Description
This article describes the Morrell method for estimating the specific energy of comminution circuits (Morrell et al., 2016).[1]
The Morrell method estimates the specific energy required to grind ore in comminution circuits, based on empirical models calibrated with laboratory test results. The method integrates ore hardness parameters from standardised testing with proposed circuit grind sizes to compute energy consumption across different equipment types.
Model theory
 This content is available to registered users. Please log in to view.
|
Comminution circuit specific energy
General equation
Tumbling mills
Coarse particle tumbling mill
Fine particle tumbling mill
Crushers
High pressure grinding rolls
Size distribution correction
Hardness parameters
Estimating P80
Estimating breakage parameters
Excel
Coarse particle tumbling mill specific energy
The coarse particle tumbling mill specific energy calculation may be invoked from the Excel formula bar with the following function call:
=mdSMC_Wa(K1 as Double, Mia as Double, x1 as Double, Optional returnCalcs as Boolean = false)
Invoking the function with no arguments will print Help text associated with the model, including a link to this page.
The input parameters and calculation results are defined below in matrix notation, along with an example image showing the selection of the same cells and arrays in the Excel interface:
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{align} K1 & = \big [ K_1 \big ]\\ \mathit{Mia} & = \big [M_{\rm ia}\text{ (kWh/t)} \big ]\\ x1 & = \big [x_1\text{ (}\mu\text{m)} \big ]\\ \mathit{returnCalcs} & = \big [(\text{True / False)} \big ] \end{align}}
|
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathit{mdSMC\_Wa} = \begin{bmatrix} W_{\rm a}\text{ (kWh/t)}\\ f(x_1)^*\\ f(x_2)^*\\ \end{bmatrix}}
|
|
where:
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle K_1=1}
for all circuits without a recycle pebble crusher, and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle K_1=0.95}
where circuits have a pebble crusher
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle M_{\rm ia}}
is the coarse ore (> 750 μm) work index in tumbling mill circuits (kWh/t)
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x_1}
is the 80% passing size of the feed (μm)
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathit{returnCalcs}}
indicates whether to return the optional results marked with the Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle ^*}
superscript (default is to omit)
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x_1)}
and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x_2)}
are exponents of the F80 and P80 equation terms, respectively
|
|
 Figure 1. Example showing the selection of the input parameters (shaded blue, red and purple frames), and Results (green frame) array in Excel. The parameter Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathit{returnCalcs}=\text{False}}
in this example.
|
Fine particle tumbling mill specific energy
The fine particle tumbling mill specific energy calculation may be invoked from the Excel formula bar with the following function call:
=mdSMC_Wb(Mib as Double, x3 as Double, Optional returnCalcs as Boolean = false)
Invoking the function with no arguments will print Help text associated with the model, including a link to this page.
The input parameters and calculation results are defined below in matrix notation, along with an example image showing the selection of the same cells and arrays in the Excel interface:
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{align} \mathit{Mib} & = \big [M_{\rm ib}\text{ (kWh/t)} \big ]\\ x3 & = \big [x_3\text{ (}\mu\text{m)} \big ]\\ \mathit{returnCalcs} & = \big [(\text{True / False)} \big ] \end{align}}
|
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathit{mdSMC\_Wb} = \begin{bmatrix} W_{\rm b}\text{ (kWh/t)}\\ f(x_1)^*\\ f(x_2)^*\\ \end{bmatrix}}
|
|
where:
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle M_{\rm ib}}
is the fine ore (< 750 μm) work index in tumbling mill circuits (kWh/t)
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x_3}
is the 80% passing size of the final grind product (μm)
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathit{returnCalcs}}
indicates whether to return the optional results marked with the Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle ^*}
superscript (default is to omit)
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x_1)}
and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x_2)}
are exponents of the F80 and P80 equation terms, respectively
|
|
 Figure 2. Example showing the selection of the input parameters (shaded blue and red frames), and Results (green frame) array in Excel. The parameter Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathit{returnCalcs}=\text{False}}
in this example.
|
Conventional crushing specific energy
The conventional crushing specific energy calculation may be invoked from the Excel formula bar with the following function call:
=mdSMC_Wc(K2 as Double, Mic as Double, x1 as Double, x2 as Double, Optional returnCalcs as Boolean = false)
Invoking the function with no arguments will print Help text associated with the model, including a link to this page.
