Gradient-reactor

Figure 1 Gradient reactor configuration, three catalysts.

TABLE 2 Gradient Reactor Configuration, Three Catalysts... 

Further extensions of this chemistry (equation 2) include the addition of alkanols - particularly tert-butanol or methanol - to the acetone feed streams, thereby generating, in one step, a mix of DIPE with IPTBE, MTBE, etc (9). Again, these one-step, multi-ether syntheses can be conducted in the gradient reactor system without the co-production of large quantities of undesirable C-3 and C-4 gaseous co-products. Typical alkanol feed concentrations may be in the 10 to 70% range (9). 

We conclude that of the three unit configurations considered in this research program, the gradient reactor design has the triple advantages of ... 

Optimal environmental operating conditions (for temperature, pH, and Po-) can be maintained in such gradient reactors. 

Non-gradient reactor. Non-gradient reactors have many different names and types, and can be roughly divided into external circulation, internal circulation and continuous stirred kettle -style by the gas flowing mode. However, it is necessary to achieve the flow phase with constant temperature and ideal mixing, and the elimination of mass transfer resistance between phases in reactor. At the same time, on the premise of elimination of the gradient of temperature and concentration, it should be the same that the reaction rate equation is obtained from the circulation flow system or the ideal hybrid system. 

The characteristic of external circulation of non-gradient reactor, also known as plug-shaped reactor or flow cycle device, recycles gas after reaction through the loop in outside of reactors to carry out cycle. Generally, circulation pump is used to drive gas circulation as shown in Fig. 7.2. 

Plug-flow reactors have a decreasing concentration gradient from inlet to outlet, which means that toxic compounds in the feed remain undiluted during their passage along the reactor, and this may inhibit or kill many of the microorganisms within the... 

In the Godrej-Lurgi process, olefins are produced by dehydration of fatty alcohols on alumina in a continuous vapor-phase process. The reaction is carried out in a specially designed isothermal multitube reactor at a temperature of approximately 300°C and a pressure of 5—10 kPa (0.05—0.10 atm). As the reaction is endothermic, temperature is maintained by circulating externally heated molten salt solution around the reactor tubes. The reaction is sensitive to temperature fluctuations and gradients, hence the need to maintain an isothermal reaction regime. 

Catalyst Effectiveness. Even at steady-state, isothermal conditions, consideration must be given to the possible loss in catalyst activity resulting from gradients. The loss is usually calculated based on the effectiveness factor, which is the diffusion-limited reaction rate within catalyst pores divided by the reaction rate at catalyst surface conditions (50). The effectiveness factor E, in turn, is related to the Thiele modulus,

first-order rate constant, a the internal surface area, and the effective diffusivity. It is desirable for E to be as close as possible to its maximum value of unity. Various formulas have been developed for E, which are particularly usehil for analyzing reactors that are potentially subject to thermal instabilities, such as hot spots and temperature mnaways (1,48,51). 

In cases where a large reactor operates similarly to a CSTR, fluid dynamics sometimes can be estabflshed in a smaller reactor by external recycle of product. For example, the extent of soflds back-mixing and Hquid recirculation increases with reactor diameter in a gas—Hquid—soflds reactor. Consequently, if gas and Hquid velocities are maintained constant when scaling and the same space velocities are used, then the smaller pilot unit should be of the same overall height. The net result is that the large-diameter reactor is well mixed and no temperature gradients occur even with a highly exothermic reaction. 

The smaller reactor approaches plug-flow behavior and exhibits a large temperature gradient. In this case, external recycle provides the same degree of back-mixing as is provided by internal circulation in the larger diameter reactor. 

Deviations from the ideal frequentiy occur in order to avoid system complexity, but differences between an experimental system and the commercial unit should always be considered carefully to avoid surprises on scale-up. In the event that fundamental kinetic data are desired, it is usually necessary to choose a reactor design in which reactant and product concentration gradients are minimized (36), such as in the recycle (37) or spinning basket reactor designs (38,39). 

Unsteady-State Direct Oxidation Process. Periodic iatermption of the feeds can be used to reduce the sharp temperature gradients associated with the conventional oxidation of ethylene over a silver catalyst (209). Steady and periodic operation of a packed-bed reactor has been iavestigated for the production of ethylene oxide (210). By periodically varyiag the inlet feed concentration of ethylene or oxygen, or both, considerable improvements ia the selectivity to ethylene oxide were claimed. 

A differential equation for a function that depends on only one variable, often time, is called an ordinary differential equation. The general solution to the differential equation includes many possibilities the boundaiy or initial conditions are needed to specify which of those are desired. If all conditions are at one point, then the problem is an initial valueproblem and can be integrated from that point on. If some of the conditions are available at one point and others at another point, then the ordinaiy differential equations become two-point boundaiy value problems, which are treated in the next section. Initial value problems as ordinary differential equations arise in control of lumped parameter models, transient models of stirred tank reactors, and in all models where there are no spatial gradients in the unknowns. 

Packed Red Reactors The commonest vessels are cylindrical. They will have gradients of composition and temperature in the radial and axial directions. The partial differential equations of the material and energy balances are summarized in Table 7-10. Example 4 of Modeling of Chemical Reactions in Sec. 23 is an apphcation of such equations. 

In tubular reactors of only a few cm in diameter, the temperature is substantially uniform over the cross section so only an axial gradient occurs in the heat balance. 

Peclet number independent of Reynolds number also means that turbulent diffusion or dispersion is directly proportional to the fluid velocity. In general, reactors that are simple in construction, (tubular reactors and adiabatic reactors) approach their ideal condition much better in commercial size then on laboratory scale. On small scale and corresponding low flows, they are handicapped by significant temperature and concentration gradients that are not even well defined. In contrast, recycle reactors and CSTRs come much closer to their ideal state in laboratory sizes than in large equipment. The energy requirement for recycle reaci ors grows with the square of the volume. This limits increases in size or applicable recycle ratios. 

The concentration gradient normal to the outside of the catalyst particle. The rate is expressed on catalyst-filled reactor volume, with e void fraction for this smaller volume the rate must be higher to keep Vrr=Vcr< . This is calculated from the continuity requirement that was mentioned above ... 

Pirjamali et al (1972) developed a correction procedure for interparticle gradients in recycle reactors. Their study involved recycle ratios n from 36 to 1000 (as defined in this book) that relates to their recycle ratio P... 

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