Reactor Methods

Monte Carlo Calculations for Enriched Uranium Metal Assemblies, D. C. Irving and John T. Mihalczo (ORNL) 

The capability of the general geometry subroutine GEOM as used in the 05R Code for handling complicated three-dimensional geometries exactly has been tested in a series of calculations of unmoderated and unreflected critical assemblies of 93.2% U -enriched uranium metal (p - 18.69 g/cm ). Descriptions of the assemblies are given in Pig. 1 and Table I. The upper section of each assembly was built on a 30-in. diam stainless-steel diaphragm, and the lower section was supported by a low-mass frame that could be raised remotely. 

GEOM will treat all geometries in which material interfaces are describable by functions that are at most quadratic (e.g., planes, cylinders, cones, spheres, etc.). The quadratic material boundaries may intersect each other and be oriented in any possible manner. The com- 

Multiplication constants calculated with GEOM for the experimental assemblies are shown in Table L Although the calculated values are 1.4 to 2.1% larger than those 

TobU I. Critical Momi and Caloulolad Mwltiplicafian Contlonls of 93.2 wt% -Enriched Uranium Metal 

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By incorporating the entire analytical scheme (enzyme reaction and electrochemical detection) into the flow system a great improvement in precision can be realized. Sample manipulation is minimized because only a single injection into the flow system is required versus sampling of aliquots for the off-line method. Precision is also improved because the timing of the enzyme reaction and detection are much better controlled in the flow system. Finally, less of both enzyme and sample are needed with on-line enzyme reactor methods. 

Principles of the adiabatic reactor method have been discussed elsewhere [67,68], Under adiabatic conditions, assuming constant heat capacity, constant heat of reaction, and homogeneous reaction, temperature rise data yields fractional conversion, X [68] ... 

The pulse reactor method is similar to semibatch in that all the ingredients except HCN are placed in a small, well-mixed vessel in a thermostated bath. Very small amounts of HCN are then rapidly injected into the reaction mixture with vigorous mixing and the exotherm is monitored. Repeated pulses are made only after the reaction mixture has come back to temperature equilibrium with the bath. In this manner, kinetic information may be obtained. 

Effect of ion doping. Since (photo)-electronic processes are involved at the surface of titania, this oxide was modified by ion doping, both of p- and n-type, by dissolving either tri-(Ga3+, 3+) or pentavalent (Sb5+, V +) heterocations during the preparation by the flame reactor method (ref. 16), which produced homodispersed and homogeneously doped non-... 

The static reactor method used for absolute rate determinations, and almost always for ortho -para deuterium studies, is generally that based on the micro-Pirani gauge analysis chamber as adapted by Ashmead et al. (3). The time necessary for a single determination of the extrinsic field effect by this method is unfortunately likely to be measured in hours or days rather than in seconds as for the flow reactor. To date the only application of this method to the extrinsic field effect appears to be that of Eley et al. (4). Van Cauwelaert and Hall (5) have described a recirculating adaptation of the static reactor that would seem to be useful for studying the field effect. 

Tien (1987) studied the kinetics of heavy metal sorption-desorption on sludge using the stirred-flow reactor method of Carski and Sparks (1985). Sorption-desorption reactions were rapid with an equilibrium reached in 30 min. The sorption-desorption reactions were reversible. The sorption rate coefficients were of the order Hg > Pb > Cd > Cu > Zn > Co > Ni, while the desorption rate coefficients were of the order Cd > Cu > Hg >... 

Figure 8. Sodium hydroxide extraction of Morwell coal in a semi-continuous reactor (method A).

Other methods that have been used to determine Koc values are the so-called box method (Macintyre et al., 1991), the continuous stirred reactor method (de Jonge et al., 1999) and headspace methods, which are especially useful for volatile chemicals (Garbarini and Lion, 1985). Delle Site (2001) has recently reviewed the available methods for the determination of Koc values. 

In order to provide a logical framework for the discussion, an example will be worked out in enough detail to illustrate the methods used. There is no question of providing a recipe for designing nonisothermal reactors methods of working that are useful will be presented, and their application to a more or less typical problem will be described. 

In the sections that follow, we introduce terminology commonly used in the analysis of combustion reactors and discuss material balance calculations for such reactors. Methods of determining the energy that can be obtained from combustion reactions are given in Chapter 9. 

Katz, S. 1960b. Best temperature prohles in plug flow reactors Methods of the calculus of variations. Annals N. Y. Acad. Sci., 84, 441—478. 

