Unmixed reactors

A reactor will be isothermal at the feed inlet temperature Tq if (1) reactions do not generate or absorb significant heat or (2) the reactor is thermostatted by contact with a temperature bath at coolant temperature Tq. For any other situation we will have to solve the energy-balance equation long with the mass balance to find the temperature in the reactor. We therefore must set up these equations for our mixed and unmixed reactors. 

Flow pattern Next one decides whether a batch or continuous reactor is suitable and, if flow, whether a mixed of unmixed reactor is preferred. Initially one may do calculations for PFTR and CSTR to bracket all flow patterns. This is the subject of Chapters 3 and 4. The choice of catalyst and heat removal method will be very important in deciding the best flow pattern. 

Thus far we have considered only two flow patterns the completely mixed reactor and the completely unmixed reactor. This is because only for these flow patterns can we completely ignore the fluid flow configurations in the reactor. In this chapter we will begin to see how reactors that have more complex flow patterns should be treated. We will not attempt to describe the fluid mechanics completely. Rather, we will hint at how one would go about solving more realistic chemical reactor problems and examine the errors we have been making by using the completely mixed and unmixed approximations. 

Diffusion is important in reactors with unmixed feed streams since the initial mixing of reactants must occur inside the reactor under reacting conditions. Diffusion can be a slow process, and the reaction rate will often be limited by diffusion rather than by the intrinsic reaction rate that would prevail if the reactants were premixed. Thus, diffusion can be expected to be important in tubular reactors with unmixed feed streams. Its effects are difficult to calculate, and normal design practice is to use premixed feeds whenever possible. 

We turn now to the numerical solution of Equations (9.1) and (9.3). The solutions are necessarily simultaneous. Equation (9.1) is not needed for an isothermal reactor since, with a flat velocity profile and in the absence of a temperature profile, radial gradients in concentration do not arise and the model is equivalent to piston flow. Unmixed feed streams are an exception to this statement. By writing versions of Equation (9.1) for each component, we can model reactors with unmixed feed provided radial symmetry is preserved. Problem 9.1 describes a situation where this is possible. 

The difference between complete segregation and maximum mixedness is largest when the reactor is a stirred tank and is zero when the reactor is a PFR. Even for the stirred tank case, it has been difficult to find experimental evidence of segregation for single-phase reactions. Real CSTRs approximate perfect mixing when observed on the time and distance scales appropriate to industrial reactions, provided that the feed is premixed. Even with unmixed... 

Segregation may also be important if the reactants are fed to a reactor in an unmixed condition. This could be the case in any continuously fed reactor, either tubular (Fig. 5.133) or tank (Fig. 5.134). 

Figure 5.133. Feeding of unmixed reactants to a tubular reactor.

Another Lagrangian-based description of micromixing is provided by multienvironment models. In these models, the well macromixed reactor is broken up into sub-grid-scale environments with uniform concentrations. A four-environment model is shown in Fig. 5.16. In this model, environment 1 contains unmixed fluid from feed stream 1 environments 2 and 3 contain partially mixed fluid and environment 4 contains unmixed fluid from feed stream 2. The user must specify the relative volume of each environment (possibly as a function of age), and the exchange rates between environments. While some qualitative arguments have been put forward to fit these parameters based on fluid dynamics and/or flow visualization, one has little confidence in the general applicability of these rules when applied to scale up or scale down, or to complex reactor geometries. 

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. 

We win develop mass balances in terms of mixing in the reactor. In one limit the reactor is stirred sufficiently to mix the fluid completely, and in the other limit the fluid is completely unmtxed. In any other situation the fluid is partially mixed, and one cannot specify the composition without a detailed description of the fluid mechanics. We wiU consider these nonideal reactors in Chapter 8, but until then all reactors wiU be assumed to be either completely mixed or completely unmixed. 

Reactors have volume V. Continuous-flow reactors have volumetric flow rate V, and constant-density reactors have residence time X = V/v. Until Chapter 8 all continuous reactors are either completely mixed (the CSTR) or completely unmixed (the PFTR). 

Consider the injection of a pulse into an arbitrary reactor with a partially mixed flow pattern. Now p(t) will be somewhere between the limits of unmixed and mixed, and 0 < tr < t. 

Until this chapter all reactors were assumed to be either totally unmixed or totally mixed. These are clearly limits of a partially mixed reactor, and thus these simple calculations estabhsh bounds on any chemical reactor. We have developed models of several simple partially mixed reactors, and we showed that pit is somewhere between the S fimction of the PFTR and the exponential of the CSTR. We show these models in Figure 8-13 for increasing backmixing. 

As before, we consider only two ideal continuous reactors the PFTR and the CSTR, because any other reactor involves detailed consideration of the fluid mechanics. For a phase a the mass balance if the fluid is unmixed is... 

If an isolated drop or bubble rises or falls in the reactor, then the flow pattern in this phase is clearly unmixed, and this phase should be described as a PFTR. However, drops and bubbles may not have simple trajectories because of stirring in the reactor, and also drops and bubbles can coalesce and breakup as they move through the reactor. 

For the following continuous multiphase chemical reactors construct a table indicating the phases, whether they are mixed or unmixed, the major reactions, and in what phase(s) the reaction is occurring. A sketch may be helpful. 

The reaction A B products occurs in an unmixed flow reactor, with B entering in the continuous aqueous phase and A in the orgarric phase. Reaction occurs by A transferring from the orgarric phase into the aqueous phase, where reaction occurs. The organic phase forms... 

However, the fluid is now passing from a mixed region to an unmixed plug-flow region again as in a stirred-tank reactor, the fluid leaving the reactor must have the same concentration of reactant as the fluid just inside the outlet plane. Thus, if CL is the concentration at z = L- just inside the reactor and Cex is the concentration in the fluid leaving, then CL = C . But if Ci, = Cex, then from the equality of flux (equation 2.40) we must have ... 

By minimizing the residence time of the reactive or spent gases above the wafer, the designers of this reactor attempt to minimize gas phase reactions and subsequent generation of particles. Since the SiH4 and Oj are introduced unmixed just above the wafer at high velocity, deposition rates as high as 10,000... 

Figure 2. Extension of the BPT model to the case of a reactor having two inlets (two unmixed feedstreams of respective flowrates Q, and C ). The picture shows how to build the overall RTD from those of each separate feedstream by associating tubes having the same residence time.

The case of reactors with two unmixed feedstreams is especially interesting (6), because more realistic for applications. It has been thoroughly investigated in a series of papers by researchers of Exeter University (UK). The BPT model offers a convenient picture of the reactor where both feed streams have their own RTD and the two bundles are placed side by side in such a manner that particles with the same life expectancy are situated as usual on the same vertical line (figure 6). In a first paper (60), a distinction is made between age mixedness and species mixedness Maximum age and species mixedness is achieved if particles with the same life expectancy are mixed. A more restrictive case is that where particles are able to mix only if they have both the same... 

Figure 6. Mixing in a flow reactor with two unmixed feedstreams (60). Left, Maximum age, maximum species mixedness middle, minimum age, maximum species mixedness (mixing in this case can also he assumed to occur by molecular diffusion between two tubes having the same and (T9.)) and right, mixing between particles of the same life expectancy by a random-coalescence process (77).

Figure 7. Top, extension of Spencer and Leshaw s model to the case of a reactor having two inlets (unmixed feedstreams). In the general case, there are four environments (two entering, two leaving). Bottom, when the segregation function only depends on residence time, this representation is also valid (78). Three environment model with three parameters R s = exp(-R t ), ...

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