Reactors limiting conditions, 65

Some batch reactions have the potential for very high energy levels. If all the reactants (and sometimes catalysts) are put into a kettle before the reaction is initiated, some exothermic reactions may result in a runaway. The use of continuous or semi-batch reactors to limit the energy present and to reduce the risk of a runaway should be considered. The term semi-batch refers to a system where one reactant and, if necessary, a catalyst is initially charged to a batch reactor. A second reactant is subsequently fed to the reactor under conditions such that an upset in reacting conditions can be detected and the flow of the reactant stopped, thus limiting the total amount of potential energy in the reactor. 

Equations 11 and 12 are only valid if the volumetric growth rate of particles is the same in both reactors a condition which would not hold true if the conversion were high or if the temperatures differ. Graphs of these size distributions are shown in Figure 3. They are all broader than the distributions one would expect in latex produced by batch reaction. The particle size distributions shown in Figure 3 are based on the assumption that steady-state particle generation can be achieved in the CSTR systems. Consequences of transients or limit-cycle behavior will be discussed later in this paper. 

Finally, to conclude our discussion on coupling with chemistry, we should note that in principle fairly complex reaction schemes can be used to define the reaction source terms. However, as in single-phase flows, adding many fast chemical reactions can lead to slow convergence in CFD simulations, and the user is advised to attempt to eliminate instantaneous reaction steps whenever possible. The question of determining the rate constants (and their dependence on temperature) is also an important consideration. Ideally, this should be done under laboratory conditions for which the mass/heat-transfer rates are all faster than those likely to occur in the production-scale reactor. Note that it is not necessary to completely eliminate mass/heat-transfer limitations to determine usable rate parameters. Indeed, as long as the rate parameters found in the lab are reliable under well-mixed (vs. perfect-mixed) conditions, the actual mass/ heat-transfer rates in the reactor will be lower, leading to accurate predictions of chemical species under mass/heat-transfer-limited conditions. 

The point is that the same population dynamics are applicable to remediation systems. The principal difference is that in a soil/water system, one has essentially the growth rate of the bacteria as a limiting condition. This is also akin to another type of system known as the Sequencing Batch Reactor or SBR. 

Attempts have been made to expand the technique to include the analysis of soil biotransformations f23.29V While the hydrodynamic nature and physical structure of soil systems vary widely and are difficult to establish with certainty, two limiting conditions may be specified. The first is where the soil particles are suspended and all phases are well-mixed. This case is not typically found in nature, but is found in various types of engineered soil-slurry reactors. The reactors currently used in our systems experiments include continuous stirred tank reactors (CSTRs) operated to minimize soil washout. 

The batch reactor, above described, permits both to operate at quasi-zero conversion per pass and to evaluate the cat ytic activity at finite values of the reagents conversion. A typical test performed on Si02 catalyst at 600°C is presented in Figure 1. It is remarkable how in our approach the product selectivity is unaffected by the methane conversion. A special care was taken to avoid oxygen-limiting conditions and, hence, methane conversion data obtained for oxygen conversions below 20% only have been used for the calculation of reaction rates. 

Reductive alkylation is an efficient method to synthesize secondary amines from primary amines. The aim of this study is to optimize sulfur-promoted platinum catalysts for the reductive alkylation of p-aminodiphenylamine (ADPA) with methyl isobutyl ketone (MIBK) to improve the productivity of N-(l,3-dimethylbutyl)-N-phenyl-p-phenylenediamine (6-PPD). In this study, we focus on Pt loading, the amount of sulfur, and the pH as the variables. The reaction was conducted in the liquid phase under kinetically limited conditions in a continuously stirred tank reactor at a constant hydrogen pressure. Use of the two-factorial design minimized the number of experiments needed to arrive at the optimal solution. The activity and selectivity of the reaction was followed using the hydrogen-uptake and chromatographic analysis of products. The most optimal catalyst was identified to be l%Pt-0.1%S/C prepared at a pH of 6. 

Ideal reactors work under very simple limiting conditions, mainly concerning the residence time distribution. The operation of an ideal reactor is essentially controlled by chemical kinetics and thus the kinetic analysis of a chemical reaction is facilitated by the use of such a reactor. Furthermore, most laboratory and industrial reactors operate under conditions very near to ideality or may be modelled by simple combinations of ideal reactors. There are three main types of ideal reactors ... 

