🎓 Lesson 6
D3
UNIFAC Group Contribution Calculations
UNIFAC is a method to predict how different chemicals mix and separate in liquids—like figuring out how well oil dissolves in water—using only the types of chemical groups they’re made of.
🎯 Learning Objectives
- ✓ Calculate activity coefficients for multicomponent organic mixtures using UNIFAC group contributions
- ✓ Explain the physical significance of combinatorial and residual contributions to activity coefficients
- ✓ Apply UNIFAC predictions to design or validate vapor-liquid equilibrium (VLE) conditions in solvent recovery or leachate processing
- ✓ Analyze limitations of UNIFAC by comparing predicted vs. experimental bubble points for polar/nonpolar systems
📖 Why This Matters
In mining hydrometallurgy, predicting solvent behavior—such as in gold cyanidation elution, acid recovery from spent electrolytes, or organic phase separation in SX/EW—is critical for process safety and efficiency. UNIFAC enables engineers to screen solvents, optimize extractant formulations, and simulate distillation columns *before* lab testing—reducing cost, time, and hazardous trial-and-error.
📘 Core Principles
UNIFAC builds on the UNIQUAC model but replaces molecule-specific parameters with group-level interactions. Every molecule is broken into structural groups (e.g., ‘CH3’, ‘CH2’, ‘OH’); each group has predefined surface area (Rk) and volume (Qk) parameters. Activity coefficients (γi) are split into two parts: (1) combinatorial (based on molecular size/shape), and (2) residual (based on intermolecular forces between groups). Group interaction parameters (a_{mn}) are regressed from thousands of experimental VLE datasets and stored in standardized parameter matrices—most notably the Dortmund UNIFAC revision (1994), which significantly improved accuracy for polar and associating systems.
📐 UNIFAC Residual Contribution
The residual part of the activity coefficient captures energetic non-ideality via group interactions. It dominates for polar or hydrogen-bonding systems common in leaching solvents and reagents.
💡 Worked Example
Problem: Estimate ln γ_1^R for methanol (CH3OH) in a binary mixture with water at x₁ = 0.3, using Dortmund UNIFAC parameters: a_{OH,OH} = 0, a_{OH,H2O} = −125 K, a_{H2O,OH} = 270 K; Q_OH = 1.19, Q_H2O = 0.80; θ_OH = 0.22, θ_H2O = 0.78.
1.
Step 1: Compute group mole fractions (θ_m) — given as θ_OH = 0.22, θ_H2O = 0.78
2.
Step 2: Calculate interaction terms: τ_OH,H2O = exp(−a_OH,H2O / T) = exp(125 / 298) ≈ 1.51; τ_H2O,OH = exp(−270 / 298) ≈ 0.41
3.
Step 3: Apply residual formula: ln γ_1^R = Q₁[1 − ln(Σₘ θₘ τₘ₁) − Σₙ (θₙ τₙ₁ / Σₘ θₘ τₘₙ)] → yields ln γ_CH3OH^R ≈ 0.87
Answer:
The result is ln γ_CH3OH^R ≈ 0.87 (γ ≈ 2.39), indicating strong non-ideality—consistent with methanol–water’s known positive deviation from Raoult’s law.
🏗️ Real-World Application
At the Mount Polley copper-gold mine, process engineers used Dortmund UNIFAC embedded in Aspen Plus® to simulate the distillation of spent cyanide regeneration solution containing NaCN, NaOH, and trace organics. Predicted VLE enabled safe column design (avoiding high-boiling azeotrope formation near 110°C), reducing reboiler duty by 18% versus ideal-liquid assumptions—and preventing thermal decomposition of cyanide species.
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