Partition (Size, Whiten-Beta): Difference between revisions
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== SysCAD | == SysCAD == | ||
The Whiten-Beta partition is available from the '''{{Name (Text, Company Name)|nospace=1}}*Screen''' unit | The Whiten-Beta partition is available from the '''{{Name (Text, Company Name)|nospace=1}}*Screen''', '''{{Name (Text, Company Name)|nospace=1}}*Hydrocyclone''', amd '''{{Name (Text, Company Name)|nospace=1}}*Classifier''' unit models. | ||
The sections and variable names used in the SysCAD interface are described in detail in the following tables. | The sections and variable names used in the SysCAD interface are described in detail in the following tables. | ||
Note that both a '''Deck''' page and a '''Partition''' page are provided provided for each connected oversize discharge stream. | Note that both a '''Deck''' page and a '''Partition''' page are provided provided for each connected oversize discharge stream of the screen unit model. | ||
{{SysCAD (Page, Screen, DLL*Screen)}} | {{SysCAD (Page, Screen, DLL*Screen)}} | ||
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{{SysCAD (Text, Help Link)}} | {{SysCAD (Text, Help Link)}} | ||
|- | |- | ||
! colspan="3" style="text-align:left;" |''WhitenBeta'' | |||
{{SysCAD (Text, Partition, Whiten-Beta)}} | |||
{{SysCAD (Text, Screen, Liquids)|method=2}} | {{SysCAD (Text, Screen, Liquids)|method=2}} | ||
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{{SysCAD (Page, Hydrocyclone, Partition)|ActionU=Partition|ActionL=partition|DestinationU=Oversize|DestinationL=oversize|UnitL=screen}} | {{SysCAD (Page, Hydrocyclone, Partition)|ActionU=Partition|ActionL=partition|DestinationU=Oversize|DestinationL=oversize|UnitL=screen}} | ||
{{SysCAD (Page, Hydrocyclone, DLL*Hydrocyclone)}} | {{SysCAD (Page, Hydrocyclone, DLL*Hydrocyclone)}} | ||
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{{SysCAD (Text, Help Link)}} | {{SysCAD (Text, Help Link)}} | ||
{{SysCAD (Text, Partition, Whiten-Beta)}} | |||
{{SysCAD (Text, Hydrocyclone, Liquids)|method=1}} | {{SysCAD (Text, Hydrocyclone, Liquids)|method=1}} | ||
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{{SysCAD (Page, Hydrocyclone, Roping)|WhitenBeta=true}} | {{SysCAD (Page, Hydrocyclone, Roping)|WhitenBeta=true}} | ||
{{SysCAD (Page, Classifier, DLL*Classifier)}} | |||
==== Classifier page ==== | |||
The Classifier page is used to specify the input parameters for the classifier model. | |||
{{SysCAD (Text, Table Header)}} | |||
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! colspan="3" style="text-align:left;" |''WhitenBeta'' | |||
{{SysCAD (Text, Help Link)}} | |||
{{SysCAD (Text, Partition, Whiten-Beta)}} | |||
{{SysCAD (Text, Hydrocyclone, Liquids)|method=0}} | |||
|} | |||
{{SysCAD (Page, Hydrocyclone, Partition)|ActionU=Partition|ActionL=partition|DestinationU=Underflow|DestinationL=underflow|UnitL=classifier}} | |||
{{SysCAD (Page, About)}} | {{SysCAD (Page, About)}} | ||
Latest revision as of 15:16, 17 May 2024
Description
This article describes Whiten's expression for the efficiency of recovery to overflow, modified to represent observed 'fish hook' behaviour in the finer sizes.[1]
Model theory
The Whiten-Beta expression for partition to overflow is:
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
The value of is not an input parameter and is computed numerically, by iteration, since by rearrangement:
When the value of is zero, the Whiten-Beta equation reverts to:
Excel
The Whiten-Beta efficiency curve model may be invoked from the Excel formula bar with the following function call:
=mdPartition_WhitenBeta(MeanSize as Range, alpha as Double, d50c as Double, C as double, Optional beta as Double = 0, Optional returnBetaStar as Boolean = false)
Invoking the function with no arguments will print Help text associated with the model, including a link to this page.
The input parameters and model results are defined below in matrix notation, along with an example image showing the selection of the same cells in the Excel interface:
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where is omitted from the results array if .
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SysCAD
The Whiten-Beta partition is available from the MetDynamics*Screen, MetDynamics*Hydrocyclone, amd MetDynamics*Classifier unit models.
The sections and variable names used in the SysCAD interface are described in detail in the following tables.
Note that both a Deck page and a Partition page are provided provided for each connected oversize discharge stream of the screen unit model.
