Number of Absorption Stages by Kremser Equation Calculator

✖The Solute Free Mole Fraction of Gas in Inlet is the mole fraction of the Solute in the Gas stream entering the column on solute free basis.ⓘ Solute Free Mole Fraction of Gas in Inlet [Y_N+1]			+10% -10%
✖The Equilibrium constant for Mass Transfer is the proportionality constant between gas phase mole fraction and liquid phase mole fraction and could be given as the ratio between the two.ⓘ Equilibrium Constant for Mass Transfer [α]			+10% -10%
✖The Solute Free Mole Fraction of Liquid in Inlet is the mole fraction of the solute in the solvent (liquid) in inlet of the column on solute free basis.ⓘ Solute Free Mole Fraction of Liquid in Inlet [X₀]			+10% -10%
✖The Solute Free Mole Fraction of Gas in Outlet is the mole fraction of the solute in the exit gas stream of the column on solute free basis.ⓘ Solute Free Mole Fraction of Gas in Outlet [Y₁]			+10% -10%
✖The Absorption Factor is the ratio of slopes of operating line of absorption to the equilibrium line. If equilibrium line is a curve then the absorption factor is the average at the two ends.ⓘ Absorption Factor [A]			+10% -10%

✖The Number of Stages is defined as the Ideal number of stages required to achieve the desired separation.ⓘ Number of Absorption Stages by Kremser Equation [N]

⎘ Copy

👎

Formula

✖

Number of Absorption Stages by Kremser Equation

Formula

`"N" = log10((("Y"_{"N+1"}-("α"*"X"_{"0"}))/("Y"_{"1"}-("α"*"X"_{"0"})))*(1-(1/"A"))+(1/"A"))/(log10("A"))`

Example

`"2.353434"=log10((("0.8"-("1.5"*"0.0099"))/("0.1"-("1.5"*"0.0099")))*(1-(1/"2"))+(1/"2"))/(log10("2"))`

Calculator

LaTeX

Reset

👍

Download Gas Absorption & Stripping Formula PDF

Number of Absorption Stages by Kremser Equation Solution

STEP 0: Pre-Calculation Summary

Formula Used

Number of Stages = log10(((Solute Free Mole Fraction of Gas in Inlet-(Equilibrium Constant for Mass Transfer*Solute Free Mole Fraction of Liquid in Inlet))/(Solute Free Mole Fraction of Gas in Outlet-(Equilibrium Constant for Mass Transfer*Solute Free Mole Fraction of Liquid in Inlet)))*(1-(1/Absorption Factor))+(1/Absorption Factor))/(log10(Absorption Factor))
N = log10(((Y_N+1-(α*X₀))/(Y₁-(α*X₀)))*(1-(1/A))+(1/A))/(log10(A))
This formula uses 1 Functions, 6 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

Number of Stages - The Number of Stages is defined as the Ideal number of stages required to achieve the desired separation.
Solute Free Mole Fraction of Gas in Inlet - The Solute Free Mole Fraction of Gas in Inlet is the mole fraction of the Solute in the Gas stream entering the column on solute free basis.
Equilibrium Constant for Mass Transfer - The Equilibrium constant for Mass Transfer is the proportionality constant between gas phase mole fraction and liquid phase mole fraction and could be given as the ratio between the two.
Solute Free Mole Fraction of Liquid in Inlet - The Solute Free Mole Fraction of Liquid in Inlet is the mole fraction of the solute in the solvent (liquid) in inlet of the column on solute free basis.
Solute Free Mole Fraction of Gas in Outlet - The Solute Free Mole Fraction of Gas in Outlet is the mole fraction of the solute in the exit gas stream of the column on solute free basis.
Absorption Factor - The Absorption Factor is the ratio of slopes of operating line of absorption to the equilibrium line. If equilibrium line is a curve then the absorption factor is the average at the two ends.

