Predicting oxygen transfer of fine bubble diffused aeration systems—model issued from dimensional analysis

Abstract

The standard oxygenation performances of fine bubble diffused aeration systems in clean water, measured in 12 cylindrical tanks (water depth from 2.4 to 6.1 m), were analysed using dimensional analysis. A relationship was established to estimate the scale-up factor for oxygen transfer, the transfer number ( N T ) N T = k L a 20 U G ( ν 2 g ) 1 / 3 = 7.77 × 1 0 - 5 ( S p S ) 0.24 ( S p S a ) - 0.15 ( D h ) 0.13 . The transfer number, which is written as a function of the oxygen transfer coefficient ( k L a 20 ) , the gas superficial velocity ( U G ) , the kinematic viscosity of water ( ν ) and the acceleration due to gravity ( g ) , has the same physical meaning as the specific oxygen transfer efficiency. N T only depends on the geometry of the tank/aeration system [the total surface of the perforated membrane ( S p ) , the surface of the tank ( S ) or its diameter ( D ) , the total surface of the zones covered by the diffusers (“aerated area”, S a ) and the submergence of the diffusers ( h ) ]. This analysis allowed to better describe the mass transfer in cylindrical tanks. Within the range of the parameters considered, the oxygen transfer coefficient ( k L a 20 ) is an increasing linear function of the air flow rate. For a given air flow rate and a given tank surface area, k L a 20 decreases with the water depth (submergence of the diffusers). For a given water depth, k L a 20 increases with the number of diffusers, and, for an equal number of diffusers, with the total area of the zones covered by the diffusers. The latter result evidences the superiority of the total floor coverage over an arrangement whereby the diffusers are placed on separate grids. The specific standard oxygen transfer efficiency is independent of the air flow rate and the water depth, the drop in the k L a 20 being offset by the increase of the saturation concentration. For a given tank area, the impact of the total surface of the perforated membrane ( S p ) and of the aerated area ( S a ) is the same as on the oxygen transfer coefficient.