Total heat generation rate in a bacterial fermentation system is the sum of all of non-negligible sources of heat generation
and heat loss that typically consist of cellular metabolism, agitator motion, evaporation, feed addition, and gas addition.
The following formula can be used to calculate the net rate of heat generation (Hnet) in a fermentation system:
in which Hmetab is the heat generation because of cellular metabolism, Hagit is the heat generation because of mechanical motion of the agitator(s), Hevap is the heat loss due to evaporation, Hfeed is the heat loss because of addition of feed held at room temperature, and Hgas is the heat loss because of addition of supply air/O2 at room temperature.
The component Hmetab can be directly correlated to OUR and has been shown to account for approximately 80% of the net heat generation (i.e., heat
generation from agitator motion accounts for ~20% of heat generation). However, when all major sources of process-related
heat loss are taken into account, Hnet ≈ Hmetab. Because culture temperature is typically controlled at a constant setpoint during a fermentation process, Hnet = Hcooling. Hence, metabolic heat generation rate can be measured fairly accurately by calculating the amount of heat removed from the
cooling jacket (Hmetab ≈ Hcooling).
Rate of Heat Removal
The rate of heat removal through the cooling jacket and cooling coils can be determined from the outputs of the temperature
control system on the fermenter. In a commonly used control configuration, the temperature of water recirculated through the
jacket or coils is regulated by an incremental addition of chilled water. The water in the jacket is warmed up through contact
with the fermenter wall, and after it exits the jacket, a regulated amount of chilled water is added to cool down the water.
It then enters the jacket again through a loop, acting as a heat exchange fluid to remove as much heat as needed from the
fermenter to control the temperature at the setpoint. Using this setup, the heat removal rate can be calculated using the
in which Qwater is the volumetric flow rate of the water in the jacket (L/min), ρwater is the density of water (kg/L), Cp, water is the mass heat capacity of water (kJ/kg–K), Tout is the temperature of the water in the jacket downstream of the fermenter (°C), Tin is the temperature of the water in the jacket upstream of the fermenter (°C), and mculture is the mass of the culture in the fermenter (kg). By measuring the volumetric flow rate of the water in the jacket and the
temperature of the water at both the inlet and the outlet of the jacket, one can determine the heat removal rate from the
cooling jacket at any given moment over the course of a fermentation process.