# Guidelines for using recycled plastics in food packaging: Appendix

## Appendix I. Sample calculation of the estimated residual concentration of a contaminant in a PET finished packaging article

Probable daily intake (PDI) is calculated as:

PDI = [(Caq.*Faq.) + ( Cac.* Fac.) + (Calc. * Falc.) + (Cfat. * Ffat.)] DpMpKp/ Bw

Where:

PDI
probable daily intake; mg/kg bw/day.
C
concentration; mg/g of chemical amount extracted in aqueous, acidic, alcoholic and fatty food simulants, normalized to an exposure (or packaging) ratio of 5g/in2
F
intake of aqueous, acidic, alcoholic and fatty foods in the daily diet (2 kg/day or 2000g/day for adults).
Dp
distribution (as a fraction) of types of food packaging materials such as plastic or paper. For plastic, Dp = 0.4 (meaning 40% of food is packaged in plastic)
Mp
distribution (as a fraction) of plastic or paper types used in food packaging such as polyethylene (PE) or polypropylene (PP) for plastic. For PET, Mp = 0.06 (meaning only 6% of plastic is PET but for drinks, we generally assume 100% of bottles are made of PET because PET is very popular for beverage bottles)
Kp
market penetration of the packaging material, 100% for recycled PET
Bw
the average adult body weight (70 kg).

Cµg/gfood = PDI (mg/kg-bw/day) × Bw (kg) ÷ [(DpMpKP) x F (g/day)].

Cµg/gfood = [PDI (mg/kg-bw/day) × Bw (kg)/ F (g/day)] ÷ (DpMpKP)

Cµg/gfood = [0.025 mg/kg-bw/day × 70 kg/ 2000 g/day] ÷ (DpMpKP)

Cµg/gfood = (0.000875µg/gfood) ÷ (DpMpKP).

Using a food-packaging ratio of 5g of food per in2, the concentration of migrating contaminant is [(0.000875µg/gfood) ÷ (DpMpKP)] ×5gfood/in2

Cµg/in2 = 0.004375 µg/in2 ÷ (DpMpKP).

The residual amount (Cresidue) of contaminant in a recycled resin will be assumed migrate 100% into food. Using the density (d, g/cm) of each type of plastic and assuming a thickness of 20 mils of the packaging materials (0.02 in or 0.0508 cm), we can calculate the concentration of the contaminant in the recycled resin.

Cµg/in2 = (d g/cm3)× (0.02 in) × (16.4 cm3/in3) × Cresidue (μg/g).

0.004375 µg/in2 ÷ (DpMpKP) =(d g/cm3)× (0.02 in) × (16.4 cm3/in3) × Cresidue (μg/g)

Cresidue (μg/g) = [0.004375 µg/in2 ÷ (DpMpKP)]÷ [d g/cm 3) × (0.328 cm3/in2)]

Cresidue (μg/g) = 0.01333 ÷ [ (DpMpKP) x d]

Cresidue (μg/g) = 0.01333 ÷ [ (DpMpKP) x d]; DpKP =0.4

Cresidue (μg/g) = (0.01333 ÷ 0.4) ÷[ Mp x d]

Cresidue (μg/g) = 0.0333÷[ Mp x d]

Using PET as an example with a density of PET = 1.4g/cm3 and a material type of 6%, the maximum residue in a recycled PET is 0.0333/1.4/0.06 = 0.3964 mg/g PET or 396.4µg/kg PET

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