Erlang

The Erlang number /leriang. nd the variances O (t ) and 0 (t) are single parameter characterizations of RTD curves. The skewness y (t), and higher moments can be used to represent RTD curves more closely if the data are accurate enough. 

Distribution models are curvefits of empirical RTDs. The Gaussian distribution is a one-parameter function based on the statistical rule with that name. The Erlang and gamma models are based on the concept of the multistage CSTR. RTD curves often can be well fitted by ratios of polynomials of the time. 

FIG. Tracer responses to n-stage continuous stirred tank batteries the Erlang model (a) impulse inputs, (h) step input. 

Numerical solutions of the maximum mixedness and segregated flow equations for the Erlang model have been obtained by Novosad and Thyn (Coll Czech. Chem. Comm., 31,3,710-3,720 [1966]). A few comparisons are made in Fig. 23-14. In some ranges of the parameters n or fte ihe differences in conversion or reaclor sizes for the same conversions are substantial. On the basis of only an RTD for the flow pattern, perhaps only an average of the two calculated extreme performances is justifiable. 

The solution of this partial differential equation is recorded in the literature (Otake and Kunigata, Kngaku Kogaku, 22, 144 [1958]). The plots of E(t ) against t are bell-shaped, resembling the corresponding Erlang plots. A relation is cited later between the Peclet number,... 

The Erlang (or gamma) and dispersion models can be related by equating the variances of their respective E(E) functions. The result for the closed-ends condition is... 

Figure 8-38 shows the residenee time distributions of some eom-mereial and fixed bed reaetors. These shapes ean be eompared with some statistieal distributions, namely the Gamma (or Erlang) and the Gaussian distribution funetions. However, these distributions are represented by limited parameters that define the asymmetry, the peak. 

Erkundigung, /. inqmry, erlangen, t.i. reach, obtain, attain, acquire. Erlanger-blau, n. Erlanger blue (a kind of Prussian blue), -leder, n. glove kid. 

Of the researchers in this field, only Erlanger (80, 81) believes that the phenyl of D24 represents the phenyl of a benzoyl group. Hein and Niemann have criticized his view (75), saying that it cannot explain why D24 is so much more reactive (4 x 10 times) in the enzymatic process than the Lisomer, which has approximately the same reactivity as N-benzoyl-Lalanine methyl ester. 

Perry HM, Erlanger MW. 1978. Pressor effects of chronically feeding cadmium and lead together. In Hemphill DD, ed. Trace substances in environmental health. Vol. 12. Columbia, MO University of Missouri-Columbia, 268-275. 

Perry HM Jr, Erlanger MW, Perry EF. 1988. Increase in the blood pressure of rats chronically fed low levels of lead. Environ Health Perspect 78 107-111. 

B.F. Erlanger, B.X. Chen, M. Zhu, and L. Brus, Binding of an anti-fullerene IgG monoclonal antibody to single wall carbon nanotubes. Nano Lett. 1, 465-467 (2001). 

When n is integral, this model goes by the name Erlang when it is non integral it is called Gamma. Further details of the derivation are in problem P5.01.02. 

Erlang with time delay expC-t Vd + t2s/n)n The last item is of a PFR and an n-stage CSTR in series. More complex combinations are the subject of problems P5.01.33, P5.03.10, P5.03.02 and... 

In the general field of statistics, the RTD of an n-stage CSTR battery is called an Erlang distribution, or a Gamma distribution when n is not integral. Then (n-1) is replaced by r(n) in the equation given in Section... 

The Gaussian is a one parameter model, the variance. The RTD curves are bell shaped. At smaller values of the variance (or the larger values of n of the Erlang), the Erlang and Gaussian RTD curves approach each other, and the... 

Construct the third and fourth order Gram-Charlier distributions corresponding to an Erlang with cr2(tr) = 0.5 or n = 2. 

The third order Gram-Charlier approximates the Erlang more closely than does the fourth order. 

P5.06.12. REACTORS WITH CSTR. ERLANG AND GAUSSIAN BEHAVIOR... 

Compare conversions in CSTRs and in segregated flow with Erlang or Gaussian RTDs, for second order reactions. 

For first order the Erlang yields are the same as those of the CSTRs. The results are summarized in the tables. 

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