Plug flow reactor constant fluid density

This equation is the basic relation for the mean residence time in a plug flow reactor with arbitrary reaction kinetics. Note that this expression differs from that for the space time (equation 8.2.9) by the inclusion of the term (1 + SAfA) and that this term appears inside the integral sign. The two quantities become identical only when 5a is zero (i.e., the fluid density is constant). The differences between the two characteristic times may be quite substantial, as we will see in Illustration 8.5. Of the two quantities, the reactor... 

For constant fluid density the design equations for plug flow and batch reactors are mathematically identical in form with the space time and the holding time playing comparable roles (see Chapter 8). Consequently it is necessary to consider only the batch reactor case. The pertinent rate equations were solved previously in Section 5.3.1.1 to give the following results. 

The concentrations of reactant and products at the outlet of a packed bed reactor can be easily calculated with the mass balances for each compound supposing ideal plug flow behavior. For irreversible first-order consecutive reactions (Eq. (11.5)), the concentrations at the reactor outlet depend on the inlet concentration, Cj g, the rate constant, and the residence time, r. For reaction systems with constant fluid density, the residence time corresponds to the space-time defined as, r = V/Vg, with V the reactor volume and Vq the volumetric inlet flow. The space time... 

D, which has the same dimension unit as the molecular diffusion coefficient D. Usually is much larger than because it incorporates all effects that may cause deviation from plug flow, such as radial velocity differences, eddies, or vortices. The key parameter determining the width of the RTD is the ratio between the axial dispersion time and the space-time r, which corresponds to the mean residence time in the reactor t at constant fluid density. This ratio is often called Bodenstein number Bo). 

For a plug-flow reactor, the concentration of A (and all other species) in the bulk fluid and at the surface of the catalyst particle will depend on where the catalyst particle is located in the reactor. If the external transport resistances are negligible, the surface concentrations are the same as the bulk concentrations at every point. Moreover, the bulk concentrations can be written as functions of xp, as we did in Chapter 4. For example, for a reaction that occurs at constant density,... 

At constant pressure and granted ideal plug flow, the behavior of a tubular reactor at steady state is mathematically analogous to that of a batch reactor A volume element of the reaction mixture has no means of knowing whether it is suspended tea bag-style in a batch reactor or rides elevator-style through a tubular reactor being exposed to the same conditions it behaves in the same way in both cases. As in a batch reactor, what is measured directly are concentrations—here in the effluent—and a finite-difference approximation is needed to obtain the rate from experiments with different reactor space times and otherwise identical conditions. For a reaction without fluid-density variation ... 

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