Ideal mixed flow reactor

Figure 4.1. The three types of ideal chemical reactors. The ideal batch reactor (BR) is well mixed but closed to mass transfer. The ideal mixed flow reactor (MFR) is well mixed and subject to continuous mass transfer.The fluid in an ideal plug flow reactor (PFR) moves as slugs, which are closed to mass transfer with each other and therefore act as batch reactors moving through space.

Adding a tracer spike to an ideal mixed flow reactor produces a step increase in the tracer concentration just as in the batch reactor case, but in this case the tracer s concentration declines over time as the reactor s effluent carries it away. If the amount of solution in the reactor remains constant and no more tracer is added by the feed solution or by generation in the reactor, the continuity equation simplifies to make the rate of accumulation equal to the rate of loss by the effluent flow. 

If a tracer is added to an ideal mixed flow reactor at a constant rate, the rate of accumulation of the tracer in the reactor amounts to the difference between the rate of input by the feed stream and the rate of removal in the effluent stream. 

The simplest box model consists of one reservoir that is fed by a constant flux (Fg) (Figure 8.2). The flux out of a reservoir is the product of the mass of the substance (A/) in the reservoir and a mass transfer constant (k). Box model reservoirs are simply gigantic ideal mixed flow reactors (see Chapter 4) where there is no net generation or consumption of the substance. Over geologic time spans these reactors tend to attain a steady state so that the flux into a reservoir is matched by the flux out, which means that the rate of accumulation in the reservoir is zero and M is constant (M j). The flux out of the reservoir equals a mass transfer constant (k, yr ) times the mass of the substance in the reservoir. 

There are two important types of ideal, continuous-flow reactors the piston flow reactor or PFR, and the continuous-flow stirred tank reactor or CSTR. They behave very diflerently with respect to conversion and selectivity. The piston flow reactor behaves exactly like a batch reactor. It is usually visualized as a long tube as illustrated in Figure 1.3. Suppose a small clump of material enters the reactor at time t = 0 and flows from the inlet to the outlet. We suppose that there is no mixing between this particular clump and other clumps that entered at different times. The clump stays together and ages and reacts as it flows down the tube. After it has been in the piston flow reactor for t seconds, the clump will have the same composition as if it had been in a batch reactor for t seconds. The composition of a batch reactor varies with time. The composition of a small clump flowing through a piston flow reactor varies with time in the same way. It also varies with position down the tube. The relationship between time and position is... 

Figure 5.4a compares the profiles for a mixed-flow and plug-flow reactor between the same inlet and outlet concentrations, from which it can be concluded that the mixed-flow reactor requires a larger volume. The rate of reaction in a mixed-flow reactor is uniformly low as the reactant is instantly diluted by the product that has already been formed. In a plug-flow or ideal-batch reactor,... 

In practice, it is often possible with stirred-tank reactors to come close to the idealized mixed-flow model, providing the fluid phase is not too viscous. For homogenous reactions, such reactors should be avoided for some types of parallel reaction systems (see Figure 5.6) and for all systems in which byproduct formation is via series reactions. 

Solution As much as possible, the production of di- and triethanolamine needs to be avoided. These are formed by series reactions with respect to monoethanolamine. In a mixed-flow reactor, part of the monoethanolamine formed in the primary reaction could stay for extended periods, thus increasing its chances of being converted to di- and triethanolamine. The ideal batch or plug-flow arrangement is preferred to carefully control the residence time in the reactor. 

The responses of this system to ideal step and pulse inputs are shown in Figure 11.3. Because the flow patterns in real tubular reactors will always involve some axial mixing and boundary layer flow near the walls of the vessels, they will distort the response curves for the ideal plug flow reactor. Consequently, the responses of a real tubular reactor to these inputs may look like those shown in Figure 11.3. 

If free-radical polymerisation is carried out in an ideal back-mixed flow reactor, the concentrations of the reactant species become constant and the molecular weight distributions can be obtained from eqns. (83) and (84). Figure 8 shows how changes in P /Pn with conversion compare for the two reactor types. These plots represent idealised behaviour, in practice, Pw/Pn will be influenced by changes in at high conversion and by the occurrence of chain transfer reactions. 

Figure 5.1 The three types of ideal reactors (a) batch reactor, or BR (b) plug flow reactor, or PFR and (c) mixed flow reactor, or MFR.

The other ideal steady-state flow reactor is called the mixed reactor, the backmix reactor, the ideal stirred tank reactor, the C " (meaning C-star), CSTR, or the CFSTR (constant flow stirred tank reactor), and, as its names suggest, it is a reactor in which the contents are well stirred and uniform throughout. Thus, the exit stream from this reactor has the same composition as the fluid within the reactor. We refer to this type of flow as mixed flow, and the corresponding reactor the mixed flow reactor, or MFR. 

