Operating Procedure for Liquid-Liquid Extraction in Packed Column

Liquid-Liquid Extraction Calculator

Solute:

Solvent:

Saturation Concentration in Solvent (mol/L):

Distribution Coefficient:

Volume of Aqueous Phase (L):

Volume of Solvent Phase (L):

Liquid-liquid extraction, familiarly called as solvent extraction is a unit operation which involves the liquid-liquid contact method. It is based on the principle of separation of individual components of a solution mixture by using another insoluble liquid. The extraction phenomena work on solubility property of the liquid mixture and on the pure solvent used in the separation or purification process. Operation of the liquid-liquid extractor entirely differs from the operation procedure of distillation column. For a packed extraction column operating procedure can be understood at the startup of the column for a plant operator or an engineer.

A standard procedure designed for most packed extraction columns:

• The heavy liquid (solution) which has more density is fed from the top side of the column and the light liquid (pure or recycled solvent) from the bottom. 
• At initial condition, the light liquid is passed into the column through the distributors and the steady flow rate is maintained.
• Then the heavy liquid is passed with the flow rates approximately to the ratio based on the density of the heavy liquid and light liquid, that of light liquid flow rates.
• The above step leads to attaining the concentration gradient of the solute which diffuses into the light liquid.
• And so heavy liquid pass down the column having contact with the fresh light liquid.
• The sample analysis is made to confirm the concentration at bottom of the column when the bottom outlet control valve is opened.
• The pressure at bottom of the column is maintained in such a way to determine the position of the interface in the column.

For an extraction column, two control valves play an important role in controlling the complex process. 

1. Heavy liquid outlet Bottom control valve.
2. The interface level control valve.

Mass transfer occurs at the interface of the two phases so, the interface position is important in achieving the maximum distribution of solute. The interface control valve placed at above the heavy liquid distributor maintains the level and used to remove the particles or foam material formed during the operation.

A detailed diagram can help to understand the operation of the solvent extractor.

Decaffeination of Coffee Beans: A Mathematical Modeling Approach to Liquid-Liquid Extraction

The quest for the perfect cup of coffee has led to innovations in decaffeination, a process often relying on liquid-liquid extraction (LLE). This method selectively removes caffeine from green coffee beans using solvents that are unharmful. We'll explore the mathematical underpinnings of this process, developing a model to estimate caffeine extraction potential on a global scale.

The Essence of Liquid-Liquid Extraction

LLE leverages the principle of differential solubility. Green coffee beans are contacted with a solvent, and caffeine, more soluble in the solvent, migrates from the beans into the solvent phase. The caffeine-rich solvent is then separated, leaving behind decaffeinated beans.

Mathematical Modeling: Quantifying the Unseen

Mathematical models provide a powerful tool to understand and optimize this process. We'll build a model based on equilibrium, mass balance, and extraction efficiency.

1. Equilibrium: The distribution of caffeine between the beans and solvent at equilibrium is described by the distribution coefficient (K):

K = [Caffeine]_solvent / [Caffeine]_bean

Where:

 K is the distribution coefficient (dimensionless).

 [Caffeine]_solvent is the concentration of caffeine in the solvent (e.g., kg/m³).

 [Caffeine]_bean is the concentration of caffeine in the coffee beans (e.g., kg/kg bean).

K is temperature-dependent and may also vary with concentration: 

K = f(T, [Caffeine]_bean).

 Accurate K values, often determined experimentally, are crucial for model accuracy. At low concentrations, a linear relationship is often a reasonable assumption.

2. Mass Balance: A mass balance on caffeine dictates:

M_initial = M_extracted + M_remaining

Where:

• M_initial is the initial mass of caffeine in the beans (kg).
• M_extracted is the mass of caffeine extracted (kg).
•  M_remaining is the mass of caffeine remaining (kg).

Expressing these in terms of concentrations and masses/volumes:

[Caffeine]_initial * m_beans = [Caffeine]_solvent * V_solvent + [Caffeine]_final * m_beans

Where:

[Caffeine]_initial is the initial caffeine concentration in the beans (kg/kg bean).

m_beans is the mass of the coffee beans (kg).

 V_solvent is the volume of the solvent (m³).

 [Caffeine]_final is the final caffeine concentration in the beans (kg/kg bean).

3. Extraction Efficiency: The extraction efficiency (E) is:

E = (M_extracted / M_initial) * 100% = (1 - ([Caffeine]_final / [Caffeine]_initial)) * 100%

4. Model Application & Solution: Combining equilibrium and mass balance (substituting [Caffeine]_solvent = K * [Caffeine]_bean):

[Caffeine]_final = ([Caffeine]_initial * m_beans) / (K * V_solvent + m_beans)

E = (1 - m_beans / (K * V_solvent + m_beans)) * 100%

Example Calculation:

Assume: 

 

• K = 10 
•  [Caffeine]_initial = 0.02 kg caffeine/kg beans (2% w/w) 
•  m_beans = 100 kg
•  V_solvent = 0.05 m³ (50 L) 

 [Caffeine]_final ≈ 0.0199 kg caffeine/kg beans

 E ≈ 0.497% 

 This indicates a ~0.5% extraction efficiency, extracting approximately 0.010 kg of caffeine.

Global Caffeine Footprint: A Hypothetical Scenario

Using global coffee bean production data (e.g., from the ICO or FAO) and assuming an average caffeine content range (1-3%), we can estimate a *theoretical maximum* caffeine extraction potential. For instance, 10 billion kg of coffee beans at 2% caffeine content *could* yield 200 million kg of caffeine. However, this is a highly idealized scenario. Not all coffee is decaffeinated, and real-world extraction rates are influenced by many factors.

Model Refinement: Beyond the Basics

Real-world decaffeination is more complex. Advanced models incorporate:

Multi-Stage Extraction: Multiple extraction stages significantly improve efficiency. The model would need to be adapted for each stage.

Mass Transfer Limitations: Caffeine diffusion isn't instantaneous. Mass transfer coefficients (k) are introduced, leading to differential equations:

d[Caffeine]_bean/dt = -k * a * ([Caffeine]_bean - [Caffeine]_solvent/K)

Where 'a' is the surface area for mass transfer.

Non-Ideal Solutions: K can vary with concentration. Thermodynamic models and activity coefficients become necessary.

Temperature & Pressure Effects: K is temperature-dependent, and pressure matters in supercritical CO2 extraction. Empirical or theoretical relationships are added.