Partition (Density, Stochastic): Difference between revisions

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== Description ==
== Description ==


This article describes Rao's '''Stochastic''' equation for the partition of particles by size and density in batch jigs.{{Rao (2021)}}
This article describes the '''Stochastic''' equation for the partition of particles by size and density in gravity separators.{{Rao et al. (2003)}}{{Rao (2021)}}
 
The Stochastic formulation is applicable to both dense medium separators and gravity concentration processes.


== Model theory ==
== Model theory ==


{{Under construction|section}}
{{Restricted content}}
 
<hide>
[[File:PartitionStochastic2.png|thumb|500px|Figure 1. Stochastic model partition to sinks. Each coloured line represents a particle class with the geometric mean size indicated in the series label. The pivot point is evident at a density of 2.53 t/m<sup>3</sup>.]]
 
[[File:PartitionStochastic3.png|thumb|500px|Figure 2. Stochastic model partition to sinks, using the same model parameters as Figure 1. Each coloured line represents a density class with the specific gravity indicated in the series label.]]
 
[[File:PartitionStochastic4.png|thumb|500px|Figure 3. Modified Stochastic model partition to sinks, using the same model parameters as Figure 1 except time, <math>t</math>, which is half the original value. Each coloured line represents a density class with the specific gravity indicated in the series label.]]
 
Rao et al (2003) proposed a model that describes the size-density partition surface in both dense-medium and gravity separators. The Stochastic model is derived from a statistical consideration of particle settling phenomena, and for a steady-state process is:{{Rao et al. (2003)}}
 
:<math>Y_{ij} = \dfrac{1}{2}\left [ 1 + {\rm erf} \left (B - A{{\bar d}_i}^c ((\rho_{\rm S})_{ij} - \rho_{\rm p})\right ) \right ]</math>
 
where:
* <math>i</math> is the index of the size interval, <math>i = \{1,2,\dots,q\}</math>, <math>q</math> is the number of size intervals
* <math>j</math> is the index of the density class, <math>j = \{1,2,\dots,m\}</math>, <math>m</math> is the number of density classes
* <math>Y_{ij}</math> is the fraction of the mass of particles in size class <math>i</math> and density class <math>j</math> which are partitioned (recovered) to the underflow/concentrate/sinks stream (frac)
* <math>A</math> is a model parameter that accounts for gravitational and viscous forces of the separation (-)
* <math>c</math> is a model parameter that accounts for turbulence in the separation (-)
* <math>B</math> is a model parameter that accounts for fluid drift force of the separation (-)
* <math>\bar d_{i}</math> is the [[Conversions|geometric mean size]] of particles in size interval <math>i</math> (mm)
* <math>\rho_{\rm S}</math> is the particle density (kg/m<sup>3</sup>)
* <math>\rho_{\rm p}</math> is a model parameter representing the pivot density of separation (kg/m<sup>3</sup>)
 
Rao (2021) extended the Stochastic model to represent the partition surface of an entire batch jig bed in terms of both slice (cut) height and jigging time.{{Rao (2021)}} The modified Stochastic model is:
 
:<math>
\begin{array}{c}
Y_{ij} = \dfrac{1}{2} \left [ 1 + {\rm erf} \left ( \dfrac{(h_{\rm l} - h_{\rm f})}{tD} + B - A{{\bar d}_i}^c ((\rho_{\rm S})_{ij} - \rho_{\rm p}) \right ) \right ] & \text{for } 0 \leq h_{\rm l} \leq 1 \text{ and } 0 \leq t \leq t_{\rm eq}\\
\end{array}
</math>
 
where:
* <math>h_{\rm l}</math> is the relative slice position of the bed, where 0 is the bottom of the bed and 1 is the top of the bed (m/m)
* <math>h_{\rm f}</math> is the feed particle input bed position, a model parameter (m/m)
* <math>D</math> is a model parameter that accounts for the standard deviation of particle velocities in the separator (-)
* <math>t</math> is thje jigging time of the particles (s)
* <math>t_{\rm eq}</math> is the jigging time required to attain dynamic equilibrium (s)
 
The modified Stochastic model reduces to the original formulation when <math>(h_{\rm l} - h_{\rm f}) \to 0</math> or <math>t \to \infty</math>, i.e. steady-state.
 