These findings differ from ordinary nth-order reactions (n > 0) where the plug flow reactor is always more efficient than the mixed flow reactor. In addition, we should note that a plug flow reactor will not operate at all with a feed of pure reactant. In such a situation the feed must be continually primed with product, an ideal opportunity for using a recycle reactor. 

In the ideal plug-flow reactor (Figure 11.16) the continuous phase flows as a plug through the reactor i.e., there is no mixing or, in other words, no axial dispersion. Consequently, if a compound is consumed or produced, a concentration gradient will exist in the direction of flow. The mass balance is therefore first set up over an infinite small slice perpendicular to the direction of the flow with volume dV of the bioreactor. Assuming steady state and F =Fq=F, Equation (11.5) then is reduced to ... 

In real tubular (or column) reactors there is, usually, a back-mixing effect which influences the performance of the ideal plug-flow reactor. This axial dispersion is higher for fluidized-bed reactors than for packed-bed reactors, although comparatively lower than for continuous-feed stirred-tank reactors, where the mixing is complete. 

The modeling of real immobilized-enzyme column reactors, mainly the fluidized-bed type, has been described (Emeiy and Cardoso, 1978 Allen, Charles and Coughlin, 1979 Kobayashi and Moo-Young, 1971) by mathematical models based on the dispersion concept (Levenspiel, 1972), by incorporation of an additional term to account for back-mixing in the ideal plug-flow reactor. This term describes the non-ideal effects in terms of a dispersion coefficient. 

Plug-flow tubular reactor (PFTR) This reactor is operated under steady-state condition. The reactor is of tubular shape, the reactants enter at the inlet and the composition is a function of the distance from the inlet. However, the composition is not a function of time. The ideal plug-flow reactor is characterized by the absence of mixing in the direction of flow and complete mixing in the transverse direction. 

A mixed-flow reactor requires uniform composition of the fluid phase throughout the volume while the fluid is constantly flowing through it. This requires a special design in order to be achieved in the case of gas-solid systems. These reactors are basically experimental devices, which closely approach the ideal flow conditions and have been devised by Carbeny (Levenspiel, 1972). This device is called a basket-type mixed reactor (Figure 3.6). The catalyst is contained in four rapidly spinning wire baskets. 

Continuous stirred tank reactor Sometimes called a continuous-flow stirred-tank reactor, ideal mixer, or mixed-flow reactor, all describing reactors with continuous input and output of material. The outlet concentration is assumed to be the same as the concentration at any point in the reactor. 

The continuous-stirred tank reactor is one of the two primary types of ideal flow reactors. It is also referred to as a mixed-flow reactor, back-mix reactor, or constant-flow stirred-tank reactor. 

The RTD in a system is a measure of the degree to which fluid elements mix. In an ideal plug flow reactor, there is no mixing, while in a perfect mixer, the elements of different ages are uniformly mixed. A real process fluid is neither a macrofluid nor a microfluid, but tends toward one or the other of these extremes. Fluid mixing in a vessel, as reviewed in Chapter 7, is a complex process and can be analyzed on both macroscopic and microscopic scales. In a non-ideal system, there are irregularities that account for the fluid mixing of different... 

The reactive transport of contaminants in FePRBs has been modeled using several approaches [179,184,186,205-208]. The simplest approach treats the FePRB as an ideal plug-flow reactor (PFR), which is a steady-state flow reactor in which mixing (i.e., dispersion) and sorption are negligible. Removal rates (and therefore required wall widths, W) can be estimated based on first-order contaminant degradation and residence times calculated from the average linear groundwater velocity [Eq. (27)]. The usefulness of... 

The fluidized-bed reactor involves a rapid movement of the solid catalytic particles throughout the bed so that the operation can come close to one of uniform temperature throughout the reactor. The actual flow pattern for the operation of a fluidized bed is very complex and is between that for the ideal back-mix reactor and the ideal plug-flow reactor so that special methods for design may be required to approximate the real situation. 

Classical chemical reaction engineering provides mathematical concepts to describe the ideal (and real) mass balances and reaction kinetics of commonly used reactor types that include discontinuous batch, mixed flow, plug flow, batch recirculation systems and staged or cascade reactor configurations (Levenspiel, 1996). Mixed flow reactors are sometimes referred to as continuously stirred tank reactors (CSTRs). The different reactor types are shown schematically in Fig. 8-1. All these reactor types and configurations are amenable to photochemical reaction engineering. 

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