Residence time effect

The variance approach may also be used to determine n. From Illustration 11.2 the variance of the response data based on dimensionless time is 30609/(374.4)2, or 0.218. From equation 11.1.76 it is evident that n is 4.59. Thus the results of the two approaches are consistent. However, a comparison of the F(t) curves for n = 4 and n = 5 with the experimental data indicates that these approaches do not provide very good representations of the data. For the reactor network in question it is difficult to model the residence time distribution function in terms of a single parameter. This is one of the potential difficulties inherent in using such simple models of reactor behavior. For more advanced methods of modeling residence time effects, consult the review article by Levenspiel and Bischoff (3) and textbooks written by these authors (2, 4). 

Ainsworth C.C., Pilon J.L., Gassman P.L., Van Der Sluys W.G. Cobalt, cadmium, and lead sorption to hydrous iron oxide Residence time effect. Soil Sci Soc Am J 1994 58 ... 

Arai Y, Sparks DL (2002) Residence time effects on arsenate surface speciation at the aluminum oxide-water interface. Soil Sci 167 303-314... 

Fischer-Tropsch synthesis, 28 80, 97, 103, 30 166-168, 34 18, 37 147, 39 221-296 activation energy and kinetics, 39 276 added olefin reactions, 39 251-253 bed residence time effects on chain growth probability and product functionality, 39 246-250... 

Paracrystallinity, Cu/ZnO/AIjOj, 31 295 2"-Paracyclophanes, 32 453 Paracyclophanes, macrocycles, 29 206-208 Paraffin, see also Alkanes alkylation, 10 165, 27 98 carbon selectivity, bed residence time effects, 39 249-250 cracking, 39 283 cyclization, 28 295 rates, 28 301, 302 double cyclization, 28 312-314 in exhaust gases, 24 66, 67 hydrogenolysis, 30 43-44 hydroisomerization, 39 183 oxidation, 32 118-121 solubility enhanced hydrogeolysis, 39 285 Parahydrogen conversion rate correlations, 27 48-50... 

Residence time effects on arsenate ad-sorption/desorption mechanisms on goethite. Soil Sci. Soc. Am. J. 65 67-77... 

The shear viscosity can be used for relating the polymer flow properties to the processing behavior, extruder design, and many other high shear rate applications. Elongational viscosity, die swell measurements as well as residence time effects can be estimated. Typical data are shown in Figure 6. 

The model was developed from experiments conducted in a downflow reactor, where gas residence times are greater than solid residence times. The model may not be able to predict residence time effect in a fluid bed or upflow reactor where solid residence times are greater than gas residence times. But it does give useful information for pressure and temperature effects in these reactors. 

Steady-state temperature Coolant temperature Feed flowrate Feed concentration Pre-exponential factor Heat transfer parameter (UAi Residence time Effective liquid volume... 

C, Bed Residence Time Effects on Chain Growth Probability and Product Functionality... 

Bed residence time effects on olefin and paraffin selectivity for a given hydrocarbon size also show that chain initiation by readsorbed olefins is the predominant reaction of a-olefins during FT synthesis at high reactant pressure (>500 kPa) on both Co and Ru catalysts. Olefins are selectively consumed in readsorption reactions only to reappear (with a certain probabil-... 

Fig. 12. Secondary reactions of primary synthesis products at low CO concentrations (Co/SiO, 2700 kPa, H2/CO = 3.0, 6.2 wt% Co, 4.8% dispersion), (a) Bed residence time effects on CO conversion and C5+ selectivity (b) CO depletion effects on propylene and propane carbon selectivity.

Dimensional analysis of the coupled kinetic-transport equations shows that a Thiele modulus (4> ) and a Peclet number (Peo) completely characterize diffusion and convection effects, respectively, on reactive processes of a-olefins [Eqs. (8)-(14)]. The Thiele modulus [Eq. (15)] contains a term ( // ) that depends only on the properties of the diffusing molecule and a term ( -) that includes all relevant structural catalyst parameters. The first term introduces carbon number effects on selectivity, whereas the second introduces the effects of pellet size and pore structure and of metal dispersion and site density. The Peclet number accounts for the effects of bed residence time effects on secondary reactions of a-olefins and relates it to the corresponding contribution of pore residence time. 

Bed residence time effects can also be described by the convective terms included in the olefin readsorption model [Eqs. (13) and (14)]. Convection-limited removal of a-olefins, characterized by the Peclet number, accounts... 

Fig. 19. Comparison of model and experimental results. Bed residence time effects on total chain termination probability (experimental/model same as in Fig. 16).

O Reilly, S. E., Strawn, D. G., and Sparks, D. L., 2001, Residence time effects on arsenate adsorption/desorption mechanisms on goethite Soil Science Society of America Journal, v. 65, p. 67-77. 

The integral model is a development of a simple scale-up model which allows for mixing and residence time effects, first suggested for fluidized beds by Vanecek et al. (1964, 1966). The mean outlet moisture content is given by summing the product of the particle moisture content and the probability that it emerges at time t ... 

The formation of metal hydroxide surface precipitates and subsequent residence time effects on natural sorbents can greatly affect metal release and hysteresis. It has generally been thought that the kinetics of formation of surface precipitates was slow. However, recent studies have shown that metal hydroxide precipitates can form on time scales of minutes. In Figure 3.7 one can see that mixed Ni-Al hydroxide precipitates formed on pyrophyllite within 15 minutes, and they grew in intensity as time increased. Similar results have been observed with other soil components and with soils (Scheidegger et ak, 1998 Roberts et ak, 1999 Sparks, 2002, 2005). 

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