Reactor concentric spherical

The reactor, in which the gas phase will be virtually pure hydrogen, will operate under a pressure of 2 MN/m2 (20 bar). The catalyst will consist of porous spherical particles 3 mm in diameter, and the voidage, that is the fraction of bed occupied by gas plus liquid, will be 0.4. The diameter of the bed will be such that the superficial liquid velocity will be 0.002 m/s. The concentration of the aniline in the liquid feed will be 0.055 kmol/m3. 

The concentration and temperature Tg will, for example, be conditions of reactant concentration and temperature in the bulk gas at some point within a catalytic reactor. Because both c g and Tg will vary with position in a reactor in which there is significant conversion, eqns. (1) and (15) have to be coupled with equations describing the reactor environment (see Sect. 6) for the purpose of commerical reactor design. Because of the nonlinearity of the equations, the problem can only be solved in this form by numerical techniques [5, 6]. However, an approximation may be made which gives an asymptotically exact solution [7] or, alternatively, the exponential function of temperature may be expanded to give equations which can be solved analytically [8, 9]. A convenient solution to the problem may be presented in the form of families of curves for the effectiveness factor as a function of the Thiele modulus. Figure 3 shows these curves for the case of a first-order irreversible reaction occurring in spherical catalyst particles. Two additional independent dimensionless paramters are introduced into the problem and these are defined as... 

Figure 12-10 Sketches of reactant concentration Ca around a spherical bubble or drop that reacts after migrating from ftie gas phase into the liquid phase in bubble column and spray tower reactors.

The concentration profile for a reactant A which must migrate from a drop or bubble into the continuous phase to react might be as shown in Figure 12-10. There is a concentration drop around the spherical drop or bubble because it is migrating outward, but, as with a planar gas-liquid interface in the falling film reactor, there should be a discontinuity in at the interface due to the solubility of species A and a consequent equilibrium distribution between phases. 

Figure 12-15 Sketch of concentration profiles between a spherical bubble and a solid spherical catalyst particle in a continuous liquid phase (upper) in a gas-liquid sluny reactor or between a bubble and a planar solid wall (lower) in a catalytic w bubble reactor, It is assmned that a reactant A must migrate from the bubble, tirough the drop, md to tiie solid catdyst smface to react. Concentration variations may occur because of mass transfer limitations around both bubble and solid phases.

This paper deals mainly with the condensation of trace concentrations of radioactive vapor onto spherical particles of a substrate. For this situation the relation between the engineering approach, the molecular approach, and the fluid-dynamic approach are illustrated for several different cases of rate limitation. From these considerations criteria are derived for the use of basic physical and chemical parameters to predict the rate-controlling step or steps. Finally, the effect of changing temperature is considered and the groundwork is thereby laid for a kinetic approach to predicting fallout formation. The relation of these approaches to the escape of fission products from reactor fuel and to the deposition of radon and thoron daughters on dust particles in a uranium mine is indicated. 

Because the subject is vast, the presentation is limited to a discussion of the uptake of a tracer from the vapor phase by spherical particles. This is the viewpoint of one concerned with fallout formation. The reverse process—escape from spherical particles—is the viewpoint of one concerned with reactor fuels. For the idealized case the treatment is exactly the same for the two situations. The fact that we deal with trace quantities and concentration means that we can neglect changes in the particle properties as the reaction proceeds and that we need not be concerned with surface nucleation. 

The Static Reactor Static reactors are conceptually simple. They consist typically of a spherical vessel that is filled with the reactive mixture. The gas phase reactants are, at least initially, maintained at the desired temperature by an oven or a thermostated bath. The progress of reaction is observed by measuring the change in pressure (reaction takes place at constant volume) or by detecting concentrations as function of time for one or several species. 

In designing modules of mono- or multilamp immersion-type photochemical reactors, again the concept of convergence of light distribution and reactor geometries is followed, and knowledge of light penetration in a suspension of optimal photocatalyst concentration is therefore essential. Optimal thickness of annular irradiated reaction volume is best determined by a spherical probe under conditions where only absorption by the photocatalyst has to be taken into account [12, 78, 98, 99]. The radiant power P = f(r) within the limits of r and rR, respectively, has been simulated by the Monte Carlo method on the basis of... 

The values of KM and rmax for an enzyme (21°C and pH = 7.1) are 0.004 kmol/m3and 10 kmol/m3s, respectively. We immobilized this enzyme by attaching it covalently to acrylamide-based polymers that can be assumed to have spherical shape (diameter = 1 mm). The effectiveness of the immobilized enzyme was found to be 70 percent of the free enzyme when the concentration of the substrate was 0.5 kmol/m3. The reaction was carried out in a stirred reactor with an agitation speed of 50 rpm. (a) Estimate the concentration of the substrate at the surface of the immobilized enzyme, (b) Estimate ks a. 

In a fixed-bed the reactor vessel is filled with catalyst particles having sizes in the range 1-3 mm. The catalyst particles may be spherical, cylindrical, or of more sophisticated forms, including eggshell catalysts, with active species concentrated near the outer surface of the particle. The gas and liquid phases are passed through the bed. 

The catalyst plays a crucial role in the technology. A typical modern catalyst consists of 0.15-1.5 wt% Pd, 0.2-1.5 wt% Au, 4-10 wt% KOAc on silica spherical particles of 5 mm [8]. The very fast reaction takes place inside a thin layer (egg-shell catalyst). Preferred conditions are temperatures around 150 to 160 °C and pressures 8 to 10 bar. Hot spots above 200 °C lead to permanent catalyst deactivation. The excess of ethylene to acetic acid is 2 1 to 3 1. Because of explosion danger, the oxygen concentration in the reaction mixture should be kept below 8%. Small amount of water in the initial mixture are necessary for catalyst activation. The dilution of the reaction mixture with inert gas is necessary because of high exothermic effect. Accordingly, the reactor is designed at low values of the per-pass conversions, namely 15 - 35% for the acetic acid and 8-10% for ethylene. The above elements formulate hard constraints both for design and for plantwide control. 

This is a different kind of heterogeneous reaction—a gas-solid noncatalytic one. Let us examine the process at initial conditions (t 0), so that there has been no opportunity for a layer of UF4.(5) to be formed around the UO pellet The process is much like that for gas-solid catalytic reactions. Hydrogen fluoride gas is transferred from the bulk gas to the surface of the UO2 pellets and reacts at the pellet-gas interface, and H2O diffuses out into the bulk gas. If the pellet is nonporous, all the reaction occurs at the outer surface of the UO2 pellet, and only an external transport process is possible. Costa studied this system by suspending spherical pellets 2 cm in diameter in a stirred-tank reactor. In one run, at a bulk-gas temperature of 377°C, the surface temperature was 462°C and the observed rate was — Tuo = 6.9 x 10 mole U02/(sec) (cm reaction surface). At these conditions the concentrations of... 

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