Eerikainen, H. Watanabe, W. Kauppinen, E.I. Ahonen, P.P. Aerosol flow reactor method for synthesis of drug nanoparticles. Eur. J. Pharm. Biopharm. 2003, 55 (3), 357-360. 

The whole polymerization kinetics has been followed by means of the adiabatic reactor method (3.6). which allows to simultaneously determine polymerization times and rates. In Table V data, related to the overall polymerization time, tp, as well as to the initial and maximum rates of polymerization, are given. All these parameters are, of course, very relevant to RIM technology. 

S. Katz, Best Temperature Profiles in Plug Flow Reactors Methods of the Calculus of Variations, Annals N. /. Acad. Sci., 84, 441 (1960). 

I tp 7. Stirred-flow reactor method experimental setup. Background solution and solute are pumped from (he reservoir through thc stirred reactor containing the solid phase and are. (tlkcied us aliquots by (he fraction collector. Separation of solid and liquid phases is accom-plished by a membrane filter al the oiillel end of the stirred reactor. 

As with the batch reactor method, radiotracers are an excellent means of following the extent of kinetic reactions in flow methods. Flow methods using radiotracers are identical to those where other analytical methods are used to determine the solute of interest except that a radiolabeled solute is used. Radiotracers have been used numerous times in column transport studies but apparently have not as yet been used with thin-disk and stirred-flow methods. 

These are all devices which reduce both the product concentration and residence time in the gas phase and so minimize product losses through subsequent reactions. Methods (1), (2), and (3) are means of controlling selectively the residence time and concentrations of certain specific products in the discharge and a choice can only be made between them in the light of the physical properties of the various constituents of the gas phase. The fourth method, which does not discriminate between the concentrations or residence times of reactants and products, can only be evaluated when the relative rates of the competing reactions are known. Of the various techniques available, simultaneous reaction and absorption in a heterogeneous reactor (Method 2) opens up interesting... 

The second (syringe-reactor) method permits the study of the kinetics of the activation in the absence of the gas phase. Though the solubility of alkanes in water or sulfuric acid is very low it is sufficient to follow the decreasing concentration of RH in the solution by GLC tool. The competitive versions of the method (when two substrates, RaH and RbH, are used in the same experiment), based on the equation... 

Provided that all these reactions are completely irreversible, we can calculate productivities from the differences in the tracer concentrations before and after the reactor (method of tracer dilution). 

CARTA, M., GRANGET, G., PALMIOTTI, G., SALVATORES, M., SOULE, R., Control Rod Heterogeneity Effects in Liquid Metal Fast Breeder Reactors Method Developments and Experimental Validation, Nuclear Science and Engineering, 100 (1988) pp. 269-276. 

The discussion above suggests an approximate minimum value of 5 = 7 for most reactions. For neat supercritical CO2,5 falls below 7 at a temperature of 83 C at 6000 psi and at 130 C at 10,000 psi using equation 6. The lower temperature limit is set by the critical temperature of CO2 31. TC. Thus, for most workers, the useful range for synthesis in supercritical CO2 is likely to be 31 < T < 83 C, P < 6000 psi. The outer Imiit, without die use of fairly specialized and expensive equipment is 31 < T < 130 C, P < 10,000 psi. If higher pressures are required, they may be most easily achieved using flow reactors, (which also scale more easily). How reactor methods for synthesis in supercritical carbon dioxide have been pioneered by Poliakoff and coworkers. 74) In practice, such reactors closely resemble those ady used for hydrothermal processing. 

The net result of these differences is that one cannot simply take over the theory developed for thermal reactors and apply it to the fast reactor. In the early estimates for fast reactors, the analyses bore only a slight resemblance to the thermal calculations. However, as the energy spectrum of fast reactors has been continually degraded toward lower energies because of the natural trend toward larger cores and oxide and carbide fuels, some of the thermal reactor methods with appropriate modifications have been useful, and the tabulations of the J functions are used extensively. 

The RCP part of the mixture is designed to have ethylene contents on the order of 40-65% ethylene and is termed the rubber phase. The rubber phase can be mechanically blended into the ICP by mixing rubber and HPP in an extruder or it can be polymerized in situ in a two-reactor system. The HPP is made in the first reactor and the HPP with active catalyst still in it is conveyed into a second reactor where a mixture of ethylene and propylene monomer is polymerized in the voids and interstices of the HPP polymer powder particle. The amount of rubber phase that is blended into the HPP by mechanical or reactor methods is determined by the level of impact resistance needed. The impact resistance of the ICP product is determined not only by its rubber content but also by the size, shape, and distribution of the rubber particles throughout the ICP product. Reactor products usually give better impact resistance at a given rubber level for this reason. 

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