Primary cementing flows: Accurate computation of multi-fluid displacement sequences

A successful primary cementing operation is critical to maintaining the integrity of oil and gas wells. This operation includes injecting multi-fluid sequences into a narrow eccentric annulus, i.e., displacing the drilling mud first with a wash, followed by a spacer fluid, and finally, one or more cement slurries. We modify the two-dimensional gap averaged and the dispersive two-dimensional gap averaged models for multi-fluid displacement sequences. In particular, we implement a monotone numerical scheme, namely, the local Lax–Friedrichs scheme, for the evolution of the concentrations to ensure that individual fluid concentration bounds between 0≤c¯≤1, and the fluid concentrations sum to 1. The strong conservative properties of the numerical scheme are validated by achieving negligible relative errors (on the order of ∼10−15) for five distinct scenarios. The outcomes of this study can bring a significant improvement in designing the primary cementing operation, where an exact evaluation of fluid volumes is essential.