Thermal utilization

The term n is the total neutron density in each lattice region integrated over all energies up to 100 kev and vq is 2200 n s. 

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Authors have proposed a novel process not to dispose to landfill sites both waste PVC and waste glass but to utilize them to produce fuel and neutralize each other at the same moment. It has been successfully demonstrated that hydrogen chloride produced during flash pyrolysis of PVC was completely neutralized by the fixed glass bed and thus chlorine-lree fuel was produced [1-2]. To carry forward our proposed process we need to know the kinetics of the neutralization process. Also we have to solve the problem of formation of metal chlorides in the product char during pyrolysis of PVC, which is a critical issue for its thermal utilization. Consequently, in the present study the evaluations of neutralization kinetics of glass cullets and the decomposition of CaCl2 in char by steam were conducted. 

Xiao, C., Luo, H., Tang, R., Zhong, H. 2004. Solar thermal utilization in China. Renew Energy 29 1549-1556. 

The cross sections for neutron capture increase for all atoms for thermal energy neutrons. As a result, even though low cross section materials are used some neutrons are captured by the structural and moderator materials. The probability for the non-capture of thermal neutrons in this fashion is signified by/, the thermal utilization factor, which in our case can be assumed to be 0.9. Thus of the original N neutrons 112 thermal neutrons remain in the second generation to cause fission in the nuclear fuel. 

A cubic unreflected graphite moderated natural uranium reactor contains 3 % enriched uranium as UC homogeneously dispersed in the graphite matrix the weight ratio CIV = 10. The resoiunce passage and thermal utilization factors ate both assumed to be 0.9 c = 1.00. Make an estimate of the critical size of the cube. 

Some special parameters (e.g., flash point, heating value, water content) must be determined for wastes that are to be disposed of or thermally utilized by combustion. All data for a given waste are documented in a multi-page survey form. The plant manager is responsible for the correctness of the information. After thorough checking, including a check for completeness of analysis data, the necessary pretreatment and the... 

Pla.stics to be recycled after use must be collected in the purest possible form. The recyclable portion of the waste must be separated into classes of valuable substances or individual substances. The fractions that result can be recycled for valuable constituents, recycled for feedstocks, or thermally utilized, depending on the type of plastic. 

Spherical Harmonics Method. Wigner recognized that the diffusion theory approximation in all of these calculations was deficient. However, he was reluctant to invoke more complicated transport theory because the neutrons were not monoenergetic, and any transport correction to the diffusion theory would be obscured by the error caused by the assumption that the thermal neutrons were monoenergetic. He and Breit had used the spherical harmonics method in their original calculations of the size of a bomb, and he supervised the later work at Chicago on the application of the spherical harmonics expansion to calculate the thermal utilization. 

The work in Princeton was concerned with three problems the diffusion length of thermal neutrons in uranium oxide and that in metal was measured, which permitted a more exact calculation of the thermal utilization than... 

In order to better estimate the effect of the water, a comparison calculation for a 2 region system consisting of a 1.25 cm radius metal cylinder concentric with an 11.1 cm radius graphite cylinder has been carried out. The distributions at thermal and resonance energies are shown in the figures. The thermal utilization factor, for such an arrangement is 1.185, the resonance absorption factor, is 1.100 and so n = x - = 1.304. 

To compute the thermal utilization from the thermal neutron densities in the three regions, we must first compute the total slowing down powers, Pq and P2 of the water and the graphite. Taking the effective hydrogen scattering cross section to be 15 X 10 (which underestimates the scattering power of the water), we have... 

In Paper 30 Wigner derived the simplest expression for the thermal utilization in a spherical cell, and also showed that the error caused by sphericizing a cubic cell was very small. 

T. Plass, G.N. and Wigner, E. P., Values of the Thermal Utilization, Resonance Absorption, and Fast Neutron Effect for Oxide and Metal Spheres and Cylinders , CP-372, December 14, 1942. 

It is evident that the system deflned by (13) and (17) is identical with the set of equations used to calculate the thermal utilization in a cell (CP-103, 104, 161). Consequently, the standard formulas given for the thermal utilization apply here, namely... 

The above approximations make the calculation very simple. At least in the case of a face centered or a body centered lattice, it is a very good approximation to replace the cell by a sphere of equal volume and to assume that the neutron density has zero radial derivative on the surface of the sphere. This is a less good approximation for a simple cubic lattice and the corresponding correction will be given below. This correction constitutes, from the point of view of thermal utilization, the only difference between the simple cubic and face and body centered lattice. For a finite lattice, corrections must be introduced which decrease the thermal utilization. These will be also discussed below. 

