Residence times limiting conditions

The experiments were carried out at a pressure of 1.5 bar and a flow rate of 80-270 Ncm3 min-1. At 200 °C no deactivation of the catalyst was observed. As the rate of reaction was found to show a linear dependence on the residence time, differential conditions were assumed for the measurements. Because of the determined high activation energy of 5 6 kj mol-1, mass transport limitations were excluded. A power law kinetic expression of the following form was determined for methanol steam reforming ... 

The advantage of this technology is that melting and homogenization can be carried out gently under optimum processing conditions, since the two processes are separated from one another. Other than for PE processing, this process may also be used for other residence-time limited materials. 

Yq = 1.56x10 kgmole/m s, cannot be used easily. Indeed, it is calculated from the condition Oq > 3.7 proposed in Table IX, that Tq = 8.9 s and tq < 2.U s. Such a small gas residence time limits the applicability of this chemical method to the small scale units. This may explain why interfacial areas have been measured in tanks the volume of which are not bigger than 1 m, with gas superficial velocity as high as 0.047 m /m s (24). Complementary information for the case of shrinking bubbles may be found in ref. (22). 

The following conditions are stipulated the catalyst decomposition rate constant must be one hour or greater the residence time of the continuous reactor must be sufficient to decompose the catalyst to at least 50% of the feed level the catalyst concentration must be greater than or equal to 0.002 x Q, where the residence time, is expressed in hours. An upper limit on the rate of radical formation was also noted that is, when the rate of radical formation is greater than the addition rate of the primary radicals to the monomers, initiation efficiency is reduced by the recombination of primary radicals. 

The quantity of coproduct acetylene produced is sensitive to both the feedstock and the severity of the cracking process. Naphtha, for example, is cracked at the most severe conditions and thus produces appreciable acetylene up to 2.5 wt % of the ethylene content. On the other hand, gas oil must be processed at lower temperature to limit coking and thus produces less acetylene. Two industry trends are resulting in increased acetylene output (/) the ethylene plant capacity has more than doubled, and (2) furnace operating conditions of higher temperature and shorter residence times have increased the cracking severity. 

Various theoretical and empirical models have been derived expressing either charge density or charging current in terms of flow characteristics such as pipe diameter d (m) and flow velocity v (m/s). Liquid dielectric and physical properties appear in more complex models. The application of theoretical models is often limited by the nonavailability or inaccuracy of parameters needed to solve the equations. Empirical models are adequate in most cases. For turbulent flow of nonconductive liquid through a given pipe under conditions where the residence time is long compared with the relaxation time, it is found that the volumetric charge density Qy attains a steady-state value which is directly proportional to flow velocity... 

With the above as an introduction, we now consider the important operational case of filtration performed under constant pressure. In practice, all the parameters defined above are nearly constant under steady state conditions except V and r, which are varied by the operator. We may therefore integrate the working expression for filtration over the limits of volume from 0 to V, and for residence time over the limits of 0 to x ... 

In this way, the operational range of the Kolbe-Schmitt synthesis using resorcinol with water as solvent to give 2,4-dihydroxy benzoic acid was extended by about 120°C to 220°C, as compared to a standard batch protocol under reflux conditions (100°C) [18], The yields were at best close to 40% (160°C 40 bar 500 ml h 56 s) at full conversion, which approaches good practice in a laboratory-scale flask. Compared to the latter, the 120°C-higher microreactor operation results in a 130-fold decrease in reaction time and a 440-fold increase in space-time yield. The use of still higher temperatures, however, is limited by the increasing decarboxylation of the product, which was monitored at various residence times (t). 

The equilibrium values are not reached at a rhodium catalyst on a micro structured reactor within the limits of the experimental conditions and the constructional constraints [3]. As possible explanations post-catalytic reactions at lower temperatures or, more likely, insufficient catalyst activity concerning the short residence times are seen. 

Given that the long residence time of uranium should place limits on how much the marine value could change over Late Quaternary time scales, several workers have used models to determine what these limits should be (see Henderson and Anderson 2003). Chen et al. (1986) and Edwards (1988) used a simple one-box model and assumed steady state conditions. They showed that ... 

In this paper we have looked firstly at the effect that the catalyst concentration, secondly at the effect that the reactor temperature and finally at the effect that the residence time at temperature have on the chemical structure of the oils (hexane soluble product) produced on hydropyrolysis (dry hydrogenation) of a high volatile bituminous coal. Generally, the hydropyrolysis conditions used in this study resulted in oil yields that were considerably higher than the asphaltene yields and this study has been limited to the effects that the three reaction conditions have on the chemical nature of the oils produced. 

The design q>roblem can be approached at various levels of sophistication using different mathematical models of the packed bed. In cases of industrial interest, it is not possible to obtain closed form analytical solutions for any but the simplest of models under isothermal operating conditions. However, numerical procedures can be employed to predict effluent compositions on the basis of the various models. In the subsections that follow, we shall consider first the fundamental equations that must be obeyed by all packed bed reactors under various energy transfer constraints, and then discuss some of the simplest models of reactor behavior. These discussions are limited to pseudo steady-state operating conditions (i.e., the catalyst activity is presumed to be essentially constant for times that are long compared to the fluid residence time in the reactor). 

Our main motivation to develop the specific transient technique of wavefront analysis, presented in detail in (21, 22, 5), was to make feasible the direct separation and direct measurements of individual relaxation steps. As we will show this objective is feasible, because the elements of this technique correspond to integral (therefore amplified) effects of the initial rate, the initial acceleration and the differential accumulative effect. Unfortunately the implication of the space coordinate makes the general mathematical analysis of the transient responses cumbersome, particularly if one has to take into account the axial dispersion effects. But we will show that the mathematical analysis of the fastest wavefront which only will be considered here, is straight forward, because it is limited to ordinary differential equations dispersion effects are important only for large residence times of wavefronts in the system, i.e. for slow waves. We naturally recognize that this technique requires an additional experimental and theoretical effort, but we believe that it is an effective technique for the study of catalysis under technical operating conditions, where the micro- as well as the macrorelaxations above mentioned are equally important. 

Figure 12.8 Calculated trajectories of fluid particles in the combustor with flame holder (solid lines) and the curves of constant dimensionless residence time t/tr (dashed curves). The residence time tr is defined as the time taken for the fluid particle to reach the turning point at the limiting trajectory (marked by the arrow). Conditions are similar to Fig. 12.66... 

Figure 12.9 To the determination of the limiting inlet velocity for the stabilized combustion of the stoichiometric methane-air mixture in the combustor with open-edge V-gutter flame holders. Solid curves correspond to the calculated residence time b- Dashed curves correspond to the calculated reaction time tc. Flame holders with H = 10 cm (f), 5 cm (2), and 2 cm (3). Conditions are similar to those in Figs. 12.6 and 12.7...

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