7.6 Extraction

Principles of Liquid-Liquid Extraction

Liquid-liquid extraction separates a solute from one liquid into another immiscible liquid, based on differences in solubility. It's one of the core separation techniques in chemical engineering, used when distillation isn't practical (for example, when components have similar boiling points or are heat-sensitive).

Fundamentals of Liquid-Liquid Extraction

The basic idea: you have a solute dissolved in one liquid (the feed), and you contact it with a second liquid (the solvent) that doesn't mix with the first. The solute moves into whichever phase it's more soluble in. At equilibrium, the solute distributes itself between the two phases according to its partition coefficient.

The two phases are typically an aqueous phase and an organic solvent phase. After mixing and settling, you get two streams:

• Extract phase — the solvent phase, now enriched with the solute
• Raffinate phase — the original feed phase, now depleted of the solute

Applications of Liquid-Liquid Extraction in Chemical Engineering

• Recovering valuable components from mixtures — extracting antibiotics from fermentation broths, recovering metals from aqueous leach solutions
• Purifying products — removing organic acids from wastewater, extracting sulfur compounds or contaminants from crude oil
• Concentrating dilute solutions — selectively pulling the desired component into a smaller volume of solvent, which increases its concentration for downstream processing

Factors Affecting the Effectiveness of Liquid-Liquid Extraction

Four main factors control how well an extraction works:

• Choice of solvent — determines how strongly the solute partitions into the extract phase
• Distribution coefficient — quantifies the solute's preference for one phase over the other
• Phase ratio — the volume ratio of extract phase to raffinate phase; more solvent generally means more recovery, but at higher cost
• Number of extraction stages — more stages means more complete separation

Distribution Coefficients and Selectivity

Distribution Coefficient (K)

The distribution coefficient tells you how a solute splits between the two phases at equilibrium. It's defined as:

$K = \frac{C_E}{C_R}$

where $C_E$ is the solute concentration in the extract phase and $C_R$ is the concentration in the raffinate phase.

A large $K$ means the solute strongly prefers the extract phase, which is what you want. $K$ is affected by temperature, the solute's relative solubility in each phase, and the presence of other dissolved components.

Selectivity (β)

When your feed contains more than one solute, you need to know how well the solvent can separate them. Selectivity is the ratio of the distribution coefficients for two solutes:

$\beta = \frac{K_1}{K_2}$

where $K_1$ is the distribution coefficient of the desired solute and $K_2$ is that of the undesired one. A selectivity of 1 means no separation at all. The further $\beta$ is from 1, the easier the separation.

Determination of Distribution Coefficients and Selectivity

Both $K$ and $\beta$ are determined experimentally:

1. Mix the solute with both liquid phases and allow the system to reach equilibrium.
2. Separate the phases and measure the solute concentration in each using analytical techniques like gas chromatography or UV-vis spectroscopy.
3. Calculate $K$ from the concentration ratio.

These values are then used to evaluate whether an extraction is feasible and to estimate the number of stages needed for a given recovery target.

Design of Extraction Processes

Single-Stage Extraction

In a single-stage extraction, the feed and solvent are mixed in one vessel, allowed to reach equilibrium, and then separated into extract and raffinate streams. This is the simplest setup, but it's limited. Even with a favorable $K$, a single stage rarely achieves complete solute recovery. The fraction of solute extracted depends on both $K$ and the phase ratio.

Multistage Extraction

To get higher recovery, you repeat the extraction across multiple equilibrium stages. The raffinate leaving one stage becomes the feed for the next. Two common flow configurations:

• Cross-current extraction — fresh solvent is added at each stage. Simple to analyze, but uses a lot of solvent.
• Countercurrent extraction — the feed and solvent flow in opposite directions through a series of stages. More solvent-efficient and the standard approach in industrial practice.

The number of theoretical stages required can be determined using:

• Graphical methods like the McCabe-Thiele diagram (adapted for extraction)
• Analytical equations like the Kremser equation, which works well when the distribution coefficient is roughly constant across stages

Design Considerations for Extraction Processes

• Equipment selection — mixer-settlers (good for systems needing long contact time) vs. extraction columns (packed, pulsed, or agitated columns for continuous operation)
• Flow configuration — countercurrent is generally preferred for efficiency
• Operating conditions — temperature, pressure, and mixing intensity all affect mass transfer rates and phase separation

Factors Affecting Extraction Efficiency

Solvent Selection

Choosing the right solvent is often the most important design decision. A good extraction solvent should have:

• High selectivity for the target solute over other components
• Low miscibility with the feed phase (so the two phases separate cleanly)
• Favorable physical properties — a density different enough from the feed for easy phase separation, low viscosity for good mixing, and reasonable surface tension
• Practical considerations — inexpensive, non-toxic, non-flammable, and easy to recover and recycle

Common solvent families include hydrocarbons (hexane, kerosene), alcohols (ethanol, isopropanol), ethers (diethyl ether, MTBE), and halogenated solvents (chloroform, dichloromethane).

Phase Ratio

The phase ratio is the volume of extract phase divided by the volume of raffinate phase. Increasing the phase ratio (using more solvent) generally improves recovery, but there's a tradeoff: more solvent means higher costs for both the solvent itself and the downstream separation needed to recover it.

The optimal phase ratio balances the distribution coefficient, the target solute recovery, and economic constraints. In practice, you want to use just enough solvent to hit your recovery target without excess.

Other Factors Affecting Extraction Efficiency

• Temperature — changes the distribution coefficient and solubility. Higher temperatures can improve mass transfer rates but may reduce selectivity.
• pH — particularly important for ionizable solutes. Adjusting pH can shift a solute between its ionized and un-ionized forms, dramatically changing its partitioning behavior.
• Other dissolved components — can compete for solvent capacity (co-extraction) or stabilize emulsions that make phase separation difficult.