🎓 Lesson 20
D5
Column Mass Transfer Coefficient Selection Guidelines
The column mass transfer coefficient tells us how quickly a substance (like a gas or chemical) moves from a flowing fluid into a packed bed or column — like how fast oxygen dissolves into water in a mining leach tank.
🎯 Learning Objectives
- ✓ Calculate the overall liquid-phase mass transfer coefficient (kₗa) from experimental absorption data using log-mean concentration driving force
- ✓ Design a leaching column by selecting appropriate kₗa values for copper oxide ore in dilute sulfuric acid based on particle size and superficial velocity
- ✓ Analyze the effect of gas flow rate and liquid spray density on kₐ in a packed CO₂ absorption column used in mine ventilation air methane (VAM) abatement
- ✓ Explain how column scaling from lab to industrial size impacts kₐ due to changes in holdup, channeling, and effective interfacial area
- ✓ Apply correlations (e.g., Onda et al.) to estimate kₐ for structured packing in gold cyanidation columns
📖 Why This Matters
In mining operations, mass transfer governs critical unit processes: heap leaching kinetics, solvent extraction efficiency, acid-gas scrubbing in tailings gas treatment, and carbon-in-pulp adsorption. Choosing the wrong mass transfer coefficient leads to undersized columns (poor recovery, environmental non-compliance) or oversized ones (wasted capital, higher operating costs). This lesson bridges lab-scale measurements to robust industrial design — where 10% error in kₐ can mean $2M/year in reagent overuse or 5% lost metal recovery.
📘 Core Principles
Mass transfer in columns occurs across phases (e.g., aqueous leach solution ↔ solid ore; CO₂ gas ↔ amine solution). The overall coefficient Kₐ reflects combined resistances: bulk fluid diffusion, interfacial reaction, and stagnant film transport. For gas–liquid systems, Kₐ = 1 / (1/k₉a + H/kₗa), where H is the Henry’s law constant; for liquid–solid (leaching), kₗa dominates and depends on liquid velocity, particle porosity, and diffusion coefficients. Key insight: kₐ is not intrinsic — it’s a *system property*, not a fluid property — and must be determined experimentally or via validated correlations for each column configuration and operating point.
📐 Onda Correlation for kₗa in Packed Columns
The Onda correlation is widely used for estimating kₗa in randomly packed columns under turbulent flow. It accounts for liquid and gas flow rates, physical properties, and packing characteristics — making it essential for scaling leach columns or SX contactors.
💡 Worked Example
Problem: Estimate kₗa (s⁻¹) for a 1.2 m diameter column packed with 25 mm Raschig rings, processing 80 L/s of 5 g/L CuSO₄ solution (ρₗ = 1020 kg/m³, μₗ = 0.95 cP, Dₗ = 1.2×10⁻⁹ m²/s) at 25°C. Superficial liquid velocity = 0.071 m/s; void fraction ε = 0.72; specific surface area a = 120 m²/m³.
1.
Step 1: Compute Reynolds number Reₗ = (ρₗ uₗ dₚ)/μₗ = (1020 × 0.071 × 0.025)/(0.00095) ≈ 1910 → turbulent regime
2.
Step 2: Compute Schmidt number Sc = μₗ/(ρₗ Dₗ) = 0.00095/(1020 × 1.2×10⁻⁹) ≈ 778
3.
Step 3: Apply Onda: kₗa = 0.0051 Reₗ⁰·⁷ Sc⁰·⁵ (uₗ a/ε) = 0.0051 × (1910)⁰·⁷ × (778)⁰·⁵ × (0.071 × 120 / 0.72)
4.
Step 4: Calculate: (1910)⁰·⁷ ≈ 124.5; (778)⁰·⁵ ≈ 27.9; term = 0.0051 × 124.5 × 27.9 × 11.83 ≈ 206 s⁻¹
Answer:
The estimated kₗa is 206 s⁻¹, which falls within the typical range of 150–300 s⁻¹ for 25 mm ceramic Raschig rings under these leaching conditions.
🏗️ Real-World Application
At the Tenke Fungurume copper mine (DRC), a pilot-scale agitated leach column was scaled to full production using kₗa values derived from bench-scale column tests with crushed oxide ore (P₈₀ = 1.8 mm). Measured kₗa ranged from 185–220 s⁻¹ at 15% pulp density and 20 L/min/m² spray density. Engineers applied the Onda correlation with correction factors for ore fines (−12% kₗa) and temperature (kₗa ∝ exp(−Eₐ/RT)), validating design against 3-month plant trial data showing <3% deviation in Cu extraction rate — enabling accurate CAPEX estimation and avoiding costly retrofitting.
🔧 Interactive Calculator
🔧 Open Fluid Flow & Transport Phenomena Calculator📋 Case Connection
📋 Heat Integration in Ethylene Oxide Absorption Column
Poor CO₂ co-absorption leading to catalyst deactivation and product loss
📋 CFD-Guided Mixer Redesign in Pharmaceutical Bioreactor
Oxygen mass transfer limitation causing cell viability drop at large scale