SCF Extraction System Mass Balance

Reference ID: MET-0E97 | Process Engineering Reference Sheets Calculation Guide

Introduction & Context

Supercritical CO₂ (SCF) extraction is a high‑pressure separation process widely utilized in the food, pharmaceutical, and chemical industries for the selective removal of compounds (e.g., caffeine from coffee, essential oils from botanicals), making it a key technology for natural flavor and fragrance extraction. The process relies on the unique solvent properties of CO₂ above its critical point, where it exhibits liquid‑like density and gas‑like diffusivity.

The mass balance of an SCF system is critical for process design, as it dictates the solvent-to‑feed ratio, compressor sizing, and energy consumption; a thorough economic assessment of SCF extraction builds on this foundation to evaluate cost drivers and profitability. Because CO₂ behaves as a non‑ideal fluid in the supercritical regime, standard ideal gas laws are insufficient for design. Accurate mass balance requires real‑fluid property data (enthalpy, entropy, and density) to ensure the system operates within the feasible solubility window while maintaining mechanical integrity.

Methodology & Formulas

The following formulas define the mass and energy balance for a closed-loop SCF extraction system. All enthalpy and entropy values must be sourced from certified real-fluid property databases.

1. Solute Extraction Rate
The mass flow rate of the extracted solute is determined by the solute mass flow rate in the feed material and the target recovery efficiency:

\[ \dot{m}_{\text{solute,ext}} = \dot{m}_{\text{solute,feed}} \cdot R \]

2. Solvent Loading
The loading factor represents the mass of solute per unit mass of solvent. This must be maintained below the equilibrium solubility limit to ensure mass transfer kinetics:

\[ Y = \frac{\dot{m}_{\text{solute,ext}}}{\dot{m}_{\text{CO}_2}} \]

3. Solvent-to-Feed Ratio
This ratio defines the process intensity and is a primary design specification for extraction efficiency:

\[ \frac{S}{F} = \frac{\dot{m}_{\text{CO}_2}}{\dot{m}_{\text{feed}}} \]

4. Compressor Power Requirements
The power required for re-pressurization is calculated using the isentropic enthalpy change, adjusted for the compressor's isentropic efficiency:

\[ \dot{W}_{\text{c}} = \frac{\dot{m}_{\text{CO}_2} \cdot (h_{2s} - h_{1})}{\eta_{\text{c}}} \]

5. Specific Energy Consumption
This metric evaluates the efficiency of the extraction loop in terms of energy input per unit of solvent circulated:

\[ E_{\text{spec}} = \frac{\dot{W}_{\text{c}}}{\dot{m}_{\text{CO}_2}} \]

Operational Validity Bounds

Parameter	Constraint/Condition	Engineering Rationale
Extraction Phase	\( P > 73.8 \text{ bar}, T > 31.1 \text{ °C} \)	Ensures CO₂ is in the supercritical regime.
Loading Limit	\( Y \leq 0.7 \cdot Y_{\text{equilibrium}} \)	Prevents solute breakthrough and ensures kinetic feasibility.
Compressor Discharge	\( T_{2s} < 180 \text{ °C} \)	Protects mechanical seals and lubricant integrity.
Compressor Efficiency	\( 0.70 \leq \eta_{\text{c}} \leq 0.95 \)	Standard empirical range for industrial CO₂ compressors.

To ensure accurate mass balance closure, process engineers must account for all mass streams entering and exiting the supercritical fluid loop. Follow these steps:

Measure the mass flow rate of the CO₂ solvent at the pump inlet using the mass_flow_meter variable.
Quantify the mass of the raw feed material loaded into the extractor and the mass of the spent biomass removed post-extraction.
Collect and weigh the total extract collected in the separator vessel.
Calculate the difference between the total input mass and the sum of the output streams to determine the system loss percentage.

