Residence time distribution curve

Fig. 3. Typical residence-time distribution curves in a gas-liquid dispersion [after Gal-Or and Resnick (G8)].

Figure 3.42 Evolution of a pulse at the entrance of a micro channel for different diffusion coefficients. Calculated concentration profile (left) and cumulative residence time distribution curve (channel 300 pm x 300 pm x 20 mm flow velocity 1 m s f = 10 s) [27],...

Residence time distribution curves for dispersion model. 

In addition to the aforementioned slope and variance methods for estimating the dispersion parameter, it is possible to use transfer functions in the analysis of residence time distribution curves. This approach reduces the error in the variance approach that arises from the tails of the concentration versus time curves. These tails contribute significantly to the variance and can be responsible for significant errors in the determination of Q)L. 

ILLUSTRATION 11.4 COMPARISON OF CONVERSION LEVELS ATTAINED IN TWO DIFFERENT REACTOR COMBINATIONS HAVING THE SAME RESIDENCE TIME DISTRIBUTION CURVE—FIRST-ORDER REACTION... 

The dispersion and stirred tank models of reactor behavior are in essence single parameter models. The literature contains an abundance of more complex multiparameter models. For an introduction to such models, consult the review article by Levenspiel and Bischoff (3) and the texts by these individuals (2, 4). The texts also contain discussions of the means by which residence time distribution curves may be used to diagnose the presence of flow maldistribution and stagnant region effects in operating equipment. 

In a two-part series. Zeme discusses the importance of good separator hydraulics. A poor hydraulic design can make a good separation scheme ineffective. Zemel provides the methods and procedures to run a tracer test to identify short-circuiting, stagnant-flow regions, and shear forces. Analysis of the residence-time distribution curve that results is presented. Actual tests run on separators indicate that the most successful separator was the sequential dispersed-gas flotation cell, which closely followed the tanks-in-serie< model. This is contrasted with the poor performance of a conventional 2, 006-hbl [3 0-ms] wash tank The tracer responses of a pressurized flotation cell, a 15j000-bbl [2400 mJj wash tank, and a horizontal free-water knockout with and without baffles are also discussed. 

Regions of stagnancy are often caused by baffles and by interference due to pipes and fittings in corners and other places where abrupt changes in flow paths can occur. It is evidenced principally by long tails in the residence time distribution curve and in extreme cases, by a mean residence time which is very much shorter than that calculated by the volume divided by the flow rate. 

As predicted from the model, the residence time distribution curve shown in Fig. 3.11 exhibits the feature of perfect mixing with a certain lag time, that is, the feature of plug flow-perfect mixing flow in series. All the experiments yield the results of RTD exhibiting the same feature. 

Determinations of Peclet number were carried out by comparison between experimental residence time distribution curves and the plug flow model with axial dispersion. Hold-up and axial dispersion coefficient, for the gas and liquid phases are then obtained as a function of pressure. In the range from 0.1-1.3 MPa, the obtained results show that the hydrodynamic behaviour of the liquid phase is independant of pressure. The influence of pressure on the axial dispersion coefficient in the gas phase is demonstrated for a constant gas flow velocity maintained at 0.037 m s. 

The residence time distribution curve (Fig. 13.4) provides further insight into the origins of the bimodal distribution. The peak in the residence time curve falls in the size range 0.1 < dp < 1.0 (im corresponding to the accumulation mode. Although the coarse mode has a short residence time, it is continually reinforced by fresh injections of crustal material and. perhaps, anthropogenic sources. Thus the two modes are essentially uncoupled. 

The residence time distribution curve (RTD) can be inscribed by its statistical moments, of which the centroid of distribution T and spread of distribution a are the most important numerical values. Thus, for a C curve, the zeroth moment is... 

Figure 3.10. Residence time distribution curves in a coiled tube computed with the aid of Speberg s model [3.3]. (a) For = 0 the familiar Taylor s solution is obtained. When the function E is included, then RTD curves showing isodispersion points are obtained for both mixing cup detector b) and area average (across the flow) detector (c).

The similarity of these breakthrough curves to residence-time distribution curves is apparent, and in fact we can think of them as a kind of residence-time distribution for the adsorbate, although the processes occuring within the bed and leading to the observed breakthrough are much more complex than those occuring in a simple tracer experiment. 

Figure 8.1 Residence time distribution curves for IVr equal-size CSTRs in series. Curves are for the same total volume. V, with Vr = V/A r...

The mathematical relations expressing the different amounts of time that fluid elements spend in a given reactor may be expressed in a variety of forms [see, e.g., Leven-spiel (1-3) and Himmelblau and Bischoff (4)]. In this book we utilize the cumulative residence-time distribution curve [F(0], as defined by Danckwerts (5) for this purpose. For a continuous flow system. Fit) is the volume fraction of... 

Figure 11.9 Cumulative residence time distribution curves for the /i-CSTR model.

ILLUSTRATION 11.4 Comparison of Conversion Levels Attained in Two Different Reactor Combinations Having the Same Residence-Time Distribution Curve First-Order Reaction... 

W. Zhu and Y. laluria [Polym. Eng. ScL, 41, 1280-1291 (2001)] determined residence time distribution curves for a twin-screw extruder in which gelatinization of commeal... 

Figure 3.7 Cumulative residence time distribution curves of a cascade of stirred tanks, parameter number of tanks. (Adapted from Ref. [4], Figure 6.30b Copyright 2013, Wiley-...

The analysis of residence time distribution curves thus far refers to situations... 

Figure 6.25 Comparison of residence time distribution curves for various reactors [125].

Figure 7.158 Residence time distribution curves for several power law index values...

Figure 4.10.59 Example of an RTD (residence time distribution) curve (open vessel boundary condition, see Figures 4.10.55 and 4.10.57).

Figure 7.16 Comparison of various reactors residence time distribution curves...

B.12 Residence Time Distribution Curved Channel Model (Pinto and Tadmor, 1970). The residence time disAibution (RTD) funcAon for Aow of a Newtonian Auid in a rectangular channel was developed in SecAon 8.5.1. Derive the RTD for the case in which curvature is included. A Auid parAcle located at position r in the extruder channel will turn over when it hits the screw Aight and start moving in the opposite direcAon at a posiAon r. ... 

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