💧 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
📊 Solver Telemetry
● ACTIVE
💧 Counter-Current Liquid-Liquid Extraction Column Simulation
Real-time visual simulation of heavy aqueous feed descending & light solvent droplets rising counter-currently📝 Configuration & Presets
🧪 Acetic Acid / Ethyl Acetate
💊 Penicillin / Amyl Acetate
🛢️ Phenol Removal with MIBK
🥛 Lactic Acid Broth
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
📊 Output Summary
Theoretical Equilibrium Stages (N)
N = 7.50 stages (≈ 8 stages)
Packed Height: Z = 5.69 meters (NTU = 9.48)
E = 1.63
Extraction Factor (E = m·S/F)
1.632
Favorable Extraction
Mass Solute Extracted
99.00 kg/h
99.0 % Recovery
Final Raffinate Concentration (xN)
0.040 %
Feed: 4.00 %
Rich Extract Concentration (y₁)
16.500 %
Solvent Product
📈 Required Stages (N) vs Solvent-to-Feed Ratio (S/F)
📉 Packed Height Z (m) vs Solute Recovery Yield (%)
================================================================= THERMOFLUIDCALC — COUNTER-CURRENT EXTRACTION REPORT ================================================================= Case Title : Wastewater Phenol Dephenolization with MIBK Solvent Feed / Solvent Flow Rate : 2500.0 kg/h / 600.0 kg/h (S/F = 0.24) Feed Solute Concentration : 4.00 wt% (Inlet Solvent = 0.00 %) Partition Coefficient (KD) : 6.80 (y/x) EXTRACTION FACTOR (E) : 1.632 ----------------------------------------------------------------- THEORETICAL STAGES (N) : 7.50 stages (Kremser) Number of Transfer Units : 9.48 NTU_OL PACKED COLUMN HEIGHT (Z) : 5.69 meters (HTU = 0.60 m) Target Recovery Yield : 99.00 % Raffinate Solute (xN) : 0.0400 wt% Extract Solute (y1) : 16.5000 wt% Mass Solute Extracted : 99.00 kg/h =================================================================
📘 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.