Reactivity coefficient

PFBR (India) -1.8/-1.2 (fiesh/equil.) -0.64/-0.57 (fiesh/equil.) +4.3 

EBR-II (USA) value is very small, approximately -0.0003 sodium-in therefore no sodium-out calculations have been made 

The temperature distribution radially across a fuel pin is approximately linear in terms of the volume of annular regions. It departs from a linear variation because of the dependence of thermal conductivity on temperature and when there is a central hole in the pin. For a fast reactor spectrum the effective temperature is estimated to be close to the average [4.91]. 

In a transient the temperature of the fuel depends on the specific heat, which is temperature dependent. Fuel melting at the centre of the pin can change the temperature distribution and these effects must be taken into account in calculations of Doppler reactivity feedback. Gas gap conductivity is another source of uncertainty in the calculation of effective fuel temperature. The temperature change across the fuel-clad gas gap is about 25% of the 

A study of the effect of heterogeneity is described in ref [4.92] which presents a general review. The effect can be separated into two components, the fuel pin heterogeneity effect and the subassembly wrapper effect. Compared with the homogenised model both effects are found to increase the Doppler constant by 2.5% giving a total increase of 5%. 

Experimental Validation. The following types of measurement have been used to evaluate the accuracy of Doppler effect calculations (a) the South-west Experimental Fast Oxide Reactor (SEFOR) was built and operated specifically to measure Doppler effects (or fast-acting fuel reactivity feedback effects with expansion effects minimised) (b) the dependence of reactivity on temperature in operating power reactors, such as PHENDC and SUPER-PHENDC (fi-om the non-linearity of the temperature coefficient, for example) (c) the ZEBRA 5 Doppler Loop experiments, in which a test zone was heated. Experiments were performed with and without sodium present (d) the temperature dependence of the reactivity worths of small samples oscillated at the centre of critical assemblies (e) the differences in reaction rates in samples irradiated at different temperatures and (f) temperature dependent thick sample transmission and self-indication measurements, which are usually analj ed together with the differential nuclear data to provide average resonance parameter data. The uncertainties in extrapolating fi-om these comparisons to the conditions in an operating power reactor must also be taken into account. 

Small sample Doppler Experiments and the steel Doppler ect. Small sample Doppler measurements have been made in several critical facilities, including the ANL ZPR and ZPPR facilities, SNEAK and FCA [93]. Measurements made for U-238 samples in ZPPR have been analysed using ENDF/B-IV data giving C/E values in the range 0.85 to 0.90. Measurements made in SNEAK and analysed using KFKINR data give C/E values of about 0.89. These two data sets give similar values for the Doppler constants in the SEFOR cores. Measurements of the Doppler effect of iron samples have been made in FCA Assemblies V-2 (a mock-up of JOYO) and VI-2 (a mock-up of MONJU). The samples were heated from room temperature to 823°K and 1073°K. 

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Control of the core is affected by movable control rods which contain neutron absorbers soluble neutron absorbers ia the coolant, called chemical shim fixed burnable neutron absorbers and the intrinsic feature of negative reactivity coefficients. Gross changes ia fission reaction rates, as well as start-up and shutdown of the fission reactions, are effected by the control rods. In a typical PWR, ca 90 control rods are used. These, iaserted from the top of the core, contain strong neutron absorbers such as boron, cadmium, or hafnium, and are made up of a cadmium—iadium—silver alloy, clad ia stainless steel. The movement of the control rods is governed remotely by an operator ia the control room. Safety circuitry automatically iaserts the rods ia the event of an abnormal power or reactivity transient. 

Copolymers. Although many copolymers of ethylene can be made, only a few have been commercially produced. These commercially important copolymers are Hsted in Table 4, along with their respective reactivity coefficient (see Co polymers. The basic equation governing the composition of the copolymer is as follows, where and M2 are the monomer feed compositions, and r2 ate the reactivity ratios (6). 

A two-site immunometric assay of undecapeptide substance P (SP) has been developed. This assay is based on the use of two different antibodies specifically directed against the N- and C-terminal parts of the peptide (95). Affinity-purified polyclonal antibodies raised against the six amino-terminal residues of the molecule were used as capture antibodies. A monoclonal antibody directed against the carboxy terminal part of substance P (SP), covalently coupled to the enzyme acetylcholinesterase, was used as the tracer antibody. The assay is very sensitive, having a detection limit close to 3 pg/mL. The assay is fiiUy specific for SP because cross-reactivity coefficients between 0.01% were observed with other tachykinins, SP derivatives, and SP fragments. The assay can be used to measure the SP content of rat brain extracts. 

Figure 7.3 Comparative evolution of the concentration for a non-reactive species and a reactive species when the input concentration is doubled at t=0. In this particular case, th = 0.2 is the water residence time in time units, a,- = 4 the reactivity coefficient, equation (7.2.8), of the reactive species.

Let agr be the common value of the reactivity coefficients for both isotopes. Replacing the subscripts liq by SW , in by runoff and evaluating, we get the rate of change of 87Sr/86Sr as... 

