Fine Wet Screen (Mwale): Difference between revisions

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== Description ==
== Description ==


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


== Model theory ==
== Model theory ==


{{Restricted content}}
{{Under construction|section}}
 
<hide>
[[File:DenseMediumBaguley4.png|thumb|450px|Figure 1. Example of the partition curves generated by the Baguley dense medium drum model (lines) for an industrial data set (markers) (after Baguley, 1988.{{Baguley (1988)}}). Chart series represent density classes.]]
 
[[File:DenseMediumBaguley5.png|thumb|450px|Figure 2. Example of the partition curves generated by the Baguley dense medium drum model (lines) for the same industrial data set (markers) as Figure 1 (after Baguley, 1988.{{Baguley (1988)}}). Chart series represent size intervals.]]
 
Baguley and Napier-Munn (1996) proposed a model of dense-medium drum separators where the partitioning behaviour is related to the hydrodynamic properties of particles, such as terminal velocity in a fluid.{{Baguley and Napier-Munn (1996)}}
 
An empirical function is adopted for the fraction of feed particles reporting to the sinks stream, <math>P</math> (frac):
 
:<math>
P_{ij} =
\begin{cases}
\left [ 1 - (V_{100} - V_{{\rm t}_{ij}})^2 \right]^x & V_{\rm t} < V_{100}\\
1 & V_{\rm t} \geq V_{100}
\end{cases}
</math>
 
where particle size effects are incorporated via the <math>x</math> term:
 
:<math>\ln(x) = \dfrac{A}{{\bar d_i}^2} + B</math>
 
and:
* <math>i</math> is the index of the size interval, <math>i = \{1,2,\dots,q\}</math>, <math>q</math> is the number of size intervals
* <math>j</math> is the index of the density class, <math>j = \{1,2,\dots,m\}</math>, <math>m</math> is the number of density classes
* <math>V_{100}</math> is the terminal velocity of particles of which 100% report to sinks (m/s)
* <math>V_{\rm t}</math> is the terminal velocity of particles (m/s)
* <math>A</math> is a coefficient of the size expression (-)
* <math>B</math> is constant of the size expression (-)
* <math>\bar d_{i}</math> is the [[Conversions|geometric mean size]] of particles in size interval <math>i</math> (mm)
 
In order to compute the terminal velocity, the series of expressions described below are used.
 
The dimensionless terminal velocity, <math>V_{\rm t}^* </math>, is computed for each particle size (<math>i</math>) and density class (<math>j</math>) from:
 
:<math>V_{\rm t}^* = \dfrac{{\delta_0}^2}{4d^*} \left [ \left ( 1 + \dfrac{4{d^*}^{1.5}}{{C_0}^{0.5} {\delta_0}^2} \right )^{0.5} - 1 \right ]^2</math>
 
where <math>d^*</math> is the dimensionless particle size computed from:
 
:<math>d^* = \dfrac{\bar d}{p}</math>
 
and <math>\bar d</math> is the [[Conversions|geometric mean size]] of particles in a size interval (with units of m in the <math>d^*</math> equation).
 
The particle-fluid characteristic size parameter, <math>p</math>, is:
 
:<math>p = \left ( \dfrac{3 \mu^2}{4 (\Delta \rho) \rho_{\rm m} g} \right )^{\frac{1}{3}}</math>
 
where:
* <math>\mu</math> is the apparent equivalent Newtonian medium viscosity (Pa.s)
* <math>\Delta\rho</math> is density difference between a particle and the medium (kg/m<sup>3</sup>)
* <math>\rho_{\rm m}</math> is medium density (kg/m<sup>3</sup>)
* <math>g</math> is acceleration due to gravity (m/s<sup>2</sup>)
 
The shape-dependent parameters <math>C_0</math> and <math>\delta_0</math> are calculated from:
 
:<math>\ln C_0 = -5.99k + 1.95</math>
 
:<math>\delta_0 = 9.97k + 2.94</math>
 
where <math>k</math> is a particle shape coefficient, assumed to be 0.225 for spheres.
 
