Minimum Number of Distillation Stages by Fenske's Equation Calculator

✖The Mole Fraction of More Volatile comp in Distillate of Distillation Column is the mole fraction of More Volatile Component in the distillate stream of distillation column.ⓘ Mole Fraction of More Volatile Comp in Distillate [x_D]			+10% -10%
✖The Mole Fraction of More Volatile comp in Residue of Distillation Column is the mole fraction of More Volatile Component in the residue stream of distillation column.ⓘ Mole Fraction of More Volatile Comp in Residue [x_W]			+10% -10%
✖The Average Relative Volatility is the ratio of the volatility of the More Volatile component to the volatility of the Less Volatile component, averaged at top and bottom column conditions.ⓘ Average Relative Volatility [α_avg]			+10% -10%

✖The minimum number of stages in the distillation column is the minimum stages required to achieve a specified separation.ⓘ Minimum Number of Distillation Stages by Fenske's Equation [N_m]

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Minimum Number of Distillation Stages by Fenske's Equation Solution

STEP 0: Pre-Calculation Summary

Formula Used

Minimum Number of Stages = ((log10((Mole Fraction of More Volatile Comp in Distillate*(1-Mole Fraction of More Volatile Comp in Residue))/(Mole Fraction of More Volatile Comp in Residue*(1-Mole Fraction of More Volatile Comp in Distillate))))/(log10(Average Relative Volatility)))-1
N_m = ((log10((x_D*(1-x_W))/(x_W*(1-x_D))))/(log10(α_avg)))-1
This formula uses 1 Functions, 4 Variables

Functions Used

log10 - The common logarithm, also known as the base-10 logarithm or the decimal logarithm, is a mathematical function that is the inverse of the exponential function., log10(Number)

Variables Used

Minimum Number of Stages - The minimum number of stages in the distillation column is the minimum stages required to achieve a specified separation.
Mole Fraction of More Volatile Comp in Distillate - The Mole Fraction of More Volatile comp in Distillate of Distillation Column is the mole fraction of More Volatile Component in the distillate stream of distillation column.
Mole Fraction of More Volatile Comp in Residue - The Mole Fraction of More Volatile comp in Residue of Distillation Column is the mole fraction of More Volatile Component in the residue stream of distillation column.
Average Relative Volatility - The Average Relative Volatility is the ratio of the volatility of the More Volatile component to the volatility of the Less Volatile component, averaged at top and bottom column conditions.

STEP 1: Convert Input(s) to Base Unit

Mole Fraction of More Volatile Comp in Distillate: 0.9 --> No Conversion Required
Mole Fraction of More Volatile Comp in Residue: 0.2103 --> No Conversion Required
Average Relative Volatility: 3.2 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

N_m = ((log10((x_D*(1-x_W))/(x_W*(1-x_D))))/(log10(α_avg)))-1 --> ((log10((0.9*(1-0.2103))/(0.2103*(1-0.9))))/(log10(3.2)))-1

Evaluating ... ...

N_m = 2.02655734016058

STEP 3: Convert Result to Output's Unit

2.02655734016058 --> No Conversion Required

FINAL ANSWER

2.02655734016058 ≈ 2.026557 <-- Minimum Number of Stages

(Calculation completed in 00.004 seconds)

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Minimum Number of Distillation Stages by Fenske's Equation Formula

LaTeX Go

What is Fenske's Equation?

The Fenske equation in continuous fractional distillation is an equation used for calculating the minimum number of theoretical plates required for the separation of a binary feed stream by a fractionation column that is being operated at total reflux (i.e., which means that no overhead product distillate is being withdrawn from the column).
The equation was derived in 1932 by Merrell Fenske, a professor who served as the head of the chemical engineering department at the Pennsylvania State University from 1959 to 1969.
When designing large-scale, continuous industrial distillation towers, it is very useful to first calculate the minimum number of theoretical plates required to obtain the desired overhead product composition.

How to Calculate Minimum Number of Distillation Stages by Fenske's Equation?

Minimum Number of Distillation Stages by Fenske's Equation calculator uses Minimum Number of Stages = ((log10((Mole Fraction of More Volatile Comp in Distillate*(1-Mole Fraction of More Volatile Comp in Residue))/(Mole Fraction of More Volatile Comp in Residue*(1-Mole Fraction of More Volatile Comp in Distillate))))/(log10(Average Relative Volatility)))-1 to calculate the Minimum Number of Stages, The Minimum Number of Distillation Stages by Fenske's Equation formula is defined as minimum number of stages required to achieve a specified separation in distillation column based on Fenske's method. Minimum Number of Stages is denoted by N_m symbol.

How to calculate Minimum Number of Distillation Stages by Fenske's Equation using this online calculator? To use this online calculator for Minimum Number of Distillation Stages by Fenske's Equation, enter Mole Fraction of More Volatile Comp in Distillate (x_D), Mole Fraction of More Volatile Comp in Residue (x_W) & Average Relative Volatility (α_avg) and hit the calculate button. Here is how the Minimum Number of Distillation Stages by Fenske's Equation calculation can be explained with given input values -> 2.778056 = ((log10((0.9*(1-0.2103))/(0.2103*(1-0.9))))/(log10(3.2)))-1.

FAQ

What is Minimum Number of Distillation Stages by Fenske's Equation?

The Minimum Number of Distillation Stages by Fenske's Equation formula is defined as minimum number of stages required to achieve a specified separation in distillation column based on Fenske's method and is represented as N_m = ((log10((x_D*(1-x_W))/(x_W*(1-x_D))))/(log10(α_avg)))-1 or Minimum Number of Stages = ((log10((Mole Fraction of More Volatile Comp in Distillate*(1-Mole Fraction of More Volatile Comp in Residue))/(Mole Fraction of More Volatile Comp in Residue*(1-Mole Fraction of More Volatile Comp in Distillate))))/(log10(Average Relative Volatility)))-1. The Mole Fraction of More Volatile comp in Distillate of Distillation Column is the mole fraction of More Volatile Component in the distillate stream of distillation column, The Mole Fraction of More Volatile comp in Residue of Distillation Column is the mole fraction of More Volatile Component in the residue stream of distillation column & The Average Relative Volatility is the ratio of the volatility of the More Volatile component to the volatility of the Less Volatile component, averaged at top and bottom column conditions.

How to calculate Minimum Number of Distillation Stages by Fenske's Equation?

The Minimum Number of Distillation Stages by Fenske's Equation formula is defined as minimum number of stages required to achieve a specified separation in distillation column based on Fenske's method is calculated using Minimum Number of Stages = ((log10((Mole Fraction of More Volatile Comp in Distillate*(1-Mole Fraction of More Volatile Comp in Residue))/(Mole Fraction of More Volatile Comp in Residue*(1-Mole Fraction of More Volatile Comp in Distillate))))/(log10(Average Relative Volatility)))-1. To calculate Minimum Number of Distillation Stages by Fenske's Equation, you need Mole Fraction of More Volatile Comp in Distillate (x_D), Mole Fraction of More Volatile Comp in Residue (x_W) & Average Relative Volatility (α_avg). With our tool, you need to enter the respective value for Mole Fraction of More Volatile Comp in Distillate, Mole Fraction of More Volatile Comp in Residue & Average Relative Volatility and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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