Feed Solute Concentration for N-number of Ideal Stage Extraction Calculator

Formula Used:

\[ z_C = \frac{X_N}{\left(\frac{F'}{F' + (E' \times K_{Solute})}\right)^N} \]

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

Solute Free Feed Flowrate (F'):

kg/s

Solute Free Extract Phase Flowrate (E'):

kg/s

Distribution Coefficient of Solute (K_Solute):

Number of Equilibrium Stages (N):

Mass Fraction of Solute in the Feed (z_C):

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1. What is Feed Solute Concentration for N-number of Ideal Stage Extraction?

Definition: This calculator determines the initial mass fraction of solute in the feed stream based on the performance of N-number of ideal extraction stages in liquid-liquid extraction.

Purpose: It helps chemical engineers design and analyze liquid-liquid extraction processes by determining the required feed concentration to achieve a desired raffinate purity.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ z_C = \frac{X_N}{\left(\frac{F'}{F' + (E' \times K_{Solute})}\right)^N} \]

Where:

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

Explanation: The formula calculates the required feed concentration based on the equilibrium relationship between the raffinate and extract phases across multiple stages.

3. Importance of Feed Solute Concentration Calculation

Details: Accurate determination of feed concentration is crucial for designing efficient extraction processes, predicting separation performance, and optimizing solvent usage.

4. Using the Calculator

Tips: Enter the raffinate solute fraction, solute-free flowrates of both phases, solute distribution coefficient, and number of equilibrium stages. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the distribution coefficient (K_Solute)?
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 by focusing on the carrier and solvent flows independent of solute concentration.

Q3: What's a typical range for K_Solute?
A: Typically between 0.1 and 10, depending on the solute-solvent system and operating conditions.

Q4: How does number of stages affect the calculation?
A: More stages generally allow for lower feed concentrations to achieve the same raffinate purity.

Q5: What if I get unrealistic results?
A: Check your input values, especially K_Solute and flowrates, as they significantly impact the calculation.