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]

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Formula

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Number of Absorption Stages by Kremser Equation

Formula

N = \log 10 \frac{(\frac{Y N+1 - (α \cdot X 0)}{Y 1 - (α \cdot X 0)}) \cdot (1 - (\frac{1}{A})) + (\frac{1}{A})}{\log 10 (A)}

Example

2.353434 = \log 10 \frac{(\frac{0.8 - (1.5 \cdot 0.0099)}{0.1 - (1.5 \cdot 0.0099)}) \cdot (1 - (\frac{1}{2})) + (\frac{1}{2})}{\log 10 (2)}

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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 00.020 seconds)

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< 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))

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)

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)

< Important Formulas in Gas Absorption and 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))

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)

Stripping Factor given Absorption Factor

Go Stripping Factor = 1/Absorption 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))

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