A 3D model for annular displacements of wellbore completion fluids with casing movement

During mud circulation and cementing operations, non-Newtonian completion fluids are injected along the wellbore annular space formed by the gap between the outer wall of the casing and the rock face. During such processes, these fluids displace each-other and follow a complex path given by pressure gradients, rheology and density contrasts, casing rotation and reciprocation and by the actual shape and orientation of the annulus. Muds and cement slurries also often exhibit a yield stress which may represent additional challenge for optimal fluid removal and cement coverage. This paper presents a novel approach to solving the 3D flow and displacement of completion fluids in the annulus. In particular, this work extends a model published in Tardy and Bittleston (2015) which solves the flow in the 2D axial-azimuthal plane, to now capture fluid distribution and velocity profiles across the gap width in the 3D axial-azimuthal-radial space. The new 3D model is derived using the so-called narrow-gap approximation for the momentum balance equations. This approximation provides a mean to solve the 3D velocity and concentration fields while solving a 2D-only elliptic pressure equation, which is significantly faster to solve than the original 3D pressure equation, and without suffering any significant loss of accuracy.