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

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* <math>D_{\rm L}</math> is the discharge rate of liquids from the mill, normally assumed to equal <math>D_n</math> (h<sup>-1</sup>).
* <math>D_{\rm L}</math> is the discharge rate of liquids from the mill, normally assumed to equal <math>D_n</math> (h<sup>-1</sup>).


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=== Calculation sequence ===
=== Calculation sequence ===
</div><hide>


The Variable Rates AG/SAG model uses a range of sub-models to quantify the breakage rate (<math>R</math>), appearance function (<math>A</math>), and discharge function (<math>D</math>) terms of the perfect mixing model, and hence compute the mill load (<math>s</math>) and product (<math>p</math>) at steady-state.
The Variable Rates AG/SAG model uses a range of sub-models to quantify the breakage rate (<math>R</math>), appearance function (<math>A</math>), and discharge function (<math>D</math>) terms of the perfect mixing model, and hence compute the mill load (<math>s</math>) and product (<math>p</math>) at steady-state.
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The sub-models are described in further detail below.
The sub-models are described in further detail below.


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=== Breakage rates ===
=== Breakage rates ===
</div><hide>


[[File:AGSAGVariableRates12.png|thumb|450px|Figure 4. Breakage rate distribution characterised by cubic spline interpolation.]]
[[File:AGSAGVariableRates12.png|thumb|450px|Figure 4. Breakage rate distribution characterised by cubic spline interpolation.]]


The breakage rate at each size interval, <math>R_i</math> (h<sup>-1</sup>), is generated by [[Interpolation|cubic spline interpolation]] between five breakage rate knots (<math>R1 - R5</math>) at the 0.25, 4, 16, 44 and 128 mm particle size positions.{{Leung et al. (1987)}}
{{Model theory (Text, AG/SAG Mill, Variable Rates, Breakage Rates)|4}}


Morrell and Morrison (1996) described the following set of empirical equations which relate the breakage rate knots <math>R1 - R5</math> to mill operating conditions:{{Morrell and Morrison (1996)}}
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:<math>
\begin{array}{l}
\ln(R1) = \mathit{RConst}_1 + \dfrac{k_{11} + k_{12} \ln (R2) - k_{13} \ln (R3) + J_{\rm B} (k_{14} - k_{15} F_{80}) - D_{\rm B}}{S_{\rm b}}\\
\ln(R2) = \mathit{RConst}_2 + k_{21}+ k_{22}\ln(R3) - k_{23} \ln(R4) - k_{24} F_{80}\\
\ln(R3) = \mathit{RConst}_3 + S_{\rm a} + \dfrac{k_{31} + k_{32} \ln(R4) - k_{33} R_{\rm r}}{S_{\rm b}}\\
\ln(R4) = \mathit{RConst}_4 + S_{\rm b} (k_{41} + k_{42} \ln(R5) + J_{\rm B} (k_{43} - k_{44} F_{80}))\\
\ln(R5) = \mathit{RConst}_5 + S_{\rm a} + S_{\rm b} \left (k_{51} + k_{52} F_{80} + J_{\rm B} (k_{53} - k_{54} F_{80}) - 3.0 D_{\rm B} \right )\\
\end{array}
</math>
 
where:
* <math>\mathit{RConst}_1 - \mathit{RConst}_5</math> are user-defined constants which can be used to adjust modelled breakage rates to observed values
* <math>J_{\rm B}</math> is the fraction of total mill volume occupied by balls and associated voids (% v/v)
* <math>F_{80}</math> is the 80% passing size of new feed (mm)
* <math>k_{ij}</math> are the regression coefficients specified in Table 1.
 
:{| class="wikitable"
|+ Table 1. Breakage rate regression coefficients (after Morrell and Morrison, 1996).{{Morrell and Morrison (1996)}}
 
|-
! <math>j</math> !! <math>k_{1j}</math> !! <math>k_{2j}</math> !! <math>k_{3j}</math> !! <math>k_{4j}</math> !! <math>k_{5j}</math>
|-
| 1 || 2.504|| 4.682|| 3.141|| 1.057|| 1.894
|-
| 2 || 0.397|| 0.468|| 0.402|| 0.333|| 0.014
|-
| 3 || 0.597|| 0.327|| 4.632 || 0.171|| 0.473
|-
| 4 || 0.192|| 0.0085|| -|| 0.0014|| 0.002
|-
| 5 || 0.002 || - || -|| -|| -
|}
 
The mill rotational speed scaling factor, <math>S_{\rm a}</math>, is computed from the mill rotational speed (rpm) as:
 
:<math>S_{\rm a} = \ln \left ( \dfrac{\text{Mill speed (rpm)}}{23.6} \right )</math>
 
Similarly, the mill fraction critical speed scaling factor, <math>S_{\rm b}</math>, is computed from the [[Tumbling Mill (Speed)|mill fraction critical speed]], <math>\phi</math> (frac), as:
 
:<math>S_{\rm b} = \dfrac{\phi}{0.75}</math>
 
The ball diameter scaling factor, <math>D_{\rm B}</math>, is computed from the ball top size, <math>d_{\rm B,Top}</math> (mm), as:
 
:<math>D_{\rm B} = \ln \left ( \dfrac{d_{\rm B,Top}}{90} \right )</math>
 
The recycle ratio, <math>R_{\rm r}</math>, is the ratio of the mass flowrate of recycled -20+4 mm material to the total mass flowrate of all new feed plus recycled -20+4 mm material, i.e.
 
