Air Classifier (Altun)

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Description

This article describes the Altun and Benzer (2014) model for high efficiency air classifiers.[1]

High efficiency air classifiers may be alternatively described as dynamic or third generation air classifiers.

Model theory

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Corrected cut size

Sharpness of separation

Fines bypass

Fish-hook parameter

Equation parameters

Multi-component modelling

Partition metrics

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)

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})_{p1}\text{ (t/h)} & \dots & (Q_{\rm M,F})_{pm}\text{ (t/h)}\\ \end{bmatrix},\;\;\;\;\;\; }[/math]

where:

  • [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{ (Q_{\rm M,F})_{\rm L} }[/math] is the mass flow rate of liquids in the feed (t/h)

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)}\\ d_{50}\text{ (mm)}\\ E_{\rm p}\text{ (mm)}\\ I\\ \end{bmatrix} \begin{array}{cccccc} \begin{bmatrix} \bar d_1\text{ (mm)}\\ \vdots\\ \bar d_p\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})_{p1}\text{ (t/h)} & \dots & (Q_{\rm M,UF})_{pm}\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})_{p1}\text{ (t/h)} & \dots & (Q_{\rm M,OF})_{pm}\text{ (t/h)}\\ \end{bmatrix} & \begin{bmatrix} (E_{\rm oa})_1\text{ (frac)}\\ \vdots\\ (E_{\rm oa})_p\text{ (frac)} \end{bmatrix} \\ \\ \\ \\ \\ \\ \\ \end{array} \end{bmatrix} }[/math]


where:

  • [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)

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

The sections and variable names used in the SysCAD interface are described in detail in the following tables.

MD_Classifier page

The first tab page in the access window will have this name.

Tag (Long/Short) Input / Display Description/Calculated Variables/Options
Tag Display This name tag may be modified with the change tag option.
Condition Display OK if no errors/warnings, otherwise lists errors/warnings.
ConditionCount Display The current number of errors/warnings. If condition is OK, returns 0.
GeneralDescription / GenDesc Display This is an automatically generated description for the unit. If the user has entered text in the 'EqpDesc' field on the Info tab (see below), this will be displayed here.

If this field is blank, then SysCAD will display the unit class ID.

Requirements
On CheckBox This enables the unit. If this box is not checked, then the MassFracToUF option appears below.
MassFracToUF Input Only appears if the On field above is not checked. Specifies the fraction of feed mass that reports to the underflow stream when the model is off.
NumParallelUnits Input The number of parallel, identical units to simulate:
  • Feed is divided by the number of parallel units before being sent to the unit model.
  • Unit model products are multiplied back by the same value and returned to the SysCAD product streams.
  • All unit model result values are shown per parallel unit.
Method Partition (User) The partition to underflow for each size interval is defined by the user. Different values can be used for different solids.
Partition (Reid-Plitt) The partition to underflow for each size interval is defined by a Reid-Plitt efficiency curve. Different parameters can be used for different solids.
Partition (Whiten-Beta) The partition to underflow for each size interval is defined by a Whiten-Beta efficiency curve. Different parameters can be used for different solids.
Air Classifier (Altun) The Altun air classifier model is used to determine the partition of solids to underflow for each size interval.
Gravity (Plitt-Flintoff) The Plitt-Flintoff gravity classifier model is used to determine the partition of solids to underflow for each size interval.
Options
ShowQFeed CheckBox QFeed and associated tab pages (eg Sp) will become visible, showing the properties of the combined feed stream.
ShowQOF CheckBox QOF and associated tab pages (eg Sp) will become visible, showing the properties of the overflow stream.
ShowQUF CheckBox QUF and associated tab pages (eg Sp) will become visible, showing the properties of the underflow stream.
SizeForPassingFracCalc Input Size fraction for % Passing calculation. The size fraction input here will be shown in the Stream Summary section.
FracForPassingSizeCalc Input Fraction passing for Size calculation. The fraction input here will be shown in the Stream Summary section.
Stream Summary
MassFlow / Qm Display The total mass flow in each stream.
SolidMassFlow / SQm Display The Solids mass flow in each stream.
LiquidMassFlow / LQm Display The Liquid mass flow in each stream.
VolFlow / Qv Display The total Volume flow in each stream.
Temperature / T Display The Temperature of each stream.
Density / Rho Display The Density of each stream.
SolidFrac / Sf Display The Solid Fraction in each stream.
LiquidFrac / Lf Display The Liquid Fraction in each stream.
Passing Display The mass fraction passing the user-specified size (in the field SizeForPassingFracCalc) in each stream.
Passes Display The user-specified (in the field FracForPassesSizeCalc) fraction of material in each stream will pass this size fraction.

