Spouting pressure drop

Fig. 11. Spouting pressure drop data. Wheat (T2) O wheat (M3) A rapeseed...

As previously mentioned, the vertical pressure gradient in a spouting bed increases from zero at the base to a maximum near the top of the bed. A total spouting pressure drop APgg at the maximum spoutable bed depth can be estimated by the following relation ... 

APsb Total spouting pressure drop at maximum spoutable bed depth (M/ LP)... 

McNab, G.S. and Bridgwater, J. (1977) Spouted Beds - Estimation of Spouted Pressure Drop and the Particle Size for Deepest Beds , Proc. Europ. Congr. on Particle Technology, Nuremberg. 

Figure 11.10(b) can be modeled as a piston flow reactor with recycle. The fluid mechanics of spouting have been examined in detail so that model variables such as pressure drop, gas recycle rate, and solids circulation rate can be estimated. Spouted-bed reactors use relatively large particles. Particles of 1 mm (1000 pm) are typical, compared with 40-100 pm for most fluidizable catalysts. 

The pressure drop over a spouted bed is normally lower than that for a fluidised bed, because part of the weight of the solids is supported by the frictional force between the... 

Minimum Spouting Velocity and Pressure Drop in Spouted Beds. Can. J. Chem. Eng.,... 

By taking into account the pressure gradient in the spout in relation to gas velocity and tube contour, it could be shown that the pressure drop through the spout can be computed by integrating the equation... 

Or alternately, the pressure drop through the locked solids in the spout has to satisfy the condition... 

If control gas at point 1 in Fig. 37 is admitted to unlock the solids above this point, the A Pc peak, shown in Fig. 37, will first be lowered to APcl, which is, however, still above the value (AP, — APcy — APD). If the unlocking gas streams at point 2 and point 3 are successively turned on, the new peak Pc0 is eventually reached, which is below (AP, — APcy — APD). The unlocked spout now drops to its normal operating pressure drop APc0 for moving-bed uptransport, and the solids of Reactor 1 will now flow rather rapidly to Reactor 2 under the driving force (AP, — APcy — APD) — APc0. 

Fig. 3. Variation of solids level in dipleg L, pressure drop through conical spout APc and solids discharge rate S in intermittent solids flow (Li et al, 1981).

Integration of Eqn (5) from h = Oto h = hv gives the pressure drop equation of the trapezoidal spout ... 

Gas pressure drop across the spout, APv, and gas flow rate through the spout, Ggv, are the more important variables for the design and operation of the V-valve. From Eqs. (6) and (7), we can see that in order to calculate APv and Ggv, the gas-solids relative velocity (uro - up0) must be known. The value of (Wf0 - uPo) can be calculated by solving the simultaneous differential Eqs. (2) to (5) for the trapezoidal spout, with the boundary conditions of simultaneous equations consists of a trial-and-error process for the numerical method. 

Gas pressure drop across the spout was found to be independent of gas and solids flow rates, Fgv and Gp, respectively, as shown in Figs. 9 and 10. These results are also in conformity with the preceding theory. It can be seen from Eq. (6) that the gas-solids relative velocity (uf0 — up0) is also constant for a gas-solids-spout system. 

Gas pressure drop in the dipleg depends on pressure balance of the overall system. Let the pressure at the outlet of the tapered spout be pb, and at the top of the dipleg be pa. Then the following relation is obtained ... 

Pressure drop through the spout can be computed by integrating Eq (17) ... 

Actual integration and substitution of Eq. (19) for Qt gives the ratio of the actual pressure drop in the spout with flaring cross-section to that due to gravity of the solids ... 

APco is eventually reached, which is below (APt — APcy — APD). The unlocked spout now drops to its normal operating pressure drop APco for moving-bed uptransport, and the solids of Reactor 1 will now flow rather rapidly to Reactor 2 under the driving force (AP, - APcy — APD) - APeo. 

When unlocked, the spout operates in moving bed uptransport with a pressure drop given by Eq. (20) ... 

The first mode of operation described above possesses certain shortcomings. There is a tendency towards channeling and backmixing of liquid which makes true countercurrent operation impossible. Good design can minimize these channeling problems.5,36,9S An alternative to this mode of operation is a three-phase spouted-bed column. The hydrodynamics (i.e., pressure drop, bed expansion, and the liquid holdup) of this type of column have been studied by Vukovic et... 

Figure 9-4 Pressure drop versus flow rate curves Tor a three-phase spouted-bed column (after data from Vukovic et al. ).

The mechanism by which a bed of particulate solids transforms to the spouted state is best explained by following the changes that occur in the pressure drop across the bed, with varying rate of gas flow (Fig. 4). 

With further increases in gas flow, the cavity elongates to an internal spout (Fig. ob). The arch of compacted material stUl exists above the internal spout, so that the pressure drop across the bed rises further until it reaches a maximum value (Fig. 4, point B). 

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