Outlet residence time distribution

Nonreacdive substances that can be used in small concentrations and that can easily be detected by analysis are the most useful tracers. When making a test, tracer is injected at the inlet of the vessel along with the normal charge of process or carrier fluid, according to some definite time sequence. The progress of both the inlet and outlet concentrations with time is noted. Those data are converted to a residence time distribution (RTD) that tells how much time each fracdion of the charge spends in the vessel. 

Example 14.6 derives a rather remarkable result. Here is a way of gradually shutting down a CSTR while keeping a constant outlet composition. The derivation applies to an arbitrary SI a and can be extended to include multiple reactions and adiabatic reactions. It is been experimentally verified for a polymerization. It can be generalized to shut down a train of CSTRs in series. The reason it works is that the material in the tank always experiences the same mean residence time and residence time distribution as existed during the original steady state. Hence, it is called constant RTD control. It will cease to work in a real vessel when the liquid level drops below the agitator. 

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. 

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 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. ... 

Positive Step Changes and the Cumulative Distribution. Residence time distributions can also be measured by applying a positive step change to the inlet of the reactor Cm = Cout = 0 for r<0 and C = Co for r>0. Then the outlet response, F i) = CouMICq, gives the cumulative distribution function. ... 

The completely segregated stirred tank can be modeled as a set of piston flow reactors in parallel, with the lengths of the individual piston flow elements being distributed exponentially. Any residence time distribution can be modeled as piston flow elements in parallel. Simply divide the flow evenly between the elements and then cut the tubes so that they match the shape of the washout function. See Figure 15.12. A reactor modeled in this way is said to be completely segregated. Its outlet concentration is found by averaging the concentrations of the individual PFRs ... 

The characterization is performed by means of residence time distribution (RTD) investigation [23]. Typically, holdup is low, and therefore the mean residence time is expected to be relatively short Consequently, it is required to shorten the distance between the pulse injection and the reactor inlet. Besides, it is necessary to use specific experimental techniques with fast time response. Since it is rather difficult, in practice, to perfectly perform a Dirac pulse, a signal deconvolution between inlet and outlet signals is always required. 

One method of characterising the residence time distribution is by means of the E-curve or external-age distribution function. This defines the fraction of material in the reactor exit which has spent time between t and t -i- dt in the reactor. The response to a pulse input of tracer in the inlet flow to the reactor gives rise to an outlet response in the form of an E-curve. This is shown below in Fig. 3.20. 

If this is the case, the design and configuration of the gas outlet in the freeboard region can have an important effect on the fines residence time distribution and holdup above the bed. The importance of the freeboard region for further reaction of fines merits greater emphasis in both experimental and theoretical studies. 

In a laminar flow reactor (LFR), we assume that one-dimensional laminar flow (LF) prevails there is no mixing in the (axial) direction of flow (a characteristic of tubular flow) and also no mixing in the radial direction in a cylindrical vessel. We assume LF exists between the inlet and outlet of such a vessel, which is otherwise a closed vessel (Section 13.2.4). These and other features of LF are described in Section 2.5, and illustrated in Figure 2.5. The residence-time distribution functions E(B) and F(B) for LF are derived in Section 13.4.3, and the results are summarized in Table 13.2. 

The integral for a batch reaction is tabulated in the first two columns. A potential reactor has the residence time distribution E(t) given in column 3. Find the outlet concentration in segregated flow. 

The IEM model is a simple example of an age-based model. Other more complicated models that use the residence time distribution have also been developed by chemical-reaction engineers. For example, two models based on the mixing of fluid particles with different ages are shown in Fig. 5.15. Nevertheless, because it is impossible to map the age of a fluid particle onto a physical location in a general flow, age-based models cannot be used to predict the spatial distribution of the concentration fields inside a chemical reactor. Model validation is thus performed by comparing the predicted outlet concentrations with experimental data. 

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. 

P 62] A Lagrangian particle tracking technique, i.e. the computation of trajectories of massless tracer particles, which allows the computation of interfacial stretching factors, was coupled to CFD simulation [47]. Some calculations concerning the residence time distribution were also performed. A constant, uniform velocity and pressure were applied at the inlet and outlet, respectively. The existence of a fully developed flow without any noticeable effect of the inlet and outlet boundaries was assured by inspection of the computed flow fields obtained in the third mixer segment for all Reynolds numbers under study. 

The following example examines the SDF in drag flow between parallel plates. In this particular flow geometry, although the shear rate is constant throughout the mixer, a rather broad SDF results because of the existence of a broad residence time distribution. Consequently, a minor component, even if distributed at the inlet over all the entering streamlines and placed in an optimal orientation, will not be uniformly mixed in the outlet stream. 

This common measure is the variance of the residence-time distribution. In the absence of reaction, a sudden change in inlet conditions will be followed by a spread-out change in outlet conditions. The spreading can be described by common statistical parameters, the mean, variance, skewness, and so on. 

Real reactors deviate more or less from these ideal behaviors. Deviations may be detected with residence time distributions (RTD) obtained with the aid of tracer tests. In other cases a mechanism may be postulated and its parameters checked against test data. The commonest models are combinations of CSTRs and PFRs in series and/or parallel. Thus, a stirred tank may be assumed completely mixed in the vicinity of the impeller and in plug flow near the outlet. 

A well-known traditional approach adopted in chemical engineering to circumvent the intrinsic difficulties in obtaining the complete velocity distribution map is the characterization of nonideal flow patterns by means of residence time distribution (RTD) experiments where typically the response of apiece of process equipment is measured due to a disturbance of the inlet concentration of a tracer. From the measured response of the system (i.e., the concentration of the tracer measured in the outlet stream of the relevant piece of process equipment) the differential residence time distribution E(t) can be obtained where E(t)dt represents... 

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