Transient plug flow reactors

In Chapter 3, the analytical method of solving kinetic schemes in a batch system was considered. Generally, industrial realistic schemes are complex and obtaining analytical solutions can be very difficult. Because this is often the case for such systems as isothermal, constant volume batch reactors and semibatch systems, the designer must review an alternative to the analytical technique, namely a numerical method, to obtain a solution. For systems such as the batch, semibatch, and plug flow reactors, sets of simultaneous, first order ordinary differential equations are often necessary to obtain the required solutions. Transient situations often arise in the case of continuous flow stirred tank reactors, and the use of numerical techniques is the most convenient and appropriate method. 

The plug flow reactor is increasingly being used under transient conditions to obtain kinetic data by analysing the combined reactor and catalyst response upon a stimulus. Mostly used are a small reactant pulse (e.g. in temporal analysis of products (TAP) [16] and positron emission profiling (PEP) [17, 18]) or a concentration step change (in step-response measurements (SRE) [19]). Isotopically labeled compounds are used which allow operation under overall steady state conditions, but under transient conditions with respect to the labeled compound [18, 20-23]. In this type of experiments both time- and position-dependent concentration profiles will develop which are described by sets of coupled partial differential equations (PDEs). These include the concentrations of proposed intermediates at the catalyst. The mathematical treatment is more complex and more parameters are to be estimated [17]. Basically, kinetic studies consist of ... 

Fig.4.4-5a demonstrates the effect of p on the transient response of C2 and Cn, i.e. the first and the last perfectly mixed reactors in the upper plug flow reactor in Fig.4.4-5. The tracer was introduced into reactor 2. It is obsereved that by increasing p from 80 to 800, the number of oscillations for reaching the steady state concentration 1/22 in the system is increased. It should also be noted that for p = 800, the distance between two successive peaks corresponding to C2 and Cn is...

Reactors do not always run at steady state. In fact, many pharmaceuticals are made in a batch mode. Such problems are easily solved using the same techniques presented above because the plug flow reactor equations are identical to the batch reactor equations. Even CSTRs can be run in a transient mode, and it may be necessary to model a time-dependent CSTR to study the stability of steady solutions. When there is more than one solution, one or more of them will be unstable. Thus, this section considers a time-dependent CSTR as described by Eq. (8.51) ... 

Compute the transient behavior of the dispersed plug-flow reactor for the isothermal, liquid-phase, second-order reaction... 

We turn now to the plug flow reactor. Here, as we have said, there is absolutely no mixing in the direction of flow but perfect mixing perpendicular to it, that is, between the centerline and the walls. This special case of a tubular reactor can be operated transiently or in the steady state, but it is the latter mode that is most often considered for kinetics and design. Consider the reactor shown in Figure 4 in which A is converted to B irreversibly and with linear kinetics. 

Simple transient state experiments in laboratory plug flow reactors can qualitatively tell whether the surface processes mentioned above are instantaneous or not. For example, a step composition change can lead to two types of results. Either the outlet composition follows what is expected from tlie steady state rate equations or not. In the fonner case, one may assume quasi steady state. In the latter case, one is facing a slow surface step (oxidation/reduction of rhodiiun, oxygen storage/release, transient deactivation by SO2, etc.) that affects the main reaction mechanism. 

Because the transient data for methanation reaction are more accurate than those for C2-C5 hydrocarbons. By decoupling the methanation reaction, rate coefficients for the initial part of the mechanism can be fixed, followed by correct account of readsorption of reactive olefins during subsequent modeling based on a plug-flow reactor model. 

Happel, I, Walter, E., Lecourtier, Y. (1990) Modeling transient tracer studies in plug-flow reactors. /. Catal., 123, 12-20. 

In the case of transient operation, an accumulation term, that is, a differential term with respect to time, has to be added to equations 79 and 80 for being able to describe the observations. A batch reactor with uniform concentrations throughout the entire reactor but without continuous feed addition and effluent removal, is inherently operating in a transient regime. The corresponding reactor model equation is analogous to that of a plug flow reactor with the derivative taken with respect to time rather than with respect to position ... 

