Measurement of the RTD

The RTD is determined experimentally by injeeting an inert chemical, molecule, or atom, called a tracer, into the reactor at some time t = 0 and then measuring the tracer concentration, C, in the effluent stream as a function of time. In addition to being a nomeaetive species that is easily detectable, the tracer should have physical properties similar to those of the reacting mixture and be completely soluble in the mixture. It also should not adsorb on the walls or other smfaces in the reaetor. The latter requirements are needed so that the tracer s behavior will honestly refleet that of the material flowing 

of through the reactor. Colored and radioactive materials are the two most com- 

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Residence-Time Distribution (RTDj Function Measurement of the RTD 871... 

As explained in Section 12.3, the RTD can be calculated a posteriori from a PDF or CFD calculation, allowing comparison with an experimental RTD or avoiding the measurement of the RTD. 

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. 

The RTD quantifies the number of fluid particles which spend different durations in a reactor and is dependent upon the distribution of axial velocities and the reactor length [3]. The impact of advection field structures such as vortices on the molecular transit time in a reactor are manifest in the RTD [6, 33], MRM measurement of the propagator of the motion provides the velocity probability distribution over the experimental observation time A. The residence time is a primary means of characterizing the mixing in reactor flow systems and is provided directly by the propagator if the velocity distribution is invariant with respect to the observation time. In this case an exact relationship between the propagator and the RTD, N(t), exists... 

The exit-age distribution function is a measure of the distribution of the ages of fluid elements leaving a vessel, and hence is an RTD function. As a function of time, f, it is defined as ... 

An RTD curve, for instance, can be represented in algebraic form in more than one way and for different purposes. The characteristic bell shape of many RTDs is evident in the real examples of Figure 5.4. Such shapes invite comparison with some well-known statistical distributions and representation of the RTD by their equations. Or a realistic mechanism may be postulated, such as a network of reactor elements and a type of flow pattern, and the parameters of that mechanism evaluated from a measured RTD. 

The response of the RTDs and the temperature of the screw were tested with the screw not rotating. For this experiment, the temperatures were first measured with the extruder at ambient conditions. Next, the barrel temperature set points were increased to 200, 220, and 240 °C for Zones 1, 2, and 3, respectively. The downstream die system was heated at the same time as the barrel and at a set point temperature equal to Zone 3 (240 °C). The temperature profile of the screw as a function of axial length is shown in Fig. 10.19 for select heating times. For heating... 

The RTD in a system is a measure of the degree to which fluid elements mix. In an ideal plug flow reactor, there is no mixing, while in a perfect mixer, the elements of different ages are uniformly mixed. A real process fluid is neither a macrofluid nor a microfluid, but tends toward one or the other of these extremes. Fluid mixing in a vessel, as reviewed in Chapter 7, is a complex process and can be analyzed on both macroscopic and microscopic scales. In a non-ideal system, there are irregularities that account for the fluid mixing of different... 

Here, C (t) is the concentration of the tracer at time t on the RTD curve at position i, U is the real mean axial velocity of the phase being considered, L is the distance between two measuring points, fit is the first moment and zrfjs the second moment of the RTD curve. Since the first moment of the response curve is essentially the mean of that curve, the average residence time of the tracer can be calculated by taking the difference of the first moment of the response curves... 

The second moment of the response curves indicates the spread of the RTD curve and the difference of the second moments is a measure of the amount of backmixing occurring between the two measuring points. For the.opea system, the second moment has been derived analytically by Levenspiel and Smith58 as... 

Heaviside Step Function This function implies measurements of the integrated function of the distribution curve, cumulative RTD function F t). This can be established by changing one liquid (usually water) from one steady value to another with a detectable tracer. The equation that relates this measurement to the tracer impulse method is F i) = E t)dt. 

The Helium injection occurs via secondary air flow to determine the state of mixedness in the SCC (see Figure 4), Square waves with a period of 30 s are used to excite the system during 5 minutes. Therefore 10 step responses in both directions result, such that every 15 seconds new measurement data of the state of mixedness are provided. Each step response is evaluated individually as shown in Figure 7 and thus the model parameters are determined off-line for every 15 sec. This corresponds to the time resolution of the RTD measurement system. 

The measured mean residence time and shape of the RTD curve provide valuable information on the flow of the reacting fluid in the reactor. Based on fundamental physical concepts, the mean residence time is the quotient of the volume of the reacting fluid in the reactor and its volumetric flow rate ... 

Now, consider a second example, that of turbulent flow through the tube. Again there exists some sort of velocity profile, but in addition there is some level of micromixing due to eddy motion among the elements. In this case it is possible to identify a distribution of residence times for individual molecules within the system, not volume elements, and the RTD is a measure of the combined effects of macro-and micromixing. 

Using the analogy with proltobility theory, a useful measure of the width of the RTD is the variance with respect to the mean residence time ... 

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