STEP 1: Convert Input(s) to Base Unit

Solute Free Mole Fraction of Gas in Inlet: 0.8 --> No Conversion Required
Equilibrium Constant for Mass Transfer: 1.5 --> No Conversion Required
Solute Free Mole Fraction of Liquid in Inlet: 0.0099 --> No Conversion Required
Solute Free Mole Fraction of Gas in Outlet: 0.1 --> No Conversion Required
Absorption Factor: 2 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

N = log10(((Y_N+1-(α*X₀))/(Y₁-(α*X₀)))*(1-(1/A))+(1/A))/(log10(A)) --> log10(((0.8-(1.5*0.0099))/(0.1-(1.5*0.0099)))*(1-(1/2))+(1/2))/(log10(2))

Evaluating ... ...

N = 2.35343436124061

STEP 3: Convert Result to Output's Unit

2.35343436124061 --> No Conversion Required

FINAL ANSWER

2.35343436124061 ≈ 2.353434 <-- Number of Stages

(Calculation completed in 00.004 seconds)

You are here -

Home » Engineering » Chemical Engineering » Mass Transfer Operations » Gas Absorption & Stripping » Gas Absorption » Number of Absorption Stages by Kremser Equation

Credits

Created by Vaibhav Mishra

DJ Sanghvi College of Engineering (DJSCE), Mumbai

Vaibhav Mishra has created this Calculator and 300+ more calculators!

Verified by Soupayan banerjee

National University of Judicial Science (NUJS), Kolkata

Soupayan banerjee has verified this Calculator and 800+ more calculators!

< 10+ Gas Absorption Calculators

Number of Absorption Stages by Kremser Equation

Go Number of Stages = log10(((Solute Free Mole Fraction of Gas in Inlet-(Equilibrium Constant for Mass Transfer*Solute Free Mole Fraction of Liquid in Inlet))/(Solute Free Mole Fraction of Gas in Outlet-(Equilibrium Constant for Mass Transfer*Solute Free Mole Fraction of Liquid in Inlet)))*(1-(1/Absorption Factor))+(1/Absorption Factor))/(log10(Absorption Factor))

Maximum Gas Rate for Absorption Column

Go Maximum Gas Flowrate on Solute Free Basis = Liquid Flowrate on Solute Free Basis/((Solute Free Mole Fraction of Gas in Inlet- Solute Free Mole Fraction of Gas in Outlet)/((Solute Free Mole Fraction of Gas in Inlet/Equilibrium Constant for Mass Transfer)-Solute Free Mole Fraction of Liquid in Inlet))

Minimum Liquid Rate for Absorption Column

Go Minimum Liquid Flowrate on Solute Free Basis = Gas Flowrate on Solute Free Basis*(Solute Free Mole Fraction of Gas in Inlet-Solute Free Mole Fraction of Gas in Outlet)/((Solute Free Mole Fraction of Gas in Inlet/Equilibrium Constant for Mass Transfer)-Solute Free Mole Fraction of Liquid in Inlet)

Minimum Operating Line Slope for Absorption Column

Go Minimum Operating Line Slope of Absorption Column = (Solute Free Mole Fraction of Gas in Inlet-Solute Free Mole Fraction of Gas in Outlet)/((Solute Free Mole Fraction of Gas in Inlet/Equilibrium Constant for Mass Transfer)-Solute Free Mole Fraction of Liquid in Inlet)

Gas Flowrate for Absorption Column on Solute Free Basis

Go Gas Flowrate on Solute Free Basis = Liquid Flowrate on Solute Free Basis/((Solute Free Mole Fraction of Gas in Inlet-Solute Free Mole Fraction of Gas in Outlet)/(Solute Free Mole Fraction of Liquid in Outlet-Solute Free Mole Fraction of Liquid in Inlet))

Liquid Flowrate for Absorption Column on Solute Free basis

Go Liquid Flowrate on Solute Free Basis = Gas Flowrate on Solute Free Basis*(Solute Free Mole Fraction of Gas in Inlet-Solute Free Mole Fraction of Gas in Outlet)/(Solute Free Mole Fraction of Liquid in Outlet-Solute Free Mole Fraction of Liquid in Inlet)

