Mass Transfer Coefficient for Batch Leaching Calculator

Mass Transfer Coefficient Formula:

\[ K_L = \frac{-V_{Leaching}}{A \times t} \times \ln\left(\frac{C_S - C}{C_S}\right) \]

Volume of Leaching Solution:

m³

Area of Leaching:

m²

Time of Batch Leaching:

Concentration of Saturated Solution:

kg/m³

Concentration in Bulk Solution:

kg/m³

Mass Transfer Coefficient (mol/s·m²):

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1. What is Mass Transfer Coefficient for Batch Leaching?

Definition: This calculator determines the mass transfer coefficient (K_L) for batch leaching processes, which quantifies the rate of solute transfer from solid to liquid phase.

Purpose: It helps chemical engineers and process designers optimize leaching operations in industries like mining, metallurgy, and food processing.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ K_L = \frac{-V_{Leaching}}{A \times t} \times \ln\left(\frac{C_S - C}{C_S}\right) \]

Where:

\( K_L \) — Mass transfer coefficient (mol/s·m²)
\( V_{Leaching} \) — Volume of leaching solution (m³)
\( A \) — Area of leaching (m²)
\( t \) — Time of batch leaching (s)
\( C_S \) — Concentration of saturated solution (kg/m³)
\( C \) — Concentration in bulk solution at time t (kg/m³)

Explanation: The formula accounts for solution volume, contact area, time, and concentration differences to determine the mass transfer rate.

3. Importance of Mass Transfer Coefficient

Details: The coefficient is crucial for designing efficient leaching systems, predicting extraction rates, and scaling up laboratory results to industrial processes.

4. Using the Calculator

Tips: Enter all required parameters in consistent units. Ensure C_S > C for valid results. Typical values range from 10^-5 to 10^-3 mol/s·m².

5. Frequently Asked Questions (FAQ)

Q1: What affects the mass transfer coefficient?
A: Factors include temperature, agitation, particle size, solvent properties, and solute characteristics.

Q2: How does this differ from continuous leaching?
A: Batch leaching has finite contact time, while continuous systems operate at steady state with constant feed and product streams.

Q3: What if I get negative values?
A: The coefficient is always positive. Negative results indicate input errors (typically C > C_S).

Q4: How to improve leaching efficiency?
A: Increase surface area, optimize temperature, improve mixing, or use more effective solvents.

Q5: What are typical industrial values?
A: For mineral processing, values typically range from 10^-4 to 10^-3 mol/s·m² depending on the system.