Residence time distribution flow pattern

As the Figure 8.12 reveals, the flow pattern deviates from plug flow. The residence time distribution function E(l) is calculated from the experimentally recorded responses, after which the F(t) function was obtained from integration of E(t). The experimental functions are compared to the theoretical ones. The expressions of E(t) and F(t) obtained from the analytical solution of the dynamic, non-reactive axial dispersion model with closed Danckwerts boundary conditions were used in comparison. A comparison of the results shown in Figure 8.12 suggests that a reasonable value for the Peclet number is Pe=3. 

A distinc tion is to be drawn between situations in which (1) the flow pattern is known in detail, and (2) only the residence time distribution is known or can be calculated from tracer response data. Different networks of reactor elements can have similar RTDs, but fixing the network also fixes the RTD. Accordingly, reaction conversions in a known network will be unique for any form of rate equation, whereas conversions figured when only the RTD is known proceed uniquely only for hnear kinetics, although they can be bracketed in the general case. 

Glaser and Litt (G4) have proposed, in an extension of the above study, a model for gas-liquid flow through a b d of porous particles. The bed is assumed to consist of two basic structures which influence the fluid flow patterns (1) Void channels external to the packing, with which are associated dead-ended pockets that can hold stagnant pools of liquid and (2) pore channels and pockets, i.e., continuous and dead-ended pockets in the interior of the particles. On this basis, a theoretical model of liquid-phase dispersion in mixed-phase flow is developed. The model uses three bed parameters for the description of axial dispersion (1) Dispersion due to the mixing of streams from various channels of different residence times (2) dispersion from axial diffusion in the void channels and (3) dispersion from diffusion into the pores. The model is not applicable to turbulent flow nor to such low flow rates that molecular diffusion is comparable to Taylor diffusion. The latter region is unlikely to be of practical interest. The model predicts that the reciprocal Peclet number should be directly proportional to nominal liquid velocity, a prediction that has been confirmed by a few determinations of residence-time distribution for a wax desulfurization pilot reactor of 1-in. diameter packed with 10-14 mesh particles. 

For a few highly idealized systems, the residence time distribution function can be determined a priori without the need for experimental work. These systems include our two idealized flow reactors—the plug flow reactor and the continuous stirred tank reactor—and the tubular laminar flow reactor. The F(t) and response curves for each of these three types of well-characterized flow patterns will be developed in turn. 

Different reactor networks can give rise to the same residence time distribution function. For example, a CSTR characterized by a space time Tj followed by a PFR characterized by a space time t2 has an F(t) curve that is identical to that of these two reactors operated in the reverse order. Consequently, the F(t) curve alone is not sufficient, in general, to permit one to determine the conversion in a nonideal reactor. As a result, several mathematical models of reactor performance have been developed to provide estimates of the conversion levels in nonideal reactors. These models vary in their degree of complexity and range of applicability. In this textbook we will confine the discussion to models in which a single parameter is used to characterize the nonideal flow pattern. Multiparameter models have been developed for handling more complex situations (e.g., that which prevails in a fluidized bed reactor), but these are beyond the scope of this textbook. [See Levenspiel (2) and Himmelblau and Bischoff (4).]... 

In the previous section we indicated how various mathematical models may be used to simulate the performance of a reactor in which the flow patterns do not fit the ideal CSTR or PFR conditions. The models treated represent only a small fraction of the large number that have been proposed by various authors. However, they are among the simplest and most widely used models, and they permit one to bracket the expected performance of an isothermal reactor. However, small variations in temperature can lead to much more significant changes in the reactor performance than do reasonably large deviations inflow patterns from idealized conditions. Because the rate constant depends exponentially on temperature, uncertainties in this parameter can lead to design uncertainties that will make any quantitative analysis of performance in terms of the residence time distribution function little more than an academic exercise. Nonetheless, there are many situations where such analyses are useful. 

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... 

Each flow pattern of fluid through a vessel has associated with it a definite clearly defined residence time distribution (RTD), or exit age distribution function E. The converse is not true, however. Each RTD does not define a specific flow pattern hence, a number of flow patterns—some with earlier mixing, others with later mixing of fluids—may be able to give the same RTD. 

Figure 8-1 Sketch of response to a pulse injection 5(0 of a traca (uppa) md response toastepinjectionofatracer(lower)inasteady state chanicd reactor wtii ai abiti flow pattern. The response to a pitise injection is the residence time distribution p(t). and the derivative of tiie step response is p(t),...

These possible flow patterns of a drop or bubble phase are shown in Figure 12-12. At the left is shown an isolated bubble which rises (turn the drawing over for a falling drop), a clearly unrtuxed situation, ff the bubble is in a continuous phase which is being stirred, then the bubble wiU swirl around the reactor, and its residence time will not be fixed but will be a distributed function. In the limit of very rapid stirring, the residence time of drops or bubbles wiU have a residence time distribution... 

However with stirring and coalescence and breakup, both effects tend to mix the contents of the bubbles or drops, and this situation should be handled using the CSTR mass balance equation. As you might expect, for a real drop or bubble reactor the residence time distribution might not be given accurately by either of these limits, and it might be necessary to measure the RDT to correctly describe the flow pattern in the discontinuous phase. 

Figure 12-12 Sketches of possible flow patterns of bubbles rising through a liquid phase in a bubble column. Stirring of the continuous phase will cause the residence time distribution to be broadened, and coalescence and breakup of drops will cause mixing between bubbles. Both of these effects cause the residence time distribution in the bubble phase to approach that of a CSTR. For falling drops in a spray tower, the situation is similar but now the drops fall instead of rising in the reactor.

The mixing pattern in an n-stage CSTR battery is intermediate between segregated and maximum mixed flow and is characterized by residence time distribution with variance o2 = 1/n. Conversion in the CSTR battery is found by solving n successive equations... 

The design of the jet spouted bed requires the rigorous definition of the gas flow pattern in order for the residence time distribution to be considered. In previous papers, the regime of jet spouted bed and its hydrodynamics correlations have been defined [2-8]. The minimum jet spouting velocity is calculated by the following correlation [7]. 

In this section of the studies, the flow patterns of two-phase flow in the investigated packings (monoliths, Sulzer DX , and Sulzer katapak S ) are discussed. Further, the resulting residence time distribution (RTD), flooding limits, and mass transfer behavior are compared. 

Residence time distribution measurements, together with a theoretical model, provide a method to calculate the rate of mass transfer between the liquid flowing through the column, the dynamic holdup, and the stagnant pockets of liquid in between the particles. We have chosen the cross flow model (10). It has to be noted that the model starts from the assumption that the flow pattern has a steady-state character, which is in conflict with reality. Nevertheless, average values of the number of mass transfer units can be calculated as well as the part of the liquid being in the stagnant situation. 

The residence time distribution of the recycle reactor was determined by tracer experiments. This permitted the interpretation of the flow patterns in the reactor, so that the degree of mixing could be quantified. 

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... 

For a continuous reactor with a nonideal flow pattern, characterized by the differential residence time distribution E t), the following expression holds for the conversion nonideai. which is attained in case complete segregation of all fluid elements passing through the reactor can be assumed ... 

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