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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Formula

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Minimum Number of Distillation Stages by Fenske's Equation

Formula

`"N"_{"m"} = ((log10(("x"_{"D"}*(1-"x"_{"W"}))/("x"_{"W"}*(1-"x"_{"D"}))))/(log10("α"_{"avg"})))-1`

Example

`"2.026557"=((log10(("0.9"*(1-"0.2103"))/("0.2103"*(1-"0.9"))))/(log10("3.2")))-1`

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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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Home » Engineering » Chemical Engineering » Mass Transfer Operations » Distillation » Continuous Distillation » Minimum Number of Distillation Stages by Fenske's Equation

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< 13 Continuous Distillation Calculators

Minimum Number of Distillation Stages by Fenske's Equation

Go 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

Murphree Efficiency of Distillation Column Based on Vapour Phase

Go Murphree Efficiency of Distillation Column = ((Average Mole Fraction of Vapour on Nth Plate-Average Mole Fraction of Vapour at N+1 Plate)/ (Average Mole Fraction at Equilibrium on Nth Plate-Average Mole Fraction of Vapour at N+1 Plate))*100

Feed Q-Value in Distillation Column

Go Q-value in Mass Transfer = Heat Required to Convert Feed to Saturated Vapor/Molal Latent Heat of Vaporization of Saturated Liq

Internal Liquid Reflux Flowrate based on Internal Reflux Ratio

Go Internal Reflux Flowrate to Distillation Column = Internal Reflux Ratio*Distillate Flowrate from Distillation Column

Liquid Reflux Flowrate based on External Reflux Ratio

Go External Reflux Flowrate to Distillation Column = External Reflux Ratio*Distillate Flowrate from Distillation Column

Distillate Flowrate based on External Reflux Ratio

Go Distillate Flowrate from Distillation Column = External Reflux Flowrate to Distillation Column/External Reflux Ratio

Distillate Flowrate based on Internal Reflux Ratio

Go Distillate Flowrate from Distillation Column = Internal Reflux Flowrate to Distillation Column/Internal Reflux Ratio

External Reflux Ratio

Go External Reflux Ratio = External Reflux Flowrate to Distillation Column/Distillate Flowrate from Distillation Column

Internal Reflux Ratio

Go Internal Reflux Ratio = Internal Reflux Flowrate to Distillation Column/Distillate Flowrate from Distillation Column

Bottom Product based on Boil-up Ratio

Go Residue Flowrate from Distillation Column = Boil-Up Flowrate to the Distillation Column/Boil-Up Ratio

Vapor Reflux based on Boil-Up Ratio

Go Boil-Up Flowrate to the Distillation Column = Boil-Up Ratio*Residue Flowrate from Distillation Column

Boil-Up Ratio

Go Boil-Up Ratio = Boil-Up Flowrate to the Distillation Column/Residue Flowrate from Distillation Column

Overall Efficiency of Distillation Column

Go Overall Efficiency of Distillation Column = (Ideal Number of Plates/Actual Number of Plates)*100

< 20 Important Formulas in Distillation Mass Transfer Operation Calculators

Total Steam Required to Vaporize Volatile Component

Go Total Steam Required to Vaporize Volatile Comp = (((Total Pressure of System/(Vaporizing Efficiency*Vapor Pressure of Volatile Component))-1)*(Initial Moles of Volatile Component-Final Moles of Volatile Component))+((Total Pressure of System*Moles of Non-Volatile Component/(Vaporizing Efficiency*Vapor Pressure of Volatile Component))*ln(Initial Moles of Volatile Component/Final Moles of Volatile Component))

Moles of Volatile component Volatilized from mixture of Non-Volatiles by Steam

Go Moles of Volatile Component = Moles of Steam*((Vaporizing Efficiency*Mole Fraction of Volatile Comp in Non-Volatiles*Vapor Pressure of Volatile Component)/(Total Pressure of System-Vaporizing Efficiency*Mole Fraction of Volatile Comp in Non-Volatiles*Vapor Pressure of Volatile Component))

