💧 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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📅 Released Jun 2026

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💧 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

💧 Feed & Solvent Flows

Aqueous Feed Flow F [kg/h]:

Extracting Solvent Flow S [kg/h]:

🧪 Equilibrium & Target Recovery

Feed Solute Concentration x_F [wt%]:

Partition Coefficient K_D = y/x: Equilibrium distribution ratio

Target Solute Recovery [%]:

Height of Transfer Unit HTU [m]: Typical packed column HTU: 0.4 to 1.0 m

Kremser Extraction Formulations:
• Extraction Factor: E = (m · S) / F
• Theoretical Stages: N = ln[ ( (x_F − y_S/m) / (x_N − y_S/m) ) (1 − 1/E) + 1/E ] / ln E
• NTU_OL = [ E / (E − 1) ] · ln[ (1 − 1/E) ( (x_F − y_S/m) / (x_N − y_S/m) ) + 1/E ]
• Packed Column Height: Z = NTU_OL × HTU_OL

📊 Extraction Sizing Results

📊 Output Summary
💾 Fortran Source

Theoretical Equilibrium Stages (N)

N = 3.89 stages (≈ 4 stages)

Packed Height: Z = 4.02 meters (NTU = 4.73)

E = 1.50

Extraction Factor (E = m·S/F) 1.500 Favorable Extraction

Mass Solute Extracted 88.32 kg/h 92.0 % Recovery

Final Raffinate Concentration (x_N) 0.960 % Feed: 12.00 %

Rich Extract Concentration (y₁) 17.664 % 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                 : Fermentation Broth Lactic Acid Reactive Extraction
Feed / Solvent Flow Rate   : 800.0 kg/h / 500.0 kg/h (S/F = 0.62)
Feed Solute Concentration  : 12.00 wt% (Inlet Solvent = 0.00 %)
Partition Coefficient (KD) : 2.40 (y/x)
EXTRACTION FACTOR (E)      : 1.500
-----------------------------------------------------------------
THEORETICAL STAGES (N)     : 3.89 stages (Kremser)
Number of Transfer Units   : 4.73 NTU_OL
PACKED COLUMN HEIGHT (Z)   : 4.02 meters (HTU = 0.85 m)
Target Recovery Yield      : 92.00 %
Raffinate Solute (xN)      : 0.9600 wt%
Extract Solute (y1)        : 17.6640 wt%
Mass Solute Extracted      : 88.32 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.

ThermoFluidCalc Engineering Report