AG/SAG Mill (Variable Rates, Dynamic): Difference between revisions

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== Description ==
== Description ==


This article describes a '''''dynamic''''' implementation of the Autogenous (AG) and Semi-Autogenous (SAG) mill model originated by Leung (1987) and extended with variable breakage rates by Morrell and Morrison (1996).{{Napier-Munn et al. (1996)}}{{Leung et al. (1987)}}{{Morrell and Morrison (1996)}}
This article describes a '''''dynamic''''' implementation of the ''Variable Rates'' Autogenous (AG) and Semi-Autogenous (SAG) mill model originated by Leung (1987) and extended with variable breakage rates by Morrell and Morrison (1996).{{Napier-Munn et al. (1996)}}{{Leung et al. (1987)}}{{Morrell and Morrison (1996)}}{{Morrell et al. (2001)}}{{Valery_and_Morrell_(1995)}}


The formulation is referred to in the associated literature as the "Variable Rates" model (Morrell et al., 2001).{{Morrell et al. (2001)}}
The dynamic version uses the same underlying theory and structure as the steady-state Variable Rates AG/SAG mill model. For a full description of the steady-state model, see ''[[AG/SAG Mill (Variable Rates)]]''.


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


{{Under construction|section}}
{{Restricted content}}
 
<hide>
 
[[File:AGSAGVariableRates7.png|thumb|450px|Figure 2. Schematic diagram of internal AG/SAG mill processes (after Napier-Munn et al., 1996).{{Napier-Munn et al. (1996)}}]]
 
{{Model theory (Text, Mill, Perfect Mixing, Population Balance, Dynamic)|Variable Rates AG/SAG|2}}
 
The schematic diagram in Figure 2 illustrates the primary processes of ''feed'', ''breakage'', ''classification'' and ''discharge'' occurring within AG/SAG mills.
 
</hide><div class="user-show">
=== Time step discretisation ===
</div><hide>
 
{{Model theory (Text, Mill, Perfect Mixing, Dynamic, Time Step)}}
 
</hide><div class="user-show">
=== Breakage rates ===
</div><hide>
 
[[File:AGSAGVariableRates12.png|thumb|450px|Figure 3. Breakage rate distribution characterised by cubic spline interpolation.]]
 
{{Model theory (Text, AG/SAG Mill, Variable Rates, Breakage Rates)|3}}
 
</hide><div class="user-show">
 
=== Discharge rates ===
</div><hide>
 
The discharge rates (<math>D_i</math>) are related to the hold-up of slurry in the mill and particle classification at the discharge grates.
 
</hide><div class="user-show">
==== Slurry discharge ====
</div><hide>
 
[[File:AGSAGVariableRates9.png|thumb|450px|Figure 4. Principal dimensions of an AG/SAG mill.]]
 
The volumetric flow rate of slurry discharged from an AG/SAG mill depends on the level of slurry hold-up within the mill, similar to the flow from the bottom of a filled tank. The principal dimensions of an AG/SAG mill required to compute slurry hold-up and other properties are shown in Figure 4.
 
The semi-empirical model proposed by [[Tumbling Mill (Slurry Flow)|Morrell and Stephenson]] (1996) relates the discharge rate to slurry hold-up, grate design, and mill speed using the following equations:{{Morrell_and_Stephenson_(1996)}}
 
{{Model theory (Text, Slurry Flow, Morrell and Stephenson)}}, assume <math>r_{\rm n} = 1</math> for consistency with the steady-state Variable Rates model.
 
The mean radial position of the grate apertures, <math>\gamma</math>, is defined as:
 
:<math>\gamma = \frac{\sum{r_ia_i}}{r_{\rm m} \sum{a_i}}</math>
 
where:
* <math>a_i</math> is the open area of all holes (m<sup>2</sup>) at radial position <math>r_i</math> (m)
* <math>r_{\rm m}</math> is the radius of the mill inside the liners (m)
 
In addition to fine slurry, particles up to the grate aperture size will also discharge from the mill. To estimate total discharge flow rate, <math>Q</math> (m<sup>3</sup>/h), Morrell and Stephenson (1996) suggest the following correction:
 
:<math>Q = k_{\rm g} (Q_{\rm m} + Q_{\rm t})</math>
 
where <math>k_{\rm g}</math> is a factor to account for coarse material, typically taking the values shown in Table 1.
 