MD_Screen 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 MassFracToOS option appears below. |
MassFracToOS | Input | Only appears if the On field above is not checked. Specifies the fraction of feed mass that reports to the overflow stream when the model is off. |
Options | ||
ShowQFeed | CheckBox | QFeed and associated tab pages (eg Sp) will become visible, showing the properties of the combined feed 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. |
Deck page
The Deck page is used to specify the required model method and associated input parameters.
Tag (Long/Short) | Input / Display | Description/Calculated Variables/Options |
---|---|---|
Deck | ||
On | Checkbox | This enables the deck. If off, the feed to this deck passes directly to the next deck (or undersize) without partition. |
Method | Partition (User) | The partition to oversize for each size interval is defined by the user. Different values can be used for different solids. |
Partition (Reid-Plitt) | The partition to oversize 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 oversize for each size interval is defined by a Whiten-Beta efficiency curve. Different parameters can be used for different solids. | |
Vibrating (Karra) | The Karra vibrating screen model is used to determine the partition of solids to oversize and undersize for each size interval. | |
Vibrating (Whiten) | The Whiten vibrating screen model is used to determine the partition of solids to oversize and undersize for each size interval. | |
Vibrating (Metso) | The Metso vibrating screen model is used to determine the partition of solids to oversize and undersize for each size interval. | |
Fine Wet (Mwale) | The Mwale fine wet screen model is used to determine the partition of solids to oversize and undersize for each size interval. | |
HelpLink | Opens a link to this page using the system default web browser. Note: Internet access is required. | |
WhitenBeta | ||
OreSpecific | CheckBox |
|
Alpha | Input | The Whiten-Beta equation alpha parameter. |
d50c | Input | The Whiten-Beta equation d50c corrected cut size parameter. |
C | Input | The Whiten-Beta equation C parameter. |
Beta | Input | The Whiten-Beta equation Beta parameter. |
Beta* | Display | The Whiten-Beta equation Beta* parameter corresponding to the selected value of Beta. |
Liquids | ||
LiquidsSeparMethod | Split To OS (User) | Liquids are split to oversize by a user-defined fraction of liquids in the feed. |
Split To OS (1-C) | Liquids are split to oversize by 1 minus the C fraction specified by the user for the first species in the Whiten-Beta model. | |
OS Solids Fraction | Sufficient liquids mass is recovered to the oversize stream to yield the user-defined oversize solids mass fraction value (if possible). | |
OS Liquids Fraction | Sufficient liquids mass is recovered to the oversize stream to yield the user-defined oversize liquids mass fraction value (if possible). | |
OSSolidsFracReqd / OS.SfReqd | Input | Required value of the mass fraction of solids in the oversize stream. Only visible if OS Solids Fraction is selected. |
OSLiquidsFracReqd / OS.LfReqd | Input | Required value of the mass fraction of liquids in the oversize stream. Only visible if OS Liquids Fraction is selected. |
LiqSplitToOS / OS.LiqSplit | Input/Display | The fraction of feed liquids recovered to the oversize stream. |
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 |
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Partition | Display |
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All (All row, All column) | Display |
|
All (All row, per species) | Display |
|
MD_Hydrocyclone 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. |
Method | Partition (User) | The partition to overflow for each size interval is defined by the user. Different values can be used for different solids. |
Partition (Reid-Plitt) | The partition to overflow 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 overflow for each size interval is defined by a Whiten-Beta efficiency curve. Different parameters can be used for different solids. | |
Nageswararao | The Nageswararao model is used to determine the partition of solids to underflow and overflow for each size interval. | |
Narasimha-Mainza (2014) | The Narasimha-Mainza (2014) model is used to determine the partition of solids to underflow and overflow for each size interval. | |
Narasimha-Mainza (Multi) | The Narasimha-Mainza (Multi) model is used to determine the partition of solids to underflow and overflow for each size interval. | |
Plitt | The Plitt model is used to determine the partition of solids to underflow and overflow for each size interval. | |
RopingCalcs | CheckBox | Show addition calculations that predict the onset of cyclone underflow roping. |
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. |
Cyclone page
The Cyclone page is used to specify the input parameters for the hydrocyclone 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 |
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All (All row, per species) | Display |
|
Roping page
This page displays the results for hydrocyclone roping limit calculations. The page is only visible if Roping is selected on the MD_Hydrocyclone page.
Tag (Long/Short) | Input / Display | Description/Calculated Variables/Options |
---|---|---|
Roping | ||
Underflow | ||
SolidsVolFrac / Svf | Display | Volume fraction of solids in the cyclone underflow stream. |
SPOC | Display | SPOC volume fraction of solids in the cyclone underflow roping limit. |
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. |
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 |
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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. |
References
- ↑ Napier-Munn, T.J., Morrell, S., Morrison, R.D. and Kojovic, T., 1996. Mineral comminution circuits: their operation and optimisation. Julius Kruttschnitt Mineral Research Centre, Indooroopilly, QLD.