View source for Fine Wet Screen (Mwale)

== Description ==

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

== Model theory ==

{{Under construction|section}}

== Excel ==

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)</syntaxhighlight>

{{Excel (Text, Help, No Arguments)}}

=== Inputs ===

{{Excel (Text, Inputs)}}

:<math>Parameters=
\begin{bmatrix}
x_{\rm a} \text{ (mm)}\\
A_{\rm o}\text{ (m}^2\text{)}\\
s\text{ (w/w)}\\
K\text{ (t/h.m}^2\text{)}\\
\delta\text{ ((t/h)}^{-1}\text{)}\\
\alpha\text{ (-)}\\
\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}
</math>


where:
* <math>x_{\rm a}</math> is the screen aperture (mm)
* <math>A_{\rm o}</math> is the screen open area (m<sup>2</sup>)
* <math>s</math> is the mass fraction of solids in the feed slurry (w/w)
* <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>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+1}<d_i<d_{i-1}</math>, i.e. descending size order from top size (<math>d_{1}</math>) to sub mesh (<math>d_{n}=0</math> mm)
* <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)

=== Results ===

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

:<math>
\mathit{mdUnit\_Screen\_Mwale} = 
\begin{bmatrix}

\begin{array}{c}
\begin{bmatrix}
E_{\rm US}\\
\end{bmatrix}
\\
\\
\\
\end{array}

&

\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{bmatrix}
</math>


where:
* <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,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 ===

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

{| 
|- style="vertical-align:top;"
| [[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), 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.]]
|}

== 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.

{{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
|-
|BypassConstant / Delta
|Input
|Mwale model bypass constant
|-
|SharpnessConstant / Alpha
|Input
|Mwale model sharpness constant

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

|-
! colspan="3" style="text-align:left;" |''Results''
|-
|Feed.Sf
|style="background: #eaecf0" | Display
|Mass fraction of solids in the feed (includes solids without PSD quality)
|-
|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}}

== References ==

[[Category:Excel]]
[[Category:SysCAD]]