:{| class="wikitable"
|+ Table 1. Recommended values for <math>k_{\rm g}</math>.
|-
! Aperture !! <math>k_{\rm g}</math>
|-
| Grates only; <19mm || 1.05 - 1.1
|-
| Grates only; 19mm - 28mm|| 1.1 - 1.15
|-
| Grates >38mm or pebble ports || 1.15 - 1.25
|-
| Pebble port open area > Grate open area|| 1.25
|}
 
The slurry pool discharge coefficient is empirically related to grinding zone coefficient by <math>k_{\rm t} = \frac{935}{6100} k_{\rm m}</math>, based on Morrell and Stephenson's observed values.{{Morrell_and_Stephenson_(1996)}}
 
The net fraction of mill volume occupied by slurry (<math>J_{\rm p}</math>) is defined as the fraction of total mill volume, <math>V</math> (m<sup>3</sup>), occupied by both liquid and solids smaller than the grate aperture size <math>x_{\rm g}</math> (mm).
 
The volume of the mill, <math>V</math>, is calculated as the sum of a cylinder and two right circular frustums:{{Gupta and Yan (2016)}}
 
:<math>V = \pi {R_{\rm m}}^2L + 2 \cdot \bigg[ \dfrac{\pi}{3} (R_{\rm m} - R_{\rm t}) \cdot \tan \alpha_{\rm c} \cdot \left ( {R_{\rm m}}^{2} + R_{\rm m} R_{\rm t} + {R_{\rm t}}^{2} \right) \bigg]</math>
 
where:
* <math>R_{\rm m}</math> is the radius of the mill inside the liners (m), equal to half of the diameter of the mill inside the liners, <math>D</math> (m)
* <math>R_{\rm t}</math> is the radius of the discharge trunnion (m), equal to half of the diameter of the discharge trunnion, <math>D_{\rm t}</math> (m)
* <math>L</math> is the length of the cylindrical (belly) section of the mill (m)
* <math>\alpha_{\rm c}</math> is the cone angle, measured as the angular displacement of the cone surface from the vertical direction (rad)
 
The total open area of the grates, <math>A</math> (m<sup>2</sup>), can be replaced with an expression combining the grate ''open area fraction'',  <math>A_{\rm OF}</math> (m<sup>2</sup>/m<sup>2</sup>), and mill cross-sectional area:
 
:<math>A = \pi \left ( \dfrac{D}{2} \right )^2 A_{\rm OF}</math>
 
The fraction of mill volume occupied by the charge (<math>J_{\rm t}</math>) is computed from the total ore, balls, and liquid content in the mill. See [[#Charge_properties|Charge properties]] below for more detail.
 
The steady-state Variable Rates AG/SAG mill relates slurry hold-up to discharge flow with the following empirical relationship:{{Napier-Munn et al. (1996)}}
 
:<math>L_{\rm V} = m_1 \left ( \dfrac{F}{V} \right )^{m_2}</math>
 
where:
* <math>L_{\rm V}</math> is the fraction of mill volume occupied by below grate size solids and water (v/v)
* <math>F</math> is the volumetric flow rate of slurry discharged from the mill (m<sup>3</sup>/min)
* <math>m_1</math> is a constant related to grate design and mill speed
* <math>m_2</math> is a constant assumed to take the value of 0.5.{{Kojovic et al. (2012)}}
 
Substituting <math>L_{\rm V} = J_{\rm p}</math> and <math>F = Q</math> gives:
 
:<math>m_1 = \dfrac{J_{\rm p}}{\left (\dfrac{Q}{60 \cdot V} \right )^{m_2}} </math>
 
which is provided for compatibility with the steady-state Variables Rates model results.
 
Thus, slurry discharge (<math>Q</math>) can be computed at each time step for the current mill load, mill speed and given grate design.
 
</hide><div class="user-show">
 
==== Classification and discharge ====
</div><hide>
 
[[File:AGSAGVariableRates10.png|thumb|450px|Figure 5. Classification function, <math>C_i</math>, with pebble port open are fraction, <math>f_p</math>, specified.]]
 
[[File:AGSAGVariableRates11.png|thumb|450px|Figure 6. Classification function, <math>C_i</math>, where pebble port open are fraction, <math>f_p</math>, is zero, i.e grates only.]]
 
