Material Balance in Leaching Process

Oct 4, 2024

Material Balance Problem: Leaching Process with Mixing and Recycle Streams

Introduction

  • Objective: Solve a material balance problem involving a mixing point and a recycle stream using degree of freedom analysis.
  • Leaching Concept: Separation process where a solid component is removed into a liquid phase (e.g., caffeine removal from coffee beans).

Process Description

  • Schematic Overview:
    • Coffee beans and decaffeinating solvent (DCS) enter a mixing tank.
    • Beans move to a dryer, where some solvent evaporates and returns to the mixing tank.
    • Treated beans exit with less caffeine and some solvent residue.
    • Dirty solvent with extracted caffeine exits the mixing tank and enters a separation unit.
    • Two streams from the separation unit: high-solvent stream (recycled) and high-purity caffeine product.

Problem Statement

  • Goals:
    • Determine DCS needed per 100 kg of coffee beans.
    • Determine the ideal composition of the recycled stream.
  • Given Data:
    1. 100 kg coffee beans contain 1.5 kg caffeine.
    2. DCS removes 90% of caffeine.
    3. 20 kg solvent leaves with beans to the dryer; 90% recovered.
    4. Solvent entering the mixing tank: 95% solvent.
    5. Solvent entering the settling unit: 88% solvent.
    6. Waste solution: 5% solvent.

Strategy

  1. Basis: Use 100 kg of coffee beans entering the process.
  2. Degree of Freedom Analysis:
    • Overall Process:
      • Unknowns: M2, M4, M5.
      • Balance equations: DCS and caffeine.
      • Degree of Freedom (DoF): 0 (solvable).
    • Mixing Tank:
      • Unknowns: M3, M4.
      • Balance equations: caffeine and DCS.
      • DoF: 0 (solvable).
    • Extraction Unit:
      • Unknowns: M6, X.
      • Balance equations: caffeine and DCS.
      • DoF: 0 (solvable).
    • Mixing Point:
      • Unknowns: M2, M3, M6, X.
      • Balance equations: caffeine and DCS.
      • DoF: 2 (not solvable).
  3. Plan:
    • Solve for overall caffeine and DCS balances.
    • Use balances around the mixing tank and extraction unit.

Calculations

  1. Overall Caffeine Balance:
    • 1.5 kg caffeine enters; 0.15 kg exits in bean stream.
    • Solve for M5: 1.42 kg.
  2. Overall DCS Balance:
    • Solve for M2: 2.07 kg of solvent required.
  3. Mixing Tank Balances:
    • Caffeine and solvent balances to solve M3 (20.4 kg) and M4 (19.75 kg).
  4. Recycle Stream and Composition:
    • Overall balance around mixing point: M6 = 18.75 kg.
    • Solvent balance: X = 0.944 (94.4% solvent composition).

Conclusion

  • Results:
    • Require 2.07 kg of DCS per 100 kg of coffee beans.
    • Recycle stream composition: ~94.4% solvent.
  • Considerations:
    • Potential for improved separation unit to reduce caffeine backflow.
  • Learning Outcome: Effective approach to solving material balance problems with multiple units using degree of freedom analysis.