Number of Extraction Stages by Kremser Equation Solution

STEP 0: Pre-Calculation Summary
Formula Used
Number of Equilibrium Extraction Stages = log10(((Mass Fraction of Solute in the Feed-(Mass Fraction of Solute in the Solvent/Distribution Coefficient of Solute))/(Mass Fraction of Solute in the Raffinate-(Mass Fraction of Solute in the Solvent/Distribution Coefficient of Solute)))*(1-(1/Extraction Factor))+(1/Extraction Factor))/(log10(Extraction Factor))
N = log10(((zC-(ys/KSolute))/(xC-(ys/KSolute)))*(1-(1/ε))+(1/ε))/(log10(ε))
This formula uses 1 Functions, 6 Variables
Functions Used
log10 - Common logarithm function (base 10), log10(Number)
Variables Used
Number of Equilibrium Extraction Stages - The Number of Equilibrium Extraction Stages is the number of Ideal Equilibrium stages required for Liquid-Liquid Extraction.
Mass Fraction of Solute in the Feed - The Mass Fraction of Solute in the Feed is the mass fraction of the solute in the Feed to the Liquid-Liquid Extraction operation.
Mass Fraction of Solute in the Solvent - The Mass Fraction of Solute in the Solvent is the mass ratio of the solute in the inlet solvent to the solvent mass in Liquid-Liquid Extraction operation.
Distribution Coefficient of Solute - The distribution coefficient of solute is defined as the concentration of solute in the extract phase divided by the concentration of solute in the raffinate phase.
Mass Fraction of Solute in the Raffinate - The Mass Fraction of Solute in the Raffinate Phase is the mass fraction of the solute in the raffinate phase after separation of the ternary mixture.
Extraction Factor - The Extraction Factor is defined as the ratio of the slope of equilibrium line to the slope of operating line.
STEP 1: Convert Input(s) to Base Unit
Mass Fraction of Solute in the Feed: 0.5 --> No Conversion Required
Mass Fraction of Solute in the Solvent: 0.05 --> No Conversion Required
Distribution Coefficient of Solute: 2.6 --> No Conversion Required
Mass Fraction of Solute in the Raffinate: 0.35 --> No Conversion Required
Extraction Factor: 2.4 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
N = log10(((zC-(ys/KSolute))/(xC-(ys/KSolute)))*(1-(1/ε))+(1/ε))/(log10(ε)) --> log10(((0.5-(0.05/2.6))/(0.35-(0.05/2.6)))*(1-(1/2.4))+(1/2.4))/(log10(2.4))
Evaluating ... ...
N = 0.268089954216616
STEP 3: Convert Result to Output's Unit
0.268089954216616 --> No Conversion Required
FINAL ANSWER
0.268089954216616 <-- Number of Equilibrium Extraction Stages
(Calculation completed in 00.000 seconds)

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DJ Sanghvi College of Engineering (DJSCE), Mumbai
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6 Kremser's Equation for Liquid-Liquid Extraction Calculators

Number of Extraction Stages by Kremser Equation

Number of Extraction Stages by Kremser Equation

Formula
`"N" = log10((("z"_{"C"}-("y"_{"s"}/"K"_{"Solute"}))/("x"_{"C"}-("y"_{"s"}/"K"_{"Solute"})))*(1-(1/"ε"))+(1/"ε"))/(log10("ε"))`

Example
`"0.26809"=log10((("0.5"-("0.05"/"2.6"))/("0.35"-("0.05"/"2.6")))*(1-(1/"2.4"))+(1/"2.4"))/(log10("2.4"))`

Calculator
LaTeX
Go Number of Equilibrium Extraction Stages = log10(((Mass Fraction of Solute in the Feed-(Mass Fraction of Solute in the Solvent/Distribution Coefficient of Solute))/(Mass Fraction of Solute in the Raffinate-(Mass Fraction of Solute in the Solvent/Distribution Coefficient of Solute)))*(1-(1/Extraction Factor))+(1/Extraction Factor))/(log10(Extraction Factor))
Number of Stages for Extraction Factor equal to 1

Number of Stages for Extraction Factor equal to 1

Formula
`"N" = (("z"_{"C"}-("y"_{"s"}/"K"_{"Solute"}))/("x"_{"C"}-("y"_{"s"}/"K"_{"Solute"})))-1`

