective density calculated by Allen equation were between 0.85 kg·m-3 and 66.70 kg·m-3 when Logan-Allen equation showed the range were 1.04～76.96 kg·m-3; free setting rates were 1.96～45.27mm·s-1.During free setting process with equal rates for these granules, the ratio between the average diameters for them in each stage at horizontal projected view and at vertical projected view was nearly constant, but every stage was different.Their mass fractal dimensions Df, calculated by bi-logarithm relation between setting rates and equivalent circle diameters, were 2.019～2.905 during the process of ABR start-up, and were 2.097～2.801 after that. Moreover, the Df value for granules in the 5th compartment was the highest one among them, indicating that the most compact granules were formed. The least compact granules were observed in the 4th compartment, and the granules in the 1st and 2nd compartments show close compactness. However, the highest average setting rate for granules was detected in the 1st compartment.In addition, the relation among the calculated fractal dimensions in 1-D and 2-D topological spaces for these ABR granules with image analysis method gives accordance with the relation among theirtheory equations. The fractal dimensions in 2-D topological space for these granules based on the projected area-maximum diameter bi-logarithm relation were 1.39～1.87 during the process of ABR start-up and between 1.69～1.84 after that, and they show an order of D2 values: in 3rd compartment > in 1st compartment > in 5th compartment > in 4th compartment > in 2nd compartment. The fractal dimensions in 1-D topological space of 0.99～1.03 indicate little irregular boundary of these granules and no distinct difference in the five compartments.