Mixing lateral

As can be seen from the plots, the minimum TAC is about 55,OOQ/yr. The opdmal permeate composition is about 0.0005 kmol/m which conesponds to a feed pressure of 48 atm. It is interesting to note that the optimum value of Cp is significantly less than the required target composition (0.0012 kmol/m ). In other words, more separation can be obtained for less cost It is also worth mentioning that in some cases, environmental regulations tnay allow the bypass of a fraction of the feed and later mix it with the over-separated permeate to attain the requited target composition. In such cases, lower costs than the ones shown in Figs. 11.5 and 11.6 can be accomplished. 

It is important that combustion of the coke in the spent catalyst occur in the dense bed of catalyst. Without the catalyst bed to absorb this heat of combustion, the dilute phase and flue gas temperatures increase rapidly. This phenomenon is called afterburning. It is critical that spent catalyst and combustion/lift air are being introduced into the regenerator as evenly as possible across the catalyst bed. It is also important to note that vertical mixing is much faster than lateral mixing. 

By independence we mean that the fluid loses its memory as it passes from vessel to vessel. Thus, a faster-moving fluid element in one vessel does not remember this fact in the next vessel and doesn t preferentially flow faster (or slower) there. Laminar flow often does not satisfy this requirement of independence however, complete (or lateral) mixing of fluid between units satisfies this condition. 

Each flow pattern of fluid through a vessel has associated with it a definite clearly defined residence time distribution (RTD), or exit age distribution function E. The converse is not true, however. Each RTD does not define a specific flow pattern hence, a number of flow patterns—some with earlier mixing, others with later mixing of fluids—may be able to give the same RTD. 

For reactions with rates that are linear in concentration, conversions cannot be calculated from tracer information alone, since a given tracer curve can represent a range of flow patterns with earlier or later mixing... 

Vertical Mixing by Turbulence Lateral Mixing by Turbulence Longitudinal Mixing by Dispersion... 

Note that incomplete lateral mixing of Cw does not alter the average surface concentration provided that vertical mixing is complete. Thus, Eq. 24-21 remains... 

By analogy to vertical mixing, the time and distance characteristic of lateral mixing can be expressed as ... 

Second, remembering the picture of the railway tracks we used in Section 22.4 to describe dispersion, we concluded that if the number of streamlines (tracks) is limited, then the dispersion coefficient should be inversely related to lateral diffusivity. Thus, from the concept of lateral mixing time (Eq. 24-38) one expects... 

Yet, this is not the only, and usually not even the most important reason why the concentration measured at a fixed location is asymmetric in time. In many cases chemicals enter the river from outfalls (see Fig. 24.4). Remember that vertical mixing usually occurs over a short distance, whereas lateral mixing may need more time (or distance). As discussed before, it is mostly the lateral mixing (or rather its slowness ) which allows longitudinal dispersion. As long as not all streamlines are occupied , the dispersion coefficient is small and the concentration front steep. 

Vertical and lateral mixing are not considered here. It is assumed that a given mass flux of a compound is mixed instantaneously into the corresponding volume flux of water. Of course, close to the input, vertical and lateral mixing are the most important mechanisms to reduce the concentration in the river. Also note that processes 3, 4, and 5 are only effective in reducing the concentration of the compound for the case of an episodic input. If a compound is continuously added to the river, the sediments reach an equilibrium with the river water and thus do not act as a sink anymore. Similarly, dispersion does not reduce the concentration of a compound that is permanently added to the river. 

Since not enough information is available on the exact input mode of the polluted water into the River Rhine, the initial mixing phase will not be considered. In fact, a hydroelectric power station located a few kilometers downstream of the spill significantly accelerated vertical and lateral mixing. The total mass of disulfoton, which had entered the river, was indirectly calculated from water samples taken at Village Neuf located about 10 km downstream of the power station. In these samples the concentration of disulfoton was about 100 ig L-1. 

These polyesters are primarily copolyesters of propylene glycol with maleic and phthalic acids, dissolved in styrene monomer, and cured by peroxides activators (1, 4, 5). In a typical general-purpose polyester, a 103 excess of propylene glycol is cooked with an equimolar mixture of maleic and phthalic anhydrides for eight or more hours at 150-200°C to produce a viscous liquid polyester of 1000-5000 molecular weight. This is then partially cooled, diluted about 60/40 with styrene monomer, cooled to room temperature, and stored. It is later mixed... 

Huber et al. (loc. cit.) and Yuan and Spiegel [Chem. Ing. Tech. 54, 774 (1982)] added lateral mixing to the model. Lateral deflection of liquid by the packing particles tends to homogenize the liquid, thus counteracting the channeling and pinching effect. 

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