Example
`"0.453488"=(("0.5"-("0.05"/"2.6"))/("0.35"-("0.05"/"2.6")))-1`

Calculator
LaTeX
Go Number of Equilibrium Extraction Stages = ((Mass Fraction of Solute in the Feed-(Mass Fraction of Solute in the Solvent/Distribution Coefficient of Solute))/(Mass Fraction of Solute in the Raffinate-(Mass Fraction of Solute in the Solvent/Distribution Coefficient of Solute)))-1
Extraction Factor based on Raffinate Point Slope

Extraction Factor based on Raffinate Point Slope

Formula
`"ε" = "m"_{"R"}*"S'"/"F'"`

Example
`"1.95"="3.3"*"65kg/s"/"110kg/s"`

Calculator
LaTeX
Go Extraction Factor = Raffinate Point Slope of Equilibrium Curve*Solute Free Solvent Flowrate in Extraction/Solute Free Feed Flowrate in Extraction
Extraction Factor at Feed Point Slope of Equilibrium Curve

Extraction Factor at Feed Point Slope of Equilibrium Curve

Formula
`"ε" = "m"_{"F"}*"S'"/"F'"`

Example
`"1.831818"="3.1"*"65kg/s"/"110kg/s"`

Calculator
LaTeX
Go Extraction Factor = Feed Point Slope of Equilibrium Curve*Solute Free Solvent Flowrate in Extraction/Solute Free Feed Flowrate in Extraction
Extraction Factor at Mean Slope of Equilibrium Curve

Extraction Factor at Mean Slope of Equilibrium Curve

Formula
`"ε" = "m"*"S'"/"F'"`

Example
`"1.890909"="3.2"*"65kg/s"/"110kg/s"`

Calculator
LaTeX
Go Extraction Factor = Mean Slope of Equilibrium Curve*Solute Free Solvent Flowrate in Extraction/Solute Free Feed Flowrate in Extraction
Geometric Mean of Equilibrium Line Slope

Geometric Mean of Equilibrium Line Slope

Formula
`"m" = sqrt("m"_{"F"}*"m"_{"R"})`

Example
`"3.198437"=sqrt("3.1"*"3.3")`

Calculator
LaTeX
Go Mean Slope of Equilibrium Curve = sqrt(Feed Point Slope of Equilibrium Curve*Raffinate Point Slope of Equilibrium Curve)

Number of Extraction Stages by Kremser Equation Formula

Number of Equilibrium Extraction Stages = log10(((Mass Fraction of Solute in the Feed-(Mass Fraction of Solute in the Solvent/Distribution Coefficient of Solute))/(Mass Fraction of Solute in the Raffinate-(Mass Fraction of Solute in the Solvent/Distribution Coefficient of Solute)))*(1-(1/Extraction Factor))+(1/Extraction Factor))/(log10(Extraction Factor))
N = log10(((zC-(ys/KSolute))/(xC-(ys/KSolute)))*(1-(1/ε))+(1/ε))/(log10(ε))

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).

What is Liquid-Liquid Extraction?

Liquid–liquid extraction (LLE), also known as solvent extraction, is a method to separate compounds or metal complexes, based on their relative solubilities in two different immiscible liquids, usually water (polar) and an organic solvent (non-polar). There is a net transfer of one or more species from one liquid into another liquid phase, generally from aqueous to organic. The transfer is driven by chemical potential, i.e. once the transfer is complete, the overall system of chemical components that make up the solutes and the solvents are in a more stable configuration (lower free energy). The solvent that is enriched in solute(s) is called extract. The feed solution that is depleted in solute(s) is called the raffinate.

How to Calculate Number of Extraction Stages by Kremser Equation?

Number of Extraction Stages by Kremser Equation calculator uses Number of Equilibrium Extraction Stages = log10(((Mass Fraction of Solute in the Feed-(Mass Fraction of Solute in the Solvent/Distribution Coefficient of Solute))/(Mass Fraction of Solute in the Raffinate-(Mass Fraction of Solute in the Solvent/Distribution Coefficient of Solute)))*(1-(1/Extraction Factor))+(1/Extraction Factor))/(log10(Extraction Factor)) to calculate the Number of Equilibrium Extraction Stages, The Number of Extraction Stages by Kremser Equation formula is defined as the calculation for number of stages for extraction operation according to the Kremser Souders Brown equation. Number of Equilibrium Extraction Stages is denoted by N symbol.

