Introduction & Context
The Oxygen Transmission Rate (OTR) requirement is a critical parameter in food science and process engineering for the design of modified atmosphere and barrier packaging. For non‑respiring, oxygen‑sensitive products, the shelf life is primarily limited by oxidative degradation, which leads to rancidity, nutrient loss, and microbial spoilage. By calculating the maximum allowable OTR, engineers can select the appropriate packaging barrier function and choose suitable polymer films or metallized laminates to ensure the internal oxygen concentration remains below the product's critical tolerance threshold throughout the intended storage duration.
Methodology & Formulas
The calculation follows a mass-balance approach, determining the total allowable oxygen ingress based on product mass and tolerance, then normalizing this value against the package surface area and shelf life. Environmental factors, specifically temperature and relative humidity, are applied to adjust the theoretical requirement to standard laboratory test conditions.
The allowable oxygen volume is defined as:
\[ V_{allow} = M \cdot Tol \]The required OTR under ambient air conditions is calculated as:
\[ OTR_{air,req} = \frac{V_{allow}}{A \cdot t} \]To account for environmental deviations, the Arrhenius equation is used to adjust for temperature differences between storage and testing:
\[ F_{Arrhenius} = \exp\left( \frac{E_{a}}{R} \cdot \left( \frac{1}{T_{test}} - \frac{1}{T_{store}} \right) \right) \]The humidity correction factor accounts for the increased permeability of hydrophilic films (e.g., EVOH, Nylon) at higher relative humidity levels. This factor is an empirical linear approximation; for precise design, use experimental permeability data at the target relative humidity, and consult the water vapor transmission rate (WVTR) requirement for complementary moisture‑control criteria.
\[ F_{humidity} = 1 + (C_{h} \cdot RH_{store}) \]The final required OTR for a standard 100% oxygen test condition, including a safety factor to account for seal integrity and process variability, is:
\[ OTR_{test,100} = \frac{OTR_{air,req}}{F_{Arrhenius} \cdot F_{humidity} \cdot P_{O2,air} \cdot SF} \]Nomenclature and Units
| Symbol | Description | Units |
|---|---|---|
| M | Product mass | kg |
| Tol | Oxygen tolerance (allowable O2 uptake per product mass) | mL O2/kg |
| Vallow | Total allowable oxygen ingression volume | mL (at standard conditions) |
| A | Package surface area | m² |
| t | Intended shelf life | days |
| OTRair,req | Required OTR under atmospheric conditions (21% O2) | mL/(m²·day) (cc/(m²·day)) |
| Ea | Activation energy for oxygen permeation (material dependent; e.g., 40–50 kJ/mol for common barrier polymers) | J/mol |
| R | Universal gas constant | 8.314 J/(mol·K) |
| Ttest | Absolute temperature during standard OTR test (e.g., 296 K for 23°C) | K |
| Tstore | Absolute storage temperature | K |
| Ch | Humidity coefficient (material specific; typically 0.005–0.02 per %RH for hydrophilic films) | dimensionless |
| RHstore | Relative humidity in storage (expressed as integer, e.g., 75 for 75% RH) | %RH |
| PO2,air | Partial pressure fraction of oxygen in ambient air | dimensionless (0.21) |
| SF | Safety factor (recommended 1.5 – 2.0) | dimensionless |
| OTRtest,100 | Required OTR specification for quality control under 100% O2 test condition | cc/(m²·day) (mL/(m²·day)) |
| Regime | OTR Range (cc/m²/day) | Typical Material |
|---|---|---|
| High Barrier | < 0.5 | Al-foil, Metallized PET |
| Medium Barrier | 0.5 – 50 | EVOH, Nylon |
| Low Barrier | > 50 | LDPE, PET |
| Parameter | Condition/Threshold |
|---|---|
| Product Tolerance | 1.0 – 20.0 mL O₂/kg |
| Temperature Sensitivity | OTR doubles per 10°C rise (typical rule of thumb) |
| Safety Factor | 1.5 – 2.0 (Recommended) |