Superficial velocity fixed beds

Generally, gas-liquid-solid fixed-bed reactors can operate in hydrodynamically different regimes whose boundaries depend on gas and liquid superficial velocities, catalyst bed and fluid properties. 

Few fixed-bed reactors operate in a region where the intrinsic kinetics are applicable. The particles are usually large to minimize pressure drop, and this means that diffusion within the pores. Steps 3 and 7, can limit the reaction rate. Also, the superficial fluid velocity may be low enough that the external film resistances of Steps 2 and 8 become important. A method is needed to estimate actual reaction rates given the intrinsic kinetics and operating conditions within the reactor. The usual approach is to define the effectiveness factor as... 

Fixed-bed systems are the most common, but some countercurrent fluidized beds are in use. Flow diagrams are given in reference 47. The superficial velocities of gases in fixed beds should be about 1 ft/sec (0.3 m/sec) and those for liquids about 1 ft/min (0.3 m/min).48 See references 48 and 49 for more design information. 

This section is a continuation of Section 21.3.2 dealing with pressure drop (-AP) for flow through a fixed bed of solid particles. Here, we make further use of the Ergun equation for estimating the minimum superficial fluidization velocity, ump In addition, by analogous treatment for free fall of a single particle, we develop a means for estimating terminal velocity, ur as a quantity related to elutriation and entrainment. 

At low gas velocities, the bed of particles is practically a packed bed, and the pressure drop is proportional to the superficial velocity. As the gas velocity is increased, a point is reached at which the bed behavior changes from fixed particles to suspended particles. The superficial velocity required to first suspend the bed particles is known as minimum fluidization velocity (umf). The minimum fluidization velocity sets the lower limit of possible operating velocities and the approximate pressure drop can be used to approximate pumping energy requirements. For agglomeration process in the fluid-bed processor, air velocity required is normally five to six times the minimum fluidization velocity. 

Before analyzing the subject of gas holdup, it has to pointed out that while ub is the bubble rising velocity and Z/ub is the bubble residence time, the superficial gas velocity present in the following equation is equivalent to the superficial gas velocity in fixed beds ... 

Furthermore, the superficial gas velocity usG in slurry reactors is equivalent to the superficial gas velocity in a fixed bed ... 

In the following equations, the Reynolds number is based on the superficial velocity. Fu and Tan correlation has been derived from experiments conducted in three-phase fixed beds packed with spherical particles and for particle diameters between 0.5 and 1.9 mm. Fixed bed operated under downflow conditions and a liquid distributor was used. The correlation was derived for Rep between 0.1 and 10 (Fu and Tan, 1996) ... 

In this equation, Re is tlie particle Reynolds number based on the minimum superficial velocity for fluidization. Moreover, for fixed-beds, we can set = 1 and sf = s. The correlation is applicable for void fractions between 0.4 and 0.8 with particle density up to 480 lb/ft3. Note that by changing the Rep number, the fluidized bed voidage ef is changed. 

Hashimoto et al. (1977) studied the removal of DBS from an aqueous solution in a carbon fixed-bed adsorber at 30 °C. The dimensions of the bed were D = 20 mm and Z = 25.1 cm. Carbon particles of 0.0322-cm radius were used, with 0.82 g/cm3 particle density, and 0.39 g/cm3 bulk density. The concentration of the influent stream was 99.2 rng/L and the superficial velocity was 0.0239 cm/s. The fixed bed was operated under upflow condition. Furthermore, the isotherm of the DBS-carbon system at 30 °C was found to be of Freundlich type with Fr = 0.113 and = 178 (mg/g)(L/mg)0113. Finally, the average solid-phase diffusion coefficient was found to be 2.1 X 10 10 cm2/s. The approximate value of 10 9 m2/s could be used for DBS liquid-phase diffusion coefficient. 

Here, it has to be noted that for calculating the Peclet number in fixed beds, the actual velocity has to be used, i.e. the interstitial velocity, which influences the degree of mixing. In slurry bubble column reactors, the real velocity of the fluid is the bubble velocity, which is much higher than the gas superficial velocity. The mean bubble rise velocity for a batch liquid is (eq (3.201))... 

For constant superficial velocity (zero expansion factor) and negligible pressure drop (see the subsection Nonisobaric fixed-bed operation), the general mass and thermal energy continuity equations for the catalytic fixed-bed reactor are... 

Note that in an adiabatic fixed bed, the temperature varies from inlet to the outlet of the bed and thus the fluid density, volumetric flow rate, and superficial velocity are not constant. However, the product pus in the above equation is the mass flow rate per unit cross-sectional area of the bed (kg/rn2 s), which is constant throughout the bed length. 

In Figure 5.13, the maximum superficial velocity and the corresponding minimum contact time for keeping aZIPi lower than 0.1 is shown for a typical fixed bed with no reaction. 

It is clear that the limit in aZIPi can be easily satisfied in fixed beds with particles larger than about 1 mm, where the bed can be operated in a wide range of superficial fluid velocities up to values in the vicinity of 100 cm/s. 

Fluidized bed For the specified system and particle size, the minimum fluidization velocity is 4.24 cm/s (eq. 3.451). Flere, we note that the operating superficial velocity in the fixed bed is higher than the minimum fluidization velocity. This means that to retain a fixed-bed operation, we should operate in a downflow mode. 

Hydrodynamics The particle size can be evaluated from the superficial velocity at incipient fluidization fm and the Ergun equation by trial and error (eq. (3.451)). For this calculation, we need the bed porosity at incipient fluidization for the assumed particle size, which can be evaluated by using the relationship of Broadhurt and Becker (eq. (3.466)). Note, that the resulting value cannot be lower than the fixed-bed porosity. Since we assume spherical particles, a reasonable value of bed porosity is 0.41. This procedure results in a particle size of 0.077 mm and sfm = 0.47. 

Fig. 23. MR visualization of water flowing within a fixed bed of spherical glass beads the beads have no MR signal intensity associated with them and are identified as black voxels. Flow velocities in the (a) Z-, (b) x-, and (c) y-directions are shown with slices taken in the xy, yz, and vz planes for each of the velocity components. In each xy-image the positions at which the slices in the other two directions were taken are identified. Voxel resolution is 195 pm x 195 pm x 195 pm. The glass beads were of diameter 5mm and were packed within a column of internal diameter 46 mm. Typically, 40% of the flow was carried by approximately 20% of the inter-particle space within any 2-D slice section through the bed, perpendicular to the direction of superficial flow. Regions of high- and low-flow velocity in the direction of superficial flow are highlighted in (a). Reprinted from reference (77), with pennission from Elsevier, Copyright (2001).

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