A Computer Simulation of Thermal Sterilization of Canned Foods With Sub-Freezing Initial Temperatures

A Computer Simulation of Thermal Sterilization of Canned Foods With Sub-Freezing Initial Temperatures

Can. Inst. Sci. Technol. J. Vo!. 24, No. 1/2, pp. 95-98, 1991 RESEARCH NOTE A Computer Simulation of Thermal Sterilization of Canned Foods With Sub-...

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Can. Inst. Sci. Technol. J. Vo!. 24, No. 1/2, pp. 95-98, 1991


A Computer Simulation of Thermal Sterilization of Canned Foods With Sub-Freezing Initial Temperatures P. Richard I, T. D. Durance2 and G. M. M. Sandberg 3 IDepartment of Bio-Resource Engineering, University of British Columbia, 2357 Main Mall, Vancouver, B,C. 2Department of Food Science, University of British Columbia, 6650 NW Marine Drive, Vancouver, B.C, 3Lipton Puritan Ltd., Vulcan Way, Richmond, B,C.

ingredients previously stored frozen, such as some meat and fish products, current processes require complete thawing before processing. Thawing at room temperature increases the potential for product deterioration. Sterilization from a frozen state was thus seen as an attractive alternative. This raises three basic questions. For the process to be effective and safe, how much must retort time be increased when the product is initially frozen? Also, if this added time is considerable, the material on the sides of the cans will be exposed to high temperatures for a long duration while the center is thawing; does this result in an excessive loss of nutrients or other quality attributes? Finally, what are the effects of the operating variables, such as retort temperature, initial product temperature, and product size? In this study, a computer simulation using finite difference techniques was used to provide an initial answer to these questions.

Abstract Certain types of canned foods are best handled as a frozen slurry and retorting such products from an initially frozen state would be advantageous from the standpoint of materials handling. However, there is currently little information on this process. Accordingly, a computer simulation using finite difference techniques was developed to determine the added process time required to achieve commercial sterilization. Total required processing time could not be approximated as being the sum of the thawing time and the sterilization time as calculated by conventional methods. Total concentration of heat labile nutrient was found to be unaffected by the process and was independent of initial product temperature, despite the longer exposure of the product to high retort temperatures.

Resume Il y a certains aliments en conserve qu'il vaut mieux traiter 11 I' etat de pate congelee, La sterilisation de tels produits initialement sous la forme congelee serait avantageuse du point de vue manutention des matieres premieres, Toutefois, 11 ce jour, il existe peu d'information sur ce procede. En consequence, nous avons developpe une simulation par ordinateur, en se servant de techniques differentes, pour etablir la dun~e supplementaire du procede afin d'atteindre la sterelisation commerciale. La duree etre evaluee en additionnant le temps totale du procede ne peut pas totale du procede ne peut pas etre evaluee en additionnant le temps ~ degel au temps de sterilisation tels que calcules par les methodes ~nventionnelles. La concentration totale des nutriments therptosensibles ne fut pas affectee par le procede et fut independante 1le la temperature initiale du produit, malgre I'exposition plus ,tongue du produit aux temperatures elevees de I'autoclave,

Methods A finite difference model was developed in order to simulate heat penetration and nutrient degradation in the food package. This approach was selected because there exists no analytical solutions of the heat transfer equation in a situation where both latent heat and sensible heat are important. The use of Plank's or similar methods may be adequate to calculate thawing time but the resulting non-uniform temperature profile in the can after thawing precludes the use of a straight forward analytical solution to predict the time-temperature profile after thawing.

lntroduction In current commercial practice, retort sterilization of low acid foods invariably begins with all food anaterial in an unfrozen state. In the case of

Copyright © 1991 Canadian Institute of Food Science and Technology


A fully explicit one-dimensional finite difference formulation with variable parameters was used as shown in equation 1: T+I=T!+~X 2 I





(q, X Cp)j

[k l + 1/2 X (Tt + 1/2 - T j )




1/2 x (Tt _ I - T[ - I)]


where: T is the temperature the superscripts refer to the time step 6t the subscripts to the space step 6x. The subscripts i + 1/2 and i - 1/2 refer to properties evaluated half-way between the nodes. The values of the thermal conductivity (k) were taken as 1.56 w/mC and 0.45 w/mC below and above freezing, respectively, after the data of Heldman and Gorby (1975) for ham. Heat capacity (){ (C p) was taken as the change in enthalpy per unit temperature change in order to account for latent heat. The equations of Levy (1979) for pork were used, as: (2)

C p = 3600 @ T > T f



115.5 x [0.0276 + 0.0183 x

(T f


T)]-2 @ 0 :5 (T f

C p = 25617.1 x (T f




T) :5 6

T)[email protected] (T f

These were obtained using cans filled with 40010 (v/w) bentonite retorted at 125°C from an initial frozen state at -20°C. Bentonite suspensions were prepared and conditioned as described by Neikamp et af. (1984) and sealed into 307 x III metal 2-piece cans. Hypothetical nutrient concentrations (averaged over the container volume) and sterilization effectiveness at the center were computed using well known numerical integration techniques (e.g., Loncin and Merson, 1979). Each simulation was performed until a target lethality Fo of 12 min was achieved. The concentrations of an arbitrarily selected heat labile nutrient were calculated using a decimal reduction temperature (z) of 22 Co and a decimal reduction time (D) of 83.3 min. The j-factor (Jag factor) and the apparent initial temperature Ta were computed from the simulated results using Ball's method (Loncin and Merson, 1979).