Finally, the particle terminal velocity, <math>v_{\rm t}</math> (m/s), is computed from:
 
:<math>V_{\rm t} = V_{\rm t}^* q</math>
 
where the particle-fluid characteristic velocity parameter, <math>q</math>, is:
 
:<math>q = \left ( \dfrac{4 (\Delta \rho) \mu g}{3 {\rho_{\rm m}}^2} \right )^{\frac{1}{3}}</math>
</hide>


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


<syntaxhighlight lang="vb">=mdUnit_Screen_Mwale(Parameters as Range, Size as Range, Feed as Range, OreSG as Range)</syntaxhighlight>
<syntaxhighlight lang="vb">=mdUnit_Screen_Mwale(Parameters as Range, Size as Range, Feed as Range)</syntaxhighlight>


{{Excel (Text, Help, No Arguments)}}
{{Excel (Text, Help, No Arguments)}}
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:<math>Parameters=
:<math>Parameters=
\begin{bmatrix}
\begin{bmatrix}
K\text{ (t/h.m}^2\text{)}\\
\delta\text{ ((t/h)}^{-1}\text{)}\\
\alpha\text{ (-)}\\
A_{\rm o}\text{ (m}^2\text{)}\\
x_{\rm a} \text{ (mm)}\\
x_{\rm a} \text{ (mm)}\\
A_{\rm o}\text{ (m}^2\text{)}\\
s\text{ (w/w)}\\
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},\;\;\;\;\;\;
\end{bmatrix},\;\;\;\;\;\;


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\vdots & \ddots & \vdots\\  
\vdots & \ddots & \vdots\\  
(Q_{\rm M,F})_{n1}\text{ (t/h)} & \dots & (Q_{\rm M,F})_{nm}\text{ (t/h)}\\  
(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}
\end{bmatrix}
</math>
</math>




where:
where:
* <math>K</math> is the kinetic parameter (t/h.m<sup>2</sup>)
* <math>\delta</math> is a bypass parameter ((t/h)<sup>-1</sup>)
* <math>\alpha</math> is the sharpness parameter (-)
* <math>A_{\rm o}</math> is the screen open area (m<sup>2</sup>)
* <math>x_{\rm a}</math> is the screen aperture (mm)
* <math>s</math> is the mass fraction of solids in the feed slurry (w/w)
* <math>n</math> is the number of size intervals
* <math>n</math> is the number of size intervals
* <math>d_i</math> is the size of the square mesh interval that feed mass is retained on (mm)
* <math>d_i</math> is the size of the square mesh interval that feed mass is retained on (mm)
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* <math>m</math> is the number of ore types
* <math>m</math> is the number of ore types
* <math>Q_{\rm M,F}</math> is feed solids mass flow rate by size and ore type (t/h)
* <math>Q_{\rm M,F}</math> is feed solids mass flow rate by size and ore type (t/h)
* <math>(Q_{\rm M,F})_{\rm L}</math> is the mass flow feed rate of liquids in the feed (t/h)
* <math>\rho_{\rm S}</math> is the density of solids in the feed (t/m<sup>3</sup>)
* <math>\rho_{\rm L}</math> is the density of liquids in the feed (t/m<sup>3</sup>)


=== Results ===
=== Results ===
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\begin{array}{c}
\begin{array}{c}
\begin{bmatrix}
\begin{bmatrix}
\alpha\text{ (-)}\\
E_{\rm US}\\
\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{bmatrix}
\\
\\
\\
\end{array}
\end{array}


\begin{array}{cccccc}
&


\begin{bmatrix}
\begin{bmatrix}
Line 183: Line 101:


\begin{bmatrix}
\begin{bmatrix}
(E_{i \rm o})_1\text{ (frac)}\\
(E_{\rm oa})_1\text{ (frac)}\\
\vdots\\
\vdots\\
(E_{i \rm o})_n\text{ (frac)}
(E_{\rm oa})_n\text{ (frac)}
\end{bmatrix}
\end{bmatrix}


\\
\\
\\
\\
\\
\\


\end{array}
\end{bmatrix}
\end{bmatrix}
</math>
</math>
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where:
where:
* <math>E_{\rm US}</math> is the efficiency of undersize removal achieved by the screen (frac)
* <math>E_{\rm US}</math> is the efficiency of undersize removal achieved by the screen (frac)
* <math>\bar d_{i}</math> is the [[Conversions|geometric mean size]] of particles in size interval <math>i</math> (mm)
* <math>Q_{\rm M,OS}</math> is mass flow rate of solids to the oversize stream (t/h)
* <math>Q_{\rm M,OS}</math> is mass flow rate of solids to the oversize stream (t/h)
* <math>Q_{\rm M,US}</math> is mass flow rate of solids to the undersize stream (t/h)
* <math>Q_{\rm M,US}</math> is mass flow rate of solids to the undersize stream (t/h)
* <math>E_{\rm oa}</math> is the partition to oversize (frac)


