International Journal of Chemical Engineering / 2016 / Article / Tab 1

Research Article

Comparison of the Accuracy and Performance of Different Numbers of Classes in Discretised Solution Method for Population Balance Model

Table 1

Calibration parameters and error of simulation using different numbers of classes in discretised solution method for PBM at different velocity gradients.

Number of classesRatio of breakage rate coefficient and collision efficiency, (m−1⋅s−1)Average error of volume Computational time (s)Dimensionless number , DNote

 s−124 (k = 2.0)10320.024713.80.0900The total simulation time at which the steady-state PSD can be obtained was 5400 s. The possible values of the parameter were chosen in the range of , and a constant step-length 1 was applied in the exhaust algorithm for parameter calibration.
28 (k = 1.8)10450.023518.70.0980
35 (k = 1.6)10250.018130.40.0760
48 (k = 1.4)10520.016361.50.0977
88 (k = 1.2)10500.0128213.30.0900

 s−124 (k = 2.0)26020.02437.60.0900The total simulation time at which the steady-state PSD can be obtained was 3000 s. The possible values of the parameter were chosen in the range of , and a constant step-length 1 was applied in the exhaust algorithm for parameter calibration.
28 (k = 1.8)25980.023110.10.1020
35 (k = 1.6)26170.016514.60.0640
48 (k = 1.4)26110.015025.50.0770
88 (k = 1.2)26260.012389.40.0900

 s−124 (k = 2.0)42670.02875.50.0900The total simulation time at which the steady-state PSD can be obtained was 2500 s. The possible values of the parameter were chosen in the range of , and a constant step-length 1 was applied in the exhaust algorithm for parameter calibration.
28 (k = 1.8)41850.02688.20.1130
35 (k = 1.6)42280.021410.30.0842
48 (k = 1.4)42260.018518.70.0959
88 (k = 1.2)41990.014955.60.0900

: the cumulative volume percentage distribution was first calculated from the simulated PSD using different numbers of classes and then interpolated at the pivots of the measured PSD grid. Finally, the average error of volume percentage was recalculated by comparing with the measured PSD.
: a dimensionless number; : relating error and computational time; see (10).