Dewatering Screen (Ng)

Description

This article describes the Ng (1990) model for a dewatering screen, with additions for particle classification.

Model theory

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Dewatering

Bed transport

Dewatering rate

Dewatering capacity

Classification

Simple partition

Partition by size

Additional notes

Excel

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

=mdUnit_Screen_Dewatering_Ng(Parameters as Range, Size as Range, Feed as Range, Optional 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 ($i$) x column ($j$) format:

${\mathit {Parameters}}={\begin{bmatrix}{\text{Classification Method}}\\h{\text{ (mm)}}\\L{\text{ (m)}}\\w{\text{ (m)}}\\N{\text{ (rpm)}}\\A{\text{ (m)}}\\\theta {\text{ (deg.)}}\\\zeta {\text{ (deg.)}}\\S_{\infty }{\text{ (w/w)}}\\p{\text{ (-)}}\\q_{1}{\text{ (-)}}\\q_{2}{\text{ (-)}}\\a{\text{ (-)}}\\b_{1}{\text{ (-)}}\\b_{2}{\text{ (-)}}\\d_{\rm {AR}}{\text{ (mm/mm)}}\\R_{\rm {f}}{\text{ (frac)}}\\\lambda \\(E_{\rm {US}})_{\rm {T}}{\text{ (frac)}}\\n_{\rm {L}}{\text{ (/m)}}\\(Q_{\rm {M,F}})_{\rm {L}}{\text{ (t/h)}}\\\end{bmatrix}},\;\;\;\;\;\;{\mathit {Size}}={\begin{bmatrix}d_{1}{\text{ (mm)}}\\\vdots \\d_{n}{\text{ (mm)}}\\\end{bmatrix}},\;\;\;\;\;\;{\mathit {Feed}}={\begin{bmatrix}(Q_{\rm {M,F}})_{11}{\text{ (t/h)}}&\dots &(Q_{\rm {M,F}})_{1m}{\text{ (t/h)}}\\\vdots &\ddots &\vdots \\(Q_{\rm {M,F}})_{n1}{\text{ (t/h)}}&\dots &(Q_{\rm {M,F}})_{nm}{\text{ (t/h)}}\\\end{bmatrix}},\;\;\;\;\;\;{\mathit {Rows}}={\begin{bmatrix}L_{1}{\text{ (m)}}&(D_{1})_{1}{\text{ (mm)}}&(D_{2})_{1}{\text{ (mm)}}&(f_{\rm {o}})_{1}{\text{ (m}}^{2}{\text{/m}}^{2}{\text{)}}\\\vdots &\vdots &\vdots &\vdots \\L_{p}{\text{ (m)}}&(D_{1})_{p}{\text{ (mm)}}&(D_{2})_{p}{\text{ (mm)}}&(f_{\rm {o}})_{p}{\text{ (m}}^{2}{\text{/m}}^{2}{\text{)}}\\\end{bmatrix}}^{*}\;\;\;\;\;\;$

where:

• ${\text{Classification Method}}$ indicates whether the model applies a user-specified $n_{L}$ parameter or solves the $n_{L}$ value required to achieve a user-specified target efficiency (0 = Simple (US Partition = Rw), 1 = Whiten (Efficiency = R_w), 2 = Whiten (Specify n_L), 3 = Whiten (Specify Efficiency))
• $n_{\rm {L}}$ is number of trials parameter (/m) applied if ${\text{Method}}=2$, ignored otherwise
• $(E_{\rm {US}})_{\rm {T}}$ is the target screen efficiency (frac) if ${\text{Method}}=3$, ignored otherwise
• $d_{i}$ is the size of the square mesh interval that feed mass is retained on (mm)
• $m$ is the number of ore types
• $Q_{\rm {M,F}}$ is feed solids mass flow rate by size and ore type (t/h)
• $(Q_{\rm {M,F}})_{\rm {L}}$ is the mass flow feed rate of liquids to the screen (t/h)
• $^{*}$ indicates the ${\mathit {Rows}}$ array is only required when the ${\text{Classification Method}}$ is 1, 2 or 3 (Whiten classification).