Rao (2021) does not indicate whether the modified Stochastic model is applicable to dense-medium or gravity concentration processes other than batch jigging. The modified Stochastic model should be applied with caution in such cases.
 
</hide><div class="user-show">
=== Partition Metrics ===
</div><hide>
 
Several metrics are provided to characterise the Stochastic model partition curve.
 
The <math>d_{50}</math>, also known as the ''cut or separation size'', is defined as the size of a particle of a given density which has an even (50%) chance of appearing in either the sinks (concentrate) or floats (tail) stream. The <math>d _{50}</math> size is obtained by rearranging the modified Stochastic model:
 
:<math>d_{50} =\left ( \dfrac{\frac{(h_{\rm l} - h_{\rm f})}{tD} + B}{A(\rho - \rho_{\rm p})} \right )^{\frac{1}{c}}</math>
 
The <math>\rho_{50}</math>, also known as the ''cut or separation density'', is defined as the density of a particle of a given size which has an even (50%) chance of appearing in either the sinks (concentrate) or floats (tail) stream. The <math>\rho _{50}</math> density is obtained by rearranging the modified Stochastic model:
 
:<math>\rho_{50} = \rho_{\rm p} + \left ( \dfrac{\frac{(h_{\rm l} - h_{\rm f})}{tD} + B}{Ad^c} \right )</math>
 
The ''Ecart Probable'', or <math>E_{\rm p}</math>, is a measure of the deviation of a partition curve from a perfect separation, and is found as:
 
:<math>E_{\rm p} = - \dfrac{0.476936}{Ad^c}</math>
 
Finally, the partition coefficient at the pivot point, <math>Y_{\rm p}</math> (frac), is:
 
:<math>Y_{\rm p} = \dfrac{1}{2} \left [ 1 + {\rm erf} \left ( \dfrac{(h_{\rm l} - h_{\rm f})}{tD} + B) \right ) \right ] </math>
 
As with the modified Stochastic model, the partition metrics above reduce to their steady-state counterparts as <math>(h_{\rm l} - h_{\rm f}) \to 0</math> or <math>t \to \infty</math>.
 
</hide><div class="user-show">
=== Cumulative recovery ===
</div><hide>
 
{{Model theory (Text, Gravity Concentrator, Middlings)}}
</hide>


== Excel ==
== Excel ==
{{Under construction|section}}


The Stochastic partition equation may be invoked from the Excel formula bar with the following function call:
The Stochastic partition equation may be invoked from the Excel formula bar with the following function call:


<syntaxhighlight lang="vb">=mdPartition_StochasticRao(MeanSize as Range, RD as Range, A as Double, c as Double, B as Double, rhop as Double, hf as Double, D as double, hl as Double, t as Double)</syntaxhighlight>
<syntaxhighlight lang="vb">=mdPartition_Stochastic(MeanSize as Range, RD as Range, A as Double, c as Double, B as Double, rhop as Double, Optional hf as Double = 0, Optional D as double = 0, Optional hl as Double = 0, Optional t as Double = 0, Optional returnPartitionMetrics as Bool = false)</syntaxhighlight>