T) ~ 6


where: T f is the freezing point, given as - 0.9°C. Volume changes were to be negligible and the density (ct» was given a single value of 1040 kg/m (Heldman and Gorby, 1975).

The conditions simulated were simplified in order to clearly identify the effects due solely to thawing. Accordingly the simulation did not include come-up time or cooling time, and a perfect thermal contact at the surface of the cans was assumed. A simpler one-dimensional situation was chosen in the model as the inclusion of more dimensions would not appreciably add to the analysis of the situation. Several combinations of temperatures and sizes were simulated in order to identify the effects that are important during the transient heating period. These include conditions of high temperature which are not achieved in conventional retorts. The accuracy of the model was tested by comparing simulation results with experimental data.

Results and Discussion

Effects of processing temperature In order to test the validity of the model, actual heat penetration data of cans of bentonite clay with an initial temperature of -20°C were collected. The data from 4 cans were compared with the predictions of the mathematical model and the results are presented in Figure 1. Bentonite was selected as a model food because of its homogeneity and its demonstrated ability to emulate the thermal properties of food. Although there was some variability in the experimental data, the fit to the predictions of the model was considered adequate to indicate the usefulness of the model. Figure 2 shows the evolution of the center temperature over time for a can thickness of 1.9 cm initially frozen at -lOoe as predicted by the mathematical model. The retort temperatures, ranging from 120°C to 160°C, of course had a very clear



::: t


~ 100 ~

!l a; ~





Can 112 Can 113



1: 20 I

Can 114 -6,-



:; '§.,


E Qj



" i " - 40 4-'-..L.L-,+.L..L.L..Lt-'--.L.L.~'-L-LL..j-'-'-'-'-+-'....L..L.L+-'-' 5 o 10 15 20 25 30 35 Time (min)

Fig. I. A comparison of simulated and experimental results.

96 / Richards et al.

75 50







01-::-. .- - - - - - - - - - - - - - - . - - - I

-254-L L.L..L.f-L.l-"--,-+"-' , , I ' , , , I ' , , , I ' " I"" I 0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 Time (m;n)

Fig. 2. Time-temperature distribution in the center of cans initially at -10°C exposed to varying temperatures. J. Inst. Can. Sci. Technol. Aliment. Vol. 24. No. 1/2. 1991

effect on the process duration required to achieve an F oof 12 min. The process was fairly lengthy at l20oe, most of the sterilization being achieved while the can was near thermal equilibrium. By contrast, center temperatures rose rapidly above 121°e in the cans exposed to a hotter environment, resulting in rapid processing under transient heating. There was comparatively little effect of the retort temperature on the time required to complete thawing. Under the conditions simulated, thawing was relatively short (4 min or less) and appeared as a simple lag in the temperature profile curves. In all cases, thawing time was much shorter than processing time after thaw. Thawing time was also approximated using Plank's equation (Loncin and Merson, 1979), and found to be equal to 3.0 min for a retort temperature of l20oe. This was somewhat shorter than the value obtained using the numerical solution since Plank's equation neglected the sensible heating of the thawed portion. However, heating of the center following thawing was appreciably faster than if it were heated directly from an initial uniform temperature of oDe. This was because of the considerable temperature rise of the thawed fraction while the center slowly thawed. In this comparison, if the processing time was calculated by simply adding the computed time of thawing to the conventional processing time obtained when retorting the thawed product, the processing time would have been overestimated by a full two thirds of the thawing time, i.e., two min in this case. The average hypothetical nutrient concentration remaining after processing was also affected little by retort temperature, as seen in Figure 3. Though the nutrients were destroyed at a faster rate under hotter conditions, this was compensated for by the fact that processing time was much shorter under such conditions. Nevertheless, there was a clear optimum temperature (in this case, BO°C) for nutrient

1. 2



"~ u





"c U° 0





130 C

-4- 1.0 C 0.2

-8- 150 C •

0.0 1 1

-l!- 160 C '











I '





























I '


Time (min)

Fig. 3. Nutrient losses from cans initially at _10°C exposed varying temperatures.


retention. These findings are consistent with the existence of a similar optimum for retorting of cans initially at room temperature observed by Teixeira et al. (1969).

