Normalized residence time distribution

Continuous stirred tank reactor Dispersion coefficient Effective diffusivity Knudsen diffusivity Residence time distribution Normalized residence time distribution... 

The entire residence time distribution can be made dimensionless. A normalized distribution has the residence time replaced by the dimensionless residence time, X = t/t. The first moment of a normalized distribution is 1, and all the moments are dimensionless. Normalized distributions allow flow systems to be compared in a manner that is independent of their volume and throughput. For example, all CSTRs have the same normalized residence time distribution, W(x) = exp(—t). Similarly, all PFRs have f(r) = S(x — 1). 

E(t) E(t,) residence time distribution, p. 507, 508 normalized residence time distribution, p. 508... 

E E(t) E(tr) f. Fit) Activation energy Residence time distribution Normalized residence time distribution Fraction of A remaining unconverted, Ca /Ca0 or nja0 Age function of tracer kJ/(kgmol) Btu/(lb-mol)... 

These expressions demonstrate that the normalized mean residence time and variance of the normalized residence time distribution increase with increased values of the axial dispersion number Dj. In the limit of = 0, the signal is convected and behavior corresponding to the parallel tube model is approximated the normalized residence time fi= 1 and Act = 0. For very large values of D, the behavior corresponds to a single well-mixed compartment. 

Fig. 7.43 Normalized residence time distributions derived from the measured data of Fig. 7.41 in comparison writh the tanks-in-series model at (a) 500m h" (b) 700m h of fluidization air.

To measure a residence-time distribution, a pulse of tagged feed is inserted into a continuous mill and the effluent is sampled on a schedule. If it is a dry miU, a soluble tracer such as salt or dye may be used and the samples analyzed conductimetricaUy or colorimetricaUy. If it is a wet mill, the tracer must be a solid of similar density to the ore. Materials hke copper concentrate, chrome brick, or barites have been used as tracers and analyzed by X-ray fluorescence. To plot results in log-normal coordinates, the concentration data must first be normalized from the form of Fig. 20-15 to the form of cumulative percent discharged, as in Fig. 20-16. For this, one must either know the total amount of pulse fed or determine it by a simple numerical integration... 

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. 

Liquid residence-time distributions in mechanically stirred gas-liquid-solid operations have apparently not been studied as such. It seems a safe assumption that these systems under normal operating conditions may be considered as perfectly mixed vessels. Van de Vusse (V3) have discussed some aspects of liquid flow in stirred slurry reactors. 

The residence time distribution is normally considered a steady-state property of a flow system, but material leaving a reactor at some time 8 wiU have a distribution of residence times regardless of whether the reactor is at steady... 

Two template examples based on a capillary geometry are the plug flow ideal reactor and the non-ideal Poiseuille flow reactor [3]. Because in the plug flow reactor there is a single velocity, v0, with a velocity probability distribution P(v) = v0 16 (v - Vo) the residence time distribution for capillary of length L is the normalized delta function RTD(t) = T 1S(t-1), where x = I/v0. The non-ideal reactor with the para-... 

Residence time distributions are expressed in two forms normalized,... 

Any process takes a certain amount of time and the length of the residence time often dictates the occasions when particular equipment or technology can be used. On the other hand, in almost all chemical unit processes the driving forces vary from time to time, and therefore time has the nature of non-equivalence, i.e., an equal time interval yields different, even greatly different, results for the early and later stages of a process. The result mentioned here means the processing amount accomplished, such as the increments of reaction conversion, absorption efficiency, moisture removal etc. Normally, these parameters vary as parabolic curves with time. Because of the nature of the non-equivalence of time, in addition to the mean residence time, the residence time distribution (RTD) affects the performance of equipment, and thus receives common attention. 

The residence time distribution of particles is related to the properties of the particles and the gas flow, including the size distribution, and the velocity of gas flow and its profile. In practically applicable impinging stream devices, the particles being processed usually have relatively narrower size distribution the diameter of the tube to particles size ratio, d Jd,h is normally very large ( 15) while the gas velocity is high... 

In all the just-mentioned examples, quantitative prediction and design require the detailed knowledge of the residence time distribution functions. Moreover, in normal operation, the time needed to purge a system, or to switch materials, is also determined by the nature of this function. Therefore the calculation and measurement of RTD functions in processing equipment have an important role in design and operation. 

Bypassing the reactor showed that the broadening of the pulse caused by the feed and effluent lines was negligible. Hence, the normalized pulse response is the residence time distribution (RTD) of the recycle reactor. 

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