Air Classifier (Altun)
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
The Altun air classifier model applies the Whiten-Beta efficiency curve to partition particles to the overflow stream:
where:
- is the index of the size interval, , is the number of size intervals
- is the fraction of particles of size interval in the feed reporting to the overflow stream (frac)
- is the geometric mean size of particles in size interval (mm)
- is the corrected size at which 50% of the particle mass reports to underflow and 50% to overflow (mm)
- is the fraction of feed liquids (or fines) split to overflow (frac)
- is a parameter representing the sharpness of separation
- is a term introduced to accommodate the so-called fish-hook effect, and controls the initial rise in the efficiency curve at finer sizes
- is computed to ensure the Whiten-Beta function preserves the definition of in the presence of the fish-hook, i.e. at
Additional relations link terms of the efficiency curve equation with operating parameters.
Corrected cut size
The corrected cut size, (mm), is:
where:
- is the classifier air flow rate (m3/h)
- is the rotor speed of the classifier (m/s)
- is the flow rate of -36+3 µm size particles in the feed (t/h)
- and are the coefficient and exponent, respectively, of the cut size equation.
Sharpness of separation
The sharpness of separation term, , is estimated by:
where:
- is the classifier chamber diameter (m)
- is the dust loading of the classifier feed (kg/m3)
- and are the coefficient and exponent, respectively, of the sharpness of separation equation.
The dust loading, (kg/m3), is calculated from the feed and air flow rates:
where is the mass flow rate of solids in the feed (t/h)
Fines bypass
The fraction of the finest particles reporting to overflow, (frac), is:
where and are the coefficient and exponent, respectively, of the fines bypass equation.
Fish-hook parameter
The parameter controlling the initial rise of the efficiency curve in fines sizes (fish-hook), , is:
where , and are the coefficient, exponent and constant, respectively, of the fish-hook equation.
Altun and Benzer (2014) also provide an equation for the term of the efficiency equation. However, Whiten's definition of requires its value to be computed in complement to the specified value of in the efficiency equation (see Partition (Size, Whiten-Beta) for more information).
Therefore, the equation is excluded from this implementation of Altun and Benzer's (2014) air classifier model.
Equation parameters
Altun and Benzer's (2014) test work was conducted on a range of Sepol, Sepax and Sepmaster industrial scale dynamic air classifiers. The parameter values in Table 1 were derived by regression analyses of their industrial sampling results.
Table 1. Air classifier model equation parameters (after Altun and Benzer, 2014).[1] Equation Coefficient, Exponent, Constant, 0.905 1.2679 - 0.4048 0.7775 - 10.467 1.4171 - 0.4417 1.4171 0.1293
This implementation of the air classifier model allows a user to specify the values of the equation coefficients, exponents and constants directly. Altun and Benzer's (2014) values may be used, or new values derived from specific industrial or laboratory test work programmes.
Multi-component modelling
Altun and co-workers have published subsequent journal articles outlining similar model treatments for multi-component feeds, where particle density differences and agglomeration are observed to affect classification performance.[2][3]
However, this work was only conducted on laboratory scale equipment rather than operating industrial air classifiers. Additional non-standard material measurements are also required (e.g. fluidity index). As such, these model implementations are not included here.
Partition metrics
Several metrics are provided to characterise the partition curve.
The , also known as the cut or separation size, is defined as the size of a particle which has an even (50%) chance of appearing in either the underflow or overflow stream. The size is estimated via a log-linear interpolation of geometric mean size () against the uncorrected partition to underflow of all solids in the feed.
The Ecart Probable, or , is a measure of the deviation of a partition curve from a perfect separation, and is typically defined for size classification as:[4]
where and are the sizes of particles which have a 75% and 25% probability, respectively, of appearing in the underflow stream. The and sizes are estimated by log-linear interpolation of geometric mean size against the uncorrected partition to underflow of all solids in the feed.
The Imperfection, , is a normalised measure of the sharpness of separation, which is suggested to be independent of the magnitude of the , and is typically defined for size classification as:[4]
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 () x column () format:
where:
- is the number of size intervals
- is the number of ore types
- is the size of the square mesh interval that mass is retained on (mm)
- , i.e. descending size order from top size () to sub mesh ( mm)
- 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:
where:
- is the mass flow rate of liquids to the overflow stream (t/h)
- 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.
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:
|
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.
Partition page
The Partition page is used to specify or display the partition by species 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 |
|
Partition | Display |
|
All (All row, All column) | Display |
|
All (All row, per species) | Display |
|
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 | Opens a link to the Installation and Licensing page using the system default web browser. Note: Internet access is required. | |
Information | 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 | 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
References
- ↑ 1.0 1.1 Altun, O. and Benzer, H., 2014. Selection and mathematical modelling of high efficiency air classifiers. Powder Technology, 264, pp.1-8.
- ↑ Altun, O., Toprak, A., Benzer, H. and Darilmaz, O., 2016. Multi component modelling of an air classifier. Minerals Engineering, 93, pp.50-56.
- ↑ Altun, O., 2022. Air classification performances of the components within the varied feed blends. Powder Technology, 399, p.117092.
- ↑ 4.0 4.1 Gupta, A. and Yan, D.S., 2016. Mineral processing design and operations: an introduction. Elsevier.