Effect of container size Table 1 shows the effects of can size on process duration and nutrient retention. The thickness was changed by a factor of five to see the effect of this variable and was not meant to imply actual container sizes. At 160o e, the duration of the process increased approximately 20 times for the larger container size. The fraction of the processing time during which the center of the can remained frozen also increased with size; these values ranged from 0.11 for the smaller size to 0.32 for the larger size. These findings are a

Table 1. Summary of simulated results. Can Size (mm)

To 1

T '" 2 (0C)

Duration (min)

Nutrient retention (N/No)3

End temperature


19 19 19 19 19 19 19 19 19 95 95 3.8 3.8

- 13 -10 20 40 - 10 - 10 -10 - 10 20 - 10 20 -10 20

160 160 160 160 150 140 130 120 120 160 160 160 160

12.3 12.0 9.7 8.9 13.8 16.5 21.7 38.6 35.4 252.6 192.7 0.6 0.5

0.530 0.530 0.530 0.531 0.573 0.624 0.646 0.574 0.576 0.167 0.167 0.887 0.890

133.3 133.3 133.3 133.3 131.8 129.8 126.5 119.9 119.9 120.8 120.8 145.1 145.1


Ta4 77.7 -66.0 19.1 39.4 -66.8 -67.0 -66.8 -67.8 19.6 -65.5 19.2 -64.4 19.2

1.25 1.33 1.01 1.01 1.28 1.38 1.41 1.44 1.01 1.33 1.01 1.32 1.01

(Initial product temperature). 2Constant temperature environment at the surface of the can (i.e., retort temperature). 3Ratio of concentration of nutrient after certain time temperature combination to initial concentration. ;4Apparent initial temperature. . sL ag factor.


Can. Inst. Food Sci. Technol. J. Vol. 24. No. 112, 1991

Richards et al. / 97

straight forward consequence of the effect of size on heat penetration. Similarly, hypothetical nutrient losses dramatically increased with container size.

Effect of initial temperature As shown in Table I, the time required to sterilize a 19mm thick can, initiallY at room temperature, represented approximately 80010 of the duration required for a can initially frozen. This relatively small difference was due to the fact that the actual sterilization required much more time than the thawing, as seen in Figure 2, for a hot retort temperature. This was even more pronounced for a cooler environment (l20°C), where the difference in time required was less than 10% (35 min versus 30 min). However, the larger the can size, the bigger the difference in processing time became, due to the delay in thawing the center. Latent heat of melting was the dominant factor in this delay since the difference in duration between frozen cans at -30 o e or _lODe was much larger than the difference between thawed cans at 20 0 e or 40 0 e as seen in Table 1. The delay in processing due to the frozen state could be expressed as a larger value of the lag factor (j). As shown in Table 1, the apparent initial temperature (T J from which j was computed, was relatively insensitive to variables other than actual initial temperature. The initial temperature and state of the product had a negligible effect on hypothetical nutrient losses. As can be seen in Table 1, the nutrient concentration after sterilization remained the same regardless of the initial temperature. This arose because the nutrients remaining were concentrated towards the center, which was subjected to a relatively similar duration of exposure to high temperatures, regardless of its initial state. By contrast, the edges of the can were exposed to high temperatures for a longer duration if the can was initially frozen. However, since the overall exposure of the edges was much longer than that of the center, the contribution of the nutrients remaining along the edges to the overall average was insignificant. Only in the case of a very thin package rapidly flashed to hot temperatures was there a difference, albeit very small.

98 / Richards et al.

Thus it appears that the initial state and temperature of the food affected only the process duration, not the end results, i.e., the nutrient loss and final temperature profile. This last observation has interesting consequences for the operation of the system. Any difference in the lag factor arising from different initial temperatures, come-up time, or retort type would be likely to affect only the process duration but not the nutrient retention. Likewise, any further nutrient loss arising from the cooling period would be the same regardless of the initial temperature. This would indicate that the simplifying assumption of constant retort temperature did not severely limit the validity of the results. Much work remains to be done to test the validity of the assumptions used here and to compare the results of the model to heat penetration results of actual foods. Nevertheless, findings based on the present model and model food indicated that only the lag factor and duration of the process were affected when the cans were sterilized with subfreezing initial temperatures, but not the effectiveness of the process nor product quality. Furthermore, the relatively small increase in the process duration required, and its potential for easy monitoring, attest to the feasibility of sterilizing canned foods with subfreezing initial temperatures.

References Heldman, D.R. and Gorby, D.P. 1975. Prediction of thermal conductivity in frozen foods. Trans. Am. Soc. Agric. Eng.18:156. Levy, F.L. 1979. Enthalpy and specific heat of meat and fish in the freezing range. 1. Food Technol. 14:549. Loncin, M. and Merson, R.L. 1979. Food Enginering:Principles and Selected Applications. Academic Press, Inc., New York, NY. Neikamp, A., Unklesbay, K., Unklesbay, N. and Ellersieck, M. 1984. Thermal properties of bentonite-water dispersions used for modelling foods. J. Food Sci. 49:28. Teixeira, A.A., Dixon, J.R.D., Zahradnik, J.W. and Zinsmeister, G.E. 1969. Computer optimization of nutrient retention in the thermal processing of conduction-heated foods. Food Technol. 23:137. Submitted July 28, 1989 Revised August 14, 1990 Accepted August 14, 1990

J. Inst. Can. Sci. Technol. Aliment. Vo!. 24, No. 112. 1991