Number of Stages for Absorption Factor Equal to 1

Go Number of Stages = (Solute Free Mole Fraction of Gas in Inlet-Solute Free Mole Fraction of Gas in Outlet)/(Solute Free Mole Fraction of Gas in Outlet-(Equilibrium Constant for Mass Transfer*Solute Free Mole Fraction of Liquid in Inlet))

Operating Line Slope for Absorption Column

Go Operating Line Slope of Absorption Column = (Solute Free Mole Fraction of Gas in Inlet-Solute Free Mole Fraction of Gas in Outlet)/(Solute Free Mole Fraction of Liquid in Outlet-Solute Free Mole Fraction of Liquid in Inlet)

Absorption Factor

Go Absorption Factor = Liquid Flowrate on Solute Free Basis/(Equilibrium Constant for Mass Transfer*Gas Flowrate on Solute Free Basis)

Absorption Factor given Stripping Factor

Go Absorption Factor = 1/Stripping Factor

< 24 Important Formulas in Gas Absorption & Stripping Calculators

Number of Stripping Stages by Kremser Equation

Go Number of Stages = (log10(((Solute Free Mole Frac of Liquid in Stripping Inlet-(Solute Free Mole Frac of Gas in Stripping Inlet/Equilibrium Constant for Mass Transfer))/(Solute Free Mole Frac of Liquid in Stripping Out-(Solute Free Mole Frac of Gas in Stripping Inlet/Equilibrium Constant for Mass Transfer)))*(1-(1/Stripping Factor))+(1/Stripping Factor)))/(log10(Stripping Factor))

Number of Absorption Stages by Kremser Equation

Maximum Gas Rate for Absorption Column

Minimum Liquid Rate for Absorption Column

Minimum Operating Line Slope for Absorption Column

Gas Flowrate for Absorption Column on Solute Free Basis

Liquid Flowrate for Absorption Column on Solute Free basis

Number of Stages for Absorption Factor Equal to 1

Point Efficiency of Absorption Operation

Go Point Efficiency of Absorption Column in Percent = ((Local Mole Fraction of Vapor Leaving Nth Plate-Local Mole Fraction of Vapor Entering Nth Plate)/(Local Eqm Mole Fraction of Vapor on Nth Plate-Local Mole Fraction of Vapor Entering Nth Plate))*100

Murphree Tray Efficiency of Absorption Operation

Go Murphree Efficiency of Absorption 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

Operating Line Slope for Absorption Column

Corrected Murphree Efficiency Percentage for Liquid Entrainment

Go Corrected Murphree Efficiency for Absorption = ((Murphree Efficiency of Absorption Column/100)/(1+((Murphree Efficiency of Absorption Column/100)*(Fractional Entrainment/(1-Fractional Entrainment)))))*100

Overall Tray Efficiency for Absorption Column given Murphree Efficiency

Go Overall Tray Efficiency of Absorption Column = (ln(1+(Murphree Efficiency of Absorption Column/100)*((1/Absorption Factor)-1))/ln(1/Absorption Factor))*100

Murphree Efficiency of Absorption Operation Based on Point Efficiency for Plug Flow

Go Murphree Efficiency of Absorption Column = (Absorption Factor*(exp(Point Efficiency of Absorption Column in Percent/(Absorption Factor*100))-1))*100

Stripping Factor

Go Stripping Factor = (Equilibrium Constant for Mass Transfer*Gas Flowrate on Solute Free Basis for Stripping)/Liquid Flowrate on Solute Free Basis for Stripping

Absorption Factor

Go Absorption Factor = Liquid Flowrate on Solute Free Basis/(Equilibrium Constant for Mass Transfer*Gas Flowrate on Solute Free Basis)

Liquid Flowrate on Solute Free Basis for Inlet Conditions by Solute Free Mole Fraction