{{Excel (Text, Help, No Arguments)}}
{{Excel (Text, Help, No Arguments)}}
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:
:{|
|- style="vertical-align:top;"
|
<math>
\begin{align}
\mathit{MeanSize} & =
\begin{bmatrix}
\bar{d}_1\text{ (mm)}\\
\vdots\\
\bar{d}_n\text{ (mm)}\\
\end{bmatrix}\\
\\
\mathit{RD} & = \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}\\
\\
A & = \big [A \big ]\\
B & = \big [B \big ]\\
c & = \big [c \big ]\\
\mathit{rhop} & = \big [\rho_{\rm p} \text{ (t/m}^3\text{))}\big ]\\
\mathit{hf} & = \big [h_{\rm f}\text{ (m/m)} \big ]\\
\mathit{hl} & = \big [h_{\rm l}\text{ (m/m)} \big ]\\
D & = \big [D \big ]\\
t & = \big [t\text{ (s)} \big ]\\
\mathit{returnPartitionMetrics} & = \big [(\text{True / False)} \big ]\\
\\
\\
\mathit{mdPartition\_StochasticRao} & =
\begin{bmatrix}
\begin{bmatrix}
Y_{11}\text{ (t/h)} & \dots & Y_{1m}\text{ (t/h)}\\
\vdots & \ddots & \vdots\\
Y_{n1}\text{ (t/h)} & \dots & Y_{nm}\text{ (t/h)}\\
\end{bmatrix}
&
\begin{bmatrix}
(\rho_{50})_1\text{ (t/m}^3\text{)}\\
\vdots\\
(\rho_{50})_n\text{ (t/m}^3\text{)}\\
\end{bmatrix}
&
\begin{bmatrix}
(E_{\rm p})_1\text{ (t/m}^3\text{)}\\
\vdots\\
(E_{\rm p})_n\text{ (t/m}^3\text{)}\\
\end{bmatrix}
&
\begin{array}{c}
\begin{bmatrix}
(d_{50})_{1}\text{ (mm)} & \dots & (d_{50})_m\text{ (mm)}\\
\end{bmatrix}^{\rm *}
\\
\\
\\
\\
\end{array}
\end{bmatrix}
\end{align}</math>
where:
* <math>n</math> is the number of size intervals
* <math>m</math> is the number of density classes
* <math>^*</math> indicates optional results returned if <math>\mathit{returnPartitionMetrics = True}</math>
|- style="vertical-align:top;"
| [[File:PartitionStochastic1.png|frame|Figure 2. Example showing the selection of the input parameters (purple, green, pink, brown, teal, blue, red and purple cells), and the '''MeanSize''' (blue frame), '''RD''' (red frame) and '''Results''' (light blue frame) arrays in Excel. The parameter <math>\mathit{returnPartitionMetrics} =\text{True}</math> in this example.]]
|}


== SysCAD ==
== SysCAD ==


{{Under construction|section}}
The Stochastic partition is available from the '''{{Name (Text, Company Name)|nospace=1}}*GravityConcentrator''' and '''{{Name (Text, Company Name)|nospace=1}}*DenseMedium''' unit models.
 
The sections and variable names used in the SysCAD interface are described in detail in the following tables.
 
=== Gravity concentrator ===
 
Note that a '''Con''' and '''Partition''' page is provided for each connected concentrate discharge stream.
 
{{SysCAD (Page, Gravity Concentrator, DLL*GravityConcentrator)}}
 
==== Con page ====
 
The Con page is used to specify the required model method and associated input parameters.
 
{{SysCAD (Text, Table Header)}}
 
{{SysCAD (Text, Gravity Concentrator, Con)}}
 
{{SysCAD (Text, Help Link)}}
 
|-
! colspan="3" style="text-align:left;" |''Stochastic''
 
{{SysCAD (Text, Partition, Stochastic)}}
 
{{SysCAD (Text, Gravity Concentrator, Liquids)|method=0}}
 
|}
 
{{SysCAD (Page, Hydrocyclone, Partition)|ActionU=Partition|ActionL=partition|DestinationU=Concentrate|DestinationL=concentrate|UnitL=gravity concentrator|GravityMetrics=true|Cumulative=true}}
 
{{SysCAD (Page, About)}}
 
==== Additional notes ====
 
{{SysCAD (Text, No PSD Splits)|gasstream=tail}}
 
=== Dense medium separator ===
 
{{SysCAD (Page, Dense Medium, DLL*DenseMedium)|ViscosityModel=true}}
 
==== Stochastic page ====
 
The Stochastic page is used to specify the required model method and associated input parameters.
 
{{SysCAD (Text, Table Header)}}
 
|-
! colspan="3" style="text-align:left;" |''Stochastic''
 
{{SysCAD (Text, Help Link)}}
 
{{SysCAD (Text, Partition, Stochastic)}}
 
|-
! colspan="3" style="text-align:left;" |''Medium''
|- style="vertical-align:top;"
|MediumSolids 
|Input / List
|Specifies which species should be considered as the medium solids by the model.
* The drop down list will contain all solids species in the project, plus "-" for no selection.
* See [[#Medium_solids|Medium solids]] for more information.
|- style="vertical-align:top;"
|rowspan="4" | MedSolSeparMethod
|None
|Medium solids are split as if the default ''MediumSolids'' parameter "-" was selected. See above.
|- style="vertical-align:top;"
|Split to Sinks (User)
|The user specifies the fractional split of the selected medium solids species to the sinks stream.
|- style="vertical-align:top;"
|Follow Solids
|The fractional split of the selected medium solids species to the sinks stream is equal to the overall mass split of all other solids to the sinks stream.
|- style="vertical-align:top;"
|Follow Liquids
|The fractional split of the selected medium solids species to the sinks stream is equal to the mass split of liquids to the sinks stream.
|-
|MedSolSplitToSinks
|style="background: #eaecf0" | Input / Display
|Value of the fractional mass split of the selected medium solids to the sinks stream.
 
{{SysCAD (Text, Dense Medium, Liquids)|method=0}}
 
|}
 
{{SysCAD (Page, Hydrocyclone, Partition)|ActionU=Partition|ActionL=partition|DestinationU=Sinks|DestinationL=sinks|UnitL=dense medium separator|GravityMetrics=true}}
 
==== Viscosity page ====
 
This page displays the inputs and results for [[Properties (Dense Medium Viscosity)|dense medium viscosity]] calculations. The page is only visible if ''ViscosityModel'' is selected on the '''{{SysCAD (Text, UnitType Prefix)}}DenseMedium''' page.
 
{{SysCAD (Page, About)}}
 
{{SysCAD (Text, Dense Medium, Medium Solids)}}
 
==== Additional notes ====
 
{{SysCAD (Text, No PSD Splits)|gasstream=floats}}
 
== See also ==
* [[Partition (Density, Pivot)]]
* [https://help.syscad.net/Met_Dynamics_-_Gravity_Concentrator Met Dynamics - Gravity Concentrator (help.syscad.net)]
* [https://help.syscad.net/Met_Dynamics_-_Dense_Medium_Separator Met Dynamics - Dense Medium Separator (help.syscad.net)]


== References ==
== References ==

Latest revision as of 06:35, 27 June 2025

Description

This article describes the Stochastic equation for the partition of particles by size and density in gravity separators.[1][2]

The Stochastic formulation is applicable to both dense medium separators and gravity concentration processes.

Model theory

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Partition Metrics

Cumulative recovery

Excel

The Stochastic partition equation may be invoked from the Excel formula bar with the following function call: 

=mdPartition_Stochastic(MeanSize as Range, RD as Range, A as Double, c as Double, B as Double, rhop as Double, Optional hf as Double = 0, Optional D as double = 0, Optional hl as Double = 0, Optional t as Double = 0, Optional returnPartitionMetrics as Bool = 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:


where:

  • is the number of size intervals
  • is the number of density classes
  • indicates optional results returned if


Figure 2. Example showing the selection of the input parameters (purple, green, pink, brown, teal, blue, red and purple cells), and the MeanSize (blue frame), RD (red frame) and Results (light blue frame) arrays in Excel. The parameter in this example.

SysCAD

The Stochastic partition is available from the MetDynamics*GravityConcentrator and MetDynamics*DenseMedium unit models.

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

Gravity concentrator

Note that a Con and Partition page is provided for each connected concentrate discharge stream.

MD_GravityConcentrator 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 MassFracToCon option appears below.
MassFracToCon Input Only appears if the On field above is not checked. Specifies the fraction of feed mass that reports to the concentrate 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.
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.

Con page

The Con page is used to specify the required model method and associated input parameters.

