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(((YN+1-(α*X0))/(Y1-(α*X0)))*(1-(1/A))+(1/A))/log10(A)
This formula uses 1 Functions, 6 Variables
Functions Used
log10 - Common logarithm function (base 10), 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: 0.01 --> 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(((YN+1-(α*X0))/(Y1-(α*X0)))*(1-(1/A))+(1/A))/log10(A) --> log10(((0.8-(1.5*0.01))/(0.1-(1.5*0.01)))*(1-(1/2))+(1/2))/log10(2)
Evaluating ... ...
N = 2.35548065459839
STEP 3: Convert Result to Output's Unit
2.35548065459839 --> No Conversion Required
FINAL ANSWER
2.35548065459839 <-- Number of Stages
(Calculation completed in 00.000 seconds)

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10+ Gas Absorption Calculators

Number of Absorption Stages by Kremser Equation
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) Go
Maximum Gas Rate for Absorption Column
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)) Go
Minimum Liquid Rate for Absorption Column
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) Go
Minimum Operating Line Slope for Absorption Column
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) Go
Gas Flowrate for Absorption Column on Solute Free Basis
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)) Go
Liquid Flowrate for Absorption Column on Solute Free basis
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) Go
Number of Stages for Absorption Factor Equal to 1
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)) Go
Operating Line Slope for Absorption Column
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) Go
Absorption Factor
Absorption Factor = Liquid Flowrate on Solute Free Basis/(Equilibrium Constant for Mass Transfer*Gas Flowrate on Solute Free Basis) Go
Absorption Factor based on Stripping Factor
Absorption Factor = 1/Stripping Factor Go

Number of Absorption Stages by Kremser Equation Formula

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(((YN+1-(α*X0))/(Y1-(α*X0)))*(1-(1/A))+(1/A))/log10(A)

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 (YN+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*0.01))/(0.1-(1.5*0.01)))*(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(((YN+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 (YN+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 1 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))
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