A study of the thermodynamic and rheological properties of polymer and polyelectrolyte dilute solutions
An incompressible fluid flowing through a porous medium must undergo local velocity fluctuations as the local flow path cross-sectional area varies. If a small amount of a linear polymer is dissolved in the fluid, the fluid drag forces elongate the solvated polymer coils where the fluid is accelerating and compress the polymer coils where the fluid is decelerating. Polymer coil resistance to such deformations can result in a great increase in the fluid apparent viscosity as compared to the solvent apparent viscosity in absence of dissolved polymer. An apparent correlation exists between dilute polymer solution flow resistance in porous media and the average size of a dissolved polymer coil. A measure of polymer coil size in solution is the solution zero-shear intrinsic viscosity. A model equation was developed from existing theory to describe polymer solution intrinsic viscosity as a function of polymer molecular weight and fluid temperature. The model was verified using intrinsic viscosity data collected experimentally and gathered from the scientific literature. A second model equation was derived from empirical results describing the solution intrinsic viscosity of a charged polymer as a function of solution ionic strength. The model relates three dimensionless groups of parameters that describe a polyelectrolyte in solution. An extensive assembly of experimental data and of data from the scientific literature was used to test the predictive capability of the model. A nearuniversal correlation was established between dimensionless quantities, but data for two polymer types deviated from the trend. A custom extensional rheometer was used to test the correlation of solution extensional flow resistance with polymer hydrodynamic size. A packed bed of small mesh screens simulated fluid flow through a porous medium, thus creating an extensional fluid flow field. Dilute polymer solution resistances to flow through the packed bed were measured, and polymer coil extensional viscosities were derived from the experimental results. A critical fluid strain rate was identified beyond which polymer coils experience extensional strain and enhance the solution viscosity. Finally, polymer coil extensional viscosity was related to solution intrinsic viscosity, and the fluid yield flow rate for coil extension was related to the polymer coil hydrodynamic diameter. The model equations can, therefore, be used to predict dilute polymer solution flow resistance in porous media based on macromolecular chemical structure and solution conditions.