Mixing Horsepower by Aeration

The theoretical agitation effect of aeration alone can be easily calculated. There are two separate forces, the first caused by the free rise of bubbles. The bubbles rise from the sparger at a pressure equal to the hydrostatic pressure of the liquid and as they rise to the surface, the gas bubble pressure remains in constant equilibrium with the hydrostatic pressure above it until it escapes fi om the liquid surface. The temperature of the air in the bubble is equal to the fermentation temperature and remains constant due to heat transfer from the fermentation broth. These conditions describe an isothermal expansion of gas gas pressure and gas volume change at constant temperature. Using the formula from Perry and Chilton,the theoretical horsepower for the isothermal expansion of air can be calculated. 

The effect of aeration scale-up by superficial linear velocity (SLV) is not proportional to P V). However, by using these curves scale-up at constant P/V) can be used to determine the required SLV. 

Experience indicates that the P/V relationship is not affected by non-Newtonian fluids below 6000 cps apparent viscosity. 

If the air temperature at the bottom of the fermenter is less than the liquid temperature, there is a gain in P/V. This is due to the fact that at a lower temperature, the air density is greater, and heat is transferred from the broth to the bubbles (isothermal expansion) resulting in more work (P/V) or kinetic energy imparted to the broth by turbulence. 

If the fermenter vent valve is restricted to increase the pressure above the broth, it has the effect of reducing P/V, but oxygen transfer increases due to the greater partial pressure of oxygen. 

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