WLIMS (King and Schneider)
Description
This article describes the King and Schneider (1995) model for drum-type Wet Low Intensity Magnetic Separators (WLIMS).[1]
Model theory
Recovery to non-magnetics
Recovery to magnetics
Excel
The King and Schneider WLIMS model may be invoked from the Excel formula bar with the following function call:
=mdUnit_WLIMS_KingSchneider(Parameters as Range, Size as Range, Feed as Range, MagneticsVolGrade 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{ \mathit{Parameters} = \begin{bmatrix} \text{Recover to NM (true/false)}\\ \mathit{SI}\text{ (-)}\\ g_{50}\text{ (v/v)}\\ \kappa\text{ (frac)}\\ \zeta\text{ (mm}^{-1}\text{)}\\ \end{bmatrix},\;\;\;\;\;\; \mathit{Size} = \begin{bmatrix} d_{1}\text{ (mm)}\\ \vdots\\ d_n\text{ (mm)}\\ \end{bmatrix},\;\;\;\;\;\; \mathit{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},\;\;\;\;\;\; }[/math]
- [math]\displaystyle{ \mathit{MagneticsVolGrade} = \begin{bmatrix} (g_{\rm v})_{11}\text{ (v/v)} & \dots & (g_{\rm v})_{1m}\text{ (v/v)}\\ \vdots & \ddots & \vdots\\ (g_{\rm v})_{n1}\text{ (v/v)} & \dots & (g_{\rm v})_{nm}\text{ (v/v)}\\ \end{bmatrix}\;\;\; \text{or}\;\;\; \begin{bmatrix} (g_{\rm v})_{1}\text{ (v/v)} & \dots & (g_{\rm v})_{m}\text{ (v/v)}\\ \end{bmatrix},\;\;\;\;\;\; }[/math]
where [math]\displaystyle{ \text{Recover to NM} }[/math] indicates whether the recovery equations are for King and Schnieder's (1995) original recovery to the non-magnetics stream (true), or the alternative recovery to magnetics stream (false).
Note that [math]\displaystyle{ \mathit{MagneticsVolGrade} }[/math] can be specified on a per particle size per ore type basis, or with a singular value for all particle sizes of a given ore type.
Results
The results are displayed in Excel as an array corresponding to the matrix notation below:
- [math]\displaystyle{ \mathit{mdUnit\_WLIMS\_KingSchneider} = \begin{bmatrix} \begin{array}{c} \begin{bmatrix} R_{\rm M}\text{ (frac)}\\ \end{bmatrix} \\ \\ \\ \end{array} \begin{array}{cccccc} \begin{bmatrix} \bar d_1\text{ (mm)}\\ \vdots\\ \bar d_n\text{ (mm)} \end{bmatrix} & \begin{bmatrix} (Q_{\rm M,M})_{11}\text{ (t/h)} & \dots & (Q_{\rm M,M})_{1m}\text{ (t/h)}\\ \vdots & \ddots & \vdots\\ (Q_{\rm M,M})_{n1}\text{ (t/h)} & \dots & (Q_{\rm M,M})_{nm}\text{ (t/h)}\\ \end{bmatrix} & \begin{bmatrix} (Q_{\rm M,NM})_{11}\text{ (t/h)} & \dots & (Q_{\rm M,NM})_{1m}\text{ (t/h)}\\ \vdots & \ddots & \vdots\\ (Q_{\rm M,NM})_{n1}\text{ (t/h)} & \dots & (Q_{\rm M,NM})_{nm}\text{ (t/h)}\\ \end{bmatrix} & \begin{bmatrix} (R_{\rm M})_{11}\text{ (frac)} & \dots & (R_{\rm M})_{1m}\text{ (frac)}\\ \vdots & \ddots & \vdots\\ (R_{\rm M})_{n1}\text{ (frac)} & \dots & (R_{\rm M})_{nm}\text{ (frac)}\\ \end{bmatrix} & \begin{bmatrix} (R_{\rm M})_1\text{ (frac)}\\ \vdots\\ (R_{\rm M})_n\text{ (frac)} \end{bmatrix} & \begin{array}{c} \begin{bmatrix} (R_{\rm M})_1 & \dots & (R_{\rm T})_m\\ \end{bmatrix} \\ \\ \\ \end{array} & \begin{bmatrix} \alpha_1\text{ (frac)}\\ \vdots\\ \alpha_n\text{ (frac)} \end{bmatrix} \end{array} \end{bmatrix} }[/math]
where:
- [math]\displaystyle{ Q_{\rm M,M} }[/math] is mass flow rate of solids to the magnetics stream (t/h)
- [math]\displaystyle{ Q_{\rm M,NM} }[/math] is mass flow rate of solids to the non-magnetics stream (t/h)
Example
The images below show the selection of input arrays and output results in the Excel interface.
