## Spiral Cooler

Sterilized product to fermenter

### Raw product

Fig. 5.11. Flow diagram of a typical continuous sterilization system employing spiral heat exchangers (Alfa-Laval Engineering Ltd., Brentford, Middlesex).

process is that temperature may be used as a variable in scaling up a continuous process so that the increased V factor may be achieved whilst maintaining the nutrient quality constant. Deindoerfer and Humphrey (1961) attempted to rationalize the choice of time-temperature regime by the use of a Nutrient Quality Criterion (Q), based on similar logic to the Del factor:

where x0 is the concentration of essential heat labile nutrient in the original medium, x, is the concentration of essential heat labile nutrient in the medium after a sterilization time, t.

As considered earlier, the destruction of a nutrient may be considered a first-order reaction:

xt/xo = e k' where k is the reaction rate constant or x0/xt = ekt.

Thus, taking natural logarithms,

The relationship between k and absolute temperature is described by the Arrhenius equation:

therefore, substituting for k:

Therefore, as for the Del factor equation, by taking natural logarithms, and rearranging, the following equation is obtained

Thus, a plot of the natural logarithms of the time required to achieve a certain Q value against the reciprocal of the absolute temperature will yield a straight line, the slope of which is dependent on the activation energy; that is, a very similar plot to Fig. 5.5 for the Del factor relationship. If both plots were superimposed on the same figure, then a continuous sterilization performance chart is obtained. The example put forward by Deindoerfer and Humphrey (1961) is shown in Fig. 5.12. Thus, in Fig. 5.12 each line of a constant Del factor specifies temperature-time regimes giving the same fractional reduction in spore number and each line of a constant nutrient quality criterion specifies temperature-time regimes giving the same destruction of nutrient. By considering the effect of nutrient destruction on product yield, limits may be imposed on Fig. 5.12 indicating the nutrient quality criterion below which no further increase in yield is achieved (i.e. the nutrient is in excess) and the nutrient quality criterion at which the product yield is at its lowest (i.e. there is no nutrient remaining). Thus, from such a plot a temperature-time regime may be chosen which gives the required Del factor and does not adversely affect the yield of the process.

The adoption of Deindoerfer and Humphrey's approach is possible only if the limiting heat-labile nutrient is identified and the Arrhenius constant and activation energy for its thermal destruction experimentally  