Delineation of the effective viscosity controls of diluted polymer solutions at various flow regimes

Carreau's model is a well-established standard in the scientific community for estimating the viscosity of polymer solutions as a function of shear rate. It accurately predicts effective viscosity in power-law and Newtonian flow regimes, distinguished by distinct asymptotic values at extremely low and high shear rates. However, existing analytical models for determining Carreau's parameters (zero-shear-viscosity, μp∘, power-law index, n, and relaxation-time constant, λ) have limitations. Typically expressed in terms of polymer solution concentration (Cp), these models often overlook critical variables such as solvent salinity (CNaCl), hardness (Cca++), solution density (ρs), and polymer molecular weight (M). Additionally, many of these models lack dimensional consistency.This study introduces a robust scientific method for modeling Carreau's parameters, integrating dimensional analysis with non-linear regression to delineate the factors influencing these parameters. The analysis indicates that the power-law index is primarily influenced by Cp, CNaCl, and Cca++. The zero-shear-viscosity (μp∘) is governed by Cp, CNaCl, Cca++, M, ρs, pressure (P), and n, while the time constant (λ) is mainly determined by Cp, CNaCl, Cca++, n, and μp∘. The derived empirical models demonstrate a direct dependence of zero-shear viscosity on P, M3,ρs6, and an exponential dependence on Cp, aligning with experimental observations. Incorporating variables like solution density, molecular weight, and pressure was crucial for enhancing the precision of μp∘ and λ predictions. These models, validated against rheological measurements of three dilute EOR polymer solutions (HPAM and AMPS-based) in various conditions, have shown superior precision and impartiality compared to prominent existing models, representing a significant advancement in the field.