Mass Balancing (Three-Product Formula): Difference between revisions
Jump to navigation
Jump to search
imported>Scott.Munro mNo edit summary |
imported>Scott.Munro m (→Model theory) |
||
| (One intermediate revision by the same user not shown) | |||
| Line 5: | Line 5: | ||
== Model theory == | == Model theory == | ||
{{Restricted content}} | |||
<hide> | |||
The three-product formula estimates the mass flow split of solids and the recovery of two assayed components from a process step with one feed and three product streams.{{Gupta and Yan (2016)}} | The three-product formula estimates the mass flow split of solids and the recovery of two assayed components from a process step with one feed and three product streams.{{Gupta and Yan (2016)}} | ||
| Line 18: | Line 21: | ||
* <math>A</math> and <math>B</math> indicate each of the two components assayed. | * <math>A</math> and <math>B</math> indicate each of the two components assayed. | ||
By rearranging the three-product mass balance equations, the solids split to concentrate and middlings is: | By rearranging the three-product mass balance equations, the solids split to concentrate, <math>S_C</math> (frac), and middlings, <math>S_M</math> (frac), is: | ||
:<math>S_C = \dfrac{C}{F} = \dfrac{ (f_A - t_A)(m_B - t_B) - (f_B - t_B)(m_A - t_A) }{ (c_A - t_A)(m_B - t_B) - (c_B - t_B)(m_A - t_A) }</math> | :<math>S_C = \dfrac{C}{F} = \dfrac{ (f_A - t_A)(m_B - t_B) - (f_B - t_B)(m_A - t_A) }{ (c_A - t_A)(m_B - t_B) - (c_B - t_B)(m_A - t_A) }</math> | ||
| Line 24: | Line 27: | ||
:<math>S_M = \dfrac{M}{F} = \dfrac{ (f_A - t_A)(c_B - t_B) - (f_B - t_B)(c_A - t_A) }{ (m_A - t_A)(c_B - t_B) - (m_B - t_B)(c_A - t_A) }</math> | :<math>S_M = \dfrac{M}{F} = \dfrac{ (f_A - t_A)(c_B - t_B) - (f_B - t_B)(c_A - t_A) }{ (m_A - t_A)(c_B - t_B) - (m_B - t_B)(c_A - t_A) }</math> | ||
The recovery of the two assayed components to concentrate and middlings is: | The recovery, <math>R</math> (frac), of the two assayed components to concentrate and middlings is: | ||
:<math>(R_A)_C = \dfrac{C}{F} . \dfrac{c_A}{f_A}</math> | :<math>(R_A)_C = \dfrac{C}{F} . \dfrac{c_A}{f_A}</math> | ||
| Line 37: | Line 40: | ||
Mineral compositions, particle size distributions and water fractions can be substituted in place of metal assays in the formula. | Mineral compositions, particle size distributions and water fractions can be substituted in place of metal assays in the formula. | ||
</hide> | |||
== Excel == | == Excel == | ||
Latest revision as of 11:38, 4 December 2024
Description
This article describes the classical two-product formula for estimating the separation efficiency of a process.
Model theory
 This content is available to registered users. Please log in to view.
|
Excel
The three-product formula may be invoked from the Excel formula bar with the following function call:
=mdMassBal_ThreeroductFormula(Assay as Range, Optional AbsSD as Range)
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:
|
| ||||
