TANK CALIBRATION DATA EVALUATION

Over the past several years, the International Atomic Energy Agency (IAEA) has been faced with the increasing need for standardized procedures for the evaluation of calibration data gathered in nuclear process tanks equipped with bubbling tubes for measuring liquid content. Any process measurement of solution volume performed in such a tank can only be as good as the quality of the calibration function and the related uncertainties determined from data gathered during the calibration exercise. The determination of the calibration function consists of a three-step process: 1) Gathering of calibration measurement data; 2) Standardization of the measurement data; and 3), Fitting of a calibration equation to the standardized data and the determination of the associated uncertainties. This paper details the procedures that the IAEA has developed for completing the latter two steps of this process. Standardization of calibration measurement data is necessary to account for buoyancy effects and the inevitable temperature fluctuations encountered during the multiple calibration runs required for any given tank. Buoyancy corrections must be applied to gravimetric increment measurements to determine the exact mass of calibration liquid added to the tank. Thermal expansion corrections must be applied to account for the changing volume of the tank with changing temperature. The necessary equations for applying these corrections are presented and show that other effects, such as relative humidity or the height of the manometers above the tips of the bubbling probes, are negligible in comparison with the uncertainties associated with the temperature corrections. Tank calibration data has traditionally been evaluated using a rather haphazard methodology, which offered no satisfactory error modeling. A new statistical model for determining the calibration equation and its associated uncertainties are presented. The basic statistical equations from which all estimates are derived are given, including the algorithm used to calculate the contribution of the random and systematic errors (fully taking into account the covariances) to the uncertainty of the estimation of the fitted calibration parameters.