4.5 Product Formation Kinetics

Product formation kinetics fall into one of the following three types.

• Growth Associated Product Formation
• Non-Growth Associated Product Formation
• Mixed Mode Product Formation

Figure 4-5a Growth Associated Product Formation

Figure 4-5b Non-Growth Associated Product Formation

Figure 4-5c Mixed Mode Product Formation

Typical time-profiles of these three cases are illustrated above. In Type I shown in Fig 4-5a, product is formed simultaneously with growth of cells. That is product concentration increases with cell concentration. The metabolic quotient for P can be expressed as a function of µ,

It is clear from the above, the proportionality constant, a is the yield coefficient, YP/X. Anaerobic fermentation of sugars by Saccharomyces cerevisae is an example of Type I. Illustrated below are actual data for this bioprocess.

Figure 4-5 Ethanol Fermentation data for yeast illustrates Type I product formation kinetics. Note that formation of alcohol is proportional to cell concentration.

In Type II, product formation is unrelated to growth rate, but is a function of cell concentration. This is expressed as

Antibody formation by hybridoma, and some antibiotic fermentation exhibit this type of behavior.

In the third category, product formation is a combination of growth rate and cell concentration. That is,

Many biochemical processes fall into this category. Note that if b is zero and a is YP/X, this case reduces to Type I. If a = 0, it reduces to non-growth associated case. Therefore let us consider this more general case for further analysis.

In a batch reactor, product accumulation can be obtained by carrying out mass balance on the product.

Rate of Product Formation = Accumulation of Product

For constant V,

If we consider exponential phase only, X = X0 Exp(µmt). That is, substituting in the above gives

Integrating from t = 0, P = P0 we get

The above expression can be used to calculate the amount of product concentration at the end of a growth cycle.

Example 4-1

McCallion reported growth of Thermoanaerobacter ethanolicus under controlled pH of 7.0. Using appropriate graphs calculate YX/G and YLA/G, where G and LA refer to glucose and lactate. Is lactic acid formation growth associated ? Can you estimate an approximate value for qglucose?

 Time [h] Glucose [g/L] Lactate (LA) [g/L] Cell (X) [g/L] 0 19.50 0.45 0.01 13 16.88 3.88 0.41 14 14.85 4.94 0.54 16 13.11 6.98 0.92 18 10.40 8.98 0.99 19 8.91 10.30 1.05 20 7.75 10.83 1.15 22 5.18 12.57 1.30 24 3.64 14.58 1.35 37 0.25 16.03 0.69

Solution

First plot cell concentration versus time. The slope in the exponential growth phase is approximately 0.24 h-1. Notice that the culture growth slows down shortly after 15 h. One could also analyze the information numerically. Such an approach unfortunately will lack a good overview of the phases of growth.

Now plot LA vs X and S vs X.

Plot above shows that the exponential behavior deviates at t = 16 h. A straight line drawn during the exponential phase gives growth rate.

Except for one point, all others lie nearly on a straight line. The data at 0.7 g/L of cell corresponds to the declining phase of growth, which may be ignored for current analysis. The line has a negative slope because glucose decreases as cell concentration increases.

Yields from the above graphs: