How to Design Modified Atmosphere Packaging (MAP)

How to Design Modified Atmosphere Packaging

I. Design Objectives and Overall Approach

The essence of designing modified atmosphere packaging (MAP) is to balance the "respiration/transpiration of the product" with the "gas transmission capacity of the packaging material", keeping the O₂, CO₂, and water vapor inside the package within a safe range that is conducive to freshness throughout the shelf life [1][2][3][4].

The entire process can be broken down into 7 major steps:

Define the product and application scenarios
Obtain/set the target atmosphere and storage conditions
Quantify the physiological parameters of the product (respiration, transpiration)
Calculate target OTR (Oxygen Transmission Rate) and CO₂ transmission capacity
Select and configure packaging film materials (including multi-layer structures and micro-perforations)
Select packaging format and gas filling method (active/passive MAP)
Perform numerical verification and safety checks using mass balance equations

Let's unfold these step by step.

II. Step 1: Product and Scenario Definition (Input Parameters)

2.1 List of Necessary Input Parameters

Note:
The respiration rate RR can be measured directly through experiments, or looked up from literature tables (e.g., $r_{O_2}$, $r_{CO_2}$ for different fruits and vegetables at 20℃) [3].

For "respiring products" like fruits and vegetables, these parameters are the core of the design; for non-respiring products like meat/snacks, the main concerns are microorganisms and oxidation.

III. Step 2: Set Target Atmosphere and Storage Conditions

3.1 Target Gas Concentration Range

Based on literature and practical experience, there are recommended suitable O₂ / CO₂ ranges for different fruits and vegetables [3]:

When designing, you need to select a target combination. For example, for strawberries, choose:

$O_{2\_pkg} = 5\%$
$CO_{2\_pkg} = 10\%$

At the same time, set:

External atmosphere: $O_{2\_out} \approx 21\%$, $CO_{2\_out} \approx 0.04\%$
Target relative humidity: $RH \approx 80–90\%$ (to avoid excessive water loss while preventing condensation) [3]
Temperature: T (e.g., 4℃, 10℃, etc.)

3.2 Safety and Quality Boundary Conditions

The following safety constraints must be met [2][3]:

O₂ must not be lower than 1–2%, otherwise there is a risk of anaerobic respiration and pathogenic bacteria
CO₂ must not be higher than the tolerable upper limit of the product (usually no more than 15% for strawberries, and 10–20% for most vegetables)
Temperature control must be stable (fluctuations will lead to changes in RR, destroying the designed atmosphere)

IV. Step 3: Quantify Product Respiration and Transpiration (Kinetic Models)

4.1 Respiration Rate and Michaelis-Menten Model

For many fruits and vegetables, the dependence of respiration rate on O₂ and CO₂ can be modeled using the MMU model [3]:

O₂ consumption rate:

r_{O_2} = \frac{r_{O_{2max}} \, y_{O_2}}{K_{mO_2} + y_{O_2} \left( 1 + \frac{y_{CO_2}}{K_{muCO_2}} \right)}

CO₂ generation rate:

r_{CO_2} = \frac{r_{CO_{2max}} \, y_{O_2}}{K_{mCO_2} + y_{O_2} \left( 1 + \frac{y_{CO_2}}{K_{mu'_{CO_2}}} \right)}

Where:

$r_{O_2}, r_{CO_2}$: O₂ consumption and CO₂ generation rates (cm³/kg·d)
$r_{O_{2max}}, r_{CO_{2max}}$: Maximum respiration rates
$K_{mO_2}, K_{mCO_2}$: Michaelis constants
$K_{muCO_2}, K_{mu'_{CO_2}}$: CO₂ inhibition constants
$y_{O_2}, y_{CO_2}$: Mole fractions of O₂ and CO₂ in the packaging headspace

In actual design, if there is no time for complete kinetic fitting, the average $r_{O_2}$, $r_{CO_2}$, and RQ given in the literature can be used as an approximation.

