Thermal processing: D, z and F values
How heat kills microbes in canned and pasteurised foods, what D, z and F values mean, the botulinum cook, and how to calculate process lethality.
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Heating is the oldest and still the most widely used way to make food safe and keep it. Canning, retorting, pasteurisation and UHT treatment all depend on one idea: microbes die at a predictable rate when heated, and that rate can be measured and calculated. Three numbers describe it: the D value, the z value and the F value.
Thermal death kinetics is one of the highest-yield topics in food technology and dairy technology exams, and the calculations appear in almost every food engineering paper.
How microbes die in heat
When a population of microbes or spores is held at a constant lethal temperature, the number of survivors falls by the same fraction in each equal interval of time. Plotted on a logarithmic scale, the survivors fall in a straight line. This is first-order (logarithmic) death kinetics.
The D value
The decimal reduction time, D, is the time at a stated temperature needed to kill 90 per cent of the population, a one-log reduction. It is written with the temperature as a subscript, for example D121.
N0 is the starting number, N the number after t minutes. Heating for 2D leaves 1 per cent; 5D leaves 0.001 per cent. The count never reaches zero; it only becomes a smaller and smaller probability of a survivor.
The z value
The D value depends strongly on temperature. The z value is the temperature change needed to change the D value tenfold. For bacterial spores, z is often about 10 °C; for vegetative cells, enzymes and nutrients the values differ, which is why processes can be chosen to kill microbes while sparing quality.
The F value and the botulinum cook
The F value is the total lethal effect of a heat process, expressed as the equivalent number of minutes at a reference temperature. For low-acid canned foods the reference is 121.1 °C (250 °F) with z = 10 °C, and the value is called F0.
The organism that sets the standard for low-acid canned foods is Clostridium botulinum, whose spores survive ordinary cooking and, in a sealed, low-oxygen, low-acid can, can germinate and produce botulinum toxin, one of the most potent toxins known. Its spores have a D121 of roughly 0.2 minutes (0.21 is a commonly used value).
The classic safety target is the 12D process (the "botulinum cook"): enough heating to reduce the spore population by twelve log cycles.
A 12D process means that if every can started with one spore, only one can in 1012 would be expected to contain a survivor. In practice, commercial processes often use higher F0 values to control more heat-resistant spoilage organisms, such as Geobacillus stearothermophilus (flat sour spoilage), which are not dangerous but spoil the product.
Acid and low-acid foods
C. botulinum does not grow or make toxin below pH 4.6. This dividing line shapes the whole of canning:
- Low-acid foods (pH above 4.6, and water activity above 0.85): most vegetables, meat, fish, milk, soups. They need a sterilising process at temperatures above 100 °C, under pressure in a retort, delivering at least the botulinum cook. The result is commercial sterility: free of microbes capable of growing under normal storage, rather than absolutely sterile.
- Acid and acidified foods (pH 4.6 or below): most fruits, tomatoes (sometimes acidified), pickles, many juices. Spore-formers cannot grow, so the target is acid-tolerant yeasts, moulds and bacteria, and a process below 100 °C, a hot fill or a boiling-water bath, is usually enough.
Pasteurisation
Pasteurisation is a milder heat treatment that kills pathogenic vegetative microbes and most spoilage organisms, but not spores. The product still needs refrigeration or another hurdle. For milk, the established conditions include:
| Method | Typical time–temperature | Notes |
|---|---|---|
| Low-temperature long-time (batch) | 63 °C for 30 minutes | the original method |
| High-temperature short-time (HTST) | 72 °C for 15 seconds | the usual continuous process |
| UHT (ultra-high temperature) | about 135–150 °C for a few seconds | with aseptic packaging, shelf-stable for months |
Milk pasteurisation standards were set to destroy the most heat-resistant common pathogen in raw milk, historically Mycobacterium tuberculosis and later Coxiella burnetii. Adequate pasteurisation is checked with the alkaline phosphatase test: this natural milk enzyme is slightly more heat-resistant than the target pathogens, so if it is inactivated, the milk was properly heated.
Calculating process lethality
A real can does not jump instantly to 121 °C; its slowest-heating point, the cold point, heats and cools over many minutes. Each moment contributes some lethality. The lethal rate at temperature T, relative to 121.1 °C, is:
The F value is the sum (integral) of lethal rates over the process time. Adding them from measured temperatures at the cold point is the general method, first described by W. D. Bigelow and colleagues in 1920; C. Olin Ball's formula method (1923) estimates lethality from the shape of the heating curve.