The units of space velocity are the reciprocal of time. Usually, the hourly volumetric feed-gas flow rate is calculated at 60 °F (15.6 C) and 1.0 atm (1.01 bar). The volumetric liquid-feed flow rate is calculated at 60 F (15.6 °C). Space velocity depends on the design of the reactor, reactor inlet conditions, catalyst type and diameter, and fractional conversion. Walas [7] has tabulated space velocities for 102 reactions. For exanple, for the homogeneous conversion of benzene to toluene in the gas phase, the hoiuly-volumetric space velocity is 815 h . This means that 815 reactor volumes of benzene at standard conditions will be converted in one hoiu. Although space velocity has limited usefulness, it allows estimating the reaction volume rapidly at specified conditions. Other conditions require additional space velocities. A kinetic model is more useful than space velocities, allowing the calculation of the reaction volume at different operating conditions, but a model requires more time to develop, and frequently time is not available. 

Some aspects of fluidized-bed reactor performance are examined using the Kunii-Levenspiel model of fluidized-bed reactor behavior. An ammonia-oxidation system is modeled, and the conversion predicted is shown to approximate that observed experimentally. The model is used to predict the changes in conversion with parameter variation under the limiting conditions of reaction control and transport control, and the ammonia-oxidation system is seen to be an example of reaction control. Finally, it is shown that significant differences in the averaging techniques occur for height to diameter ratios in the range of 2 to 20. 

Armed with this knowledge, we then set out to examine the fluid mechanics of the reactor. Limiting asymptotic solutions are obtained for some of the flow equations which allow the determination of the optimum flow configuration for actual conditions which approximate those assumed. Outside the domain of validity of the asymptotic solutions, numerical integration must be applied, of course. These results substantiate conclusions arrived at using the asymptotic solutions, even in parametric regions where the... 

The excessive formation of powders occurs only under limited conditions, although powder formation has been observed in reactors of different designs and types of discharge and with various monomers, particularly in a specific section of a reactor that is related to the flow pattern of gas. Therefore, powder formation provides an excellent opportunity for examining the basic principles of the polymer deposition mechanism. 

The ten possibilities outlined above are collected in Table 3.1.1. Next, ideal reactors will be illustrated in the contexts of the limiting conditions of their operation. 

The variables that influence reactor operation imder each of the limiting conditions just discussed are shown in Table 12-3. 

So we have a second scale-up problem what is the suitable equipment for complying with these demands This means more precisely how can the reactor performance be achieved over a broad range of reaction velocities Different equipment may be chosen to combine reaction and distillation within the limiting conditions of reaction velocity, relative volatility and catalysis. 

The other common reactor type is a cold-wall reactor. Here only the substrate is heated, and the gas in the forced convection region as well as the reactor walls are considerably colder than the substrate. This design has limited capacity the substrate is usually coated on one face only and although uniform gas ffow to the substrate is easier to control, heating the substrate is relatively difficult. These reactors are usually operated under mass transport limited conditions. Heating is accomplished in one of four ways ... 

Propane dehydrogenation is a highly endothermic process. High temperatures and relatively low pressures are used to get a reasonable conversion of propane. The reaction is equilibrium limited. The amount of olefin in the reactor effluent is dependent on the reactor outlet conditions. Thermal cracking reactions limit the maximum practical temperature, and pressure, therefore, becomes the dominant variable. 

The steady state temperature of the catalyst surface under mass-transport-limited conditions can exceed the adiabatic flame temperature if the rate of mass transport of fuel to the surface is faster than the rate of heat transport from the surfaee. The ratio of mass diffusivity to heat dilTusivity in a gas is known as the Lewis number. Reactor models [9] show that for gases with a Lewis number close to unity, such as carbon monoxide and methane, the catalyst surface temperature jumps to the adiabatic flame temperature of the fuel/air mixture on ignition. However, for gases with a Lewis number significantly larger than unity the rate of mass transport to the surface is much faster than the rate of heat transport from the surface, and so the wall temperature can exceed the adiabatic gas temperature. The extreme case is... 

Then, the expression of the current density for the reactor under limiting conditions is... 

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