{{Model theory (Text, AG/SAG Mill, Variable Rates, Classification)}}
 
Figure 5 shows an example classification function with pebble ports included, whilst Figure 6 shows the same function with a grate-only mill.
 
The value of <math>d_{\rm max}</math> is computed at each time step from the current mill load volume and discharge flow rate:
 
:<math>d_{\rm max} = \dfrac{Q}{\dfrac{s_{\rm w}}{\rho_{\rm L}} + \sum\limits_{i=1}^n C_i \dfrac{s_{i}}{\rho_{\rm S}}}</math>
 
where <math>\rho_{\rm S}</math> and <math>\rho_{\rm L}</math> are the densities of solids and liquids in the load, respectively (t/m<sup>3</sup>).
 
</hide><div class="user-show">
 
=== Appearance function ===
 
{{Model theory (Text, AG/SAG Mill, Variable Rates, Appearance Function)}}
 
=== Charge properties ===
</div><hide>
 
The load within the mill is characterised by <math>J_{\rm t}</math> (v/v), the fraction of mill volume occupied by the charge, which includes coarse ore, balls, slurry, and void spaces.
 
Morrell (1992) provides relations for the mass of coarse ore, slurried ore, water and balls in a mill.{{Morrell (1992)}} Converting from mass to fraction of mill volume, these relations are:
 
:<math>\frac{V_{\rm co}}{V} = (J_{\rm t} - J_{\rm B})(1 - \varepsilon), \quad \frac{V_{\rm so}}{V} = J_{\rm t} \varepsilon U S, \quad \frac{V_{\rm L}}{V} = J_{\rm t} \varepsilon U (1 - S), \quad \frac{V_{\rm B}}{V} = J_{\rm B} (1 - \varepsilon)</math>
 
where:
* <math>V_{\rm co}</math>, <math>V_{\rm so}</math>, <math>V_{\rm L}</math>, and <math>V_{\rm B}</math> are the volumes of coarse ore, slurried ore, liquids, and balls in the mill, respectively (m<sup>3</sup>)
* <math>S</math> is the volume fraction of solids in the mill discharge (v/v)
* <math>U</math> is the fraction of void space between the coarse ore particles and balls that is filled with slurry (v/v)
 
The total volume of ore in the mill, <math>V_{\rm o}</math> (m<sup>3</sup>), is computed by the perfect mixing model, i.e.:
 
:<math>V_{\rm o} = \sum_{i=1}^n s_i</math>
 
Subtracting the slurried ore component from the total ore volume, the coarse ore volume is:
 
:<math>\frac{V_{\rm co}}{V} = \frac{V_{\rm o}}{V} - \frac{V_{\rm so}}{V} \implies (J_{\rm t} - J_{\rm B})(1 - \varepsilon) = \frac{\sum_{i=1}^n s_i}{V} - J_{\rm t} \varepsilon U S</math>
 
and rearranging for <math>J_{\rm t}</math> yields:
 
:<math>J_{\rm t} = \dfrac{J_{\rm B} (\varepsilon - 1) - \frac{\sum_{i=1}^n s_i}{V}}{\varepsilon (1 - U S) - 1}</math>
 
The value of <math>U</math> in the above equation is unknown, and is itself a function of <math>J_{\rm t}</math>. To simplify the calculations, <math>J_{\rm t}</math> is estimated for a given mill load and discharge by assuming <math>U = 1</math>.
 
Having computed an estimate for <math>J_{\rm t}</math>, the value of <math>U</math> may be approximated by:
 
:<math>U = \dfrac{L_{\rm V}}{\varepsilon J_{\rm t}}</math>
 
and the apparent density of the charge, <math>\rho_{\rm c}</math>, is:{{Morrell (1992)}}
 
:<math>\rho_{\rm c} =
\begin{cases}
\dfrac{J_{\rm t} \rho_{\rm S} (1 - \varepsilon + \varepsilon U S) + J_{\rm B}( \rho_{\rm B} - \rho_{\rm S})(1 - \varepsilon) + J_{\rm t} \varepsilon U (1 - S)}{J_{\rm t}}, & U \leq 1\\
\dfrac{J_{\rm t} \rho_{\rm S} (1 - \varepsilon + \varepsilon U S) + J_{\rm B}( \rho_{\rm B} - \rho_{\rm S})(1 - \varepsilon) + J_{\rm t} \varepsilon U (1 - S)}{J_{\rm t} [1 + \varepsilon (U - 1)]}, & U > 1\\
\end{cases}
</math>
 
</hide><div class="user-show">
 
=== Slurry filling and discharge ===
</div><hide>
 
The unsteady-state population balance and liquid hold-up models described above compute the quantity of slurry in the mill at each discrete time step.
 