Go Liquid Flowrate on Solute Free Basis = Inlet Liquid Flowrate/(1+Solute Free Mole Fraction of Liquid in Inlet)

Solute Free Mole Fraction of Liquid in Inlet based on Mole Fraction

Go Solute Free Mole Fraction of Liquid in Inlet = Liquid Inlet Mole Fraction/(1-Liquid Inlet Mole Fraction)

Gas Flowrate on Solute Free Basis for Inlet Conditions by Solute Free Mole Fraction

Go Gas Flowrate on Solute Free Basis = Inlet Gas Flowrate/(1+Solute Free Mole Fraction of Gas in Inlet)

Solute Free Mole Fraction of Gas in Inlet based on Mole Fraction

Go Solute Free Mole Fraction of Gas in Inlet = Gas Inlet Mole Fraction/(1-Gas Inlet Mole Fraction)

Liquid Flowrate on Solute Free Basis for Inlet Conditions using Mole Fraction

Go Liquid Flowrate on Solute Free Basis = Inlet Liquid Flowrate*(1-Liquid Inlet Mole Fraction)

Gas Flowrate on Solute Free Basis for Inlet Conditions by Mole Fraction

Go Gas Flowrate on Solute Free Basis = Inlet Gas Flowrate*(1-Gas Inlet Mole Fraction)

Stripping Factor given Absorption Factor

Go Stripping Factor = 1/Absorption Factor

Absorption Factor given Stripping Factor

Go Absorption Factor = 1/Stripping Factor

Number of Absorption Stages by Kremser Equation Formula

What is the Kremser - Souders - Brown Equation?

In unit operation design calculations, it is useful to find out the quality of separation for a given number of stages. It is also useful to find the required number of stages if the product recovery is specified. The development was first given by Kremser in 1930, and by Souders and Brown in 1932. The resulting equations are referred to as the KSB or Kremser equations.
These equation were originally developed for gas absorption operation in a plate column, however, it is applicable to other mass transfer operations as well (for example, counter current adsorption).

How to Calculate Number of Absorption Stages by Kremser Equation?

Number of Absorption Stages by Kremser Equation calculator uses Number of Stages = log10(((Solute Free Mole Fraction of Gas in Inlet-(Equilibrium Constant for Mass Transfer*Solute Free Mole Fraction of Liquid in Inlet))/(Solute Free Mole Fraction of Gas in Outlet-(Equilibrium Constant for Mass Transfer*Solute Free Mole Fraction of Liquid in Inlet)))*(1-(1/Absorption Factor))+(1/Absorption Factor))/(log10(Absorption Factor)) to calculate the Number of Stages, The Number of Absorption Stages by Kremser Equation formula is defined as the calculation for number of stages for dilute systems having straight operating line in absorption algebraically. Number of Stages is denoted by N symbol.

How to calculate Number of Absorption Stages by Kremser Equation using this online calculator? To use this online calculator for Number of Absorption Stages by Kremser Equation, enter Solute Free Mole Fraction of Gas in Inlet (Y_N+1), Equilibrium Constant for Mass Transfer (α), Solute Free Mole Fraction of Liquid in Inlet (X₀), Solute Free Mole Fraction of Gas in Outlet (Y₁) & Absorption Factor (A) and hit the calculate button. Here is how the Number of Absorption Stages by Kremser Equation calculation can be explained with given input values -> 2.355481 = log10(((0.8-(1.5*0.0099))/(0.1-(1.5*0.0099)))*(1-(1/2))+(1/2))/(log10(2)).

FAQ

What is Number of Absorption Stages by Kremser Equation?

