💧 Counter-Current Extraction (Kremser)
Calculate theoretical equilibrium stages (N), Extraction Factor (E), Number of Transfer Units (NTU), and packed column height (Z) for liquid-liquid extraction.
⚡ Fortran 90 Engine
Double Precision (IEEE 754)
✓ ISO / ASME Validated
Mass Transfer
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Kremser Extraction Formulations:
• Extraction Factor: E = (m · S) / F
• Theoretical Stages: N = ln[ ( (xF − yS/m) / (xN − yS/m) ) (1 − 1/E) + 1/E ] / ln E
• NTUOL = [ E / (E − 1) ] · ln[ (1 − 1/E) ( (xF − yS/m) / (xN − yS/m) ) + 1/E ]
• Packed Column Height: Z = NTUOL × HTUOL
• Extraction Factor: E = (m · S) / F
• Theoretical Stages: N = ln[ ( (xF − yS/m) / (xN − yS/m) ) (1 − 1/E) + 1/E ] / ln E
• NTUOL = [ E / (E − 1) ] · ln[ (1 − 1/E) ( (xF − yS/m) / (xN − yS/m) ) + 1/E ]
• Packed Column Height: Z = NTUOL × HTUOL
📊 Extraction Sizing Results
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📘 Calculation Methodology & Extraction Standards
Kremser Analytical Sizing
For dilute immiscible liquid-liquid systems with linear distribution equilibrium $y^* = K_D x$, the Kremser equation solves the exact number of theoretical equilibrium stages:
N = ln[ (xF / xN)(1 − 1/E) + 1/E ] / ln E
Extraction Factor Criterion
When $E = \frac{K_D S}{F} > 1.3$, sharp extraction is achieved with very few stages. Operating below $E = 1$ requires excessive stages or column height.
Key Engineering Assumptions
- Constant liquid phase flow rates (immiscible carrier and solvent).
- Linear distribution partition equilibrium $K_D$.
- Height of a Transfer Unit $HTU_{OL}$ based on packing hydraulics.