The oilfield primary cementing process is vital to successful and safe extraction. It is the first cementing operation performed after the casing string has been placed in the newly drilled wellbore, and is critical to prevent loss of well control or contamination of water sources. While a conceptually simple operation, real-world cementing operations are complicated by a slew of operation specific issues such as high wellbore deviation, weak formation walls, and high bottom hole formation pressure. This makes a quantitative understanding of the cement slurry rheology imperative. Cement slurry rheometry can be difficult in practice due to its non-linear stress-strain behaviour. Complicating matters further, the cement slurries we are interested in contain suspensions of relatively large particles---micro beads---that are problematic for convential measurement tools such as concentric cylinder rheometers. This motivates a computational treatment.

There are two overriding aspects to modelling suspensions in viscoplastic fluid flows. Firstly, for fully resolved particle suspensions---regardless of the carrier fluid---the discretisation scheme must cope with disparate length scales at the particle boundaries and wider flow field. In this work we adopt the overset grid method, allowing each particle to be explicitly represented with a curvilinear grid, thereby enabling cost-effective resolution of boundary layer flows. Secondly, the governing equations of viscoplatic fluid flow are non-linear, even in the absence of inertia, requiring specialised solution strategies. We adopt an augmented Lagrangian approach that allows for an exact treatment of the constitutive equation, enabling truly unyielded zones in our solutions.

Even with an efficient discretisation scheme, the solution of viscoplatic fluid flow problems remains prohibitively expensive. In this work, we are primarily interested in yield stress effects, and so we use the ideal Bingham constitutive model as a proxy for our cement slurry. We begin by investigating the viscoplatic squeeze flow between approaching particles, finding that under certain conditions yield stress effects external to the closing gap contribute greatly to the lubrication force. This enables viscoplastic lubrication theory to be used as a sub-grid scale model in coarse grained suspension simulations.

By restricting ourselves to quasi-steady, non-inertial, two-dimensional suspensions of infinite circular cylinders we are able to simulate suspension flows with two orders of magnitude more particles than in the literature. We first investigate the yielding transition in negatively buoyant suspensions under quiescent flow conditions. We identify three distinct sedimentation regimes, including a mixed regime where clusters of particles preferentially settle while isolated particles remain fixed. Finally, we investigate neutrally buoyant suspensions under shear, where we find that unyielded material may act as additional particles, increasing the apparent solid volume fraction, and extend an existing micro-mechanical model to take this in to account.