Residence time distribution , for reactors

SECnON 6-4 RESIDENCE-TIME DISTRIBUTIONS FOR REACTORS WITH KNOWN MIXING STATES 251... 

Residence-time Distributions for Reactors with Known Mixing States... 

RESIDENCE TIME DISTRIBUTION FOR A LAMINAR FLOW TUBULAR REACTOR... 

Glaser and Litt (G4) have proposed, in an extension of the above study, a model for gas-liquid flow through a b d of porous particles. The bed is assumed to consist of two basic structures which influence the fluid flow patterns (1) Void channels external to the packing, with which are associated dead-ended pockets that can hold stagnant pools of liquid and (2) pore channels and pockets, i.e., continuous and dead-ended pockets in the interior of the particles. On this basis, a theoretical model of liquid-phase dispersion in mixed-phase flow is developed. The model uses three bed parameters for the description of axial dispersion (1) Dispersion due to the mixing of streams from various channels of different residence times (2) dispersion from axial diffusion in the void channels and (3) dispersion from diffusion into the pores. The model is not applicable to turbulent flow nor to such low flow rates that molecular diffusion is comparable to Taylor diffusion. The latter region is unlikely to be of practical interest. The model predicts that the reciprocal Peclet number should be directly proportional to nominal liquid velocity, a prediction that has been confirmed by a few determinations of residence-time distribution for a wax desulfurization pilot reactor of 1-in. diameter packed with 10-14 mesh particles. 

Two template examples based on a capillary geometry are the plug flow ideal reactor and the non-ideal Poiseuille flow reactor [3]. Because in the plug flow reactor there is a single velocity, v0, with a velocity probability distribution P(v) = v0 16 (v - Vo) the residence time distribution for capillary of length L is the normalized delta function RTD(t) = T 1S(t-1), where x = I/v0. The non-ideal reactor with the para-... 

The residence time distribution for a continuous stirred tank reactor may be represented in terms of the F(t) curve as... 

These relationships are of profound importance for, once a reactor has been described by means of a transfer function, they enable the residence time distribution for that reactor to be chsiracterised in terms of its mean, variance, skewness, etc. Such a characterisation in terms of a few low-order moments is often entirely adequate for the requirements of chemical reaction engineering. 

Generally, alkoxide-derived monodisperse oxide particles have been produced by batch processes on a beaker scale. However, on an industrial scale, the batch process is not suitable. Therefore, a continuous process is required for mass production. The stirred tank reactors (46) used in industrial process usually lead to the formation of spherical, oxide powders with a broad particle size distribution, because the residence time distribution in reactor is broad. It is necessary to design a novel apparatus for a continuous production system of monodispersed, spherical oxide particles. So far, the continuous production system of monodisperse particles by the forced hydrolysis... 

Isothermality in this reactor is difficult to maintain however, wall heat transfer is better than for fixed-bed reactors. Salt or sand baths may be required for isothermality. Residence-time distributions for all three phases can be measured accurately. At low velocity, slip between phases is a problem, but more... 

If recirculation rates are 10 to 15 times the feed rate, the reactor would tend to operate nearly isothermally. High velocities past the bed of particles could eliminate almost completely any external mass-transfer influence on the reactor performance. By varying the circulation rates, the reaction condition for which the mass transfer effect is negligible can be established. Except for the rapidly-decaying catalyst system, steady state can be achieved effectively. Sampling and product analysis can be obtained as effectively as in the fixed-bed reactor. Residence-time distributions for the fluid phases can be measured easily. High fluid velocities would cause less flow-maldistribution problems. 

Residence-time distributions for the gas and liquid phases in this type of reactor can be evaluated easily. The reactor is operated under transient conditions if the catalyst decays rapidly. Otherwise, steady-state operation is obtained. Baffles can be installed to obtain better contact. When both homogeneous and heterogeneous reactions occur simultaneously, their rates can be separated by obtaining the results at various stirrer speeds. This type of reactor has several dis-... 

By applying the mass balance equation to each reactor (see Exercise 7.9.2), it can be shown that just as Pi(z), the residence time distribution for one stage, is so in general... 

Octave Levenspiel, Chemical Reaction Engineering, John Wiley Sons, Inc., New York, 1962. A complete text for undergraduate students. The emphasis is rather more on homogeneous and noncatalytic reactors than on catalytic ones. Effects of residence-time distribution on reactor performance are treated in detail. 

Figure 831 Residence-time distribution for the optima reactor configuration.

Consider two arrangements of a PFR and CSTR of equal volume in series as shown in Figure 8.13. What are the residence-time distributions for the two reactor systems What are the oyerall cpoverslon.s for the two systems ... 

Residence time the residence time t takes into account the time in which each fluid element or molecule passes through the reactor and it depends on the molecules velocity inside the reactor therefore, it depends on the flow in the reactor. Residence time is equal to space time if the velocity is uniform in a cross section of the reactor, as in ideal tubular reactors. This situation is not valid to tank reactors, since the velocity distribution is not uniform. In most nonideal reactors, the residence time is not the same for all molecules, leading to variations in radial concentrations along the reactor and therefore, the concentration in the tank and at the reactor outlet is not uniform. That means we need to define initially the residence time and calculate the residence time distribution for each system. 

Joshi et al. (30) proposed reactor models based on the shrinking core mechanism. Since the particles take part in the reaction their role was evaluated based on the residence time distribution. For extremely fine pyrite particles, (< 100 ym), it has been shown (31) that the RTD of the solid and liquid phases can be asstimed to be identical and the RTD of the solid phase is given by the diffusion-sedimentation model. Various rate controlling steps that were considered are (1) gas-liquid mass transfer (2) liquid-solid mass transfer (3) ash diffusion (4) chemical reaction and, (5) intraparticle diffusional resistance (for particles encased in the coal matrix). 

The wide residence time distribution for an ideal backmix reactor is detrimental to high conversion of solids. However, the residence time distribution can be considerably narrowed by staging. The residence time distribution for a system with a N stages of fluidized beds of equal size can be estimated by... 

There is another practical method for estimating conversions in reactors with residence time distribution, for perfect micro-mixing, that is also applicable to other reaction orders. To this end the reactor is simulated by a model that consists of a cascade on N perfectly mixed equal reactors (section 3.3.3). The RTD-function of the cascade with total residence time x can be calculated ... 

An effective temperature control, which is a general problem with gas phase processes, can be realized for solid/gas processes by choosing a fluidized bed reactor. TTiis type of reactor usually has a good thermal stability. However, the residence time distribution for the gas phase in a fluidized bed is relatively large, which may limit the attainable degree of conversion. 

Broad or narrow residence time distribution (for continuous reactors). 

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