Mathematical Problems in Engineering

Research Article

Simulation of Floc Size Distribution in Flocculation of Activated Sludge Using Population Balance Model with Modified Expressions for the Aggregation and Breakage

Table 2

Results of parameters calibration and modeling errors of four methods.


		Constant for collision efficiency ()	Parameter of Eq. (3) for collision efficiency ()	breakage rate coefficient (E, m⁻¹·s⁻¹)	maximum breakage rate (, s⁻¹)	Average error of volume percentage (Err₁, %)	Average error of mean size (Err₂, μm)

G = 28.2s⁻¹	Method 1	0.33		363		4.67 × 10⁻¹	18.86
	Method 2	0.32		328		4.51 × 10⁻¹	15.07
	Method 3		0.58	271		3.17 × 10⁻¹	13.86
	Method 4		0.78	389	0.16	2.25 × 10⁻¹	0.69

G = 64.7s⁻¹	Method 1	0.21		573		4.76 × 10⁻¹	16.01
	Method 2	0.23		593		4.54 × 10⁻¹	15.76
	Method 3		0.30	351		3.38 × 10⁻¹	13.42
	Method 4		0.34	413	0.16	2.48 × 10⁻¹	0.52

G = 101.7s⁻¹	Method 1	0.09		405		4.95 × 10⁻¹	16.77
	Method 2	0.09		381		4.79 × 10⁻¹	14.49
	Method 3		0.16	310		3.51 × 10⁻¹	13.46
	Method 4		0.22	447	0.16	2.47 × 10⁻¹	0.36

G = 149.8s⁻¹	Method 1	0.05		362		5.58 × 10⁻¹	15.46
	Method 2	0.05		350		5.62 × 10⁻¹	16.34
	Method 3		0.08	252		4.33 × 10⁻¹	14.62
	Method 4		0.15	481	0.16	3.58 × 10⁻¹	0.23

: The fractal dimension D₂ = 1.83 was used in the expressions for the collision frequency and breakage rate. The maximum breakage rate, which is assumed to be independent on the velocity gradient, was calibrated to be 0.16 from the floc size distribution of activated sludge at the velocity gradient of 28.2, 64.7, 101.7 and 149.8 s⁻¹.