Trend curves

Original trend curves given in the Russian Code were constructed on the basis of test results obtained after irradiation within the material qualification programmes in experimental reactors. Thus, their lead factor (relation between neutron flux in the experiment and in the RPV) was more than 100, and such a large factor is not allowed by current standards. Moreover, the database of results was relatively small at that time and irradiation embrittlement of 15Kh2NMFA-type steel was studied only on steePwelds with nickel content lower than 1.5 mass %, as this was the original intention for this type of steel. 

The generic form of the critical temperature of brittleness due to operation ageing mechanisms has the following form  

Tk is the current value of critical temperature of brittleness during operation  

---

A numerical value is obtainable by integrating the trend curve for the flow received from the Flow Recorder (FR), from the start of the reaction to a time selected. Doing this from zero to each of 20 equally spaced times gives the conversion of the solid soda. Correlating the rates with the calculated X s, a mathematical model for the dependence of rate on X can be developed. 

Trend data also must be adjusted for maintenance and repair activities. Figure 44.34 illustrates an average trend curve that indicates a sharp rise in vibration levels. It also reflects that, after repair, the levels drop radically. At this point, all baseline and reference values should be reset. If this does not occur, the automatic trending capabilities of the computer-based system do not function properly. 

Rj Ratio of the average temperature-dependent trend curve value of tensile strength to the room temperature tensile strength ... 

Also he speculated that citrus juices contain two cloud-coagulating enzymes of different thermostabilities. One enzyme, most active at low pH and temperature, appeared to be destroyed by heating the juice at 65 to 70°C (149 to 158°F). The second enzyme, most active at pH 3.0 to 3.3 and about 35°C (95°F), appeared to require heating to 888C (191°F) for inactivation (12). Stevens (13) described a rapid test for pectic enzymes in citrus juice. It involved adding pectin under controlled conditions of temperature and sample preparation, and measuring the time required for flocculation. Stevens, and coworkers (14) further elaborated on the patent work (12, 13). They produced a trend curve of the... 

Figure 11.12. Estimation of time-trend curve of p,p -DDT and p,p DDE residues in human breast milk in Vietnam.

FIGURE 15-2 Titration curves for the Fe(II)-KMn04 reaction Qett) and the Fe(II)-K2Cr207 reaction (right). The downward trending curve is for the reverse titration of dichromate with Fe(II). (From Smith. )... 

FIGURE 13.5 Concentrations of dissolved Pb, Cd, Zn, Cu and calculated trend curves above and below the halocline between 1993 and 2005 at Station 271. (n.s., not significant), (p < 0.01, significant on the 99% level). Oxygen and hydrogen sulfide (expressed as negative oxygen equivalents) over 15 years in the 200-m depth horizon (Nausch et al., 2003). (See color plate)... 

FIGURE 13.5 Concentrations of dissolved Pb, Cd, Zn, Cu and calculated trend curves above and... 

A markedly nonlinear trend in the exploratory plot of the empirical logit versus exposure or a covariate of interest would indicate that the assumptions of the linear logistic model are not met. In this case, a more complex nonlinear model can be evaluated using a shght modification to the models already presented. Let s suppose that the plot of the empirical logit versus AUC had a distinctly concave trend, curving upward similarly at each end of the observed AUC distribution. With appropriate precautions and care in interpretation, especially outside the range of the data, a quadratic model may be implemented ... 

Methoxyl Content. The saponification method of von Fellenberg (, ff) was used to determine the methoxyl content, and the results in Table I are expressed on the basis of 100% calcium pectate for uniformity. The methoxyl content of the calcium pectinates prepared by acid de-esterification ranged from 3.1 to 6.4% Trend curves, showing a comparison of de-esterification as denoted by the methoxyl contents of the alcohol-recovered samples and calcium-precipitated samples, are presented in Figure 2. Under comparable conditions of pH and time of treatment, the methoxyl contents of the alcohol- and the calcium-precipitated samples prepared by acid de-esterification at 60 C. were similar. 

Grades ranged from 68 to 204 for the alcohol-precipitated pectinates, and from 92 to 244 for the comparable acid-alcohol-treated calcium pectinates. Trend curves in Figure 3 show that the calcium pectinates treated with acid-alcohol are superior in grade to the alcohol-precipitated products (17). The effect of the addition of calcium and sodium hexametaphosphate upon the grade of acid-alcohol-treated cal-... 

