Baseline Mass-Transfer Coefficient and Interpretation of Nonsteady State Submerged Bubble-Oxygen Transfer Data

Numerous testing of data reported in the relevant scientific literature widely available to the public has led to the discovery of several physical mathematical models in nature applicable to the subject of oxygenation in water from submerged bubble aeration. The mass transfer coefficient commonly symbolized as ${\mathrm{K}}_{\mathrm{L}}\mathrm{a}$ is the product of the overall liquid film coefficient ${\mathrm{K}}_{\mathrm{L}}$ and the overall gas-liquid interfacial area that the gas flux passes through, expressed by the letter $\mathrm{a}$. The rate of mass transfer (the rate at which the solute gas dissolves into a given liquid) is a function of the mass transfer coefficient ${\mathrm{K}}_{\mathrm{L}}\mathrm{a}$ and the driving force exerted against the fluid being aerated. In a nonsteady state test where the oxygen content of the water is usually lowered to approximately zero prior to initiating the test, the driving force gradually diminishes as the dissolved oxygen increases until it reaches saturation. Given that ${\mathrm{K}}_{\mathrm{L}}\mathrm{a}$ is a function of many variables, in order to have a unified test result, it is necessary to create a baseline mass transfer coefficient ${\mathrm{K}}_{\mathrm{L}}{\mathrm{a}}_0$, so that all tests will have the same measured baseline. ${\mathrm{K}}_{\mathrm{L}}\mathrm{a}$ is an exponential function of this new coefficient and dependent on the height of the liquid column ${\mathrm{Z}}_{\mathrm{d}}$ through which the gas flow stream passes. The mass transfer coefficient ${\mathrm{K}}_{\mathrm{L}}\mathrm{a}$ is dependent on the gas average flow rate (${\mathrm{Q}}_{\mathrm{a}}$) passing through the liquid column. ${\mathrm{Q}}_{\mathrm{a}}$ is expressed in terms of volume of gas per unit time and is calculated by the universal gas law, or Boyle’s Law, if the liquid temperature is uniform throughout the liquid column, taking the arithmetic mean of the flow rates over the tank column. ${\mathrm{K}}_{\mathrm{L}}\mathrm{a}$ is directly proportional to this averaged gas flow rate to power $q$, where $q$ is usually less than unity for water in a fixed column height and a fixed gas supply rate at standard conditions. This paper provides case studies that verify this concept of a standardized specific baseline mass transfer coefficient $({\mathrm{K}}_{\mathrm{L}}{\mathrm{a}}_0{)/\mathrm{Q}}_{\mathrm{a}}^{\mathrm{q}}$ that is applicable to submerged bubble aeration tests.