Template:Model theory (Text, Stirred Mill, Perfect Mixing, Breakage Scaling)

The scaling factors are defined as:

${\begin{array}{lll}f_{\rm {Ds}}=\left({\dfrac {(D_{\rm {s}})_{\rm {Sim}}}{(D_{\rm {s}})_{\rm {Orig}}}}\right)^{e_{1}},&&f_{\rm {Hb}}=\left({\dfrac {(H_{\rm {b}})_{\rm {Sim}}}{(H_{\rm {b}})_{\rm {Orig}}}}\right)^{e_{2}},&&f_{\rm {Ns}}=\left({\dfrac {(N_{\rm {s}})_{\rm {Sim}}}{(N_{\rm {s}})_{\rm {Orig}}}}\right)^{e_{3}}\\f_{\rm {S}}=\left({\dfrac {S_{\rm {Sim}}}{S_{\rm {Orig}}}}\right)^{e_{4}},&&f_{\rm {T}}=\left({\dfrac {T_{\rm {Sim}}}{T_{\rm {Orig}}}}\right)^{e_{5}},&&f_{\rm {Db}}=\left({\dfrac {(D_{\rm {b}})_{\rm {Orig}}}{(D_{\rm {b}})_{\rm {Sim}}}}\right)^{e_{6}}\\f_{\rm {WI}}=\left({\frac {{\rm {WI}}_{\rm {Orig}}}{{\rm {WI}}_{\rm {Sim}}}}\right)^{e_{7}}\end{array}}$

where:

• the ${\rm {Orig}}$ subscript refers to the original mill from which $R_{i}/D_{i}^{*}$ was derived
• the ${\rm {Sim}}$ subscript refers to the mill being simulated (scaled)
• $e_{1}\dots e_{7}$ are scaling exponents, $e_{1}=3$, $e_{2}\dots e_{6}=1$, and $e_{7}=0.8$

The Work Index scaling factor, $f_{\rm {WI}}$, is retained from the Perfect Mixing ball mill model, where ${\rm {WI}}$ is the Bond Ball Work Index value of the ore (kWh/t).

The model user may optionally change the values of $e_{1}\dots e_{7}$ to suit specific test work results or operating data.