Fine Wet Screen (Mwale)

Description

This article describes an implementation of the Mwale et al. (2016) model for fine wet screening.

Model theory

Efficiency curve

Mwale et al. (2016) proposed a phenomenological model of fine wet screening where the partition to oversize, $E_{i{\rm {o}}}$ (frac), is related to properties of both the screen and the feed:

$E_{i{\rm {o}}}=\exp \left[-{\dfrac {A_{\rm {o}}K}{F_{\rm {f}}s\left({\dfrac {{\bar {d}}_{i}}{a}}\right)^{\alpha }}}\right]+{\dfrac {\delta .F_{\rm {f}}}{100(1-s)}}\left[\exp \left(-{\dfrac {{\bar {d}}_{i}}{a}}\right)\right]^{\alpha }$

where:

• $A_{\rm {o}}$ is the total screen open area (m²)
• $F_{\rm {f}}$ is the solids feed rate (t/h)
• $s$ is the mass fraction of solids in the feed (w/w)
• $x_{\rm {a}}$ is the aperture size (mm)
• ${\bar {d}}_{i}$ is the geometric mean size of the size interval $i$ (mm)
• $K$ is the kinetic constant (t/hr.m²)
• $\alpha$ is the sharpness of separation parameter (-)
• $\delta$ is the fines bypass parameter (h/t)

Sharpness constant

Mwale et al. (2018) suggest the following equation to estimate the sharpness constant, $\alpha$, as a function of screen design and feed conditions:

$\alpha =k_{1}\left({\dfrac {{\rho _{\rm {p}}}^{2}F_{\rm {f}}{A_{\rm {o}}}^{3.5}}{\mu a^{2}{M_{\rm {u}}}^{2}}}\right)+k_{2}\left({\dfrac {A_{\rm {o}}}{a^{2}}}\right)+k_{3}$

where:

• $\rho _{\rm {p}}$ is the density of the feed slurry (t/m³)
• $M_{\rm {u}}$ is the mass flow rate of particles in the feed which are smaller than the aperture (t/h)
• $k_{1}$, $k_{2}$ and $k_{3}$ are coefficients of the sharpness equation

The apparent viscosity of slurry in the feed, $\mu$ (Pa.s), is estimated by the classical Krieger-Dougherty (1959) equation:

$\mu =\mu _{\rm {0}}\left(1-{\dfrac {\phi _{\rm {Eff}}}{\phi _{\rm {m}}}}\right)^{-k\phi _{\rm {m}}}$

where:

• $\mu _{0}$ is the viscosity of the carrier fluid, i.e. water (Pa.s)
• $\phi _{\rm {m}}$ is maximum packing fraction of particles (v/v), assumed to be 0.64
• $k$ is a particle shape constant, assumed to be 2.5

The sharpness constant can be specified directly as the value of coefficient $k_{3}$ when coefficients $k_{1}$ and $k_{2}$ are set to zero.

Bypass constant

Mwale et al. (2018) suggest the following simple linear relationship to estimate the bypass constant, $\delta$,:

$\delta =C_{1}.F_{\rm {f}}+C_{2}.s+C_{3}.x_{\rm {a}}+C_{4}$

where $C_{1}-C_{4}$ are coefficients of the bypass equation.

The bypass constant can be specified directly as the value of coefficient $C_{4}$ when coefficients $C_{1}-C_{3}$ are set to zero.

Excel

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

=mdUnit_Screen_Mwale(Parameters as Range, Size as Range, Feed as Range, OreSG 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:

$Parameters={\begin{bmatrix}x_{\rm {a}}{\text{ (mm)}}\\A_{\rm {o}}{\text{ (m}}^{2}{\text{)}}\\K{\text{ (t/h.m}}^{2}{\text{)}}\\k_{1}{\text{ (-)}}\\k_{2}{\text{ (-)}}\\k_{3}{\text{ (-)}}\\C_{1}{\text{ (-)}}\\C_{2}{\text{ (-)}}\\C_{3}{\text{ (-)}}\\C_{4}{\text{ (-)}}\\(Q_{\rm {M,F}})_{\rm {L}}{\text{ (t/h)}}\\\rho _{\rm {L}}{\text{ (t/m}}^{\text{3}}{\text{)}}\\\mu _{0}{\text{ (mPa.S)}}\\\end{bmatrix}},\;\;\;\;\;\;Size={\begin{bmatrix}d_{1}{\text{ (mm)}}\\\vdots \\d_{n}{\text{ (mm)}}\\\end{bmatrix}},\;\;\;\;\;\;Feed={\begin{bmatrix}(Q_{\rm {M,F}})_{11}{\text{ (t/h)}}&\dots &(Q_{\rm {M,F}})_{1m}{\text{ (t/h)}}\\\vdots &\ddots &\vdots \\(Q_{\rm {M,F}})_{n1}{\text{ (t/h)}}&\dots &(Q_{\rm {M,F}})_{nm}{\text{ (t/h)}}\\\end{bmatrix}},\;\;\;\;\;\;{\mathit {OreSG}}={\begin{bmatrix}(\rho _{\rm {S}})_{1}{\text{ (t/m}}^{\text{3}}{\text{)}}&\dots &(\rho _{\rm {S}})_{m}{\text{ (t/m}}^{\text{3}}{\text{)}}\\\end{bmatrix}}$

where:

