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, ${\mu }_p^{\circ }$, power-law index, $n$, and relaxation-time constant, $\lambda$) have limitations. Typically expressed in terms of polymer solution concentration ($C_p$), these models often overlook critical variables such as solvent salinity $\left(C_{\mathrm{NaCl}}\right)$, hardness ($C_{c{a}^{++}}$), solution density (${\rho }_s$), 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 $C_p$, $C_{NaCl}$, and $C_{c{a}^{++}}$. The zero-shear-viscosity $\left({\mu }_p^{\circ }\right)$ is governed by $C_p$, $C_{NaCl}$, $C_{c{a}^{++}}$, $M$, ${\rho }_s$, pressure ($P$), and $n$, while the time constant ($\lambda$) is mainly determined by $C_p$, $C_{NaCl}$, $C_{c{a}^{++}}$, $n$, and ${\mu }_p^{\circ }$. The derived empirical models demonstrate a direct dependence of zero-shear viscosity on $\sqrt{P}$, $\sqrt[3]{M},\sqrt[6]{{\rho }_s}$, and an exponential dependence on $C_p$, aligning with experimental observations. Incorporating variables like solution density, molecular weight, and pressure was crucial for enhancing the precision of ${\mu }_p^{\circ }$ and $\lambda$ 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.