HPGR (Morrell-Tondo-Shi)

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Description

This article describes the Morrell-Tondo-Shi (Morrell et al., 1997) model for comminution by High Pressure Grinding Rolls (HPGR), verified for simulation and scale-up by Daniel and Morrell (2004).[1][2]

Model theory

Figure 1. Schematic diagram showing the Whiten crusher sub-model arrangement of the Morrell-Shi-Tondo approach (after Morrell et al., 1997).[1]

The Morrell-Tondo-Shi (Morrell et al., 1997) model simulates HPGR size reduction by linking three separate instances of the Whiten crusher model.[1] The crusher instances represent comminution by the sub-processes of pre-crushing, edge crushing, and compressed bed crushing, as illustrated in Figure 1.

Pre, edge and bed crushers

Main article: See Crusher (Whiten) for a full description of the Whiten crusher model.

Behaviour of the pre-crusher process is determined by the critical gap, (mm), which is defined as the largest particle in the feed which will be nipped and comminuted in the HPGR machine. The critical gap can be estimated by the relation:

where:

  • is the diameter of the rolls (m)
  • is the working gap (m)
  • is the bulk density of the discharge cake solids (t/m3)
  • is the bulk density of the feed solids (t/m3)

The pre, edge and bed Whiten crusher parameter values in Table 1 are recommended by Morrell et al. (1997):

Whiten crusher parameter values for the Morrell-Tondo-Shi HPGR model (after Morrell et al., 1997).[1]
Pre-crusher Edge crusher Bed crusher

Particles in the pre-crusher and edge crusher zones are assumed to undergo a single-particle breakage process, much like a conventional cone crusher:

  • The appearance function and energy-size reduction parameters determined from drop weight tests characterise single particle breakage behaviour.

Particles in the bed crusher are subject to contact forces from surrounding particles and undergo a compressed bed breakage process:

  • Compressed bed appearance function and energy-size reduction parameters may be determined from piston and die tests, and are notably different from the single particle breakage parameters for the same ore.
  • The appearance function and energy-size reduction matrices for compressed bed breakage are specified at intervals, rather than the intervals of single particle breakage, due to the additional size reduction obtained from HPGR devices.

Edge split

The split of pre-crushed material to the edge crusher process, (frac), is given by:

where:

  • is the edge split factor (-)
  • is the length of the rolls (m)

Throughput

The throughput capacity of an HPGR machine may be estimated from:[2]

where

  • is the HPGR throughput solids mass flow rate (t/h)
  • is the circumferential velocity of the rolls (m/s)
  • is the length of the rolls (m)
  • is the working gap (m)
  • is the discharge cake solids bulk density (t/m3)

The parameter is a correction factor applied to the theoretical throughput to account for material slip at the rolls face:

where is the measured throughput of an HPGR unit (t/h) and is the theoretical throughput calculated from (t/h).

Morrell et al. (1997) suggests material slip is a function of rolls speed and the dimensionless rolls gap, and that the correction factor exhibits a linear relationship of the form , i.e.:

The parameters and can be determined from measurements on an operating HPGR at various throughputs, roll speeds and working gaps.

Power

The gross power draw of the HPGR machine, (kW), is computed as:

where:

  • is the no-load (idling) power draw of the machine (kW)
  • is the power draw estimated by the pre-crusher model (kW)
  • is the power draw estimated by the edge crusher model (kW)
  • is the power draw estimated by the compressed bed crusher model (kW)
  • and are user-defined scaling factors that correct model-estimated power to observed power (kW/kW)

The specific comminution energy, (kWh/t), of an HPGR is defined as:

Excel

The Morrell-Tondo-Shi HPGR model may be invoked from the Excel formula bar with the following function call:

=mdUnit_HPGR_MorrellTondoShi(Parameters as Range, Size as Range, HPGRFeed as Range, SP_Appearance as Range, SP_Ecst10Size-t10-size as Range, Bed_Appearance as Range, Bed_Ecst10Size 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 number of size intervals
  • is the number of ore types
  • is the size of the square mesh interval that mass is retained on (mm)
  • , i.e. descending size order from top size () to sub mesh ( mm)
  • is the mass flow rate of particles in the crusher feed (t/h)
  • is the fraction of mass passing one-th the size of a parent particle (%) when passes one-tenth the size of a parent particle (%), , and or
  • is the size of a parent particle subject to breakage for Energy-Size Reduction relationship testing (mm)
  • is the number of particle sizes subject to breakage for Energy-Size Reduction relationship testing
  • is the specific comminution energy required to break a parent particle of size into a distribution of progeny particles with passing one-tenth of the parent size (kWh/t)
  • the subscript indicates properties associated with single particle breakage
  • the subscript indicates properties associated with bed compression breakage

