The P-µ-T Cubic Equation of Viscosity for Reservoir Oils

Abstract

Summary Oil recovery simulation sensitivity increases with heavier oils for the existing viscosity models, driving into higher levels of difficulty when fitting viscosity data for rising oil heaviness, particularly below the saturation pressure. Keeping in view the similarity of trends of viscosity and density with isothermal pressures for reservoir oils, the P-μ-T cubic viscosity model, which was developed for pure hydrocarbon components, was extended to reservoir oils. Two parameters in the P-μ-T cubic viscosity model for mixtures with pure and pseudocomponents are identified for adjusting the viscosity data fitting: Kc for controlling the viscosity gradient with pressure and the “ε” shifting trends for increasing viscosity direction. These two parameters are treated as the adjustable parameters required for fitting the viscosity data. A total of 129 reservoir oils from different sources are used to validate the reliability of the P-μ-T viscosity model. The default model (where ε and Kc are 1 and 45, respectively), extended to 71 light oils, resulted in 31% of average absolute relative deviation (AARD) in viscosity prediction. However, separate adjusted parameters are obtained per oil for more accurate viscosity data fitting. Application of the model in this work results in (post-fitting) AARD% of 2.86% average for 36 low-viscosity oil data, 5.68% for 9 high-viscosity oil data, 9% for five oil blends, and 4.11% for bitumen blends. The model gives an AARD of 3.06% in the undersaturated region and 3.79% in the saturated region for the oil considered. The model predicts better the viscosity above saturation pressure for low-viscosity oils and below saturation pressure for high-viscosity oils. A comparative analysis of the P-μ-T cubic viscosity model vs. other models demonstrates its ability to successfully capture viscosity trends of oil and blends in all viscosity ranges. For simplicity, the P-μ-T cubic viscosity model is proposed with only two optimizing parameters even though using a third parameter improves the matching in heavy oils.