The mill may be in one of a number of slurry filling states at any time:
 
# Empty (balls only, no slurry)
# Charge void space partially filled with slurry
# Charge void space fully filled with slurry and a slurry pool formed at the toe of the tumbling charge
# Charge void space fully filled, slurry pool is overflowing the trunnion of the mill
 
The slurry filling states are illustrated visually in Figure 7 below:
 
:{|
|+ '''Figure 7. Tumbling mill slurry filling states, profile view.'''
|- style="vertical-align:top;"
| [[File:BallMillPerfectMixingDynamic2.png|thumb|325px|1. Empty (balls only, no slurry).]]
| [[File:BallMillPerfectMixingDynamic3.png|thumb|325px|2. Charge void space partially filled with slurry.]]
| [[File:BallMillPerfectMixingDynamic4.png|thumb|325px|3. Charge void space fully filled with slurry and a slurry pool formed at the toe of the tumbling charge.]]
| [[File:BallMillPerfectMixingDynamic5.png|thumb|325px|4. Charge void space fully filled, slurry pool is overflowing the discharge trunnion lip.]]
|}
 
The filling states are numbered are in progressive order as a mill is filled from an empty state. A mill may transition between the states in forward or backward direction during dynamic simulation as the feed and milling conditions change.
 
Slurry will commence discharging from an AG/SAG mill from step 2, once the slurry level inside the charge exceeds the level of the outermost apertures in the grate (<math>r_{\rm n}</math>). The discharge rate then increases as the level of slurry held-up in the mill increases.
 
As described [[#Slurry_discharge|above]], the [[Tumbling Mill (Slurry Flow)|method of Morrell and Stephenson]] (1996) is used to compute the volumetric discharge flow rate of slurry for mill filling states 2 and 3:{{Morrell_and_Stephenson_(1996)}}
 
If the mill continues to fill due to excessive feed rate or insufficient discharge capacity, the slurry level will eventually overflow the trunnion lip (filling state 4). The volumetric discharge rate of pulp from the mill is then, for practical purposes, equal to the instantaneous volumetric feed rate.
 
The quantity of slurry in the mill at the point of trunnion overflow is determined by the mill dimensions and charge geometry. The [[Ball Mill (Overfilling)#Shi|method described by Shi (2016)]] is used to compute the volumetric sum of slurry within the charge void space and slurry pool at the overflow condition.{{Shi_(2016)}}
 
</hide><div class="user-show">
 
=== Power draw===
</div><hide>
 
[[File:BallMillPerfectMixingDynamic6.png|thumb|375px|Figure 8. Simplified charge and slurry pool shapes.]]
 
{{Model theory (Text, Mill Power, Hilden and Powell)|Variable Rates AG/SAG|8}}
 
</hide><div class="user-show">
 
=== Internal mesh series ===
</div><hide>
 
{{Model theory (Text, AG/SAG Mill, Variable Rates, Internal Mesh)}}
 
</hide><div class="user-show">
 
=== Multicomponent modelling ===
</div><hide>
 
{{Model theory (Text, AG/SAG Mill, Variable Rates, Multicomponent)}}
 
</hide><div class="user-show">
 
=== Additional notes ===
</div><hide>
 
</hide><div class="user-show">
==== Breakage rates and mill load ====
</div><hide>
 
An important, and potentially overlooked, limitation of the Variable Rates AG/SAG mill model is the insensitivity of the breakage rate relationships to mill load. Mill simulations should therefore use mill loads close or equal to the load observed during model fitting, or 25% for design activities.{{Bailey et al. (2009)}}
 
</hide><div class="user-show">
==== Slurry pool ====
</div><hide>
 
Published descriptions of the Variable Rates AG/SAG mill suggest that slurry pooling phenomena are excluded from slurry hold-up and power draw estimations.{{Morrell and Morrison (1996)}}{{Kojovic et al. (2012)}}{{Bueno et al. (2013)}}
* The dynamic Variable Rates AG/SAG mill model implemented here reintroduces slurry pooling, which may develop during periods of mill overfilling and is important for accurate unsteady-state simulation.
* The dynamic model remains compatible with the original steady-state formulation when slurry pooling is absent.
 
