Dispersed plug flow model determination

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 ... 

Explain carefully the dispersed plug-flow model for representing departure from ideal plug flow. What are the requirements and limitations of the tracer response technique for determining Dispersion Number from measurements of tracer concentration at only one location in the system Discuss the advantages of using two locations for tracer concentration measurements. 

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,. ... 

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

If we know the number N of the tanks-in-series model, we calculate the conversion by Eq. (4.10.32) for example, for Do = 1 we obtain a conversion of 59.0%, which almost equals the values as determined by the axially dispersed plug flow model (58.6% and 58.3%). 

Both the tank in series (TIS) and the dispersion plug flow (DPF) models require traeer tests for their aeeurate determination. However, the TIS model is relatively simple mathematieally and thus ean be used with any kineties. Also, it ean be extended to any eonfiguration of eompartments witli or without reeycle. The DPF axial dispersion model is eomplex and therefore gives signifieantly different results for different ehoiees of boundary eonditions. 

We have discussed methods for experimentally finding dispersion coefficients for the various classes of dispersion models. Although the models were treated completely separately, there are interrelations between them such that the simpler plug-fiow models may be derived from the more complicated general models. Naturally, we would like to use the simplest possible model whenever possible. Conditions will be developed here for determining when it is justifiable to use a simpler plug-flow model rather than the more cumbersome general model. 

Predictions of the column height required for any given separation can be obtained by using either a staged approach or a transfer unit approach. The plug flow models for determining the height of a column are of limited value due to the effect of axial dispersion, which is caused by... 

Determinations of Peclet number were carried out by comparison between experimental residence time distribution curves and the plug flow model with axial dispersion. Hold-up and axial dispersion coefficient, for the gas and liquid phases are then obtained as a function of pressure. In the range from 0.1-1.3 MPa, the obtained results show that the hydrodynamic behaviour of the liquid phase is independant of pressure. The influence of pressure on the axial dispersion coefficient in the gas phase is demonstrated for a constant gas flow velocity maintained at 0.037 m s. 

Dynamic analysis of TBR by sitimules response technique has been succesfully applied to determine the extent of liquid axial mixing. There are number of learning and predictive models proposed in literature 2. Among them the ones having less number of parameters such as cross-flow model and axially dispersed plug flow ADPF model are the most adequate ones. A more realistic model profound for a TBR can be the one which includes the simultaneous effect of interphase and intraparticle transport rates, and the adequate hydrodynamic model, to minimize the relative importance of liquid mixing on these rates. 

The value of Dax of this plug flow model with axial dispersion can also be calculated based on correlations given in Section 4.10.6.3. Example 4.10.8 gives an example to highlight the methods used to determine the conversion based on RTD measurements. 

The model is referred to as a dispersion model, and the value of the dispersion coefficient De is determined empirically based on correlations or experimental data. In a case where Eq. (19-21) is converted to dimensionless variables, the coefficient of the second derivative is referred to as the Peclet number (Pe = uL/De), where L is the reactor length and u is the linear velocity. For plug flow, De = 0 (Pe ) while for a CSTR, De = oo (Pe = 0). To solve Eq. (19-21), one initial condition and two boundary conditions are needed. The closed-ends boundary conditions are uC0 = (uC — DedC/dL)L=o and (dC/BL)i = i = 0 (e.g., see Wen and Fan, Models for Flow Systems in Chemical Reactors, Marcel Dekker, 1975). Figure 19-2 shows the performance of a tubular reactor with dispersion compared to that of a plug flow reactor. 

The other two methods are subject to both these errors, since both the form ofi the RTD and the extent of micromixing are assumed. Their advantage is that they permit analytical solution for the conversion. In the axial-dispersion model the reactor is represented by allowing for axial diffusion in an otherwise ideal tubular-flow reactor. In this case the RTD for the actual reactor is used to calculate the best axial dififusivity for the model (Sec. 6-5), and this diffusivity is then employed to predict the conversion (Sec. 6-9). This is a good approximation for most tubular reactors with turbulent flow, since the deviations from plug-flow performance are small. In the third model the reactor is represented by a series of ideal stirred tanks of equal volume. Response data from the actual reactor are used to determine the number of tanks in series (Sec. 6-6). Then the conversion can be evaluated by the method for multiple stirred tanks in series (Sec. 6-10). 

Here we wish to determine the axial diffusivity from response measurements, in preparation for using the dispersion model for conversion calculations. According to this model, the actual reactor can be represented by a tubular-flow reactor in which axial dispersion takes place according to the effective diffusivity D. It is supposed that the axial velocity u and the concentration are uniform across the diameter, as in a plug-flow reactor. 

In the few case where more complex description of the bulk gas phase is necessary, the one-dimensional model of the bulk gas phase can be extended to a two dimensional model or the assumption of plug flow in the axial direction can be relaxed and an axial dispersion term superimposed. However, this should only be carried out when there are strong justifications, for although these extensions of the bulk gas phase modelling are quite simple mathematically, they increase the computational effort considerably and also require the determination of a larger number of parameters. 

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