Tubular reactor linear

It is common practice to use geometric similarity in the scaleup of stirred tanks (but not tubular reactors). This means that the production-scale reactor will have the same shape as the pilot-scale reactor. All linear dimensions such as reactor diameter, impeller diameter, and liquid height will change by the same factor, Surface areas will scale as Now, what happens to tmix upon scaleup ... 

Tubular reactors are used for some polycondensations. Para-blocked phenols can be reacted with formalin to form linear oligomers. When the same reactor is used with ordinary phenol, plugging will occur if the tube diameter is above a critical size, even though the reaction stoichiometry is outside the region that causes gelation in a batch reactor. Polymer chains at the wall continue to receive formaldehyde by diffusion from the center of the tube and can crosslink. Local stoichiometry is not preserved when the reactants have different diffusion coefficients. See Section 2.8. 

The importance of the linear arrangement of mixer/funnel/tubular reactor is shown when processing in a set-up with a curved flow element (0.3 m long bent Teflon tube of 0.3 mm inner diameter) in between the funnel and tubular reactor [78]. If a straight tube of equal dimensions as given above is used, plugging occius after 30 s. Hence even short curved flow passages are detrimental for micro-chan-nel-based amidation studies. 

A tubular reactor is considered in which the gas-phase reaction leads to a change in the molar flow rate and thus in the linear gas velocity. The reaction stoichiometry is represented by... 

If AW AW the process of finding a linear-mixture basis can be tedious. Fortunately, however, in practical applications Nm is usually not greater than 2 or 3, and thus it is rarely necessary to search for more than one or two combinations of linearly independent columns for each reference vector. In the rare cases where A m > 3, the linear mixtures are often easy to identify. For example, in a tubular reactor with multiple side-injection streams, the side streams might all have the same inlet concentrations so that c(2) = = c(iVin). The stationary flow calculation would then require only AW = 1 mixture-fraction components to describe mixing between inlet 1 and the Nm — I side streams. In summary, as illustrated in Fig. 5.7, a turbulent reacting flow for which a linear-mixture basis exists can be completely described in terms of a transformed composition vector ipm( defined by... 

It is well known that self-oscillation theory concerns the branching of periodic solutions of a system of differential equations at an equilibrium point. From Poincare, Andronov [4] up to the classical paper by Hopf [12], [18], non-linear oscillators have been considered in many contexts. An example of the classical electrical non-oscillator of van der Pol can be found in the paper of Cartwright [7]. Poore and later Uppal [32] were the first researchers who applied the theory of nonlinear oscillators to an irreversible exothermic reaction A B in a CSTR. Afterwards, several examples of self-oscillation (Andronov-PoincarA Hopf bifurcation) have been studied in CSTR and tubular reactors. Another... 

Table V compares M, M and M values for two polyethylenes analyzed by SEC in TCB solution at l45°C. Sample C is a linear low density material listed in Table 1. NBS 1 476 is low density polyethylene which is stated to be a low conversion tubular reactor product with density 0.931 gem and melt index 1.2 (11). IL and are little af fected by the existence of aggregates in these two samples but values are more severely influenced.

Tubular reactors are most often used, although autoclave reactors are also employed. Tubular reactors consist of a number of sections, each with an inner diameter of 2-6 cm and length of 0.5-1.5 km, arranged in the shape of an elongated coil. The polymerization mixture has very high linear velocities (>10m s-1) with short reaction times (0.25-2 min). Trace amounts of oxygen (<300 ppm) are typically used as the initiator, often in combination... 

A tubular reactor model that may apply to viscous fluids such as polymers has a radial distribution of linear velocities represented by... 

If the points lie close to a straight line, this is taken as confirmation that a second-order equation satisfactorily describes the kinetics, and the value of the rate constant k2 is found by fitting the best straight line to the points by linear regression. Experiments using tubular and continuous stirred-tank reactors to determine kinetic constants are discussed in the sections describing these reactors (Sections 1.7.4 and 1.8.S). 

First we introduce the reader to the principles of such problems and their solution in Sections 5.1.2 and 5.1.2. As an educational tool we use the classical axial dispersion model for finding the steady state of one-dimensional tubular reactors. The model is formulated for the isothermal case with linear kinetics. This case lends itself to an otherwise rare analytical solution that is given in the book. From this example our students can understand many characteristics of such systems. 

Block diagrams of the linear openloop process are shown in Figure 7.4. The two alternative flowsheets are labeled FS1, in which no furnace is used, and FS2, in which a furnace is used. The reactor transfer function is GR(s), representing the adiabatic tubular reactor. The reactor by itself is openloop-stable. In Figure 7.4a a simple first-order... 

For a tubular (plug flow) reactor, the conditions at any point in the reactor are independent of time, and the linear velocity v of the reacting mixture is the same at every point in a cross-section S perpendicular to the flow direction and equal to (G/pS). The composition of the reaction mixture depends on the distance L from the inlet point. 

The model is referred to as a dispersion model, and the value of the dispersion coefficient De is determined empirically based on correlations or experimental data. In a case where Eq. (19-21) is converted to dimensionless variables, the coefficient of the second derivative is referred to as the Peclet number (Pe = uL/De), where L is the reactor length and u is the linear velocity. For plug flow, De = 0 (Pe ) while for a CSTR, De = oo (Pe = 0). To solve Eq. (19-21), one initial condition and two boundary conditions are needed. The closed-ends boundary conditions are uC0 = (uC — DedC/dL)L=o and (dC/BL)i = i = 0 (e.g., see Wen and Fan, Models for Flow Systems in Chemical Reactors, Marcel Dekker, 1975). Figure 19-2 shows the performance of a tubular reactor with dispersion compared to that of a plug flow reactor. 

As our first example, we consider the case of a first-order homogeneous reaction A -> B in a laminar flow tubular reactor for which the global equation is linear in c (i.e. r( c)) — (c)) and is therefore completely closed. To obtain the range of convergence of the two-mode model, we need to consider only the local equation. In this specific case, the reduced model equations to all orders of p are then given by... 

When comparing different solar collectors it is important to take into account the different quantities of radiation collected in each case. For a given receiver, the radiative power collected increases with aperture size (i.e., with concentration). However, this is not a linear effect and, for instance, a CPC with a two suns concentration ratio provides twice the aperture area of a nonconcentrating CPC. Nevertheless the power received by the tubular absorber is not doubled, because the former CPC misses around half of the diffuse radiation. Other important consideration is the fact that concentrating reactors are faster simply because they collect more radiation, which is associated with larger collector area. 

A chrome -alumel thermocouple was set in close proximity to the sample inside a reactor. The reactor was made of a quartz tube which was surrounded by a tubular furnace. In a typical coal pyrolysis run, the coal sample (20-30 mg) was placed in a platinum boat which was suspended from the quartz beam of the TGA balance. The coal particle size used was 100-200 mesh. Samples were heated to desired temperatures at linear heating rates or heated iso-thermally under various gaseous environments. 

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