</hide>


== Excel ==
== Excel ==


{{Under construction|section}}
The dynamic Variable Rates AG/SAG mill model is not implemented in Excel for practical purposes. Excel is not a convenient platform for dynamic simulation and SysCAD (or similar) is preferred.


== SysCAD ==
== SysCAD ==


{{Under construction|section}}
The sections and variable names used in the SysCAD interface are described in detail in the following tables.
 
{{SysCAD (Page, Mill, DLL*Mill)|PowerModels=true|MediaTraj=true|MediaStrings=true}}
 
{{SysCAD (Page, AG/SAG Mill, Variable Rates, Mill)|method=1}}
 
{{SysCAD (Page, AG/SAG Mill, Variable Rates, Ore)}}
 
{{SysCAD (Page, AG/SAG Mill, Variable Rates, Results)}}
 
{{SysCAD (Page, AG/SAGMill, Variable Rates, Ri/Di)}}
 
{{SysCAD (Page, AG/SAGMill, Variable Rates, Load)|Filling=true}}
 
{{SysCAD (Page, Tumbling Mill, Power)|modelpage={{SysCAD (Text, UnitType Prefix)}}Mill|HildenPowell=true}}
 
{{SysCAD (Page, Tumbling Mill, MediaStrings)|modelpage={{SysCAD (Text, UnitType Prefix)}}Mill}}
 
{{SysCAD (Page, Tumbling Mill, MediaTraj)|modelpage={{SysCAD (Text, UnitType Prefix)}}Mill}}
 
{{SysCAD (Page, About)}}


== See also ==
== See also ==


* [[AG/SAG Mill (Variable Rates)]]
* [[AG/SAG Mill (Variable Rates)]]
* [[Tumbling Mill (Slurry Flow)]]
== External links ==
* [https://help.syscad.net/Met_Dynamics_-_Mill Met Dynamics - Mill (help.syscad.net)]
* [https://help.syscad.net/Met_Dynamic_-_Dynamic_Example_Projects#Dynamic_Grinding_Example Dynamic Grinding Example project (help.syscad.net)]


== References ==
== References ==
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[[Category:Excel]]
[[Category:Excel]]
[[Category:SysCAD]]
[[Category:SysCAD]]
[[Category:Dynamic]]

Latest revision as of 05:59, 23 September 2025

Description

This article describes a dynamic implementation of the Variable Rates Autogenous (AG) and Semi-Autogenous (SAG) mill model originated by Leung (1987) and extended with variable breakage rates by Morrell and Morrison (1996).[1][2][3][4][5]

The dynamic version uses the same underlying theory and structure as the steady-state Variable Rates AG/SAG mill model. For a full description of the steady-state model, see AG/SAG Mill (Variable Rates).

Model theory

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Time step discretisation

Breakage rates

Discharge rates

Slurry discharge

Classification and discharge

Appearance function

High energy

Ball load

Low energy

Combined appearance function

Charge properties

Slurry filling and discharge

Power draw

Internal mesh series

Multicomponent modelling

Additional notes

Breakage rates and mill load

Slurry pool

Excel

The dynamic Variable Rates AG/SAG mill model is not implemented in Excel for practical purposes. Excel is not a convenient platform for dynamic simulation and SysCAD (or similar) is preferred.

SysCAD

The sections and variable names used in the SysCAD interface are described in detail in the following tables.

