Volumetric solid flow rate

This equation gives the local volumetric solid flow rate (Qv) according to the kiln radius (R), the different operating variables (6, n), the angle of repose of materials (fi) and the local depth of the solid bed (II). The spatial variable (z) is defined from the kiln end for example, H(z = 0) corresponds to the depth of the solid bed at the exit of the kiln. Two views of the kiln are presented in Fig. 2 with the main variables used in the equations. 

In the stationary regime and for a non-reactive solid, the volumetric solid flow rate is constant and equal to the inlet flow rate given by the vibrating feeder (Qv ). From Eq. (1), the following ordinary differential equation is directly obtained and can be solved with a boundary condition (exit height fixed) in order to compute the bed profile along the kiln ... 

Now, the actual linear velocity with respect to the retaining vessel of a fluid flowing through a fluidized bed of voidage e is m0/e, where u0 is the superficial fluid velocity, that is, the volumetric fluid flow rate divided by the horizontal cross-sectional area of the otherwise empty retaining vessel, being positive for the upward direction. Similarly, the actual linear velocity of the particles with respect to the retaining wall is ud/(l - e), where ud is the solid mass flow rate... 

Figure 15 maps the variation of this volume-specific intensity with gas velocity Ut and solids flow rate Gs. The subfigure at the top shows the shadowed cross-section for Gs = 80 kg/(m2s). Maximal Iv corresponds to the most efficient particle-fluid contacting per unit volume, and IFst should be integrated volumetrically to yield the global effectiveness of particle-fluid contacting in a reactor. 

D8. In the leaching of sugar from sugar cane, water is used as the solvent. Typically about 11 stages are used in a countercurrent Rotocel or other leaching system. On a volumetric basis liquid flow rate/solid flow rate = 0.95. The effective equilibrium constant is i% = 1.18, where m = (concentration, g/liter, in liquid)/(concentration, liter, in solid) fSchwartzberg. 19801. If pure water is used as the inlet solvent, predict the recovery of sugar in the solvent. 

D12. A countercurrent leaching system is recovering oil from soybeans. The system has five stages. On a volumetric basis, liquid flow rate/solids flow rate = 1.36. 97.5% of the oil entering with the nonsoluble solids is recovered with the solvent. Solvent used is pure. Determine the effective equlibrium constant, m, where m is (kg/m of solute in solvent)/(kg m of solute in solid) and is given by the equation y = m x. 

Using such a formalism (Davis et al, 1989), we can obtain the following mass balance relations for the total volumetric flow rate, total solids flow rate and the flow rate of solids having a particular settling velocity Up t (subscript j = 1, overflow subscriptj = 2, underflow) ... 

Figure 6-32, taken from Govier and Aziz, schematically indicates four flow pattern regions superimposed on a plot of pressure gradient vs. mixture velocity = Vl -t- V5 = Qj + ( s)/A where and Vs are the superficial liquid and solid velocities, Qi, and ( 5 are liquid and solid volumetric flow rates, and A is the pipe cross-sectional area. is the transition velocity above which a bed exists in the bottom of the pipe, part of which is stationary and part of which moves by saltation, with the upper particles tumbling and bouncing over one another, often with Formation of dunes. With a broad particle-size distribution, the finer particles may be fully suspended. Near V 4, the pressure gra-... 

One manner in which size may be computed, for estimating purposes, is by employing a volumetric heat-transfer concept as used for rotary diyers. It it is assumed that contacting efficiency is in the same order as that provided by efficient lifters in a rotaiy dryer and that the velocity difference between gas and solids controls, Eq. (12-52) may be employed to estimate a volumetric heat-transfer coefficient. By assuming a duct diameter of 0.3 m (D) and a gas velocity of 23 m/s, if the solids velocity is taken as 80 percent of this speed, the velocity difference between the two would be 4.6 m/s. If the exit gas has a density of 1 kg/m, the relative mass flow rate of the gas G becomes 4.8 kg/(s m the volumetric heat-transfer coefficient is 2235 J/(m s K). This is not far different from many coefficients found in commercial installations however, it is usually not possible to predict accurately the acdual difference in velocity between gas and soRds. Furthermore, the coefficient is influenced by the sohds-to-gas loading and particle size, which control the total solids surface exposed to the gas. Therefore, the figure given is only an approximation. 

Let Q, Qo, Qfi = Volumetric flow-rates of feed, overflow and sediment (m /s), W = Mass flowrate of solids (kg/s), F = Mass ratio of liquid to solid in feed (kg/kg) and S = Mass ratio of liquid to solid in sediment (kg/kg). 

Superticial Velocity. The velocity of the gas through the vessel or pipe without any solids present. It is a volumetric flow rate of fluidization gas divided by the cross-sectional area. 

Where u, is the mobile phase velocity at the column outlet, Fg the column volumetric flow rate, and Ag the column cross-sectional area available to the mobile phase. In a packed bed only a fraction of the column geometric cross-sectional area is available to the mobile phase, the rest is occupied by the solid (support) particles. The flow of mobile phase in a packed bed occurs predominantly through the interstitial spaces the mobile phase trapped within the porous particles is largely stagnant (37-40). 

Design a cyclone to recover solids from a process gas stream. The anticipated particle size distribution in the inlet gas is given below. The density of the particles is 2500 kg/m3, and the gas is essentially nitrogen at 150°C. The stream volumetric flow-rate is 4000 m3/h, and the operation is at atmospheric pressure. An 80 per cent recovery of the solids is required. 

Effect of Downcomer Aeration. When only the central gas flows (No. 7 and No. 8 flows) were employed without downcomer aeration, the solids circulation rate depended primarily on the entrainment rate of the jets. The linear relationship for both bed materials (hollow epoxy and polyethylene) in Fig. 8 shows that the volumetric concentration of the solids inside the draft tube after acceleration (or the gas voidage) is approximately constant, independent of particle density. This can be readily realized by expressing the volumetric solid loading in the draft tube as follows ... 

A value of 1290 kg/m3 for underflow concentration was selected from a retention time test. Estimate the underflow volumetric flow rate assuming total separation of all solids and that a clear overflow is obtained. 

The velocity of the plug in the downchannel (z) and tangential (0) directions can be vectorially visualized in Fig. 5.3. Notice that the volumetric flow rate, 0, as well as all of the plug velocities are dependent upon the unknown solids forwarding angle q>. 

According to Perry and Green (1999), if the experimental data are plotted in N (T - 1) versus CIC0 graph, the C/C0 at which N (T - 1) and thus 7 - 1 equals zero is called the stoichiometric point, and is independent of the volumetric flow rate. This is the point where the amount of solute that has leaked past the reference point in the bed exactly equals the residual unfilled capacity of the solid contained before that point. The characteristic C/C0 versus N Cl - 1) curves are shown in Figure 4.32. 

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