Vibrating Screen (Karra): Difference between revisions

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The basic capacity equation assumes a woven wire mesh screening surface, and is corrected for other surfaces via the <math>OA</math> factor:
The basic capacity equation assumes a woven wire mesh screening surface, and is corrected for other surfaces via the <math>OA</math> factor:


:<math>\mathit{OA} = 21.5 \log_{10} h + 37</math>
:<math>{\rm OA} = 21.5 \log_{10} h + 37</math>


The basic capacity computed above is then adjusted by the open area factor:
The basic capacity computed above is then adjusted by the open area factor:


:<math>\dfrac{A \times \text{Open area fraction (} \% \text{)}}{\mathit{OA}}</math>
:<math>\dfrac{A \times \text{Open area fraction (} \% \text{)}}{{\rm OA}}</math>


where <math>\text{Open area fraction}</math> (%) is the fraction of screening area consisting of apertures.
where <math>\text{Open area fraction}</math> (%) is the fraction of screening area consisting of apertures.
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The deck location factor, <math>D</math> is:
The deck location factor, <math>D</math> is:


:<math>D = 1.1 =0.1 S</math>
:<math>D = 1.1 - 0.1 S</math>


where <math>S</math> is the location of the deck, i.e. <math>S = 1</math> is the top deck, <math>S = 2</math> is the second deck etc.
where <math>S</math> is the location of the deck, i.e. <math>S = 1</math> is the top deck, <math>S = 2</math> is the second deck etc.
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where:
where:
* <math>i</math> is the index of the size interval, <math>i = \{1,2,\dots,n\}</math>, <math>n</math> is the number of size intervals
* <math>i</math> is the index of the size interval, <math>i = \{1,2,\dots,n\}</math>, <math>n</math> is the number of size intervals
* <math>E_{{\rm oc}i}</math> is the fraction of particles of size interval <math>i</math> in the feed reporting to the oversize stream (frac)
* <math>E_{{\rm os}i}</math> is the fraction of particles of size interval <math>i</math> in the feed reporting to the oversize stream (frac)
* <math>\bar d_{i}</math> is the [[Conversions|geometric mean size]] of the size interval <math>i</math> (mm)
* <math>\bar d_{i}</math> is the [[Conversions|geometric mean size]] of the size interval <math>i</math> (mm)


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The screen ''efficiency'' is defined as the fraction of sub-aperture material in the feed that is actually recovered to undersize, i.e.:
The screen ''efficiency'' is defined as the fraction of sub-aperture material in the feed that is actually recovered to undersize, i.e.:


:<math>\text{Efficiency} = \dfrac{ Q_{\rm M, US} }{(Q_{\rm M, F})_{P_{h_{\rm T}}}}</math>
:<math>\text{Efficiency} = \dfrac{ Q_{\rm M, US}}{(Q_{\rm M, F})_{P_{h_{\rm T}}} }</math>


== Excel ==
== Excel ==
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P_{0.5h_{\rm T}}\text{ (frac)}\\
P_{0.5h_{\rm T}}\text{ (frac)}\\
(P_{1.25h_{\rm T}} - P_{0.75h_{\rm T}})\text{ (frac)}\\
(P_{1.25h_{\rm T}} - P_{0.75h_{\rm T}})\text{ (frac)}\\
OA\text{ (frac)}\\
{\rm OA}\text{ (frac)}\\
\text{Required area (m}^2\text{)}\\
\text{Required area (m}^2\text{)}\\
d_{50}\text{ (mm)}\\
d_{50}\text{ (mm)}\\
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The sections and variable names used in the SysCAD interface are described in detail in the following tables.
The sections and variable names used in the SysCAD interface are described in detail in the following tables.


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


{{SysCAD (Page, Screen, DLL*Screen)}}
{{SysCAD (Page, Screen, DLL*Screen)}}
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|User defined factor for adjusting the theoretical screen capacity.
|User defined factor for adjusting the theoretical screen capacity.


{{SysCAD (Text, Screen, Liquids)}}
{{SysCAD (Text, Screen, Liquids)|method=0}}


|-
|-
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|}
|}


{{SysCAD (Page, Hydrocyclone, Partition)}}
{{SysCAD (Page, Hydrocyclone, Partition)|ActionU=Partition|ActionL=partition|DestinationU=Oversize|DestinationL=oversize|UnitL=screen}}


{{SysCAD (Page, About)}}
{{SysCAD (Page, About)}}

Latest revision as of 02:24, 28 October 2023

Description

This article describes the Karra model for vibrating screen classification.[1]

Model theory

Karra provides a method of computing the classification of particles by size on a vibrating screen.[1][2]

Capacity

The capacity of a screen with particular properties is defined by the theoretical undersize transmission rate, (t/h):

where:

  • is the basic capacity of the screen (t/h/m2)
  • is the oversize factor
  • is the half-size factor
  • is the deck location factor
  • is the wet screening factor
  • is the bulk density factor
  • is the near-size factor
  • is a user defined factor
  • is the length x width of the screening area.

Basic capacity (A)

The basic capacity of a screen is defined by the throughfall aperture, (mm), defined as the effective size of the aperture that a particle is presented to:

where:

  • is the actual aperture of the screen (mm)
  • is the width of the wire or distance between apertures (mm)
  • is the angle of inclination of the screen (deg.)

