Flow measurement of liquid hydrocarbons with positive displacement meters: the correction for slippage

In the oil industry, the economical and fiscal impact of the measurements accuracy on the custody transfer operations implies fulfilling strict requirements of legal metrology. In this work, we focus on the positive displacement meters (PD meters) for refined liquid hydrocarbons. The state of the art of the lack of accuracy due to slippage flow in these meters is revised. The slippage flow due to the pressure drop across the device has been calculated analytically by applying the Navier-Stokes equation. No friction with any wall of the slippage channel has been neglected and a more accurate formula than the one found in the literature has been obtained. PD meters are calibrated against a bidirectional prover in order to obtain their meter factor which allows correction of their indications. Instead of the analytical model, an empirical one is proposed to explain the variation of the meter factor of the PD meters with flow rate and temperature for a certain hydrocarbon. The empirical model is based on the historical calibration data, of 9 years on average, of 25 m with four types of refined hydrocarbon. This model has been statistically validated by linear least-squares fitting. By using the model parameters, we can obtain the meter factor corresponding to different conditions of temperature and flow rate from the conditions in which the devices were calibrated. The flow parameter is such that a 10% flow rate variation implies a meter factor variation lower than 0.01%. A rule of thumb value for the temperature parameter is 0.005% per degree Celsius. The model residuals allow surveillance of the device drift and quantifying its contribution to the meter factor uncertainty. The observed drift is 0.09% at 95% confidence level in the analyzed population of meters.