Residence time, average experimental determination

Experimental work was undertaken (G8) to provide the information necessary to permit a test of this theoretical model. The system used bore complete geometrical and chemical similarity to that used by Cooper et al. (C9) so that their mass-transfer rate measurements, along with the average residence-time and power-consumption results determined in the experimental work (see Section II,D), were used to compare the experimental values with the model. 

Our aim is to determine the concentration of A in the reactor as a function of time and in terms of the experimental conditions (inflow concentrations, pumping rates, etc.). We need to obtain the equation which governs the rate at which the concentration of A is changing within the reactor. This mass-balance equation will have contributions from the reaction kinetics (the rate equation) and from the inflow and outflow terms. In the simplest case the reactor is fed by a stream of liquid with a volume flow rate of q dm3 s 1 in which the concentration of A is a0. If the volume of the reactor is V dm3, then the average time spent by a molecule in the reactor is V/q s. This is called the mean residence time, tres. The inverse of fres has units of s-1 we will call this the flow rate kf, and see that it plays the role of a pseudo-first-order rate constant. We denote the concentration of A in the reactor itself by a. 

A disadvantage of the differential reactor is the inaccuracy in the determination of conversion and selectivity due to the small concentration changes. The second difficulty in the treatment of experimental data is caused by possible flow nonuniformities. Since the average residence time is short and the fluid elements moving with different axial velocities do not mix, the simplified Equation 5.30 may not be valid. This is because the reactor operates as a segregated flow reactor rather than a plug flow or ideal mixed reactor, on which Equation 5.30 is based. 

Chromatographic Considerations. The experimental problem is now reduced to the far from trivial one of determining the ratio of the retention volumes of the two isotopically substituted molecules. Consider a typical chromatogram for two difficultly resolvable isomers such as is sketched in Figure 1. Here to is the time from injection that a completely inert nonadsorbed material is eluted t2 and ti are the corrected retention times P2/P1 = ti/t2) (21) t is the average residence time in the column and tv is the peak width. 

For continuous (cascade) operation, the plate is lowered in the bowl so that a certain volume always remains inside. This residual volume can be either measured experimentally or calculated, assuming that the cross section of the rope resembles a fourth of a circle (quarter torus). If material is fed to the unit at a constant rate, the average residence time, f, a most important parameter that had been previously determined during testing, can be calculated... 

In Illustration 11.1 we considered the response of an arbitrary reactor to a pulse stimulus and used these data to determine the average residence time and the F(0 curve. If the pulse is assumed to be perfect, what value of T)JuL gives a reasonable fit of the experimental data Use the slope and variance methods to evaluate this parameter. 

It is necessary to know the density function, E t), if the segregation model is applied. E(t) can be determined either experimentally or theoretically. Since it is possible to derive the residence time functions for many flow models, the segregation model is very flexible. According to the segregation model, the average concentration at the reactor outlet is obtained from the relation... 

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