MD_Mill 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 material will pass straight through the mill with no change to the size distribution.
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 product is multiplied back by the same value and returned to the SysCAD product stream.
  • All unit model result values are shown per parallel unit.
Method Fixed Discharge The discharge particle size distribution is user defined. Different distributions can be used for different solids.
AG/SAG (Variable Rates) The Variable Rates AG/SAG mill model (steady-state or dynamic) is used to determine the mill product size distribution. Different parameters can be used for different solids.
Rod Mill (Lynch) The Lynch rod mill model is used to determine the mill product size distribution. Different parameters can be used for different solids.
Ball (Perfect Mixing) The Perfect Mixing ball mill model (steady-state or dynamic) is used to determine the mill product size distribution. Different parameters can be used for different solids.
Stirred (Perfect Mixing) The Perfect Mixing stirred mill model (steady-state or dynamic) is used to determine the mill product size distribution. Different parameters can be used for different solids.
Mill (Herbst-Fuerstenau) The Herbst-Fuerstenau model is used to determine the mill product size distribution. Different parameters can be used for different solids.
PowerModels CheckBox Show alternative mill power model calculations on the Power page.
MediaTrajectory CheckBox Show mill media rolling, sliding and free flight trajectory computations on the MediaTraj page.
MediaStrings CheckBox Show media size distributions at recharge equilibrium on the MediaStrings page.
Options
ShowQFeed CheckBox QFeed and associated tab pages (eg Sp) will become visible, showing the properties of the combined feed stream.
ShowQProd CheckBox QProd and associated tab pages (eg Sp) will become visible, showing the properties of the products.
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.

Mill page

The Mill page is used to specify the input parameters for the mill model.

Tag (Long/Short) Input / Display Description/Calculated Variables/Options
VariableRates
HelpLink ButtonModelHelp.png Opens a link to this page using the system default web browser. Note: Internet access is required.
Mode Steady State
  • The steady-state Variable Rates AG/SAG mill model is used in SysCAD Dynamic simulation mode used instead of the dynamic Variable Rates AG/SAG model described here.
  • This approach may be useful when very large SysCAD step sizes are used and steady-state operation can be assumed between each time step.
Dynamic The dynamic Variable Rates AG/SAG mill model described here is used to determine the mill product size distribution. Different parameters can be used for different solids.
MaxSubStepSize Input The maximum allowed size of internal sub-steps for each SysCAD step.
SubStepSize Display The actual size of internal sub-steps for each SysCAD step.
SubSteps Display The actual number of internal models steps taken per SysCAD step. May be affected by breakage/discharge rates or the user-specified MinSubSteps parameter.
Mill
Diameter Input The inside liner diameter of the mill.
BellyLength Input The inside liner belly length of the mill, excluding cones.
TrunnionDiameter Input The inside liner trunnion diameter of the mill.
ConeAngle Input Angle of the feed and discharge end cones, measured as positive displacement from the vertical direction.
FracCS Input The fraction critical speed of the mill.
Grate
OpenAreaFrac Input Open area fraction of the grate.
PebblePortFrac / fp Input Pebble port area fraction.
PebblePortAperture / xp Input Pebble port aperture size.
GrateAperture / xg Input Grate aperture size.
FineSize / xm Input Fine size, size at which particles behave like water.
MeanRadialPosition / gamma Input Mean radial position of the grate apertures.
SlurryDischCoeff / k Input Slurry discharge coefficient.
Ball
BallLoad Input Ball load fraction.
BallSG Input Density (Specific Gravity) of ball media.
NumBallMeshSizes Input Number of ball mesh sizes below the top size, including the submesh.
BallTopSize Input Top size of new ball media.
Size Input / Display Ball sizing intervals.
Load Input Mass fraction retained of ball media in each ball sizing interval.
RFunction
RSize Display Spline knot positions.
RConst Input Values of at each spline knot position.
Other
ReferenceF80 Input Reference F80 size.
InternalMeshTopSize Input Top size of internal mesh series.
Voidage Input Volumetric fraction of void space in charge.
NetPowerAdjust Input Net Power Adjust factor of mill power equation.

Ore page

This page is used to define the comminution properties of SysCAD species with the size distribution quality in the project.

Tag (Long/Short) Input / Display Description/Calculated Variables/Options
Ore
OreSpecific CheckBox
  • Ore-specific parameters, allows the ore breakage parameters to be separately input for all species.
  • Default is all species have the same set of single input properties.
  • This option is only available if there is more than one species in the project with the size distribution property.
A Input / Display Impact ore breakage parameter.
b Input / Display Impact ore breakage parameter.
ta Input / Display Abrasion ore breakage parameter.
AGSAGVariableRates5.png AGSAGVariableRates6.png

Results page

This page is used to display the model results.

