Theoretical Translation of Clean Water to Wastewater Oxygen Transfer Rates

In wastewater treatment design, it is common practice to test aeration equipment in clean water first, and then extrapolate the result to wastewater via a correction factor. In addition to the many variables, such as the organic loading and physicochemical properties of the water, that affect its magnitude, there is evidence that biochemical reactions play an important role in oxygen transfer in wastewater. The proposed model for in-process oxygen transfer is based on the novel concept of a resistance to gas transfer due to the microbial activity in the field. The hypothesis proposed in this study is that the alpha factor alpha, or the relative mass transfer coefficient, which is the ratio of the mass transfer coefficient in wastewater KLaf to the mass transfer coefficient in water KLa, is independent of microbial activities in an aeration basin, and the corresponding performance ratio in terms of efficiencies is the same function as alpha=OTEf/OTE, where subscript f denotes field water characteristics. The common approach is to report the OTEf from off-gas measurements in the field and translate this value to KLaf, giving alpha as the ratio OTEpw/OTE that gives only a false or apparent alpha, where the subscript pw denotes process water undergoing biological stabilization due to microbial metabolism. The field-determined OTE pw is affected by the respiration rate R, which is dictated by the microbial activity, which is mathematically associative to the transfer process by addition and not associative by multiplication with a scalar quantity. A gas-phase mass balance for oxygen around a completely mixed aeration tank confirmed the association nature of the alpha factor. Examination of test data extracted from the literature indicates that the field-determined OTE pw is indeed affected by the respiration rate R. Using the data collected from previous investigators, the alpha factor has a consistent magnitude of about 0.8 for domestic sewage.