Rt

where y is the amount of component j produced (+ sign) or consumed (— sign) per unit of contaminant consumed (see "Nutrient Addition and Start-Up").

The description of the driving force for mass transfer in terms of the log-mean concentration difference in the second term of this equation follows from the assumption of plug flow of the gas. The expression is not strictly correct when the pressure drop through the bioreactor is large, as in a tall bubble column, because the contaminant partial pressure in the influent is then (J + h)n; but this complication is rarely included in practice. The essential points here are that the mass-transfer factor, kJa, is an empirically determined parameter, that it can be based on different forms of the driving force, and that the best choice depends on the reactor type and must be clearly understood by everyone involved in a project.

Equation 3 can be rearranged to give the fractional removal of the contaminant from the gas, only the product (subscript m) being considered in the last term:

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