Residence-time distribution experimental measurement

Washout experiments can be used to measure the residence time distribution in continuous-flow systems. A good step change must be made at the reactor inlet. The concentration of tracer molecules leaving the system must be accurately measured at the outlet. If the tracer has a background concentration, it is subtracted from the experimental measurements. The flow properties of the tracer molecules must be similar to those of the reactant molecules. It is usually possible to meet these requirements in practice. The major theoretical requirement is that the inlet and outlet streams have unidirectional flows so that molecules that once enter the system stay in until they exit, never to return. Systems with unidirectional inlet and outlet streams are closed in the sense of the axial dispersion model i.e., Di = D ut = 0- See Sections 9.3.1 and 15.2.2. Most systems of chemical engineering importance are closed to a reasonable approximation. 

Figure 5.1.7 shows the propagator of the motion measured for a clean and a biofilm impacted capillary [14,15] and the residence time distributions calculated for each from these velocity distributions. The clean capillary gives an experimental propagator equal to the theoretical velocity distribution convolved with a Gaussian diffusion curve [14], as shown in Figure 5.1.2. For the flow around the biofilm structure note the appearance of a high velocity tail indicating higher probability of large displacements relative to the clean capillary. The slow flow peak near zero displacement results from the protons trapped within the EPS gel matrix where the...

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 ... 

METHOD FOR EXPERIMENTAL MEASUREMENT OF PARTICLES RESIDENCE TIME DISTRIBUTION... 

Obviously, if no special restriction is exerted on the input signal, the experimental measurement of residence time distribution of solid particles would become simpler and much more convenient. 

The experimental SCISR is the same as that used for the measurements of macromixing and residence time distribution, as shown in Fig. 10.2, while its major dimensions are shown in Fig. 10.6 and the equipment system scheme is illustrated in Fig. 10.7. 

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 ... 

The extent of gas dispersion can usually be computed from experimentally measured gas residence time distribution. The dual probe detection method followed by least square regression of data in the time domain is effective in eliminating error introduced from the usual pulse technique which could not produce an ideal Delta function input (Wu, 1988). By this method, tracer is injected at a point in the fast bed, and tracer concentration is monitored downstream of the injection point by two sampling probes spaced a given distance apart, which are connected to two individual thermal conductivity cells. The response signal produced by the first probe is taken as the input to the second probe. The difference between the concentration-versus-time curves is used to describe gas mixing. 

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

For an impulse of a tracer dye, the mean and variance of the experimentally measured residence time distribution are given by the following moment equations... 

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... 

Mixing effects may be found experimentally, by measuring the residence time distribution of the phases. Mixing flow models are used to convert the results into half empirical correlations (see, for example, [0.4]) ... 

The experimental measurement and typical results for different residence time distributions in a continuous reactor are summarized in Fig. 3.4. The same arrangements used for determining the mixing time are appropriate for determining the residence time distribution in a reactor. A signal in the form of a pulse or step function or a periodic function is formed at the input, and the response is measured at the output. 

In this equation, t = t/il with T being the mean residence time. The Bodenstein number is therefore the parameter of the dispersion model used in quantifying the residence time distribution, and it may be obtained from the experimentally measured curves using Equ. 3.6a with particular boundary conditions (see Levenspiel and Smith, 1957) ... 

The influence of residence time distribution (RTD) on performance, selectivity and yield is the same in microreactors as in conventional reactors. Therefore, the eflfects are well understood. Nonetheless, the demonstration of this at the microscale has hardly been reported so far. However, some experimental techniques have been developed to measure RTDs in microchannel flows which allow comparison between different types of flows or flows run at different parameters so that at least optimal flow conditions with regard to RTD can be found. 

It should be noted that CARPT experiments in the gas—soHd riser produced for the first time the definitive soHds residence time distribution in the riser itself (Fig. 1.12). Precise monitoring of the time when the tracer particle enters the system across the inlet plane, and the time when it exits across either inlet or exit plane, provides its actual residence time in the riser. Ensemble averaging for several thousand particle visits yields the solids RTD. The first passage time distribution is also readily be obtained. This information cannot be obtained by measuring the response at the top of the riser to an impulse injection of tracer at the bottom. By using CARPT, true descriptions ofsoHds residence time distributions can be obtained in the riser (Bhusarapu et al., 2004, 2006). One task of CFD modelers is to develop codes that can predict the experimental observations of CARPT. Here, it... 

Nevertheless, the blast furnace is an instructive example to examine the question of to what extent this reactor can be regarded as an ideal plug reactor. As deduced in Section 4.10.5.1, we need the residence time distribution, which was measured in 1969 by a pulse experiment with the injection of Kr into the blast air (Standish and Polthier, 1975, see also Levenspiel, 1999). Figures 6.5.22 and 6.5.23 give the dimensions of the blast furnace and the experimental results. 

RTD methods are based on the concept of age distribution functions and make use of the experimentally measured or calculated residence time distribution of fluid elements in a reactor vessel (Figure 12.3-1, C and D). A Lagrangian perspective is taken and the age of a fluid element is defined as the time elapsed since it entered the reactor. In what follows, steady state operation of a vessel fed with a volumetric flow rate F is considered. A residence time distribution (RTD) experiment can be performed with inert tracers, such that at an instant of time all fluid elements entering a reactor or process vessel are marked. The injection of an impulse of tracer into the vessel at time zero can be mathematically represented by means of the Dirac delta function or perfect unit impulse function ... 

Eq. (7.16) is plotted in figure 7.4 for different vdues of N, It can be used for modelling a real reactor with a non-ideal residence time distribution. The RTD-funcdon can be found from tracer-response measurements. By fitting eq. (7.16) with the experimental RTD-curve the fictituous number N can be determined. Tliis number merely is a measure of the residence time distribution of the real reactor. Then the chemical conversion is calculated for the cascade with N reactors, on the basis of reaction kinetics, using eq. (3.50), for which the conversion in each successive reactor is calculated with eq. (3.49), or one of the previous equations. 

Figure 2. Experimental arrangement for the measurement of residence time distribution...

Comparison of experimentally measured and CFD simulated dimensionless residence time distribution (Eg) versus dimensionless time (0). 

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