Liquid-Liquid Extraction Theory
What is Liquid-Liquid Extraction?
Liquid-liquid extraction (LLE), also called solvent extraction, is a separation process where one or more components are transferred from one liquid phase to another immiscible or partially miscible liquid phase. The solvent is chosen to preferentially dissolve the desired component(s).
LLE is widely used in the pharmaceutical, chemical, petrochemical, and food industries for purification, separation, and recovery operations.
Distribution Coefficient
The distribution coefficient (K) or partition coefficient describes the equilibrium distribution of a solute between two immiscible phases:
K = y / x
where y = solute concentration in extract phase, x = solute concentration in raffinate phase
- K > 1: Solute prefers the extract (solvent) phase - favorable extraction
- K < 1: Solute prefers the raffinate (feed) phase - poor extraction
- K ≈ 1: Equal distribution - many stages required
Extraction Factor
The extraction factor (A) relates the distribution coefficient to the solvent-to-feed ratio:
A = K × (S/F)
where S = solvent flow rate, F = feed flow rate
- A > 1.5: Efficient extraction with fewer stages
- A ≈ 1: Many stages required (Kremser equation becomes undefined)
- A < 1: Very difficult extraction - consider alternative methods
Number of Stages - Kremser Equation
For countercurrent extraction with constant K and flow rates, the Kremser equation relates the number of stages to extraction performance:
When A ≠ 1:
N = ln[(xF - yS/K) / (xR - yS/K) × (1 - 1/A) + 1/A] / ln(A)
When A ≈ 1:
N = (xF - xR) / [xF(1 - xR)]
where xF = feed composition, xR = raffinate composition, yS = solvent composition (usually 0 for pure solvent)
Single-Stage vs Multi-Stage Extraction
| Type | Advantages | Disadvantages |
|---|---|---|
| Single Stage | Simple equipment, low capital cost | High solvent requirement, lower recovery |
| Crosscurrent | Moderate efficiency, flexible | Higher solvent use than countercurrent |
| Countercurrent | Most efficient, lowest solvent requirement | More complex equipment, control challenges |
Solvent Selection Criteria
Choosing the right solvent is critical for successful extraction:
- Selectivity: High K for target solute, low K for contaminants
- Immiscibility: Should not dissolve significantly in feed phase
- Density difference: Large difference aids phase separation
- Interfacial tension: Moderate value for good mass transfer but easy separation
- Viscosity: Low viscosity improves mass transfer rates
- Chemical stability: No reactions with feed or product
- Cost and availability: Economically feasible, readily available
- Safety: Low toxicity, non-flammable, environmentally acceptable
- Recoverability: Easy to regenerate and recycle
Common Applications
Pharmaceutical Industry
- • Antibiotic recovery
- • Vitamin purification
- • API extraction
Petrochemical Industry
- • Aromatics extraction (BTX)
- • Lube oil dewaxing
- • Sulfur removal
Metal Processing
- • Copper extraction (SX-EW)
- • Uranium recovery
- • Rare earth separation
Food Industry
- • Caffeine extraction
- • Vegetable oil refining
- • Flavor extraction
Design Considerations
Important: The calculator uses simplified assumptions (constant K, immiscible phases, ideal mixing). Real systems may require:
- Triangular equilibrium diagrams for partially miscible systems
- Activity coefficient corrections for non-ideal behavior
- Temperature effects on distribution coefficients
- Pilot testing to validate stage efficiency
References
- Treybal, R.E., "Liquid Extraction", 2nd Edition, McGraw-Hill (1963)
- Seader, J.D., Henley, E.J., Roper, D.K., "Separation Process Principles", 4th Edition, Wiley (2016)
- Lo, T.C., Baird, M.H.I., Hanson, C., "Handbook of Solvent Extraction", Wiley-Interscience (1983)
- Kremser, A., "Theoretical Analysis of Absorption Process", National Petroleum News, 22(21) (1930)