WHIMS (Dobby and Finch)

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Description

This article describes the Dobby and Finch (1977) model for Wet High Intensity Magnetic Separator (WHIMS) and High Gradient Magnetic Separator (HGMS) machines.[1][2][3]

Model theory

Dobby and Finch (1977) describe an empirical model of a laboratory-scale High Gradient Magnetic Separator (HGMS), which may be applicable to Wet High Intensity Magnetic Separators (WHIMS) and other similar machines.[1][2][3]

The authors suggest the total recovery of material to the magnetics stream, (frac), is the sum of recovery by the mechanisms of magnetic capture, (frac), and physical capture by entrapment, (frac). For a particle within a given size interval and magnetic susceptibility class , the total recovery is:

The magnetic recovery () is related to particle and separating machine properties by the following relations:

where is the recovery curve slope and is the magnetic cut point. Both and are machine-specific parameters, independent of the material being separated.[3]

For free-draining separation chambers, the machine and material parameters are related by the group :

where:

  • is the applied magnetic field strength (T)
  • is the magnetic field gradient (T)
  • is the saturated magnetic field strength (T)
  • is the particle density (kg/m3)
  • is the mass magnetic susceptibility (m3/kg)
  • is the material magnetic susceptibility exponent
  • is the geometric mean size of particles in size interval (m)
  • is the mean interstitial velocity of slurry though the chamber (m/s)
  • is the matrix loading, the ratio of the mass of magnetics in the chamber to the mass of the matrix (kg/kg)

Dobby and Finch found the value of was 1.8 for a group of minerals with a wide susceptibly range, which included haematite, ilmenite, sphalerite and chalcopyrite. When the low susceptibity sphalerite and chalcopyrite were removed from the regression procedure, a better fit was obtained with a of 3.9. The value of may require re-fitting to specific data sets when applying the model.

The recovery by physical capture per size interval, is specified by the user.

Excel

The Dobby and Finch WHIMS model may be invoked from the Excel formula bar with the following function call:

=mdUnit_WHIMS_DobbyFinch(Parameters as Range, Size as Range, Feed as Range, Density As Range, Susceptibility As Range, Optional Rp As Range = 0)

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

Inputs

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




where:

  • is feed solids mass flow rate by size and ore type (t/h)
  • indicates an optional input, default values of for are assumed if is omitted

Note that both and 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:


where:

  • is mass flow rate of solids to the magnetics stream (t/h)
  • 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.

Figure 1. Example showing the selection of the Parameters (blue frame) array in Excel.
Figure 2. Example showing the selection of the Size (red frame), Feed (purple frame), Density (green frame), Susceptibility (pink frame) and Rp (brown frame) arrays in Excel.
Figure 3. Example showing the outline of the Results (light blue frame) array in Excel.

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.
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.

WHIMS page

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

Tag (Long/Short) Input / Display Description/Calculated Variables/Options
WHIMS
HelpLink ButtonModelHelp.png Opens a link to this page using the system default web browser. Note: Internet access is required.
Parameters
MagneticFieldStrength / H Input Magnetic field strength.
SatMagFieldStrength / Hs Input Saturation magnetic field strength.
SlurryVelocity / u Input Average velocity of slurry flow through the matrix.
MatrixLoading / Lm Input Ratio of the mass of magnetic solids to the mass of the matrix in the separation chamber.
MagneticCutPoint / M50 Input Magnetic cut point.
RecoveryCurveSlope / B Input Slope of the recovery curve, i.e. coefficient of the log term.
SusceptibilityExponent / Beta Input Exponent of the susceptibility equation term.
Liquids
LiquidsSeparMethod Split To Mags (User) Liquids are split to magnetics by a user-defined fraction of liquids in the feed.
Mags Solids Fraction Sufficient liquids mass is recovered to the magnetics stream to yield the user-defined magnetics solids mass fraction value (if possible).
Mags Liquids Fraction Sufficient liquids mass is recovered to the magnetics stream to yield the user-defined magnetics liquids mass fraction value (if possible).
MagsSolidsFracReqd / Mags.SfReqd Input Required value of the mass fraction of solids in the magnetics stream. Only visible if Mags Solids Fraction is selected.
MagsLiquidsFracReqd / Mags.LfReqd Input Required value of the mass fraction of liquids in the magnetics stream. Only visible if Mags Liquids Fraction is selected.
LiqSplitToMags Input/Display The fraction of feed liquids recovered to the magnetics stream.

Susceptibility page

This page is used to specify the magnetic mass susceptibility 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.
Susceptibility
Selection Stream A single mass susceptibility value is specified for all species and sizes.
Species Mass susceptibility values are specified per species, for all sizes of that species.
Size Mass susceptibility values are specified per size interval, for all species in that interval.
Species-Size Individual mass susceptibility 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.
Rp Input Fraction recovered to magnetics by physical capture of particles.
Susceptibility Input / Display Mass susceptibility for each size interval, in each solid species.

WHIMSDobbyFinch4.png WHIMSDobbyFinch5.png

WHIMSDobbyFinch6.png WHIMSDobbyFinch7.png

Recovery page

The Recovery page is used to specify or display the recovery 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.
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
  • Actual overall recovery to magnetics of all solid species, for each size interval.
  • Excludes solid species not present in the magnetic separator feed.
Recovery Display
  • Recovery to magnetics 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 magnetic separator feed or not.
All (All row, All column) Display
  • Displays the actual, total, recovery of all solids with a particle size distribution property in the feed to magnetics.
  • Excludes solid species not present in the magnetic separator feed.
All (All row, per species) Display
  • Actual overall recovery to magnetics for each solid species, for all size intervals in that species.
  • Excludes solid species not present in the magnetic 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.

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.

References

  1. 1.0 1.1 Dobby, G.S. and Finch, J.A., 1977. An Empirical Model Of Capture In A High Gradient Magnetic Separator And Its Use In Performance Prediction. 1977 AIME Annual Meeting, Atlanta, Georgia - March 6-10, 1977.
  2. 2.0 2.1 Dobby, G. and Finch, J.A., 1977. Capture of mineral particles in a high gradient magnetic field. Powder Technology, 17(1), pp.73-82. Elsevier.
  3. 3.0 3.1 3.2 King, R.P., 2012. Modeling and Simulation of Mineral Processing Systems. Elsevier.