Vibrating Screen (Whiten): Difference between revisions

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{{Model theory (Text, Screen Efficiency)}}
{{Model theory (Text, Screen Efficiency)}}


The efficiency of a given screen feed and deck configuration is a function of the <math>n_{\rm L}</math> model parameter.
The efficiency of a given screen feed and deck configuration is a function of the <math>n_{\rm L}</math>, <math>R_{\rm f}</math> and <math>\lambda</math> model parameters.


Alternatively, the <math>n_{\rm L}</math> value required to achieve a target efficiency value for a given screen and feed may be found by the model with a numerical root-finding algorithm.
Alternatively, the <math>n_{\rm L}</math> value required to achieve a target efficiency value for a given screen, feed and <math>R_{\rm f}</math>, <math>\lambda</math> parameters may be found by the model with a numerical root-finding algorithm.


=== Multiple decks ===
=== Multiple decks ===

Latest revision as of 05:38, 20 December 2023

Description

This article describes an implementation of the Whiten and White (1977) model for multi-row vibrating screen classification, with extensions by Dehghani et al. (2002) and Firth and Hart (2008).[1][2][3]

Model theory

Figure 1. Example panel layout for a vibrating screen deck.
Figure 2. Schematic diagram of three screens in series.
Figure 3. Schematic diagram of three panel rows in series, analogous to the three screens in series of Figure 2.

The Whiten screen model combines particle classification with a relationship for screening across sequential rows of panels with differing aperture and open area properties.

Classification

This model applies a modified version of the Whiten and White (1977) expression for classification of particles to oversize:[1]

where:

  • is the index of the size interval, , is the number of size intervals
  • is the corrected fraction of particles of size interval in the feed reporting to the oversize stream (frac)
  • is the geometric mean size of the size interval (mm)
  • is the number of trials per unit length parameter (/m)
  • is the length of the screening area (or panel) in the direction of flow (m)
  • is the fraction open area of the screen deck/panels (m2/m2)
  • is length (the longer side) of the screen deck/panel aperture (m)
  • is width (the shorter side) of the screen deck/panel aperture (m)

Whiten and White's equation was modified by Dehghani et al. (2002) to include a term for irregularly shaped particles, and is generalised to:[2]

where:

and is the representative aspect ratio of the particle population, the ratio of the second longest to the longest dimensions of a particle (mm/mm)

The aspect ratio property, , allows for the balanced screening of 'flaky' or 'elongated' particles on slotted meshes. Dehghani et al.'s relation reduces to Whiten and White's original equation when .

Firth and Hart (2008) suggested a simple modification to a partition curve to account for the observed entrainment of fine particles in an oversize stream, with decreasing probability as particle size increases:[3]

where:

  • is the actual fraction of particles of size interval in the feed reporting to the oversize stream (frac)
  • is the fraction of the finest particles or feed liquids split to the oversize stream (frac)
  • is the size constant

Multi-row screening

Figure 1 indicates a typical arrangement of screen panels on a screen deck. Each row of panels may exhibit a unique set of properties. Particles in the screen feed may therefore experience changing apertures sizes or open area fractions during screening, in the order of row arrangement in the flow direction.

Screening across the rows of a deck with differing properties is analogous to an arrangement of screens in series, where the oversize from the first screen (row) becomes the feed to the next screen (row), and so on. This concept is illustrated in Figures 2 and 3.

Mathematically, this is stated as:

and adjusted for the entrainment of fines by:

where:

  • is the corrected fraction of the feed to the screen deck in size interval recovered to the deck oversize stream (frac)
  • is the corrected fraction of the feed to panel row in size interval recovered to the row oversize stream (frac)
  • is the actual fraction of the feed to the screen deck in size interval recovered to the deck oversize stream (frac)
  • is the number of panel rows with apertures permitting the passage of particles

Classification for each row is computed via the modified Whiten and White equation presented above. The same parameter is applied to all rows as a simplification.

Screen efficiency

Screen efficiency, or the efficiency of undersize removal, (frac), is defined as "the fraction of sub-aperture material in the feed stream which is actually recovered to the undersize stream". Formally,

where:

  • is the mass flow rate of particles in the undersize stream (t/h)
  • is the mass flow rate of particles in the feed stream (t/h)
  • is the mass fraction of particles in the feed which are smaller than the aperture size (w/w)

The efficiency of a given screen feed and deck configuration is a function of the , and model parameters.

