Axial dispersed plug flow model

This model is referred to as the axial dispersed plug flow model or the longitudinal dispersed plug flow model. (Dg)j. ean be negleeted relative to (Dg)[ when the ratio of eolumn diameter to length is very small and the flow is in the turbulent regime. This model is widely used for ehemieal reaetors and other eontaeting deviees. 

Comparison of solutions of the axially dispersed plug flow model for different boundary conditions... 

The axial dispersion plug flow model is used to determine the performanee of a reaetor with non-ideal flow. Consider a steady state reaeting speeies A, under isothermal operation for a system at eonstant density Equation 8-121 reduees to a seeond order differential equation ... 

When there is no radial variation in composition in the fluid flowing in the cylindrical vessel, the only observable dispersion takes place in the direction of fluid flow. In this situation Eq. (1-4) reduces to Eq. (1-5), and we get the axial-dispersed plug-flow model with parameters D r and u. 

Experimental Schemes Used in Relation to the Axial-Dispersed Plug-Flow Model... 

Thus we may drop the primed notation on the coefiicient for the axial-dispersed plug-flow model and identify this coeflScient with the one for the dispersed plug-flow model. 

The solution of Eq. (173) poses a rather formidable task in general. Thus the dispersed plug-flow model has not been as extensively studied as the axial-dispersed plug-flow model. Actually, if there are no initial radial gradients in C, the radial terms will be identically zero, and Eq. (173) will reduce to the simpler Eq. (167). Thus for a simple isothermal reactor, the dispersed plug flow model is not useful. Its greatest use is for either nonisothermal reactions with radial temperature gradients or tube wall catalysed reactions. Of course, if the reactants were not introduced uniformly across a plane the model could be used, but this would not be a common practice. Paneth and Herzfeld (P2) have used this model for a first order wall catalysed reaction. The boundary conditions used were the same as those discussed for tracer measurements for radial dispersion coefficients in Section II,C,3,b, except that at the wall. 

Axial dispersion coefficient, axial-dispersed plug, flow model shown equal to Dl in Eq. (72) Mean value of Dl(R) Axial dispersion coefficient, uniform dispersion model... 

In most adsorption processes the adsorbent is contacted with fluid in a packed bed. An understanding of the dynamic behavior of such systems is therefore needed for rational process design and optimization. What is required is a mathematical model which allows the effluent concentration to be predicted for any defined change in the feed concentration or flow rate to the bed. The flow pattern can generally be represented adequately by the axial dispersed plug-flow model, according to which a mass balance for an element of the column yields, for the basic differential equation governing llie dynamic behavior,... 

The pattern of flow through a packed adsorbent bed can generally be described by the axial dispersed plug flow model. To predict the dynamic response of the column therefore requires the simultaneous solution, subject to the appropriate initial and boundary conditions, of the differential mass balance equations for an element of the column,... 

The determination of volumetric mass transfer coefficients, kLa, usually requires additional knowledge on the residence time distribution of the phases. Only in large diameter columns the assumption is justified that both phases are completely mixed. In tall and smaller diameter bubble columns the determination of kLa should be based on concentration profiles measured along the length of the column and evaluated with the axial dispersed plug flow model ( 5,. ... 

There are numerous models that have been formulated to describe nonideal flow in vessels. Here, the axial dispersion or axially-dispersed plug flow model is described, since it is widely used. Consider the situation illustrated in Figure 8.4.1. (The steady-state PFR is described in Chapter 3 and the RTD for a PFR discussed in Section 8.2.)... 

The length-based Peclet number (PeL) is determined with the axial dispersed plug flow model and it is defined as... 

Several parameters have been used to gather information about sample dispersion in flow analysis peak variance [109], time of appearance of the analytical signal, also known as baseline-to-baseline time [110], number of tanks in the tanks-in-series model [111], the Peclet number in the axially dispersed plug flow model [112], the Peclet number and the mean residence time in the diffusive—convective equation [113]. 

S.D. Kolev, E. Pungor, Description of an axially-dispersed plug flow model for the flow pattern in elements of fluid systems, Anal. Chim. Acta 185 (1986) 315. 

By analogy to the one-dimensional axial dispersion plug flow model, Randolph and White (1977) proposed the random fluctuation (RF) model, in which growth rate fluctuations were represented by the growth rate diffusivity. Do, which interacts with the average linear growth rate G as follows... 

There are several types of models that have found useful applications, but two are most common—at least when found to be adequate to represent the physical situation. The first is usually termed the axial dispersion or axial dispersed plug flow model, Levenspiel and Bischoff [1], and takes the form of the one-... 

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. 

As in Section 8.1 we consider an element of the bed through which a stream containing concentration c,(z,r) of adsorbabie species / is flowing. Assuming that the flow pattern can be described by the axially dispersed plug flow model, the differential fluid phase mass balance equation for each component is... 

El-Temtamy SA, El-Shamoubi YO, El-Halwagi MM. Liquid dispersion in gas—liquid fluidized beds part I axial dispersion. The axially dispersed plug-flow model. Chem. Eng. J. 1979 18 151-159. 

Ruthven, D.M., Axial-dispersed plug-flow model for continuous countercurrent adsorbers, Can. J. Chem. Eng., 61(6), 881-883 (1983). 

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