Inert tracer

For operation with an inert tracer, the material balances are conveniently handled as Laplace transforms. For a stirred tank, the differential equation... 

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. 

Negative Step Changes and the Washout Function. Suppose that an inert tracer has been fed to a CSTR for an extended period of time, giving C, = Cout = Co for r < 0. At time r = 0, the tracer supply is suddenly stopped so that = 0 for r > 0. Equation (14.2) governs the transient response of the system. For t > 0,... 

The use of inert tracer experiments to measure residence time distributions can be extended to systems with multiple inlets and outlets, multiple phases within the reactor, and species-dependent residence times. This discussion ignores these complications, but see Suggestions for Further Reading. ... 

Thus, t can be found from inert tracer experiments. It can also be found from measurements of the system inventory and throughput since... 

Agreement of the t values calculated by these two methods provides a good check on experimental accuracy. Occasionally, Equation (15.13) is used to determine an unknown volume or an unknown density from inert tracer data. 

The Piston Flow Reactor. Any input signal of an inert tracer is transmitted through a PFR without distortion but with a time delay of F seconds. When the input is a negative step change, the output will be a delayed negative step change. Thus, for a PFR,... 

Solution The dynamic model governing the flow of an inert tracer through an unsteady PFR is Equation (14.13) with =0 ... 

This result allows the unsteady output to be calculated when component A reacts with first-order kinetics. The case k = 0, corresponding to an inert tracer, is also of interest ... 

Example 15.11 Suppose the input of an inert tracer to a CSTR varies sinusoidally ... 

C(t, z) capacity model Concentration of inert tracer in an unsteady tubular Exam. 15.4... 

Concentration of inert tracer in the side tank of the Exam. 15.7 capacity model... 

K. Luby-Phelps, P. E. Castle, D. L. Taylor, and F. Lanni, Hindered diffusion of inert tracer particles in the cytoplasm of mouse 3T3 cells, Proc. Natl. Acad. Sci. USA 84, 4910 (1987). 

We now want to use an impulse input of equivalent "strength," /.e.. same amount of inert tracer added. The amount of additional tracer in the rectangular pulse is... 

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 ... 

Equation (2.2) can be considered as the fundamental governing equation for the concentration of an inert constituent in a turbulent flow. Because the flow in the atmosphere is turbulent, the velocity vector u is a random function of location and time. Consequently, the concentration c is also a random fimction of location and time. Thus, the dispersion of a pollutant (or tracer) in the atmosphere essentiaUy involves the propagation of the species molecules through a random medium. Even if the strength and spatial distribution of the source 5 are assumed to be known precisely, the concentration of tracer resulting from that source is a random quantity. The instantaneous, random concentration, c(x, y, z, t), of an inert tracer in a turbulent fluid with random velocity field u( c, y, z, t) resulting from a source distribution S x, y, z, t) is described by Eq. (2.2). 

We have now derived two fundamentally different expressions for the mean concentration of an inert tracer in a turbulent flow Eqs. (2.7) and (2.19). To compute the mean concentration c from Eq. (2.7) requires only that p(x, y, z, t x, y, z, t ), the transition probability density, be specified, whereas the mean velocities and eddy diffiisivities must be prescribed to obtain c from Eq. (2.19). In the next section we see how forms of c are obtained from Eqs. (2.7) and (2.19). 

The residence time distribution is measured by monitoring the outlet concentration of an inert tracer that can be analyzed for accuracy. The shape of response curve is compared with that of a thoroughly (ideally) mixed tank. 

In the most useful form the test consists of a momentary injection of a known amount of inert tracer at the inlet of the operating vessel and monitoring of its concentration at the outlet. The data are used most conveniently in reduced form, as E — C/C0 in terms of tr — t/t, where... 

The Airborne Submillimeter SIS Radiometer (ASUR), operated on-board the German research aircraft FALCON, measures thermal emission lines of stratospheric trace gases at submillimeter wavelength. Measurement campaigns with respect to ozone depletion in the Arctic winter stratosphere were carried out in yearly intervals from 1992-97 to investigate the distributions of the radical chlorine monoxide (CIO), the reservoir species hydrochloric acid (HC1), the chemically inert tracer nitrous oxide (N20), and ozone (O3). The high sensitivity of the receiver allowed to take spatially well resolved measurements inside, at the edge, and outside of the Arctic polar vortex. This paper focuses on the results obtained for CIO from... 

Mass transport in laminar flow is dominated by diffusion and by the laminar velocity profile. This combined effect is known as dispersion and the underlying model for the theoretical derivation of a kinetic study had to be derived from the dispersion model, which Taylor [91] and Aris [92] developed. Taylor concluded that in laminar flow the speed of an inert tracer impulse initially given to a channel will have the same speed as the steady laminar carrier gas flow originally prevailing in this channel. 

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