4.2 Respiratory Quotient (RQ)

Definition:

RQ = \frac{r_{CO_2}}{r_{O_2}}

The RQ range for general fruits and vegetables: 0.7–1.3
A significantly high RQ often suggests anaerobic metabolism (producing alcohol and off-odors) [3].

4.3 Transpiration Rate Model (Optional)

The transpiration rate $r_{H_2O}$ (cm³/kg·d) can be obtained from energy and mass balances [3]:

r_{H_2O} = \frac{q}{\lambda} \left( \frac{RT}{P M_{H_2O}} \right) + k(a_{wp} - a_{wat})

$q$: Heat transferred to the product to evaporate moisture (kJ/d)
$\lambda$: Latent heat of vaporization of water (kJ/kg)
$R$: Gas constant
$T$: Temperature (K)
$P$: Pressure (atm)
$M_{H_2O}$: Molar mass of water
$k$: Overall mass transfer coefficient (cm³/kg·d)
$a_{wp}$: Water activity of the product
$a_{wat}$: Water activity of the environment

Measured or empirical values are often used in application.

V. Step 4: Establish MAP Mass Balance Equations (Core Mathematical Framework)

5.1 Mass Balance for Flexible Packaging (Pouches)

Let:

$V$: Headspace volume (cm³)
$y_{O_2}, y_{CO_2}, y_{H_2O}, y_{N_2}$: Mole fractions of each gas
$K_{TRi}$: Transmission coefficient through perforations (cm³/d)
$Q_i$: Permeability coefficient of the material for gas i (cm³·mm·m⁻²·atm⁻¹·d⁻¹) [3]
$A$: Surface area of the film (m²)
$L$: Film thickness (mm)
$W$: Product weight (kg)

For flexible packaging, the headspace pressure is approximately constant, and the volume can change with the amount of gas [3]:

O₂:

V\frac{dy_{O_2}}{dt} = K_{TRO_2}(y_{O_{2out}} - y_{O_2}) + \frac{APQ_{O_2}}{L}(y_{O_{2out}} - y_{O_2}) - r_{O_2}W - y_{O_2}\frac{dV}{dt}

CO₂:

V\frac{dy_{CO_2}}{dt} = K_{TRCO_2}(y_{CO_{2out}} - y_{CO_2}) + \frac{APQ_{CO_2}}{L}(y_{CO_{2out}} - y_{CO_2}) + r_{CO_2}W - y_{CO_2}\frac{dV}{dt}

Water Vapor:

V\frac{dy_{H_2O}}{dt} = K_{TRH_2O}(y_{H_2O_{out}} - y_{H_2O}) + \frac{APQ_{H_2O}}{L}(y_{H_2O_{out}} - y_{H_2O}) + r_{H_2O}W - y_{H_2O}\frac{dV}{dt}

N₂:

V\frac{dy_{N_2}}{dt} = K_{TRN_2}(y_{N_{2out}} - y_{N_2}) + \frac{APQ_{N_2}}{L}(y_{N_{2out}} - y_{N_2}) - y_{N_2}\frac{dV}{dt}

Volume Change:

\frac{dV}{dt} = W(r_{CO_2} - r_{O_2} + r_{H_2O}) + \sum_{i=O_2,CO_2,H_2O,N_2} (y_{iout} - y_i) \left( K_{TRi} + \frac{APQ_i}{L} \right)

In a steady state (equilibrium atmosphere), the concentration of each gas no longer changes with time, i.e., $dy/dt = 0$. At this point:

\left(K_{TRO_2}+\frac{APQ_{O_2}}{L}\right)(y_{O_{2out}}-y_{O_{2eq}}) - r_{O_2}W - y_{O_{2eq}}\frac{dV}{dt}=0

These equations are used to solve for the required film area A and (or) the required hole diameter/number of holes [3].

