Continuous flow reactors residence time distribution

The residence times in a continuous flow reactor have a distribution that can be characterized by any of a trio of functions. One of these is the cumulative probability function F(t), which is the fraction of exiting material that was in the reactor for a time less than t. 

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. 

The time that a molecule spends in a reactive system will affect its probability of reacting and the measurement, interpretation, and modeling of residence time distributions are important aspects of chemical reaction engineering. Part of the inspiration for residence time theory came from the black box analysis techniques used by electrical engineers to study circuits. These are stimulus-response or input-output methods where a system is disturbed and its response to the disturbance is measured. The measured response, when properly interpreted, is used to predict the response of the system to other inputs. For residence time measurements, an inert tracer is injected at the inlet to the reactor, and the tracer concentration is measured at the outlet. The injection is carried out in a standardized way to allow easy interpretation of the results, which can then be used to make predictions. Predictions include the dynamic response of the system to arbitrary tracer inputs. More important, however, are the predictions of the steady-state yield of reactions in continuous-flow systems. All this can be done without opening the black box. 

Washout experiments can be used to measure the residence time distribution in continuous-flow systems. A good step change must be made at the reactor inlet. The concentration of tracer molecules leaving the system must be accurately measured at the outlet. If the tracer has a background concentration, it is subtracted from the experimental measurements. The flow properties of the tracer molecules must be similar to those of the reactant molecules. It is usually possible to meet these requirements in practice. The major theoretical requirement is that the inlet and outlet streams have unidirectional flows so that molecules that once enter the system stay in until they exit, never to return. Systems with unidirectional inlet and outlet streams are closed in the sense of the axial dispersion model i.e., Di = D ut = 0- See Sections 9.3.1 and 15.2.2. Most systems of chemical engineering importance are closed to a reasonable approximation. 

This study investigates the hydrodynamic behaviour of an aimular bubble column reactor with continuous liquid and gas flow using an Eulerian-Eulerian computational fluid dynamics approach. The residence time distribution is completed using a numerical scalar technique which compares favourably to the corresponding experimental data. It is shown that liquid mixing performance and residence time are strong functions of flowrate and direction. 

For a few highly idealized systems, the residence time distribution function can be determined a priori without the need for experimental work. These systems include our two idealized flow reactors—the plug flow reactor and the continuous stirred tank reactor—and the tubular laminar flow reactor. The F(t) and response curves for each of these three types of well-characterized flow patterns will be developed in turn. 

These possible flow patterns of a drop or bubble phase are shown in Figure 12-12. At the left is shown an isolated bubble which rises (turn the drawing over for a falling drop), a clearly unrtuxed situation, ff the bubble is in a continuous phase which is being stirred, then the bubble wiU swirl around the reactor, and its residence time will not be fixed but will be a distributed function. In the limit of very rapid stirring, the residence time of drops or bubbles wiU have a residence time distribution... 

Figure 12-12 Sketches of possible flow patterns of bubbles rising through a liquid phase in a bubble column. Stirring of the continuous phase will cause the residence time distribution to be broadened, and coalescence and breakup of drops will cause mixing between bubbles. Both of these effects cause the residence time distribution in the bubble phase to approach that of a CSTR. For falling drops in a spray tower, the situation is similar but now the drops fall instead of rising in the reactor.

The following equations are written for absorption (of any gas) in a continuous-flow stirred tank reactor (CFSTR) under the assumption that the gas and liquid phases are ideally mixed (Figure B 1-2). The assumption of an ideally mixed phase can be checked by determining the residence time distribution in the reactor (e. g. Levenspiel, 1972 Lin and Peng, 1997 Huang et al., 1998). 

The significant conclusion of this work is that although mixing of the fluid in the direction of flow has a strong influence on the stability of a continuous flow reactor, as can be seen by the way the parameters of the residence-time distribution are involved, the quantitative criterion for stability is independent of the mechanism by which such mixing occurs. The criterion applies equally well to imperfectly-... 

Particles of polypropylene are continuously formed at low pressure in the reactor (1) in the presence of catalyst. Evaporated monomer is partially condensed and recycled. The liquid monomer with fresh propylene is sprayed onto the stirred powder bed to provide evaporative cooling. The powder is passed through a gas-lock system (2) to a second reactor (3). This acts in a similar manner to the first, except that ethylene as well as propylene is fed to the system for impact co-polymer production. The horizontal reactor makes the powder residence time distribution approach that of plug-flow. The stirred bed is well suited to handling some high ethylene co-polymers that may not flow or fluidize well. 

The polymerization time in continuous processes depends on the time the reactants spend in the reactor. The contents of a batch reactor will all have the same residence time, since they are introduced and removed from the vessel at the same times. The continuous flow tubular reactor has the next narrowest residence time distribution, if flow in the reactor is truly plug-like (i.e., not laminar). These two reactors are best adapted for achieving high conversions, while a CSTR cannot provide high conversion, by definition of its operation. The residence time distribution of the CSTR contents is broader than those of the former types. A cascade of CSTR s will approach the behavior of a plug flow continuous reactor. 

For a continuous reactor with a nonideal flow pattern, characterized by the differential residence time distribution E t), the following expression holds for the conversion nonideai. which is attained in case complete segregation of all fluid elements passing through the reactor can be assumed ... 

The residence time distribution (RTD), also referred to as the distribution of ages, is based on the assumption that each element traveling through the column takes a different route and will therefore have a different residence time. Different methods are developed to determine the RTD in a module or in a reactor [190]. The RTD of a chromatographic column is defined by a function E (Figure 3.20), such that E dt is the fraction of material in the exit stream with an age between t and f - - dt. The -curve lies between the extremes of plug flow and continuously stirred tank reactor. The surface below the curve between f = 0 and t = oo has to be equal to unity E t) dt = 1, because all elements that enter the module must also exit the module. 

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