Reactors dead zones

The available models mostly refer to ideal reactors, STR, CSTR, continuous PFR. The extension of these models to real reactors should take into account the hydrodynamics of the vessel, expressed in terms of residence time distribution and mixing state. The deviation of the real behavior from the ideal reactors may strongly affect the performance of the process. Liquid bypass - which is likely to occur in fluidized beds or unevenly packed beds - and reactor dead zones - due to local clogging or non-uniform liquid distribution - may be responsible for the drastic reduction of the expected conversion. The reader may refer to chemical reactor engineering textbooks [51, 57] for additional details. 

An ideal reactor model is composed of complete mix reactors with leaky dead zones that are also complete mixed. Assuming a pulse input to reactor 1, derive the concentration versus time equation for the third reactor-dead zone combination. Derive the concentration versus time equation for the nth reactor-dead zone combination. 

Often, complete mixing cannot be approached for economic reasons. Inactive or dead zones, bypassing, and limitations of energy input are common causes. Packed beds are usually predominantly used in plug flow reactors, but they may also have small mixing zones... 

Elow intensification is made with the use of apparatuses in which flow follows a perfect plug flow the internal parts of the reactor have to be designed accordingly. Indeed, dead zones, that is, reactant accumulation, must be avoided not only in order to have better selectivity and yield but also to avoid formation of hot spots, which would generate safety problems. 

Figure 3.25. Stirred-tank reactor with dead zones.

In this model of non-ideal reactor mixing, a fraction, fi, of the volumetric feed rate, F, completely by-passes the mixing in the reactor. In addition, a fraction, f2, of the reactor volume, V, exists as dead space. F3 is the volumetric rate of exchange between the perfectly mixed volume Vi and the dead zone volume V2 of the reactor. 

Tank reactor, with a bypass and a dead-zone. The bypass Is modelled by a series of tanks. The reaction is nth-order. 

Dead Zones - Dead zones in a complete mix reactor do not participate in the mixing process. They effectively reduce the reactor size, with no exchange between the dead zone and the reactor. An example might be a wetland at the edge of... 

Bypass - A bypass is a parallel path taken by a portion of the fluid that skips the reactor altogether without any residence time. As with dead zones, a bypass is not very useful unless a plug flow or mixed tank reactor is placed into the bypass, resulting in a parallel-flow reactor system. 

The skew in the fit of the tracer curve in Example 6.7 occurs because the tails are not modeled well. This is a problem with the reactors-in-series model and most computational models as well. A solution to this curve-fit problem will be discussed in the next section on leaky dead zones. For most applications, in transport modeling. 

There are many real-life situations resulting in a tracer pulse or front with a long tail, where the pulse or front does not decay nearly as quickly as it rises. The fit of the tanks-in-series to the tracer pulse in Example 6.7 is typical of the trailing edge problem. These can be solved by employing a leaky dead-zone model. There are physical arrangements of transport problems where the need of a leaky dead zone seems apparent, such as a side embayment on a lake or river, or a stratified lake where a well-mixed reactor will be used to model the lake. These are illustrated in... 

Figure 6.8. But, the need of a leaky dead zone is more ubiquitous than these examples imply. To develop a model with a fit, which does not have a strong bias at certain parts of a tracer pulse curve for any reactor or river, for example, a leaky dead zone is a better model.

The concept of a leaky dead zone is illustrated in Figure 6.9. A complete mix reactor is connected to a leaky dead zone through the inflow and outflow discharges to and from the dead zone, Qd. The dead zone is, in itself, a complete mix reactor, but it is not part of the main flow system with discharge Q. The independent parameters that can be ht to a tracer pulse or front are the volume of the primary complete mix reactor, Vi, the volume of the dead zone, Vd, and the discharge into and out of the dead zone, Qd. 

There are two mass transport equations - the main reactor and the dead-zone reactor - that need to be solved for the reactor combination given in Figure 6.9. These are... 

Figure 6.9. Illustration of a complete mix reactor with a leaky dead zone.

A reactor modeled as a complete mix reactor with a leaky dead zone will have a concentration front from Q =0to Q = Co applied. Develop an equation for the concentration in the outflow of the reactor. 

Figure E6.8.2. Solution of a complete mix reactor with a leaky dead zone to a step-down concentration front applied at f = 0 with ty = 1.2 hrs and h = 1 hr.

Boundary condition 1 occurs because the pulse is instantaneously mixed only into the primary reactor in the model. Boundary condition 2 indicates that, as the dead zone disappears, the reactor becomes a standard complete mix reactor. Applying boundary condition 1 gives... 

With this definition for the initial value of Co will generally be greater than 1. Note that equations (E6.9.1) and (E6.9.5) result in = 0. The solution to a pulse tracer input to a complete mix reactor with a leaky dead zone is thus... 

Stochastic modeling is used when a measurable output is available but the inputs or causes are unknown or cannot be described in a simple fashion. The black-box approach is used. The model is determined from past input and output data. An example is the description of incomplete mixing in a stirred tank reactor, which is done in terms of contributions of dead zones and short circuiting. In these cases, a sequence of output called a time series is known, but the inputs or causes are numerous and not known in addition, they may be unobservable. Though the causes for the response of the system are unknown, the development of a model is important to gain understanding of the process, which may be used for future planning. 

The continuous-stirred tank reactor (CSTR) has continuous input and output of material. The CSTR is well mixed with no dead zones or bypasses in ideal operation. It may or may not include baffling. The assumptions made for the ideal CSTR are (1) composition and temperature are uniform everywhere in the tank, (2) the effluent composition is the same as that in the tank, and (3) the tank operates at steady state. 

This implies that the necessary recirculation ratio is not a fixed value, but depends on the reaction under consideration and the conversion level. At low conversions, the recirculation rate need not be high according to this criterion (good mixing, eq 5, is still required to avoid dead zones in the reactor), and a differential PFR model can be used. At high conversions, the recirculation rate must increase. It can easily be seen that a recirculation ratio of 20 limits the conversion for a first-order and a second-order reaction to 50% and 25%, respectively. 

From an operational point of view, the choice of an appropriate polymerization reactor depends on six requirements temperature control mixing product accumulation and reactor foul-up follow-up separation processes the desired form of the product and safety. Heats of polymerization are typically high, so that maintaining the reactor at a desired temperature level is not always a simple task. Temperature can become spatially nonuniform and globally out of control (causing inconsistency of the reaction medium). Nonuniformity in temperature can lead to localized zones of poor mixing or even dead zones. In a polymerization reactor, temperature, mixing, viscosity,... 

Flow maldistribution of the phases can render the evaluation of RTD data very difficult. In some cases, maldistribution may exist in small units but it may not exist in large-scale units (e g., trickle-bed reactors). While in some other cases, such as three-phase fluidized-bed reactors, nonuniform gas distribution in large-scale units may cause undesirable recirculation and dead zones. Uniform gas distribution can usually be achieved in the small-scale fluidized-bed reactor. 

---