Residence time distribution of solids in staged spouted beds

A new type of multistage spouted bed is developed for a counterflow of gas and solids. A one-stage and a three-stage units are studied, the RTD's of solids therein are measured, and a solids flow compartment model is developed to represent obtained family of RTD curves.; Colored particles, identical to those used as a bed material {dollar}rm(Dsb{lcub}ave{rcub}=1.78{dollar} mm, {dollar}rmrhosb{lcub}s{rcub}=2.64{dollar} grams/cm{dollar}sp3),{dollar} are adopted as tracer particles in impulse-response experiments. The RTD of solids is measured in both one-stage and three-stage columns of spouted beds with draft tubes. The hold-up of particles in each stage is self controlled by a specially designed feature of the bed. The recirculation of solids within each stage is controlled by the flow of gas (air) through the draft tube. The solids are continuously withdrawn from the system through a modified "L-valve" which operates with oscillating air pressure for a more uniform throughflow of solid material.; A simple compartment model consisting of a plug-flow vessel, with dead space, in series with a continuous-stirred-tank vessel is developed to represent the flow of solids through a single spouted bed vessel:{dollar}{dollar}rm E(t)=cases{lcub}{lcub}0 &for t {dollar}<{dollar} taurmsb{lcub}p{rcub}{rcub}crcr{lcub}{lcub}1overtaurmsb{lcub}M{rcub}{rcub}exp leftlbrack{lcub}{lcub}-{rcub}left(rm t-tausb{lcub}p{rcub}right)overtausb{lcub}rm M{rcub}{rcub}rightrbrack &for t getaurmsb{lcub}p{rcub}cr{rcub}{rcub}{dollar}{dollar}; A self-convolution of the above model/equation yields the residence time distribution expression for the three-stage column,{dollar}{dollar}rm E(t)=cases{lcub}{lcub}0 &for t {dollar}<{dollar} 3taurmsb{lcub}pi{rcub}{rcub}crcr{lcub}{lcub}left(rm t-3tausb{lcub}pi{rcub}right)sp2over2tausbsp{lcub}rm Mi{rcub}{lcub}3{rcub}{rcub}{rcub}expleftlbrack{lcub}{lcub}-{rcub}left(rm t-3tausb{lcub}pi{rcub}right)overtausb{lcub}rm Mi{rcub}{rcub}rightrbrack &for rm t ge3taurmsb{lcub}pi{rcub}cr{rcub}{dollar}{dollar}; System parameters {dollar}rmtausb{lcub}p{rcub}{dollar} and {dollar}rmtausb{lcub}M{rcub}{dollar} (or {dollar}rmtausb{lcub}pi{rcub}{dollar} and {dollar}rmtausb{lcub}Mi{rcub}){dollar} are correlated to operating variables (solid flow rate, S{dollar}rmsb{lcub}o{rcub},{dollar} gas flow rate, GFR, and recirculation time, {dollar}rm tsb{lcub}R{rcub}){dollar} by,{dollar}{dollar}rm{lcub}tausb{lcub}p{rcub}overtau{rcub}=alpha expleftlbrack{lcub}-{rcub}beta(tsb{lcub}Ro{rcub}-tsb{lcub}R{rcub})rightrbrack{dollar}{dollar}where {dollar}alpha{dollar} and {dollar}beta{dollar} are functions of the solid flow rate, S{dollar}rmsb{lcub}o{rcub}.{dollar} This correlation is tested with an independent set of data. The correlation represents data well in the solid flow range of 6.0 to 17.0 g/sec, and in the gas flow range of 3.5 to 3.7 lit/sec.; This particular multistage spouted bed design has clear operating and scale-up advantages over previous reported designs. It can tolerate a wide range of solid flow, it starts operating without difficulties, and when shut down it empties readily. The countercurrent system, also can be easily transformed in a cross-current multistage system.