Development of a model to determine mass transfer coefficient and oxygen solubility in bioreactors

The objective of this paper is to present an experimentally validated mechanistic model to predict the oxygen transfer rate coefficient (Kla) in aeration tanks for different water temperatures. Using experimental data created by Hunter and Vogelaar, the formula precisely reproduces experimental results for the standardized Kla at 20 °C, comparatively better than the current model used by ASCE 2-06 based on the equation Kla₂₀ = Kla. ([Formula: see text])^(20-T) where T is in °C. Currently, reported values for [Formula: see text] range from 1.008 to 1.047. Because it is a geometric function, large error can result if an incorrect value of [Formula: see text] is used. Establishment of such value for an aeration system can only be made by means of series of full scale testing over a range of temperatures required. The new model predicts oxygen transfer coefficients to within 1% error compared to observed measurements. This is a breakthrough since the correct prediction of the volumetric mass transfer coefficient (Kla) is a crucial step in the design, operation and scale up of bioreactors including wastewater treatment plant aeration tanks, and the equation developed allows doing so without resorting to multiple full scale testing for each individual tank under the same testing condition for different temperatures. The effect of temperature on the transfer rate coefficient Kla is explored in this paper, and it is recommended to replace the current model by this new model given by: [Formula: see text] where T is in degree Kelvin, and the subscripts refer to degree Celsius; E, ρ, σ are properties of water. Furthermore, using data from published data on oxygen solubility in water, it was found that solubility bears a linear and inverse relationship with the mass transfer coefficient.