59th Annual Report on Research 2014

Introduction and Objectives:

Increasing energy costs have attracted oil companies to tap into heavy crude oil reserves. Heavy crude oil is a colloidal suspension of aggregates of many compounds (resins and asphaltenes), which give rise to very unusual rheological properties such as non-Newtonian behavior and very high viscosity. Such high viscosity leads to difficulties in the production/transportation of heavy crude oil. To optimize processes to lower viscosity and improve flow properties of heavy crude oil, a better understanding of the relationship between micro-structure and macro rheological behavior is required. Here we propose to study the effects of micro-structure (size, shape, polydispersity, concentration, etc.) on the rheology of heavy crude oil using state-of-the-art numerical simulations without the simplifying assumptions of previous theoretical models.

Methods:

We use our well-validated, sharp-interface immersed boundary method to simulate colloidal suspensions of asphaltene with their experimentally observed micro-structure.  We have incorporated the methods for calculating the particle stresses that affect the bulk stress of the suspension, from which the effective viscosity of the suspension is determined. Moreover, we separately calculate different terms affecting the bulk stress, to identify the relative importance of different mechanisms of stress generation in the suspension.

Results:

We have validated our methods against analytical and experimental results for single particles in the shear flow. We have investigated the effects of inertia, shape, and concentration of the aggregates on the viscosity of the suspension through our simulations. Figure 1 shows the pressure field and streamlines around the ellipsoid in the symmetric mid-plane (plane perpendicular to the vorticity vector and passing the center of ellipsoid) in a semi-dilute suspension at Re=0.01. The background plane is colored by pressure where dark and bright colors indicate high-pressure and low-pressure regions, respectively.

Figure 1 Visualization of pressure field and streamlines around the ellipsoid

We found that inertia would generally increase the Reynolds-scaled shear stresslet (dominant term of the particle stress) of suspensions, which results in increasing total particle stress and the relative viscosity of suspensions. For finite and moderate inertial regimes of dilute and semi-dilute suspensions while keeping the volume fraction constant, the relative viscosity of suspensions increase when the aspect ratio of particles increases. Another influence of inertia is that other components of particle stress, i.e. acceleration stress would be the order of 10% of the total particle stress for Reynolds number of O(10) for the ellipsoids.

Figure 2 Relative viscosity of suspension of mono disperse particles as a function of volume fraction for

Figure 2 shows the relative viscosity of suspension of ellipsoids with constant aspect ratio Ar  = 2 as a function of volume fraction. Analytical solution of Jeffery (1922) for this aspect ratio is also plotted in comparison with numerical results. As it is expected, up to the boundary of semi-dilute suspension the linear equation is an accurate fit. However, for suspension of higher volume fractions effect of other particles reinforce inertial effects and accelerate the relative viscosity as a function of volume fraction.

The results of this research have been presented at two conferences (APS DFD 2013, and ASME CIE 2014). Furthermore, the work has resulted in two peer-reviewed conference proceeding papers, and a journal paper is being submitted.

Future work:

For the next year we will focus on more complex geometries based on the experimentally observed micro-structure.  Furthermore, we will look into the effect of polydispersity on all mechanisms of stress generation and the relative viscosity of the suspension