Parametric Estimation - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 321

level of 1.10% is the limit of acceptability. One limit on the shelf life of yogurt is
“postacidification” or continued production of acid by the yogurt cultures during

TABLE P7.7 Cell Concentration, 10 10 cells/L, as Functions of Time and Sucrose Concentration

Sucrose

Time, h 10 g/L 50 g/L 100 g/L 150 g/L

0.00 3.00 2.00 2.00 1.33

1.00 4.16 3.78 6.71 5.27

2.00 5.34 5.79 1.11 0.30

3.00 7.35 5.72 3.78

4.00 6.01 9.36 3.71 7.65

5.00 8.61 6.68 8.32 10.3

6.00 10.1 17.6 21.1 17.0

7.00 18.8 35.5 37.6 38.4

8.00 28.9 66.1 74.2 70.8

9.00 36.2 143 180 194

10.0 42.4 160 269 283

11.0 44.4 170 237 279

12.0 46.9 165 256 306

13.0 46.9 163 249 289

storage. Table P7.8 shows acid production (% lactic acid) in yogurt versus time at four
different temperatures.

For the purpose of this problem, assume that the saturation constant is large (very rarely
in reality) and thus the acid production follows first-order kinetics with respect to the
consumption of lactose in the yogurt to produce lactic acid. At the start of acidproduction,
the lactose concentration is about 1.5%, the bacteria concentration is 10 11 cells/L, and the
acid concentration at which all metabolic activity ceases is 1.4% lactic acid.

35 F 40 F 45 F 50 F

Time, days

1 1.02 1.02 1.02 1.02

14 1.03 1.05 1.14 1.19

28 1.05 1.06 1.15 1.24

35 1.09 1.10 1.22 1.26

42 1.09 1.12 1.22 1.31

49 1.10 1.12 1.22 1.32

56 1.09 1.13 1.24 1.32

63 1.10 1.14 1.25 1.32

70 1.10 1.16 1.26 1.34