PROCESS OPTIMIZATION 1 O BJECTIVE F UNCTIONS

The principle objective of thermal process optimization is to maximize product quality and profits while minimizing undesirable changes and cost. At all times, a minimal process must be maintained to exclude the danger from microorgan- isms of public health and spoilage concern. Five elements common to all optimization problems are performance or objective function (quality factors, nutrients, texture, and sensory characteristics), decision variables (retort tem- perature and process time), constraints (practical limits for temperatures and required minimal lethality), mathematical model (analytical, finite differences, and finite element), and optimization technique (search, response surface, and linear or nonlinear programming).

Optimization theory makes use of the different temperature sensitivities of microbial and quality factor destruction rates. Microorganisms have lower deci- mal reduction times (less resistant to heat) and a lower Z value (more sensitive to temperature) than most quality factors. Hence, a higher temperature will result in preferential destruction of microorganisms over the quality factor. Especially applied to liquid product, either in a batch mode (in-container) or in continuous aseptic systems, the higher temperature with shorter time offers a great potential for quality optimization. However, for conduction-heating foods, one of the major limitations is the slower heating. All higher temperatures do not necessarily favor the best quality retention because they also expose the product nearer the surface to more severe temperatures than the product at the center, which might result in diminished overall quality.

3.7.2 THERMAL DEGRADATION OF QUALITY FACTORS

Optimum combinations of retort temperature and process time that maximize quality or nutrient retention can be found if the kinetic parameters describing the thermal degradation kinetics of the quality factors are known. Using the numerical computer simulation (deterministic) models described earlier, process times

needed at different retort temperatures to achieve the same process lethality can be quickly calculated over a range of retort temperatures that fall within the operating performance limitations of the retort. A plot of these equivalent retort temperature–process time combinations produces an isolethality curve, such as the one shown in Figure 3.13 for the case of pea puree in No. 2 cans.9

The total level of nutrient/quality retention can be quickly calculated for each set of equivalent process conditions by replacing the kinetic parameters in the model for microbial inactivation with those for quality degradation. Table 3.4 gives exam- ples of such kinetic parameters for the thermal degradation of selected quality FIGURE 3.13 Isolethality curve showing combinations of retort temperature and process

time that deliver the same level of lethality for pea puree in No. 2 cans. (From Teixeira, A.A. et al., Food Technol., 23, 137–143, 1969.)

TABLE 3.4

Kinetic Parameters for Thermal Degradation of Quality Factors in Selected Thermally Processed Foods

Quality Factor in

Food System D121ºC (min) K121ºC (min–1) Z (ºC) Ea (kcal/mol)

Thiamine in beans 329.77 6.9837 × 10–3 _{27.95 25.416}

Lysine in beans 178.28 9.051 × 10–2 _{25.44 27.32}

Texture in beans 101.68 2.260 × 10–2 _{20.62 35.44}

Source: Thermobacteriology Laboratory, Food Science Department, Food Engi-

neering Faculty, UNICAMP, Campinas, Sao Paulo, Brazil.

0 20 40 60 80 100 120 140 160

Process time (min)

Retor t temper ature ( °C) 149 138 127 116

factors in specific food systems. A plot of nutrient retention vs. equivalent process conditions reveals the range of process conditions that result in maximum nutrient retention, as shown in Figure 3.14 for the case of pea puree in No. 2 cans. Note that the same exercise is also useful when seeking to minimize process time, because these results reveal the price that is paid in lower quality retention caused by the higher surface temperatures needed to allow for shorter process time.

3.7.3 VOLUME AVERAGE DETERMINATION OF QUALITY RETENTION

Quality retention in thermally processed conduction-heated foods is a nonuni- formly distributed parameter. Relatively long exposure to the higher temperatures near the product surface causes much more quality degradation in products near the surface than will occur in products near the cold spot, or center. This is because temperature distribution throughout the food container is nonuniformly distributed as heating and cooling proceed during the process. For this reason, quality retention must be calculated by volume integration of the different levels of retention at different locations. This is done by taking advantage of the finite element feature of the numerical simulation model. As the computer iterations make each sweep across the finite element nodes in carrying out the heat transfer calculations, the small change in nutrient concentration that occurs in that time FIGURE 3.14 Optimization curve showing percent thiamine retention for pea puree in

No. 2 cans after various retort temperature and process time combinations that deliver the same level of lethality. (From Teixeira, A.A. et al., Food Technol., 23, 137–143, 1969.)

40 (145) 60 (129) 80 (122) 100 (118) 120 (116) 50 40 30 20

Process time (min) Retort temperature (°C)

interval can be calculated from the momentary value of rate constant, which prevails at the local temperature at that time. When the process simulation is ended, a different final nutrient/quality concentration will exist within each volume element. Recall that the volume elements are in the shape of concentric rings with known dimensions, from which the volume of each different-size ring can be calculated. Total nutrient retention within each ring is calculated by multiplying the final nutrient concentration within the ring by the volume of that ring. Total nutrient retention in the product is the summation of final retention in all the rings and is known as volume average retention.