Tubular reactors residence-time distribution

Tanks-in-series reactor configurations provide a means of approaching the conversion of a tubular reactor. In modelling, they are employed for describing axial mixing in non-ideal tubular reactors. Residence time distributions, as measured by tracers, can be used to characterise reactors, to establish models and to calculate conversions for first-order reactions. 

Problem. Think about the overall strategy that must be implemented to account for the effect of interpellet axial dispersion on ihe outlet concentration of reactant A when Langmuir-Hinshelwood kinetics and Hougen-Watson models are operative in a packed catalytic tubular reactor. Residence-time distribution effects are important at small mass transfer Peclet numbers. 

The most commonly used model of a mixed vessel is the fractional tubularity (delay-lag) model in which some part of the reactor is taken as exhibiting plug-flow conditions and contributing a delay and the rest of the reactor is taken as perfectly mixed (uniform concentrations) contributing a first-order lag (/( ,). The delay and lag in series are taken as describing the reactor residence time distribution (RTD). The delay-lag representation was validated using both CFD analysis and experimental residence time distributions (Walsh, 1993). 

Figure 2.10 Homopolymer/copolymer distribution for impact copolymers made in a series of two tubular reactors or two CSTRs. The wide residence time distribution of the CSTRs is reflected in the non-uniform homopolymer/copolymer distribution in the particles. The distribution of homopolymer (light gray) and copolymer (dark gray) phases is only to illustrate the effect of reactor residence time distribution. In reality, one phase is dispersed into the other.

Even though tubular reactors are not used industrially for the production of impact copolymers, some reactor technologies (such as gas phase horizontal reactors) were developed to narrow the reactor residence time distribution and, consequently, produce impact copolymer with narrower homopolymer/copolymer distributions. 

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

Figure 3.12 Residence time distribution in a micro reactor which is tightened by different means. ( ) Glued reactor without catalyst coating (X) glued reactor with catalyst coating ( ) reactor with graphite joints. Calculated curves for tubular reactors with the Bodenstein number Bo = 33 (solid line) and Bo = 70 (dashed line).

Chemical Kinetics, Tank and Tubular Reactor Fundamentals, Residence Time Distributions, Multiphase Reaction Systems, Basic Reactor Types, Batch Reactor Dynamics, Semi-batch Reactors, Control and Stability of Nonisotheimal Reactors. Complex Reactions with Feeding Strategies, Liquid Phase Tubular Reactors, Gas Phase Tubular Reactors, Axial Dispersion, Unsteady State Tubular Reactor Models... 

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. 

In a laminar flow reactor (LFR), we assume that one-dimensional laminar flow (LF) prevails there is no mixing in the (axial) direction of flow (a characteristic of tubular flow) and also no mixing in the radial direction in a cylindrical vessel. We assume LF exists between the inlet and outlet of such a vessel, which is otherwise a closed vessel (Section 13.2.4). These and other features of LF are described in Section 2.5, and illustrated in Figure 2.5. The residence-time distribution functions E(B) and F(B) for LF are derived in Section 13.4.3, and the results are summarized in Table 13.2. 

Figure 8-5 Residence time distribution in a laminar flow tubular reactor. The dashed curve indicates the p t) curve expected in laminar flow after allowing for radial diffusion, which makes p(t) closer to the plug flow.

Tubular reactor advantages include their well-defined residence time distributions, turbulent mixing reactants, ease of obtaining and applying kinetic data, efficient use of reactor volume, and mechanical simplicity. However, great care must be taken when applying the correct flow model (e.g., plug... 

The three ideal reactors form the building blocks for analysis of laboratory and commercial catalytic reactors. In practice, an actual flow reactor may be more complex than a CSTR or PFR. Such a reactor may be described by a residence time distribution function F(t) that gives the probability that a given fluid element has resided in the reactor for a time longer than t. The reactor is then defined further by specifying the origin of the observed residence time distribution function (e.g., axial dispersion in a tubular reactor or incomplete mixing in a tank reactor). 

In stirred tanks, the power input to agitate the tank will depend on the physical properties of the liquid. In tubular reactors, the axial dispersion in empty tubes may be estimated [e.g., Wen in Petho and Noble (eds.), Residence Time Distribution Theory in Chemical Engineering, Verlag Chemie, 1982] as... 

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. 

In a multichannel monolith with cocurrent downflow, each channel will have the same residence time and a residence-time distribution close to an ideal tubular reactor. But due to nonuniform flow distribution, the gas-liquid ratio, the volume reactant per volume catalyst, and, consequently, the conversion can be very different in different channels. 

Tubular reactors with different designs are often used in chemical reaction ingineering as hold-up sections for completing the reaction of the reaction mixture, because they offer a much narrower residence time distribution than tanks in series. 

An alternative to filling or coating with a catalyst layer the microcharmels, with the related problems of avoiding maldistribution, which leads to a broad residence time distribution (RTD), is to create the microchannels between the void space left from a close packing of parallel filaments or wires. This novel MSR concept has been applied for the oxidative steam reforming of methanol [173]. Thin linear metallic wires, with diameters in the millimeter range, were close packed and introduced into a macro tubular reactor. The catalyst layer was grown on the external surface of these wires by thermal treatment. 

Fig. 6-7 Residence-time distribution in a laminar-flow tubular reactor (segregated flow)...

The reactor in which chemical reactions lake place is fhe mosl imporlanl piece of equipmenl in each chemical planl. A variety of reactors are used in induslry, bul all of Ihem can be assigned to cerlain basic types or a combination of fhese ideal reactors [53] (1) bafch slirred-lank reactor, (2) continuous slirred-lank reactor, and (3) lubular reactor. The ideal slirred-lank bafch reactor is characterized by complete mixing, while in the ideal tubular reactor, plug flow is assumed. In contrast to the stirred-tank batch reactor with well-defined residence time, the continuous stirred-tank reactor has a very broad residence-time distribution. In... 

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