Second-Stage Dipleg Solids Backup

If py is the pressure in the vessel s dilute phase (above the fluid bed) then  

In addition, for equilibrium between the pressures on the two sides of the flapper valve, which occurs when it is just about to open  

ps is the pressure within and near the bottom of the second-stage dip-leg Appr, Aps are the pressure drops across the primary and second-stage cyclones, respectively, ps and pb are the bulk densities of the dense-phase 

A worked example for the calculation of solids back-up in diplegs is included in Appendix 11. A. In addition, a quantitative estimation of the different contributions to the solid back-up in diplegs on basis of a moment balance on flapper valves is included in Appendix ll.B. 

One may wonder why the flapper valve is ever used if the second-stage cyclone s dipleg is submerged (and therefore, sealed) below the surface of the 

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Figure 11.4.1 is a simple illustration of an internal, two-stage cyclone system contained within a fluidized bed vessel (typically a reactor or regenerator). We wish to compute the backup h of the solids within the second-stage dipleg above the fluid bed level, which is at the vessel s lower cylindrical/conical transition. 

The second term is the manometer effect and accounts for the difference in solids densities in the bed outside the flapper valve and that inside the valve. If there is no difference in these densities, or if the dipleg is not submerged, this term vanishes. In lightly-loaded (that is, second or third-stage) cyclones for which Eq. (11.B.8) mainly applies, the dipleg solids density is normally less than that of the bed. This results in a positive contribution to the solids backup, h. We may note that the backup increases as the submergence increases and with a decrease in dipleg solids density. 

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