5.2 Mass Balance for Rigid Packaging (Trays) (Brief)

For rigid packaging, the volume V is approximately constant, but the pressure P changes. The equations are similar, except that $dV/dt$ is replaced by $dP/dt$, and a Poiseuille flow term (flowing through holes according to Poiseuille's law) is added [3]. The details are omitted here. In engineering applications, detailed calculations are usually only performed for active MAP in flexible pouches or highly permeable films, while empirical data and simulation software are more commonly used for rigid trays.

VI. Step 5: Calculate Target OTR and Material Selection

6.1 Empirical Formula: Target OTR Calculation (Commonly Used in Engineering)

White papers provide a simplified engineering formula for fresh-cut fruits and vegetables (OTR per mil thickness) [2]:

OTR = RR_{O_2} \cdot t \cdot \frac{W}{A} \cdot (O_{2air} - O_{2pkg})

$OTR$: Film oxygen transmission rate (converted based on 1 mil thickness, cc/100in²/mil/atm/day)
$RR_{O_2}$: Respiration rate (ml O₂/kg·hr or converted to cm³/kg·d)
$t$: Film thickness (mil)
$W$: Product weight (kg)
$A$: Effective mass transfer area (cm²)
$O_{2air}$: 21%
$O_{2pkg}$: Target O₂ concentration inside the package (%)

Note: If the actual film thickness is 2 mils, the "OTR in the database (labeled for 1 mil)" needs to be divided by 2 to get the actual OTR of the structure.

6.1.1 Simple Calculation Example (Fresh-cut Strawberries)

Assuming: $RR_{O_2} = 1100$ cm³/kg·d (referencing the average $r_{O_2}$ of strawberries at 20℃ [3]), $W = 0.5$ kg, $A = 300$ cm², $t = 1$ mil. Target: $O_{2\_pkg} = 5\%$

For simplicity, ignore the difference in unit conversions first (in engineering, it can be unified as "relative magnitude" judgments). Calculate:

OTR \approx 1100 \times 1 \times \left(\frac{0.5}{300}\right) \times (21 - 5) \approx 1100 \times 0.001667 \times 16 \approx 29.3 \ (\text{relative units})

Then compare with the material database (OTR of LDPE, PP, etc.), and select the film structure (or micro-perforation combination) closest to 30 as a candidate.

6.2 OTR Calculation for Multi-layer Film Structures

If it is a multi-layer co-extruded or laminated film, the overall OTR is calculated as "resistors in series" [2]:

\frac{1}{OTR_{total}} = \frac{t_1}{OTR_1} + \frac{t_2}{OTR_2} + \cdots + \frac{t_n}{OTR_n}

$t_i$: Thickness of the i-th layer (mil)
$OTR_i$: OTR of the i-th layer material at 1 mil thickness

Conclusion: The overall OTR will never be higher than that of the layer with the worst barrier properties (i.e., the layer with the minimum OTR dominates the lower limit) [2].

VII. Step 6: Calculation of Gas Transmission Capacity Through Films and Micro-perforations

7.1 Gas Permeation Through Films (Fick's Law)

The permeation flux of gas i through a uniform film [3]:

J_{fi} = -\frac{Q_i A (p_i - p_{i,out})}{L} \cdot \frac{P}{RT}

$J_{fi}$: Molar flow rate of gas through the film (mol/d)
$Q_i$: Permeability coefficient of the gas in the material (cm³·mm·m⁻²·atm⁻¹·d⁻¹)
$A$: Film area (m²)
$L$: Thickness (mm)
$p_i, p_{i,out}$: Partial pressures inside and outside the film
$P$: System pressure
$R, T$: Gas constant and temperature

7.2 Gas Diffusion Through Micro-perforations (KTR Calculation)

Micro-perforation transmission coefficient [3]:

K_{TRi} = \frac{D_i A_h}{L + \varepsilon}

$D_i$: Diffusion coefficient of gas i in air (cm²/s)
$A_h$: Total cross-sectional area of all holes (cm²)
$L$: Film thickness (mm, for holes, this is the length of the hole)
$\varepsilon$: Diffusion channel resistance correction term, approximately $0.5 \times d_e$
$d_e$: Equivalent diameter, $d_e = \sqrt{N} \cdot d$
$N$: Number of holes
$d$: Diameter of a single hole

Key technical points of micro-perforations: Micro-perforation diameter is usually 40–200 μm; The CO₂/O₂ transmission rate ratio (Beta value) of micro-perforated structures is $\approx 1$, while for polymer films it is about 2–5 [2][3].

