Independent guide to pasteurisation F-value calculations using Bigelow's log-linear inactivation model.

Time-temperature equivalence for HTST, batch and ESL processes, with C.

burnetii z-value of 4.34°C

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The Formula

The fundamental relationship for thermal equivalence is Bigelow's first-order log-linear inactivation model. For a given microorganism, the time required to achieve equivalent lethality at two different temperatures is:

t₂ = t₁ × 10^{(T₁ − T₂)/z} t = exposure time at temperature T (s) · z = temperature change for 10× rate change (°C)

The z-value represents the temperature increase required to reduce the thermal death time by a factor of 10. For pasteurisation of Coxiella burnetii in milk (the regulatory target organism for HTST pasteurisation), the published z-value is 4.34°C. Other process targets use different z-values: general thermal inactivation z ≈ 7–10°C, alkaline phosphatase z ≈ 5°C.

Worked Example

Problem: A dairy operates HTST pasteurisation at 72°C for 15 seconds (the UK statutory minimum). For an audit, the QA manager needs to demonstrate this delivers equivalent lethality to a batch pasteuriser running at 63°C. How long must the batch process run?

Step 1. Apply Bigelow's formula with z=4.34°C: t₂ = 15 × 10^{(72−63)/4.34}

Step 2. Calculate the exponent: (72-63)/4.34 = 9/4.34 = 2.074

Step 3. 10^2.074 = 118.5. So t₂ = 15 × 118.5 = 1,777 seconds = 29.6 minutes.

Conclusion: 30 minutes at 63°C delivers equivalent C. burnetii lethality to 15 seconds at 72°C. This is the basis for the UK statutory batch pasteurisation time of 30 minutes at 63°C, matching the HTST 72°C/15s spec used in continuous plants.

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Frequently Asked Questions

What is the z-value for milk pasteurisation?

For Coxiella burnetii (the regulatory target for milk pasteurisation), the z-value is 4.34°C as established by Enright et al. (1957) and confirmed in subsequent studies. This is the value used in UK pasteurisation regulations.

Why is 72°C/15s equivalent to 63°C/30 min?

Both processes deliver equivalent lethality of Coxiella burnetii. Using Bigelow's z-value model with z=4.34°C, the math gives approximately 30 minutes at 63°C as equivalent to 15 seconds at 72°C. The UK statutes specify both as acceptable processes.

Can I use this for sterilisation (UHT) calculations?

The same model applies but with different z-values. For sterilisation targeting Clostridium botulinum spores, z is typically 10°C. F₀ values for UHT are calculated at the reference 121.1°C. The principles are identical.

Need expert support on pasteurisation f-value? Watson Dairy Consulting provides independent support including process design, plant audit, and troubleshooting. Contact Watson Dairy Consulting.

References & Further Reading

Bigelow, W. D. (1921). "The logarithmic nature of thermal death time curves." Journal of Infectious Diseases, 29(5), 528-536.
Enright, J. B., Sadler, W. W., & Thomas, R. C. (1957). "Pasteurisation of milk containing the organism of Q fever." American Journal of Public Health, 47(6), 695-700.
UK Statutory Instruments: The Food Safety and Hygiene (England) Regulations 2013, Schedule 6 Heat Treatments.
Codex Alimentarius: CAC/RCP 57-2004 Code of Hygienic Practice for Milk and Milk Products.
Lewis, M., & Heppell, N. (2000). Continuous Thermal Processing of Foods. Aspen.

Further reading: John Watson publishes articles on dairy industry topics on LinkedIn. Browse all articles by John Watson on LinkedIn →

Disclaimer: This calculator and the calculations on this page are provided for educational and indicative purposes only. Real plant performance depends on many factors not captured by simple models. Always verify against your specific plant data, ingredient specifications, regulatory requirements and safety procedures. Watson Dairy Consulting accepts no liability for production, regulatory, safety or commercial decisions made on the basis of this calculator alone. For project-specific support, please contact Watson Dairy Consulting.

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