Results

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

$mdUnit\_Screen\_Dewatering\_Ng={\begin{bmatrix}{\begin{array}{c}{\begin{bmatrix}{\text{Iterations}}\\\omega {\text{ (rad/s)}}\\A_{x}{\text{ (m)}}\\A_{y}{\text{ (m)}}\\G_{y}{\text{ (-)}}\\b{\text{ (-)}}\\q{\text{ (-)}}\\{\dot {X}}{\text{ (-)}}\\u{\text{ (m/s)}}\\t{\text{ (s)}}\\S_{0}{\text{ (w/w)}}\\S{\text{ (w/w)}}\\S_{\rm {actual}}{\text{ (w/w)}}\\F_{80}{\text{ (mm)}}\\W{\text{ (t/h.m)}}\\Q_{\rm {W}}{\text{ (t/h)}}\\{\text{Load (frac)}}\\R_{\rm {US}}{\text{ (frac)}}\\R_{\rm {w}}{\text{ (frac)}}\\(E_{\rm {US}})_{\rm {A}}\\n_{\rm {L}}{\text{ (/m)}}\\\end{bmatrix}}&\\&\\\end{array}}&{\begin{array}{c}{\begin{bmatrix}{\bar {d}}_{1}{\text{ (mm)}}\\\vdots \\{\bar {d}}_{n}{\text{ (mm)}}\end{bmatrix}}&{\begin{bmatrix}(Q_{\rm {M,OS}})_{11}{\text{ (t/h)}}&\dots &(Q_{\rm {M,OS}})_{1m}{\text{ (t/h)}}\\\vdots &\ddots &\vdots \\(Q_{\rm {M,OS}})_{n1}{\text{ (t/h)}}&\dots &(Q_{\rm {M,OS}})_{nm}{\text{ (t/h)}}\\\end{bmatrix}}&{\begin{bmatrix}(Q_{\rm {M,US}})_{11}{\text{ (t/h)}}&\dots &(Q_{\rm {M,US}})_{1m}{\text{ (t/h)}}\\\vdots &\ddots &\vdots \\(Q_{\rm {M,US}})_{n1}{\text{ (t/h)}}&\dots &(Q_{\rm {M,US}})_{nm}{\text{ (t/h)}}\\\end{bmatrix}}&{\begin{bmatrix}(E_{\rm {oa}})_{1}{\text{ (frac)}}\\\vdots \\(E_{\rm {oa}})_{n}{\text{ (frac)}}\end{bmatrix}}\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\end{array}}\end{bmatrix}}$

where:

• $(E_{\rm {US}})_{\rm {A}}$ is the actual efficiency of undersize removal achieved by the screen (frac)
• $n_{\rm {L}}$ is number of trials parameter (/m) specified by the user if ${\text{Classification Method}}=2$, or required to achieve the target efficiency if ${\text{Classification Method}}=1{\text{ or }}3$
• $Q_{\rm {M,OS}}$ is mass flow rate of solids to the oversize stream (t/h)
• $Q_{\rm {M,US}}$ 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 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.
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.