:<math>R_{\rm r} = \dfrac{Q_{\rm M,R} (P_{20\text{mm,R}} - P_{4\text{mm,R}})}{Q_{\rm M,F} + Q_{\rm M,R}(P_{20\text{mm,R}} - P_{4\text{mm,R}})}</math>
 
where:
* <math>Q_{\rm M,F}</math> is new feed mass flow rate (t/h)
* <math>Q_{\rm M,R}</math> is recycle feed mass flow rate (t/h)
* <math>P_{20\text{mm,R}}</math> and <math>P_{4\text{mm,R}}</math> are the fraction of recycle feed passing 20 mm and 4 mm size, respectively (frac)
 
The recycle ratio, <math>R_{\rm r}</math>, is only applicable when the coarse recycled feed component consists of mill pebbles (scats) which have not undergone an intervening breakage step such as pebble crushing.
 
Figure 4 presents an example breakage rate distribution constructed from the five breakage rate knots and a continuous cubic spline.


=== Discharge rates ===
=== Discharge rates ===
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The discharge rates (<math>D</math>) are related to the hold-up of slurry in the mill and particle classification at the discharge grates.
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.


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==== Slurry hold-up ====
==== Slurry hold-up ====
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[[File:AGSAGVariableRates9.png|thumb|450px|Figure 5. Principal dimensions of an AG/SAG mill.]]
[[File:AGSAGVariableRates9.png|thumb|450px|Figure 5. Principal dimensions of an AG/SAG mill.]]
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* <math>r_{\rm m}</math> is the radius of the mill inside the liners (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 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:{{Morrell and Stephenson (1996)}}
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:{{Morrell and Stephenson (1996)}}


:<math>Q = k_{\rm g} Q_{\rm m}</math>
:<math>Q = k_{\rm g} Q_{\rm m}</math>
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Thus, slurry hold-up, <math>L_{\rm V}</math>, can be computed for a given feed/discharge flow rate, grate design and mill.
Thus, slurry hold-up, <math>L_{\rm V}</math>, can be computed for a given feed/discharge flow rate, grate design and mill.


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==== Classification and discharge ====
==== Classification and discharge ====
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[[File:AGSAGVariableRates10.png|thumb|450px|Figure 6. Classification function, <math>C_i</math>, with pebble port open are fraction, <math>f_p</math>, specified.]]
[[File:AGSAGVariableRates10.png|thumb|450px|Figure 6. Classification function, <math>C_i</math>, with pebble port open are fraction, <math>f_p</math>, specified.]]
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[[File:AGSAGVariableRates11.png|thumb|450px|Figure 7. Classification function, <math>C_i</math>, where pebble port open are fraction, <math>f_p</math>, is zero, i.e grates only.]]
[[File:AGSAGVariableRates11.png|thumb|450px|Figure 7. Classification function, <math>C_i</math>, where pebble port open are fraction, <math>f_p</math>, is zero, i.e grates only.]]


The discharge rate of solids from the grate of a perfectly mixed mill is:{{Kojovic et al. (2012)}}
{{Model theory (Text, AG/SAG Mill, Variable Rates, Classification)}}
 
:<math>p_i = D_i.s_i</math>
 
where:
:<math>D_i = d_{\rm max}.C_i</math>
:<math> C_i =
    \begin{cases}
      1 & \bar d_i \leq x_{\rm m}\\
      \left ( 1 - \dfrac{\ln \bar d_i -\ln x_{\rm m}}{\ln x_{\rm g} - \ln x_{\rm m} } \right )(1 - f_{\rm p}) + f_{\rm p} & x_{\rm m}<\bar d_i\leq x_{\rm g}\\   
      \left ( 1 - \dfrac{\ln \bar d_i -\ln x_{\rm g}}{\ln x_{\rm p} - \ln x_{\rm g} } \right ) .f_{\rm p}  & x_{\rm g}<\bar d_i\leq x_{\rm p}\\   
      0 & \bar d_i>x_{\rm p}\\
    \end{cases}
</math>
 
and:
* <math>d_{\rm max}</math> is the fraction of load presented to the mill discharge per unit of time (h<sup>-1</sup>)
* <math>C_{i}</math> is the classification function, the fraction of particles of size <math>i</math> reporting to the mill product (frac)
* <math>\bar d_i</math> is the [[Conversions|geometric mean size]] of particles in size interval <math>i</math> (mm)
* <math>x_{\rm m}</math> is the particle size below which all mass in the size interval reports to mill product (mm), i.e. like water
* <math>x_{\rm g}</math> is the grate aperture size (mm)
* <math>x_{\rm p}</math> is the pebble port size (mm)
* <math>f_{\rm p}</math> is the fraction of open area occupied by pebble ports (m<sup>2</sup>/m<sup>2</sup>)


