Scaling oxygen mass transfer in agitated fermentors

There are many scaling formulas that predict the oxygen mass transfer coefficient as k(L).a = constant.(Hp/V)(alpha)Vs(beta) Exponents alpha and beta frequently are scale dependent themselves. A general formula has been derived from the work of Calderbank,(1) Miller,(2) and Tilton,(3) resulting in k(L).a = C(1) phi + C(2) log (Pm/V) phi where phi equals the gas-holdup fraction and Pm/V equals the effective mechanical power input per unit of volume. This formula is consistent with the formula of Westerterp(4) modified by Miller.(2) Gas holdup can be predicted in several ways. Gas-sparged isothermal expansion power input, used for predicting phi, demonstrates that scaling can be done by using either superficial air velocity or volume per volume per minute for aeration.The importance of mixing in replenishing oxygen at the boundary layers of microorganisms will be assessed and compared with the k(L).a as the oxygen transfer ratelimiting step.