Classifier page

The Classifier page is used to specify the input parameters for the classifier model.

Tag (Long/Short) Input / Display Description/Calculated Variables/Options
Altun
HelpLink ButtonModelHelp.png Opens a link to this page using the system default web browser. Note: Internet access is required.
Parameters
Diameter / D Input Chamber diameter
AirFlowRate / AF Input Flow rate of air into chamber.
RotorSpeed / RS Input Velocity of the rotor.
Alpha Input Coefficient (k) and exponent (n) of the alpha equation.
d50c Input Coefficient (k) and exponent (n) of the d50c equation.
Beta Input Coefficient (k), exponent (n) and constant (c) of the beta equation.
Liquids
LiquidsSeparMethod Split To UF (User) Liquids are split to underflow by a user-defined fraction of liquids in the feed.
Split To UF (1-C) Liquids are split to underflow by the C (overflow) fraction specified for the first species in the model.
UF Solids Fraction Sufficient liquids mass is recovered to the underflow stream to yield the user-defined underflow solids mass fraction value (if possible).
UF Liquids Fraction Sufficient liquids mass is recovered to the underflow stream to yield the user-defined underflow liquids mass fraction value (if possible).
UFSolidsFracReqd / UF.SfReqd Input Required value of the mass fraction of solids in the underflow stream. Only visible if UF Solids Fraction is selected.
UFLiquidsFracReqd / UF.LfReqd Input Required value of the mass fraction of liquids in the underflow stream. Only visible if UF Liquids Fraction is selected.
LiqSplitToUF / UF.LiqSplit Input/Display The fraction of liquids recovered to underflow.
Results
DustLoading / Feed.DL Display Dust loading of the feed.
FineSolidMassFlow / F Display Mass flow rate of -36+3 um solids in the feed.
Alpha Display Value of the alpha parameter of the Whiten Beta efficiency curve.
d50c Display Value of the d50c parameter of the Whiten Beta efficiency curve.
C Display Value of the C parameter of the Whiten Beta efficiency curve.
Beta Display Value of the beta parameter of the Whiten Beta efficiency curve.
BetaStar Display Value of the beta star parameter of the Whiten Beta efficiency curve.
d50 Display The separation size, d50, of all solid particles in the feed.
EcartProbable / Ep Display The value of the Ecart Probable of the separation.
Imperfection / I Display The value of the Imperfection of the separation.

Partition page

The Partition page is used to display (or specify) the partition by species/component/element/individual phase and size values.

Tag (Long/Short) Input / Display Description/Calculated Variables/Options
Distribution
Name Display Shows the name of the SysCAD Size Distribution (PSD) quality associated with the feed stream.
IntervalCount Display Shows the number of size intervals in the SysCAD Size Distribution (PSD) quality associated with the feed stream.
SpWithPSDCount Display Shows the number of species in the feed stream assigned with the SysCAD Size Distribution (PSD) quality.
Partition
Method Model / User Select model-calculated or user-defined partition to separate each solids species type.
Density Display Density of each solid species.
Size Display Size of each interval in mesh series.
MeanSize Display Geometric mean size of each interval in mesh series.