=== Example ===
=== Example ===
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|- style="vertical-align:top;"
|- style="vertical-align:top;"
| [[File:FineWetScreenMwale1.png|left|frame|Figure 1. Example showing the selection of the '''Parameters''' (blue frame) array in Excel.]]  
| [[File:FineWetScreenMwale1.png|left|frame|Figure 1. Example showing the selection of the '''Parameters''' (blue frame) array in Excel.]]  
| [[File:FineWetScreenMwale2.png|left|frame|Figure 2. Example showing the selection of the '''Size''' (red frame), '''Feed''' (purple frame) and '''OreSG''' (green frame) arrays in Excel.]]   
| [[File:FineWetScreenMwale2.png|left|frame|Figure 2. Example showing the selection of the '''Size''' (red frame), and '''Feed''' (purple frame) arrays in Excel.]]   
| [[File:FineWetScreenMwale3.png|left|frame|Figure 3. Example showing the outline of the '''Results''' (light blue frame) array in Excel.]]
| [[File:FineWetScreenMwale3.png|left|frame|Figure 3. Example showing the outline of the '''Results''' (light blue frame) array in Excel.]]
|}
|}
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== SysCAD ==
== SysCAD ==


The sections and variable names used in the SysCAD interface are described in detail in the following tables.
{{Under construction|section}}
 
Note that a '''Deck''' and '''Partition''' page is provided for each connected oversize discharge stream.
 
{{SysCAD (Page, Screen, DLL*Screen)}}
 
==== Deck page ====
 
The Deck page is used to specify the required model method and associated input parameters.
 
{{SysCAD (Text, Table Header)}}
 
{{SysCAD (Text, Screen, Deck)}}
 
{{SysCAD (Text, Help Link)}}
 
|-
! colspan="3" style="text-align:left;" |''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
 
{{SysCAD (Text, Screen, Liquids)|method=0}}
 
|-
! colspan="3" style="text-align:left;" |''Results''
|-
|SharpnessConstant / Alpha
|style="background: #eaecf0" | Display
|Mwale model sharpness constant
|-
|BypassConstant / Delta
|style="background: #eaecf0" | Display
|Mwale model bypass constant
|-
|Feed.SQm
|style="background: #eaecf0" | Display
|Mass flow rate of solids in the feed (excludes solids without PSD quality)
|-
|Feed.SQmSubAp
|style="background: #eaecf0" | Display
|Mass flow rate of particles in the feed which are smaller than the aperture size (sub-aperture)
|-
|Feed.Sf
|style="background: #eaecf0" | Display
|Mass fraction of solids in the feed (excludes solids without PSD quality)
|-
|Feed.SLRho
|style="background: #eaecf0" | Display
|Density of slurry in the feed
|-
|SlurryViscosity / mu
|style="background: #eaecf0" | Display
|Apparent viscosity of slurry in the feed
|-
|Efficiency
|style="background: #eaecf0" | Display
|Fraction of total sub-aperture sized material in feed that is actually recovered to the undersize stream.
|}
 
{{SysCAD (Page, Hydrocyclone, Partition)|ActionU=Partition|ActionL=partition|DestinationU=Oversize|DestinationL=oversize|UnitL=screen}}
 
{{SysCAD (Page, About)}}
 
==== Additional notes ====
 
{{SysCAD (Text, No PSD Splits)|gasstream=undersize}}
 
== External links ==
 
* [https://help.syscad.net/Met_Dynamics_-_Screen Met Dynamics - Screen (help.syscad.net)]


== References ==
== References ==

Revision as of 01:53, 15 October 2025

Description

This article describes an implementation of the Mwale (Mwale et al., 2016) model for fine wet screening.[1]

Model theory

Under construction icon-blue.svg.png This section is currently under construction. Please check back later for updates and revisions.

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)

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 the kinetic parameter (t/h.m2)
  • is a bypass parameter ((t/h)-1)
  • is the sharpness parameter (-)
  • is the screen open area (m2)
  • is the screen aperture (mm)
  • is the mass fraction of solids in the feed slurry (w/w)
  • is the number of size intervals
  • is the size of the square mesh interval that feed mass is retained on (mm)
  • , i.e. descending size order from top size () to sub mesh ( 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 efficiency of undersize removal achieved by the screen (frac)
  • is the geometric mean size of particles in size interval (mm)
  • 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 the partition to oversize (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 3. Example showing the outline of the Results (light blue frame) array in Excel.

SysCAD

Under construction icon-blue.svg.png This section is currently under construction. Please check back later for updates and revisions.

References

  1. ↑ Mwale, A.N., Mainza, A.N., Bepswa, P.A., Simukanga, S., Masinja, J.H., 2016. MODEL FOR FINE WET SCREENING. In XXVIII International Mineral Processing Congress Proceedings. Canadian Institute of Mining, Metallurgy and Petroleum.
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