A simple model of the rheological curve of HPAM solutions at different temperatures

The oil and gas industry faces two significant challenges, including rising global temperatures and depletion of reserves. Enhanced recovery techniques such as polymer flooding have positioned themselves as an alternative that attracts international attention thanks to increased recovery factors with low CO2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {CO}_2$$\end{document} emissions. However, existing physical models need further refinement to improve predictive accuracy and prevent design failures in polymer flooding projects. In particular, disposing of adequate rheological models is vital as they are intimately associated with the sweep efficiency of the fluid. The rheological curves of polymeric solutions of partially hydrolyzed polyacrylamide (HPAM) can be obtained from a viscosity measurement at a single shear rate using the recently reported PAMA technique. This methodology provides the coefficients of the Carreau-Yasuda Law (viscosity at zero shear rates (eta 0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta _0$$\end{document}), power law index (n), and the shear relaxation time (lambda\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda$$\end{document})) when the temperature of solutions is close to 298 K. Nevertheless, the values of these coefficients at various temperatures are not linked through simple expressions of the Arrhenius type, limiting the validity of rheological curves to a narrow range of temperatures. This article presents a new model-referred to as PAMA-T-that extends the PAMA methodology to a temperature range of 298-343 K. We demonstrate that PAMA-T provides satisfactory predictions of rheological curves at various temperatures, also using as input a single measurement performed with a Brookfield viscometer at a single solution temperature. The method relies on the intrinsic viscosity's slight or null dependence on temperature and on a master surface, which is specified in the space spanned by the following three parameters: the power-law index, relative viscosity, and nondimensional shear relaxation time. The solvent viscosity and relaxation time-employed as references to define these parameters-are functions of temperature. On the master surface, while the power coefficient of Carreau-Yasuda (n) exhibits only a slight dependency on temperature, the relative viscosity depends monotonically on this variable. Moreover, the concentration regime of the fluid significantly influences the temperature dependence of the nondimensional relaxation parameter. Solutions included in this study are those formed with polymers with a molecular weight ranging from 8 to 26 MDa-with concentrations between 0.03 and 5.876 g/L-and for brines with a wide range of salinity and ionic composition. The methodology gives rheological curves for shear rates comprised between 0.01 and 1000 s-1 excluding the shear thickening behavior of the HPAM polymer solutions. The regression model developed was fitted with a training dataset and has exhibited satisfactory results, as tested with additional experimental datasets from different authors. The metrics used to quantify the agreement of viscosities between the model and experiments demonstrate satisfactory behavior in the shear thinning range of shear rates and the shear range lower than 7.3 s-1.