Nonlinear Rheology, Yielding, and Constitutive Modeling of Waxy Crude Oils

In this work, the rheological behavior of a group of model crude oils is experimentally studied at temperatures below their wax appearance temperature (WAT). We consider both a two-component wax-oil system and a three-component oil-water emulsion that is partially stabilized by precipitated wax. We characterize the shear-localization and yielding using a combined approach of bulk rheometry and localized velocimetric measurements (RheoPIV) [1]. In particular, Large Amplitude Oscillatory Shear (LAOS) is used in order to map out the non-linear behavior of the material. Along with this, simultaneous local velocity measurements within the fluid are carried out using Particle Image Velocimetry (PIV). The capabilities of the Rheo-PIV apparatus allow deviations from a linear velocity profile to be determined within a single cycle of oscillatory shear and continuously monitored over several cycles. These deviations are correlated to simultaneous measurements of the oscillating stress-strain response of the fluid. The combination of LAOS and local PIV measurements also allows for a more in-depth study of the yielding mechanisms and stress-dependent wallslip in the model wax-oil system. The new insights gained using this approach are used to develop an appropriate elasto-plastic constitutive model that captures both the small strain elastic behavior as well as the large deformation rate-dependent plastic flow that occurs in these fluids. The constitutive model adapts a behavior known as nonlinear kinematic hardening, a concept frequently encountered in the solid mechanics and plasticity literature. This behavior is implemented through the introduction of an evolving internal structural parameter (similar to the structure parameters utilized in certain thixotropy models [2]) that describes the current state of the material. One of the advantages of taking this approach towards constitutive modeling of crude oils is that there exists a robust formalism that allows the model to be extended to frame invariant, thermodynamically consistent, 3D tensorial form. The 3D form of the model can then be implemented into numerical packages in order to simulate various scenarios, e.g. pipeline restart of a gelled crude oil.