Modeling dispersion in cementing flows: From vertical to horizontal wells

Primary cementing often involves a laminar displacement flow of miscible fluids at a high Péclet number (Pe≥107) along an inclined narrow eccentric annulus. As the displacing fluid penetrates ahead of the mean flow in the center of the annular gap, significant dispersion may result. In this study, we explore the impact of dispersion on horizontal well cementing flows in detail by comparing both quantitative and qualitative results obtained from three-dimensional (3D) simulations, the dispersive two-dimensional gap-averaged (D2DGA) model, and the earlier two-dimensional gap-averaged (2DGA) model. Unlike in vertical wells, buoyancy acts transverse to the main flow direction, but surprisingly the 3D and D2DGA models predict very similar flows. Further external verification of the D2DGA approach was provided by comparing with existing experimental results in the literature. Outcomes from both 3D and D2DGA models reveal pronounced dispersive fronts that are largely absent in the 2DGA model. The results suggest that advective dispersion smears the fronts in both 3D and D2DGA models, thereby retarding the growth of fingering instabilities arising from an unfavorable viscosity or density gradients, as found in the 2DGA model results. Consequently, advective dispersion can significantly alter the flow structures and, perhaps remarkably, lead to less fingering-dominated flow patterns.