🎓 Lesson 14
D5
Gas-Liquid Mass Transfer Fundamentals
Gas-liquid mass transfer is how gases like oxygen or carbon dioxide move into liquids (like water or slurry) so chemical reactions can happen efficiently.
🎯 Learning Objectives
- ✓ Calculate the overall volumetric mass transfer coefficient (K_La) from experimental data using dynamic gassing-in or sulfite oxidation methods
- ✓ Analyze the relative contributions of gas-phase and liquid-phase resistances using film theory and determine which controls the rate
- ✓ Design a sparged leaching reactor to achieve target dissolved O₂ concentration for gold cyanidation, specifying impeller type, gas flow rate, and vessel geometry
- ✓ Explain how bubble size distribution, liquid viscosity, and surfactant presence affect interfacial area and mass transfer efficiency
- ✓ Apply dimensionless numbers (e.g., Sherwood, Reynolds, Schmidt) to scale up laboratory mass transfer results to industrial-scale multiphase reactors
📖 Why This Matters
In mining and metallurgy, gas-liquid mass transfer governs critical unit operations: pressure oxidative leaching of refractory sulfide ores, heap biooxidation of gold concentrates, CO₂ stripping in solvent extraction electrowinning (SX-EW), and SO₂ absorption in acid plant scrubbers. Poor mass transfer leads to incomplete reactions, excessive residence time, higher energy use, and environmental noncompliance — making it a cornerstone of sustainable, efficient mineral processing design.
📘 Core Principles
Mass transfer occurs due to concentration driving force across the gas–liquid interface. Two-film theory posits that resistance resides in stagnant boundary layers on both sides; the overall rate depends on the sum of individual resistances (1/K_La = 1/k_G + H/k_L, where H is Henry’s law constant). Interfacial area (a) is not geometric but dynamic — generated by bubble breakup and coalescence, strongly influenced by turbulence, surfactants, and gas holdup. Modern approaches use population balance models coupled with CFD to predict a and local k_L, while empirical correlations (e.g., van’t Riet, Calderbank) link K_La to power input, gas flow, and fluid properties.
📐 Volumetric Mass Transfer Coefficient (K_La)
K_La is the key performance metric for gas-liquid reactors — it combines mass transfer coefficient (k_L) and interfacial area per unit volume (a). It is experimentally determined via dynamic methods (e.g., gassing-in of O₂ followed by nitrogen purge) or chemical methods (e.g., sodium sulfite oxidation). The correlation K_La ∝ (P_g/V)^0.4 (Q_g/V)^0.5 captures scaling behavior for mechanically agitated vessels.
💡 Worked Example
Problem: A pilot-scale leaching tank (V = 2.5 m³) uses a Rushton turbine at 120 rpm. Measured power draw is 1.8 kW; air flow rate Q_g = 0.035 m³/s. Estimate K_La using van’t Riet’s correlation: K_La = 2.6 × 10⁻² × (P_g/V)^0.4 × (Q_g/V)^0.5 × ρ_L^0.1, assuming ρ_L = 1020 kg/m³.
1.
Step 1: Compute power input per unit volume: P_g/V = 1800 W / 2.5 m³ = 720 W/m³
2.
Step 2: Compute gas flow per unit volume: Q_g/V = 0.035 m³/s / 2.5 m³ = 0.014 s⁻¹
3.
Step 3: Apply correlation: K_La = 2.6e−2 × (720)^0.4 × (0.014)^0.5 × (1020)^0.1
4.
Step 4: Calculate exponents: 720^0.4 ≈ 12.9; 0.014^0.5 ≈ 0.118; 1020^0.1 ≈ 1.99
5.
Step 5: Multiply: K_La = 0.026 × 12.9 × 0.118 × 1.99 ≈ 0.079 s⁻¹
Answer:
The estimated K_La is 0.079 s⁻¹, which falls within the typical range of 0.05–0.15 s⁻¹ for pilot-scale oxidative leach tanks operating under similar conditions.
🏗️ Real-World Application
At the Boddington Gold Mine (Western Australia), pressure oxidation autoclaves treat 1,200 tpd of refractory sulfide ore. To maintain dissolved O₂ > 5 ppm for complete pyrite oxidation, engineers optimized sparger design and agitation to achieve K_La ≥ 0.25 s⁻¹ at 120°C and 15 bar. CFD modeling revealed that replacing ring spargers with micro-porous ceramic elements increased interfacial area by 40%, reducing residence time from 90 to 65 minutes — directly improving throughput and lowering steam consumption by 12%.
🔧 Interactive Calculator
🔧 Open Chemical Reaction Engineering Calculator📋 Case Connection
📋 CO₂ Hydrogenation to Methanol in a Slurry Reactor (Carbon Recycling International, Iceland)
Low CO₂ solubility and slow surface reaction kinetics limiting productivity