Residence time distribution experimental determination

A best way is to determine the residence time distribution experimentally as described in Chapter 4. From the experimentally determined variance (a) of a pulse experiment, the longitudinal Peclet number is easily obtained by an iterative solution o =... 

Chapter 14 and Section 15.2 used a unsteady-state model of a system to calculate the output response to an inlet disturbance. Equations (15.45) and (15.46) show that a dynamic model is unnecessary if the entering compound is inert or disappears according to first-order kinetics. The only needed information is the residence time distribution, and it can be determined experimentally. 

An investigation into the applicability of numerical residence time distribution was carried out on a pilot-scale annular bubble column reactor. Validation of the results was determined experimentally with a good degree of correlation. The liquid phase showed to be heavily dependent on the liquid flow, as expected, but also with the direction of travel. Significantly larger man residence times were observed in the cocurrent flow mode, with the counter-current mode exhibiting more chaimeling within the system, which appears to be contributed to by the gas phase. 

Experimental Determination of Residence Time Distribution Functions... 

For a few highly idealized systems, the residence time distribution function can be determined a priori without the need for experimental work. These systems include our two idealized flow reactors—the plug flow reactor and the continuous stirred tank reactor—and the tubular laminar flow reactor. The F(t) and response curves for each of these three types of well-characterized flow patterns will be developed in turn. 

The variance approach may also be used to determine n. From Illustration 11.2 the variance of the response data based on dimensionless time is 30609/(374.4)2, or 0.218. From equation 11.1.76 it is evident that n is 4.59. Thus the results of the two approaches are consistent. However, a comparison of the F(t) curves for n = 4 and n = 5 with the experimental data indicates that these approaches do not provide very good representations of the data. For the reactor network in question it is difficult to model the residence time distribution function in terms of a single parameter. This is one of the potential difficulties inherent in using such simple models of reactor behavior. For more advanced methods of modeling residence time effects, consult the review article by Levenspiel and Bischoff (3) and textbooks written by these authors (2, 4). 

The movement of the particles in this stage is very complex and extremely random, so that to determine accurately the residence time distribution and the mean residence time is difficult, whether by theoretical analysis or experimental measurement. On the other hand, the residence time distribution in this stage is unimportant because this subspace is essentially inert for heat and mass transfer. Considering the presence of significant back-mixing, the flow of the particles in this stage is assumed also to be in perfect mixing, as a first-order approximation, and thus the residence time distribution probability density function is of the form below ... 

Using the experimental residence time distribution data of Levenspiel and Smith in Example 8-2, determine the number of ideal tanks N, the variance, dispersion number, and Peclet number. 

Fig. 8.16. Schematic flowsheet for the experimental determination of pressure drop, flooding limits, residence time distribution (RTD), and mass transfer.

The rate-based stage model parameters describing the mass transfer and hydrodynamic behavior comprise mass transfer coefficients, specific contact area, liquid hold-up, residence time distribution characteristics and pressure drop. Usually they have to be determined by extensive and expensive experimental estimation procedures and correlated with process variables and specific internals properties. 

The extruder flow model suggested by Carley et al. (9) is chosen, by virtue of its simplicity and good agreement with experimentally determined residence time distributions, throughput and power requirements, to illustrate the methodology of this approach. 

Experimental Methods for Determining Mixing Quality and Residence Time Distribution... 

However, if the reactor is filled, for example, with a catalyst, the situation becomes more complicated. The Vr would be the empty volume of the reactor, which is then difficult to determine, for instance, using settled apparent densities. The residence time can also be experimentally determined, usually resulting in a residence time distribution however, the experimental effort for such experiments is often large. Therefore, it is useful to apply a modified residence time, as shown in Equation (27), which defines the ratio of the mass of the catalyst and the gas flow, two easily measurable values ... 

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. 

The HDU can also be experimentally determined by measuring the residence time distribution of the two phases in the extractor unit. 

In [211] the flow conditions in a Kenics mixer consisting of six mixing elements were mathematically investigated with a commercially available software packet, in which the path of the mixing elements was followed through the flow field. In this way the residence time distribution, the layer formation and the variance coefficient were determined as a function of the number of mixing elements. The results obtained agreed very well with the published experimental data. 

It is most convenient to define these distributions quantitatively within the context of the experimental methods normally used for the determination of the residence-time distribution. Once again we base the vocabulary and the development on the pioneering work of Danckwerts [P.V. Danckwerts, Chem. Eng. ScL, 2, 1 (1953)]. 

Experimental data on exit-age or residence-time distributions most often take the form of discrete values of tracer concentration measured at successive time intervals after introduction of the tracer. Thus, the integrals involved can be replaced by summations in the analysis of actual data. We will illustrate the procedure for the analysis of a pulse-response experiment. Available are tracer concentrations in the effluent, C t) and corresponding times, and from these data we would like to determine the exit-age distribution, or E 0)d6, the distribution in terms of the residencetime variable 6. First determine E t) from C t) versus t by... 

One common approach to determining the model parameter, is to perform a residence time-distribution test on the reactor, and choose the value D, so that the model solution and experimental output curve agree [e.g., by least squares techniques (see Sec. 12.5. c)]. Figure 12.5.a-l shows the (d )—curves of the model for an impulse input with closed boundaries (here ff = OF IV = flu/L, with L s length of the reactor) ... 

Design equations can be developed for partial mixing in either or both phases. The first step is to experimentally determine the residence time distribution for each phase. But the procedures tend to be quite involved, and are outside the scope of this treatment (see Kastanek et al., 1993, for a comprehensive exposition). 

To determine the function F(t) from experimental data, we use the property G, as shown in Chapter 1. If G is any property (conductivity, ionization, wavelength, etc.) proportional to the concentration, in which Gi is the magnitude at the inlet and Gi at the outlet, then the cumulative residence time distribution function, which remained in the reactor at an instant shorter than t, will be ... 

In these models, the interactions between the chemical reaction and the transport processes are described in some more details than in first category. The numerous elementary transport processes are lumped together into some effective terms, using different simplification rules. These models are generally based on the Residence Time Distribution (R.T.D.) of the fluid phases. This formulation is convenient because the R.T.D. can be determined experimentally by well established stimulus-response techniques. The resultant R.T.D. reflects bulk pheno-... 

Correction using Murphree stage efficency coefficients determined experimentally Determination of the apparatus dimensions with respect to the flooding limit or based on the required mean residence time and residence time distribution. 

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