HEAT INPUTS

The heat input from the feeds can alternately be a heat loss depending on the conditions of the feed itself. If the feed is hotter than the fermentation broth temperature, then it will act as a heat input. If the feed is cooler than the fermentation broth, then it will act as a heat loss. The use of certain chemical additions, such as sulfuric acid for pH control, can also add reaction heat, but these generally represent a small portion of heat from feed inputs, and are routinely ignored. The operating conditions of the particular process in use will dictate the actual role that the feeds play with regard to the heat balance. The heat from the temperature difference between the feed and fermentation broth is calculated though the use of Equation 1:

R_Hs heat from substrate (W)

Q_s = flow of substrate (m³/s)

ρ_s = density of substrate (kg/m³)

C_ρs = heat capacity of substrate (J/kg/°K)

ΔT = temperature difference between broth and feed (°K)

The heat input from air is very similar to that of the feed additions. Again, as in the case of the feeds, this may not be the case for smaller scale fermentations, and needs to be dealt with as such. The heat input from airflow can be calculated from Equation 2:

in which:

R_HA = heat from air (W)

Q_A = flow of air (m³/s)

ρ_A = density of air (kg/m³)

C_ρA = heat capacity of air (J/kg/°K)

ΔT = temperature difference between broth and air (°K)

The heat from the recirculation pumps that are used to force coolant through the jacket or coils is usually ignored, because it does not contribute much to the overall heat balance. This is another aspect of the system that should be investigated, depending on the particular fermenter layout.

The heat from the metabolic activity of the cells is the largest heat input component, especially when dealing with fast growing bacteria such as E. coli. As the cells respire, they release heat, in the same manner as a person working up a sweat while running on a treadmill. If the oxygen uptake rate is known, the amount of heat from the respiration of the cells can be determined using Equation 3:

in which:

R_HM = heat from metabolism (W)

OUR = oxygen uptake rate (mmol/kg/hr)

G = weight of fermentation broth (kg)

The factor, 430, represents the amount of heat that is released per mmol of oxygen that the cells consume.^1,2 This empirical factor may vary slightly from cell line to cell line, but as seen in previous work, there does not appear to be much variation, and this number can be adjusted as needed to meet the cellular requirements of the fermentation based on experimental data.¹

The heat from the agitator can be calculated from theoretical models, which use the power number, the speed, and physical characteristics of the stirrer blade.² The primary challenge with using the theoretical models is that there are many assumptions that have to be made about the agitation of the fermenter, especially when dealing with multiple impellers and a gassed system. It is simpler to determine the power draw of the agitator from direct electrical measurement. When measuring the power draw directly, the value will need to be multiplied by the efficiency of the motor to determine how much power is transferred to the fermentation broth. All of the power that is transferred to the fermentation broth is dissipated as heat. If the power draw for an agitator is 100 KW and the motor's efficiency is 0.9, then 90 KW of heat will be added to the heat balance of the fermenter.