Tag (Long/Short) Input / Display Description/Calculated Variables/Options
Stage
On Checkbox This enables the stage. If off, the feed to this stage passes directly to the next stage (or tail) without partition.
Method Partition (User) The partition to concentrate for each size interval is defined by the user.
Partition (Rho50-Ep) The partition to concentrate for each species and size interval is defined by the Rho50-Ep model.
Partition (Pivot) The partition to concentrate for each species and size interval is defined by the Pivot model.
Partition (Stochastic) The partition to concentrate for species and each size interval is defined by the Stochastic model.
Partition (Bazin) The partition to concentrate for species and each size interval is defined by the Bazin model.
Jig (King) The partition to concentrate for species and each size interval is defined by the King jig stratification model.
Spiral (Tucker) The partition to concentrate for each species and size interval is defined by the Tucker spiral concentrator model.
Shaking Table (Tucker) The partition to concentrate for each species and size interval is defined by the Tucker shaking table model.
HelpLink ButtonModelHelp.png Opens a link to this page using the system default web browser. Note: Internet access is required.
Stochastic
A Input Partition surface parameter, gravitation and viscous forces.
B Input Partition surface parameter, fluid drift force.
c Input Partition surface parameter, turbulence.
PivotDensity / Rhop Input Density at pivot point.
hf Input Feed particle input bed position.
hl Input Slice position of the particle bed.
D Input Partition surface parameter, standard deviation of particle velocities.
t Input Separation period of particles.
Liquids
LiquidsSeparMethod Split To Con (User) Liquids are split to concentrate by a user-defined fraction of liquids in the feed.
Con Solids Fraction Sufficient liquids mass is recovered to the concentrate stream to yield the user-defined concentrate solids mass fraction value (if possible).
Con Liquids Fraction Sufficient liquids mass is recovered to the concentrate stream to yield the user-defined concentrate liquids mass fraction value (if possible).
ConSolidsFracReqd / Con.SfReqd Input Required value of the mass fraction of solids in the concentrate stream. Only visible if Con Solids Fraction is selected.
ConLiquidsFracReqd / Con.LfReqd Input Required value of the mass fraction of liquids in the concentrate stream. Only visible if Con Liquids Fraction is selected.
LiqSplitToCon / Con.LiqSplit Input/Display The fraction of feed liquids recovered to the concentrate stream.

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.

CumulativePartition
Method Model / User Select model-calculated or user-defined cumulative 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 cumulative partition to concentrate of all solid species, for each size interval.
  • Excludes solid species not present in the gravity concentrator feed.
CumulativePartition Display
  • Cumulative partition to concentrate 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 gravity concentrator feed or not.
All (All row, All column) Display
  • Displays the actual, total, cumulative partition of all solids with a particle size distribution property in the feed to concentrate.
  • Excludes solid species not present in the gravity concentrator feed.
All (All row, per species) Display
  • Actual overall cumulative partition to concentrate for each solid species, for all size intervals in that species.
  • Excludes solid species not present in the gravity concentrator feed.
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 concentrate of all solid species, for each size interval.
  • Excludes solid species not present in the gravity concentrator feed.
Partition Display
  • Partition to concentrate 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 gravity concentrator 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 concentrate.
  • Excludes solid species not present in the gravity concentrator feed.
All (All row, per species) Display
  • Actual overall partition to concentrate for each solid species, for all size intervals in that species.
  • Excludes solid species not present in the gravity concentrator 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 concentrate of all solid components, for each size interval.
  • Excludes solid components not present in the gravity concentrator feed.
CmpPartition Display
  • Partition to concentrate 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 gravity concentrator 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 concentrate.
  • Excludes solid components not present in the gravity concentrator feed.
All (All row, per component) Display
  • Actual overall partition to concentrate for each solid component, for all size intervals in that component.
  • Excludes solid components not present in the gravity concentrator 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 concentrate of all solid elements, for each size interval.
  • Excludes solid elements not present in the gravity concentrator feed.
ElePartition Display
  • Partition to concentrate 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 gravity concentrator 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 concentrate.
  • Excludes solid elements not present in the gravity concentrator feed.
All (All row, per element) Display
  • Actual overall partition to concentrate for each solid element, for all size intervals in that component.
  • Excludes solid elements not present in the gravity concentrator 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 concentrate of all solid individual phases, for each size interval.
  • Excludes solid individual phases not present in the gravity concentrator feed.
IPhPartition Display
  • Partition to concentrate 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 gravity concentrator 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 concentrate.
  • Excludes solid individual phases not present in the gravity concentrator feed.
All (All row, per individual phase) Display
  • Actual overall partition to concentrate for each solid individual phase, for all size intervals in that component.
  • Excludes solid individual phases not present in the gravity concentrator feed.

