Dense Medium Cyclone (Dunglison)

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Description

This article describes the Dunglison (1999) model for dense medium cyclones.[1] The model is applicable to both minerals (e.g. iron ore, diamonds) and coal separations.

The Dunglison model is a comprehensive description of dense medium cyclone performance, and does not have any parameters that require calibration or "fitting" to plant or laboratory data.

Model theory

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Flowrate and pressure

Volumetric flow rate

Feed inlet pressure

Medium split

Medium:Ore ratio

Medium viscosity

Shear rate

Shi viscosity model

Medium classification

Pulp-split function

Underflow and overflow densities

Medium properties

Ore partitioning

Pulp-split function

Cut density and Ecart Probable

Particle velocity

Centrifugal acceleration

Hindered settling velocity

Feed medium density adjustment

Excel

The Dunglison dense medium cyclone model may be invoked from the Excel formula bar with the following function call:

=mdUnit_DMCyclone_Dunglison(Parameters as Range, Size as Range, Density As Range, Feed as Range, MediumSize as Range, MediumDist as Range)

Invoking the function with no arguments will print Help text associated with the model, including a link to this page.

Inputs

The required inputs are defined below in matrix notation with elements corresponding to cells in Excel row () x column () format:


where:

  • specifies the flow-pressure calculation mode to apply (0 = Compute flow rate at specified pressure, 1 = Compute pressure at specified flow rate)
  • is the volumetric flow rate of medium in the cyclone feed (m3/h)
  • specifies the type of solid media (0 = Atomised FeSi, 1 = Milled FeSi, 2 = Magnetite)
  • is the temperature of the medium (deg. C)
  • is feed solids mass flow rate by size and ore type (t/h)
  • is the particle density (t/m3)

Results

The results are displayed in Excel as an array corresponding to the matrix notation below:


where:

  • (m) is the geometric mean size of a medium particle in size interval (mm)
  • is mass flow rate of solids to the underflow (sinks) stream (t/h)
  • is mass flow rate of solids to the overflow (floats) stream (t/h)
  • is the actual partition of all mass to the sinks stream, computed as (frac)
  • is the actual partition of all particles of size to the underflow (sinks) stream, computed as (frac)
  • is the actual partition of all particles of density class to the underflow (sinks) stream, computed as (frac)

Example

The images below show the selection of input arrays and output results in the Excel interface.

Figure 2. Example showing the selection of the Parameters (blue frame) array in Excel.
Figure 3. Example showing the selection of the Size (red frame), Feed (green frame), Density (purple frame), MediumSize (pink frame), and MediumDist (brown frame) arrays in Excel.
Figure 4. Example showing the outline of the left side of the Results array (shaded area) in Excel.
Figure 5. Example showing the outline of the right side of the Results array (shaded area) in Excel.

SysCAD

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.
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.

