Model axially dispersed plug flow

The dispersion model (axially dispersed plug flow)... 

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,... 

Figure 3-11 A mixing model for the trickle-bed reactor which comprises an axially dispersed plug flow with mass exchange with stagnant areas.106...

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... 

Beste et al. [104] compared the results obtained with the SMB and the TMB models, using numerical solutions. All the models used assumed axially dispersed plug flow, the linear driving force model for the mass transfer kinetics, and non-linear competitive isotherms. The coupled partial differential equations of the SMB model were transformed with the method of lines [105] into a set of ordinary differential equations. This system of equations was solved with a conventional set of initial and boundary conditions, using the commercially available solver SPEEDUP. Eor the TMB model, the method of orthogonal collocation was used to transfer the differential equations and the boimdary conditions into a set of non-linear algebraic equations which were solved numerically with the Newton-Raphson algorithm. 

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. 

The mathematical model for the mass transfer of an adsorbate in the LC column packed with the silicalite crystal particles is based on the assumptions of (1) axial—dispersed plug—flow for the mobile phase with a constant interstitial flow velocity (2) Fickian diffusion in the silicalite crystal pore with an intracrystalline diffus— ivity independent of concentration and pressure and (3) spherical silicalite crystal particles with a uniform particle size distribution. A detailed discussion of these assumptions can be found in (13). The differential mass balances over an element of the LC column and silicalite crystal result in the following two partial differential equations ... 

The above discussion can be illustrated for an isothermal packed bed tubular reactor with negligible diffusional resistances ( /= 1.0) and negligible axial dispersion (plug flow) and instantaneous radial dispersion (one-dimensional model) ... 

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