Alternatively, the value required to achieve a target efficiency value for a given screen, feed and , parameters may be found by the model with a numerical root-finding algorithm.

Multiple decks

Screens with multiple decks can be simulated by stacking model instances, i.e.:

  • The undersize stream from the first deck becomes the feed to the next deck, and so on.
  • Each deck yields an oversize stream, which can remain separated or combined into an overall oversize stream, depending on the screen and circuit configuration.

The overall efficiency of a multi-deck screen may be computed with the screen feed and final deck undersize streams in place of deck feed and deck undersize.

Excel

The Whiten vibrating screen model may be invoked from the Excel formula bar with the following function call:

=mdUnit_Screen_Whiten(Parameters as Range, Size as Range, Feed as Range, Rows 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:

  • indicates whether the model applies a user-specified parameter or solves the value required to achieve a user-specified target efficiency (0 = Specify nL, 1 = Specify Efficiency)
  • is the target screen efficiency (frac) if , ignored otherwise
  • is number of trials parameter (/m) applied if , ignored otherwise
  • is the size of the square mesh interval that feed mass is retained on (mm)
  • is the number of ore types
  • is feed solids mass flow rate by size and ore type (t/h)

Results

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


where:

  • is the actual efficiency of undersize removal achieved by the screen (frac)
  • is number of trials parameter (/m) specified by the user if , or required to achieve the target efficiency if if
  • is mass flow rate of solids to the oversize stream (t/h)
  • is mass flow rate of solids to the undersize stream (t/h)

Example

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

Figure 4. Example showing the selection of the Parameters (blue frame) array in Excel.
Figure 5. Example showing the selection of the Rows (green frame) array in Excel.
Figure 6. Example showing the selection of the Size (red frame), and Feed (purple frame) arrays in Excel.
Figure 7. Example showing the outline of the Results (light blue frame) array in Excel.

SysCAD

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

Note that both a Deck page and a Partition page are provided provided for each connected oversize discharge stream.

MD_Screen page

The first tab page in the access window will have this name.

Tag (Long/Short) Input / Display Description/Calculated Variables/Options
Tag Display This name tag may be modified with the change tag option.
Condition Display OK if no errors/warnings, otherwise lists errors/warnings.
ConditionCount Display The current number of errors/warnings. If condition is OK, returns 0.
GeneralDescription / GenDesc Display This is an automatically generated description for the unit. If the user has entered text in the 'EqpDesc' field on the Info tab (see below), this will be displayed here.

If this field is blank, then SysCAD will display the unit class ID.

Requirements
On CheckBox This enables the unit. If this box is not checked, then the MassFracToOS option appears below.
MassFracToOS Input Only appears if the On field above is not checked. Specifies the fraction of feed mass that reports to the overflow stream when the model is off.
Options
ShowQFeed CheckBox QFeed and associated tab pages (eg Sp) will become visible, showing the properties of the combined feed stream.
SizeForPassingFracCalc Input Size fraction for % Passing calculation. The size fraction input here will be shown in the Stream Summary section.
FracForPassingSizeCalc Input Fraction passing for Size calculation. The fraction input here will be shown in the Stream Summary section.
Stream Summary
MassFlow / Qm Display The total mass flow in each stream.
SolidMassFlow / SQm Display The Solids mass flow in each stream.
LiquidMassFlow / LQm Display The Liquid mass flow in each stream.
VolFlow / Qv Display The total Volume flow in each stream.
Temperature / T Display The Temperature of each stream.
Density / Rho Display The Density of each stream.
SolidFrac / Sf Display The Solid Fraction in each stream.
LiquidFrac / Lf Display The Liquid Fraction in each stream.
Passing Display The mass fraction passing the user-specified size (in the field SizeForPassingFracCalc) in each stream.
Passes Display The user-specified (in the field FracForPassesSizeCalc) fraction of material in each stream will pass this size fraction.

