Ideal flows, reactors with

In another land of ideal flow reactor, all portions of the feed stream have the same residence time that is, there is no mixing in the axial direction but complete mixing radially. It is called a.plugflow reactor (PFR), or a tubular flow reactor (TFR), because this flow pattern is characteristic of tubes and pipes. As the reaction proceeds, the concentration falls off with distance. 

As i the term in brackets above tends to exp (vit/V) for t < V/v), and F becomes zero(7>. Thus, for an infinite number of tanks the fraction of tracer that has escaped is zero for all times less than the residence time V/v. This is exactly the same as for the case of an ideal tubular reactor with plug flow. 

Ideal plug-flow conditions can also be established in so-called nano-flow reactors with catalyst particle sizes from 50 to 200 pm. These reactors were operated in 16-and 64-barrel mode at Avantium for the regression of intrinsic kinetics [4],... 

An important advantage of the use of EOF to pump liquids in a micro-channel network is that the velocity over the microchannel cross section is constant, in contrast to pressure-driven (Poisseuille) flow, which exhibits a parabolic velocity profile. EOF-based microreactors therefore are nearly ideal plug-flow reactors, with corresponding narrow residence time distribution, which improves reaction selectivity. 

Another model, which will not be analyzed, is the plug-flow reactor with recycle shown in Fig. 6-1. The reactor itself behaves as an ideal tubular type, but mixing is introduced by the recycle stream. When the recycle rate becomes very large, ideal stirred-tank performance is obtained, and when the recycle is zero, plug-flow operation, results. The response data on the actual reactor are used to evaluate the recycle rate and then the conversion is estimated for a plug-flow reactor with this recycle rate. 

Fig. 6-1 Ideal tubular-flow reactor with recycle...

Figure 7.1c and d show two types of the steady-state flow reactors with a continuous supply of reactants and continuous removal of product(s). Figure 7.1c shows the continuous stirred-tank reactor (CSTR) in which the reactor contents are perfectly mixed and uniform throughout the reactor. Thus, the composition of the outlet flow is constant, and the same as that in the reactor. Figure 7.Id shows the plug flow reactor (PFR). Plug flow is the idealized flow, with a uniform fluid velocity across the entire flow channel, and with no mixing in the axial and radial...

As the main responsible for the changes in the material balance, the chemical reactor must be modelled accurately from this point of view. Basic flowsheeting reactors are the plug flow reactor (PFR) and continuous stirred tank reactor (CSTR), as shown in Fig. 3.17. The ideal models are not sufficient to describe the complexity of industrial reactors. A practical alternative is the combination of ideal flow models with stoichiometric reactors, or with some user programming. In this way the flow reactors can take into account the influence of recycles on conversion, while the stoichiometric types can serve to describe realistically selectivity effects, namely the formation of impurities, important for separations. Some standard models are described below. 

The integral in the second term is a form of the exponential integral, normally tabulated as Ei z) [M. Abramowitz and LA. Stegun, Handbook of Mathematical Functions, Dover, New York, NY, (1965)]. Further discussion of the ideal laminar-flow reactor with a first-order reaction is given by Cleland and Wilhelm [F.A. Cleland and R.H. Wilhelm, Amer. Inst. Chem. Eng. J., 2, 489 (1956)]. 

Fig. 2.2-4 Cumulative residence-time function F t/z) for an ideal continuous stirred tank (1), an ideal tubular reactor with plug flow (2), and laminar flow in a tubular reactor (3).

Here n - the only parameter of cellular model equal to cells (reactors) number in cascade of ideal stirred reactors, ideal stirring regime is achieved at n —> oo [3], It is accepted [22], that if cells number in reactor n S 8, then such apparatus can be calculated as plug-flow reactor with enough for industrial practice accuracy. 

On the other hand, for the ideal tubular reactor with a plug-flow-like profile (PER), the material balance has to be made over a differential element of volume, dV = Adz, where A is the cross-sectional area of the bioreactor and dz is a differential thickness of the bioreactor (Figure 7.4). The material balance thus becomes... 

It was realised by Rowe in the early 1980s that the uniform supersonic flows obtained by the correct design of a Laval nozzle and used for decades in rarefied wind tunnels for aerodynamic studies could provide an ideal flow reactor for the study of chemical reactivity at low and very low temperature. This was the cornerstone around which the CRESU technique has been developed. At the exit of the Laval nozzle, as there is no further expansion downstream of the nozzle exit, the flow parameters (i.e. temperature, density, pressure and velocity) do not exhibit any axial and radial variations at least in the centre of the jet (typically 10 to 20 mm in diameter) where the flow is isentropic for several tens of centimetres. The diffusion velocity is always negligible with respect to the bulk velocity therefore avoiding the major problem of condensation associated with the use of cryogenically cooled cells. As a consequence, in such expansions, heavily supersaturated conditions prevail and condensable species such as water, ammonia or even polycyclic aromatic hydrocarbons (PAHs hereafter), can be maintained in the gas phase at very low temperatures. 

The CFD simulation results were compared with conventional ideal flow reactor model predictions — combinations of plug flow and completely mixed... 

The derivative of a step change is a delta function, and f(t) = 8(t — t). Thus, a piston flow reactor is said to have a delta distribution of residence times. The variances for these ideal cases are = 1 for a CSTR and 0 = 0 for a PFR, which are extremes for well-designed reactors in turbulent flow. Poorly designed reactors and laminar flow reactors with little molecular diffusion can have 0 values greater than 1. 

According to the idealized flow patterns (Hlavacek and Kubicek, 1972), the slice of the bed cut in the radial direction can be considered as a fixed-bed with the inlet condition at r = Rx and the outlet condition at r — Rz- Conservation equations written for this slice should be applicable to the whole length of the bed. Therefore, the conservation equations of l s. 9.27 through 9.36 are applicable to radial flow reactors with the convection terms 9c/dz and bT/bz replaced by bc/br and bT/br. This model is then identical to the one-dimensional model with axial dispersion as for the usual fixed-bed reactor. The same boundary conditions as those of Eqs. 9.10 and 9.11 apply, but this time Eq. 9.10 applies at r = Ri and Eq. 9.11 at r = R2. with z replaced by r for the flow pattern (a) in Figure 9.12. Unless the bed depth is quite shallow, the dispersion term can be neglected, resulting in a plug-flow model in the radial direction. 

The following experiments were carried out at 120 °C in an ideal plug flow reactor with a feed consisting of pure ethanol at 1.0 atm. The same reactor was used for all experiments. 

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