Minimum Number of Distillation Stages by Fenske's Equation

Mole Fraction of MVC in Feed from Overall and Component Material Balance in Distillation

Go Mole Fraction of More Volatile Component in Feed = (Distillate Flowrate*Mole Fraction of More Volatile Comp in Distillate+Residue Flowrate from Distillation Column*Mole Fraction of More Volatile Comp in Residue)/(Distillate Flowrate+Residue Flowrate from Distillation Column)

Moles of Volatile component Volatilized from mixture of Non-Volatiles by Steam at Equilibrium

Go Moles of Volatile Component = Moles of Steam*(Mole Fraction of Volatile Comp in Non-Volatiles*Vapor Pressure of Volatile Component/(Total Pressure of System-Mole Fraction of Volatile Comp in Non-Volatiles*Vapor Pressure of Volatile Component))

Moles of Volatile component Volatilized by Steam with Trace amounts of Non-Volatiles

Go Moles of Volatile Component = Moles of Steam*((Vaporizing Efficiency*Vapor Pressure of Volatile Component)/(Total Pressure of System-(Vaporizing Efficiency*Vapor Pressure of Volatile Component)))

Murphree Efficiency of Distillation Column Based on Vapour Phase

Relative Volatility using Mole Fraction

Go Relative Volatility = (Mole Fraction of Component in Vapor Phase/(1-Mole Fraction of Component in Vapor Phase))/(Mole Fraction of Component in Liquid Phase/(1-Mole Fraction of Component in Liquid Phase))

Total Pressure using Mole Fraction and Saturated Pressure

Go Total Pressure of Gas = (Mole Fraction of MVC in Liq Phase*Partial Pressure of More Volatile Component)+((1-Mole Fraction of MVC in Liq Phase)*Partial Pressure of Less Volatile Component)

Moles of Volatile component Volatilized by Steam with Trace amounts of Non-Volatiles at Equilibrium

Go Moles of Volatile Component = Moles of Steam*(Vapor Pressure of Volatile Component/(Total Pressure of System-Vapor Pressure of Volatile Component))

Feed Q-Value in Distillation Column

Go Q-value in Mass Transfer = Heat Required to Convert Feed to Saturated Vapor/Molal Latent Heat of Vaporization of Saturated Liq

Relative Volatility using Vapour Pressure

Go Relative Volatility = Saturated Vapour Pressure of More Volatile Comp/Saturated Vapour Pressure of Less Volatile Comp

External Reflux Ratio

Go External Reflux Ratio = External Reflux Flowrate to Distillation Column/Distillate Flowrate from Distillation Column

Internal Reflux Ratio

Go Internal Reflux Ratio = Internal Reflux Flowrate to Distillation Column/Distillate Flowrate from Distillation Column

Equilibrium Vaporization Ratio for Less Volatile Component

Go Equilibrium Vaporization Ratio of LVC = Mole Fraction of LVC in Vapor Phase/Mole Fraction of LVC in Liquid Phase

Equilibrium Vaporization Ratio for More Volatile Component

Go Equilibrium Vaporization Ratio of MVC = Mole Fraction of MVC in Vapor Phase/Mole Fraction of MVC in Liquid Phase

Boil-Up Ratio

Go Boil-Up Ratio = Boil-Up Flowrate to the Distillation Column/Residue Flowrate from Distillation Column

Total Feed Flowrate of Distillation Column from Overall Material Balance

Go Feed Flowrate to Distillation Column = Distillate Flowrate+Residue Flowrate from Distillation Column

Relative Volatility using Equilibrium Vaporization Ratio

Go Relative Volatility = Equilibrium Vaporization Ratio of MVC/Equilibrium Vaporization Ratio of LVC

Overall Efficiency of Distillation Column

Go Overall Efficiency of Distillation Column = (Ideal Number of Plates/Actual Number of Plates)*100

Minimum Number of Distillation Stages by Fenske's Equation Formula

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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