Modeling Tools for Environmental Engineers and Scientists

eactant(s) flows through a tubular reactor packed with the solid phase. Thesolid phase is retained within the reactor. The reaction occurs at the externalor internal sites on the solid phase. Packed bed reactors can be engineeredwith immobile beds, expanded beds, or fluidized beds. In expanded bed reactors,the fluid velocity, U, is slightly greater than the settling velocity, U s , ofthe solid particles, i.e., U > U s ; in fluidized bed reactors, the fluid velocity issignificantly greater than the settling velocity, i.e., U >> U s .The process model is essentially the same whether the bed is stationary,expanded, or fluidized. Reactor-scale macro-transport and element-scalemicro-transport features of the three packed bed configurations are illustratedin Figure 5.6. In this example, the following assumptions are made: the reactionis first-order, and the fluid flow is nonideal, with advection and dispersion.The steady state MB equation for the reactant in fluid phase can be developedas follows:0 = QC – Q C d Cdz dz EA d C –dzEA d C d dzd z EA d Cdz0 = Q d C ddz – dzd z EA d Cdzdz – Na(Adz)2 dz – Na(Adz)0 = –u d C – E d Cdzdz2 – Na (5.31)where E is the dispersion coefficient (L 2 T –1 ), a is the specific reactive area perunit volume of the reactor (L 2 L –3 ), N is the interphase transport flux normal toa) Macro-scale processes b) Micro-scale processesFixed bedExpanded bed Fluidized bedQ, Cout Q, Cout Q, Cout123IntraphasetransportInterphasetransportzQC+d[QC)]/dzdzdEA dC [EA dCdz + dz dz]Q, CinQ, CinQ, CinQ.CAdvectionEA dCdzDispersionFigure 5.6 Macro-scale and micro-scale representations of packed bed reactors (1—fluid phase;2—laminar sublayer; 3—porous solid phase).© 2002 by CRC Press LLC