Axial effect

The axial effective conductivity 2 > - of the DPF is well known to be the product of the solid fraction (1—eA) and the conductivity of the wall material ,. The open area fraction (equivalent to the porosity) of a square honeycomb structure is... 

Ab initio MP2/GIAO/NBO study of the delta-syn-axial effect in 13CNMR spectroscopy105... 

Axial effective diffusivity in tubular reactor (m /h) Radial effective diffusivity in tubular reactor (m /h) Bulk diffusivity of component i (m /h)... 

S. Yagi, D. Kunii, and N. Wakao, Studies on Axial Effective Thermal Conductivities in Packed Beds, AlChE J, (6) 543-546,1960. 

Figure II.6-1 Peclel number for axial effective diffusion, based on particle diameter, versus Reynolds number. I McHenry and Wilhelm 2 Ebadi and White 3 Carberry and Bretton 4 Strang artd Geankoplis 5 Cairns and Prausnitz 6 Hiby 7 Hiby, without wall effect (from Froment [76]). 

The magnitude of the axial effective diffusivity determines which of the two conditions, Eq. 11.6-4 or 11.6-10, is stronger. For a first-order irreversible reaction carried out in an adiabatic reactor, Eq.ll. 6-10 leads to... 

This figure clearly illustrates that the range within which multiple steady states can occur is very narrow. It is true that, as Hlavacek and Hofmann calculated, the adiabatic temperature rise is sufficiently high in ammonia, methanol and oxo-synthesis and in ethylene, naphthalene, and o-xylene oxidation. None of the reactions are carried out in adiabatic reactors, however, although multibed adiabatic reactors are sometimes used. According to Beskov (mentioned in Hlavacek and Hofmann) in methanol synthesis the effect of axial mixing would have to be taken into account when Pe < 30. In industrial methanol synthesis reactors Pe is of the order of 600 and more. In ethylene oxidation Pe would have to be smaller than 200 for axial effective transport to be of some importance, but in industrial practice Pe exceeds 2500. Baddour et al. in their simulation of the TVA ammonia synthesis converter found that the axial diffusion of heat altered the steady-state temperature profile by less than 0.6°C. Therefore, the length of... 

The axial effective diffusivity for the liquid phase has been correlated by Elenkov... 

Since the liquid flow rates are generally rather low it may be necessary to account for axial mixing in the liquid phase. This is done in terms of axial effective diffusion. The axial effective diffusivity for the liquid phase is given by Bdxkes [40] ... 

The liquid flow pattern in a bubble column of 15 cm diameter was investigated by Kojima et al. [63] at superficial liquid and gas velocites of the order of 1 cm/s. The liquid flow was found to be complicated and to vary continuously with time. The flow was mainly upward in the central part, but in other parts both upward and downward, although mainly downward near the wall. Radial flow was present across the entire cross section as a result of the pumping effect of the wakes of bubble swarms when the volume of liquid pumped per unit time by the wakes of the bubbles exceeds that of the liquid fed, downward flow has to occur, inducing radial flow. These observations confirm those of Towell and Ackerman [64] who, in addition, expressed the mixing in terms of axial effective diffusivities for the... 

In particulate systems, the order of magnitude of the radial and axial effects is not uniform. Some hypotheses can be made for simplicity, neglecting the radial and axial effects, approaching them to the ideal conditions. 

In some cases, it is assumed a pseudohomogeneous. That is, considering negligible the radial and axial effects. In other cases, the reaction can occur in the tube wall (monolith). 

In general, a minimum value for db/dp is usually reported, whereas for axial effects, a minimum L/dp is required. However, some discrepancy in the values of these ratios exists. 

Elsari M, Hughes R. Axial effective thermal conductivities of packed beds. Applied Thermal Engineering 2002 22 1969-1980. 

Discuss briefly, why reactivity worth of an individual rod can be variable throughout operation in a cycle. Include both radial and axial effects in discussion. Assume constant boron content. 

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