Figure 6 shows an example classification function with pebble ports included, whilst Figure 7 shows the same function with a grate-only mill.
Figure 6 shows an example classification function with pebble ports included, whilst Figure 7 shows the same function with a grate-only mill.


The value of <math>d_{\rm max}</math> is adjusted during the calculation sequence (Figure 3) to ensure the fraction of solids less than <math>x_{\rm g}</math> plus water retained in the mill load computed by the perfect mixing population balance matches the slurry hold-up determined by the [[AG/SAG Mill (Variable Rates)#Slurry_flow|slurry flow]] calculations.
The value of <math>d_{\rm max}</math> is adjusted during the calculation sequence (Figure 3) to ensure the fraction of solids less than <math>x_{\rm g}</math> plus water retained in the mill load computed by the perfect mixing population balance matches the slurry hold-up determined by the [[AG/SAG Mill (Variable Rates)#Slurry_flow|slurry flow]] calculations.
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=== Appearance function ===
=== Appearance function ===


The appearance function, <math>A</math>, is defined as the mass-by-size distribution of progeny particles resulting from the breakage of parent particles.
{{Model theory (Text, AG/SAG Mill, Variable Rates, Appearance Function)}}
 
Two types of particle breakage are theorised to occur occur within AG/SAG mills:
 
# ''High energy'' breakage from the impact of cataracting balls and large rocks at the toe of the charge, and
# ''Low energy'' breakage from the abrasion and attrition of particles within the charge bed.
 
The appearance function for an AG/SAG mill is constructed from the combination of appearance functions for the high energy, <math>A_{\rm HE}</math>, and low energy, <math>A_{\rm LE}</math>, breakage regimes.
 
An appearance function is a lower triangular matrix as all broken particles are, by definition, smaller than their parent particle.
 
==== High energy ====
 
Leung et al. (1987) related the amount of energy available for high energy impact breakage in a mill to the mean size of the top 20% of the charge, <math>S_{20}</math> (mm). The <math>S_{20}</math> is defined as:{{Leung et al. (1987)}}
 
:<math>S_{20} = \left (P_{100} \cdot P_{98} \cdot P_{96} \dots P_{80} \right )^{\frac{1}{11}} </math>
 
where <math>P_{x}</math> is the size passing fraction <math>x</math> (mm) of the charge, which includes ore and balls (if present).
 
A particle of representative size <math>S_{20}</math> falling through the full height of the mill converts the following potential energy into impact (kinetic) energy:
 
:<math>E_q = \dfrac{\frac{4}{3} \pi \left ( \dfrac{S_{20}}{2000} \right )^3 \rho_{\rm S} g D}{3600}</math>
 
where:
* <math>E_q</math> is the energy level in the mill applied to particles in size fraction <math>q</math> (kWh)
* <math>q</math> is defined as the index of the size interval containing the largest particle in the feed, <math>1 \leq q \leq n</math>
* <math>\rho_{\rm S}</math> is the density of solids in the mill (t/m<sup>3</sup>)
* <math>g</math> is acceleration due to gravity (m/s<sup>2</sup>)
* <math>D</math> is the mil diameter (m)
 
and the above equation has been corrected from Leung et al. (1987) for particle radius and measurement units.
 
The energy level, <math>E_q</math>, is converted to the specific comminution energy applied to a particle in size fraction <math>q</math>, <math>(E_{\rm cs})_q</math> (kWh/t), by:{{Bueno et al. (2013)}}
 
:<math>(E_{\rm cs})_q = \dfrac{E_p}{\frac{4}{3} \pi \left ( \dfrac{\bar d_q}{2000} \right )^3 \rho_{\rm S}}</math>
 
where <math>\bar d_q</math> is the [[Conversions#Geometric_mean_size|geometric mean size]] (mm) of a particle in size interval <math>q</math>, and the equation is again corrected for radius and units.
 