Tag (Long/Short) Input / Display Description/Calculated Variables/Options
Results
Mill Properties
MillVolume Display Internal volume of the mill.
MillSpeed Display Rotational speed of the mill.
MillFeedRate / Feed.SLQv Display Volumetric feed rate of pulp into the mill.
Mill Contents
OreMass Display Mass of ore (solids with PSD) in the mill.
LiquidMass Display Mass of liquids in the mill.
BallMass Display Mass of ball media in the mill.
TotalChargeMass Display Total mass of ore, liquids and balls in the mill.
VolTotalLoad Display Volumetric fraction of mill volume of total charge (ore, liquids, balls and void space).
Mill Discharge
m1 Display Parameter of the Austin mill holdup relationship.
m2 Display Parameter of the Austin mill holdup relationship.
dMax Display Maximum discharge rate of load volume through the grate.
Charge Properties
S20 Display Size of the top (largest) 20% of the load.
ChargeDensity Display Density of the charge.
U Display Fraction of charge void space filled with slurry.
ThetaShoulder Display Angular position of the charge shoulder.
ThetaToe Display Angular position of the charge toe.
ChargeSurfaceRadius Display Radius of the inner charge surface.

RiDi page

This page displays the breakage and discharge rates for each size interval computed by the model.

Tag (Long/Short) Input / Display Description/Calculated Variables/Options
Rates
Size Display Size of each interval in internal mesh series.
MeanSize Display Geometric mean size of each interval in internal mesh series.
R Display Value of breakage rate, , for each size interval, for each ore species.
D Display Value of discharge rate, , for each size interval.
Ecs Display Value of the specific comminution energy for each size interval.

Load page

This page displays information about the balls, solids and liquids that currently comprise the mill load.

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.
Filling
SLCapacity / SLVtCap Display The maximum volume of slurry the mill can contain before overflow.
SLCharge / SLVtCharge Display The maximum volume of slurry that can fill the charge void space.
SLVolume / SLVt Display The total volume of slurry currently in the mill.
SLLevel / SLLvl Display The current slurry volume (SLVolume) as a fraction of the maximum slurry volume before overflow (SLCapacity).
Load
SolidMass / SMt Display The mass of solids with the SysCAD size distribution property currently in the mill.
LiquidMass / LMt Display The mass of liquids currently in the mill.
BallMass / BMt Display The mass of ball media in the mill.
Size Display Size of each interval in the external mesh series.
MeanSize Display Geometric mean size of each interval in the external mesh series.
Load Display The mass of solids with the SysCAD size distribution property currently in the mill, by size and species.}}

Power page

This optional page displays the inputs and results for alternative mill power models. The page is only visible if PowerModels is selected on the MD_Mill page.

Tag (Long/Short) Input / Display Description/Calculated Variables/Options
Power
HildenPowell CheckBox Shows inputs and results for tumbling mill power calculations using the Hilden and Powell method.

MediaStrings page

This page displays the inputs and results for grinding mill media string calculations. The page is only visible if MediaStrings is selected on the MD_Mill page.

MediaTraj page

This page displays the inputs and results for tumbling mill media trajectory calculations. The page is only visible if MediaTrajectory is selected on the MD_Mill page.

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.

See also

External links

References

  1. ↑ Napier-Munn, T.J., Morrell, S., Morrison, R.D. and Kojovic, T., 1996. Mineral comminution circuits: their operation and optimisation. Julius Kruttschnitt Mineral Research Centre, Indooroopilly, QLD.
  2. ↑ Leung, K., Morrison, R.D. and Whiten, W.J., 1987. An Energy Based Ore Specific Model for Autogenous and Semi-autogenous Grinding, Copper 87, Vina del Mar, Vol. 2, pp 71 - 86
  3. ↑ Morrell, S. and Morrison, R.D., 1996. AG and SAG mill circuit selection and design by simulation. In International Conference on Autogenous and Semiautogenous Grinding Technology (Vol. 2, pp. 769-790).
  4. ↑ Morrell, S., Valery, W., Banini, G. and Latchireddi, S., 2001. Developments in AG/SAG mill modelling. Proceedings of Autogenous and Semiautogenous Grinding Technology, Vancouver, pp.71-84.
  5. ↑ Valery Jnr, W. and Morrell, S., 1995. The development of a dynamic model for autogenous and semi-autogenous grinding. Minerals engineering, 8(11), pp.1285-1297.
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