Tracer impulse method

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. 

Tracer impulse method In this method, a certain amount of tracer is injected (very short time interval) into the system and the concentration is measured at the outlet of the column. The concentration followed in time can directly be converted to the E(f) curve as described earlier. 

As for the RTD study in the gas phase, we have used the method of two injections. The response of the conductimetric probe to the input and output injections, with a Dirac tracer impulse, is shown in figure 6. In order to model the liquid flow, several theoretical models were tested. The liquid flow corresponded to plug flow with axial dispersion as shown in figure 7. 

Measurement techniques for the gas phase in CFB risers are becoming increasingly more sophisticated and accurate, and many find application in industrial-size equipment. In this section, we classify the different methods into five categories intrusive probes, steady state tracers, impulse (non-steady state) tracers, chemical reaction, and optical tracers. No single tracer technique is capable of quantifying... 

Frequently used macro-PDFs are the so-called Internal Age Distribution, /(a), and related Residence Time Distribution (RTD), E 6), which are closely related to the macro-PDF of the velocity, (v). The characteristics and practical use of the RTD are discussed in more detail in the next sub-sections. RTD methods are commonly based on the response of the reactor to a tracer impulse or step given at the reactor inlet. This implies statistically non-stationary calculations, for which (12.6.1-1) can be extended to... 

Since all tracer entered the system at the same time, t = 0, the response gives the distribution or range of residence times the tracer has spent in the system. Thus, by definition, eqn. (8) is the RTD of the tracer because the tracer behaves identically to the process fluid, it is also the system RTD. This was depicted previously in Fig. 3. Furthermore, eqn. (8) is general in that it shows that the inverse of a system transfer function is equal to the RTD of that system. To create a pulse of tracer which approximates to a dirac delta function may be difficult to achieve in practice, but the simplicity of the test and ease of interpreting results is a strong incentive for using impulse response testing methods. 

For many cases in which the RTD cannot be calculated theoretically, experimental techniques have been developed to measure it. Such techniques are used by introducing a tracer material into the system and recording its concentration at the exit.9 These methods are discussed in great detail in the literature. In general, a step change in tracer concentration results directly in the F(t) function, and an impulse type of tracer injection results directly in the/(f) function. 

The methods used in determining the RTD are an impulse signal and a step-change or a periodic input of the tracer. The following reviews these methods of injecting a tracer to analyze the RTD in flow systems. 

Vergnes107 has outlined a simple method for the determination of the Peclet number when the tracer injection is sharp enough to be considered as a true Dirac 6 impulse and the response equation is described by the solution of the dispersion model for a system open at both ends. The method does not require knowledge of the tracer quantity added, the sensitivity of the recorder, or the chart speed. 

Table 2.4 shows the power spectra of some input functions. Impulse and stochastic functions have high limit frequencies. Therefore impulse or stochastic methods should be prefered for tracer experiments in soil columns. 

The principle of a tracer experiment is the one of any common method impulse-response (Figure 4-1) injection of a tracer in the entrance of a system and a recording of the concentration-time curve at the exit. 

EXPERIMENTAL METHODS, 264 Intrusive Probes, 265 Steady State Tracers, 267 Impulse Tracers, 269 Optical Tracers, 274 Chemical Reaction, 276... 

As suggested, RTD measurements should be combined with other techniques to best quantify riser gas-phase hydrodynamics. Injection and detection methods are critical to interpreting the data. Iso-kinetic injection at different radii may help deconvolute inlet boundary conditions and flow structure. Multiple detectors along the riser length also are preferred. However, combining radial gas sampling, as practiced with steady state tracers, with radioactive impulse experiments could provide sufficient data to completely characterize riser gas-phase hydrodynamics. 

Program subroutine to calculate E versus theta from the impulse tracer test data Program subroutine to evaluate the integral value by trapezoidal method Program subroutine to calculate mean and variance from impulse tracer test data Program subroutine to calculate number of tanks n in tanks in series model Program subroutine to calculate Peclet number Pe... 

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 ... 

In the pulse method, the tracer is introduced momentarily (as a pulse) and the resulting response shows a maximum as illustrated in Figure 4.6a. If the tracer is introduced over a very short time interval—infinitesimally short—the pulse is called an impulse, and the mathematical treatment then becomes quite simple. The tracer can also be introduced by including several consecutive pulses of varying lengths in the system. In this case, we discuss a so-called pulse train. 

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