# The Synthetic Scale-up Data Generated by the Austin model and Their Estimation by the Kotake–Kanda Model

The Excel spreadsheet contains the synthetic scale-up data generated by the Austin model and their estimation using the Kotake–Kanda (KK) model, which overall yields the information presented in **Table 2** of the manuscript. In view of all scale-up (SU) cases in **Table 2**, the Austin model, via Eqn. (12) of the manuscript, was used to produce the synthetic scale-up data, i.e., the specific breakage rate *S*_{i}*, to which the *S*_{i}* generated by the KK model, via Eqn. (13) of the manuscript, were compared (SU1–SU4 in **Table 2**). In SU1–SU4, standard values of the scale-up correction exponents, i.e., *N*_{1} = 0.5 and *N*_{2} = 0.2, were used. In SU5–SU8, *N*_{1} and *N*_{2} were estimated by fitting Eqn. (13) to the synthetic scale-up data for each diameter ratio *D*/*D*_{T} separately. In SU9–SU12, they were fitted to the synthetic scale-up data for all *D*/*D*_{T} data together. These two separate types of fits are presented in the Excel spreadsheet, which contains two separate spreadsheets entitled “Separately fitted” and “Simultaneously fitted.” For simplicity,* S*_{i}* was replaced by Si in the Excel spreadsheet. Columns A and B yield, respectively, the ball size *d*_{B} values and the particle size *x*_{i} values from which the artificial *S*_{i} values were calculated using the Austin model for different values of *D*/*D*_{T}. A summary table is included at the far right side of the Excel spreadsheet, which presents the values used in **Table 2 **of the manuscript.

Nomenclature

Si,A and Si,K: *S*_{i}* calculated by the Austin model and estimated by the KK model

Si,Kmod: *S*_{i}* estimated by the KK model with modified (fitted) *N*_{1} and *N*_{2}

Sqrt(Si,A) and Sqrt(Si,K): Square root of Si,A and Si,K

Sqrt(Si,Kmod): Square root of Si,Kmod

SE original: square error between the Austin and the KK model for* N*_{1} = 0.5 and *N*_{2} = 0.2

SE modified: square error between the Austin and the KK model for fitted* N*_{1} and *N*_{2}