Advances in Water Treatment and Enviromental Management

144 WATER TREATMENTThe overall volumetric transfer coefficient k, characterizes the attainable mass—transfer in a gas-liquid system. In process applications it is influenced by– dimensions of the reactor (geometry of the reactor and the air diffusersystem etc.)– operation parameters (flux of water and air, pressure etc.)– chemical and physical properties of the two phases (surface tension,viscosity etc.)These free selected parameters fix not only bubble characteristics such as form,size and residence time but also the material properties and hydrodynamic conditionsof the two phases and the interface boundary layer. Now these dependent parametersare related to the final desired values: the efficiency and the energy demand of themass-transfer processes.Integrating equation (2) yield:This equation corresponds to a kinetic reaction model of first order and leads to thedetermination of k.(3)2.2 Overall volumetric mass-transfer coefficient kFor practical transfer processes, it is not possible to identify separately the twovalues k L and a. To dimension and regulate a mass transfer reactor, it is of greatimportance, knowing the parameters which influence these values, to take suitableengineering actions for their variation. For this, it is necessary to clarify the physicalconditions in the neighbourhood of the interfacial boundary layer.The replacement of the liquid in the region of the interfacial boundary, is oftendescribed in terms of renewal models. A comparison of the various theories anddefinition equations for the transfer coefficient k L is listed in table 1.All formulate k L as a function of the terms:The following assumptions are common to all models:– the oxygen diffusion through the interfacial area is a molecularprocess,– the interface boundary layer consists of fluid elements which arecontacting with the molecules from the gaseous phase during a certaintime unit t’,– after the contacting time, new fluid elements from the water bulk(concentration C L ) push aside the elements with increased oxygenconcentration.The residence time t’ of the fluid elements at the interface is a function of the flowcharacteristics, i.e., the turbulence of the flow. The formulations of the models 6, 7and 8 (table 1) describe this influence of the turbulent flow on the transfer of the(4)