Accuracy Needed In Shelf-life Modelling

Dr Brady Carter on modelling shelf life with water activity

The shelf life of a product is defined as the practical time that it remains desirable to consumers. It dictates the radius of distribution for the product, how it must be stored and its best-by date. Failure to match this expected shelf life can result in customer complaints, product recalls and tarnished reputation. Consequently, correctly determining the optimal production process and handling that maximises the shelf life and then monitoring to make sure those conditions are met is the difference between profitability and lost revenue.

However, correctly determining the shelf life of a product can be a challenging endeavour, often due to a lack of resources and the time to conduct full shelf-life studies. One option to speed up the shelf-life testing is to derive a model that can predict the shelf life based on the expected storage conditions of the product. To be effective, these models need to account for the effect of both water activity and temperature and not just one of these as they both impact shelf life.

The method

While there are examples of shelf-life models in scientific literature, the most well-known being the Arrhenius equation, the only fundamental model that includes both water activity and temperature is hygrothermal time.(1) It is derived from a form of the Eyring (2) equation for rate change and Gibbs equation for free energy and is given by the equation shown above.

Where T is the temperature (K), R is the gas constant (J mol-1 K-1), Ea is the activation energy (J mol-1), B is the molecular volume ratio, aw is the water activity, and r0 is the rate at the standard state. In practice, the values for B, Ea/R and r0 will be unique to each situation and are derived empirically through least squares iteration. Once the constants are known, any temperature and water activity can be used with the hygrothermal time model to determine the reaction rate at those conditions and hence the shelf life that the product will remain acceptable to the consumer.

The significance

Hygrothermal time has proven to be effective at predicting the shelf life of products where the mode of failure is related to the rate of a chemical reaction such as lipid oxidation or vitamin loss. The shelf-life model is unique because it accounts for both water activity and temperature effects. The model can predict the change in shelf life that would occur due to processing to an incorrect water activity specification or subjecting a product to abuse storage conditions. When combined with Fickian based packaging models, it can predict the change in shelf life experienced by a product in the package when stored at different ambient conditions.


1. Carter, B. P., Syamaladevi, R. M., Galloway, M. T., Campbell, G. S., & Sablani, S. S. 2017. A Hygrothermal Time Model to Predict Shelf Life of Infant Formula. In U. Klinkesorn (Ed.), Proceedings for the 8th Shelf Life International Meeting (pp. 40–45). Bangkok, Thailand: Kasetsart University.

2. Eyring, H. 1936. Viscosity, plasticity, and diffusion as examples of absolute reaction rates. J. Chem. Phys. 4:283

Dr Brady Carter is an application scientist with Novasina

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