Fermentation Design 101 Table 5. Air Compressor Horsepower per Fermenter 30 compressor compressor H/D scfm 2 3.522 429 609 2,693 327 2,219 Constant: 30,000 gal tank; 24,000 gal run vol; 0. 4 ft/sec SLV Note: Basis of hp is( 8 hp)/(0. 7) 6.3 Mixing Horsepower by Aeration The theoretical agitation effect of aeration alone can be easily calcu ted. 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 from 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, 4 the theoretical horsepower for the isothermal expansion of air can be calculated 436P In 1.000 scfm where: PI is the hydrostatic pressure(absolute) P2 is the(absolute) pressure above the liquid Figure 8 shows the curves at different superficial linear velocities and the relationship ofhorsepower to height ofliquid in a fermenter. These curve are the mixing energy (power per unit volume) released by rising bubbles to the liquidFermentation Design IO1 Table 5. Air Compressor Horsepower per Fermenter 30 psig 50 psig compressor compressor m sch (hP) (hP) 2 3,522 429 609 3 2,693 327 464 4 2,2 19 270 3 84 Constant: 30,000 gal tank; 24,000 gal run vol; 0.4 Wsec SLV. Note: Basis of hp is (8 hp)/(0.7) 6.3 Mixing Horsepower by Aeration The theoretical agitation effect of aeration alone can be easily calcu￾lated. 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 ofthe 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 from 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 ofgas; gas pressure and gas volume change at constant temperature. Using the formula from Perry and Chilt~n,['~I the theoretical horsepower for the isothermal expansion of air can be calculated. p2 1,000 sch 4 hp = 4.36P2 In - where: P, is the hydrostatic pressure (absolute) P, is the (absolute) pressure above the liquid Figure 8 shows the curves at different superficial linear velocities and the relationship ofhorsepower to height ofliquid in a fermenter. These curves are the mixing energy (power per unit volume) released by rising bubbles to the liquid