(179f) Quantification of Uncertainties in Experimental Liquid Density and Viscosity at Hthp Conditions By Using the Corresponding States Law As Arbitrator

As yet, there is no universal answer for the methodology of quantifying the uncertainties in the standard reference viscosities (i.e., Squalane, DiPEs, DIDP, TOTEM, Krytox oil) which the International Association of Transport Property (IATP) has accepted for evaluating dense viscosity to be encountered in the drilling of the Ultra-Deep Petroleum Reservoirs of the Gulf of Mexico. It may even be impossible to quantify the uncertainties in the viscosities by statistical analysis alone because the measured viscosities are based on the empirical mathematical equation that depend on equipment standard constant, K, thermodynamic properties (density (or kinematic viscosity), coefficient of expansion, heat capacity, and interfacial tension), fluid flow regimes, reliability of standard calibration fluids, fluid sample degradation, and the standard in the Worldwide Laboratory practices. While the various statistical techniques do not show complete picture of the measured data, the reliability and consistency of the reference standard viscosity are better exhibited by calibrating charts (or reduced density and reduced viscosity graphs).

As temperature and pressure are the independent variables, the corresponding states law by which the measured data is displayed as reduced density and the reduced viscosity versus the reduced temperature (T_R) and the reduced pressure (P_R) are very desirable. Consequently, the corresponding states law provides a basis of infer critical density through the reduced VdW equation of state and likewise the measured viscosity provides inference for critical viscosity through the reduced VdW transport equation of state. The uncertainty quantification is achieved by random scatter plots of the critical densities and critical viscosities back-out of the measured data versus (P_R/T_R) at the HTHP conditions. The single continuous curve through the data or lack of a single curve through the scatter plots gives an indication of the reliability and internal consistency among the experimentally measured data. The plots also provide a measure of reliability and consistency in the transport data from the various Worldwide Laboratories.

The analysis of results shows that no systematic errors in liquid densities and liquid viscosity of Squalane at HTHP conditions can be associated with neither the various densitometer designs nor the various worldwide viscometer designs. However, it is still impossible to reduce the empirical mathematical equation used to derive the measured viscosity to the dimensionless form. So, we assume the major uncertainties in the experimentally measured viscosity data are due to the lack of reference standard for the various worldwide equipment standard constant, K. Nonetheless, the CS reduced chart provides an important way of establishing viscosity at the HTHP conditions.