Lethality from heat penetration data
Temperatures at the cold point of a can, read every 5 minutes during the hold and cooling, are 110, 115, 121 and 115 °C. Take z = 10 °C.
| Temperature (°C) | Lethal rate L, with z = 10 °C | Contribution over 5 min |
|---|---|---|
| 110 | 10−1.11 = 0.078 | 0.39 |
| 115 | 10−0.61 = 0.245 | 1.23 |
| 121 | 10−0.01 = 0.977 | 4.89 |
| 115 | 0.245 | 1.23 |
| Total | F0 ≈ 7.7 min |
This exceeds the minimum botulinum cook of about 2.5 minutes. Notice how little the 110 °C period contributes: lethality is dominated by the hottest minutes.
D at a different temperature, and spores per can
C. botulinum spores have D121.1 = 0.21 min and z = 10 °C. What is D at 115 °C, and how long a hold at 115 °C gives a 12D process?
- log (D115 ⁄ 0.21) = (121.1 − 115) ⁄ 10 = 0.61, so D115 = 0.21 × 100.61 = 0.21 × 4.07 ≈ 0.86 min.
- 12D at 115 °C = 12 × 0.86 ≈ 10.3 minutes, compared with 2.5 minutes at 121.1 °C.
If a batch of cans starts with 100 spores per can (102) and receives a 12D process, the expected survivors are 102−12 = 10−10 per can: one surviving spore in ten billion cans.
Heat and quality
The same equations apply to the loss of vitamins, colour, texture and flavour, but these usually have higher z values (often 25–40 °C) than bacterial spores (about 10 °C). Raising the temperature therefore speeds microbial death much more than quality loss. This is the principle behind high-temperature short-time and UHT processes, and behind thin-profile pouches and agitating retorts that heat the cold point faster.
Key points
- Heat kills microbes logarithmically: the same fraction dies in each equal time interval.
- D value: time at a given temperature for a 90 per cent (one-log) reduction.
- z value: temperature rise that reduces D tenfold; about 10 °C for bacterial spores.
- F0: process lethality as equivalent minutes at 121.1 °C with z = 10 °C; minimum botulinum cook ≈ 12 × 0.21 ≈ 2.5 min.
- pH 4.6 divides low-acid foods (need sterilisation above 100 °C) from acid foods (milder processes).
- Milk pasteurisation: 63 °C for 30 min or 72 °C for 15 s; checked by the alkaline phosphatase test.
What the exams ask
- School-leaving and entrance papers: definitions of pasteurisation and sterilisation, and the time–temperature combinations for milk.
- Degree and research-fellowship entrances in food and dairy technology: D, z and F definitions, the 12D concept, why pH 4.6 matters, commercial sterility, and calculating D at another temperature.
- Professional and licensing examinations: process lethality from heat penetration data (general method), spoilage probability, and choosing processes that protect quality.
Described in general terms: the kind of examination, not a past paper. Laisha never reproduces exam questions.
Questions people ask
Does a 12D process mean the food is completely sterile?
No. It means the probability of a surviving spore is extremely small. Canned foods are described as commercially sterile: no organisms that can grow under normal storage conditions.
Why is 121.1 °C used as the reference?
It equals 250 °F, the reference adopted in the early days of canning science, and it is the temperature of saturated steam at about one atmosphere above normal pressure, easily reached in retorts.
Why can tomatoes be canned in a water bath but beans cannot?
Tomatoes are usually at or below pH 4.6 (often acidified to be sure), so C. botulinum cannot grow, and boiling-water temperatures suffice. Beans are low-acid, so they need a pressure process above 100 °C.
Sources
- Fellows, P. J. Food Processing Technology: Principles and Practice, 4th edition. Woodhead Publishing, 2017. Chapters on heat processing.
- Holdsworth, S. D. and Simpson, R. Thermal Processing of Packaged Foods, 3rd edition. Springer, 2016.
- Stumbo, C. R. Thermobacteriology in Food Processing, 2nd edition. Academic Press, 1973.
- Codex Alimentarius. Code of Hygienic Practice for Low and Acidified Low Acid Canned Foods (CXC 23-1979). FAO and WHO.
- Codex Alimentarius. Code of Hygienic Practice for Milk and Milk Products (CXC 57-2004). FAO and WHO.
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