Residence-time distributions measurement

In concurrent downward-flow trickle beds of 1 meter in height and with diameters of respectively 5, 10 and 20 cm, filled with different types of packing material, gas-continuous as well as pulsing flow was realized. Residence time distribution measurements gave information about the liquid holdup, its two composing parts the dynamic and stagnant holdup and the mass transfer rate between the two. 

Residence time distribution measurements, together with a theoretical model, provide a method to calculate the rate of mass transfer between the liquid flowing through the column, the dynamic holdup, and the stagnant pockets of liquid in between the particles. We have chosen the cross flow model (10). It has to be noted that the model starts from the assumption that the flow pattern has a steady-state character, which is in conflict with reality. Nevertheless, average values of the number of mass transfer units can be calculated as well as the part of the liquid being in the stagnant situation. 

This type of reactor is very widely used because it is one of the simplest to construct and it is cheap. Sampling and analysis of the product streams are generally easy, but they can be difficult to obtain effectively at low conversions. Isothermality of the reactor is generally attainable, particularly at low heat release. Residence-time distribution measurements can be difficult because of channeling problems, but this can be somewhat reduced by running the reactor vertically rather than horizontally. 

Table IV presents some data on liquid residence time distributions measured under conditions of hydrocracking in trickle flow. It can be seen that bed dilution with fine inert particles results in a considerable improvement in the plug-flow character of the reactor, which supports the idea that the dispersion is largely determined by the packing of fine particles. Since in the range of Re numbers of interest the Bodenstein number is approximately a constant (see Figure 4), the Peclet numbers for beds of equal length should be inversely proportional to the particle diameter. Dilution of the 1.5 mm particles with 0.2 mm particles should raise Pe by a factor of about 7, which is approximately in line with the data in Table IV.

Generally tomographic measurements can be carried out only for a few column experiments, because they are time consmning and costly. In this case the results should be used for a better interpretation of the residence time distribution measured with the conventional measuring technique and to make a statement about the exactness of the used hydrodynamic model. 

Residence time distribution measurements have been presented by Sakai [127], who contrasted the behavior ofthe various types of twin-screw extruders (Figure 6.26). Sakai found that intermeshing co-rotating twin screw machines produce a narrower distribution of residence time than a single-screw extruder. He argues that this is... 

Residence time distribution measurements not only generate information about the processing history of a polymer, but have also been used to characterise the conveying and self-cleaning efficiency of compounding machinery. 

Fig. 7.42 Residence time distributions measured in horizontal equipment for volume flow rates of fluidization air at (a) 500 m h (b) 700 m h (two measurements for each gas flow rate under essentially the same conditions).

Plugatyr, A. and Svishchev, I. (2008). Residence time distribution measurements and flow modeling in a snpercritical water oxidation reactor Application of transfer function concept, J. Supercrit. Fluids, 44, pp. 31-39. 

The residence time distribution measures features of ideal or nonideal flows associated with the bulk flow patterns or macromixing in a reactor or other process vessel. The term micromixing, as used in this chapter, applies to spatial mixing at the molecular scale that is bounded but not determined uniquely by the residence time distribution. The bounds are extreme conditions known as complete segregation and maximum mixedness. They represent, respectively, the least and most molecular-level mixing that is possible for a given residence time distribution. 

A survey of residence time distribution measurements by Taylor and Jenkins [66] indicates that for most free flowing materials processed in long kilns, it is reasonable to assume that the solid flow pattern approaches plug flow. It has also been shown that the solids are well mixed in any horizontal section. 

A computer model for the calculation of the temperature/tlme profile and the composition of the gas atmosphere in rotary kilns is described. The model is applied for scaling down the continuous commercial calcination of catalyst materials to batch calcination in laboratory rotary kilns as used in catalyst development work. The results of the model are compared with measurements carried out in the rotary kiln of the catalyst plant at Ghent, which produces y-alumina extrudates used as carrier for heterogeneous catalysts. The plug flow transport model assumed for the solids is confirmed by residence time distribution measurements. The measured temperature profiles are in agreement with the calculated profiles after adjustment of the kinetic rate constants. 

To measure a residence-time distribution, a pulse of tagged feed is inserted into a continuous mill and the effluent is sampled on a schedule. If it is a dry miU, a soluble tracer such as salt or dye may be used and the samples analyzed conductimetricaUy or colorimetricaUy. If it is a wet mill, the tracer must be a solid of similar density to the ore. Materials hke copper concentrate, chrome brick, or barites have been used as tracers and analyzed by X-ray fluorescence. To plot results in log-normal coordinates, the concentration data must first be normalized from the form of Fig. 20-15 to the form of cumulative percent discharged, as in Fig. 20-16. For this, one must either know the total amount of pulse fed or determine it by a simple numerical integration... 

Axial Dispersion and the Peclet Number Peclet numbers are measures or deviation from phig flow. They may be calculated from residence time distributions found by tracer tests. Their values in trickle beds are fA to Ve, those of flow of liquid alone at the same Reynolds numbers. A correlation by Michell and Furzer (Chem. Eng. /., 4, 53 [1972]) is... 

