In this work, we study the effect of borehole irregularities during primary cementing of a horizontal section of well. We use a simplified 2D gap-averaged model to compute the displacement of a drilling mud by a spacer within an elliptical annulus that represents an oval irregularity. We also present a series of 3D numerical simulations using a Volume of Fluid method to capture the interface between the fluids. The 3D model allows us to study the effects of more local irregularities such as wall roughness that can be imported from a caliper log.
The dynamics of the displacement of two fluids in a horizontal uniform circular annulus is governed by buoyancy, eccentricity and the rheology of the fluids. A positive density difference combined with a slow mean pumping speed promotes slumping of the second fluid towards the bottom of the annulus. Nevertheless, high eccentricity values (e = 1-standoff) are common due to the weight of the casing pulling downwards, opposing the buoyancy force. Finally, the rheology of the fluids is relevant to determine the presence of un-displaced layers of mud, e.g. at the walls.
The same competition described above holds true in the elliptical annulus. Results from the 2D gap-averaged model suggest that the elliptical shape incorporates an additional way of altering the velocity field around it. The effect is more evident when orienting the largest radius of the elliptical annulus at different angles. Results from 3D simulations show that the interface follows irregularities and the local roughness can improve the displacement by inducing secondary flows. However, enlargements result in poor displacement.