Cases for Measuring Kla

In real life, we place an electrode that senses dissolved oxygen right in the bioprocess fluid. A typical signal versus time is simulated in the upcoming figure. Note that the saturation concentration of oxygen is roughly 5 mg/L. This is not the D.O. concentration because there is a tug of war between supply and demand. In most industrial processes that use high concentrations of microorganisms that crave oxygen, it is very difficult to supply oxygen fast enough to stay well into the range for aerobic metabolism. Let us first consider an easier case typical of environmental engineering situations where the feed concentrations are relatively low making it fairly easy to supply oxygen rapidly enough to match the requirements of a dilute population of microorganisms. For your first experiments with selecting coefficients, focus on the reaeration rate while keeping the uptake rate at its initial position or lower. The D.O. concentration heads downwards when the valve for supplying oxygen is closed. It comes back up when aeration is resumed.

Dissolved oxygen versus time with air valve closed and opened

We get a good estimate of R × X by measuring the slope of the D.O. graph shortly after aeration is stopped.
Now consider a point about midway in the curve in the region where aeration has resumed. The tangent to the curve that is cast through that point gives the slope. This is equal to dC/dt. The D.O. corresponding to the point is C. We look up the concentration of oxygen in water at the temperature of the process or measure it with some medium that has not been inoculated. Remember that it must be aerated with ordinary air, not pure oxygen. Now we have everything we need for the equation and simply substitute to solve for Kla.
Graph with the tangent sketched in.

Industrial fermentations tend to have high uptake rates because there are rich media and dense populations of organisms. When the D.O. falls below some critical concentration that ranges usually from 0.1 to 0.5 mg/L, the rate of respiration is limited by the oxygen concentration. The equation for the mass balance for oxygen cannot use a constant value for R.

Select a value or reaeration rate that is near the middle of its scrollbar and experiment with increasing the uptake rate. Note that the line for D.O. following closure of the value is no longer straight but curves at low D.O. because the respiration is limited by oxygen. Experiments with permutations of coefficients until you get rather low D.O. concentrations. Try to avoid or ignore permutations of coefficients where the very early D.O. is not a horizontal line. Any deviation is an artifact of the way the program calculates the initial condition.

There is no problem is using the linear portion of the graph following closure of the valve to estimate R X. It is also possible to measure a slope at a point on the curve after turning the valve back on, but there is only a cramped region in which to work. If the D.O. is too close to the concentrations where oxygen is limiting, this method fails. In other words, a more voracious demand for oxygen and a lower initial D.O. would give too little room to work before approaching the critical oxygen concentration, and the method fails at low D.O. where the equations are not valid.

Index page