The specific comminution energy <math>(E_{\rm cs})_q</math> is scaled to smaller size fractions by:{{Bueno et al. (2013)}}
 
:<math>{(E_{\rm cs})_i} =
\begin{cases}
0 & i < q\\
\dfrac{(E_{\rm cs})_q}{ \left ( \dfrac{\bar d_i}{\bar d_q} \right )^{1.5}  } & q \leq i \leq n\\
\end{cases}
</math>
 
To compute the high energy appearance function, the fraction of particles passing one-tenth of the initial mean particle, the <math>t_{\rm 10}</math> (frac), is determined for the specific comminution energy applied at each size:{{Leung et al. (1987)}}
 
:<math>(t_{10})_i = A(1-{\rm e}^{-b (E_{\rm cs})_i})</math>
 
where <math>A</math> and <math>b</math> are ore-specific hardness parameters obtained from a drop weight test.{{Napier-Munn et al. (1996)}}
 
The Variable Rates AG/SAG model uses the standard matrix of cumulative fraction passing data points in Table 3 to describe the products of a high breakage event for any ore type.{{Napier-Munn et al. (1996)}}
 
Each element of the matrix, <math>t_{x,y}</math>, represents the percentage fraction of progeny particles passing one-<math>y</math>th of the original parent particle geometric mean size, when <math>x</math>% of the products pass one-tenth of the original product size (i.e. the <math>t_{10}</math>).
 
:{| class="wikitable"
|+ Table 3. Standard appearance function data used in the Variable Rates AG/SAG model.{{Napier-Munn et al. (1996)}}
!
!<math>t_{75}(\%)</math>
!<math>t_{50}(\%)</math>
!<math>t_{25}(\%)</math>
!<math>t_{4}(\%)</math>
!<math>t_{2}(\%)</math>
|-
|<math>t_{10}=10\%</math>
|2.33
|3.06
|4.98
|23.33
|50.53
|-
|<math>t_{10}=20\%</math>
|6.89
|9.41
|15.62
|61.58
|92.49
|-
|<math>t_{10}=50\%</math>
|10.32
|14.71
|25.88
|82.86
|96.47
|}
 
This matrix allows a complete breakage product size distribution for any parent size and mesh series to be reconstructed from the <math>t_{10}</math> via the following steps:
 
# A [[Interpolation#Cubic_spline_interpolation|cubic spline]] is used to interpolate <math>t_{75}</math> - <math>t_2</math> values for the <math>(t_{\rm 10})_i</math> at each particle size fraction's specific comminution energy.
# A secondary cubic spline interpolation is used to produce a distribution across the full mesh size interval range for each parent particle size.
 
The [[Crusher (Whiten)|Whiten crusher]] model also applies a similar appearance function spline interpolation procedure.
 
==== Ball load ====
 
Semi-Autogenous (SAG) mills add steel ball grinding media to the ore charge to increase size reduction.
 
The mass of balls in a mill, <math>M_{\rm B}</math> (t), is related to the volume occupied by the balls by:{{Morrell (1992)}}
 
:<math>M_{\rm B} = J_{\rm B} (1 - \varepsilon) V \rho_{\rm B}</math>
 
where
* <math>J_{\rm B}</math> is the fraction of mill volume occupied by balls and the void space between them, when the mill is at rest (v/v)
* <math>\varepsilon</math> is the void fraction, taken as 0.4 (v/v)
 
The calculation of specific comminution energy for the [[AG/SAG Mill (Variable Rates)#High_energy|high energy appearance function]] above uses the average size of the top 20% of the charge, the <math>S_{20}</math>. A charge that includes balls must incorporate the media load into the calculation of the <math>S_{20}</math>. This is achieved by considering the ball load as if each ball were an ore particle with the same mass, but a larger diameter to compensate for the density difference between steel and rock, i.e.:{{Leung et al. (1987)}}
 
:<math>
m_{\rm B} = v_{\rm B} \rho_{\rm B} = \frac{4}{3} \pi \left ( \frac{d_{\rm B}}{2} \right )^3 \rho_{\rm B}, \quad
v_{\rm S} = \frac{4}{3} \pi \left ( \frac{d_{\rm S}}{2} \right )^3 = \frac{m_{\rm B}}{\rho_{\rm S}} = \frac{\frac{4}{3} \pi \left ( \frac{d_{\rm B}}{2} \right )^3 \rho_{\rm B}}{\rho_{\rm S}} \quad
\implies d_{\rm S} = \left ( \frac{{{d_{\rm B}}^3 \rho_{\rm B}}}{\rho_{\rm S}} \right )^{\frac{1}{3}}
</math>
 
where:
* <math>m_{\rm B}</math> and <math>v_{\rm B}</math> are the mass and volume of a ball, respectively.
* <math>\rho_{\rm B}</math> is the density of a ball
* <math>d_{\rm B}</math> is the diameter of a ball
* <math>v_{\rm S}</math> is the volume of an ore particle
* <math>\rho_{\rm S}</math> is the density of ore solids in the charge
* <math>d_{\rm S}</math> is the diameter of an ore particle with equivalent mass to a ball
 
