Inert tracer transient response

Equations (11) and (12) enable the generation of the total isotopic transient responses of a product species given (a) the transient response that characterises hypothesized catalyst-surface behaviour and (b) an inert-tracer transient response that characterises the gas-phase behaviour of the reactor system. Use of the linear-convolution relationships has been suggested as an iterative means to verify a model of the catalyst surface reaction pathway and kinetics. I This is attractive since the direct determination of the catalyst-surface transient response is especially problematic for non-ideal PFRs, since a method of complete gas-phase behaviour correction to obtain the catalyst-surface transient response is presently unavailable for such reactor systems.1 1 Unfortunately, there are also no corresponding analytical relationships to Eqs. (11) and (12) which permit explicit determination of the catalyst-surface transient response from the measured isotopic and inert-tracer transient responses, and hence, a model has to be assumed and tested. The better the model of the surface reaction pathway, the better the fit of the generated transient to the measured transient. 

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,... 

Figure 6. Transient responses at two consecutive downstream stations 4 and 6 to the same slug inputs of reactant undergoing first order reaction. The flow is a stretch of natural stream for which the responses to inert tracer (k = 0) are empirical (2). c0 = m/V.

Fig. 4. Typical normalized isotopic transient responses in product species P following an isotopic switch in reactant R— R. An inert tracer, I, is introduced to determine the gas-phase holdup of the reactor system.

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 dynamic model of the system. Table 1-1 lists the types of RTDs that can be measured using tracer experiments. The simplest case is a negative step change. Suppose that an inert tracer has been fed to the system for an extended period, giving Ci = Cout = Q for t < 0. At time t = 0, the tracer supply is suddenly stopped so that Cm = 0 for t > 0. Then the tracer concentration at the reactor outlet will decrease with time, eventually approaching zero as the tracer is washed out of the system. This response to a negative step change defines the washout function, W(t). The responses to other standard inputs are shown in Table 1-1. Relationships between the various functions are shown in Table 1-2. 

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