VIII. Step 7: Two Configuration Strategies: Adjusting Area vs. Adjusting Hole Diameter

According to literature [3], design can be divided into two situations:

Packaging dimensions have not been determined:

Achieve the desired transmission capacity by changing the film area A (pouch size)
$K_{TRi}$ is taken as 0 (no holes)
Solve the system of balance equations (21)-(23) with targeted O₂eq (or CO₂eq) as known to find A

Packaging dimensions are fixed:

A is fixed, and micro-perforations need to be designed: Determine the hole diameter d and the number of holes N, and subsequently determine $K_{TRi}$
The unknowns in the balance equations are: $y_{O_{2eq}}, y_{CO_{2eq}}, y_{H_{2Oeq}}$ and d or N
Usually fix one concentration (e.g., O₂eq), and iterate to find the other two concentrations and d or N

Engineering implementation: On a website, "target O₂eq" can be set as user input, and the system automatically calculates the "recommended area/number of holes/hole diameter" based on the product RR and selected material OTR.

IX. Rules of Thumb for Gas Mixtures (Active MAP)

For meat, ready meals, snacks, etc., which commonly use actively filled MAP (not relying on respiration), the empirical ratios given by manufacturers and literature can be used for guidance [1][4].

Note: Oxygen-enriched (>21% O₂) MAP requires confirmation of equipment and safety standards [4].

X. Summary: A Step-by-Step "Practical Checklist" for MAP Design

Select Product + Set Scenario
- Specify product type, form, target market (refrigerated/ambient), and target shelf life
Look up/Measure Physiological Parameters
- Determine or look up table values for $r_{O_2}$, $r_{CO_2}$, RQ, $r_{H_2O}$ at target temperature
Set Target O₂/CO₂/RH Ranges and Temperature
- Choose specific target values referencing Table 1, e.g., O₂=3%, CO₂=5%
Build Mass Balance Model (Simplified OTR formula can be used in engineering)
- For fresh-cut fruits and vegetables: Use $OTR = RR \cdot t \cdot W/A \cdot (21–O_{2pkg})$ to estimate target OTR
Screen Films from Material Database
- Based on target OTR, screen or combine from materials like LDPE/PP/PET/EVOH, calculating the multi-layer complete OTR by $1/OTR_{total} = \Sigma(t_i/OTR_i)$
Decide Whether to Use Micro-perforations
- For high-respiration products, if the required OTR exceeds the upper limit of pure polymers, introduce micro-perforations and calculate transmission capacity via $K_{TRi} = D_i A_h/(L+\varepsilon)$
- Two Strategies:
  If packaging size is adjustable: Use balance equations to find required A
  If size is fixed: Use the same equations inversely to find hole diameter d and number of holes N
(For Meat/Cooked Food, etc.) Configure Active Gas Filling Ratio
- Directly grant 70–80% O₂ + 20–30% CO₂ etc., per empirical tables, checking mechanical and safety compatibilities
Simulate O₂/CO₂ Changes over Time using Complete Mass Balance Equations or Simplified Models
- Check if they remain within the safe and suitable range throughout the target shelf life
Experimental Verification and Fine-tuning
- Conduct small-batch trials for actual shelf life and quality; if unsatisfactory, return to steps 4–7 and adjust film material/hole diameter/gas ratio

References

[1] 332-19-024-UK-Modified-Atmosphere-Packaging-MAP-Helping-you-to-be-retail ready.pdf.
[2] map-white-paper.pdf.
[3] 54951.pdf.
[4] 24_modified.pdf.