Influence of Viscosity on Density-Unstable Fluid-Fluid Displacement in Inclined Eccentric Annuli

Abstract

Construction of wells for oil production, geothermal energy recovery or geological storage of carbon dioxide is performed in stages by drilling the rock formation to a certain vertical depth, and then isolating the drilled section by running and cementing a casing string in the hole. The conventional cementing strategy relies on displacing the annular space behind the casing from the bottom and toward the surface. The conventional circulation direction therefore places the denser cementing fluids below the original annular fluid. An alternative cement placement strategy is to displace the annular space from the surface and downward by injecting cementing fluids directly into the annulus. Such reverse circulation operations have the benefit of lower circulation pressures and a reduced risk of fracturing the formation during placement, but also leads to density-unstable displacement conditions and increased risk of fluid contamination. To better understand how the design of cementing fluids and their placement rate affect reverse circulation displacements, we performed a series of computational simulations of density-unstable displacements using a realistic three-dimensional geometrical model of a wellbore annulus. We address the effects of wellbore inclination and inner pipe eccentricity, with a particular focus on impacts of the fluid viscosity hierarchy on the annular displacement efficiency. Our results show that increasing the displaced fluid viscosity will act to suppress the tendency for buoyant backflow, while it can worsen displacement of the narrow side of the eccentric annulus. Transverse secondary flows, which are stronger in cases where the displaced fluid is less viscous, contribute to the displacement of the narrow, low side of the annulus. We also observe that increasing the imposed axial velocity will tend to stabilize the annular displacement and suppress backflow, in agreement with previous work for buoyant pipe displacements. The present computational study is a step toward understanding how buoyant, inertial, and viscous stresses affect density-unstable displacement flows for reverse circulation cementing.

Appendix 1

We performed a grid sensitivity study to ensure the results were not significantly influenced by the chosen grid resolution. The simulation with parameters Fr = 5.15 and Re = 283 and an eccentricity of e = 0.3 was run with four different grid sizes, denoted coarse, medium, fine and extra fine. The total number of cells was doubled for each level, where fine corresponds to the grid resolution used in the remainder of the work.

Figure 13 shows the gap-averaged concentration field after 8 s. The overall evolution is almost identical for all resolutions, indicating that the fine resolution is satisfactory. This is further corroborated by the calculated front velocity and total displacement efficiency (ratio of displacing fluid volume and total annulus volume), which are shown in Fig. 14. Again, the results are not significantly influenced by the grid resolution.

Fig. 13.

Grid sensitivity study. Comparison of concentration field after 8 s. From left to right: Coarse, medium, fine, and extra fine.

Fig. 14.

Grid sensitivity study. Comparison of displacement efficiency for different grid sizes.