Tracer residence time

The present section indicates how tracer residence time data may be used to predict the conversion levels that will be obtained in re-... 

In the present section we indicate how tracer residence time data may be used to predict the conversion levels that will be obtained in reactors with nonideal flow patterns. As indicated earlier, there are two types of limiting processes that can lead to a distribution of residence times within a reactor network. 

Equation (7) has been used traditionally in medicine as the Stewart-Hamilton indicator-dilution technique (23-25) to measure the unknown flow rate through isolated organs. In this method a known bolus, mr, of tracer is injected into an artery and the tracer dilution curve, Cp(t), is measured at the outflow in a major vein. In chemical engineering systems eq. (7) should be used as a basic mass balance consistency check on the accuracy of the tracer experiment. Failure to satisfy eq. (7) indicates errors and nonidealities, and requires repeats of the experiment at different mij, s to establish linearity. On occasion, only a response R(t), which is linearly proportional to tracer concentration, is measured and the mass injected m,j, is unknown. Then the experiment should be repeated to establish linearity of R(t) with respect to HLp. The obtained age density function R(t)// R(t)dt should be invariant to the mass injected. Although the above simple rules are rather evident, they are all too often neglected by practitioners. Unfortunately, not all tracers at concentrations used behave ideally, and erroneous conclusions result when the nonideal tracer residence time distribution is accepted as the F curve of the system. The tracer tests needed to determine E(t), F(t) and W(t) functions are schematically represented in Figure 1. 

Hinze, J. 0. Turbulence (New York, McGraw Hill, 1975). Danckwerts, P. V. Tracers, Residence Times, Mixing and Dispersion. Lecture Notes (Pittsburgh, University of Pittsburgh, 1976). 

Fig. 7. Residence time distributions where U = velocity, V = reactor volume, t = time, = UtjV, Cj = tracer concentration to initial concentration and Q = reactor volume (a) output responses to step changes (b) output responses to pulse inputs.

Residence Time Distribution (RTD) This is established by injecting a known amount of tracer into the feed stream and monitor-... 

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... 

The distribution of residence times of reactants or tracers in a flow vessel, the RTD, is a key datum for determining reactor performance, either the expected conversion or the range in which the conversion must fall. In this section it is shown how tracer tests may be used to estabhsh how nearly a particular vessel approaches some standard ideal behavior, or what its efficiency is. The most useful comparisons are with complete mixing and with plug flow. A glossary of special terms is given in Table 23-3, and major relations of tracer response functions are shown in Table 23-4. 

Nonreacdive substances that can be used in small concentrations and that can easily be detected by analysis are the most useful tracers. When making a test, tracer is injected at the inlet of the vessel along with the normal charge of process or carrier fluid, according to some definite time sequence. The progress of both the inlet and outlet concentrations with time is noted. Those data are converted to a residence time distribution (RTD) that tells how much time each fracdion of the charge spends in the vessel. 

Residence time distiabution (RTD) In the case of elutriation of tracer from a vessel that contained an initial average concentration the area under a plot of E t) = between the ordinates at ti and to is the fraction of the... 

The chief quantities based on tracer tests are summarized in Table 23-4. Effluent concentrations resulting from impulse and step inputs are designated Cg and C , respectively. The initial mean concentration resulting from an impulse of magnitude m into a vessel of volume is C = mfVr- The mean residence time is the ratio of the vessel volume to the volumetric flow rate, t = V fV or t = jo tCg dt/jo Cg dt. The reduced time is t = t/t. 

FIG. 23-7 Imp ulse and step inputs and responses. Typical, PFR and CSTR. (a) Experiment with impulse input of tracer, (h) Typical behavior area between ordinates at tg and ty equals the fraction of the tracer with residence time in that range, (c) Plug flow behavior all molecules have the same residence time, (d) Completely mixed vessel residence times range between zero and infinity, e) Experiment with step input of tracer initial concentration zero. (/) Typical behavior fraction with ages between and ty equals the difference between the ordinates, h — a. (g) Plug flow behavior zero response until t =t has elapsed, then constant concentration Cy. (h) Completely mixed behavior response begins at once, and ultimately reaches feed concentration. 

A distinc tion is to be drawn between situations in which (1) the flow pattern is known in detail, and (2) only the residence time distribution is known or can be calculated from tracer response data. Different networks of reactor elements can have similar RTDs, but fixing the network also fixes the RTD. Accordingly, reaction conversions in a known network will be unique for any form of rate equation, whereas conversions figured when only the RTD is known proceed uniquely only for hnear kinetics, although they can be bracketed in the general case. 

