Air Classifier (Altun)

Description

This article describes the Altun and Benzer (2014) model for air classification.

Model theory

This section is currently under construction. Please check back later for updates and revisions.

Excel

The Altun air classifier model may be invoked from the Excel formula bar with the following function call:

=mdUnit_AirClassifier_Altun(Parameters as Range, Size as Range, Feed as Range, OreSG Range)

Invoking the function with no arguments will print Help text associated with the model, including a link to this page.

Inputs

The required inputs are defined below in matrix notation with elements corresponding to cells in Excel row ([math]\displaystyle{ i }[/math]) x column ([math]\displaystyle{ j }[/math]) format:

[math]\displaystyle{ Parameters= \begin{bmatrix} D\text{ (m)}\\ \mathit{AF}\text{ (m}^3\text{/h)}\\ \mathit{RS}\text{ (m/s)}\\ k_{\alpha}\\ n_{\alpha}\\ k_{d_{50}}\\ n_{d_{50}}\\ k_{C}\\ n_{C}\\ k_{\beta}\\ n_{\beta}\\ c_{\beta}\\ (Q_{\rm M,F})_{\rm L}\text{ (t/h)}\\ \end{bmatrix},\;\;\;\;\;\; Size = \begin{bmatrix} d_{1}\text{ (mm)}\\ \vdots\\ d_p\text{ (mm)}\\ \end{bmatrix},\;\;\;\;\;\; Feed= \begin{bmatrix} (Q_{\rm M,F})_{11}\text{ (t/h)} & \dots & (Q_{\rm M,F})_{1m}\text{ (t/h)}\\ \vdots & \ddots & \vdots\\ (Q_{\rm M,F})_{n1}\text{ (t/h)} & \dots & (Q_{\rm M,F})_{nm}\text{ (t/h)}\\ \end{bmatrix},\;\;\;\;\;\; OreSG= \begin{bmatrix} (\rho_{\rm S})_{1}\text{ (t/m}^\text{3}\text{)} & \dots & (\rho_{\rm S})_m\text{ (t/m}^\text{3}\text{)}\\ \end{bmatrix} }[/math]

where:

• [math]\displaystyle{ D }[/math] is the classifier chamber diameter (m)
• [math]\displaystyle{ \mathit{AF} }[/math] is the air flow rate (m³/h)
• [math]\displaystyle{ \mathit{RS} }[/math] is rotor speed (m/s)
• [math]\displaystyle{ k }[/math] is an equation coefficient
• [math]\displaystyle{ n }[/math] is an equation exponent
• [math]\displaystyle{ c }[/math] is an equation constant
• [math]\displaystyle{ (Q_{\rm M,F})_{\rm L} }[/math] is the mass flow rate of liquids in the feed (t/h)'
• [math]\displaystyle{ p }[/math] is the number of size intervals
• [math]\displaystyle{ m }[/math] is the number of ore types
• [math]\displaystyle{ d_i }[/math] is the size of the square mesh interval that mass is retained on (mm)
• [math]\displaystyle{ d_{i+1}\lt d_i\lt d_{i-1} }[/math], i.e. descending size order from top size ([math]\displaystyle{ d_{1} }[/math]) to sub mesh ([math]\displaystyle{ d_{p}=0 }[/math] mm)
• [math]\displaystyle{ \rho_{\rm S} }[/math] is the density of solids (t/m³)

Results

The results are displayed in Excel as an array corresponding to the matrix notation below:

[math]\displaystyle{ \mathit{mdUnit\_AirClassifier\_Altun} = \begin{bmatrix} \begin{bmatrix} \mathit{DL}\text{ (kg/m}^3\text{)}\\ F\text{ (t/h)}\\ \alpha\\ d_{\rm 50c}\text{ (mm)}\\ C\text{ (frac)}\\ \beta\\ \beta^*\\ (Q_{\rm M,OF})_{\rm L}\text{ (t/h)}\\ (Q_{\rm M,UF})_{\rm L}\text{ (t/h)}\\ \end{bmatrix} \begin{array}{cccccc} \begin{bmatrix} \bar d_1\text{ (mm)}\\ \vdots\\ \bar d_n\text{ (mm)} \end{bmatrix} & \begin{bmatrix} (Q_{\rm M,UF})_{11}\text{ (t/h)} & \dots & (Q_{\rm M,UF})_{1m}\text{ (t/h)}\\ \vdots & \ddots & \vdots\\ (Q_{\rm M,UF})_{n1}\text{ (t/h)} & \dots & (Q_{\rm M,UF})_{nm}\text{ (t/h)}\\ \end{bmatrix} & \begin{bmatrix} (Q_{\rm M,OF})_{11}\text{ (t/h)} & \dots & (Q_{\rm M,OF})_{1m}\text{ (t/h)}\\ \vdots & \ddots & \vdots\\ (Q_{\rm M,OF})_{n1}\text{ (t/h)} & \dots & (Q_{\rm M,OF})_{nm}\text{ (t/h)}\\ \end{bmatrix} & \begin{bmatrix} (P_{\rm OF})_1\text{ (frac)}\\ \vdots\\ (P_{\rm OF})_n\text{ (frac)} \end{bmatrix} \\ \\ \\ \\ \\ \\ \\ \end{array} \end{bmatrix} }[/math]

where:

• [math]\displaystyle{ \mathit{DL} }[/math] is the dust loading (kg/m³)
• [math]\displaystyle{ F }[/math] is the flow rate of -36+3 µm size particles in the feed (t/h)
• [math]\displaystyle{ \alpha }[/math] is the sharpness parameter of the Whiten-Beta efficiency curve
• [math]\displaystyle{ d_{\rm 50c} }[/math] is the cut size parameter of the Whiten-Beta efficiency curve (mm)
• [math]\displaystyle{ C }[/math] is the bypass parameter of the Whiten-Beta efficiency curve (frac)
• [math]\displaystyle{ \beta }[/math] is a fish-hook parameter of the Whiten-Beta efficiency curve
• [math]\displaystyle{ \beta^* }[/math] is a fish-hook parameter of the Whiten-Beta efficiency curve
• [math]\displaystyle{ (Q_{\rm M,OF})_{\rm L} }[/math] is the mass flow rate of liquids to the overflow stream (t/h)
• [math]\displaystyle{ (Q_{\rm M,UF})_{\rm L} }[/math] is the mass flow rate of liquids to the underflow stream (t/h)
• [math]\displaystyle{ P_{\rm OF} }[/math] is the partition fraction to overflow (frac)

Example

The images below show the selection of input arrays and output results in the Excel interface.

Figure 1. Example showing the selection of the Parameters (blue frame) array in Excel.

Figure 2. Example showing the selection of the Size (red frame), OreSG (green frame) and Feed (purple frame) arrays in Excel.

Figure 3. Example showing the selection of the Results (light blue frame) array in Excel.

SysCAD

This section is currently under construction. Please check back later for updates and revisions.