Critical mass determination

Determination of critical mass for a slab type loading, 

Measurements of reactivity changes caused by water flow, air bubbles, and open beam holes. 

Measurements of neutron and gamma fluxes inside and above the fuel, in the graphite reflector outside the tank, and in the thermal shield. 

1 Critical Hsiss Determination. Several extraordinary safety precautions were taken for the initial fuel loading. For instance, a standard safety rod was rebuilt with a beryllium section in place of the fuel section 

Another precaution was the installation of separate neutron-level and period indicators at the loading platform which was 30 ft above the control room. Also, a boron fluoride neutron detector was used in addition to the 

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After completion of this "mechanical program in September, 1949, it appeared that much could be learned by converting the Mock-Up into equipment for low-power nuclear experiments such as critical mass determination, ueutron-and gamma-flux measurements, and operation of the control system. These studies occupied the period Trom February, 19S0 to September, 1950. 

The critical mass determination was begun after recording backgrounds of all the neutron detectors with the addition of four fuel pieces containing a total of 560 g of The control rods were then withdrawn completely and... 

Critical-Mass Measurements on Beryllium-Reflected, Enriched-Uranium, Spherical Systems, by O. Kolar and H, R. Ralston (VCBL-L). A scries of critical mass determinations has been made for spherical beryllium reflected systems. Cores were enriched (93.17S U-235) uranium spheres ranging in mass from 10.6 to 32.6 kg. The corresponding reflector thicknesses were 20.3 to 2.2 cm. All results were nonnalized to a core density of 18.6 g/cc. Some Los Alamos data are included for completeness and have been similarly normalized. These two sets of experiments were found to be in good agreement. The experiments and results arc discussed, together with the fit to the experimental data obtained with the spherical Si, 5-group code in use at UCRL. 

From the list of critical masses it can be concluded that appreciable deformations In shape do not Introduce large errors Into the critical mass determination. 

Since June of 1961, the Critical Mass Group at the Han-, ford Critical Mass Facility has acquired over six months operating experience while performing approximately 60 critical mass determinations. The purpose of these experiments is to determine the criticality properties of plutonium solutions of various concentrations of plutonium and nitrate, and the effects of various reflectors. 

The approach-to-critical procedure is employed in each critical mass determination, and the rod worth is simul- -taneously determined for each etqieriment. The control rod worth, in terms of solution volume, varies from about 60 ml t high plutonium concentrationsy to about 560 ml (at low plutonium concentrations) as shown in Fig. 1. When the control rod is started into the solution (sphere. not full), the flux is observed to rise, then foil off as ex-pe ed. This is because the first portion of the rod is worth more as a volume displacement (improved geometry) than as a neutron absorber. The effect is estimated to te about 5f positive reactivity experimentally, and a perturbation calculation provides an estimate of 4.3f Ak/k. 

Mass Transfer and Kinetics in Rotary Kilns. The rates of mass transfer of gases and vapors to and from the sohds iu any thermal treatment process are critical to determining how long the waste must be treated. Oxygen must be transferred to the sohds. However, mass transfer occurs iu the context of a number of other processes as well. The complexity of the processes and the parallel nature of steps 2, 3, 4, and 5 of Figure 2, require that the parameters necessary for modeling the system be determined empirically. In this discussion the focus is on rotary kilns. 

The determination of critical si2e or mass of nuclear fuel is important for safety reasons. In the design of the atom bombs at Los Alamos, it was cmcial to know the critical mass, ie, that amount of highly enriched uranium or plutonium that would permit a chain reaction. A variety of assembhes were constmcted. Eor example, a bare metal sphere was found to have a critical mass of approximately 50 kg, whereas a natural uranium reflected 235u sphere had a critical mass of only 16 kg. 

This method employs a theoretical critical mass flow based on an ideal nozzle and isothermal flow condition. For a pure gas, the mass flow can be determined from one equation ... 

Fig. 4. Critical concentrations of polystyrene/toluene and polyacrylamide/water at 25 °C in relation to molar mass determined by viscometry and light scattering... 

Minimal bounds on the production quantity are most often process dependent. Typically, a minimal campaign length is required if for example a critical mass is necessary to initiate a chemical reaction. The same is valid for maximal bounds on the production quantity. The rationale here is that a cleaning operation may be required every time a certain amount has been produced. Finally, batch size restrictions often arise in the chemical industry, if for example the batch size is determined by a reactor load or, as discussed above, the processing time for a certain production step is independent of the amount of material processed. In these scenarios, when working with model formulations using a discrete time scale, it is important that the model formulation takes into account that lot sizes may comprise of production in several adjacent periods. 

In order to compare a number of different zeolite preparations we have found it convenient to determine not the diffusivity of o-xylene per se, but to characterize the samples by measuring the time (tQ 3) it takes to sorb 30% of the quantity sorbed at infinite time. The characteristic diffusion time, t0 3, is a direct measure of the critical mass transfer property r2/D ... 