The input parameters and calculation results are defined below in matrix notation, along with an example image showing the selection of the same cells and arrays in the Excel interface:
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{align} K2 & = \big [ K_2 \big ]\\ \mathit{Mic} & = \big [M_{\rm ic}\text{ (kWh/t)} \big ]\\ x1 & = \big [x_1\text{ (}\mu\text{m)} \big ]\\ x2 & = \big [x_2\text{ (}\mu\text{m)} \big ]\\ \mathit{returnCalcs} & = \big [(\text{True / False)} \big ] \end{align}}
|
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathit{mdSMC\_Wc} = \begin{bmatrix} W_{\rm c}\text{ (kWh/t)}\\ f(x_1)^*\\ f(x_2)^*\\ {S_{\rm c}}^*\\ \end{bmatrix}}
|
|
where:
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle K_2=1}
for closed circuit crushing, and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle K_1=1.19}
for open circuit crushing
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle M_{\rm ic}}
is the ore work index in crusher circuits (kWh/t)
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x_1}
is the 80% passing size of the feed (μm)
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x_2}
is the 80% passing size of the product (μm)
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathit{returnCalcs}}
indicates whether to return the optional results marked with the Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle ^*}
superscript (default is to omit)
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x_1)}
and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x_2)}
are exponents of the F80 and P80 equation terms, respectively
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle S_{\rm c}}
is a parameter that accounts for the decrease in ore strength in coarse crushing applications
|
|
 Figure 3. Example showing the selection of the input parameters (shaded blue, red, purple and green frames), and Results (green frame) array in Excel. The parameter Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathit{returnCalcs}=\text{False}}
in this example.
|
HPGR specific energy
The HPGR specific energy calculation may be invoked from the Excel formula bar with the following function call:
=mdSMC_Wh(K3 as Double, Mih as Double, x1 as Double, x2 as Double, Optional returnCalcs as Boolean = false)
Invoking the function with no arguments will print Help text associated with the model, including a link to this page.
The input parameters and calculation results are defined below in matrix notation, along with an example image showing the selection of the same cells and arrays in the Excel interface:
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{align} K3 & = \big [ K_3 \big ]\\ \mathit{Mih} & = \big [M_{\rm ih}\text{ (kWh/t)} \big ]\\ x1 & = \big [x_1\text{ (}\mu\text{m)} \big ]\\ x2 & = \big [x_2\text{ (}\mu\text{m)} \big ]\\ \mathit{returnCalcs} & = \big [(\text{True / False)} \big ] \end{align}}
|
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathit{mdSMC\_Wh} = \begin{bmatrix} W_{\rm h}\text{ (kWh/t)}\\ f(x_1)^*\\ f(x_2)^*\\ {S_{\rm h}}^*\\ \end{bmatrix}}
|
|
where:
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle K_3=1}
for closed circuits with a screen, and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle K_3=1.19}
in open circuits
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle M_{\rm ih}}
is the ore work index in HPGR circuits (kWh/t)
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x_1}
is the 80% passing size of the feed (μm)
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x_2}
is the 80% passing size of the product (μm)
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathit{returnCalcs}}
indicates whether to return the optional results marked with the Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle ^*}
superscript (default is to omit)
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x_1)}
and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x_2)}
are exponents of the F80 and P80 equation terms, respectively
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle S_{\rm h}}
is a parameter that accounts for the decrease in ore strength in coarse crushing applications
|
|
 Figure 4. Example showing the selection of the input parameters (shaded blue, red and purple frames), and Results (green frame) array in Excel. The parameter Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathit{returnCalcs}=\text{False}}
in this example.
|
Specific energy correction for size distribution
The specific energy correction for size distribution calculation may be invoked from the Excel formula bar with the following function call:
=mdSMC_Ws(Mia as Double, x1 as Double, x2 as Double, Optional returnCalcs as Boolean = false)
Invoking the function with no arguments will print Help text associated with the model, including a link to this page.
