Average residence time profile

Fig. 8 Average residence time profile (in units of the time r between two jump attempts) of the particles in the single-file systems considered in Fig. 7. From [72] with permission...

Kinetic Measurements. The results of the shale oil cracking experiments are summarized in Table I. Oil yields are reported as a percentage of the LLNL assay result on both a condensed-oil basis and a C5+ basis. To conduct the kinetic analysis, an effective residence time had to be determined. It was assumed for simplicity that the gas-and-oil evolution profile could be approximated by a square pulse. The average residence time was calculated by multiplying the void volume of the bottom reactor by the time interval over which three-fourths of the products were evolved and then dividing by the total volume of gases and vapors at the cracking temperatures (14). The void volume was... 

These coupled first-order ODEs allow one to generate conversion and temperature profiles as a function of reactor volume. It is not appropriate to introduce average residence time unless the fluid is incompressible. If one combines these balances... 

The residence time profile for Coils 1 and 2 are shown in Figure 5. The average residence time of the SRT III coil is longer than that of Coil 1. The SRT III pyrolysis coil (Coil No. 2) had the lower hydrocarbon partial pressure profile as shown in Figure 6. 

The two commercial coil designs just discussed have identical pyrolysis selectivity despite their differences in geometrical and process characteristics. The axial gas temperature and partial pressure profiles constitute the major differences. The effect of axial temperature and axial partial pressure profiles on pyrolysis reactor selectivity are taken into account in the definitions of average residence time and hydrocarbon partial pressure. Therefore, when pyrolysis coils of different geometries and thus different temperature and partial pressure profiles are com-... 

It has been experimentally shown that the pyrolysis selectivity of two coils of different geometry, tube diameters and temperature profiles can be identical provided their average residence times and hydrocarbon partial pressures fall on the same selectivity line. The same conclusions have also been drawn from kinetic considerations. This approach has been used to extend the pyrolysis selectivity lines into the millisecond region. 

In these equations kei is the elimination rate constant and AUMC is the area under the first moment curve. A treatment of the statistical moment analysis is of course beyond the scope of this chapter and those concepts may not be very intuitive, but AUMC could be thought of, in a simplified way, as a measure of the concentration-time average of the time-concentration profile and AUC as a measure of the concentration average of the profile. Their ratio would yield MRT, a measure of the time average of the profile termed in fact mean residence time. Or, in other words, the time-concentration profile can be considered a statistical distribution curve and the AUC and MRT represent the zero and first moment with the latter being calculated from the ratio of AUMC and AUC. 

P(CO) = L(CH4). The profiles for L(CO), given in Table IX, were calculated for winter and summer again n(OH) was averaged over the effects of rainout. if we assume that n(CO) is well mixed vertically, as suggested by its estimated residence time of 0.1 to 0.3 yr, we can solve for the CO mixing ratio... 

Another approach to determining the residence time of °Pb in the atmosphere is to divide the mean air column inventory of °Pb by the flux of °Pb to the surface at a given location. This quotient yields a climatological average for the removal processes at that particular site. Graustein and Turekian (1986) used the atmospheric profiles of °Pb from Moore et al. (1973) and their own measured °Pb fluxes from soil profiles and bucket collection to obtain a value of 6 d over the central and eastern United States. As the source of Rn and thus Pb is from the ground and the major removal by precipitation is in the lower troposphere, the mean residence time is dominated by the processes of the lower troposphere. Modeling by Balkanski et al. (1993)... 

The linear chromatographic process is modeled as a composite Poisson process a chain of exponentially distributed fly times, followed by exponentially distributed adsorption times are generated. When adsorbed, the molecule is stationary the mean adsorption time is t . When desorbed, the molecule travels with the velocity of the mobile phase the mean fly time—residence time between a desorption and the subsequent adsorption—in the mobile phase is t. The elution time of the molecule is recorded when it reaches the end of the colxunn after n adsorption-desorption events on the average. The distribution of the single molecule elution times gives the band profile. 

MRT is the average time that molecules of a drug reside in the body after drug administration. It is defined as the time needed for the initial dose to decrease to He (36.8%) of the starting value, where e is the base of the natural logarithm, with a value of 2.718. When MRT is obtained by IV bolus injection (MRTiv), it is a pure intrinsic dispositional property that reflects the loss of the compound from the body. Half-life ft1/2) is the time needed for 50% reduction in concentration or amount. Both parameters characterize the elimination rate of compounds however, MRTiv is not dependent on the distributional pattern and is a time-averaged parameter that applies throughout the entire concentration versus time profile. Half-life, on the other hand, typically describes the rate of decline for a particular phase of the concentration versus time profile (e.g., the apparent terminal elimination phase). For a compound with one-compartment distribution character ... 

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