Plug flow reactor axial transport

In a plug flow reactor all fluid elements move along parallel streamlines with equal velocity. The plug flow is the only mechanism for mass transport and there is no mixing between fluid elements. The reaction therefore only leads to a concentration gradient in the axial flow direction. For steady-state conditions, for which the term IV is zero the continuity equation is a first-order, ordinary differential equation with the axial coordinate as variable. For non-steady-state conditions the continuity equation is a partial differential equation with axial coordinate and time as variables. Narrow and long tubular reactors closely satisfy the conditions for plug flow when the viscosity of the fluid is-low. 

A dynamic mathematical model of the three-phase reactor system with catalyst particles in static elements was derived, which consists of the following ingredients simultaneous reaction and diffusion in porous catalyst particles plug flow and axial dispersion in the bulk gas and liquid phases effective mass transport and turbulence at the boundary domain of the metal network and a mass transfer model for the gas-liquid interface. 

In order to deduce fundamental information on intrinsic catalyst performance it is important to reduce the influence of the chosen reactor set-up on catalyst performance to a minimum. The first reactor requirement is ideal isothermal operation conditions. The second requirement is continuously operated ideal plug flow without axial hackmixing, this being identical to a series of infinitesimally small, continuously stirred tank reactors each fulfilling the stationary concentration requirement The realization of such an optimum reactor concept is not trivial, and in 1969 Temkin and Kul kova developed a concept in which actual-size catalyst bodies could be tested under ideal conditions. Catalyst spheres and inert cylinders are alternately placed in a tube with a diameter slightly bigger than the catalyst spheres. Inert cylinders and catalyst spheres are fixed by three wires. Excellent heat transport... 

In Chapter 11, we indicated that deviations from plug flow behavior could be quantified in terms of a dispersion parameter that lumped together the effects of molecular diffusion and eddy dif-fusivity. A similar dispersion parameter is usefl to characterize transport in the radial direction, and these two parameters can be used to describe radial and axial transport of matter in packed bed reactors. In packed beds, the dispersion results not only from ordinary molecular diffusion and the turbulence that exists in the absence of packing, but also from lateral deflections and mixing arising from the presence of the catalyst pellets. These effects are the dominant contributors to radial transport at the Reynolds numbers normally employed in commercial reactors. 

If the radial diffusion or radial eddy transport mechanisms considered above are insufficient to smear out any radial concentration differences, then the simple dispersed plug-flow model becomes inadequate to describe the system. It is then necessary to develop a mathematical model for simultaneous radial and axial dispersion incorporating both radial and axial dispersion coefficients. This is especially important for fixed bed catalytic reactors and packed beds generally (see Volume 2, Chapter 4). 

If Eqn. 7.164 is fulfilled, the effect of the reactor wall on the flow pattern can be neglected. Deviation from plug flow can also occur by superposition on the plug flow of a diffusion like transport mechanism in the axial direction. This can be neglected provided Eqn. 7.165 is satisfied. A more detailed analysis is necessary for Rep < 10. 

In Eq. 12.5a-l, u is taken to be the mean (plug flow) velocity through the vessel, and is a mixing-dispersion coefficient to be found from experiments with the system of interest. One important application is to fixed beds, as discussed in detail in Chapter 11, and then it is usually termed an effective transport model, with = Z> . However, the axial dispersion model can also be used to approximately describe a variety of other reactors. 

Dynamic analysis of a trickle bed reactor is carried out with a soluble tracer. The impulse response of the tracer is given at the inlet of the column to the gas phase and the tracer concentration distributions are obtained at the effluent both from the gas phase and the liquid phase simultaneously. The overall rate process consists the rates of mass transfer between the phases, the rate of diffusion through the catalyst pores and the rate of adsorption on the solid surface. The theoretical expressions of the zero reduced and first absolute moments which are obtained for plug flow model are compared with the expressions obtained for two different liquid phase hydrodynamic models such as cross flow model and axially dispersed plug flow model. The effect of liquid phase hydrodynamic model parameters on the estimation of intraparticle and interphase transport rates by moment analysis technique are discussed. 

The assumption of plug flow is not always correct. The plug flow assumes that the convective flow (flow by velocity q/A, = v, caused by a compressor or pump) is dominating over any other transport mode. In fact, this is not always correct, and it is sometimes important to include the dispersion of mass and heat driven by concentration and temperature gradients. However, the plug flow assumption is valid for most industrial units because of the high Peclet number. We will discuss this model in some detail, not only because of its importance but also because the techniques used to handle these two-point boundary-value differential equations are similar to that used for other diffusion-reaction problems (e.g., catalyst pellets) as well as countercurrent processes and processes with recycle. The analytical analysis as well as the numerical techniques for these systems are very similar to this axial dispersion model for tubular reactors. 

The design of fixed bed catalytic reactors of the tubular type has generally been based upon a one-dimensional model. This model assumes that concentration and temperature gradients occur only in the axial direction, and that the only transport mechanism operating in this direction is the overall flow itself, considered to be of the plug-flow type. The one-dimensional model leads to average values for the temperatures and conversions. The reaction system to be considered is ... 

For the rotating cylinder electrode to be adopted as a continuous reactor, some degree of axial flow has to be superimposed on the tangential and turbulent motion in the annulus (Fig. 2.8b). If the rate of mass transport due to axial flow exceeds that due to rotation then the reactor will exhibit approximate plug-flow characteristics. If the reverse is true the behavior will tend to approach that of a continuous stirred-tank reactor (see Section 5.1.1.1). 

Hence we need respective criteria for the design and operation of a laboratory reactor to ensure negligible deviations from the ideal. Subsequently, we repeat these criteria, which were already derived in Sections 4.7, 4.10.6.5, and 4.10.7.2, and specify them for laboratory-scale experiments. In the next subsection, the criteria for ideal plug flow behavior (exclusion of an influence of axial and radial dispersion of mass and heat are covered), and in the subsequent subsection, the criteria for gradientless deal particle behavior (exclusion of an influence of interphase and intraparticle transport of mass and heat) are outlined. 

The first model associating the axial transport along the reactor (direction z) with the cross-flow transfer of volatile by product (direction y) (see Figure 3.5) is due to Amon and Denson [47] (Ault and Mellichamp [46] considered that all the polymer was in the film) and was developed for WFRs. It assumes plug flow in the pool, which implies a negligible hold-up of the liquid in the film. A time-averaged mass... 

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