Tracer concentrations

The method is based on the international standard ISO 4053/IV. A small amount of the radioactive tracer is injected instantaneously into the flare gas flow through e.g. a valve, representing the only physical interference with the process. Radiation detectors are mounted outside the pipe and the variation of tracer concentration with time is recorded as the tracer moves with the gas stream and passes by the detectors. A control, supply and data registration unit including PC is used for on site data treatment... 

The main sources of error which define the accuracy are counting statistics in tracer concentration measurements, the dispersion of the tracer cloud in the flare gas stream, and the stationarity of the flow during measurements. 

In the case, where all 3 phases are present, the detector measurements reveal the amounts of tracers in each phase and the position of the boundaries between the phases The cross section area of each phase is calculated fi-om the latter. From this the tracer concentrations and hence the volume flows of the 3 phases are calculated. 

Measurements have been made in a static laboratory set-up. A simulation model for generating supplementary data has been developed and verified. A statistical data treatment method has been applied to estimate tracer concentration from detector measurements. Accuracy in parameter estimation in the range of 5-10% has been obtained. 

Figure 3. Tracers concentration versus time at input and output of a heat exchanger.

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.

Aircraft can take vertical temperature soundings and can measure air pollutant and tracer concentrations and turbulence intensity. Airborne lidar can measure plume heights, and integrating nephelometers can determine particle size distributions. 

If the tracer concentration is X measured at each sampling position that has its position at y, on a scale along the arc (either in degrees or in meters), estimates of the mean posiHon of the plume at ground level and the variance of the groundlevel concentration distribution are given by ... 

Fig. 19-11. Example of tracer concentration measurements along a sampling arc.

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 ... 

Tracer concentration in tlie outlet (or a quantity proportional to it) at time t... 

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. 

To determine if the local supply air reaches the breathing zone, a tracer gas is used. The tracer concentrations at various heights below the supply unit are recorded as a percentage of the supply duct tracer concentration. This provides information on the degree of mixing taking place between the and ambient air. 

The mixing time will be that required for the mixture composition to come within a specified deviation from the equilibrium value and this will be dependent upon the way in which the tracer is added and the location of the detector. It may therefore be desirable to record the tracer concentration at several locations, and to define the variance... 

In gridpoint models, transport processes such as speed and direction of wind and ocean currents, and turbulent diffusivities (see Section 4.8.1) normally have to be prescribed. Information on these physical quantities may come from observations or from other (dynamic) models, which calculate the flow patterns from basic hydrodynamic equations. Tracer transport models, in which the transport processes are prescribed in this way, are often referred to as off-line models. An on-line model, on the other hand, is one where the tracers have been incorporated directly into a d3mamic model such that the tracer concentrations and the motions are calculated simultaneously. A major advantage of an on-line model is that feedbacks of the tracer on the energy balance can be described... 

Development in recent years of fast-response instruments able to measure rapid fluctuations of the wind velocity (V ) and of fhe tracer concentration (c ), has made it possible to calculate the turbulent flux directly from the correlation expression in Equation (41), without having to resort to uncertain assumptions about eddy diffusivities. For example, Grelle and Lindroth (1996) used this eddy-correlation technique to calculate the vertical flux of CO2 above a foresf canopy in Sweden. Since the mean vertical velocity w) has to vanish above such a flat surface, the only contribution to the vertical flux of CO2 comes from the eddy-correlation term c w ). In order to capture the contributions from all important eddies, both the anemometer and the CO2 instrument must be able to resolve fluctuations on time scales down to about 0.1 s. 

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. 

Impulse Response and the Differential Distribution. Suppose a small amount of tracer is instantaneously injected at time 1 = 0 into the inlet of a reactor. All the tracer molecules enter together but leave at varying times. The tracer concentration at the outlet is measured and integrated with respect to time. The integral will be finite and proportional to the total quantity of tracer that was injected. The concentration measurement at the reactor outlet is normalized by this integral to obtain the impulse response function. ... 

The Single CSTR. The washout function for a CSTR is found from its response to a negative step change in tracer concentration from Equation (15.1) ... 

A tracer is injected into the reactor and its concentration is measured at a certain location. The observed tracer concentration will oscillate whereby the amplitude of the oscillations. A, decreases with time, finally approaching the asymptote determined by the averaged concentration over the mixing zone. This relationship can be presented as ... 

This is the response, in the outlet flow, which is obtained from a step change of tracer concentration in the reactor inlet and is shown below in Fig. 3.21. 

Figure 3.21. F-curve response to a step change in tracer concentration.

The time variations of the effluent tracer concentration in response to step and pulse inputs and the frequency-response diagram all contain essentially the same information. In principle, any one can be mathematically transformed into the other two. However, since it is easier experimentally to effect a change in input tracer concentration that approximates a step change or an impulse function, and since the measurements associated with sinusoidal variations are much more time consuming and require special equipment, the latter are used much less often in simple reactor studies. Even in the first two cases, one can obtain good experimental results only if the average residence time in the system is relatively long. 

Generalized response of an arbitrary reactor to a step change in input tracer concentration. 

If we now consider a step change in tracer concentration in the feed to an open tube that can be regarded as extending to infinity in both directions from the injection point, the appropriate initial and boundary conditions on... 

If we are determining the response of the series of stirred tank reactors to a step change in inlet tracer concentration from 0 to Cq at time zero, the initial condition for this differential equation is... 

Equations 11.1.62 and 11.1.64 may be combined to obtain the equation for the tracer concentration in the effluent from the second reactor when two reactors comprise the network. 

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