Therefore, a weight fraction retained distribution of balls on any size interval series is incorporated into the the <math>S_{20}</math> calculation by the following steps:
# Scale the ball size intervals (<math>d_{\rm B}</math>) to equivalent ore size intervals (<math>d_{\rm S}</math>) as per the equation above.
# Use a [[Interpolation#Cubic_spline_interpolation|monotonic spline]] to [[Conversions#Convert_between_meshes|convert]] the ball distribution from the scaled equivalent ore size intervals (<math>d_{\rm S}</math>) to the size intervals used by the perfect mixing population balance formulation (<math>d_i</math>).
# Convert the weight fraction retained ball distribution to a mass retained distribution using the ball mass, <math>M_{\rm B}</math>.
# Convert the mass retained ball distribution to a volume retained distribution using the ore density, <math>\rho_{\rm S}</math>.
# Combine the ball volume-by-size and ore volume-by-size in the charge (<math>s_i</math>) when computing the <math>S_{20}</math>.
 
==== Low energy ====
 
The low energy appearance function is computed from the ore-specific abrasion parameter, <math>t_a</math> (%), which is obtained from the ore abrasion test described by Napier-Munn et al. (1996).{{Napier-Munn et al. (1996)}}
 
The cumulative fraction passing distribution of progeny particles arising from the abrasion breakage of a parent particle is computed by multiplying the <math>t_a</math> for a given ore by the scaling factors indicated in Table 4.{{Leung et al. (1987)}}
 
:{| class="wikitable"
|+ Table 4. Standard abrasion appearance function data.{{Leung et al. (1987)}}
|-
!  !! Cumulative fraction passing (%)
|-
| <math>t_{1}</math>|| <math>100</math>
|-
| <math>t_{1.25}</math>|| <math>2.687 \cdot t_{\rm a}</math>
|-
| <math>t_{1.5}</math>|| <math>1.631 \cdot t_{\rm a}</math>
|-
| <math>t_{10}</math>|| <math>1.0 \cdot t_{\rm a}</math>
|-
| <math>t_{100}</math>|| <math>0.9372 \cdot t_{\rm a}</math>
|-
| <math>t_{250}</math>|| <math>0.8070 \cdot t_{\rm a}</math>
|-
| <math>t_{500}</math>|| <math>0.6365 \cdot t_{\rm a}</math>
|}
 
The low energy appearance function is then determined for all parent particle sizes and across the full mesh series by spline interpolation of the cumulative fraction passing values computed above.
 
Note that a [[Interpolation#Cubic_spline_interpolation|monotonic spline]] is employed for the low energy appearance function as the sharp change in cumulative fraction passing values between the original parent size (<math>t_1</math>) and the first progeny size (<math>t_{1.25}</math>) can result in undesired oscillation and negative function values when applying a regular cubic spline.
 
==== Combined appearance function ====
 
The high and low energy appearance functions are combined based on the relative proportions of <math>t_{\rm a}</math> and the <math>t_{10}</math> at each specific comminution energy:{{Leung et al. (1987)}}
 
:<math>A = \dfrac{t_{10} . A_{\rm HE} + t_{\rm a} . A_{\rm LE}}{t_{10} + t_{\rm a}}</math>


=== Mill power ===
=== Mill power ===
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The Variable Rates AG/SAG model includes an implementation of the [[Tumbling Mill (Power, Morrell Continuum)|Morrell Continuum]] tumbling mill power model. The predicted mill power draw is not utilised by the Variable Rates model formulation in any manner, and is provided for information only.
The Variable Rates AG/SAG model includes an implementation of the [[Tumbling Mill (Power, Morrell Continuum)|Morrell Continuum]] tumbling mill power model. The predicted mill power draw is not utilised by the Variable Rates model formulation in any manner, and is provided for information only.


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==== Charge properties ====
==== Charge properties ====
</div><hide>


The power draw prediction requires an estimate of <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.
The power draw prediction requires an estimate of <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.
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:<math>\rho_{\rm c} = \frac{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}}, \quad U \leq 1</math>
:<math>\rho_{\rm c} = \frac{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}}, \quad U \leq 1</math>


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==== Power draw ====
==== Power draw ====
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:''Main article'': [[Tumbling Mill (Power, Morrell Continuum)]]
:''Main article'': [[Tumbling Mill (Power, Morrell Continuum)]]
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The complete equations are excluded here for brevity and are available at the article link above.
The complete equations are excluded here for brevity and are available at the article link above.


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=== Internal mesh series ===
=== Internal mesh series ===
</div><hide>


The Variable Rates AG/SAG mill model is formulated internally with a geometric progression of <math>n = 42</math> mesh sizes at <math>\sqrt{2}</math> intervals, i.e.
{{Model theory (Text, AG/SAG Mill, Variable Rates, Internal Mesh)}}
 
:<math>d_i =
\begin{cases}
d_1 & i=1\\
\dfrac{d_1}{i\sqrt{2}} & 1 < i < n\\
0 & i = n
\end{cases}
</math>
 
where <math>d_1</math> (mm) is the top size of the internal mesh series.
 