However, it turns out that this quantity is a rather poor indicator of the bond ionicity, as the system hardly behaves like a classical dipole consisting of two point charges, which is also illustrated by the fact that Mo depends strongly on cluster size. A much better indicator of the bond polarity is contained in the quantities M/, M2, and Ms. For all systems studied, Mj w -1.4 to -1.6, and Ms and M3 are small, and furthermore the cluster size dependence of these quantities is much less than that of Mq. (This points to a general property of cluster calculations already alluded to in Section 111.1 whereas absolute quantities may depend sensitively on cluster size, trends and slopes of trend curves show a much weaker cluster size dependence.) This linear behavior is consistent with an ionic bond where the slope. Mi, is related to the extent of ionicity. The dipole moment of two point charges +q and -q will be = -qx r and d/j/dr = M/ = -q. Hence for an ideal fully ionic halide bond, the curve is expected to be a straight line with slope M, = -l. 

FIGURE 5.1 Atmospheric carbon dioxide at the Mauna Loa Laboratory. Data prior to May 1974 are from the Scripps Institution of OceanographyfSIO, blue), data since May 1974 are from the National Oceanic and Atmospheric Administration (NOAA, red). A long-term trend curve is fitted to the monthly mean values. (U.S. Department of Commerce, National Oceanic and Atmospheric Administration Earth System Research Laboratory. http //www.esrl.noaa.gOv/media/2007/50YearC02Record.html) (v/v) in 1850 to 360 ppm in 2000. 

Another important area of process control systems is the ability to handle trend curves as part of production documentation. Recent software packages (called Historians) provide such capability over an extremely long time span and with batch production facilities which enable paperless handling of batch data that should be documented by graphical trend curves. Some... 

The proposed algorithm is not only helpful to the decision makers to solve the problems of emergency evacuation route optimization, but also to propose problems based on the two trend curves of objective functions by applying the algorithm. 

Univariate Forecasts of a given variable demand are based on a model fitted only to present and past observations of a given time series. There are several different univariate models, like Extrapolation of Trend Curves, Simple Exponential Smoothing, Holt Method, Holt-Winters Method, Box-Jenkins Procedure, and Stepwise Auto-regression, which can be regarded as a subset of the Box-Jenkins Procedure. 

There are three important databases that have been developed by (or for) the NRC PR-EDB, RVID and the so-called Eason database used for research and development of improved embrittlement correlations and trend curves. 

Abstract This chapter describes the embrittlement processes in WWER reactor pressure vessel (RPV) materials during operation - radiation embrittlement and thermal ageing. Current trend curves for both types of WWER RPV materials are given and explained. Surveillance specimen programmes are shown, as their results are used for RPV integrity and lifetime evaluation. Finally, anneahng of the RPV is proposed as the most efficient mitigation measure. 

Original trend curves given in the Russian Code have been updated in the last several years, and the current situation can be found either in the last IAEA VERLIFE procedure or in the leading Russian document. The values of Ap, n and a for specified temperatures of irradiation of materials for WWER-440 RPVs from 15Kh2MFA-type steel are given in Table 5.1. The upper boundary for 15Kh2MFA(A) materials and their welding joints... 

For calculation of 50 % (median) curves of AT i(F, t) according to Eq. 5.5, the value a = 0 should be taken, both for base and weld metal. This type of dependence is used for direct determination of radiation embrittlement parameters based on results of RPV-specilic surveillance specimen tests. Typical trend curves calculated according to the Eq. 5.4 for base metal and weld metal are shown in Figs 5.2 and 5.3. It can be seen that mean curves provide a good description of the distribution of test results from surveillance specimen programmes. 

Typical trend curves (mean and 95%) for transition temperature shift in 15Kh2NMFA(A)-type base metal (BM) with 1.1 mass % of nickel. 

Now, national regulatory bodies accept only data obtained after such re-evaluation and reconstitution - these data are also the bases for new trend curves given by Eq. 5.4. 

Empirical trend curve for SAWs based on various surveillance results. (Reproduced from USNRC NUREG/CP-0157, 1997.)... 

The trend curve was pieced together by P.N. Randall of the NRC using evaluations and analyses performed by others. The Revision 2 trend equation uses CF values that are tabulated chemistry factors (in UK units) for welds and base metals based on Cu and Ni content (wt%), and FF is a more complex fluence function (f is again expressed as lO n/cm, E>lMeV) ... 

Jones and Bolton have provided a detailed description of the approach employed by Magnox Electric for developing trend curves describing the DDR of Magnox RPVs. The authors stress that the advantage of the physically-based approach is that the trend curves underpinned in this way can be used with confidence when limited extrapolation is required into areas of neutron dose, dose rate or irradiation temperature which are not specifically covered by the surveillance database. 

Empirical trend curve for Magnox submerged-arc welds based on reactor surveillance data. 

Surveillance data and predicted trend curves of a BWR base metal with high Cu content/ ... 

M. Kirk, Revision of AT30 embrittlement trend curves, EPRIMRP/NRC PTS Re-Evaluation Meeting, RockviUe, MD, 30 August, 2000. 

---