Food Biochemistry and Food Processing (2 edition)

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38 Thermal Processing Principles 733

Table 38.4.Process Calculation by General Graphical and Numerical Integration Method

Time

(min)

Temperature

(◦F) F=TDT=Fo∗ 10 (Tr−T/z) 1 /TDT 1 /TDT∗
t

0 62 7.01E+ 10 1.4E− 11 0

4 71 2.22E+ 10 4.5E− 11 1.8E− 10

8 99 6.17E+ 08 1.6E− 09 6.5E− 09

12 134 7.01E+ 06 1.4E− 07 5.7E− 07

16 171 6.17E+ 04 1.6E− 05 6.5E− 05

20 202 1.17E+ 03 8.5E− 04 3.4E− 03

24 231 2.86E+ 01 3.5E− 02 1.4E− 01

28 241 7.97E+ 00 1.3E− 01 5.0E− 01

32 247 3.70E+ 00 2.7E− 01 1.1E+ 00

36 248 3.25E+ 00 3.1E− 01 1.2E+ 00

40 250 2.52 4.0E− 01 1.6E+ 00

44 250 2.52 4.0E− 01 1.6E+ 00

48 231 2.86E+ 01 3.5E− 02 1.4E− 01

52 181 1.72E+ 04 5.8E− 05 2.3E− 04

56 137 4.78E+ 06 2.1E− 07 8.4E− 07

60 97 7.97E+ 08 1.3E− 09 5.0E− 09

SV=(1/TDT)
t= 6.27

a trial-and-error basis until the desired lethality achieved. In

other words, this whole process is repeated until the desired SV

is obtained, and the corresponding processing time is known.

From food safety point of view and commercial processing con-

ditions, the SV should be more than unity to ensure complete

destruction of pathogens and reduction of spoilage microorgan-

isms to the level that do not cause spoilage in postprocessing

duration.

However, this graphical method is a tedious and cumbersome

approach and requires a graphical trial-and-error works. Be-

cause of this reason, several approaches have been attempted to

develop a simple approach in order to get similar information

from gathered time–temperature data. One of the methods is the

numerical integration method (Tabular Method) proposed by

Patashnik (1953) (Table 38.4 column 5). In this method, the cor-

responding SV of each temperature is numerically calculated

for each time interval, and the total SV is obtained for equal

(Equation 28) and unequal (Equation 29) interval of time.

Sterilization value=

∑(

1 /

TDT

)


t (28)

Sterilization value=

∑(

1 /

TDT
t

)

(29)

In Table 38.4, we obtained a SV of 6.14, which can be in-

terpreted that the given heat treatment is 6.14 times more than

what is required to destroy a given target microorganism. This

is definitely an overprocessing and will have an impact on the

quality of the product. Therefore, SV of 6.14 should be reduced

to the value close to unity in order to achieve the desired degree

of lethality of target microorganism.

Improved General Method

Like the original graphical approach, this method also requires

heat penetration data and the conversion of product temperature

to lethal rate. For the development of Improved General method,

the two main contributions of Ball (1928) played a significant

role. The first important point was the construction of a hypothet-

ical reference TDT curve passing through 1 minute at reference

temperature of 121.1◦C (250◦F) having a givenzvalue. In ad-

dition to this, Ball (1928) introduced the term lethal rate (L)for

a given temperature according to the following Equation 30 on

the basis of Equation 27.

FTz

F 0

= 10

(T

refz−T

)

(30)

For commercial sterilization process, the numerator on left

side of Equation 30 indicates TDT at temperatureT,whichis

equivalent to thermal treatment of 1 minute at reference temper-

ature of 121.1◦C (250◦F) (FTzref==^10121. 1 ◦C). Therefore, based upon

this concept, Equation 30 can be written as

FTz

1

= 10

(Tref−T

z

)

,

whereFTz=TDTTand after rearranging, we get

1

TDTT

=L= 10

(TT−ref

z

)

(31)

The left-hand side term refers lethal rate (L) andLis calcu-

lated as a function of temperature versus time from heat pene-

tration data at a specific temperature. The lethal effects at the

different time–temperature combinations in a thermal process

are integrated so as to account for the total accumulated lethal-

ity, since each temperature is considered to have a sterilizing