Mass Balancing (Two-Product Formula)

Description

This article describes the classical two-product formula for estimating the separation efficiency of a process.

Model theory

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Excel

The two-product formula may be invoked from the Excel formula bar with the following function call:

=mdMassBal_TwoProductFormula(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:

${\begin{aligned}{\mathit {Assay}}&={\begin{bmatrix}f\\c\\t\\\end{bmatrix}}\\\\{\mathit {AbsSD}}&={\begin{bmatrix}\sigma _{f}\\\sigma _{c}\\\sigma _{t}\\\end{bmatrix}}\\\end{aligned}}$ ${\begin{aligned}{\mathit {mdMassBal\_TwoProductFormula}}&={\begin{bmatrix}S{\text{ (frac)}}&R{\text{ (frac)}}\\\sigma _{S}{\text{ (frac)}}&\sigma _{R}{\text{ (frac)}}\\\end{bmatrix}}\end{aligned}}$ where ${\mathit {AbsSD}}$ is an optional input and the standard deviation error estimates ($\sigma _{S}$, $\sigma _{R}$) are not returned if omitted.

Figure 1. Example showing the selection of the Assay (blue frame), AbsSD (red frame), and Results (light blue frame) arrays in Excel.

See also

• Mass Balancing (Three-Product Formula)
• Mass Balancing (n-Product Formula)