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.
	Dewatering (Ng)	The Ng dewatering screen model is used to determine the moisture content of oversize material, and the partition of solids to oversize and undersize for each size interval.
HelpLink		Opens a link to this page using the system default web browser. Note: Internet access is required.
Parameters
Classification	Simple (US Partition = Rw)	The partition to US for each size interval smaller than the aperture size is set to equal the fraction of water recovered to US (Rw).
	Whiten (Efficiency =R w)	The Whiten vibrating screen model is used to determine the classification partition. The screening efficiency is set to equal the fraction of water recovered to US (Rw).
	Whiten (Specify nL)	The Whiten vibrating screen model is used to determine the classification partition. The user specifies the value of the nL parameter and efficiency is computed.
	Whiten (Specify Efficiency)	The Whiten vibrating screen model is used to determine the classification partition. The value of the nL parameter is adjusted to achieve a user-specified target efficiency value.
ScreenAperture / h	Input / Display	Representative screen aperture. Set to smallest row aperture dimension if Whiten classification method selected above.
ScreenLength / L	Input / Display	Length of screening surface. Set to sum of row lengths if Whiten classification method selected above.
ScreenWidth / w	Input	Width of the screening surface.
VibFrequency / N	Input	Vibrational frequency of the screen motion.
VibAmplitude	Input	Amplitude of vibration of the screen motion.
DeclinationAngle / Theta	Input	Angle of declination of the screen.
VibrationAngle / Zeta	Input	Angle of vibrational motion of the screen, relative to the screening surface.
SaturationMoisture / Sinf	Input	Minimum possible moisture content of material at infinite dewatering time.
SolidsParameter / p	Input	Kinetic equation parameter for solid material.
ApertureParameter1 / q1	Input	Constant of the kinetic exponent mesh size equation.
ApertureParameter2 / q2	Input	Coefficient of the kinetic exponent mesh size equation.
VelocityParameter / a	Input	Coefficient of transport velocity equation.
SlopeParameter1 / b1	Input	Constant of the screen slope transport velocity exponent equation.
SlopeParameter2 / b2	Input	Coefficient of the screen slope transport velocity exponent equation.
nL	Input	User specified value of the nL parameter. Only visible if the Whiten (Specify nL) classification method is selected above.
Efficiency	Input	User specified target value of screen efficiency. Only visible if Whiten (Specify Efficiency) classification method is selected above.
ParticleAspectRatio / ParticleAR	Input	Value of the particle aspect ratio, i.e. (second longest dimension):(longest dimension). Only visible if a Whiten classification method is selected above.
Rf	Input	Fines recovery parameter, fraction of the finest particles or liquids split to oversize stream. Only visible if a Whiten classification method is selected above.
Lambda	Input	Fines recovery parameter, shape factor. Only visible if a Whiten classification method is selected above.
Rows
NumRows	Input	Number of screen panel rows. Only visible if a Whiten classification method is selected above.
L	Input	Length of the row in the direction of travel. Only visible if a Whiten classification method is selected above.
ApertureL / D1	Input	Aperture length. Only visible if a Whiten classification method is selected above.
ApertureW / D2	Input	Aperture width. Only visible if a Whiten classification method is selected above.
OpenArea / fo	Input	Open area fraction of the row. Only visible if a Whiten classification method is selected above.
Liquids
LiquidsSeparMethod	Split To OS (User)	Liquids are split to oversize by a user-defined fraction of liquids in the feed.
	Dewatering (S)	Final moisture content of oversize (S) is determined by the Ng dewatering screen method.
	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
Iterations	Display	Number of iterations required to set US partition or screening efficiency equal to water recovery to US (Rw) value. Only visible if Simple (US Partition = Rw) or Whiten (Efficiency = Rw) classification method is selected above.
AngularVibSpeed / Omega	Display	Angular speed of vibration of the screening surface.
ParallelVibAmp / Ax	Display	Amplitude of vibration of screen motion in direction parallel to screening surface.
NormalVibAmp / Ay	Display	Amplitude of vibration of screen motion in direction normal to screening surface.
AccelerationRatio / Gy	Display	Ratio of gravitational to vibrational acceleration of screen surface motion.
VelIncParameter / b	Display	Value of the transport velocity equation exponent.
MeshProperty / q	Display	Value of the kinetic equation exponent.
DimTransportVelocity / Xdot	Display	Dimensionless transport velocity.
TransportVelocity / u	Display	Transport velocity of material along screen.
DewateringTime / t	Display	Residence time of material on screen during dewatering.
FeedMoisture / S0	Display	Moisture content of screen feed material.
OversizeMoisture / S	Display	Predicted moisture content of dewatered screen oversize material.
ActualOSMoisture / Sactual	Display	Actual, realised moisture content of dewatered screen oversize material.
WaterRecoveryToUS / Rw	Display	Fraction of feed water recovered to screen undersize stream.
ActualEfficiency	Display	Actual efficiency achieved by screen model. Only visible if a Whiten classification method is selected above.
nL	Display	Actual value of screen classification kinetic parameter. Only visible if a Whiten classification method is selected above.
SpecScreenCapacity / W	Display	Specific dewatering capacity of screen (per unit width).
ScreenCapacity	Display	Maximum dewatering capacity of screen.
Feed.SQm	Display	Feed rate of solids to screen.
ScreenLoad	Display	Ratio of screen solids feed rate to screen capacity.

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 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.
CmpPartition
Components		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 oversize of all solid components, for each size interval. Excludes solid components not present in the screen feed.
CmpPartition	Display	Partition to oversize 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 screen 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 oversize. Excludes solid components not present in the screen feed.
All (All row, per component)	Display	Actual overall partition to oversize for each solid component, for all size intervals in that component. Excludes solid components not present in the screen feed.
ElePartition
Elements		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 oversize of all solid elements, for each size interval. Excludes solid elements not present in the screen feed.
ElePartition	Display	Partition to oversize 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 screen 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 oversize. Excludes solid elements not present in the screen feed.
All (All row, per element)	Display	Actual overall partition to oversize for each solid element, for all size intervals in that component. Excludes solid elements not present in the screen feed.
IPhPartition
IPhases		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 oversize of all solid individual phases, for each size interval. Excludes solid individual phases not present in the screen feed.
IPhPartition	Display	Partition to oversize 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 screen 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 oversize. Excludes solid individual phases not present in the screen feed.
All (All row, per individual phase)	Display	Actual overall partition to oversize for each solid individual phase, for all size intervals in that component. Excludes solid individual phases 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		Opens a link to the Installation and Licensing page using the system default web browser. Note: Internet access is required.
Information		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		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

• Vibrating Screen (Whiten)
• Partition (Size, Whiten and White)

External links

• Met Dynamics - Screen (help.syscad.net)
• Gravity, Dense Medium, and Magnetic Separation Example project (help.syscad.net)