Residence-time distributions step tracer experiment

A practical method of predicting the molecular behavior within the flow system involves the RTD. A common experiment to test nonuniformities is the stimulus response experiment. A typical stimulus is a step-change in the concentration of some tracer material. The step-response is an instantaneous jump of a concentration to some new value, which is then maintained for an indefinite period. The tracer should be detectable and must not change or decompose as it passes through the mixer. Studies have shown that the flow characteristics of static mixers approach those of an ideal plug flow system. Figures 8-41 and 8-42, respectively, indicate the exit residence time distributions of the Kenics static mixer in comparison with other flow systems. 

Washout experiments can be used to measure the residence time distribution in continuous-flow systems. A good step change must be made at the reactor inlet. The concentration of tracer molecules leaving the system must be accurately measured at the outlet. If the tracer has a background concentration, it is subtracted from the experimental measurements. The flow properties of the tracer molecules must be similar to those of the reactant molecules. It is usually possible to meet these requirements in practice. The major theoretical requirement is that the inlet and outlet streams have unidirectional flows so that molecules that once enter the system stay in until they exit, never to return. Systems with unidirectional inlet and outlet streams are closed in the sense of the axial dispersion model i.e., Di = D ut = 0- See Sections 9.3.1 and 15.2.2. Most systems of chemical engineering importance are closed to a reasonable approximation. 

The deviation of a real (continuously operated) reactor from ideal systems is deduced from the residence time distribution (RTD), which is measured by a pulse or by a step experiment. For a pulse experiment, a small amount of tracer is introduced into the feed stream, and the exit tracer concentration is measured with time ( function). For a step experiment, at time t = 0 we switch to a fluid with a tracer of constant concentration, and the exit tracer concentration versus time is measured (Ffunction). 

F(t) is a probability distribution which can be obtained directly from measurements of the system s response in the outflow to a step-up tracer input in the inflow. Consider that at time t = 0 we start introducing a red dye at the entrance of the vessel into a steady flow rate Q of white carrier fluid. The concentration of the red dye in the inlet flow is C. At the outlet we monitor the concentration of the red dye, C(t . If our system is closed, i.e. if every molecule of dye can have only one entry and exit from the system (which is equivalent to asserting that input and output occur by convection only), then QC(t)/QCQ is the residence time distribution of the dye. This is evident since all molecules of the dye appearing at the exit at time t must have entered into the system between time 0 and time t and hence have residence times less than t. Only if our red dye is a perfect tracer, i.e.. if it behaves identically to the white carrier fluid, then we have also obtained the residence time distribution for the carrier fluid and F(t) = C(t)/C. To prove that the tracer behaves ideally and that the F curve is obtained, the experiment should be repeated at different levels of C. The ratio C(t)/C at a given time should be invariant to C, i.e. the tracer response and tracer input must be linearly related. If this is not the case, then C(t)/CQ is only the step response for the tracer, which includes some nonlinear effects of tracer interactions in the system, and which does not represent the true residence time distribution for the 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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