Tracer responses

Quantitatively, the efficiency at a specified conversion level, x, is defined as the ratio of the mean residence time or reactor volume in a plug flow reactor (PFR) to that of the reactor in question, 

Other measures of efficiency are derived from the experimental RTD. Such a curve is characterized at least approximately by the variance, r2(tr). This quantity is zero for plug flow and unity for complete mixing, so there are natural bounds to the variance and thus to the efficiency. The quantity, 

A related measure of efficiency is the equivalent number of stages, nErlang in a CSTR battery with the same variance as the measured RTD. The dispersion coefficient, De also is a measure of deviation from plug flow and has the merit that limited correlations in terms of operating conditions have been made. 

At present, the chief value of RTD studies is for the diagnosis of the performance of existing equipment, for instance maldistribution of catalyst in a packed reactor, or the presence of bypassing or stagnant zones in stirred tanks. No correlations have been achieved for cr2(tr) or TiErlang in terms of operating conditions, and only limited correlations for De. 

Tracer response is formulated as an unsteady material balance in terms of linear differential equations with constant coefficients that relate an input function, Cf(t), to a response function, C(t). Such equations of ordinary type have the form 

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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. 

FIG. Tracer responses to n-stage continuous stirred tank batteries the Erlang model (a) impulse inputs, (h) step input. 

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. 

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 ... 

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. 

The forms of actual tracer response curves may be used to formulate models of the actual mixing processes in the reactor. One has, however, to be careful since the tracer response curve does not give a unique solution. It does, for example, not allow one to distinguish between early and late mixing, which may be important when used in the estimation of conversion in a particular reactor-reaction system. 

More complex situations can be imagined, for example, the combination of stirred-tanks, bypassing and stagnant zones. Care must be taken to establish the model parameters carefully however and not to merely fit the tracer response data. Experimental E-curve data is given in Fig. 3.27 and a possible model for this is shown in Fig. 3.28. 

Setting k = 0, simulate the tracer response (F-curves) for 3 perfectly-stirred tanks in series. 

The pulse tracer response, giving the E-curve response, can be used directly to calculate the steady-state conversion for a first-order reaction according to the relationship... 

Obtain the tracer response curve to a step input disturbance of tracer solution by setting k = 0. 

Study the effect of varying Peclet number, Pe, on the resulting tracer response. 

Tracer response curve. Reprinted from M. J. Hopkins, A. J. Sheppard and P. Eisenklam, Chem. Eng. Sci., 24 (1131), 1969. Used with permission of Pergamon Press, Ltd. 

In an effort to determine the cause of low yields from a reactor, a tracer study was conducted. An amount m0 = 3.80 kg of an inert tracer A was injected into the feed port of the 1. 9-m3 reactor. The volumetric flow rate was constant at q0 = 3.1 L s-1. The following tracer-response data were acquired ... 

Figure 19.9 Tailing of tracer response (a) linear coordinates (b) semi-log coordinates...

Determining Pe, from Tracer Data As noted in Section 19.4.2.2.1, values of PeL, the single parameter in the axial dispersion model, may be obtained from the characteristics of the pulse-tracer response curve, C(0) = E(6). 

C(t) normalized pulse tracer response (at vessel outlet), s 1, equation 19.3-4... 

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. 

Positive tracer responses were noted in nine (9) production wells located inside the Marbel and three (3) production wells inside the Sandawa. 

A number of special terms are defined in the Glossary, Table 5.1. Equations for tracer response functions are summarized in Table 5.2. 

Normalized tracer response data for a packed bed hydrodesulfurizer are tabulated.The time will be found at which 75% of the tracer has left the vessel. The fraction of the tracer that has exited the vessel is represented by the integral of the last column. Interpolating, E(tr) - 0.75 when tr = 1.05. 

P5.02.13. TRIANGULAR RESPONSE. EQUIVALENT GAMMA AND GAUSSIAN RTD S A triangular shaped tracer response has the equation C3 = 2.5 - 0.5t, for l t 5 and zero elsewhere. The Gamma and Gaussian E(tr) with the same variance will be found. 

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