Non-additivity of substituent effects has been proposed as a criterion for the operation of the RSR so the linearity argues against its applicability in this system. In a description of transition states by structure-reactivity coefficients (Jencks and Jencks, 1977), two alternative types of behaviour were discussed. In Hammond -type reactions the more endothermic reactions have later transition states, whereas anti-Hammond behaviour is characterized by an adjustment of the transition-state structure to take advantage of favourable substituent effects. These results illustrate that different systems can display quite different behaviour in linear free energy correlations. Thus, in alkene protonations, such correlations cover vast ranges in reactivity with only modest changes in sensitivities, while in solvolytic reactions the selectivity p varies depending on the electron supply at the electron-deficient centre (Johnson, 1978). 

D.A. Jencks and W.P. Jencks, On the Characterisation of Transition States by Structure-Reactivity Coefficients, J. Am. Chem. Soc., 1977, 99, 7948. W.P. Jencks, When is an Intermediate Not an Intermediate Enforced Mechanisms of General Acid-Base Catalysed, Carbocation, Carbanion, and Ligand Exchange Reactions, Aces. Chem. Res., 1980, 13, 161. 

This is a conclusion that we remember well, because it should never have been reached. These data, and data from many other laboratories (77), are certainly consistent with a metaphosphate mechanism, but they are also consistent with a concerted substitution reaction they do not distinguish which mechanism is followed. Structure-reactivity coefficients, isotope effects, volumes and entropies of activation and similar parameters are all measures of... 

Another striking feature of these reactions actually helps us visualize how this need for reorganization can contribute to the intrinsic barrier. This feature is the disparity or imbalance in measured structure-reactivity coefficients such as Brpnsted a and (3 values. Indeed, the Brpnsted a values obtained by varying a remote substituent in the carbon acid, for example, Z in I (equation 2), are usually larger than the Brpnsted (3 values obtained by varying the base, that is, / = a — (3 > 0 (Table II). 

Imbalance as a Function of X and Y. Nucleophilic additions to olefins also show imbalances in the structure-reactivity coefficients. In analogy to the proton transfers, I = anucn — (3nucn is defined as a measure of the imbalance Pnucn is the normalized Pnuc value 4 for anucn (measure of negative... 

In nucleophilic addition reactions, the imbalance results in exceeding jSnuc i nuc e normalized structure-reactivity coefficients that are the analogs of a and /3, respectively, in proton transfers.Note that since is usually obtained from the variation of a phenyl substituent, it is equal to the normalized Hammett p value. A representative example is shown in equation (59) where = 0-67 and i nuc — 037 Again, the exalted coefficient is the result of the negative charge at the transition state 76 being closer to the Z substituent than it is in the adduct. 

The need to account for shale properties as well as pore fluid chemistry has led to the suggestion of a descriptive dimensionless parameter, the Reactivity Coefficient (Fam et al. 2003), for shales. 

To capture combined effects of surface area and pore water ionic state, the Reactivity Coefficient X has been defined and used for shale (Fam et al. 20(X)). It is a dimensionless number, the product of specific surface, Sa, mineral gravity, Oj, water density, p , and adsorbed layer thickness, 6 ... 

X - 0.15 is a good boundary between unreactive clays (X < 0.15) and high reactivity clays (X > 0.15). Intact shale data using dielectric permittivity and magnetic resonance confirm the validity of the Reactivity Coefficient concept. Dielectric data permit rapid shale reactivity evaluation in practical cases. Along with other simple tests, it can be carried out on the drill rig using drilling chips. 

The cross-reactivity coefficient is defined as curvature, a second derivative of the function that relates pA to rate = dPn /dpAig = dp,g/dpA ,. If the... 

L. B. Miller, Monte Carlo Analysis of Reactivity Coefficients in Fast Reactors General Theory and Applications, ANL-7307 (1967). 

Reactivity is an integral parameter often met by reactor physicists and engineers. Reactivity worths of control systems and reactivity coefficients are important in the performance and safety of nuclear reactors. Hence, accurate knowledge of such reactivities is essential for reliable and economical design of nuclear reactors. The accuracy of reactivity predictions is... 

Examples of perturbation parameters are reactivity worth, reactivity coefficient, and various sensitivity functions (see Section IV,B). Gandini (39) and Stacey (46) derived GPT formulations for the calculation of reactivity in altered systems. In Section V,F,2 we present Stacey s GPT formulation for calculating the effect of different system alterations on a given reactivity. Also presented is a formulation for calculating the effect of a given system alteration on different reactivities. 

E. Kiefhaber, Fine Group Calculations for Reactivity Coefficients of Structural Materials in Fast Reactors, KFK-1759. Kernforschungszentrum Karlsruhe (1973) also in USAEC CONF-720901, Vol. 2, p. 623 (1972). 

The following characteristics have been obtained in the course of NPI tests and operation power and parameters of installation, the campaign lifetime, the reactivity margin, reactivity coefficients, poisoning effects, temperature distributions, dynamic parameters, coolant radioactivity, dose rates of neutron and y-radiation behind the shield. They were in sufficiently good agreement with calculation results. 

Absence of poisoning effects in the fast reactor (FR), low value of negative temperature reactivity coefficient, compensation of fuel bum-up and slagging processes by plutonium generation as well as partial reloadings enable to ensure the operative reactivity margin to be less than delayed neutron share and to diminish or eliminate the probability of runaway by prompt neutrons in the reactor under operation conditions. 

A full scale critical experiment is important to evaluate the calculated results such as reactivity coefficients and critical conditions. As neutron leakage is enhanced in the 4S core, the conventional calculation method is not sufficient to accurately predict the core characteristics. A critical experiment is thus the most urgent R D item. 

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