Equivalent residence time

Equivalent residence time (ERT) can be found after the temperature profile has been established ... 

For an isothermal reactor operating at the fmai temperature 7 at the pyrolysis tube exit, the equivalent residence time which serves to achieve an identical conversion... 

As shown in Table III, a low heating rate (T6 min. to 3 0°C), implying a residence time of 30 minutes between 250 and 3 0°C, leads to a conversion of 20.2 7o of wood into char, when with an equivalent residence time at 3 0°C after a rapid hydropyrolysis, the production of char is only 12,k %. Moreover, a residence time of 30 minutes at 300°C without iron, leads to the formation of a black powder (it.2 %) that can be considered as an irreversible condensation product. Consequently, it appears that the residence time in the 250-300°C range is critical for the direction of the conversion of wood either into liquid compounds or on the contrary towards char, but then the liquids obtained at higher temperature are less sensible to recondensation into solids. 

From this, it is clear that an equivalent residence time for the CSTR (using mass fractions) must incorporate the ratio of catalyst mass to CSTR feed rate. Hence, in this instance... 

Instead, we propose the following coordinate transformation that for every reactor volume V, we may associate an equivalent residence time r. If we let dV/dr = Q, then substitution of this relation into the DSR expression gives the desired DSR expression in terms of residence time as follows ... 

The optimal network increases total residence time by 48 per cent when compared with an equivalent MSMPR of the same volume and throughput. This increase would translate into a similar increase in mean crystal size and a 78 per cent increase in yield. Exactly the same residence time as for the single crystallizer have been reported from simple cascade configurations previously designed for stage-wise crystallization processes for slight improvements in... 

Vertical thermosiphon Capable of very high heat transfer rates. Compact simple piping required. Low residence time in heated zone. Not easily fouled. Good controllability. Maintenance and cleaning can be awkward. Additional column skirt required. Equivalent to theoretical plate only at high recycle. 

Flooded-bundle (kettle) Easy maintenance and cleaning. Convenient when heating medium is dirty. Equivalent to theoretical plate. Contains vapor disengaging space. Lower heat transfer rates. Extra piping and space required. High residence time in heated zone. Easily fouled. 

The results of Massimilla et al., 0stergaard, and Adlington and Thompson are in substantial agreement on the fact that gas-liquid fluidized beds are characterized by higher rates of bubble coalescence and, as a consequence, lower gas-liquid interfacial areas than those observed in equivalent gas-liquid systems with no solid particles present. This supports the observations of gas absorption rate by Massimilla et al. It may be assumed that the absorption rate depends upon the interfacial area, the gas residence-time, and a mass-transfer coefficient. The last of these factors is probably higher in a gas-liquid fluidized bed because the bubble Reynolds number is higher, but the interfacial area is lower and the gas residence-time is also lower, as will be further discussed in Section V,E,3. 

Axial Dispersion. Rigorous models for residence time distributions require use of the convective diffusion equation. Equation (14.19). Such solutions, either analytical or numerical, are rather difficult. Example 15.4 solved the simplest possible version of the convective diffusion equation to determine the residence time distribution of a piston flow reactor. The derivation of W t) for parabolic flow was actually equivalent to solving... 

The figure shows the ratio of the widths of initially delta-like concentration tracers at the reactor exits as a function of the micro-channel Peclet number for different values of the porosity. Taking a value of = 0.4 as standard, it becomes apparent that the dispersion in the micro-channel reactor is smaller than that in the fixed-bed reactor in a Peclet number range from 3 to 100. Minimum dispersion is achieved at a Peclet number of about 14, where the tracer width in the micro-channel reactor is reduced by about 40% compared with its fixed-bed counterpart. Hence the conclusion may be drawn that micro-channel reactors bear the potential of a narrower residence time than fixed-bed reactors, where again it should be stressed that reactors with equivalent chemical conversion were chosen for the comparison. 

Kettle reboilers have lower heat-transfer coefficients than the other types, as there is no liquid circulation. They are not suitable for fouling materials, and have a high residence time. They will generally be more expensive than an equivalent thermosyphon type as a larger shell is needed, but if the duty is such that the bundle can be installed in the column base, the cost will be competitive with the other types. They are often used as vaporisers, as a separate vapour-liquid disengagement vessel is not needed. They are suitable for vacuum operation, and for high rates of vaporisation, up to 80 per cent of the feed. 

When choosing between different types of reactors, both continuous and batch reactors were considered from the point of view of the performance of the reactor (continuous plug-flow and ideal batch being equivalent in terms of residence time). If a batch reactor is chosen, it will often lead to a choice of separator for the reactor effluent that also operates in batch mode, although this is not always the case as intermediate storage can be used to overcome the variations with time. Batch separations will be dealt with in Chapter 14. 

Also the thermohydrolysis of the urea solution after the injection into the hot exhaust gas upstream of the SCR catalyst has been investigated at the diesel test rig. Urea solution was atomized about 3 m upstream of the SCR catalyst into the hot exhaust equivalent to a residence time in the pipe section of 0.1 s at 440°C. As expected for the thermolysis reaction, ammonia and isocyanic acid were found at the catalyst entrance at all temperatures (Figure 9.3). The 1 1 ratio of both components shows that only the thermolysis but not the hydrolysis is taking place in the gas phase. It can also be seen that the residence time of 0.1 s is not sufficient for the quantitative thermolysis of urea, as appreciable amounts of undecomposed urea were always found. The urea share even raises with lowering the flue gas temperature, although the residence time... 

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