All (All column) Display
  • Actual overall partition to underflow of all solid species, for each size interval.
  • Excludes solid species not present in the classifier feed.
Partition Display
  • Partition to underflow for each size interval, in each solid species, as determined by the selected model or user defined value.
  • Note: These values are displayed regardless of whether the solid species is present in the classifier feed or not.
All (All row, All column) Display
  • Displays the actual, total, partition of all solids with a particle size distribution property in the feed to underflow.
  • Excludes solid species not present in the classifier feed.
All (All row, per species) Display
  • Actual overall partition to underflow for each solid species, for all size intervals in that species.
  • Excludes solid species not present in the classifier feed.
CmpPartition
Components
ButtonHideComponents.png
ButtonShowComponents.png
 Hides or shows component partition table.
Size Display Size of each interval in mesh series.
MeanSize Display Geometric mean size of each interval in mesh series.
All (All column) Display
  • Actual overall partition to underflow of all solid components, for each size interval.
  • Excludes solid components not present in the classifier feed.
CmpPartition Display
  • Partition to underflow for each size interval, in each solid component, as determined by the selected model or user defined value.
  • Excludes solid components not present in the classifier feed.
All (All row, All column) Display
  • Displays the actual, total, partition of all solid components with a particle size distribution property in the feed to underflow.
  • Excludes solid components not present in the classifier feed.
All (All row, per component) Display
  • Actual overall partition to underflow for each solid component, for all size intervals in that component.
  • Excludes solid components not present in the classifier feed.
ElePartition
Elements
ButtonHideElements.png
ButtonShowElements.png
 Hides or shows element partition table.
Size Display Size of each interval in mesh series.
MeanSize Display Geometric mean size of each interval in mesh series.
All (All column) Display
  • Actual overall partition to underflow of all solid elements, for each size interval.
  • Excludes solid elements not present in the classifier feed.
ElePartition Display
  • Partition to underflow for each size interval, in each solid element, as determined by the selected model or user defined value.
  • Excludes solid elements not present in the classifier feed.
All (All row, All column) Display
  • Displays the actual, total, partition of all solid elements with a particle size distribution property in the feed to underflow.
  • Excludes solid elements not present in the classifier feed.
All (All row, per element) Display
  • Actual overall partition to underflow for each solid element, for all size intervals in that component.
  • Excludes solid elements not present in the classifier feed.
IPhPartition
IPhases
ButtonHideIPhases.png
ButtonShowIPhases.png
 Hides or shows individual phases partition table.
Size Display Size of each interval in mesh series.
MeanSize Display Geometric mean size of each interval in mesh series.
All (All column) Display
  • Actual overall partition to underflow of all solid individual phases, for each size interval.
  • Excludes solid individual phases not present in the classifier feed.
IPhPartition Display
  • Partition to underflow for each size interval, in each solid individual phase, as determined by the selected model or user defined value.
  • Excludes solid individual phases not present in the classifier feed.
All (All row, All column) Display
  • Displays the actual, total, partition of all solid individual phases with a particle size distribution property in the feed to underflow.
  • Excludes solid individual phases not present in the classifier feed.
All (All row, per individual phase) Display
  • Actual overall partition to underflow for each solid individual phase, for all size intervals in that component.
  • Excludes solid individual phases not present in the classifier feed.

CSz page

The CSz page provides composition and constituent information by particle size for QFeed, QOF, and QUF. It appears after the standard SysCAD stream information when the corresponding stream display option is selected.