It is evident, in the case of the thermal utilization, that Kiri must be smaller than 1, since, otherwise, the neutrons which become thermal at the surface of the cell have only a very small chance for reaching the U. Hence, we can write + 2 and the first factor of (11) becomes rf/3 divided by a quantity which is very nearly 1. One can write... 

If only the first two terms of (14) were present, the disadvantage factor would be just 1, i.e., the thermal utilization would be just as good as in a homogeneous mixture. Actually, however. 

Table 1 gives the thermal utilization for the oxide of density 4 as function of the radius tq of the oxide sphere and the cube root Vc + 1 of the ratio of cell d and oxide volumes. The l/p2 given in this table were calculated on the basis of (11) or (14) and the following constants (p is the density of the oxide)... 

Figure 1 gives the thermal utilization for a lattice cell which contains 21300 gr C and 2660 gr U, either in the metal or the oxide form. In the latter case, the cell contains 3140 gr UaOg. The abscissa is the density of the U, which is,... 

We shall now test the accuracy of our cellular method , i.e., the replacing of the cell-polyhedra by spheres. We shall do this by estimating the error in case of a simple cubic lattice - the cellular method is evidently much more accurate for face or body centered lattices. The correction which we shall obtain gives, at the same time, the difference between a simple cubic and a centered lattice from the point of view of thermal utilization. 

Equation (23) shows that the difference between simple cubic lattice and the face or body centered lattices is very small from the point of view of thermal utilization 2 ia is smaller than 1 for even for the largest structures that have been proposed. Furthermore, there is an opposite effect of the same order of magnitude in the resonance absorption. 

Here, r = ln(JB/ thermai) has a somewhat different definition from the usual one it is zero for neutrons, the energy E of which is thermal, (t t) is the transport cross section which may depend on the energy but does not depend on the position thermal neutrons the average logarithmic energy loss (independent of position) <7, the absorption cross section for thermal neutrons which depends on the position. q(r) is the density of fast neutrons per unit r (it is not Fermi s slowing down density Q), multiplied with the velocity, n the density of thermal neutrons times their velocity, /(r) dr is the number of fission neutrons per slow neutron captured in U, for which r is between r and r + dr. Finally pi is the chance of escaping resonance absorption and p2 the thermal utilization. The multiplication constant here... 

In these and the above equations, the a are cross sections per imit volume, the a in (8) is scattering cross section, the average loss in r per collision. The are used because the material may contain different types of atoms. The (Ta is the thermal absorption cross section r(r) the resonance absorption cross section per unit volume. The = qef is the multiplication constant divided by the resonance escape probability. The product of thermal utilization / and (Ta is the effective cross section of uranium per unit volume, i.e., its cross section per unit volume multiplied by the thermal neutron density in it and divided by the average thermal neutron density. One can write, therefore, (Tu for f(Ta- If one multiplies this with rj the result is the same as crfU where fission cross section for thermal neutrons per unit volume, p the number of fast neutrons per fission. As a result, the third term in (7) can be written also as e is the multiplication by fast effect)... 

It appears reasonable to apply the ordinary formulae for calculating p2 such as given in report (CP-104) by Christy and Monk. The only objection to this is that the cell is so great in the present case that the production of thermal neutrons is not uniform any more over the cell but shows a dip in the neighborhood of the rod. For this reason the formulae of (CP-104) give a too high thermal utilization p2 and hence tend to exaggerate the effect of the control rods. The equation (7rr is the area of a cell in which there is one control rod, (7ao = oo must be used in CP-104 since the rod is black)... 

Combustion, carbonization, gasification, and liquefaction are considered the four grand processes in the utilization of coal. In general terms, 92% of the coal production is used as fuel and 8% is carbonized to produce metallurgical coke. Coal combustion is carried out in thermal utilities for electricity production, co-generation plants, and cement factories. Coal combines with oxygen from the air giving carbon dioxide and heat ... 

Reactor design is concerned not only with eigenvalues such as the reactivity but also with weighted characteristics or ratios such as the breeding ratio, thermal utilization, etc. Such characteristics arise in steady-state systems that are either critical or subcritical with a source. 

This theory allows us to estimate perturbations in some characteristics of interest in noncritical systems. For example, the thermal utilization / is the ratio of neutrons absorbed in the fuel (with probability h/v) to the neutrons absorbed throughout the cell (with probability L v), Thus, f = j 1,/vN dxjj If vN dx. Let... 

Note that a direct first-order approximation that based the reduction in the thermal utilization on the estimate of the neutrons wastefully absorbed in the cladding, proportional to SLfvN, would not allow for the fact that only a fraction of such neutrons were originally destined to be absorbed in the fuel anyway. Since can be as low as 0.6 or 0.7 at the interface, the correction introduced by the stationary calculation is appreciable. 

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