Pharmaceutical Compound Extraction

Reference ID: MET-D8EA | Process Engineering Reference Sheets Calculation Guide

Introduction & Context

Pharmaceutical compound extraction from botanical matrices is a critical unit operation in the production of Active Pharmaceutical Ingredients (APIs). This process involves solid‑liquid leaching, where a solvent is used to selectively dissolve the target compound from the plant material; for related techniques see our guide on antioxidant extraction from plant materials. Following extraction, the solvent must be removed to produce a concentrated extract that complies with regulatory standards, such as the International Council for Harmonisation (ICH) Q3C guidelines for residual solvents.

This calculation is essential for process engineers to determine the theoretical maximum yield, assess the purity of the resulting extract, and establish the mass balance required for downstream solvent recovery equipment design. It is typically employed during the scale‑up phase of botanical drug manufacturing to ensure that extraction efficiency and drying capacity meet production targets, as described in our guide on herbal extract production for supplements.

Methodology & Formulas

The extraction process is modeled using an equilibrium-based mass balance. The system assumes that the API distributes between the liquid solvent phase and the exhausted solid phase (mare) according to a partition coefficient, \(K_d\) (L/kg).

The mass balance for the system is defined as:

\[ m_{\text{feed}} \cdot w_{\text{API},0} = C_{L} \cdot V_{\text{solvent}} + C_{S} \cdot m_{\text{mare}} \]

Given the partition equilibrium relationship \( C_{S} = K_{d} \cdot C_{L} \), the concentration of the API in the liquid phase is derived as:

\[ C_{L} = \frac{m_{\text{feed}} \cdot w_{\text{API},0}}{V_{\text{solvent}} + (K_{d} \cdot m_{\text{mare}})} \]

The recovery efficiency of the extraction process is calculated as:

\[ R = \left( \frac{C_{L} \cdot V_{\text{solvent}}}{m_{\text{feed}} \cdot w_{\text{API},0}} \right) \cdot 100 \]

The purity of the final dry extract is determined by the ratio of the recovered API mass to the total mass of the extracted solids:

\[ \text{Purity} = \left( \frac{C_{L} \cdot V_{\text{solvent}}}{m_{\text{extract,dry}}} \right) \cdot 100 \]

To ensure compliance with ICH Q3C limits, the maximum allowable mass of residual solvent in the final product is calculated based on the target parts-per-million (ppm) threshold:

\[ m_{\text{res}} = m_{\text{extract,dry}} \cdot (\text{ppm}_{\text{target}} \cdot 10^{-6}) \]

The validity of the equilibrium assumption is governed by the diffusion of the API through the botanical tissue, where the penetration depth \( \delta \) must exceed the characteristic dimension of the particle:

\[ \delta = \sqrt{4 \cdot D_{\text{eff}} \cdot t} \]

Parameter	Condition / Threshold
Equilibrium Validity	\( \delta \geq \frac{d_{\text{particle}}}{2} \)
Partition Coefficient	\( 0.01 \leq K_{d} \leq 10.0 \; \text{L/kg} \)
Mass Balance	\( V_{\text{solvent}} + (K_{d} \cdot m_{\text{mare}}) > 0 \)
ICH Q3C Class 3 Limit	\( \text{ppm}_{\text{target}} \leq 5000 \)

Selecting the appropriate solvent is critical for yield and purity. Process engineers should evaluate the following factors:

Solubility parameters of the target active pharmaceutical ingredient.
Regulatory compliance regarding residual solvent limits as defined by ICH Q3C guidelines.
Boiling point and vapor pressure to optimize downstream solvent recovery processes.
Safety profile, specifically regarding flammability and toxicity levels.

In solid-liquid extraction, the overall rate is often controlled by internal diffusion of the solute through the plant matrix. Key parameters include:

Particle size reduction: smaller particles shorten the diffusion path length and increase surface area.
Temperature: higher temperatures increase the effective diffusion coefficient, \( D_{\text{eff}} \).
Solvent viscosity: lower viscosity improves diffusivity and penetration into the matrix.
Swelling and porosity of the botanical material, which can enhance solvent access.

Maintaining process integrity during scale-up requires strict control over mass transfer and thermodynamic variables:

Power input per unit volume to maintain consistent droplet size distribution.
Residence time distribution within continuous extraction columns.
Temperature control to prevent thermal degradation of heat-sensitive compounds.
Solvent-to-feed ratio to ensure optimal extraction efficiency across different vessel geometries.

Worked Example: Pharmaceutical Compound Extraction from Botanical Material

A batch extraction is conducted to recover an active pharmaceutical ingredient (API) from dried herb. The feed consists of 100.0 kg of dried herb with an API content of 1.0% w/w. The solvent is 2000.0 L of 80% ethanol/water (hydroalcoholic mixture). The extraction is carried out at 50°C for 2 hours, assuming equilibrium conditions. A partition coefficient K_d = 0.05 L/kg (favoring the solvent) is used. After extraction, the exhausted solid (mare) mass is 90.0 kg. The liquid extract is then dried under vacuum to yield 12.0 kg of dry extract. The target residual solvent (ethanol) is below 5000 ppm (ICH Q3C Class 3 limit). The effective diffusion coefficient of the API in the plant tissue is estimated at D_eff = 1.0×10⁻¹⁰ m²/s, and the average particle size is 1.0 mm (0.001 m).