SysCAD
MD_MagneticSeparator 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 MassFracToMags option appears below. |
| MassFracToMags | Input | Only appears if the On field above is not checked. Specifies the fraction of feed mass that reports to the magnetics stream when the model is off. |
| NumParallelUnits | Input | The number of parallel, identical units to simulate:
|
| Method | User Defined | The recovery to magnetics for each size interval is defined by the user. |
| WLIMS (King & Schneider) | The recovery to magnetics for each size interval is defined by the King and Schneider model. | |
| WHIMS (Dobby and Finch) | The recovery to magnetics for each size interval is defined by the Dobby and Finch model. | |
| Options | ||
| ShowQFeed | CheckBox | QFeed and associated tab pages (eg Sp) will become visible, showing the properties of the combined feed stream. |
| ShowQMags | CheckBox | QMags and associated tab pages (eg Sp) will become visible, showing the properties of the magnetics stream. |
| ShowQNonMags | CheckBox | QNonMags and associated tab pages (eg Sp) will become visible, showing the properties of the non-magnetics 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. |
WLIMS page
The WLIMS page is used to specify the required model method and associated input parameters.
Magnetics page
This page is used to specify the volumetric grade of magnetics phase input parameters.
| 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. |
| MagneticsVolGrade | ||
| Selection | Stream | A single magnetics volumetric grade value is specified for all species and sizes. |
| Species | Magnetics volumetric grade values are specified per species, for all sizes of that species. | |
| Size | Magnetics volumetric grade values are specified per size interval, for all species in that interval. | |
| Species-Size | Individual magnetics volumetric grade values are specified for each size interval of each species. | |
| Size | Display | Size of each interval in internal mesh series. |
| MeanSize | Display | Geometric mean size of each interval in internal mesh series. |
| MagneticsVolGrade | Input / Display | Magnetics volumetric grade for each size interval, in each solid species. |
Recovery page
The Recovery page is used to display (or specify) the recovery 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. |
| Recovery | ||
| Method | Model / User | Select model-calculated or user-defined recovery 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 |
|
| Recovery | Display |
|
| All (All row, All column) | Display |
|
| All (All row, per species) | Display |
|
| CmpRecovery | ||
| Components | Hides or shows component recovery 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 |
|
| CmpRecovery | Display |
|
| All (All row, All column) | Display |
|
| All (All row, per component) | Display |
|
| EleRecovery | ||
| Elements | Hides or shows element recovery 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 |
|
| EleRecovery | Display |
|
| All (All row, All column) | Display |
|
| All (All row, per element) | Display |
|
| IPhRecovery | ||
| IPhases | Hides or shows individual phases recovery 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 |
|
| IPhRecovery | Display |
|
| All (All row, All column) | Display |
|
| All (All row, per individual phase) | Display |
|
CSz page
The CSz page provides composition and constituent information by particle size for QFeed, QMags, and QNonMags. 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 non-magnetics stream without split.
External links
- Met Dynamics - Magnetic Separator (help.syscad.net)
- Gravity, Dense Medium, and Magnetic Separation Example project (help.syscad.net)
References
- ↑ King, R.P. and Schneider, C.L., 1995. Computer simulation of taconite grinding and concentration circuits. Utah Comminution Center, University of Utah.





