OCR Text |
Show discussed in detail by Celik and Chattree (1988). 5.0 PARTICLE RESIDENCE TIME CORRELATION For the development of a panicle residence time correlation, consider an isothennal reactor oriented vertically with a uniform downward laminar flow (i.e., no recirculation zones, etc.). In such a reactor, very small particles should approximately follow the gas streamlines and the slip velocity due to gravity would be negligible. Hence, particle and gas residence times would be the same, (t gr = t pr)' and given by Eq. (2). For relatively large particles, the slip velocity arising from gravity will be significant and these particles will have a shorter residence time than t gr' In a reactive environment, coal particles will also react and particle sizes will change throughout the reactor. In some cases, when burnout (conversion) is large (say larger than 50 percent by weight), the change in panicle size will cause a significant variation in particle slip velocity as well as in particle dispersion in turbulent flows. In turbulent flows, the turbulent eddy viscosity (and hence, the mixing coefficient) is large compared to the laminar viscosity and the particle dispersion is important. Turbulent diffusion causes the particles to migrate away from the center-line of the reactor to\\'ards the wall (See Fig. 3) where the gas velocities are lower and thus indirectly increases the particle residence time. Consideration of these factors affecting the particle residence time led to the following proposed functional relation between tpr and tgr: (6) where (7) (8) (9) -f~ (~ ~ Ji sp -.r: .. where A, B, P and q are empirical constants; be is the burnout at the exit of the reactor, Retp is particle turbulence Reynolds number, and to is the residence time for a particle in stagnant gas or for a particle having a slip velocity Uslip which is given, in Stokes range, -7- |