How to calculate Number of Extraction Stages by Kremser Equation using this online calculator? To use this online calculator for Number of Extraction Stages by Kremser Equation, enter Mass Fraction of Solute in the Feed (zC), Mass Fraction of Solute in the Solvent (ys), Distribution Coefficient of Solute (KSolute), Mass Fraction of Solute in the Raffinate (xC) & Extraction Factor (ε) and hit the calculate button. Here is how the Number of Extraction Stages by Kremser Equation calculation can be explained with given input values -> 0.26809 = log10(((0.5-(0.05/2.6))/(0.35-(0.05/2.6)))*(1-(1/2.4))+(1/2.4))/(log10(2.4)).

FAQ

What is Number of Extraction Stages by Kremser Equation?
The Number of Extraction Stages by Kremser Equation formula is defined as the calculation for number of stages for extraction operation according to the Kremser Souders Brown equation and is represented as N = log10(((zC-(ys/KSolute))/(xC-(ys/KSolute)))*(1-(1/ε))+(1/ε))/(log10(ε)) or Number of Equilibrium Extraction Stages = log10(((Mass Fraction of Solute in the Feed-(Mass Fraction of Solute in the Solvent/Distribution Coefficient of Solute))/(Mass Fraction of Solute in the Raffinate-(Mass Fraction of Solute in the Solvent/Distribution Coefficient of Solute)))*(1-(1/Extraction Factor))+(1/Extraction Factor))/(log10(Extraction Factor)). The Mass Fraction of Solute in the Feed is the mass fraction of the solute in the Feed to the Liquid-Liquid Extraction operation, The Mass Fraction of Solute in the Solvent is the mass ratio of the solute in the inlet solvent to the solvent mass in Liquid-Liquid Extraction operation, The distribution coefficient of solute is defined as the concentration of solute in the extract phase divided by the concentration of solute in the raffinate phase, The Mass Fraction of Solute in the Raffinate Phase is the mass fraction of the solute in the raffinate phase after separation of the ternary mixture & The Extraction Factor is defined as the ratio of the slope of equilibrium line to the slope of operating line.
How to calculate Number of Extraction Stages by Kremser Equation?
The Number of Extraction Stages by Kremser Equation formula is defined as the calculation for number of stages for extraction operation according to the Kremser Souders Brown equation is calculated using Number of Equilibrium Extraction Stages = log10(((Mass Fraction of Solute in the Feed-(Mass Fraction of Solute in the Solvent/Distribution Coefficient of Solute))/(Mass Fraction of Solute in the Raffinate-(Mass Fraction of Solute in the Solvent/Distribution Coefficient of Solute)))*(1-(1/Extraction Factor))+(1/Extraction Factor))/(log10(Extraction Factor)). To calculate Number of Extraction Stages by Kremser Equation, you need Mass Fraction of Solute in the Feed (zC), Mass Fraction of Solute in the Solvent (ys), Distribution Coefficient of Solute (KSolute), Mass Fraction of Solute in the Raffinate (xC) & Extraction Factor (ε). With our tool, you need to enter the respective value for Mass Fraction of Solute in the Feed, Mass Fraction of Solute in the Solvent, Distribution Coefficient of Solute, Mass Fraction of Solute in the Raffinate & Extraction 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 Equilibrium Extraction Stages?
In this formula, Number of Equilibrium Extraction Stages uses Mass Fraction of Solute in the Feed, Mass Fraction of Solute in the Solvent, Distribution Coefficient of Solute, Mass Fraction of Solute in the Raffinate & Extraction Factor. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Number of Equilibrium Extraction Stages = ((Mass Fraction of Solute in the Feed-(Mass Fraction of Solute in the Solvent/Distribution Coefficient of Solute))/(Mass Fraction of Solute in the Raffinate-(Mass Fraction of Solute in the Solvent/Distribution Coefficient of Solute)))-1
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