In laminar flow reactors

CHEMICAL CONVERSION IN LAMINAR FLOW REACTORS Single w-th Order Reactions... 

Figure S-4 Velocity profiles in a tube in plug-flow aid in laminar flow reactors.

The dispersion model is also used to describe nonideal tubular reactors. In this model, there is an axial dispersion of the material, which is governed by an analogy to Pick s law of diffusion, superimposed on the flow. So in addition to transport by bulk flow, UAqC, every component in the mixture is transported through any cross section of the reactor at a rate equal to [—DaAddCldz)] resulting from molecular and convective diffusion. By convective diffusion we mean either Aris-Taylor dispersion in laminar flow reactors or turbulent diffusion resulting from turbulent eddies. 

The RTD in laminar flow reactor without radial diffusion is shown in Figure 3.8. The first volume elements reach the reactor outlet after 7/2 (0 = 0.5) and approaches zero slowly. 

Example 3.8 Repeat Example 3.7, now assuming that both the small and large reactors are in laminar flow. 

TABLE 3.2 Series Scaleup of Gas-Phase Reactors in Laminar Flow... 

Example 8.1 Find the mixing-cup average outlet concentration for an isothermal, first-order reaction with rate constant k that is occurring in a laminar flow reactor with a parabolic velocity profile as given by Equation (8.1). 

Laminar flow reactors have concentration and temperature gradients in both the radial and axial directions. The radial gradient normally has a much greater effect on reactor performance. The diffusive flux is a vector that depends on concentration gradients. The flux in the axial direction is... 

The hnal step in the design calculations for a laminar flow reactor is determination of mixing-cup averages based on Equation (8.4). The trapezoidal rule is recommended for this numerical integration because it is easy to implement and because it converges O(Ar ) in keeping with the rest of the calculations. 

Example 8.3 The reactor of Example 8.2 is actually in laminar flow with a parabolic velocity profile. Estimate the outlet concentration ignoring molecular diffusion. 

The performance of the laminar flow reactor is appreciably worse than that of a PFR, but remains better than that of a CSTR (which gives T=0.5 for kt= 1). The computed value of 0.4432 may be useful in validating more complicated codes that include diffusion. 

Example 8.4 Suppose that the reactive component in the laminar flow reactor of Example 8.2 has a diffusivity of 5x 10 m /s. Calculate the minimum number of axial steps, J, needed for discretization stability when the radial increments are sized using 7=4, 8, 16, 32, 64, and 128. Also, suggest some actual step sizes that would be reasonable to use. 

Example 8.6 Generalize Example 8.5 to determine the fraction unreacted for a first-order reaction in a laminar flow reactor as a function of the dimensionless groups and kt. Treat the case of a parabolic velocity profile. 

Figure 8.1 includes a curve for laminar flow with 3>AtlR = 0.1. The performance of a laminar flow reactor with diffusion is intermediate between piston flow and laminar flow without diffusion, aVI = 0. Laminar flow reactors give better conversion than CSTRs, but do not generalize this result too far It is restricted to a parabolic velocity profile. Laminar velocity profiles exist that, in the absence of diffusion, give reactor performance far worse than a CSTR. 

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