METABOLIC VALUE OF THE HEAT BALANCE DATA
Now that the basic heat balance around a fermenter has been described, the value of those data can now be better understood.
The goal is to use the heat data to calculate the oxygen uptake rate. This can be done by solving the heat balance for all
parts except the metabolic heat input. The equation
Equation 8 can be further simplified using information that can be gained from the starting conditions of the fermentation.
If agitation, aeration, and environmental conditions do not change, the effect of these components on the heat balance can
be summed together into a variable R_{S} (= R_{Hev} – R_{HS} – R_{HA}). This is equivalent to the amount of heating that is needed to keep the fermenter at the temperature setpoint as seen in
Figure 1. The totalized value acts as a cooling function, which results in a positive component as seen in Equation 9.
If variable agitation and aeration were used, the effective cooling at multiple conditions would be needed. It would be best
to develop a plot of the R_{S} values so they can be fit to an equation that can accommodate the differing values of R_{S} at the varied agitation and aeration conditions. The simplified metabolic heat equation (Equation 9) can then be solved using
Equation 3, therefore, the only remaining value is the OUR.
in which:
OUR = oxygen uptake rate (mmol/kg/hr)
R_{S} = summed initial heat loss (W)
R_{HC} = heat removal through cooling system (W)
G = weight of fermentation broth (kg)
Figure 2. The balanced heat removal data for the fermentation

A practical example of Equation 10 can be developed from the data given in Figure 1. The first aspect to note is that the
fermentation in the example uses fixed agitation and aeration. This implies that the heat loss seen at the beginning of the
run will remain essentially constant throughout the remaining fermentation. If agitation or aeration were changed, a new value
for the heat loss would have to be determined, as indicated earlier. Because the described system for this example does not
vary agitation or aeration, but uses oxygen supplementation to maintain dissolved oxygen, the heat removal data can be shifted
by the initial heat input data, which are shown in Figure 2. This new data can then be used in Equation 10 to calculate the
OUR from the heat removal data. This is shown in Figure 3, where the triangle symbol represents the calculated OUR value based
on heat transfer data. The solid line represents the actual OUR measurement data by a mass spectrometer with steadystate
method.