The basic capacity, (t/h/m2), is then:

The basic capacity equation assumes a woven wire mesh screening surface, and is corrected for other surfaces via the factor:

The basic capacity computed above is then adjusted by the open area factor:

where (%) is the fraction of screening area consisting of apertures.

Oversize factor (B)

The oversize factor, is related to the fraction of screen fed which is larger than the throughfall aperture:

where is the fraction of screen feed which is smaller than the throughfall aperture (frac).

Half-size factor (C)

The half-size factor, is related to the fraction of screen fed which is smaller than half the throughfall aperture size, (frac):

Deck location factor (D)

The deck location factor, is:

where is the location of the deck, i.e. is the top deck, is the second deck etc.

Wet screening factor (E)

When spray water is added or slurry is screened, the wet screening factor, , is:

where

For dry screening, .

Bulk density factor (F)

The bulk density (or material weight) factor, , is:

where is the bulk density of the feed (kg/m3). See Properties (Bulk Density) for methods to estimate bulk density based on particle size distribution.

Near-size capacity factor (Gc)

The near-size capacity factor, , is:[1]

where

  • is the fraction of screen feed which is smaller than 1.25 times the throughfall aperture (frac), and
  • is the fraction of screen feed which is smaller than 0.75 times the throughfall aperture (frac).

Classification

The partition of particles to screen oversize is:

where:

  • is the index of the size interval, , is the number of size intervals
  • is the 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)

The value of (mm) is given by:

where is the mass flow rate of particles in the feed that are smaller than the throughfall aperture (t/h).

Load and efficiency

The screen load is defined as the actual rate of transmission to undersize as a fraction of the theoretical rate of transmission to undersize:

A load value less than 1.0 indicates an underloaded, oversized screen, and greater than 1.0 an overloaded, undersized screen.

A load value of 1.0 indicates the screen is sized exactly for the feed duty. Therefore, the screening area required to treat a given feed is:

The screen efficiency is defined as the fraction of sub-aperture material in the feed that is actually recovered to undersize, i.e.:

Excel

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

=mdUnit_Screen_Karra(Parameters as Range, Size as Range, Feed 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 wet screening factor, , should be applied (True/False)
  • is the length of the screening surface in the direction of flow (m)
  • is the width of the screening surface transverse to the direction of flow (m)
  • 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 mass flow rate of solids to the oversize stream (t/h)
  • is mass flow rate of solids to the undersize stream (t/h)
  • is partition fraction of feed solids to the oversize stream (frac)

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), and Feed (purple frame) arrays in Excel.
Figure 4. 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
FeedBulkDensity / RhoBulk Input The bulk density of the feed solids.
DeckLocation / S Input Deck location, 1 = First, 2 = Second etc.
DeckInclination / Theta Input Angle of inclination of the deck.
WetScreening Input Indicates if the deck is wet screening (sprays, slurry etc).
ScreenLength Input Length of the screen.
ScreenWidth Input Width of the screen.
Aperture / h Input Size of the apertures in the deck.
WireDiameter / dw Input Diameter of the wire in the woven mesh screening surface (or distance between apertures).
OpenAreaFraction / ActualOA Input Open area fraction of the deck.
CustomFactor Input User defined factor for adjusting the theoretical screen capacity.
Liquids
LiquidsSeparMethod Split To OS (User) Liquids are split to oversize by a user-defined fraction of liquids in the feed.
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
ScreenArea Display Area of the deck.
ThroughfallAperture/ hT Display Effective aperture size experienced by particles falling under gravity.
BasicCapacity / A Display Basic capacity of the screen.
OversizeFactor / B Display Particle oversize screen capacity factor.
HalfsizeFactor / C Display Particle halfsize screen capacity factor.
OversizeFactor / B Display Oversize screen capacity factor.
DeckLocationFactor / D Display Deck location screen capacity factor.
WetScreeningFactorT / T Display Wet screening screen capacity factor calculation parameter.
WetScreeningFactor / E Display Wet screening screen capacity factor.
NearSizeFactor / Gc Display Particle near-size screen capacity factor.
TheoreticalUndersize / Th Display Theoretical undersize transmission rate of the deck.
LoadingCoefficient / K Display Ratio of flow rate of sub aperture material in the feed to the theoretical screen capacity.
Halfsize Display Fraction of feed smaller than half the throughfall aperture.
Nearsize Display Fraction of feed near the throughfall aperture size.
Oversize Display Fraction of feed larger than the throughfall aperture.
OpenAreaWire / OA Display Estimated open area fraction of woven wire mesh.
RequiredArea Display Screening area required to treat feed stream at 100% loading.
d50 Display Size at which the 50% of the feed particle mass is partitioned to oversize.
Load Display Ratio of mass flow of actual undersize to theoretical transmission rate to undersize of screen.
Efficiency Display Fraction of total sub-aperture sized material in feed that is actually recovered to the undersize stream.

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 1.2 Karra, V.K., 1979. Development of a model for predicting the screening performance of a vibrating screen. CIM Bull.;(United States), 72(804).
  2. King, R.P., 2012. Modeling and Simulation of Mineral Processing Systems. Elsevier.