Feed, load and product size fractions are automatically converted to and from the internal mesh series during model computation.


The internal mesh series chosen can have an impact on the calculated value of <math>S_{20}</math> via the <math>P_{100}</math> parameter, which subsequently affects the computed mill load and discharge. As such, the internal mesh top size, <math>d_1</math>, is specified by the user. This ensures consistency when model parameters are transferred from once instance to another.
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=== Multicomponent modelling ===
=== Multicomponent modelling ===
</div><hide>


Published formulations of the Variable Rates AG/SAG model and its predecessors only consider feeds and loads consisting of a single ore type.{{Leung et al. (1987)}}{{Kojovic et al. (2012)}}{{Bueno et al. (2013)}}
{{Model theory (Text, AG/SAG Mill, Variable Rates, Multicomponent)}}
 
In practice, mill feeds are often multicomponent, consisting of ores and minerals blended from multiple, differing sources. Recirculation of coarse, harder material for additional grinding passes adds to this complexity.


This implementation of the Variable Rates AG/SAG model addresses multicomponent feeds in a simple way:{{Bueno et al. (2013)}}
</hide><div class="user-show">
 
# Each ore type in a mill feed is assigned a separate set of density (<math>\rho_{\rm S}</math>) and hardness (<math>A</math>, <math>b</math>, <math>t_{\rm a}</math>) parameters.
# Ore masses-by-size are converted to volumes-by-size via the density parameters.
# The <math>S_{20}</math> parameter value is determined on a volumetric basis for the combined ore types (and balls).
# The <math>(E_{\rm cs})_q</math> parameter value is determined using the overall density of all ore types in the mill load (i.e. the harmonic mean).
# Different appearance functions are then applied to separate population balance computations for each ore type in the feed.
 
This multicomponent approach allows harder and coarser ore particles to accumulate in the mill load and preferentially concentrate in coarse recycle streams, as would be expected in practice.
 
Multiple ore types are excluded from the model formulations found in the previous sections of this article for clarity, but steps 1 - 5 above are automatically undertaken during model calculation.
 
The multicomponent formulation reverts to the original single ore approach when only one ore type is present, or each ore type of a multicomponent feed is assigned the same values of <math>\rho_{\rm S}</math>, <math>A</math>, <math>b</math>, and <math>t_{\rm a}</math>.


=== Additional notes ===
=== Additional notes ===
</div><hide>


</hide><div class="user-show">
==== Breakage rates and mill load ====
==== 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)}}
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 ====
==== Slurry pool ====
</div><hide>


Various 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)}}
Various 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)}}
Line 553: Line 307:
x_{\rm m}\text{ (mm)}\\
x_{\rm m}\text{ (mm)}\\
\gamma\text{ (m/m)}\\
\gamma\text{ (m/m)}\\
k\text{ (-)}\\
k_{\rm m}\text{ (-)}\\
J_{\rm B}\text{ (v/v)}\\
J_{\rm B}\text{ (v/v)}\\
\rho_{\rm B}\text{ (t/m}^3\text{)}\\
\rho_{\rm B}\text{ (t/m}^3\text{)}\\
Line 802: Line 556:
{{SysCAD (Page, Mill, DLL*Mill)|PowerModels=true|MediaTraj=true|MediaStrings=true}}
{{SysCAD (Page, Mill, DLL*Mill)|PowerModels=true|MediaTraj=true|MediaStrings=true}}


==== Mill page ====
{{SysCAD (Page, AG/SAG Mill, Variable Rates, Mill)}}
 
The Mill page is used to specify the input parameters for the mill model.
 
{{SysCAD_Table_Header}}
 
|-
! colspan="3" style="text-align:left;" |''VariableRates''
 
{{SysCAD (Text, Help Link)}}
 
|-
! colspan="3" style="text-align:left;" |''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.
|-
! colspan="3" style="text-align:left;" |''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.
|-
! colspan="3" style="text-align:left;" |''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.
|-
! colspan="3" style="text-align:left;" |''RFunction''
|-
| RSize
|style="background: #eaecf0" | Display
|Spline knot positions.
|-
| RConst
|Input
|Values of <math>\mathit{RConst}</math> at each spline knot position.
|-
! colspan="3" style="text-align:left;" |''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.
 
{{SysCAD_Table_Header}}
 
|-
! colspan="3" style="text-align:left;" |''Ore''
|- style="vertical-align:top;"
|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.
|-
|colspan="3" | [[File:AGSAGVariableRates5.png]] [[File:AGSAGVariableRates6.png]]
|}
 
==== Results page ====
 
This page is used to display the model results.
 