Tracer A substance that is used for measuring the residence time distribution in a vessel. Usually, it is inert and used in small concentrations so as not to change the physical properties of the process fluid appreciably, and analyzable for accuracy. 

Only a few investigations concerned with the measurement of gas holdup and residence-time distribution have been reported. The information regarding liquid holdup, which will be discussed in the following section, is considerably more abundant in some cases, values of gas holdup can be deduced from the reported data on liquid holdup and total voidage. 

Glaser and Lichtenstein (G3) measured the liquid residence-time distribution for cocurrent downward flow of gas and liquid in columns of -in., 2-in., and 1-ft diameter packed with porous or nonporous -pg-in. or -in. cylindrical packings. The fluid media were an aqueous calcium chloride solution and air in one series of experiments and kerosene and hydrogen in another. Pulses of radioactive tracer (carbon-12, phosphorous-32, or rubi-dium-86) were injected outside the column, and the effluent concentration measured by Geiger counter. Axial dispersion was characterized by variability (defined as the standard deviation of residence time divided by the average residence time), and corrections for end effects were included in the analysis. The experiments indicate no effect of bed diameter upon variability. For a packed bed of porous particles, variability was found to consist of three components (1) Variability due to bulk flow through the bed... 

Ross (R2) measured liquid-phase holdup and residence-time distribution by a tracer-pulse technique. Experiments were carried out for cocurrent flow in model columns of 2- and 4-in. diameter with air and water as fluid media, as well as in pilot-scale and industrial-scale reactors of 2-in. and 6.5-ft diameters used for the catalytic hydrogenation of petroleum fractions. The columns were packed with commercial cylindrical catalyst pellets of -in. diameter and length. The liquid holdup was from 40 to 50% of total bed volume for nominal liquid velocities from 8 to 200 ft/hr in the model reactors, from 26 to 32% of volume for nominal liquid velocities from 6 to 10.5 ft/hr in the pilot unit, and from 20 to 27 % for nominal liquid velocities from 27.9 to 68.6 ft/hr in the industrial unit. In that work, a few sets of results of residence-time distribution experiments are reported in graphical form, as tracer-response curves. 

Kramers et al. (K21) measured gas residence-time distribution in a mechanically agitated gas-liquid contactor of 0.6-m diameter for various gas velocities and agitator speeds. In the region where agitation has an effect on the gas-liquid interfacial area (cf. the study by Westerterp et al. (W5), Section V,D,1), the residence-time distribution was found to resemble closely that of a perfect mixer. 

The time that a molecule spends in a reactive system will affect its probability of reacting and the measurement, interpretation, and modeling of residence time distributions are important aspects of chemical reaction engineering. Part of the inspiration for residence time theory came from the black box analysis techniques used by electrical engineers to study circuits. These are stimulus-response or input-output methods where a system is disturbed and its response to the disturbance is measured. The measured response, when properly interpreted, is used to predict the response of the system to other inputs. For residence time measurements, an inert tracer is injected at the inlet to the reactor, and the tracer concentration is measured at the outlet. The injection is carried out in a standardized way to allow easy interpretation of the results, which can then be used to make predictions. Predictions include the dynamic response of the system to arbitrary tracer inputs. More important, however, are the predictions of the steady-state yield of reactions in continuous-flow systems. All this can be done without opening the black box. 

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. 

The use of inert tracer experiments to measure residence time distributions can be extended to systems with multiple inlets and outlets, multiple phases within the reactor, and species-dependent residence times. This discussion ignores these complications, but see Suggestions for Further Reading. ... 

Positive Step Changes and the Cumulative Distribution. Residence time distributions can also be measured by applying a positive step change to the inlet of the reactor Cm = Cout = 0 for r<0 and C = Co for r>0. Then the outlet response, F i) = CouMICq, gives the cumulative distribution function. ... 

Roughly speaking, the first moment, t, measures the size of a residence time distribution, while higher moments measure its shape. The ability to characterize shape is enhanced by using moments about the mean ... 

Given k fit) for nny reactor, you automatically have an expression for the fraction unreacted for a first-order reaction with rate constant k. Alternatively, given ttoutik), you also know the Laplace transform of the differential distribution of residence time (e.g., k[f(t)] = exp(—t/t) for a PER). This fact resolves what was long a mystery in chemical engineering science. What is f i) for an open system governed by the axial dispersion model Chapter 9 shows that the conversion in an open system is identical to that of a closed system. Thus, the residence time distributions must be the same. It cannot be directly measured in an open system because time spent outside the system boundaries does not count as residence but does affect the tracer measurements. 

Resident Time Distribution (RTD) is widely employed in the chemical engineering industry, as an analytical tool for characterizing flow dynamics within reactor vessels. RTD provides a quantitative measure of the back-mixing with in a reactor system [2]. However the cost and time involved in building and operating a pilot- or full scale reactor for RTD analysis can be economically prohibitive. As such we have implemented a numerical RTD technique through the FLUENT (ver. 6.1) commercial CFD package. 

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