Discrepancies often arise from measurement errors or physical losses within the high-pressure loop. Common factors include:

Incomplete depressurization of the extractor vessel leading to residual CO₂ entrapment.
Entrainment of fine particles in the CO₂ stream that bypass the separator filters.
Calibration drift in the mass_flow_meter or load cells used for vessel weighing.
Minor leaks at high-pressure flange connections or valve stems that are not captured by the primary flow sensors.

Because supercritical CO₂ is highly compressible, small changes in temperature or pressure significantly alter its density. If the system density is not corrected in real-time, the volumetric flow readings will lead to inaccurate mass balance results. Ensure that your control system uses the current pressure_transducer and temperature_sensor inputs to calculate the dynamic density value before finalizing the mass flow integration.

Worked Example: Supercritical CO₂ Extraction Mass Balance – Green Coffee Decaffeination

A decaffeination process treats 100.0 kg/h of green coffee beans containing 1.5 kg/h of caffeine. Supercritical CO₂ at 300 bar and 60 °C flows at 4,000 kg/h. The separator operates at 55 bar, 40 °C. The compressor isentropic efficiency is 0.80. The target caffeine recovery is 96%. The mass balance and required compressor power are calculated below.

Knowns:

Total feed rate: \(\dot{m}_{\text{feed}} = 100.0\) kg/h
Caffeine mass flow in feed: \(\dot{m}_{\text{solute,feed}} = 1.5\) kg/h
CO₂ flow rate: \(\dot{m}_{\text{CO}_2} = 4000.0\) kg/h
Compressor efficiency: \(\eta_{\text{c}} = 0.80\)
Recovery target: \(R = 0.96\)
Extraction pressure: \(P_{\text{ext}} = 300.0\) bar; temperature \(T_{\text{ext}} = 60.0\) °C
Separation pressure: \(P_{\text{sep}} = 55.0\) bar; temperature \(T_{\text{sep}} = 40.0\) °C
Compressor inlet (State 1): \(h_{1} = 435.0\) kJ/kg, \(s_{1} = 1.58\) kJ/(kg·K)
Isentropic discharge (State 2s): \(h_{2s} = 550.0\) kJ/kg, \(T_{2s} = 110.0\) °C

Step-by-Step Calculation:

Caffeine extracted from the beans: \[ \dot{m}_{\text{solute,ext}} = \dot{m}_{\text{solute,feed}} \cdot R = 1.5 \cdot 0.96 = 1.44\ \text{kg/h} \]
Loading (solute mass per CO₂ mass): \[ Y = \frac{\dot{m}_{\text{solute,ext}}}{\dot{m}_{\text{CO}_2}} = \frac{1.44}{4000.0} = 0.00036\ \text{kg/kg CO₂} \]
Solvent-to-feed ratio: \[ S/F = \frac{\dot{m}_{\text{CO}_2}}{\dot{m}_{\text{feed}}} = \frac{4000.0}{100.0} = 40.0 \]
Compressor power requirement:
Actual enthalpy rise per unit mass: \[ \Delta h_{\text{actual}} = \frac{h_{2s} - h_{1}}{\eta_{\text{c}}} = \frac{550.0 - 435.0}{0.80} = 143.75\ \text{kJ/kg} \] Power consumed: \[ \dot{W}_{\text{c}} = \frac{\dot{m}_{\text{CO}_2} \cdot \Delta h_{\text{actual}}}{3600} = \frac{4000.0 \cdot 143.75}{3600} = 159.722\ \text{kW} \]
Specific energy consumption: \[ E_{\text{spec}} = \frac{\dot{W}_{\text{c}}}{\dot{m}_{\text{CO}_2}} = \frac{159.722}{4000.0} = 0.040\ \text{kWh/kg CO₂} \]

Final Answer:
The recycle compressor consumes 159.722 kW of mechanical power, and the specific energy consumption is 0.040 kWh per kilogram of CO₂ circulated. The design loading (0.00036 kg/kg) lies well below the solubility limit, and the solvent-to-feed ratio of 40.0 is within the typical range for commercial decaffeination.

"Un projet n'est jamais trop grand s'il est bien conçu." — André Citroën

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