AG/SAG Mill (Variable Rates, Dynamic)

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).

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		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 ${\mathit {RConst}}$ 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.

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, $R_{i}$, for each size interval, for each ore species.
D	Display	Value of discharge rate, $D_{i}$, 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		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.

See also

• AG/SAG Mill (Variable Rates)
• Tumbling Mill (Slurry Flow)

External links

• Met Dynamics - Mill (help.syscad.net)
• Dynamic Grinding Example project (help.syscad.net)