• $n$ is the number of size intervals
• $d_{i}$ is the size of the square mesh interval that feed mass is retained on (mm)
• $d_{i+1}<d_{i}<d_{i-1}$, i.e. descending size order from top size ($d_{1}$) to sub mesh ($d_{n}=0$ 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 in the feed (t/h)
• $\rho _{\rm {S}}$ is the density of solids in the feed (t/m³)
• $\rho _{\rm {L}}$ is the density of liquids in the feed (t/m³)

Results

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

${\mathit {mdUnit\_Screen\_Mwale}}={\begin{bmatrix}{\begin{array}{c}{\begin{bmatrix}\alpha {\text{ (-)}}\\\delta {\text{ ((t/h)}}^{-1}{\text{)}}\\F_{\rm {f}}{\text{ (t/h)}}\\s{\text{ (w/w)}}\\\rho _{\rm {p}}{\text{ (t/m}}^{3}{\text{)}}\\\mu {\text{ (Pa.s)}}\\M_{\rm {u}}{\text{ (t/h)}}\\E_{\rm {US}}{\text{ (frac)}}\\\end{bmatrix}}\end{array}}{\begin{array}{cccccc}{\begin{bmatrix}{\bar {d}}_{1}{\text{ (mm)}}\\\vdots \\{\bar {d}}_{n}{\text{ (mm)}}\end{bmatrix}}&{\begin{bmatrix}(Q_{\rm {M,OS}})_{11}{\text{ (t/h)}}&\dots &(Q_{\rm {M,OS}})_{1m}{\text{ (t/h)}}\\\vdots &\ddots &\vdots \\(Q_{\rm {M,OS}})_{n1}{\text{ (t/h)}}&\dots &(Q_{\rm {M,OS}})_{nm}{\text{ (t/h)}}\\\end{bmatrix}}&{\begin{bmatrix}(Q_{\rm {M,US}})_{11}{\text{ (t/h)}}&\dots &(Q_{\rm {M,US}})_{1m}{\text{ (t/h)}}\\\vdots &\ddots &\vdots \\(Q_{\rm {M,US}})_{n1}{\text{ (t/h)}}&\dots &(Q_{\rm {M,US}})_{nm}{\text{ (t/h)}}\\\end{bmatrix}}&{\begin{bmatrix}(E_{i{\rm {o}}})_{1}{\text{ (frac)}}\\\vdots \\(E_{i{\rm {o}}})_{n}{\text{ (frac)}}\end{bmatrix}}\\\\\\\\\\\\\end{array}}\end{bmatrix}}$

where:

• $E_{\rm {US}}$ is the efficiency of undersize removal achieved by the screen (frac)
• $Q_{\rm {M,OS}}$ 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 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) and OreSG (green frame) arrays in Excel.

Figure 3. 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 a Deck and Partition page is 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		Opens a link to this page using the system default web browser. Note: Internet access is required.
Parameters
Aperture / xa	Input	Size of the apertures in the deck.
OpenArea/ Ao	Input	Open area of the screening surface
KineticParameter / K	Input	Mwale model kinetic parameter
SharpnessCoeff1 / k1	Input	Mwale model sharpness coefficient
SharpnessCoeff2 / k2	Input	Mwale model sharpness coefficient
SharpnessCoeff3 / k3	Input	Mwale model sharpness coefficient
BypassCoeff1 / C1	Input	Mwale model bypass coefficient
BypassCoeff2 / C2	Input	Mwale mode3 bypass coefficient
BypassCoeff3 / C3	Input	Mwale model bypass coefficient
BypassCoeff4 / C4	Input	Mwale model bypass coefficient
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
SharpnessConstant / Alpha	Display	Mwale model sharpness constant
BypassConstant / Delta	Display	Mwale model bypass constant
Feed.SQm	Display	Mass flow rate of solids in the feed (excludes solids without PSD quality)
Feed.SQmSubAp	Display	Mass flow rate of particles in the feed which are smaller than the aperture size (sub-aperture)
Feed.Sf	Display	Mass fraction of solids in the feed (excludes solids without PSD quality)
Feed.SLRho	Display	Density of slurry in the feed
SlurryViscosity / mu	Display	Apparent viscosity of slurry in the feed
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		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.