  • Results are available for Species, Component, Element, and Individual Phase, with views for Composition, Distribution by Size, and Stream Contribution.
  • The calculations are described in Stream Analyser - Composition by Size.
  • These combined composition-by-size results are not available in the standard SysCAD stream pages. They are particularly useful for comparing simulated results with measured size-by-size data, such as elemental assays or mineral grades by size.
Tag (Long/Short) Input / Display Description/Calculated Variables/Options
Distribution
Name Display Shows the name of the SysCAD Size Distribution (PSD) quality associated with the feed stream.
IntervalCount Display Shows the number of size intervals in the SysCAD Size Distribution (PSD) quality associated with the feed stream.
SpWithPSDCount Display Shows the number of species in the feed stream assigned with the SysCAD Size Distribution (PSD) quality.
CSz
Property Composition Displays the mass fraction of each species, component, element, or individual phase within each size interval. The All row displays the overall composition over all size intervals.
Distribution by Size Displays the fraction of each constituent's total mass that occurs in each size interval. The All column displays the distribution by size of all solids with a particle size distribution property in the selected stream.
Stream Contribution Displays each constituent and size interval mass as a fraction of the total mass of all solids with a particle size distribution property in the selected stream.
Comp
Size Display Size of each interval in the mesh series.
All (All column) Display Total composition of all solids with a particle size distribution property in each size interval. The result is 100% when the interval contains solids with a particle size distribution property and 0 when it does not.
Comp Display Mass fraction of each solid species with a particle size distribution property within each size interval.
All (All row, All column) Display Total composition of all solids with a particle size distribution property over all size intervals. The result is 100% when the selected stream contains solids with a particle size distribution property and 0 when it does not.
All (All row, per species) Display Overall mass fraction of each solid species with a particle size distribution property in the selected stream for all size intervals.
CmpComp
Components
ButtonHideComponents.png
ButtonShowComponents.png
 Hides or shows the component composition table.
Size Display Size of each interval in the mesh series.
All (All column) Display Total composition of all solids with a particle size distribution property in each size interval. The result is 100% when the interval contains solids with a particle size distribution property and 0 when it does not.
CmpComp Display Mass fraction of each displayed solid component within each size interval.
All (All row, All column) Display Total composition of all solids with a particle size distribution property over all size intervals.
All (All row, per component) Display Overall mass fraction of each displayed solid component in the selected stream over all size intervals.
EleComp
Elements
ButtonHideElements.png
ButtonShowElements.png
 Hides or shows the element composition table.
Size Display Size of each interval in the mesh series.
All (All column) Display Total composition of all solids with a particle size distribution property in each size interval. The result is 100% when the interval contains solids with a particle size distribution property and 0 when it does not.
EleComp Display Mass fraction of each displayed element within each size interval.
All (All row, All column) Display Total composition of all solids with a particle size distribution property over all size intervals.
All (All row, per element) Display Overall mass fraction of each displayed element in the selected stream over all size intervals.
IPhComp
IPhases
ButtonHideIPhases.png
ButtonShowIPhases.png
 Hides or shows the individual phase composition table.
Size Display Size of each interval in the mesh series.
All (All column) Display Total composition of all solids with a particle size distribution property in each size interval. The result is 100% when the interval contains solids with a particle size distribution property and 0 when it does not.
IPhComp Display Mass fraction of each displayed individual phase within each size interval.
All (All row, All column) Display Total composition of all solids with a particle size distribution property over all size intervals.
All (All row, per individual phase) Display Overall mass fraction of each displayed individual phase in the selected stream over all size intervals.
Dist
Size Display Size of each interval in the mesh series.
All (All column) Display Fraction of the total mass of all solids with a particle size distribution property in the selected stream that occurs in each size interval.
Dist Display Fraction of the total mass of each solid species with a particle size distribution property that occurs in each size interval.
All (All row, All column) Display Total distribution by size of all solids with a particle size distribution property. The result is 100% when the selected stream contains solids with a particle size distribution property and 0 when it does not.
All (All row, per species) Display Total distribution by size of each solid species with a particle size distribution property. The result is 100% when that species is present and 0 when it is not.
CmpDist
Components
ButtonHideComponents.png
ButtonShowComponents.png
 Hides or shows the component distribution-by-size table.
Size Display Size of each interval in the mesh series.
All (All column) Display Fraction of the total mass of all solids with a particle size distribution property in the selected stream that occurs in each size interval.
CmpDist Display Fraction of each displayed solid component's total mass that occurs in each size interval.
All (All row, All column) Display Total distribution by size of all solids with a particle size distribution property.
All (All row, per component) Display Total distribution by size of each displayed solid component. The result is 100% when that component is present and 0 when it is not.
EleDist
Elements
ButtonHideElements.png
ButtonShowElements.png
 Hides or shows the element distribution-by-size table.
Size Display Size of each interval in the mesh series.
All (All column) Display Fraction of the total mass of all solids with a particle size distribution property in the selected stream that occurs in each size interval.
EleDist Display Fraction of each displayed element's total mass that occurs in each size interval.
All (All row, All column) Display Total distribution by size of all solids with a particle size distribution property.
All (All row, per element) Display Total distribution by size of each displayed element. The result is 100% when that element is present and 0 when it is not.
IPhDist
IPhases
ButtonHideIPhases.png
ButtonShowIPhases.png
 Hides or shows the individual phase distribution-by-size table.
Size Display Size of each interval in the mesh series.
All (All column) Display Fraction of the total mass of all solids with a particle size distribution property in the selected stream that occurs in each size interval.
IPhDist Display Fraction of each displayed individual phase's total mass that occurs in each size interval.
All (All row, All column) Display Total distribution by size of all solids with a particle size distribution property.
All (All row, per individual phase) Display Total distribution by size of each displayed individual phase. The result is 100% when that individual phase is present and 0 when it is not.
Contr
Size Display Size of each interval in the mesh series.
All (All column) Display Fraction of the total mass of all solids with a particle size distribution property in the selected stream that occurs in each size interval.
Contr Display Stream Contribution of each solid species with a particle size distribution property and size interval to the total mass of all solids with a particle size distribution property in the selected stream.
All (All row, All column) Display Total stream contribution of all solids with a particle size distribution property. The result is 100% when the selected stream contains solids with a particle size distribution property and 0 when it does not.
All (All row, per species) Display Overall stream contribution of each solid species with a particle size distribution property for all size intervals.
CmpContr
Components
ButtonHideComponents.png
ButtonShowComponents.png
 Hides or shows the component stream contribution table.
Size Display Size of each interval in the mesh series.
All (All column) Display Fraction of the total mass of all solids with a particle size distribution property in the selected stream that occurs in each size interval.
CmpContr Display Stream Contribution of each displayed solid component and size interval to the total mass of all solids with a particle size distribution property in the selected stream.
All (All row, All column) Display Total stream contribution of all solids with a particle size distribution property.
All (All row, per component) Display Overall stream contribution of each displayed solid component for all size intervals.
EleContr
Elements
ButtonHideElements.png
ButtonShowElements.png
 Hides or shows the element stream contribution table.
Size Display Size of each interval in the mesh series.
All (All column) Display Fraction of the total mass of all solids with a particle size distribution property in the selected stream that occurs in each size interval.
EleContr Display Stream Contribution of each displayed element and size interval to the total mass of all solids with a particle size distribution property in the selected stream.
All (All row, All column) Display Total stream contribution of all solids with a particle size distribution property.
All (All row, per element) Display Overall stream contribution of each displayed element for all size intervals.
IPhContr
IPhases
ButtonHideIPhases.png
ButtonShowIPhases.png
 Hides or shows the individual phase stream contribution table.
Size Display Size of each interval in the mesh series.
All (All column) Display Fraction of the total mass of all solids with a particle size distribution property in the selected stream that occurs in each size interval.
IPhContr Display Stream Contribution of each displayed individual phase and size interval to the total mass of all solids with a particle size distribution property in the selected stream.
All (All row, All column) Display Total stream contribution of all solids with a particle size distribution property.
All (All row, per individual phase) Display Overall stream contribution of each displayed individual phase for all size intervals.

