Operating Line Slope for Absorption Column 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 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 Solute Free Mole Fraction of Liquid in Outlet is the Mole fraction of the solute in the liquid at the column exit on solute free basis.ⓘ Solute Free Mole Fraction of Liquid in Outlet [X_N]			+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 Operating Line Slope of Absorption Column is the slope for operating line of absorption column plotted on solute free coordinates.ⓘ Operating Line Slope for Absorption Column [LG_ratio]

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Formula

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Operating Line Slope for Absorption Column

Formula

LG ratio = \frac{Y N+1 - Y 1}{X N - X 0}

Example

2.412961 = \frac{0.8 - 0.1}{0.3 - 0.0099}

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Operating Line Slope for Absorption Column Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
LG_ratio = (Y_N+1-Y₁)/(X_N-X₀)
This formula uses 5 Variables

Variables Used

Operating Line Slope of Absorption Column - The Operating Line Slope of Absorption Column is the slope for operating line of absorption column plotted on solute free coordinates.
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.
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.
Solute Free Mole Fraction of Liquid in Outlet - The Solute Free Mole Fraction of Liquid in Outlet is the Mole fraction of the solute in the liquid at the column exit on solute free basis.
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.

STEP 1: Convert Input(s) to Base Unit

Solute Free Mole Fraction of Gas in Inlet: 0.8 --> No Conversion Required
Solute Free Mole Fraction of Gas in Outlet: 0.1 --> No Conversion Required
Solute Free Mole Fraction of Liquid in Outlet: 0.3 --> No Conversion Required
Solute Free Mole Fraction of Liquid in Inlet: 0.0099 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

LG_ratio = (Y_N+1-Y₁)/(X_N-X₀) --> (0.8-0.1)/(0.3-0.0099)

Evaluating ... ...

LG_ratio = 2.41296104791451

STEP 3: Convert Result to Output's Unit

2.41296104791451 --> No Conversion Required

FINAL ANSWER

2.41296104791451 ≈ 2.412961 <-- Operating Line Slope of Absorption Column

(Calculation completed in 00.004 seconds)

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Home » Engineering » Chemical Engineering » Mass Transfer Operations » Gas Absorption and Stripping » Gas Absorption » Operating Line Slope for Absorption Column

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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

Operating Line Slope for Absorption Column Formula

What are the factors to be considered for Solvent Selection ?

The factors to be considered are: 1. The gas solubility should be high, thus increasing the rate of absorption and decreasing the quantity of solvent required. 2. The solvent should have a low vapour pressure to reduce loss of solvent in the gas leaving an absorption column. 3. The materials of construction required for the equipment should not be unusual or expensive. 4. The solvent should be inexpensive, so that losses are not costly, and should be readily available. 5. Low viscosity is preferred for reasons of rapid absorption rates, improved flooding characteristics in packed column, low pressure drops on pumping, and good heat transfer characteristics. 6. The solvent should be non-toxic, non-flammable and chemically stable.

What is Operating Line Slope for Absorption Column ?

The Operating Line Slope for Absorption Column is given by difference of ratios of mole fraction of gas inlet and outlet to liquid inlet and outlet.
The Operating line slope is used for plotting the number of transfer units required on solute free basis. The slope of operating line is equal to the slope of equilibrium line if the absorption factor is equal to 1. If the operating line touches the equilibrium curve then that point is called the pinch point.

How to Calculate Operating Line Slope for Absorption Column?

Operating Line Slope for Absorption Column calculator uses 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) to calculate the Operating Line Slope of Absorption Column, The Operating Line Slope for Absorption Column formula is defined as the slope for operating line of absorption column plotted on solute free basis mole fraction. Operating Line Slope of Absorption Column is denoted by LG_ratio symbol.

How to calculate Operating Line Slope for Absorption Column using this online calculator? To use this online calculator for Operating Line Slope for Absorption Column, enter Solute Free Mole Fraction of Gas in Inlet (Y_N+1), Solute Free Mole Fraction of Gas in Outlet (Y₁), Solute Free Mole Fraction of Liquid in Outlet (X_N) & Solute Free Mole Fraction of Liquid in Inlet (X₀) and hit the calculate button. Here is how the Operating Line Slope for Absorption Column calculation can be explained with given input values -> 2.413793 = (0.8-0.1)/(0.3-0.0099).

FAQ

What is Operating Line Slope for Absorption Column?

The Operating Line Slope for Absorption Column formula is defined as the slope for operating line of absorption column plotted on solute free basis mole fraction and is represented as LG_ratio = (Y_N+1-Y₁)/(X_N-X₀) or 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). 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 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 Solute Free Mole Fraction of Liquid in Outlet is the Mole fraction of the solute in the liquid at the column exit on solute free basis & 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.

How to calculate Operating Line Slope for Absorption Column?

The Operating Line Slope for Absorption Column formula is defined as the slope for operating line of absorption column plotted on solute free basis mole fraction is calculated using 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). To calculate Operating Line Slope for Absorption Column, you need Solute Free Mole Fraction of Gas in Inlet (Y_N+1), Solute Free Mole Fraction of Gas in Outlet (Y₁), Solute Free Mole Fraction of Liquid in Outlet (X_N) & Solute Free Mole Fraction of Liquid in Inlet (X₀). With our tool, you need to enter the respective value for 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 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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