Thermodynamic Basis of Brine Density on Pressure, Temperature, and Chemical Composition in Ultrahigh Pressure/High Temperature Environments

Temperature change and the pressure/volume/temperature (PVT) response of wellbore annular fluids are the primary variables that control annular pressure buildup in offshore wells. Though the physics of annular pressure buildup is well understood, there is some ambiguity in the PVT models of brines. While custom tests can be performed to determine the PVT response of brines, they are time-consuming and expensive. In this light, our paper presents a method to determine the density of brines from their chemical composition, as a function of pressure and temperature. It compares theoretical predictions with the results of tests on brines used in our industry and available test data from the oil and gas and other industries. In 1987, Kemp and Thomas used the principles of chemical thermodynamics to develop equations for the density of brines as a function of pressure and temperature and their electrolytic actions. However, their paper contained two (inadvertent, and probably typographical) errors. One of the errors lay in the set of the Debye-Hückel parameters, and the other was contained in the coefficients of the series expansion for the infinite dilution molal volume. Furthermore, they (inadvertently) did not mention the role of a crucial parameter that accounts for the interaction between the ionic constituents of the salt. As a result, nearly a generation of engineers in our industry has been unable to reproduce their valuable results or apply their technically rigorous results to other brine chemistries. In this paper, we return to the basic equations of chemical thermodynamics and the principles of stoichiometry and delineate the inadvertent errors that had crept into the Kemp and Thomas equations. We then present the rectified equations and reproduce their example with the corrected results. Further, we compare the predictions from the original Kemp and Thomas work with results from a leading chemical engineering model. Finally, we compare the results of theoretical models with test measurements from the laboratory and characterize the uncertainty inherent in each model. Thereby, we have rendered the Kemp and Thomas (1987) model useful to the well design community.