About page

This page is provides product and licensing information about the Met Dynamics Models SysCAD Add-On.

Tag (Long/Short) Input / Display Description/Calculated Variables/Options
About
HelpLink ButtonLicensingHelp.png Opens a link to the Installation and Licensing page using the system default web browser. Note: Internet access is required.
Information ButtonCopyToClipboard.png Copies Product and License information to the Windows clipboard.
Product
Name Display Met Dynamics software product name
Version Display Met Dynamics software product version number.
BuildDate Display Build date and time of the Met Dynamics Models SysCAD Add-On.
License
File ButtonBrowse.png This is used to locate a Met Dynamics software license file.
Location Display Type of Met Dynamics software license or file name and path of license file.
SiteCode Display Unique machine identifier for license authorisation.
ReqdAuth Display Authorisation level required, MD-SysCAD Full or MD-SysCAD Runtime.
Status Display License status, LICENSE_OK indicates a valid license, other messages report licensing errors.
IssuedTo Display Only visible if Met Dynamics license file is used. Name of organisation/seat the license is authorised to.
ExpiryDate Display Only visible if Met Dynamics license file is used. License expiry date.
DaysLeft Display Only visible if Met Dynamics license file is used. Days left before the license expires.

Additional notes

  • Solid species that do not possess a particle size distribution property are split according to the overall mass split of the default particle size distribution species selected in the SysCAD Project Configuration.
  • If the default particle size distribution species is not present in the unit feed, the overall split of all other species with particle size distributions combined is used, as determined by the model.
  • Gas phase species report directly to the overflow stream without split.

See also

External links

References

  1. ↑ Altun, O. and Benzer, H., 2014. Selection and mathematical modelling of high efficiency air classifiers. Powder Technology, 264, pp.1-8.
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