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Number of Equilibrium Leaching Stages based on Recovery of Solute Calculator

Formula for Equilibrium Stages in Leaching:

\[ N = \frac{\log_{10}\left(1+\frac{R-1}{1-Recovery}\right)}{\log_{10}(R)} - 1 \]

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1. What is Number of Equilibrium Leaching Stages?

Definition: This calculator determines the number of theoretical equilibrium stages required in a leaching process to achieve a specified solute recovery.

Purpose: It helps chemical engineers and process designers optimize leaching operations by determining the required number of stages.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ N = \frac{\log_{10}\left(1+\frac{R-1}{1-Recovery}\right)}{\log_{10}(R)} - 1 \]

Where:

Explanation: The formula calculates the theoretical stages needed based on the discharge ratio and desired recovery efficiency.

3. Importance of Equilibrium Stages Calculation

Details: Proper stage calculation ensures efficient solute extraction, optimal equipment sizing, and cost-effective process design.

4. Using the Calculator

Tips: Enter the discharge ratio (overflow/underflow) and desired solute recovery (as decimal between 0 and 1). The recovery must be less than 1.

5. Frequently Asked Questions (FAQ)

Q1: What is an equilibrium stage in leaching?
A: A theoretical stage where the liquid and solid phases achieve equilibrium composition before being separated.

Q2: How does discharge ratio affect stages?
A: Higher ratios typically require fewer stages for the same recovery, as more solute is carried in the overflow.

Q3: What's a typical recovery value?
A: Industrial processes often aim for 90-99% recovery (0.9 to 0.99 input).

Q4: Does this account for non-ideal conditions?
A: No, this calculates theoretical stages. Actual stages needed may be higher due to efficiency factors.

Q5: Can recovery be 100%?
A: Theoretically no (would require infinite stages), practically very high recoveries (99%+) are achievable.

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