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... 

All fluid elements have some residence time, therefore, over a sufficiently long period, all tracer will eventually come out. This is represented by... 

In a time period from t = 0 to t = 6t seconds, a quantity m (g) of a tracer is introduced at the system inlet, and the tracer concentration C(t) (g/1) is measured in the exit from the system. Subject to the above conditions, the residence time density function from the measured tracer response is ... 

A table was constructed to determine the mean residence time t, variance E(6), F(6), and 1(6) parameters from the effluent tracer versus time data. 

The distribution of tracer molecule residence times in the reactor is the result of molecular diffusion and turbulent mixing if tlie Reynolds number exceeds a critical value. Additionally, a non-uniform velocity profile causes different portions of the tracer to move at different rates, and this results in a spreading of the measured response at the reactor outlet. The dispersion coefficient D (m /sec) represents this result in the tracer cloud. Therefore, a large D indicates a rapid spreading of the tracer curve, a small D indicates slow spreading, and D = 0 means no spreading (hence, plug flow). 

A practical method of predicting the molecular behavior within the flow system involves the RTD. A common experiment to test nonuniformities is the stimulus response experiment. A typical stimulus is a step-change in the concentration of some tracer material. The step-response is an instantaneous jump of a concentration to some new value, which is then maintained for an indefinite period. The tracer should be detectable and must not change or decompose as it passes through the mixer. Studies have shown that the flow characteristics of static mixers approach those of an ideal plug flow system. Figures 8-41 and 8-42, respectively, indicate the exit residence time distributions of the Kenics static mixer in comparison with other flow systems. 

In the case of tracer from a vessel that contained an initial average concentration C°, the area under a plot of E(t) = Cgff[ygj,/C° between the ordinates at tj and tj is the fraction of the molecules that have residence times in this range. In the case of step constant input of concentration Cf to a vessel with zero initial concentration, the ratio F(t) = Cgff ygj,/Cf at tj is the fraction of molecules with residence time less than tj. 

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. 

As we have said, the key to the analysis of asystemlike this one is tohave a function that approximates to the actual residence time distribution. The tracer experiment is used to find that distribution function,butwewillworkfroman assumed function to the tracer concentration-timecurvetoseewhattheexperimentaloutcomemightlooklike. 

Schiesser and Lapidus (S3), in later studies, measured the liquid residencetime distribution for a column of 4-in. diameter and 4-ft height packed with spherical particles of varying porosity and nominal diameters of in. and in. The liquid medium was water, and as tracers sodium chloride or methyl orange were employed. The specific purposes of this study were to determine radial variations in liquid flow rate and to demonstrate how pore diffusivity and pore structure may be estimated and characterized on the basis of tracer experiments. Significant radial variations in flow rate were observed methods are discussed for separating the hydrodynamic and diffusional contributions to the residence-time curves. 

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. 

Hoogendoorn and Lips (H10) carried out residence-time distribution experiments for countercurrent trickle flow in a column of 1.33-ft diameter and 5- and 10-ft height packed with -in. porcelain Raschig rings. The fluid media were air and water, and ammonium chloride was used as tracer. The total liquid holdup was calculated from the mean residence time as found... 

The residence time is the time spent in a reservoir by an individual atom or molecule. It is also the age of a molecule when it leaves the reservoir. If the pathway of a tracer from the source to the sink is characterized by a physical transport, the word transit time can also be used. Even for a single chemical substance, different atoms and molecules will have different residence times in a given reservoir. Let the probability density... 

As mentioned in Section 11.3, fluidized-bed reactors are difficult to scale. One approach is to build a cold-flow model of the process. This is a unit in which the solids are fluidized to simulate the proposed plant, but at ambient temperature and with plain air as the fluidizing gas. The objective is to determine the gas and solid flow patterns. Experiments using both adsorbed and nonadsorbed tracers can be used in this determination. The nonadsorbed tracer determines the gas-phase residence time using the methods of Chapter 15. The adsorbed tracer also measures time spent on the solid surface, from which the contact time distribution can be estimated. See Section 15.4.2. 

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. 

Transient experiments with inert tracers are used to determine residence time distributions. In real systems, they will be actual experiments. In theoretical studies, the experiments are mathematical and are applied to a d5mamic model of the system. 

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. 

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