2.2.2. Calibration and kLa Measurement
Liquid Phase Calibration. Prepare an air saturated water by passing air bubbles into a small volume (100 mL) of water. Prepare a nitrogen saturated water in the same way. Connect the fabricated DO sensor to signal amplifying circuit of Fig. 2.3b, and then measure the voltage output for both water solutions. The liquids have to be agitated at high speed to obtain proper calibration. This is so-called a 'two point' calibration.
Gas Phase Calibration. Perform the calibration in gas phase by exposing the sensor to air. Do the same using nitrogen as the gas phase. Compare the two calibrations (between liquid and gas). Should they be the same? If not, why not?
Measurement of Response Time. The other important parameter of the sensor is the response time. It can be measured by making a step change in oxygen partial pressure in the measurement medium and measuring the sensor response. The sensor can be approximated as a first order system:
where c is the oxygen concentration in the measurement sample, cp is the oxygen concentration measured by the sensor, and tp is the sensor time constant. When a step change is made in c (by transferring the sensor from air into a nitrogen saturated, stirred water), the sensor output decreases roughly exponentially (not exactly exponentially because the sensor may not be a true first order system). The time constant tp is the time when the sensor response reaches 63.7% of the ultimate response (Fig. 2.12a). The solution to Eq. (22) with the following boundary condition is an exponential function.
Note that a normalized concentration is used: c of 1 means 100% air saturation and 0 means nitrogen saturation. The solution is:
Eq. (24) indicates that when t = tp, c/cp will be 0.64. The time constant tp can also be determined conveniently by using an integral method - the area above the response curve is equal to tp (see Fig. 2.12b). This method is especially useful when there is a lot of noise in the measured signal. The integration can be carried graphically using either trapezoidal rule of Simpson's rule.
Measurement of kLa . The oxygen absorption capability of a bioreactor is represented by kLa, the liquid phase overall volumetric mass transfer coefficient. DO sensor is used frequently to measure kLa. Typically, the reactor is first sparged with nitrogen and at time zero, the nitrogen is switched to air. The oxygen mass balance in the reactor yields:
Fig. 2.12. (a) Sensor response time measurement; (b) integral method for measuring the sensor time constant.
Fig. 2.13. Measurement of kLa by integral method.
where c is the oxygen concentration in the reactor and c* is the oxygen concentration at the gas-liquid interface. This equation can be rearranged to:
Eqs. (22) and (26) can be solved simultaneously to obtain an expression for kLa. However, tk can be obtained graphically as shown in Fig. 2.13 when tp is known.
Caution in kLa Measurement. Note that the magnitude of tp depends on the liquid velocity in the vicinity of the sensor. Therefore, if a tp measured at one agitation rate is used for measuring kLa for different agitation rates, the results will be in error. A safe way is to used the same agitation rate for both tp and tk measurements. However, if tk is much greater than tp, such a precaution is not necessary.