Results

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

where:

  • is the mass flow rate of particles in the overall, combined product (t/h)
  • is the mass flow rate of particles in the edge product (t/h)
  • is the mass flow rate of particles in the bed (centre) product (t/h)

Example

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

Figure 2. Example showing the selection of the Parameters (blue frame) array in Excel.
Figure 2. Example showing the selection of the Size (red frame) and HPGRFeed (purple frame) arrays in Excel.
Figure 4. Example showing the selection of the Single Particle Appearance (green frame), Single Particle Energy-Size Reduction (pink frame), Compressed Bed Appearance (brown frame), and Compressed Bed Energy-Size Reduction (teal frame) arrays in Excel.
Figure 5. 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.

MD_HPGR 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 crusher with no change to the size distribution.
Method Fixed Discharge The discharge particle size distribution is user defined. Different distributions can be used for different solids.
Morrell-Shi-Tondo The throughput, power draw and product size distribution are determined by the Morrell-Tondo-Shi model. Different parameters can be used for different solids.
Torres The throughput, power draw and product size distribution are determined by the Torres model. Different parameters can be used for different solids.
Campos The throughput, power draw and product size distribution are determined by the Campos model. Different parameters can be used for different solids.
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.

HPGR page

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

Tag (Long/Short) Input / Display Description/Calculated Variables/Options
MorrellTondoShi
HelpLink ButtonModelHelp.png Opens a link to this page using the system default web browser. Note: Internet access is required.
Requirements
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.
Parameters
RollDiameter / D Input Diameter of the rolls.
RollLength / L Input Length of the rolls.
RollSpeed / U Input Circumferential velocity of the rolls.
Working gap / xg Input Working gap between the rolls.
FeedBulkDensity / Rhoc Input Bulk density of the feed solids.
CakeDensity / Rhog Input Bulk density of the discharge cake solids.
SplitFactor / g Input Edge split factor.
CpA Input Throughput relationship parameter.
CpB Input Throughput relationship parameter.
NoLoadPower Input No-load power draw of machine.
PowerCoeffEdge / kPEdge Input Power coefficient of edge crusher.
PowerCoeffBed / kPBed Input Power coefficient of bed crusher.
Whiten
K1Factor Input K1 parameter scaling factor for Pre and Edge crushers.
K1 Input / Display K1 parameter for Pre, Bed and Edge crushers.
K2 Display K2 parameter for Pre, Bed and Edge crushers.
K3 Input K3 parameter for Pre, Bed and Edge crushers.
t10 Input t10 parameter for Pre, Bed and Edge crushers.
Results
CriticalGap / xc Display Critical gap.
EdgeSplit / f Display Edge split fraction.
Cp Display Throughput scaling factor.
Throughput / Q Display Maximum throughput of HPGR unit.
GrossPower Display Gross power draw of HPGR unit.
Ecs Display Specific comminution energy of HPGR unit.

Ore page

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

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.
View
ColumnView CheckBox Arranges the Appearance and Energy-Size Reduction data in table format (default) or column view.

CrusherWhiten6.png CrusherWhiten7.png

Appearance
OreSpecific CheckBox Ore-specific parameters, allows the Appearance data 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.
Appearance Input Appearance function data
CrusherWhiten8.png CrusherWhiten9.png
Ecs
NumEcsSizes Input The number of original particle sizes for which Energy-Size Reduction data was obtained in the JK Drop Weight test (usually three or five).
OreSpecific CheckBox Ore-specific parameters, allows the Energy-Size Reduction data to be separately input for all species. Default is all species have the same set of single input properties.
Ecs Input Energy-Size Reduction data

CrusherWhiten10.png CrusherWhiten11.png

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.

Additional notes

When the edge stream is connected, the following applies to mass splits:

  • Solid species without a particle size distribution property are split to the edge stream 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.
  • Liquids species are split between the edge and product streams in the same proportion as solid species.
  • Gas phase species report directly to the product stream without split.

References

  1. 1.0 1.1 1.2 1.3 Morrell, S., Tondo, L.A., and Shi, F., 1997. Modelling and scale-up of high pressure grinding rolls. In Proc. XX International Mineral Processing Congress, Aachen, Germany, September 1997.
  2. 2.0 2.1 Daniel, M.J. and Morrell, S., 2004. HPGR model verification and scale-up. Minerals Engineering, 17(11-12), pp.1149-1161.