GLOBAL Formaciones

The example process calculations carried out in the preceding subsection show that for a given Z value, the specification of any one point on the straight line drawn parallel to the TDT curve but intersecting the process time at process temperature is sufficient to specify the sterilizing value of any process combina- tion of time and temperature on that line. The reference point that has been adopted for this purpose is the time in minutes at the reference temperature of

FIGURE 3.2 Thermal death time (TDT) curve showing temperature dependency of D

value given by temperature change (Z) required for 10-fold change in D value.

110 121 132 Temperature (°C) z D v alue 100 10 1.0 0.1 0.01

Simulating Thermal Food Processes Using Deterministic Models 77

TABLE 3.1

D Values for Different Classifications of Food-Borne Bacteria

Bacterial Groups D Value

Low-acid and semiacid foods (pH above 4.5) D250

Thermophiles

Flat-sour group (B. stearothermophilus) 4.0–5.0

Gaseous-spoilage group (C. thermosaccharolyticum) 3.0–4.0

Sulfide stinkers (C. nigrigicans) 2.0–3.0

Mesophiles

Putrefactive anaerobes

C. botulinum (types A and B) 0.10–1.20

C. sporogenes group (including PA 3679) 0.10–1.5

Acid foods (pH 4.0–4.5) Thermophiles

B. coagulans (facultatively mesophilic) 0.01–0.07

Mesophiles D212

B. polymyxa and B. macerans 0.10–0.50

Butyric anaerobes (C. pasteurianum) 0.10–0.50

High-acid foods (mesophilic non-spore-bearing bacteria) D150

Lactobacillus spp., Leuconostoc spp., yeast and molds. 0.50–1.00

Source: Stumbo, C.R., Thermobacteriology in Food Processing, Academic

Press, New York, 1965. With permission.

TABLE 3.2

Comparison of D_121(250F) Values for Specific Microorganisms in Selected Food Substrates

Organism Substrate TDT Method D250 (min)

PA 3679 Cream-style corn Can 2.47

PA 3679 Whole-kernel corn Can 1.52

PA 3679 Whole-kernel corn (replicate) Can 1.82

PA 3679 Phosphate buffer Tube 1.31

FS 5010 Cream-style corn Can 1.14

FS 5010 Whole-kernel corn Can 1.35

FS 1518 Phosphate buffer Tube 3.01

FS 617 Whole milk Can 0.84

FS 617 Evaporated milk Tube 1.05

Note: PA = putrefactive anaerobe; FS = facultative spore.

Source: Stumbo, C.R., Thermobacteriology in Food Processing, Academic Press,

78 Thermal Food Processing: New Technologies and Quality Issues

121°C, or the point in time where the equivalent process curve crosses the vertical axis drawn at 121°C, and is known as the F value for the process. This is often referred to as the lethality of a process, and since it is expressed in minutes at 121°C, the unit of lethality is 1 min at 121°C. Thus, if a process is assigned an

F value of 6, then the integrated lethality achieved by whatever time–temperature history is employed by the process must be equivalent to the lethality achieved from 6 min of exposure to 121°C, assuming an idealized process of instantaneous heating to 121°C followed by instantaneous cooling after the 6-min hold.

All that is required to specify the F value is to determine how many minutes at 121°C will be necessary to achieve the specified level of log cycle reduction. The D121 value is used for this purpose, since it represents the number of minutes at 121°C to accomplish one log cycle reduction. Thus, the F value is equal to

D121 multiplied by the sterilizing value (number of log cycles required in population reduction):

(3.1)

where a is the initial number of viable spores, and b is the final number of viable spores (or survivors).

In the example given earlier, assume the value D121= 1.5 min was taken from the TDT curve in Figure 3.2 and multiplied by the required sterilizing value (six log cycles). Thus, F =1.5 (6) = 9 min, and the lethality for this process has been specified as F= 9 min. This is normally the way in which a thermal process is specified for subsequent calculation of a process time at some other temperature. In this way, proprietary information regarding specific microorganisms of concern or numbers of log cycles reduction can be kept confidential and replaced by the

F value (lethality) as a process specification.

Note also that this F value serves as the reference point to specify the equivalent process design curve discussed earlier. By plotting a point at 9 min on the vertical line passing through 121°C on a TDT graph, and drawing a line parallel to the TDT curve through this point, the line will pass through all combinations of process time and temperature that deliver the same level of lethality. The equation for this straight line can be used to calculate the process time (t) at some other constant temperature (T) when F is specified.

(3.2)

The following equation becomes important in the general case when the product temperature varies with time during a process, and the F value delivered by the process must be integrated mathematically,

(3.3) F=D121(loga−log )b F=10[ (T−121) / ]Z t F T Z t t = −

∫

Simulating Thermal Food Processes Using Deterministic Models 79 At this point Equations 3.1 and 3.3 have been presented as two clearly different mathematical expressions for the process lethality, F. It is most important that the distinction between these two expressions be clearly understood. Equation 3.1 is used to determine the F value that should be specified for a process, and is deter- mined from the log cycle reduction in spore population required of the process (sterilizing value) by considering factors related to safety and wholesomeness of the processed food, as discussed in the following section. Equation 3.3 is used to determine the F delivered by a process as a result of the time–temperature history experienced by the product during the process. Another observation is that Equation 3.1 makes use of the D121 value in converting log cycles of reduction into minutes at 121°C, while Equation 3.3 makes use of the Z value in converting tempera- ture–time history into minutes at 121°C. Because a Z value of 10˚C (18˚F) is so commonly observed or assumed for most thermal processing calculations, F values calculated with a Z of 10˚C and reference temperature of 121°C are designated Fo.