The Number of Absorption Stages by Kremser Equation formula is defined as the calculation for number of stages for dilute systems having straight operating line in absorption algebraically and is represented as N = log10(((Y_N+1-(α*X₀))/(Y₁-(α*X₀)))*(1-(1/A))+(1/A))/(log10(A)) or Number of Stages = log10(((Solute Free Mole Fraction of Gas in Inlet-(Equilibrium Constant for Mass Transfer*Solute Free Mole Fraction of Liquid in Inlet))/(Solute Free Mole Fraction of Gas in Outlet-(Equilibrium Constant for Mass Transfer*Solute Free Mole Fraction of Liquid in Inlet)))*(1-(1/Absorption Factor))+(1/Absorption Factor))/(log10(Absorption Factor)). The Solute Free Mole Fraction of Gas in Inlet is the mole fraction of the Solute in the Gas stream entering the column on solute free basis, The Equilibrium constant for Mass Transfer is the proportionality constant between gas phase mole fraction and liquid phase mole fraction and could be given as the ratio between the two, The Solute Free Mole Fraction of Liquid in Inlet is the mole fraction of the solute in the solvent (liquid) in inlet of the column on solute free basis, The Solute Free Mole Fraction of Gas in Outlet is the mole fraction of the solute in the exit gas stream of the column on solute free basis & The Absorption Factor is the ratio of slopes of operating line of absorption to the equilibrium line. If equilibrium line is a curve then the absorption factor is the average at the two ends.

How to calculate Number of Absorption Stages by Kremser Equation?

The Number of Absorption Stages by Kremser Equation formula is defined as the calculation for number of stages for dilute systems having straight operating line in absorption algebraically is calculated using Number of Stages = log10(((Solute Free Mole Fraction of Gas in Inlet-(Equilibrium Constant for Mass Transfer*Solute Free Mole Fraction of Liquid in Inlet))/(Solute Free Mole Fraction of Gas in Outlet-(Equilibrium Constant for Mass Transfer*Solute Free Mole Fraction of Liquid in Inlet)))*(1-(1/Absorption Factor))+(1/Absorption Factor))/(log10(Absorption Factor)). To calculate Number of Absorption Stages by Kremser Equation, you need Solute Free Mole Fraction of Gas in Inlet (Y_N+1), Equilibrium Constant for Mass Transfer (α), Solute Free Mole Fraction of Liquid in Inlet (X₀), Solute Free Mole Fraction of Gas in Outlet (Y₁) & Absorption Factor (A). With our tool, you need to enter the respective value for Solute Free Mole Fraction of Gas in Inlet, Equilibrium Constant for Mass Transfer, Solute Free Mole Fraction of Liquid in Inlet, Solute Free Mole Fraction of Gas in Outlet & Absorption Factor and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Number of Stages?

In this formula, Number of Stages uses Solute Free Mole Fraction of Gas in Inlet, Equilibrium Constant for Mass Transfer, Solute Free Mole Fraction of Liquid in Inlet, Solute Free Mole Fraction of Gas in Outlet & Absorption Factor. We can use 3 other way(s) to calculate the same, which is/are as follows -

Number of Stages = (Solute Free Mole Fraction of Gas in Inlet-Solute Free Mole Fraction of Gas in Outlet)/(Solute Free Mole Fraction of Gas in Outlet-(Equilibrium Constant for Mass Transfer*Solute Free Mole Fraction of Liquid in Inlet))
Number of Stages = (log10(((Solute Free Mole Frac of Liquid in Stripping Inlet-(Solute Free Mole Frac of Gas in Stripping Inlet/Equilibrium Constant for Mass Transfer))/(Solute Free Mole Frac of Liquid in Stripping Out-(Solute Free Mole Frac of Gas in Stripping Inlet/Equilibrium Constant for Mass Transfer)))*(1-(1/Stripping Factor))+(1/Stripping Factor)))/(log10(Stripping Factor))
Number of Stages = (Solute Free Mole Fraction of Gas in Inlet-Solute Free Mole Fraction of Gas in Outlet)/(Solute Free Mole Fraction of Gas in Outlet-(Equilibrium Constant for Mass Transfer*Solute Free Mole Fraction of Liquid in Inlet))

Home

FREE PDFs

🔍 Search