Of laminar flow reactors

Chapter 3 introduced the basic concepts of scaleup for tubular reactors. The theory developed in this chapter allows scaleup of laminar flow reactors on a more substantive basis. Model-based scaleup supposes that the reactor is reasonably well understood at the pilot scale and that a model of the proposed plant-scale reactor predicts performance that is acceptable, although possibly worse than that achieved in the pilot reactor. So be it. If you trust the model, go for it. The alternative is blind scaleup, where the pilot reactor produces good product and where the scaleup is based on general principles and high hopes. There are situations where blind scaleup is the best choice based on business considerations but given your druthers, go for model-based scaleup. 

Bakker, A., Laroche, R.D., Wang, M.H. and Calabrese, R.V., 1997. Sliding mesh simulation of laminar flow in stirred reactors. Transactions of the Institution of Chemical Engineers, 75, 42M4. 

Solution The approach is similar to that in Example 3.7. The unknowns are Sl and (Em)2. Set (Poudi = (Pout) - Equation (3.40) is used to calculate iPm)2 nd Equation (3.41) is used to calculate Sl- Results are given in Table 3.2. The results are qualitatively similar to those for the turbulent flow of a gas, but the scaled reactors are longer and the pressure drops are lower. In both cases, the reader should recall that the ideal gas law was assumed. This may become unrealistic for higher pressures. In Table 3.2 we make the additional assumption of laminar flow in both the large and small reactors. This assumption will be violated if the scaleup factor is large. 

Solution This is the simplest, nontrivial example of a laminar flow reactor. The solution begins by integrating Equation (8.2) for a specific streamline that corresponds to radial position r. The result is... 

This integral is a special function related to the incomplete gamma function. The solution can be considered to be analytical even though the function may be unfamiliar. Figure 8.1 illustrates the behavior of Equation (8.8) as compared with CSTRs, PFRs, and laminar flow reactors with diffusion. 

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. 

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. 

The temperature counterpart of Q>aVR ccj-F/R and if ccj-F/R is low enough, then the reactor will be adiabatic. Since aj 3>a, the situation of an adiabatic, laminar flow reactor is rare. Should it occur, then T i, will be the same in the small and large reactors, and blind scaleup is possible. More commonly, ari/R wiU be so large that radial diffusion of heat will be significant in the small reactor. The extent of radial diffusion will lessen upon scaleup, leading to the possibility of thermal runaway. If model-based scaleup predicts a reasonable outcome, go for it. Otherwise, consider scaling in series or parallel. 

Consider an isothermal, laminar flow reactor with a parabolic velocity profile. Suppose an elementary, second-order reaction of the form A -h B P with rate SR- = kab is occurring with kui 1=2. Assume aj = bi . Find Uoutlam for the following cases ... 

Determine the opposite of the Merrill and Hamlin criterion. That is, find the value of QIaVR above which a laminar flow reactor closely... 

Practical applications to laminar flow reactors are still mainly in the research literature. The first good treatment of a variable-viscosity reactor is... 

The models of Chapter 9 contain at least one empirical parameter. This parameter is used to account for complex flow fields that are not deterministic, time-invariant, and calculable. We are specifically concerned with packed-bed reactors, turbulent-flow reactors, and static mixers (also known as motionless mixers). We begin with packed-bed reactors because they are ubiquitous within the petrochemical industry and because their mathematical treatment closely parallels that of the laminar flow reactors in Chapter 8. 

Laminar Pipeline Flows. The axial dispersion model can be used for laminar flow reactors if the reactor is so long that At/R > 0.125. With this high value for the initial radial position of a molecule becomes unimportant. 

FIGURE 13.9 Curved streamlines resulting from a polycondensation in the laminar flow reactor of Example 13.10. 

Example 15.6 Determine the washout function if a diffusion-free, laminar flow reactor is put in a recycle loop. Assume that 75% of the reactor effluent is recycled per pass. 

FIGURE 15.3 Effect of recycle on a laminar flow reactor. 

Stress on particles occurs in the velocity and turbulence fields of reactors. Therefore, for the initial estimate of stress according to Eqs. (1) and (2), the theoretically derived basic Eqs. of velocity fields can be used in the case of laminar flow, and the results of turbulence measurements in the case of turbulent flow. 

For a few highly idealized systems, the residence time distribution function can be determined a priori without the need for experimental work. These systems include our two idealized flow reactors—the plug flow reactor and the continuous stirred tank reactor—and the tubular laminar flow reactor. The F(t) and response curves for each of these three types of well-characterized flow patterns will be developed in turn. 

Calculate the volumes of a plug flow reactor and a laminar flow reactor required to process 0.5 m3/ksec of feed containing 1.0 kmole/m3 of species A to 95% conversion. The liquid phase... 

A laminar-flow reactor (LFR) is rarely used for kinetic studies, since it involves a flow pattern that is relatively difficult to attain experimentally. However, the model based on laminar flow, a type of tubular flow, may be useful in certain situations, both in the laboratory and on a large scale, in which flow approaches this extreme (at low Re). Such a situation would involve low fluid flow rate, small tube size, and high fluid viscosity, either separately or in combination, as, for example, in the extrusion of high-molecular-weight polymers. Nevertheless, we consider the general features of an LFR at this stage for comparison with features of the other models introduced above. We defer more detailed discussion, including applications of the material balance, to Chapter 16. 

In a laminar flow reactor (LFR), we assume that one-dimensional laminar flow (LF) prevails there is no mixing in the (axial) direction of flow (a characteristic of tubular flow) and also no mixing in the radial direction in a cylindrical vessel. We assume LF exists between the inlet and outlet of such a vessel, which is otherwise a closed vessel (Section 13.2.4). These and other features of LF are described in Section 2.5, and illustrated in Figure 2.5. The residence-time distribution functions E(B) and F(B) for LF are derived in Section 13.4.3, and the results are summarized in Table 13.2. 

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