To summarize, in the present scenario pure hadronic stars having a central pressure larger than the static transition pressure for the formation of the Q -phase are metastable to the decay (conversion) to a more compact stellar configuration in which deconfined quark matter is present (i. e., HyS or SS). These metastable HS have a mean-life time which is related to the nucleation time to form the first critical-size drop of deconfined matter in their interior (the actual mean-life time of the HS will depend on the mass accretion or on the spin-down rate which modifies the nucleation time via an explicit time dependence of the stellar central pressure). We define as critical mass Mcr of the metastable HS, the value of the gravitational mass for which the nucleation time is equal to one year Mcr = Miis t = lyr). Pure hadronic stars with Mh > Mcr are very unlikely to be observed. Mcr plays the role of an effective maximum mass for the hadronic branch of compact stars. While the Oppenheimer-Volkov maximum mass Mhs,max (Oppenheimer Volkov 1939) is determined by the overall stiffness of the EOS for hadronic matter, the value of Mcr will depend in addition on the bulk properties of the EOS for quark matter and on the properties at the interface between the confined and deconfined phases of matter (e.g., the surface tension a). 

Handling Precautions. Care must be taken in the handling of plutonium to avoid unintentional formation of a critical mass. Plutonium in liquid solutions is more apt to become critical than solid plutonium. The shape of the mass also determines criticality. Plutonium s chemical properties also increase handling difficulty, Metallic plutonium is pyrophoric, particularly... 

Purity control, molecular mass determination and molecular mass fingerprints can be performed either by electrospray ionization (ESI) or matrix-assisted laser desorption/ionization time of flight (MALDI-TOF) MS. ESI is preferred for sequence determination by MSn and MALDI-TOF for molecular mass fingerprints. Both technologies are appropriate for molecular mass determination and purity control. We have edited a critical review on the use of MS strategies for discovery and peptide sequencing of bioactive peptide (25). 

Table 8.6 lists the mass differences due to the substitutions of a given amino acid by another in the sequence of a peptide chain [101]. The accuracy of the molecular mass determination is critical for the success of the mutation characterization. The required accuracy depends not only on the determined molecular mass, but also on the detected substitution. Indeed, the characterization of Gln/Lys substitution needs less accurate mass measurement with a 1 kDa peptide than with a 40kDa protein. In the same way, the characterization of Gly/Trp substitution is easier than the characterization of Gln/Lys substitution. 

In the growth mechanism explained in Figure 5.3, the steps or cycles are repeated while gaseous reactive species collide in the gas phase. Therefore, how large the species become and how quickly their size reaches the critical mass above which they cannot stay in the luminous gas phase are dependent on the density of the gaseous species and their flow pattern, which is determined by the size and shape of the reactor. 

The development of mass transfer models require knowledge of three properties the diffusion coefficient of the solute, the viscosity of the SCF, and the density of the SCF phase. These properties can be used to correlate mass transfer coefficients. At 35 C and pressures lower than the critical pressure (72.83 atm for CO2) we use the diffusivity interpolated from literature diffusivity data (2,3). However, a linear relationship between log Dv and p at constant temperature has been presented by several researchers U>5) who correlated diffusivities in supercritical fluids. For pressures higher than the critical, we determined an analytical relationship using the diffusivity data obtained for the C02 naphthalene system by lomtev and Tsekhanskaya (6), at 35 C. 

The selection of adsorbents is critical for determining the overall separation performance of the above-described PSA processes for hydrogen purification. The separation of the impurities from hydrogen by the adsorbents used in these processes is generally based on their thermodynamic selectivities of adsorption over H2. Thus, the multicomponent adsorption equilibrium capacities and selectivities, the multi-component isosteric heats of adsorption, and the multicomponent equilibrium-controlled desorption characteristics of the feed gas impurities under the conditions of operation of the ad(de)sorption steps of the PSA processes are the key properties for the selection of the adsorbents. The adsorbents are generally chosen to have fast kinetics of adsorption. Nonetheless, the impact of improved mass transfer coefficients for adsorption cannot be ignored, especially for rapid PSA (RPSA) cycles. 

The ability to predict drop size is critical to determining both the interfadal area for mass transfer and the state of dispersion of the system. In dilute systems and in moderately concentrated systems where coalescence can be neglected, the following equation describes the maximum equilibrium (i.e., after a long time) drop diameter of an inviscid or low viscosity dispersed phase ... 

The first application of nuclear fission was in the development of the atomic bomb. How is such a bomb made and detonated The crucial factor in the bomb s design is the determination of the critical mass for the bomb. A small atomic bomb is equivalent to 20,000 tons of TNT (trinitrotoluene). Since 1 ton of TNT releases about 4 X 10 J of energy, 20,000 tons would produce 8 X 10 J. Earlier we saw that 1 mole, or 235 g, of uranium-235 liberates 2.0 X 10 J of energy when it undergoes fission. Thus the mass of the isotope present in a small bomb must be at least... 

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