Walter, E. and Happel, J. (1995) Modeling transient tracing in plug-flow reactors a... 

Insertion of these rate laws in mass balances of ideal reactors (batch/plug flow or transient CSTR) leads to systems of semi-linear, first-order, partial differential equations, with a single family of characteristics [Eq. (139)]. 

COSILAB Combustion Simulation Software is a set of commercial software tools for simulating a variety of laminar flames including unstrained, premixed freely propagating flames, unstrained, premixed burner-stabilized flames, strained premixed flames, strained diffusion flames, strained partially premixed flames cylindrical and spherical symmetrical flames. The code can simulate transient spherically expanding and converging flames, droplets and streams of droplets in flames, sprays, tubular flames, combustion and/or evaporation of single spherical drops of liquid fuel, reactions in plug flow and perfectly stirred reactors, and problems of reactive boundary layers, such as open or enclosed jet flames, or flames in a wall boundary layer. The codes were developed from RUN-1DL, described below, and are now maintained and distributed by SoftPredict. Refer to the website http //www.softpredict.com/cms/ softpredict-home.html for more information. 

The chemical reactor is the unif in which chemical reactions occur. Reactors can be operated in batch (no mass flow into or out of the reactor) or flow modes. Flow reactors operate between hmits of completely unmixed contents (the plug-flow tubular reactor or PFTR) and completely mixed contents (the continuous stirred tank reactor or CSTR). A flow reactor may be operated in steady state (no variables vary with time) or transient modes. The properties of continuous flow reactors wiU be the main subject of this course, and an alternate title of this book could be Continuous Chemical Reactors. The next two chapters will deal with the characteristics of these reactors operated isothermaUy. We can categorize chemical reactors as shown in Figure 2-8. 

Note that setting one of the terms on the left side of the equation equal to zero yields either the batch reactor equation or the steady-state PFTR equation. However, in general we must solve the partial differential equation because the concentration is a function of both position and time in the reactor. We will consider transients in tubular reactors in more detail in Chapter 8 in connection with the effects of axial dispersion in altering the perfect plug-flow approximation. 

Next consider the response of a PFTR with steady flow to a pulse injected at f = 0. Wc could obtain this by solving the transient PFTR equation written earher in this chapter, but we can see the solution simply by following the pulse down the reactor. (This is identical to the transformation we made in transforrning the batch reactor equations to the PFTR equations.) The S(0) pulse moves without broadening because we assumed perfect plug flow, so at position z the pulse passes at time z/u and the pulse exits the reactor at time T = L/u. Thus for a perfect PFTR the RTD is given by... 

An attractive property of monolithic reactors is their flexibility of application in multiphase reactions. These can be classified according to operation in (semi)batch or continuous mode and as plug-flow or stirred-tank reactor or, according to the contacting mode, as co-, counter-, and crosscurrent. In view of the relatively high flow rates and fast responses in the monolith, transient operations also are among the possibilities. 

Various laboratory reactors have been described in the literature [3, 11-13]. The most simple one is the packed bed tubular reactor where an amount of catalyst is held between plugs of quartz wool or wire mesh screens which the reactants pass through, preferably in plug flow . For low conversions this reactor is operated in the differential mode, for high conversions over the catalyst bed in the integral mode. By recirculation of the reactor exit flow one can approach a well mixed reactor system, the continuous flow stirred tank reactor (CSTR). This can be done either externally or internally [11, 12]. Without inlet and outlet feed, this reactor becomes a batch reactor, where the composition changes as a function of time (transient operation), in contrast with the steady state operation of the continuous flow reactors. 

For all values of the variables studied, the gas-phase dispersion does not show a significant effect on the steady-state or transient characteristics of the liquid-phase or surface concentration. This means that, in modeling three-phase slurry reactors, the gas phase may be assumed to move in plug flow as long as the performance of the reactor is measured in terms of the change in concentration of the liquid phase. 

A related phenomenon is the "wrong-way behavior" of packed-bed reactors, where a sudden reduction in the feed temperature leads to a transient temperature rise. This has been observed (52, 59) and satisfactorily analyzed using a plug-flow pseudohomogeneous model (60). 

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