In the completion of oil and gas wells, successful cementing operations essentially require the complete removal of the drilling mud and its substitution by the cement slurry. Therefore, the displacement of one fluid by another one is a crucial task that should be designed and optimized properly to ensure the zonal isolation and integrity of the cement sheath. Proper cementing jobs ensure safety, while poor displacements lead to multiple problems, including environmental aspects such as contamination of fresh water bearings. There are a number of factors, such as physical properties of fluids, geometrical specifications of the annulus, flow regime, and flow rate, which can remarkably affect the displacement efficiency. The shape of the interface plays an influential role during the displacement process. For a highly efficient displacement the interface has to be as flat and stable as possible. However, unstable and elongated interfaces are associated with channeling phenomenon, excessive mixing, cement contamination, and consequently unsuccessful cementing operations. Thus, the stability of the interface between the two fluids has major importance in cementing applications.

In the present work, a novel method for the prediction of interface instability and displacement efficiency is introduced. Instability analyses of the interface between the two fluids are carried out following the main ideas of the original Rayleigh-Taylor and Kelvin-Helmholtz instabilities. Moreover, using the same analyses, optimized designs for improvement of the displacement process in any specific situation are proposed. The influence of density, rheological properties, surface tension, and flow rate of the fluids on the instability and shape of the interface, and consequently on the displacement efficiency, is studied. Furthermore, an analytical solution of the displacement of fluids in the annular space that enables the calculation of the mixed volumes is developed. Additional time-dependent considerations are made for the calculations of cases with unstable interfaces. For the same cases studied, 3-D Computational Fluid Dynamics (CFD) simulations are performed, using commercially available CFD software. For the purpose of validation of the results, a number of experiments were conducted for fluids with various combinations of physical properties.

The results present the effect of physical fluid properties, geometrical configurations, and flow rate on the instability of the interface and displacement efficiency. Reasonably good agreement between the results of all three approaches presented in the paper are observed and they all emphasize the importance of the proper selection of fluid properties and flow rates for any specific sequence, to minimize the degree of contamination and mixing.

The discussions and results of this work provide insight into displacement process, invaluable guidelines for industrial applications, and compelling evidence of the importance of correct predictions and appropriate designs of the displacement of fluids in cementing operations.

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