The input parameters and calculation results are defined below in matrix notation, along with an example image showing the selection of the same cells and arrays in the Excel interface:
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{align} \mathit{Mia} & = \big [M_{\rm ia}\text{ (kWh/t)} \big ]\\ x1 & = \big [x_1\text{ (}\mu\text{m)} \big ]\\ x2 & = \big [x_2\text{ (}\mu\text{m)} \big ]\\ \mathit{returnCalcs} & = \big [(\text{True / False)} \big ] \end{align}}
|
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathit{mdSMC\_Ws} = \begin{bmatrix} W_{\rm s}\text{ (kWh/t)}\\ f(x_1)^*\\ f(x_2)^*\\ \end{bmatrix}}
|
|
where:
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle M_{\rm ia}}
is the coarse ore (> 750 μm) work index in tumbling mill circuits (kWh/t)
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x_1}
is the 80% passing size of the feed (μm)
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x_2}
is the 80% passing size of the product (μm)
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathit{returnCalcs}}
indicates whether to return the optional results marked with the Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle ^*}
superscript (default is to omit)
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x_1)}
and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x_2)}
are exponents of the F80 and P80 equation terms, respectively
|
|
 Figure 5. Example showing the selection of the input parameters (shaded blue, red and purple frames), and Results (green frame) array in Excel. The parameter Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathit{returnCalcs}=\text{False}}
in this example.
|
General comminution specific energy
The general comminution specific energy calculation may be invoked from the Excel formula bar with the following function call:
=mdSMC_W(K as Double, Mi as Double, x1 as Double, x2 as Double, Optional returnCalcs as Boolean = false)
Invoking the function with no arguments will print Help text associated with the model, including a link to this page.
The input parameters and calculation results are defined below in matrix notation, along with an example image showing the selection of the same cells and arrays in the Excel interface:
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{align} K & = \big [ K \big ]\\ \mathit{Mi} & = \big [M_{\rm i}\text{ (kWh/t)} \big ]\\ x1 & = \big [x_1\text{ (}\mu\text{m)} \big ]\\ x2 & = \big [x_2\text{ (}\mu\text{m)} \big ]\\ \mathit{returnCalcs} & = \big [(\text{True / False)} \big ] \end{align}}
|
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathit{mdSMC\_Wa} = \begin{bmatrix} W_{\rm a}\text{ (kWh/t)}\\ f(x_1)^*\\ f(x_2)^*\\ \end{bmatrix}}
|
|
where:
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle K}
is an adjustment factor
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle M_{\rm i}}
is the ore work index (kWh/t)
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x_1}
is the 80% passing size of the feed (μm)
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x_2}
is the 80% passing size of the product (μm)
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathit{returnCalcs}}
indicates whether to return the optional results marked with the Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle ^*}
superscript (default is to omit)
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x_1)}
and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x_2)}
are exponents of the F80 and P80 equation terms, respectively
|
|
 Figure 6. Example showing the selection of the input parameters (shaded blue, red, purple, green and pink frames), and Results (green frame) array in Excel. The parameter Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathit{returnCalcs}=\text{True}}
in this example.
|
Calculating P80
The P80 calculation may be invoked from the Excel formula bar with the following function call:
=mdSMC_P80(K as Double, Mi as Double, F80 as Double, W as Double, Optional returnCalcs as Boolean = false)
Invoking the function with no arguments will print Help text associated with the model, including a link to this page.
