Number of Ideal Equilibrium Extraction Stages Calculator

Formula:

\[ N = \frac{\log_{10}\left(\frac{z_C}{X_N}\right)}{\log_{10}\left(\left(\frac{K_{Solute} \cdot E'}{F'}\right) + 1\right)} \]

Mass Fraction of Solute in the Feed (zC):

N Stages Mass Fraction of Solute in Raffinate (XN):

Distribution Coefficient of Solute (KSolute):

Solute Free Extract Phase Flowrate (E'):

kg/s

Solute Free Feed Flowrate (F'):

kg/s

Number of Equilibrium Extraction Stages (N):

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1. What is the Number of Ideal Equilibrium Extraction Stages?

Definition: This calculator determines the number of theoretical equilibrium stages required for liquid-liquid extraction processes.

Purpose: It helps chemical engineers design and optimize separation processes where a solute is transferred between two immiscible liquid phases.

2. How Does the Calculator Work?

The calculator uses the Kremser equation:

\[ N = \frac{\log_{10}\left(\frac{z_C}{X_N}\right)}{\log_{10}\left(\left(\frac{K_{Solute} \cdot E'}{F'}\right) + 1\right)} \]

Where:

\( N \) — Number of equilibrium extraction stages
\( z_C \) — Mass fraction of solute in the feed
\( X_N \) — Mass fraction of solute in raffinate after N stages
\( K_{Solute} \) — Distribution coefficient of solute
\( E' \) — Solute-free extract phase flowrate (kg/s)
\( F' \) — Solute-free feed flowrate (kg/s)

Explanation: The formula calculates the theoretical number of stages needed to achieve a desired solute concentration in the raffinate phase.

3. Importance of Stage Calculation

Details: Accurate stage calculation ensures efficient separation, minimizes solvent usage, and helps design cost-effective extraction processes.

4. Using the Calculator

Tips: Enter the mass fractions (0-1), distribution coefficient, and flowrates (must be > 0). Default values are provided for demonstration.

5. Frequently Asked Questions (FAQ)

Q1: What is the distribution coefficient?
A: It's the ratio of solute concentration in the extract phase to that in the raffinate phase at equilibrium.

Q2: Why use solute-free flowrates?
A: Solute-free basis simplifies calculations as solute concentration changes between stages.

Q3: What if I get a fractional number of stages?
A: Round up to the nearest whole number since partial stages aren't practical.

Q4: How does flowrate ratio affect stages?
A: Higher extract flowrate reduces required stages but increases solvent usage.

Q5: What's a typical distribution coefficient range?
A: Typically 0.1-10, but depends on solute and solvent system.