{{SysCAD_Table_Header}}
 
|-
! colspan="3" style="text-align:left;" |''Results''
|-
! colspan="3" style="text-align:left;" |''Solver''
|-
|Iterations
|style="background: #eaecf0" | Display
|Number of iterations to converge internal load solver.
|-
|IterationError
|style="background: #eaecf0" | Display
|Numerical approximation error of internal load solver.
|-
! colspan="3" style="text-align:left;" |''Mill Properties''
|-
|MillVolume
|style="background: #eaecf0" | Display
|Internal volume of the mill.
|-
|MillSpeed
|style="background: #eaecf0" | Display
|Rotational speed of the mill.
|-
|MillFeedRate / Feed.SLQv
|style="background: #eaecf0" | Display
|Volumetric feed rate of pulp into the mill.
|-
! colspan="3" style="text-align:left;" |''Mill Contents''
|-
|OreMass
|style="background: #eaecf0" | Display
|Mass of ore (solids with PSD) in the mill.
|-
|LiquidMass
|style="background: #eaecf0" | Display
|Mass of liquids in the mill.
|-
|BallMass
|style="background: #eaecf0" | Display
|Mass of ball media in the mill.
|-
|TotalChargeMass
|style="background: #eaecf0" | Display
|Total mass of ore, liquids and balls in the mill.
|-
|VolTotalLoad
|style="background: #eaecf0" | Display
|Volumetric fraction of mill volume of total charge (ore, liquids, balls and void space).
|-
! colspan="3" style="text-align:left;" |''Mill Discharge''
|-
|m1
|style="background: #eaecf0" | Display
|Parameter of the Austin mill holdup relationship.
|-
|m2
|style="background: #eaecf0" | Display
|Parameter of the Austin mill holdup relationship.
|-
|dMax
|style="background: #eaecf0" | Display
|Maximum discharge rate of load volume through the grate.
|-
! colspan="3" style="text-align:left;" |''Charge Properties''
|-
|S20
|style="background: #eaecf0" | Display
|Size of the top (largest) 20% of the load.
|-
|ChargeDensity
|style="background: #eaecf0" | Display
|Density of the charge.
|-
|U
|style="background: #eaecf0" | Display
|Fraction of charge void space filled with slurry.
|-
|ThetaShoulder
|style="background: #eaecf0" | Display
|Angular position of the charge shoulder.
|-
|ThetaTue
|style="background: #eaecf0" | Display
|Angular position of the charge toe.
|-
|ChargeSurfaceRadius
|style="background: #eaecf0" | Display
|Radius of the inner charge surface.
|-
! colspan="3" style="text-align:left;" |''Power''
|-
|NoLoadPower
|style="background: #eaecf0" | Display
|No-load power draw of the mill.
|-
|NetPower
|style="background: #eaecf0" | Display
|Net power draw of the mill.
|-
|GrossPower
|style="background: #eaecf0" | Display
|Gross power draw of the mill.
|}
 
==== RiDi page ====
 
This page displays the breakage and discharge rates for each size interval computed by the model.
 
{{SysCAD_Table_Header}}
 
|-
! colspan="3" style="text-align:left;" |''Rates''
|-
|Size
|style="background: #eaecf0" | Display
|Size of each interval in internal mesh series.
|-
|MeanSize
|style="background: #eaecf0" | Display
|Geometric mean size of each interval in internal mesh series.
|-
| R
|style="background: #eaecf0" | Display
| Value of breakage rate, <math>R_i</math>, for each size interval, for each ore species.
|-
| D
|style="background: #eaecf0"; | Display
| Value of discharge rate, <math>D_i</math>, for each size interval.
|-
| Ecs
|style="background: #eaecf0"; | Display
| Value of the specific comminution energy for each size interval.
|}


==== Load page ====
{{SysCAD (Page, AG/SAG Mill, Variable Rates, Ore)}}


This page displays information about the balls, solids and liquids that currently comprise the mill load.
{{SysCAD (Page, AG/SAG Mill, Variable Rates, Results)|Steady-state=true}}


{{SysCAD_Table_Header}}
{{SysCAD (Page, AG/SAGMill, Variable Rates, Ri/Di)}}


{{SysCAD (Text, Distribution)}}
{{SysCAD (Page, AG/SAGMill, Variable Rates, Load)}}
 
|-
! colspan="3" style="text-align:left;" |''Load''
|-
|SolidMass / SMt
|style="background: #eaecf0" | Display
|The mass of solids with the SysCAD size distribution property currently in the mill.
|-
|LiquidMass / LMt
|style="background: #eaecf0" | Display
|The mass of liquids plus solids without the SysCAD size distribution property currently in the mill.
|-
|BallMass / BMt
|style="background: #eaecf0" | Display
|The mass of ball media in the mill.
|-
|Size
|style="background: #eaecf0" | Display
|Size of each interval in the external mesh series.
|-
|MeanSize
|style="background: #eaecf0" | Display
|Geometric mean size of each interval in the external mesh series.
|-
|Load
|style="background: #eaecf0" | Display
|The mass of solids with the SysCAD size distribution property currently in the mill, by size and species.
|}