Knowns (Input Parameters and Units)

Feed mass: \( m_{\text{feed}} = 100.0 \, \text{kg} \)
Initial API mass fraction: \( w_{\text{API},0} = 0.01 \, (1.0\% \text{ w/w}) \)
Solvent volume: \( V_{\text{solvent}} = 2000.0 \, \text{L} \)
Partition coefficient: \( K_d = 0.05 \, \text{L/kg} \)
Mare mass: \( m_{\text{mare}} = 90.0 \, \text{kg} \)
Dry extract mass: \( m_{\text{extract,dry}} = 12.0 \, \text{kg} \)
Target residual solvent: \( \text{ppm}_{\text{target}} = 5000 \, \text{ppm} \) (ethanol, ICH Q3C Class 3)
Particle size: \( d_p = 0.001 \, \text{m} \)
Effective diffusion coefficient: \( D_{\text{eff}} = 1.0 \times 10^{-10} \, \text{m}^2/\text{s} \)
Extraction time: \( t = 7200 \, \text{s} \)

Step-by-Step Calculation

Validity Check of Equilibrium Assumption:
Compute the penetration depth: \( \delta = \sqrt{4 D_{\text{eff}} t} \). Using the given values, the result is \( \delta = 1.697 \times 10^{-3} \, \text{m} \). The particle radius is \( d_p/2 = 5.0 \times 10^{-4} \, \text{m} \). Since \( \delta > d_p/2 \), the assumption of equilibrium during the 2-hour extraction is valid.
Equilibrium Mass Balance:
The mass balance for the closed system is:
\[ m_{\text{feed}} w_{\text{API},0} = C_L V_{\text{solvent}} + C_S m_{\text{mare}} \]
where \( C_L \) is the API concentration in the liquid extract (kg/L) and \( C_S \) is the concentration in the exhausted solids (kg/kg). Using the equilibrium relation \( C_S = K_d C_L \), substitute:
\[ m_{\text{feed}} w_{\text{API},0} = C_L V_{\text{solvent}} + (K_d C_L) m_{\text{mare}} \]
Solve for \( C_L \):
Rearrange to isolate \( C_L \):
\[ C_L = \frac{m_{\text{feed}} w_{\text{API},0}}{V_{\text{solvent}} + K_d m_{\text{mare}}} \]
The denominator calculates to \( 2004.5 \, \text{L} \). Plugging in:
\[ C_L = \frac{100.0 \times 0.01}{2004.5} = 4.989 \times 10^{-4} \, \text{kg/L} \]
Correspondingly, \( C_S = K_d C_L = 0.05 \times (4.989 \times 10^{-4}) = 2.494 \times 10^{-5} \, \text{kg/kg} \).
Mass of API Recovered in Liquid:
\( m_{\text{API,recovered}} = C_L V_{\text{solvent}} = (4.989 \times 10^{-4} \, \text{kg/L}) \times 2000.0 \, \text{L} = 0.9978 \, \text{kg} \).
Recovery Percentage:
Total initial API mass: \( m_{\text{feed}} w_{\text{API},0} = 100.0 \times 0.01 = 1.0 \, \text{kg} \).
\[ R = \frac{m_{\text{API,recovered}}}{m_{\text{feed}} w_{\text{API},0}} \times 100 = \frac{0.9978}{1.0} \times 100 = 99.78\% \]
Purity of Dry Extract:
\( \text{Purity} = \frac{m_{\text{API,recovered}}}{m_{\text{extract,dry}}} \times 100 = \frac{0.9978}{12.0} \times 100 = 8.315\% \).
Residual Solvent Calculation (Regulatory Target):
The maximum allowable residual ethanol mass in the final dry extract is determined by the ICH Q3C limit of 5000 ppm:
\[ m_{\text{res}} = m_{\text{extract,dry}} \times (\text{ppm}_{\text{target}} \times 10^{-6}) = 12.0 \, \text{kg} \times (5000 \times 10^{-6}) = 0.06 \, \text{kg} \]
This indicates that the drying process must reduce the ethanol content to no more than 0.06 kg in the 12 kg extract.

Final Answer

Equilibrium assumption is valid (penetration depth 1.697×10⁻³ m exceeds particle radius).
API recovery: 99.78% (0.9978 kg recovered).
Purity of dry extract: 8.315% w/w.
Maximum allowable residual ethanol: 0.06 kg (corresponding to 5000 ppm).

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

"La difficulté attire l'homme de caractère, car c'est en l'étreignant qu'il se réalise." — Charles de Gaulle