Pulse injection

Solution of the model equations shows that, for a linear isothermal system and a pulse injection, the height equivalent to a theoretical plate (HETP) is given by... 

A promising technique is cavity ringdown laser absorption spectroscopy (307), in which the rate of decay of laser pulses injected into an optical cavity containing the sample is measured. Absorption sensitivities of 5 x 10 have been measured on a ]ls time scale. AppHcations from the uv to the ir... 

Method of Moments The first step in the analysis of chromatographic systems is often a characterization of the column response to sm l pulse injections of a solute under trace conditions in the Henry s law limit. For such conditions, the statistical moments of the response peak are used to characterize the chromatographic behavior. Such an approach is generally preferable to other descriptions of peak properties which are specific to Gaussian behavior, since the statisfical moments are directly correlated to eqmlibrium and dispersion parameters. Useful references are Schneider and Smith [AJChP J., 14, 762 (1968)], Suzuki and Smith [Chem. Eng. ScL, 26, 221 (1971)], and Carbonell et al. [Chem. Eng. Sci., 9, 115 (1975) 16, 221 (1978)]. 

The characterization is performed by means of residence time distribution (RTD) investigation [23]. Typically, holdup is low, and therefore the mean residence time is expected to be relatively short Consequently, it is required to shorten the distance between the pulse injection and the reactor inlet. Besides, it is necessary to use specific experimental techniques with fast time response. Since it is rather difficult, in practice, to perfectly perform a Dirac pulse, a signal deconvolution between inlet and outlet signals is always required. 

The BCs have been previously discussed by Gleaves et al. [1], Zou et al. [3], Creten et al. [9] and others. Initial condition (2) can he accepted because its statement of an initially clean surfece is an experimental statement. BCs (3, 4) are here further discussed with refenraice to the experimental apparatus. BC (3) states that the flux at the reactor Met is a delta fimction and is the approximation that pulse injection occurs over an inflnitely short time. This is discussed using experimental data on the speed of injection of the input pulse. BC (4) is the approximation that the gas concentration is zero outside the reactor tube. It implies tiM any gas eluting firom the reactor tube is immKiiately removed, that is, the approximation is that... 

Additions to and withdrawals from the reaction zone. General indications concerning the choice between batch and continuous reactors have been discussed above. Pulsed injections might be... 

The second part of this work will be dedicated to the start of the game what are the pieces motions How can the adsorbed molecules react on the surface and among all the playground, where does the real action take place This is the so-called in situ approach for which techniques such as temperature-programmed surface reaction (TPSR) or transient analysis by pulse injection have been developed. 

For other boundary conditions or for imperfect pulse injections, modifications must be made in these expressions. For example, for a closed vessel, Levenspiel and Bischoff (9) indicate that... 

Figure 1 shows propane conversion and hydrogen production vs. the number of pulses injected. It can be seen that, although propane consumption is large already from the first pulse (figure 1 - left), hydrogen production is initially much smaller in the 2 wt.% Ga catalyst, and is actually zero with the 3 wt.% Ga catalyst (figure 1 - center). 

Solution for Closed Vessel. For a closed vessel (i.e., closed-closed, at both inlet and outlet), the flow conditions are illustrated schematically in Figure 19.18. The flow upstream of the vessel inlet (z < 0) is PF characterized by DL = 0 or Pe, = °°. Since flow inside the vessel is dispersed, and the pulse injection is at the inlet (z = 0), there is a discontinuity in cA across the inlet. There is assumed to be continuity in cA across the outlet (z = 1), even though downstream flow (z > 1) is PF. 

In studying pyrolysis kinetics, Liliedahl et al. (1991) determined the RTD of their apparatus by pulse-injection of a gaseous hydrocarbon tracer. 

Shetty et al. (1992) studied gas-phase backmixing for the air-water system in bubble-column reactors by measuring RTDs of pulse-injected helium tracer. 

Asif et al. (1991) studied distributor effects in liquid-fluidized beds of low-density particles by measuring RTDs of the system by pulse injection of methylene blue. If PF leads into and follows the fluidized bed with a total time delay of 10 s, use the following data to calculate the mean-residence time and variance of a fluid element, and find N for the US model. 

Fig. 4 Transfer rate at the time of the pulse injection, showing direction reversal.

For a CSTR we solve the transient CSTR mass-balance equation because we want the time dependence of a pulse injection without reactiou The transient CSTR equation on a species of concentration C is... 

Figure 8-1 Sketch of response to a pulse injection 5(0 of a traca (uppa) md response toastepinjectionofatracer(lower)inasteady state chanicd reactor wtii ai abiti flow pattern. The response to a pitise injection is the residence time distribution p(t). and the derivative of tiie step response is p(t),...

Next consider the response of a PFTR with steady flow to a pulse injected at f = 0. Wc could obtain this by solving the transient PFTR equation written earher in this chapter, but we can see the solution simply by following the pulse down the reactor. (This is identical to the transformation we made in transforrning the batch reactor equations to the PFTR equations.) The S(0) pulse moves without broadening because we assumed perfect plug flow, so at position z the pulse passes at time z/u and the pulse exits the reactor at time T = L/u. Thus for a perfect PFTR the RTD is given by... 

For R = 0 we have the pulse at T at the same height as the pulse injected, for the perfect PFTR. For R = 1 the first pulse containing one-half of the tracer will leave at time r/2, and the rest will recycle one-half of this wiU exit at time r, one-fourth will recycle, etc. Thus we will observe pulses at intervals t/2 with heights The sum of all of the infinite number of pulses must be the... 

Fignre 12-19 Pulse injection of gases or liquids into a chromatographic column with carrier gas or liquid for species A, B, and C. The chromatogram is recorded as the signal versus retention time in the column. 

Figure 12-20 shows the concentration profiles of these three species in the reaction above following pulse injection of pure A into the reactor, which is packed with a chromatographic sohd. Without chromatograpli, the mixture comes to equilibrium, but with chromatographic separation species B moves faster than species A, while species C moves slower. Therefore, species B and C are spatially separated and cannot react back to form A. 

Figure 6.17. Growth of tracer variance following a pulse injection. The analysis should begin downstream of X = 0.2. Adapted from Fisher et al. (1979).

We have assumed that the location 8,000 m downstream of the pulse injection will be out of the mixing region, as specified by equation (6.60). We are now ready ... 

As we proceed to the entire exhaust system scale we face the task of interfacing the DPF behavior to that of other emission control devices in the exhaust (e.g. diesel oxidation catalysts (DOC) and NOx reduction devices). An example of a coupled simulation of a DOC and a DPF in series is shown in Fig. 43. We observe how a hydrocarbon pulse injection upstream of the DOC raises the exhaust temperature and causes regeneration of the DPF. Such simulation tools are very useful for the development and optimization of postinjection strategies for DPF regeneration. 

The shape ofthe elution curve for a pulse injection can be approximated by the Gaussian error curve for AT > 100, which is almost the case for column chromatography [2]. The value of N can be calculated from the elution volume Vg (m ) and the peak width W (m ), which is obtained by extending tangents from the sides of the elution curve to the baseline and is equal to four times the standard deviation (Ty (m ) = as shown in Figure 11.7. 

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