Cyclone page

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

Tag (Long/Short) Input / Display Description/Calculated Variables/Options
DMCyclone
HelpLink ButtonModelHelp.png Opens a link to this page using the system default web browser. Note: Internet access is required.
Mode Compute Flow The model computes the cyclone volumetric flow rate at the specified feed inlet pressure.
Compute Pressure The model computes the feed inlet pressure required to achieve the specified feed volumetric flow rate.
Parameters
FeedPressure / Pi Input / Display Feed inlet pressure of the cyclone
CycloneDiameter / Dc Input Diameter of the cylindrical section of the cyclone.
ApexDiameter / Du Input Diameter of the cyclone apex (underflow) discharge.
InletDiameter / Di Input Diameter (equivalent) of the inlet to the cyclone.
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.
MediumType Atomised FeSi The dense media is atomised ferrosilicon.
Milled FeSi The dense media is milled ferrosilicon.
Magnetite The dense media is milled magnetite.
Feed.Medium.VolFlow / QfMed Input / Display The volumetric flow rate of feed medium to the cyclone.
CorrectMediumDensity / Rhocm Input / Display The density of the correct medium.
MediumSolidsDensity / Rhom Input / Display The density of the medium solids.
MediumTemperature / T Input / Display The temperature of the feed medium.
Liquids
LiquidsSeparMethod Split To Sinks (User) Liquids are split to sinks by a user-defined fraction of liquids in the feed.
Split To Sinks (Model) Liquids are split to sinks by a fraction determined by the selected model.
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.
Results
Feed.SolidMassFlow / Mf Display Mass flow of ore solids in cyclone feed.
Feed.OreDensity / RhoOre Display Mean density of all ore solids in cyclone feed.
Feed.Medium.SolVolFrac / Cvf Display Volume fraction of solids in feed medium.
Feed.Medium.Density / Rhof Display Density of feed medium to cyclone.
Feed.VolFlow / Qf Display Volumetric flow rate of feed to cyclone.
MediumOreRatio / MO Display Medium to ore volume ratio.
Feed.OreSolVolFrac / PhiOre Display Volume concentration of ore in cyclone feed.
Feed.MedSolVolFrac / PhiMed Display Volume concentration of medium solids in cyclone feed.
MediumSplitToUF / Rm Display Fractional split of feed medium to underflow (sinks) stream.
MediumSolSplitToUF / RmSolids Display Fractional split of feed medium solids to underflow (sinks) stream.
MediumLiqSplitToUF / RmLiquids Display Fractional split of feed medium liquids to underflow (sinks) stream.
MediumVelocity / Vc Display Velocity of medium in the cyclone.
PressureHead / Head Display Pressure head to cyclone feed in multiples of cyclone diameter (Dc).
ShearRate / GammaDot Display Shear rate of medium in cyclone.
MediumP80 Display 80% passing size of the medium solids.
MediumP20 Display 20% passing size of the medium solids.
ApparentViscosity / mu Display Apparent viscosity of medium in cyclone.
AccelRadius / Radius Display Radius of centrifugal acceleration.
InletVelocity / Vinlet Display Velocity of cyclone feed at inlet.
InletVelLossFactor / alphaInlet Display Inlet velocity loss factor.
TangentialVelocity / Vt Display Tangential velocity of flow in the cyclone.
CentrifugalAccel / ac Display Centrifugal acceleration of flow in the cyclone.
ReynoldsNumber / Rec Display Reynolds Number of flow in the cyclone.
MedIneffExponent / bMed Display Medium inefficiency exponent.
UF.Medium.SolVolFrac / Cvu Display Volume fraction of solids in underflow medium.
UF.Medium.Density / Rhou Display Density of medium in the underflow.
OF.Medium.Density / Rhoo Display Density of medium in the overflow.
OreIneffExponent / bOre Display Ore inefficiency exponent.
CoarseCutDensity / Rho50c Display Cut density of coarse particles in cyclone.
CutDensityParameter / c Display Cut density parameter.
CutDensity / Rho50 Display Unsized cut density (Rho50).
EcartProbable / Ep Display Unsized Ecart Probable (Ep).
Imperfection / I Display Unsized partition Imperfection (I).

MediumSz page

The MediumSz page is used to specify the size distribution properties of the dense medium solids.

Tag (Long/Short) Input / Display Description/Calculated Variables/Options
MediumSz
NumMediumSizes Input / Display Number of medium solids particle size intervals.
Size Input / Display Size of each interval in medium mesh series.
MeanSize Display Geometric mean size of each interval in medium mesh series.
WtMedium Input / Display Mass fraction of medium solids per size interval.
YiMedium Input / Display The partition to underflow (sink) of medium solids per size interval.
All Input / Display Actual overall recovery of all medium solids to underflow (sinks).

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.

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 solids species is treated by the model:

Default: -:
  • The medium properties required by the model (Feed.Medium.VolFlow, CorrectMediumDensity, MediumSolidsDensity, MediumTemperature, and Size/WtMedium) are specified by the user.
  • All solids species in the feed stream that possess the 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 medium properties required by the model (Feed.Medium.VolFlow, CorrectMediumDensity, and MediumSolidsDensity are determined by the properties of the selected medium solids species and all liquids in the feed.
  • If the SysCAD heat calculations are enabled (Edit, Project Settings, Heat Calculations), the MediumTemperature is determined by the mixed temperature of all feed streams. Otherwise, MediumTemperature is user-specified.
  • If the selected medium solids species possesses the size distribution property (PSD):
    • The Size/WtMedium properties are determined by the PSD of the medium solids species in the feed stream.
    • The selected medium species is partitioned according to the medium classification (YiMedium) determined by the model.
    • 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 species.
  • If the selected medium solids species does not possess the PSD property:
    • The Size/WtMedium values are user-specified.
    • The selected medium solids species split to the sinks stream is determined by the RmSolids model parameter.

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/floats stream without split.

See also

External links

References

  1. Dunglison, M.E., 1999. A general model of the dense medium cyclone. PhD thesis, The University of Queensland, Julius Kruttschnitt Mineral Research Centre.