The input parameters and calculation results are defined below in matrix notation, along with an example image showing the selection of the same cells and arrays in the Excel interface:
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{align} K & = \big [ K \big ]\\ \mathit{Mi} & = \big [M_{\rm i}\text{ (kWh/t)} \big ]\\ F80 & = \big [F_{80}\text{ (}\mu\text{m)} \big ]\\ W & = \big [W\text{ (kWh/t)} \big ]\\ \mathit{returnCalcs} & = \big [(\text{True / False)} \big ] \end{align}}
|
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathit{mdSMC\_P80} = \begin{bmatrix} P_{80}\text{ (}\mu\text{m)}\\ f(x_1)^*\\ f(x_2)^*\\ \end{bmatrix}}
|
|
where:
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle K}
is an adjustment factor
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle M_{\rm i}}
is the ore work index (kWh/t)
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle F_{80}}
is the 80% passing size of the feed (μm)
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle W}
is the specific energy available to the comminution stage (kWh/t)
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathit{returnCalcs}}
indicates whether to return the optional results marked with the Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle ^*}
superscript (default is to omit)
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle P_{80}}
is the 80% passing size of the product (μm)
|
|
 Figure 7. Example showing the selection of the input parameters (shaded blue, red, purple and green frames), and Results (green frame) array in Excel. The parameter Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathit{returnCalcs}=\text{False}}
in this example.
|
Estimating breakage parameters
The breakage parameter estimation may be invoked from the Excel formula bar with the following function call:
=mdSMC_AbToSMC(A as Double, b as Double, SG as Double, BWI as Double, Optional conversionMethod as Integer = 0)
Invoking the function with no arguments will print Help text associated with the model, including a link to this page.
The input parameters and calculation results are defined below in matrix notation, along with an example image showing the selection of the same cells and arrays in the Excel interface:
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{align} A & = \big [ A \text{ (}%\text{)} \big ]\\ b & = \big [ b \big ]\\ \mathit{SG} & = \big [ \rho_{\rm S}\text{ (t/m}^3\text{)} \big ]\\ \mathit{BWI} & = \big [ \mathit{Wi}_{\rm BM}\text{ (kWh/t} \big ]\\ \mathit{conversionMethod} & = \big [ \text{0 (Doll) or 1 (Chitalov)} \big ] \end{align}}
|
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathit{mdSMC\_AbToSMC} = \begin{bmatrix} {\rm DW}_{\rm i}\text{ (kWh/m}^3\text{)}\\ M_{\rm ia}\text{ (kWh/t)}\\ M_{\rm ib}\text{ (kWh/t)}\\ M_{\rm ic}\text{ (kWh/t)}\\ M_{\rm ih}\text{ (kWh/t)}\\ t_{\rm a}\text{ (-)}\\ {\rm SCSE}\text{ (kWh/t)}\\ \end{bmatrix}}
|
|
where:
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A}
is a JK Drop Weight Test impact breakage parameter (%)
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b}
is a JK Drop Weight Test impact ore breakage parameter
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \rho_{\rm S}}
is the density of solids (t/m3)
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathit{Wi}_{\rm BM}}
is the Bond Ball Work Index of the ore (kWh/t)
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathit{conversionMethod}}
indicates the correlation set to utilise (0 = Doll 2016, 1 = Chitalov 2020)
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\rm DW}_{\rm i}}
is the Drop Weight Index (kWh/m3)
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle M_{\rm ia}}
is the coarse ore (> 750 μm) work index in tumbling mill circuits (kWh/t)
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle M_{\rm ib}}
is the fine ore (< 750 μm) work index in tumbling mill circuits (kWh/t)
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle M_{\rm ic}}
is the ore work index in crusher circuits (kWh/t)
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle M_{\rm ih}}
is the ore work index in HPGR circuits (kWh/t)
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t_{\rm a}}
is the JK Drop Weight Test abrasion breakage parameter
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\rm SCSE}}
is the SAG Circuit Specific Energy parameter (kWh/t)
|
|
 Figure 8. Example showing the selection of the input parameters (shaded blue, red, purple and green frames), and Results (light blue frame) array in Excel.
|
See also
External links
References
- ↑ Morrell, S., Daniel, M. and Burke, J., 2016. Morrell method for determining comminution circuit specific energy and assessing energy utilization efficiency of existing circuits. Global Mining Standards and Guidelines Group: Ormstown, QC, Canada.
This content is available to registered users. Please log in to view.
