Modeling Tools for Environmental Engineers and Scientists

the particle surface (ML –2 T –1 ), and u = Q/A is the axial fluid velocity (LT –1 ).The interphase flux can be expressed as follows:N = k f ∆C = k f (C – C 0 ) (5.32)where k f is the mass transfer coefficient (LT –1 ) of the laminar sublayer and∆C is the concentration difference (ML –3 ) across the laminar sublayer aroundthe particle = (C – C 0 ), C 0 being the fluid phase concentration of the reactantimmediately adjacent to the solid phase (ML –3 ). The sublayer concentrationdifference can be expressed as follows:∆C = (C – C 0 ) = C – kf Ck f k (5.33)where k is the reaction rate constant, assuming it to be a first-order reaction.The above equations can now be combined, resulting in a second-orderODE. It has been solved between z = 0, C = C in and z = L, C = C out , whereL is the length of the reactor. The final solution is as follows (Weber andDiGiano, 1996): C 4 expout uL = 2E(5.34)Cinwhere f a uE = 1 + 4kL5.4.2 FLUID-FLUID SYSTEMSEnvironmental reactor configurations for processing gas-liquid systemsinclude bubble columns (e.g., ozonation), packed towers (e.g., air-stripping),sparged tanks (e.g., activated sludge), and mechanical surface-aerated tanks(e.g., stabilization ponds). Some of these reactors involve only physicalprocesses (e.g., volatilization in air-stripping towers), while some includechemical or biochemical reactions (e.g., ozonation, activated sludge). In thissection, two examples illustrating the model development process for gasliquidsystems are detailed—one featuring a physical process and anotherfeaturing a biochemical process.5.4.2.1 Packed ColumnsPacked columns in which gas and liquid phases are contacted accompaniedby transfers and/or reactions are common in many environmental andchemical engineering applications. In the environmental area, packed-column© 2002 by CRC Press LLC