PartitionMetrics
d50 Display Cut size (d50) of separation of each ore species.
Size Display Size of each interval in mesh series.
MeanSize Display Geometric mean size of each interval in mesh series.
CutDensity / Rho50 Display Cut density (Rho50) of all particles in each size interval.
EcartProbable / Ep Display Ecart Probable of all particles in each size interval.
PivotPartition / Yp Display Partition at pivot point.

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 tail stream without split.

Dense medium separator

MD_DenseMedium 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 MassFracToSinks option appears below.
MassFracToSinks Input Only appears if the On field above is not checked. Specifies the fraction of feed mass that reports to the sinks 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 sinks for each size interval and species is defined by the user.
Partition (Rho50-Ep) The partition to sinks for each species and size interval is defined by the Rh050-Ep model.
Partition (Pivot) The partition to sinks for each species and size interval is defined by the Pivot model.
Partition (Stochastic) The partition to sinks for each species and size interval is defined by the Stochastic model.
Drum (Baguley) The Baguley dense medium drum model is used to determine the partition of solids to sinks and floats for each species and size interval.
Cyclone (Dunglison) The Dunglison dense medium cyclone model is used to determine the partition of solids to sinks (underflow) and floats (overflow) for each species and size interval.
ViscosityModel CheckBox Show dense medium viscosity model on the Viscosity page.
Options
ShowQFeed CheckBox QFeed and associated tab pages (eg Sp) will become visible, showing the properties of the combined feed stream.
ShowQSinks CheckBox QSinks and associated tab pages (eg Sp) will become visible, showing the properties of the sinks stream.
ShowQFloats CheckBox QFloats and associated tab pages (eg Sp) will become visible, showing the properties of the floats 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.

Stochastic page

The Stochastic page is used to specify the required model method and associated input parameters.

Tag (Long/Short) Input / Display Description/Calculated Variables/Options
Stochastic
HelpLink ButtonModelHelp.png Opens a link to this page using the system default web browser. Note: Internet access is required.
A Input Partition surface parameter, gravitation and viscous forces.
B Input Partition surface parameter, fluid drift force.
c Input Partition surface parameter, turbulence.
PivotDensity / Rhop Input Density at pivot point.
hf Input Feed particle input bed position.
hl Input Slice position of the particle bed.
D Input Partition surface parameter, standard deviation of particle velocities.
t Input Separation period of particles.
Medium
MediumSolids Input / List Specifies which species should be considered as the medium solids by the model.
  • The drop down list will contain all solids species in the project, plus "-" for no selection.
  • See Medium solids for more information.
MedSolSeparMethod None Medium solids are split as if the default MediumSolids parameter "-" was selected. See above.
Split to Sinks (User) The user specifies the fractional split of the selected medium solids species to the sinks stream.
Follow Solids The fractional split of the selected medium solids species to the sinks stream is equal to the overall mass split of all other solids to the sinks stream.
Follow Liquids The fractional split of the selected medium solids species to the sinks stream is equal to the mass split of liquids to the sinks stream.
MedSolSplitToSinks Input / Display Value of the fractional mass split of the selected medium solids to the sinks stream.
Liquids
LiquidsSeparMethod Split To Sinks (User) Liquids are split to sinks by a user-defined fraction of liquids in the feed.
Sinks Solids Fraction Sufficient liquids mass is recovered to the sinks stream to yield the user-defined sinks solids mass fraction value (if possible).
Sinks Liquids Fraction Sufficient liquids mass is recovered to the sinks stream to yield the user-defined sinks liquids mass fraction value (if possible).
SinksSolidsFracReqd / Sinks.SfReqd Input Required value of the mass fraction of solids in the sinks stream. Only visible if Sinks Solids Fraction is selected.
SinksLiquidsFracReqd / Sinks.LfReqd Input Required value of the mass fraction of liquids in the sinks stream. Only visible if Sinks Liquids Fraction is selected.
LiqSplitToSinks / Sinks.LiqSplit Input/Display The fraction of feed liquids recovered to the sinks stream.

