Residence laminar-flow

Economic Pipe Diameter, Laminar Flow Pipehnes for the transport of high-viscosity liquids are seldom designed purely on the basis of economics. More often, the size is dictated oy operability considerations such as available pressure drop, shear rate, or residence time distribution. Peters and Timmerhaus (ibid.. Chap. 10) provide an economic pipe diameter chart for laminar flow. For non-Newtouiau fluids, see SkeUand Non-Newtonian Flow and Heat Transfer, Chap. 7, Wiley, New York, 1967). 

RESIDENCE TIME DISTRIBUTION FOR A LAMINAR FLOW TUBULAR REACTOR... 

Example 8.1 derived a specific example of a powerful result of residence time theory. The residence time associated with a streamline is t = LIVz. The outlet concentration for this streamline is ahatchit)- This is a general result applicable to diffusion-free laminar flow. Example 8.1 treated the case of a... 

Polymerizations often give such high viscosities that laminar flow is inevitable. A t5rpical monomer diffusivity in a polymerizing mixture is 1.0 X 10 ° m/s (the diffusivity of the polymer will be much lower). A pilot-scale reactor might have a radius of 1 cm. What is the maximum value for the mean residence time before molecular diffusion becomes important What about a production-scale reactor with R= 10 cm ... 

The molecule diffuses across the tube and samples many streamlines, some with high velocity and some with low velocity, during its stay in the reactor. It will travel with an average velocity near u and will emerge from the long reactor with a residence time close to F. The axial dispersion model is a reasonable approximation for overall dispersion in a long, laminar flow reactor. The appropriate value for D is known from theory ... 

The dimensionless variance has been used extensively, perhaps excessively, to characterize mixing. For piston flow, a = 0 and for a CSTR, a = l. Most turbulent flow systems have dimensionless variances that lie between zero and 1, and cr can then be used to fit a variety of residence time models as will be discussed in Section 15.2. The dimensionless variance is generally unsatisfactory for characterizing laminar flows where > 1 is normal in liquid systems. 

Laminar Flow without Diffusion. Section 8.1.3 anticipated the use of residence time distributions to predict the yield of isothermal, homogeneous reactions, and... 

FIGURE 15.9 Residence time distribution for laminar flow in a circular tube (a) physical representation b) washout function. 

In the absence of diffusion, all hydrodynamic models show infinite variances. This is a consequence of the zero-slip condition of hydrodynamics that forces Vz = 0 at the walls of a vessel. In real systems, molecular diffusion will ultimately remove molecules from the stagnant regions near walls. For real systems, W t) will asymptotically approach an exponential distribution and will have finite moments of all orders. However, molecular diffusivities are low for liquids, and may be large indeed. This fact suggests the general inappropriateness of using to characterize the residence time distribution in a laminar flow system. Turbulent flow is less of a problem due to eddy diffusion that typically results in an exponentially decreasing tail at fairly low multiples of the mean residence time. 

Micromixing Models. Hydrodynamic models have intrinsic levels of micromixing. Examples include laminar flow with or without diffusion and the axial dispersion model. Predictions from such models are used directly without explicit concern for micromixing. The residence time distribution corresponding to the models could be associated with a range of micromixing, but this would be inconsistent with the physical model. 

The pilot reactor is a tube in isothermal, laminar flow, and molecular diffusion is negligible. The larger reactor wiU have the same value for t and will remain in laminar flow. The residence time distribution will be unchanged by the scaleup. If diffusion in the small reactor did have an influence, it wiU lessen upon scaleup, and the residence time distribution will approach that for the diffusion-free case. This wiU hurt yield and selectivity. 

This is the first reactor reported where the aim was to form micro-channel-like conduits not by employing microfabrication, but rather using the void space of structured packing from smart, precise-sized conventional materials such as filaments (Figure 3.25). In this way, a structured catalytic packing was made from filaments of 3-10 pm size [8]. The inner diameter of the void space between such filaments lies in the range of typical micro channels, so ensuring laminar flow, a narrow residence time distribution and efficient mass transfer. 

