Minimum Operating Line Slope for Absorption Column Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
LsGsmin = (YN+1-Y1)/((YN+1/α)-X0)
This formula uses 5 Variables
Variables Used
Minimum Operating Line Slope of Absorption Column - The Minimum Operating Line Slope of Absorption Column is the slope for operating line of absorption column plotted on solute free coordinates for minimum liquid flow rate.
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.
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.
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
Equilibrium Constant for Mass Transfer: 1.5 --> 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
LsGsmin = (YN+1-Y1)/((YN+1/α)-X0) --> (0.8-0.1)/((0.8/1.5)-0.0099)
Evaluating ... ...
LsGsmin = 1.33732407820162
STEP 3: Convert Result to Output's Unit
1.33732407820162 --> No Conversion Required
FINAL ANSWER
1.33732407820162 1.337324 <-- Minimum Operating Line Slope of Absorption Column
(Calculation completed in 00.004 seconds)

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DJ Sanghvi College of Engineering (DJSCE), Mumbai
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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
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))
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
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)
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

Minimum Operating Line Slope for Absorption Column Formula

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)
LsGsmin = (YN+1-Y1)/((YN+1/α)-X0)

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 Minimum Operating Line Slope for Absorption Column ?

The Minimum 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 for minimum liquid requirements. The Operating line slope is used for plotting the number of transfer units required on solute free basis. The point of contact of the operating line with the equilibrium curve is called the pinch point and the driving force becomes zero at this point. If the shape of the equilibrium curve is not straight and the operating line is a tangent to it, then the point of tangency is called the pinch point.

How to Calculate Minimum Operating Line Slope for Absorption Column?

Minimum Operating Line Slope for Absorption Column calculator uses 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) to calculate the Minimum Operating Line Slope of Absorption Column, The Minimum 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 at minimum liquid requirement. Minimum Operating Line Slope of Absorption Column is denoted by LsGsmin symbol.

How to calculate Minimum Operating Line Slope for Absorption Column using this online calculator? To use this online calculator for Minimum Operating Line Slope for Absorption Column, enter Solute Free Mole Fraction of Gas in Inlet (YN+1), Solute Free Mole Fraction of Gas in Outlet (Y1), Equilibrium Constant for Mass Transfer (α) & Solute Free Mole Fraction of Liquid in Inlet (X0) and hit the calculate button. Here is how the Minimum Operating Line Slope for Absorption Column calculation can be explained with given input values -> 1.33758 = (0.8-0.1)/((0.8/1.5)-0.0099) .

FAQ

What is Minimum Operating Line Slope for Absorption Column?
The Minimum 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 at minimum liquid requirement and is represented as LsGsmin = (YN+1-Y1)/((YN+1/α)-X0) or 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). 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 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.
How to calculate Minimum Operating Line Slope for Absorption Column?
The Minimum 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 at minimum liquid requirement is calculated using 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). To calculate Minimum Operating Line Slope for Absorption Column, you need Solute Free Mole Fraction of Gas in Inlet (YN+1), Solute Free Mole Fraction of Gas in Outlet (Y1), Equilibrium Constant for Mass Transfer (α) & 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, Equilibrium Constant for Mass Transfer & 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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