Measurements of k L a. Steady-State Mass Balance Method:

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1 Measurements of k a Steady-State Mass Balance Method: In theory, the K a in an apparatus that is operating continuously under steady-state conditions could be evaluated from the flow rates and the concentrations of the gas and liquid streams entering and leaving, and the known rate of mass transfer (e.g., the oxygen consumption rate of microbes in the case of a fermenter). However, such a method is not practical, except when the apparatus is fairly large and highly accurate instruments such as flow meters and oxygen sensors (or gas analyzers) are available. Unsteady-State Mass Balance Method One widely used technique for determining K a in bubbling gas liquid contactors is the physical absorption of oxygen or O 2 into water or aqueous solutions, or the desorption of such a gas from a solution into a sparging inert gas such as air or nitrogen. The time-dependent concentration of dissolved gas is followed by using a sensor (e.g., for O 2 or O 2 ) with a sufficiently fast response to changes in concentration. Sulfite Oxidation Method The sulfite oxidation method is a classical, but still useful, technique for measuring k G a (or k a). The method is based on the air oxidation of an aqueous solution of sodium sulfite (Na 2 SO 3 ) to sodium sulfate (Na 2 SO 4 ) with a cupric ion (u 2+ ) or cobaltous ion (o 2+ ) catalyst. With appropriate concentrations of sodium sulfite (about 1N) or cupric ions (>10 3 mol l 1 ),

2 the value of K for the rate of oxygen absorption into sulfite solution, which can be determined by chemical analysis, is practically equal to k for the physical oxygen absorption into sulfate solution; in other words, the enhancement factor E, is essentially equal to unity. It should be noted that this method yields higher values of k a compared to those in pure water under the same operating conditions because, due to the effects of electrolytes mentioned before, the average bubble size in sodium sulfite solutions is smaller and hence the interfacial area is larger than in pure water. Dynamic Method This is a practical unsteady-state technique to measure k a in fermenters in operation. When a fermenter is operating under steady conditions, the air supply is suddenly turned off, which causes the oxygen concentration in the liquid, (kmolm 3 ), to fall quickly. As there is no oxygen supply by aeration, the oxygen concentration falls linearly due to oxygen consumption by microbes. From the slope of the curve during this period, it is possible to determine the rate of oxygen consumption by microbes, q o (kmol kg 1 h 1 ), by the following relationship. d dt q0x (3.18)

3 Where; x (kgm 3 ) is the concentration of microbes in the liquid medium. Upon restarting the aeration, the dissolved oxygen concentration will increase. The oxygen balance during this period is expressed by d dt K a( ) q.. (3.19) 0 x Where; (kmolm 3 ) is the liquid oxygen concentration in equilibrium with that in air. A rearrangement of Equation 3.19 gives 1 d ( )( q0x ). (3.20) K a dt Thus, plotting the experimental values of after the restarting aeration against (d /dt +q o x ) would give a straight line with a slope of (1/K a). Figure (3.4) Dynamic measurement of k a for oxygen transfer in fermenters. Example 3.3

4 In an aerated stirred tank, air is bubbled into degassed water. The oxygen concentration in water was continuously measured using an oxygen electrode such that the data shown in Table 3.1 were obtained. Evaluate the overall volumetric mass transfer coefficient of oxygen K a (in unit of h 1 ). The equilibrium concentration of oxygen in equilibrium with air under atmospheric pressure is 8.0 mg l 1 ; the delay in response of the oxygen electrode may be neglected. Solution From the oxygen balance, the following equation is obtained: d dt K a( ) Upon integration with the initial condition = 0 at t = 0; ln K at Table (3.1) Oxygen concentration in water.

5 Plots of against time on semi-logarithmic coordinate produces a straight line, from the slope of which can be calculated the value 1 of a 79h K.

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