Residence time distribution functions internal

Residence time distribution functions were developed by Danckwerts [3] and are defined as external or internal RTD functions. The external RTD function /(f) is defined such that f(t)dt is the fraction of fluid exiting the system with a residence timebetween t and t + dt and the internal RTD function g(t) is defined such that g(t)dt is the fraction of the fluid in the system with a residence time between t and t + dt. 

G(f) Cumulative internal residence time distribution function (7.3-11)... 

Internal energy per unit mass, J/kg e/i Internal energy per unit mass for phase, k, J/kg E Differential residence time distribution function, s ... 

After studying this chapter the reader will be able to describe the cumulative F(t), external age E(t), and internal age I(t) residence-time distribution functions and to recognize these functions for PFR, CSTR, and laminar flow reactions. The reader will also be able to apply these functions to calculate the conversion and concentrations exiting a reactor using the segregation model and the maximum mixedness model for both single and multiple reactions. 

Thus, either pulse-response or step-function response experiments give sufficient information to permit evaluation of exit-age, internal-age, and residence-time distributions. The average age or mean residence time, which we have defined intuitively in equation (4-13), can be more precisely stated in terms of the time average of the exit-age distribution. 

The step-function and exponential residence-time distributions of Figure 4.5 can be modeled by two different types of flow systems. For the step-function response we have already alluded to the model of plug flow through a tube, whieh is, indeed, a standard model for this response. The exponential response, deseribed previously as the result of the equality of the internal- and exit-age distributions, requires a bit more thought. In the following we will derive the equations for the mixing models and then the corresponding reactor models for these two limits. 

Two specific functions are used to describe the residence time distribution the exit age distribution and the internal age distribution. 

Major methods used to account for mixing in reactors. Illustrations on statistically stationary field of a velocity component. DNS Direct Numerical Simulation PDF Probability Density Function I Internal distribution function RTD Residence Time Distribution <> macro-scale averaged reactor-scale averaged. 

Figures 1, 2, and 3 exhibit the salient residence time study results. Figure 1 shows the residence time density, f(t), for three different configurations the analog of the existing plant reactor and two alternate internal modifications (labelled A and B, respectively). Figure 2 exhibits the residence time distribution F(t) and Figure 3 exhibits the deduced intensity function X(t).

In a manner similar to the internal age distribution function, let E be the measure of the distribution of ages of all elements of the fluid stream leaving a vessel. Thus E is a measure of the distribution of residence times of the fluid within the vessel. Again the age is measured from the time that the fluid elements enter the vessel. Let E be deflned in such a way that E dd is the fraction of material in the exit stream which has an age between 6 and 6 -I- dO. Referring to Fig. 4, the area under the E vs. 6 curve is... 

The mean residence time of solute in a flow system is of course only a partial description and corresponds to the first temporal moment [11, 23.6-3, p. 756] of exit tracer concentration for a pulse tracer input. It says nothing about the distribution of exit concentration as a function of time or the effect of the internal flow behavior. However, there are many circumstances where the shape is of no importance, and we begin by identifying some of these. 

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