Patterns plug flow

So far we have treated two flow patterns, plug flow and mixed flow. These can give very different behavior (size of reactor, distribution of products). We like these flow patterns and in most cases we try to design equipment to approach one or the other because... 

Names have been associated with different types of flow patterns of fluid in vessels. First of all, we have the two previously mentioned ideal flow patterns, plug flow and backmix flow. Flow in tubular vessels ap-... 

The classic analysis of reactors involves two idealized flow patterns— plug flow and mixed flow. Though real reactors never fully follow these flow patterns, in many cases, a number of designs approximate these ideals with negligible error. However, deviation from ideality can be considerable. Typically, in a reaction vessel, we can have several immediate cases closer to plug or mixed flow. Of course, nonideal flow concerns all types of reactors used in heterogeneous processes, i.e. fixed beds, fluidized beds, continuous-flow tank reactors, and batch reactors. However, we will focus on fixed beds and batch reactors, which are the common cases. 

Equation (5-179) and Fig. 5-22 serve as a framework for correlating the performance of furnaces with flow patterns—plug flow, parabolic... 

In Chapter 2, the design of the so-called ideal reactors was discussed. The reactor ideahty was based on defined hydrodynamic behavior. We had assumedtwo flow patterns plug flow (piston type) where axial dispersion is excluded and completely mixed flow achieved in ideal stirred tank reactors. These flow patterns are often used for reactor design because the mass and heat balances are relatively simple to treat. But real equipment often deviates from that of the ideal flow pattern. In tubular reactors radial velocity and concentration profiles may develop in laminar flow. In turbulent flow, velocity fluctuations can lead to an axial dispersion. In catalytic packed bed reactors, irregular flow with the formation of channels may occur while stagnant fluid zones (dead zones) may develop in other parts of the reactor. Incompletely mixed zones and thus inhomogeneity can also be observed in CSTR, especially in the cases of viscous media. 

All the methods above require the correct gas flow pattern (plug flow, well back-mixed, or intermediate) to convert the transfer rate to a correct kLa value unless the degree of depletion of the gas phase is very low. This can be very important, as discussed in Chapter 11. Gas flow patterns can be determined from measurements of the gas residence time distribution using tracer gas (see Section 4-7.8). Two dynamic methods avoid this problem the double response method (Chapman et al., 1982), in which the dynamic responses of both liquid and gas phases are measured, and the initial response method (Gibilaro et al., 1985). 

Classical reactor analysis and design usually assume one of two idealized flow patterns plug flow or completely backmixed flow. Real reactors may approach one of these however, it is often the nonidealities and their interaction with chemical kinetics that lead to poor reactor design and performance (Levenspiel, 1998). Nonidealities include channeling, bypassing, and dead zones, among others. 

Equilibrium Theory. The general features of the dynamic behavior may be understood without recourse to detailed calculations since the overall pattern of the response is governed by the form of the equiUbrium relationship rather than by kinetics. Kinetic limitations may modify the form of the concentration profile but they do not change the general pattern. To illustrate the different types of transition, consider the simplest case an isothermal system with plug flow involving a single adsorbable species present at low concentration in an inert carrier, for which equation 30 reduces to... 

Fresh butane mixed with recycled gas encounters freshly oxidized catalyst at the bottom of the transport-bed reactor and is oxidized to maleic anhydride and CO during its passage up the reactor. Catalyst densities (80 160 kg/m ) in the transport-bed reactor are substantially lower than the catalyst density in a typical fluidized-bed reactor (480 640 kg/m ) (109). The gas flow pattern in the riser is nearly plug flow which avoids the negative effect of backmixing on reaction selectivity. Reduced catalyst is separated from the reaction products by cyclones and is further stripped of products and reactants in a separate stripping vessel. The reduced catalyst is reoxidized in a separate fluidized-bed oxidizer where the exothermic heat of reaction is removed by steam cods. The rate of reoxidation of the VPO catalyst is slower than the rate of oxidation of butane, and consequently residence times are longer in the oxidizer than in the transport-bed reactor. 

Macromixing is estabflshed by the mean convective flow pattern. The flow is divided into different circulation loops or zones created by the mean flow field. The material is exchanged between zones, increasing homogeneity. Micromixing, on the other hand, occurs by turbulent diffusion. Each circulation zone is further divided into a series of back-mixed or plug flow cells between which complete intermingling of molecules takes place. 

Multiphase Reactors. The overwhelming majority of industrial reactors are multiphase reactors. Some important reactor configurations are illustrated in Figures 3 and 4. The names presented are often employed, but are not the only ones used. The presence of more than one phase, whether or not it is flowing, confounds analyses of reactors and increases the multiplicity of reactor configurations. Gases, Hquids, and soHds each flow in characteristic fashions, either dispersed in other phases or separately. Flow patterns in these reactors are complex and phases rarely exhibit idealized plug-flow or weU-stirred flow behavior. 

Flow Regimes in Multiphase Reactors. Reactant contacting, product separations, rates of mass and heat transport, and ultimately reaction conversion and product yields are strong functions of the gas and Hquid flow patterns within the reactors. The nomenclature of commonly observed flow patterns or flow regimes reflects observed flow characteristics, ie, armular, bubbly, plug, slug, spray, stratified, and wavy. 

Three basic fluid contacting patterns describe the majority of gas-liquid mixing operations. These are (1) mixed gas/mixed liquid - a stirred tank with continuous in and out gas and liquid flow (2) mixed gas/batch mixed liquid - a stirred tank with continuous in and out gas flow only (3) concurrent plug flow of gas and liquid - an inline mixer with continuous in and out flow. For these cases the material balance/rate expressions and resulting performance equations can be formalized as ... 

Identify the flow pattern of the prototype system by subjecting it to an impulse, step, or sinusoidal disturbance by injection of a tracer material as reviewed in Chapter 8. The result is classified as either complete mixing, plug flow, and an option between a dispersion, cascade, or combined model. 

Non-ideal reactors are described by RTD functions between these two extremes and can be approximated by a network of ideal plug flow and continuously stirred reactors. In order to determine the RTD of a non-ideal reactor experimentally, a tracer is introduced into the feed stream. The tracer signal at the output then gives information about the RTD of the reactor. It is thus possible to develop a mathematical model of the system that gives information about flow patterns and mixing. 

The eccentric rotation of filler in virtue of the variant shear rates along the extrudate cross-section has been proposed as an alternative to the plug flow mechanism to explain this orientation pattern [355]. In [357] it was noted that the cross-wise orientation of fibers at the core of molded specimens was established only after the entire mold had been filled the authors assumed this orientation to be due to the quasi-static stresses arising in the material under pressure. 

Establish ideal flow patterns This is usually assumed to be the case for plug-flow and continuously stirred tank reactors, but are all conditions for ideal mixing fulfilled For example, a rule of thumb is that the diameter d of the PFR should be at least lOx the diameter of the catalyst particles to eliminate the influence of the reactor wall. Also, the amount of catalyst should be sufficient to avoid axial gradients. Another rule is that the ratio of the bed length L to the reactor diameter d, i.e. L/d, should be >5-10. Higher values are preferable, but these may cause other problems such as temperature gradients and pressure drops. 

Plug flow A simple convective flow pattern in pipes and tubes that is characterized by a fluid velocity independent of radial position, complete mixing in the radial direction, and no mixing in the axial direction. Also called the parallel tube model or tubular flow. See Eqs. (7) and (8) and Figure 3. 

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