Description of nonlinear viscous and viscoelastic properties of polyacrylamide solution under loading

Background. Currently, the solution of the problem of describing the rheological behavior of viscoelastic and nonlinear viscous properties of liquid and solid-like materials is far from perfect. For successful application of polymer systems to enhance oil recovery and for preparation of fracturing fluids and drilling fluids, knowledge of their rheological properties is necessary. Objective. To determine the nonlinear viscous and viscoelastic properties of polyacrylamide solution. Material and methods. We made an attempt to describe the rheological behavior of a polyacrylamide solution depending on the shear rate and on the loading time. A binomial rheological model was used to describe steady-state stresses at different shear rates, which showed a high degree of accuracy. To describe the stress from time, we proposed to use a numerical solution of a system of two differential equations representing the well-known Maxwell and Kelvin–Voigt equations. To describe the initial section of the curves for times less than 0.05 s, a model with a variable modulus of elasticity was used. Results. A high degree of correspondence of experimental and design stresses with a time of more than 0.05 s was achieved. The overall solution was achieved by combining two solutions based on shear rate and shear stress. Relationships with high correlation coefficients were found between the elastic modulus, viscosities of Maxwell and Kelvin and the shear stress and shear rate. Conclusions. We show that in addition to the “ordinary” shear rate determined by the rotation of the viscometer cylinder, it is necessary to consider an additional shear rate due to stress changes in time. Due to this approach, a description of the stress maximum and its displacement from the shear rate can be made. We note that the additional shear rate occurred immediately after the start of loading, rather than at the time of stress drop, as commonly believed.