Deck page

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

Tag (Long/Short) Input / Display Description/Calculated Variables/Options
Deck
On Checkbox This enables the deck. If off, the feed to this deck passes directly to the next deck (or undersize) without partition.
Method Partition (User) The partition to oversize for each size interval is defined by the user. Different values can be used for different solids.
Partition (Reid-Plitt) The partition to oversize for each size interval is defined by a Reid-Plitt efficiency curve. Different parameters can be used for different solids.
Partition (Whiten-Beta) The partition to oversize for each size interval is defined by a Whiten-Beta efficiency curve. Different parameters can be used for different solids.
Vibrating (Karra) The Karra vibrating screen model is used to determine the partition of solids to oversize and undersize for each size interval.
Vibrating (Whiten) The Whiten vibrating screen model is used to determine the partition of solids to oversize and undersize for each size interval.
Vibrating (Metso) The Metso vibrating screen model is used to determine the partition of solids to oversize and undersize for each size interval.
Fine Wet (Mwale) The Mwale fine wet screen model is used to determine the partition of solids to oversize and undersize for each size interval.
HelpLink ButtonModelHelp.png Opens a link to this page using the system default web browser. Note: Internet access is required.
Parameters
Method Specify nL The user specifies the value of the nL parameter and efficiency is computed.
Specify Efficiency The value of the nL parameter is adjusted to achieve a user-specified target efficiency value.
nL Input User specified value of the nL parameter. Only visible if the Specify nL method is selected above.
Efficiency Input User specified target value of screen efficiency. Only visible if Specify Efficiency method is selected above.
ParticleAspectRatio / ParticleAR Input Value of the particle aspect ratio, i.e. (second longest dimension):(longest dimension).
Rf Input Fines recovery parameter, fraction of the finest particles or liquids split to oversize stream.
Lambda Input Fines recovery parameter, shape factor.
Rows
NumRows Input Number of screen panel rows.
L Input Length of the row in the direction of travel.
ApertureL / D1 Input Aperture length.
ApertureW / D2 Input Aperture width.
OpenArea / fo Input Open area fraction of the row.
Liquids
LiquidsSeparMethod Split To OS (User) Liquids are split to oversize by a user-defined fraction of liquids in the feed.
Split To OS (Rf) Liquids are split to oversize by the Rf fraction specified for the screen model.
OS Solids Fraction Sufficient liquids mass is recovered to the oversize stream to yield the user-defined oversize solids mass fraction value (if possible).
OS Liquids Fraction Sufficient liquids mass is recovered to the oversize stream to yield the user-defined oversize liquids mass fraction value (if possible).
OSSolidsFracReqd / OS.SfReqd Input Required value of the mass fraction of solids in the oversize stream. Only visible if OS Solids Fraction is selected.
OSLiquidsFracReqd / OS.LfReqd Input Required value of the mass fraction of liquids in the oversize stream. Only visible if OS Liquids Fraction is selected.
LiqSplitToOS / OS.LiqSplit Input/Display The fraction of feed liquids recovered to the oversize stream.
Results
Efficiency Display Actual efficiency of undersize removal achieved by the deck.
nL Display Value of nL used for the deck at the actual efficiency.

Partition page

The Partition page is used to specify or display the partition by species and size values.

Tag (Long/Short) Input / Display Description/Calculated Variables/Options
Distribution
Name Display Shows the name of the SysCAD Size Distribution (PSD) quality associated with the feed stream.
IntervalCount Display Shows the number of size intervals in the SysCAD Size Distribution (PSD) quality associated with the feed stream.
SpWithPSDCount Display Shows the number of species in the feed stream assigned with the SysCAD Size Distribution (PSD) quality.
Partition
Method Model/User Select model-calculated or user-defined partition to separate each solids species type.
Density Display Density of each solid species.
Size Display Size of each interval in mesh series.
MeanSize Display Geometric mean size of each interval in mesh series.
All (All column) Display
  • Actual overall partition to oversize of all solid species, for each size interval.
  • Excludes solid species not present in the screen feed.
Partition Display
  • Partition to oversize 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 screen 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 oversize.
  • Excludes solid species not present in the screen feed.
All (All row, per species) Display
  • Actual overall partition to oversize for each solid species, for all size intervals in that species.
  • Excludes solid species not present in the screen 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 undersize stream without split.

See also

References

  1. 1.0 1.1 Whiten, W.J. and White, M.E., 1977. Modelling and simulation of high tonnage crushing plants. In: Proceedings of the 12th International Mineral Processing Congress, vol. II. Sao Paulo, pp. 148–158.
  2. 2.0 2.1 Dehghani, A., Monhemius, A.J. and Gochin, R.J., 2002. Evaluating the Nakajima et al. model for rectangular-aperture screens. Minerals engineering, 15(12), pp.1089-1094.
  3. 3.0 3.1 Firth, B. and Hart, G., 2008. Some aspects of modeling partition curves for size classification. International journal of coal preparation and utilization, 28(3), pp.174-187.