Solvent Extraction Simulator: McCabe-Thiele Design for Metal Recovery

simulator intermediate ~10 min
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E = 99.2% — 3-stage copper extraction

With K_D = 5, O/A = 1, and 3 counter-current stages, 99.2% of copper is extracted from a 15 g/L feed, leaving only 0.12 g/L in the raffinate.

Formula

E = 1 - 1/(1 + K_D · O/A)^N — extraction efficiency for N stages
K_D = [M]_org / [M]_aq — distribution coefficient at equilibrium
Operating line: y = (A/O)·x + y_in — mass balance across stage

Liquid-Liquid Separation

Solvent extraction is the elegant heart of modern hydrometallurgy. Two immiscible liquids — an aqueous phase carrying dissolved metals and an organic phase containing a selective extractant — are mixed together, allowing the target metal to transfer from water to organic. The phases then separate by gravity in a settler, producing a purified aqueous raffinate and a metal-loaded organic. This deceptively simple principle enables the separation of elements that are chemically almost identical, such as adjacent rare earths or cobalt from nickel.

The McCabe-Thiele Diagram

Designing an SX circuit requires knowing how many mixer-settler stages are needed. The McCabe-Thiele graphical method plots the equilibrium isotherm (the curved line relating organic and aqueous concentrations at equilibrium) against the operating line (the straight line representing mass balance). Starting from the feed point, you step between these curves — each step represents one theoretical stage. When the steps reach the target raffinate concentration, you have your stage count. This simulation builds the diagram interactively as you adjust parameters.

The O/A Ratio Trade-off

The organic-to-aqueous volumetric flow ratio (O/A) is the key design variable. A higher O/A means more organic solvent contacts each volume of aqueous feed, improving extraction per stage but requiring more (expensive) organic inventory. A lower O/A concentrates the metal into less organic volume — desirable for downstream stripping — but needs more stages. The optimal O/A balances capital cost (more stages) against operating cost (more solvent) and is found at the intersection of economics and thermodynamics.

Industrial Practice

The world's copper supply depends on SX: over 25% of global copper is produced through leach-SX-electrowinning circuits. Rare earth separation requires dozens of SX stages in cascade due to similar K_D values between adjacent elements — a separation tour de force. Cobalt-nickel separation, uranium purification, and platinum group metal refining all rely on carefully engineered SX flowsheets. This simulator lets you explore the fundamental design principles that underpin these billion-dollar operations.

FAQ

What is solvent extraction in hydrometallurgy?

Solvent extraction (SX) is a liquid-liquid separation process where an aqueous solution containing dissolved metals is contacted with an immiscible organic phase containing a selective extractant. The target metal transfers to the organic phase, is concentrated, and then stripped back into a clean aqueous solution for downstream recovery. It is the dominant purification method for copper, uranium, rare earths, and cobalt.

What is the McCabe-Thiele method?

The McCabe-Thiele graphical method plots the equilibrium isotherm and operating line on a diagram of organic vs aqueous metal concentration. Stepping between the two curves from the feed point determines the number of theoretical stages needed for a target extraction. It remains the standard design tool for counter-current SX circuits.

What is the distribution coefficient K_D?

K_D = [Metal]_organic / [Metal]_aqueous at equilibrium. A high K_D means strong affinity of the extractant for the metal. Typical values range from 2–50 depending on extractant type, pH, and metal species. The separation factor β between two metals equals the ratio of their K_D values.

How many stages are needed for copper SX?

Industrial copper SX circuits typically use 2 extraction stages and 1 stripping stage, achieving >95% recovery. The highly selective reagents (LIX 984N, Acorga M5640) provide K_D values of 10–50 for Cu at pH 1.5–2.0, making 2 stages sufficient for most operations.

Sources

Embed

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View source on GitHub