Tubular with laminar flow

Figure 8-6 Plots of the ratio of conversions in a tubular reactor with laminar flow to that in a perfect PFTR for first- md second-order kinetics. The lower pmd shows the percent loss in conversion from l nin flow comp ed to plug flow.

In order to approach idea PFR behavior, the flow must be turbulent. For example, with an open tube, the Reynolds number must be greater than 2100 for turbulence to occur. This flow regime is attainable in many practical situations. However, for laboratory reactors conducting liquid-phase reactions, high flow rates may not be achievable. In this case, laminar flow will occur. Calculate the mean outlet concentration of a species A undergoing a first-order reaction in a tubular reactor with laminar flow and compare the value to that obtained in a PFR when kV)/u = 1 ( = average linear flow velocity). 

Dispersion in a Tubular Reactor with Laminar Flow. In a laminar flow reaetor we know that the axial veloeity varies in the radial direetion according to the Hagen-Poiseuille equation ... 

For reactors with known mixing characteristics the response curve and the RTD can be predicted no experiments are necessary. As an illustration let us deyelop the RTD for the plug-flow reactor, a single ideal stirred-tank reactor, and a tubular reactor with laminar flow. 

A tubular reactor with laminar flow has been mentioned as a good approximation to segregated flow. If the dispersion due to molecular diffusion is neglected, the approximation is exact. Since the flow is segregated and the velocity profile is known, the RTD can be calculated. It is instruc- tive to compare the calculated results with those for the ideal forms given in Fig. 6-5. The velocity in the axial direction for laminar flow is parabolic,... 

Equation (6-20) or Eq. (6-22) gives the desired RTD function for a tubular reactor with laminar flow. 

Dispersion in a Tubular Reactor with Laminar Flow... 

The derivation of the rather complicated Eq. (4.10.29) is given in other textbooks (Westerterp, van Swaaij, and Beenackers, 1998 Levenspiel, 1996, 1999). Note that Eq. (4.10.29) is only valid for Newtonian fluids. The case of non-Newtonian fluids may also be important, such as, for example, in polymerization reactors, and is treated in the literature (Wen and Fan, 1975). Table 4.10.1 gives selected values of the exponential integral in Eq. (4.10.29). Figure 4.10.17 compares the conversion reached in a plug flow reactor with that in a tubular reactor with laminar flow. 

Figure 4.10.17 Conversion in an ideal plug flow reactor (C= 1) and in a tubular reactor with laminar flow (negligible molecular diffusion) for a first-order reaction (Do = kr) approximations for laminar flow as given by Eq. (4.10.31) are also shown.

Tubular reactor with laminar flow, Newtonian fluid, negligible molecular diffusion... 

For comparison the case of a tubular reactor with laminar flow but without molecular diffusion is also shown in Figure 4.10.61, which is formally represented by Bo 6, see also Figure 4.10.58. Values of Bo that are less than this value are only reached for very low values of Re x Sc and low L/d values, whereby we have to keep in mind that the model and thus Eqs. (4.10.117b) and (4.10.114) are only applicable for L/dt > 0.04Re x Sc. 

The following equations describe transport of species, heat, and momentum in a cylindrical tubular reactor with laminar flow... 

Flow in tubular reactors can be laminar, as with viscous fluids in small-diameter tubes, and greatly deviate from ideal plug-flow behavior, or turbulent, as with gases, and consequently closer to the ideal (Fig. 2). Turbulent flow generally is preferred to laminar flow, because mixing and heat transfer... 

Laminar Versus Turbulent Flames. Premixed and diffusion flames can be either laminar or turbulent gaseous flames. Laminar flames are those in which the gas flow is well behaved in the sense that the flow is unchanging in time at a given point (steady) and smooth without sudden disturbances. Laminar flow is often associated with slow flow from small diameter tubular burners. Turbulent flames are associated with highly time dependent flow patterns, often random, and are often associated with high velocity flows from large diameter tubular burners. Either type of flow—laminar or turbulent—can occur with both premixed and diffusion flames. 

Experimental work with styrene in tubular reactors has been reported (39) where viscosities were relatively low due to conversions below 32%. However, Lynn ( ) has concluded that a laminar flow tubular reactor for styrene polymerization is probably technically infeasible due to the distortion in velocity... 

The styrene conversion versus reaction time results for runs in the laminar flow regime are plotted in Figure 8. Both the rate of polymerization and the styrene conversion increase with increasing flow rate as noted previously (7). The conversion profile for the batch experimental run (B-3) is presented as a dashed line for comparison. It can be seen that the polymerization rates for runs with (Nj e e 2850 are greater than the corresponding batch polymerization with a conversion plateau being reached after about thirty minutes of reaction. This behavior is similar to the results obtained in a closed loop tubular reactor (7J) and is probably due to an excessively rapid consumption of initiator in a... 

Consider a laminar flow tubular polymerizer with cooling at the tube wall. At what radial position will a hotspot develop at the tube wall, at the centerline, or at an intermediate radius Justify your answer. Will the situation change with heating at the wall ... 

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. 

The F(t) curve for a laminar flow tubular reactor with no diffusion is shown in Figure 11.6. Curves for the two other types of idealized flow patterns are shown for comparison. 

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. 

A special kind of tubular flow reactor has laminar flow. The specific rate of such a case is found and compared with plug flow in problem P3.09.15. 

In Sect. 3.2, the development of the design equation for the tubular reactor with plug flow was based on the assumption that velocity and concentration gradients do not exist in the direction perpendiculeir to fluid flow. In industrial tubular reactors, turbulent flow is usually desirable since it is accompanied by effective heat and mass transfer and when turbulent flow takes place, the deviation from true plug flow is not great. However, especially in dealing with liquids of high viscosity, it may not be possible to achieve turbulent flow with a reasonable pressure drop and laminar flow must then be tolerated. 

For fairly high degrees of conversion, with both first- and second-order reactions, the volume of a tubular reactor in which laminar flow occurs is about 30—50% greater than that of the plug-flow reactor in... 

Inertial forces of the fluid increase with density and the square of velocity (pv2) while viscous forces decrease with increasing diameter of tube (nv/d) and increase with viscosity and velocity. High Reynolds numbers (Re>4000) result in turbulent flow with low Reynolds number (Re<2000) the flow is laminar. Laminar flow results from formation of layers of fluid with different velocities after a certain flow distance, as illustrated in Figure 2.10A. Flow at the walls is zero and increases approaching the center of the tubes. The laminar flow pattern results from layers of mobile phase with different velocities travelling parallel to each other. The maximum flow at the center is twice the average flow velocity of the fluid. Molecules in the fluid can exchange between fluid layers by molecular diffusion. Most open tubular columns operate under laminar flow conditions. 

The intense heat dissipated by viscous flow near the walls of a tubular reactor leads to an increase in local temperature and acceleration of the chemical reaction, which also promotes an increase in temperature the local situation then propagates to the axis of the tubular reactor. This effect, which was discovered theoretically, may occur in practice in the flow of a highly viscous liquid with relatively weak dependence of viscosity on degree of conversion. However, it is questionable whether this approach could be applied to the flow of ethylene in a tubular reactor as was proposed in the original publication.199 In turbulent flow of a monomer, the near-wall zone is not physically distinct in a hydrodynamic sense, while for a laminar flow the growth of viscosity leads to a directly opposite tendency - a slowing-down of the flow near the walls. In addition, the nature of the viscosity-versus-conversion dependence rj(P) also influences the results of theoretical calculations. For example, although this factor was included in the calculations in Ref.,200 it did not affect the flow patterns because of the rather weak q(P) dependence for the system that was analyzed. 

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