{{SysCAD (Page, Tumbling Mill, Power)|modelpage={{SysCAD (Text, UnitType Prefix)}}Mill|HF=true|MorrellC=true|MorrellE=true|MorrellD=true|HildenPowell=true}}
{{SysCAD (Page, Tumbling Mill, Power)|modelpage={{SysCAD (Text, UnitType Prefix)}}Mill|HF=true|MorrellC=true|MorrellE=true|MorrellD=true|HildenPowell=true}}
Line 1,138: Line 576:
== See also ==
== See also ==


* [[Tumbling Mill (Slurry Flow)]]
* [[AG/SAG Mill (Variable Rates, Dynamic)]]
* [[Tumbling Mill (Power, Morrell Continuum)]]
 
* [[Crusher (Whiten)]]
== External links ==
* [https://help.syscad.net/Example_-_09_Met_Dynamics_Projects#Crushing_and_Grinding_Example Crushing and Grinding Example] project at [https://help.syscad.net/ help.syscad.net]
 
* [https://help.syscad.net/Met_Dynamics_-_Mill Met Dynamics - Mill (help.syscad.net)]
* [https://help.syscad.net/Example_-_09_Met_Dynamics_Projects#Crushing_and_Grinding_Example Crushing and Grinding Example project (help.syscad.net)]
* [https://help.syscad.net/Example_-_09_Met_Dynamics_Projects#Crushing,_Grinding_and_Flotation_Example Crushing, Grinding, and Flotation Example project (help.syscad.net)]


== References ==
== References ==

Latest revision as of 09:20, 9 July 2025

Description

This article describes an 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).[1][2][3]

The formulation is referred to in the associated literature as the "Variable Rates" model (Morrell et al., 2001).[4]

Model theory

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Calculation sequence

Breakage rates

Discharge rates

Slurry hold-up

Classification and discharge

Appearance function

High energy

Ball load

Low energy

Combined appearance function

Mill power

Charge properties

Power draw

Internal mesh series

Multicomponent modelling

Additional notes

Breakage rates and mill load

Slurry pool

Excel

The Variable Rates AG/SAG mill model may be invoked from the Excel formula bar with the following function call: 

=mdUnit_AGSAG_VariableRates(Parameters as Range, Size as Range, MillNewFeed as Range, OreSG as Range, BallSizing as Range, RConst as Range, OreBreakageParams as Range, Optional MillRecycleFeed as Range = Nothing)

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 mass flow feed rate of liquids into the mill (t/h)
  • is the Specific Gravity or density of liquids in the feed (- or t/m3)
  • is an index of the Appearance function to view in the results
  • is an index of the Appearance function to view in the results
  • is the number of ore types
  • is the number of intervals of the external mesh series
  • is the number of intervals of the ball mesh series below the top size, including the submesh
  • is the size of the external square mesh interval that feed mass is retained on (mm)
  • , i.e. descending size order from top size () to sub mesh ()
  • is the size of the square mesh interval that balls are retained on (mm)
  • is the mass fraction of balls retained on ball mesh series interval (% w/w)
  • indicates the array is an optional input parameter, and is set to null if omitted

Results

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

where:

  • is the number of internal computation steps required to converge the load
  • is the numerical error of the converged load approximation
  • is the flow rate of pulp into the mill (m3/h)
  • is the rotational rate of the mill (rpm)
  • is the mass of ore solids in the mill (t)
  • is the mass of liquids in the mill (t)
  • is the mass of balls in the mill (t)
  • is the total mass of ore, liquids and balls in the mill (t)
  • is product mass flow rate (t/h)
  • is the geometric mean size of the internal mesh series interval that mass is retained on (mm)

Example

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

Figure 8. Example showing the selection of the Parameters (blue frame) array in Excel.
Figure 9. Example showing the selection of the Size (dark red frame), OreSG (green frame), MillNewFeed (purple frame) and MillRecycleFeed (light red frame) arrays in Excel.
Figure 10. Example showing the selection of the BallSizing (purple frame), RConst (brown frame), and OreBreakageParams (teal frame) arrays in Excel.
Figure 11. 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_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.
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
Solver
Iterations Display Number of iterations to converge internal load solver.
IterationError Display Numerical approximation error of internal load solver.
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.
Power
NoLoadPower Display No-load power draw of the mill.
NetPower Display Net power draw of the mill.
GrossPower Display Gross power draw of the mill.

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.
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
HoggFuerstenau CheckBox Shows inputs and results for tumbling mill power calculations using the Hogg and Fuerstenau method.
MorrellC CheckBox Shows inputs and results for tumbling mill power calculations using the Morrell Continuum method.
MorrellE CheckBox Shows inputs and results for tumbling mill power calculations using the Morrell Empirical method.
MorrellD CheckBox Shows inputs and results for tumbling mill power calculations using the Morrell Discrete Shell method.
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.
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