Ideal flows, deviation from channeling

Deviation from the two ideal flow patterns can be caused by channeling of fluid, by recycling of fluid, or by creation of stagnant regions in the vessel. Figure 11.1 shows this behavior. In all types of process equipment, such as heat exchangers, packed columns, and reactors, this type of flow should be avoided since it always lowers the performance of the unit. 

Deviation from the ideal plug flow can be described by the dispersion model, which uses the axial eddy diffusivity (m s ) as an indicator of the degree of mixing in the flow direction. If the flow in a tube is plug flow, the axial dispersion is zero. On the other hand, if the fluid in a tube is perfectly mixed, the axial dispersion is infinity. For turbulent flow in a tube, the dimensionless Peclet number (Pe) deflned by the tube diameter (v dlE-Q is correlated as a function of the Reynolds number, as shown in Figure 10.3 [3] dz is the axial eddy diffusivity, d is the tube diameter, and v is the velocity of liquid averaged over the cross section of the flow channel. 

Causes for deviations from ideal plug flow are molecular diffusion in the gas and dispersion caused by flow in the interstitial channels of the bed, and uneveness of flow over the cross section of the bed. 

Deviations from ideal flow can be classified in two types. In one type of deviation elements of fluid may move through the reactor at different velocities, causing channeling and dead spots. For such behavior to occur, the elements of fluid must not completely mix locally, but remain at least partially segregated as they move through the reactor. The other deviation refers to the extent of the local or micromixing. For exam.ple, there may be some mixing or diffusion in the direction of flow in a tubular reactor. 

In Chapter 2, the design of the so-called ideal reactors was discussed. The reactor ideahty was based on defined hydrodynamic behavior. We had assumedtwo flow patterns plug flow (piston type) where axial dispersion is excluded and completely mixed flow achieved in ideal stirred tank reactors. These flow patterns are often used for reactor design because the mass and heat balances are relatively simple to treat. But real equipment often deviates from that of the ideal flow pattern. In tubular reactors radial velocity and concentration profiles may develop in laminar flow. In turbulent flow, velocity fluctuations can lead to an axial dispersion. In catalytic packed bed reactors, irregular flow with the formation of channels may occur while stagnant fluid zones (dead zones) may develop in other parts of the reactor. Incompletely mixed zones and thus inhomogeneity can also be observed in CSTR, especially in the cases of viscous media. 

Most actual reactors deviate from these idealized systems primarily because of nonuniform velocity profiles, channeling and bypassing of fluids, and the presence of stagnant regions caused by reactor shape and internal components such as baffles, heat-transfer coils, and measurement probes. Disruptions to the flow path are common when dealing with heterogeneous systems, particularly when solids are present. To model these actual reactors, various regions are compartmentalized and... 

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