Residence-time distribution characteristics

In a continuous reaction process, the true residence time of the reaction partners in the reactor plays a major role. It is governed by the residence time distribution characteristic of the reactor, which gives information on backmixing (macromixing) of the throughput. The principal objectives of studies into the macrokinetics of a process are to estimate the coefficients of a mathematical model of the process and to validate the model for adequacy. For this purpose, a pilot plant should provide the following ... 

The rate-based stage model parameters describing the mass transfer and hydrodynamic behavior comprise mass transfer coefficients, specific contact area, liquid hold-up, residence time distribution characteristics and pressure drop. Usually they have to be determined by extensive and expensive experimental estimation procedures and correlated with process variables and specific internals properties. 

For heat transfer applications the static mixer has an advantage over the empty tube in that it has a much more uniform residence time distribution characteristic, further reducing the possibility of damage to heat sensitive materials. The more uniform residence time characteristic has other advantages, particularly for the design of continuous flow tubular reactors. 

Topics that acquire special importance on the industrial scale are the quality of mixing in tanks and the residence time distribution in vessels where plug flow may be the goal. The information about agitation in tanks described for gas/liquid and slurry reactions is largely apphcable here. The relation between heat transfer and agitation also is discussed elsewhere in this Handbook. Residence time distribution is covered at length under Reactor Efficiency. A special case is that of laminar and related flow distributions characteristic of non-Newtonian fluids, which often occiu s in polymerization reactors. 

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. 

At this stage, type (1) is more apparent than type (2), and we provide some preliminary discussion of (2) here. Flow characteristics include relative times taken by elements of fluid to pass through the reactor (residence-time distribution), and mixing character-... 

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. 

Reactive Tracer. If the tracer is reactive, the measured concentrations reflect both mixing characteristics and decay of the tracer. Therefore, the data must be adjusted, such that the residence time distribution within the reactor can be obtained. Example 19-3 illustrates how to adjust the data following a step input of a reactive tracer. 

Residence time distributions can be determined in practice by injecting a non-reactive tracer material into the input flow to the reactor and measuring the output response characteristics in a similar manner to that described previously in Section 2.1.1. 

The length and the distribution of chain lengths are functions of the temperature, pressure, residence time, catalyst characteristics, and the proportion of ethylene present in the reaction, A measure of this is the mole ratio of ethylene, which measures the weight of ethylene compared to the weight of triethyl aluminum in scales related to their atomic weights. As an example, Table 15-2 shows how the distribution of chain lengths can vary, using different mole ratios of ethylene to triethyl aluminum. 

With the development of modern computation techniques, more and more numerical simulations occur in the literature to predict the velocity profiles, pressure distribution, and the temperature distribution inside the extruder. Rotem and Shinnar [31] obtained numerical solutions for one-dimensional isothermal power law fluid flows. Griffith [25], Zamodits and Pearson [32], and Fenner [26] derived numerical solutions for two-dimensional fully developed, nonisothermal, and non-Newtonian flow in an infinitely wide rectangular screw channel. Karwe and Jaluria [33] completed a numerical solution for non-Newtonian fluids in a curved channel. The characteristic curves of the screw and residence time distributions were obtained. 

In a final RTD experiment, a sheet of dye was frozen as before and positioned in the feed channel perpendicular to the flight tip. The sheet positioned the dye evenly across the entire cross section. After the dye thawed, the extruder was operated at five rpm in extrusion mode. The experimental and numerical RTDs for this experiment are shown in Fig. 8.12, and they show the characteristic residence-time distribution for a single-screw extruder. The long peak indicates that most of the dye exits at one time. The shallow decay function indicates wall effects pulling the fluid back up the channel of the extruder, while the extended tail describes dye trapped in the Moffat eddies that greatly impede the down-channel movement of the dye at the flight corners. Moffat eddies will be discussed more next. Due to the physical limitations of the process, sampling was stopped before the tail had completely decreased to zero concentration. 

From this point of view, it was tried previously to correlate the CSD to the characteristics of continuous crystallizers, under the assumption that the CSD is controlled predominantly by the flow pattern in crystallizer, namely the residence time distribution (RTD) of the crystals, and to examine the correlation thus obtained, by applying to the real data on two kinds of compounds in CEC type crystallizer. As the results, the procedures was found to be useful to inspect the characteristics of crystallizer (1). Whereupon, in order to get the correlation, the following additional assumptions were made 1) the crystal flow in the real crystallizer is expressed by the... 

Han, W., Mai, B. and Gu, T., Residence time distribution and drying characteristics of a continuous vibro-fluidized bed. Drying Tech., 9 (1991) 159-181. 

Comparative measurements of residence time for rotor designs A and B showed relatively small differences in the width of the residencetime distribution characteristics. In Figure 5, the modified Pe number [according to Levenspiel (11)] is used to demonstrate the residencetime distribution. A lower Pe number corresponds to an increased degree of mixing and will be accompanied by a broader residence time distribution. 

A characteristic of micro-channel reactors is their narrow residence-time distribution. This is important, for example, to obtain clean products. This property is not imaginable without the influence of dispersion. Considering only the laminar flow would... 

A theoretical analysis is helpful for understanding the basic characteristics of impinging stream processes and the performances of the related devices. In an impinging stream device, where the residence time distribution of particles is most important is in the impingement zone, because this zone is the major active region for heat and mass transfer between phases in such a device. Unfortunately, it is basically... 

An impinging stream contactor usually contains several flow spaces of different natures, which exhibit not only different flow characteristics but also different contributions to the residence time distribution. 

On the other hand, one of the essential conditions for correct measurement of RTD is that the tracer particles have the properties, including RTD characteristics, very close to those of the process particles. This implies that, in the time domain of t > 0, the residence time distribution functions of particles A and B in the same device should be approximately equal to each other, i.e. 

A characteristic of micro channel reactors is their narrow residence-time distribution. This is important, for example, to obtain clean products. This property is not imaginable without the influence of dispersion. Just considering the laminar flow would deliver an extremely wide residence-time distribution. The near wall flow is close to stagnation because a fluid element at the wall of the channel is, by definition, fixed to the wall for an endlessly long time, in contrast to the fast core flow. The phenomenon that prevents such a behavior is the known dispersion effect and is demonstrated in Figure 3.88. 

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