A fractional model to relative viscosity prediction of water-in-crude oil emulsions

Abstract

The objective of this work was to propose a new model based on the theory of fractional calculus to predict the relative viscosity of petroleum emulsions. For this, stable emulsions with water content ranging from 10 to 65 wt% were prepared from three Brazilian crude oils: A (API 24.6), B (API 16.8) and C (API 13.5), with different contents of saturates, aromatics, resins and asphaltenes. Stable emulsions were prepared using an Ultra-Turrax homogenizer and the viscosity data were obtained from an Anton Paar Controlled Rheometer. The proposed fractional model was able to describe the experimental data very well, yielding a mean correlation coefficient (R2¯) above 0.99 in all tests and mean deviations of the order of 6%. For comparison purposes, the models of Mooney (1951) and Pal and Rhodes (1989) were applied to the same experimental data and presented mean deviations of up to 21% and 18%, respectively. Finally, based on the formulated theory, it is shown that the fractional model parameters (k1, k2, α) may be related to the mass fraction of saturates, aromatics, resins and asphaltenes (SARA) existing in the crude oils.