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 sinks of all solid species, for each size interval.
  • Excludes solid species not present in the dense medium separator feed.
Partition Display
  • Partition to sinks 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 dense medium separator 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 sinks.
  • Excludes solid species not present in the dense medium separator feed.
All (All row, per species) Display
  • Actual overall partition to sinks for each solid species, for all size intervals in that species.
  • Excludes solid species not present in the dense medium separator 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 sinks of all solid components, for each size interval.
  • Excludes solid components not present in the dense medium separator feed.
CmpPartition Display
  • Partition to sinks 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 dense medium separator 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 sinks.
  • Excludes solid components not present in the dense medium separator feed.
All (All row, per component) Display
  • Actual overall partition to sinks for each solid component, for all size intervals in that component.
  • Excludes solid components not present in the dense medium separator 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 sinks of all solid elements, for each size interval.
  • Excludes solid elements not present in the dense medium separator feed.
ElePartition Display
  • Partition to sinks 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 dense medium separator 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 sinks.
  • Excludes solid elements not present in the dense medium separator feed.
All (All row, per element) Display
  • Actual overall partition to sinks for each solid element, for all size intervals in that component.
  • Excludes solid elements not present in the dense medium separator 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 sinks of all solid individual phases, for each size interval.
  • Excludes solid individual phases not present in the dense medium separator feed.
IPhPartition Display
  • Partition to sinks 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 dense medium separator 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 sinks.
  • Excludes solid individual phases not present in the dense medium separator feed.
All (All row, per individual phase) Display
  • Actual overall partition to sinks for each solid individual phase, for all size intervals in that component.
  • Excludes solid individual phases not present in the dense medium separator feed.

PartitionMetrics
d50 Display Cut size (d50) of separation of each ore species.
Size Display Size of each interval in mesh series.
MeanSize Display Geometric mean size of each interval in mesh series.
CutDensity / Rho50 Display Cut density (Rho50) of all particles in each size interval.
EcartProbable / Ep Display Ecart Probable of all particles in each size interval.
PivotPartition / Yp Display Partition at pivot point.

Viscosity page

This page displays the inputs and results for dense medium viscosity calculations. The page is only visible if ViscosityModel is selected on the MD_DenseMedium page.

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.

Medium solids

This model allows the user to designate any single SysCAD solids species in the project as the medium solids. Alternatively, no medium solids may be specified (default: "-").

The selected option determines how the medium species is treated by the model:

Default: -:
  • All solids species in the feed stream that possess the size distribution (PSD) property are partitioned by the model based on their size and density characteristics.
  • The All partition values shown on the Partition page include contributions from all species.
  • All solids species in the feed stream that do not possess the PSD property are split by the model based on default behaviour (see Additional notes).
[Species Name]:
  • The user may specify how the selected medium solids species is split to the sinks stream via the MedSolSeparMethod field. Options are:
    • None: Medium solids are split as if the default MediumSolids parameter "-" was selected. See above.
    • Split to Sinks (User): The user specifies the fractional split of the selected medium solids species to the sinks stream.
    • Follow Solids: The fractional split of the selected medium solids species to the sinks stream is equal to the overall mass split of all other solids to the sinks stream.
    • Follow Liquids: The fractional split of the selected medium solids species to the sinks stream is equal to the mass split of liquids to the sinks stream.
  • if the selected medium solids species posseses the PSD property:
    • The partition-by-size values for the medium species on the Partition page are displayed as zeroes.
    • The All partition values on the Partition page exclude the medium solids species.

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 floats stream without split.

See also

References

  1. ↑ Rao, B.V., Kapur, P.C. and Konnur, R., 2003. Modeling the size–density partition surface of dense-medium separators. International Journal of Mineral Processing, 72(1-4), pp.443-453.
  2. ↑ Rao, B.V., 2021. An improved stochastic model to describe partition surfaces of entire segregated batch jig bed. Minerals Engineering, 170, p.107064.
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