There will be velocity gradients in the radial direction so all fluid elements will not have the same residence time in the reactor. Under turbulent flow conditions in reactors with large length to diameter ratios, any disparities between observed values and model predictions arising from this factor should be small. For short reactors and/or laminar flow conditions the disparities can be appreciable. Some of the techniques used in the analysis of isothermal tubular reactors that deviate from plug flow are treated in Chapter 11. 

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. 

Even higher shear rates in the extruder cannot prevent laminar flow in the screw flights and therefore resultant unmixed particles being carried over the shearing sections. Lengthening of the residence time in the barrel also has to be restricted to limit unacceptable temperature build-up, which would result in scorched compound. It is thus necessary to have an effective means of... 

Laminar flow (LF) is also a form of tubular flow, and is the flow model for an LFR. It is described in Section 2.5. LF occurs at low Reynolds numbers, and is characterized by a lack of mixing in both axial and radial directions. As a consequence, fluid properties vary in both directions. There is a distribution of residence times, since the fluid velocity varies as a parabolic function of radial position. 

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. 

Develop the E(t) profile for a 10-m laminar-flow reactor which has a maximum flow velocity of 0.40 m min-1. Consider t = 0.5 to 80 min. Compare the resulting profile with that for a reactor system consisting of a CSTR followed by a PFR in series, where the CSTR has the same mean residence time as the LFR and the PFR has a residence time of 25 min. Include in the comparison a plot of the two profiles on the same graph. 

A reaction with rate equation rc = C/(1+0,2C) is conducted in a laminar flow reactor. Evaluate the ratio of the mean laminar conversion to the plug flow conversion for a range of residence times. 

Fiber orientation uniformity is also affected by small-scale or timewise variations in polymer viscosity, related to breakage of polymer chains during the extrusion process. The degradation occurs as a result of residual moisture that immediately reacts to break chains, and by thermal degradation that occurs more gradually over time. Different residence times and temperature histories within the laminar flow streamlines lead to different viscosities, and hence different average orientation levels in the different fibers. 

When the objective of the modeling effort is to develop and validate a reaction mechanism, the major uncertainty in the model must reside in the detailed chemical kinetic mechanism. Under these conditions, the process must be studied either under transport-free conditions, e.g., in plug-flow or stirred-tank reactors, or under conditions in which the transport phenomena can be modeled very precisely, e.g., under laminar flow conditions. This way. 

Note that, in a laminar-flow tubular reactor, the material on the reactor centre line has the highest velocity, this being exactly twice the average velocity, Q/A, for the whole reactor. This means that, following any tracer test, no response will be observed until the elapsed time exceeds one half of the reactor space time or mean residence time. The following values for 0 and F(0) emphasise the form of the cumulative RTD and the fact that, even up to 10 residence times after a tracer impulse test, 0.25% of the tracer will not have been eluted from the system. 

When a tube or pipe is long enough and the fluid is not very viscous, then the dispersion or tanks-in-series model can be used to represent the flow in these vessels. For a viscous fluid, one has laminar flow with its characteristic parabolic velocity profile. Also, because of the high viscosity there is but slight radial diffusion between faster and slower fluid elements. In the extreme we have the pure convection model. This assumes that each element of fluid slides past its neighbor with no interaction by molecular diffusion. Thus the spread in residence times is caused only by velocity variations. This flow is shown in Fig. 15.1. This chapter deals with this model. 

Figure 8-5 Residence time distribution in a laminar flow tubular reactor. The dashed curve indicates the p t) curve expected in laminar flow after allowing for radial diffusion, which makes p(t) closer to the plug flow.

In fact, the plug-flow approximation is even better than this calculation indicates because of radial mixing, which wiU occur in a laminar-flow reactor. A fluid molecule near the wall will flow with nearly zero velocity and have an infinite residence time, while a molecule near the center will flow with velocity 2u. However, the molecule near the wall will diffuse toward the center of the tube, and the molecule near the center will diffuse toward the wall, as shown in Figure 8-7. Thus the tail on the RTD will be smaller, and the spike at t/2 will be broadened. We will consider diffusion effects in the axial direction in the next section. 

A characteristic of micro-channel reactors is their narrow residence-time distribution. This is important, for example, to obtain clean products. This property is not imaginable without the influence of dispersion. Considering only the laminar flow would... 

---