## Gey

initial fresh matter Xo+So+WO

dry matter at time X+S of sampling biomass _ X

initial dry matter X0+S0

Fig. 14.4. Various manners in which the biomass content can be expressed. (a) The various measurements that can be made. (b) The biomass content will be calculated as a different number depending on what is included in the denominator

• grams of biomass or component per gram initial fresh sample. In this case the sample is removed and the amount of biomass or component is determined. To calculate the biomass content, the amount of biomass is divided not by the mass of fresh solids in the sample, but by the mass of fresh solids present at the time of inoculation (i.e., X/Mo);

• grams of biomass or component per gram initial dry substrate. In this case the sample is removed and the amount of biomass or component is determined. To calculate the biomass content, the amount of biomass is divided not by the mass of dry solids in the sample, but by the mass of dry solids present at the time of inoculation (i.e., X/Do).

Of course, if sufficient data is available about how the water content and total dry solids vary during the fermentation, it is possible to calculate the biomass concentration in any of the above units. It is easy to obtain sufficient data to do this in laboratory experiments, but not so easy within a bioreactor.

So which is the most appropriate set of units to use in analyzing kinetics? This question will be addressed in Sect. 14.3.5 after considering the consequences of using each set of units.

### 14.3.1 Grams of Biomass per Gram of Fresh Sample

Expressing the biomass concentration per gram of fresh sample (CXM) means that the denominator depends on changes in three factors, the mass of biomass (X), the mass of residual dry substrate (S), and the mass of water (W):

The sum of X and S is the total mass of dry solids (D). The sum of the dry solids and the water gives the total mass of the moist solids (M).

A biomass content expressed in these terms will not only be influenced by the consumption of dry matter, but will also be influenced by changes in the water content of the substrate, these changes arising from metabolic water production and evaporation. At the extreme, even if the organism is neither growing nor consuming substrate, CXM can increase due to evaporation of water from the substrate.

### 14.3.2 Grams of Biomass per Gram of Dry Sample

Expressing the biomass in terms of the amount of dry sample removes the effect of changes in the water content on the apparent biomass concentration. However, due to the conversion of solid organic matter into CO2 during the fermentation, the amount of solid material in the bioreactor can change significantly during the fermentation. In this case, the change in the biomass content expressed on the basis of "g of biomass per g of dry sample" arises from two sources: increase in the mass of biomass and decrease in the mass of solids. It is possible to have a situa tion where the microorganism is not growing, but is metabolizing to maintain itself. In such a situation the biomass concentration expressed per mass of dry sample will increase due to the loss of dry matter as CO2, despite the fact that the biomass is not increasing.

The symbol CXR (g-dry-biomass g-dry-solids-1) can be used to represent a biomass content of this kind. It is given by: