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Summary A successful cement placement can provide zonal isolation and environmental safety. Effective design of cement placement and mud removal affects all the stages of the wellbore life, from drilling ahead to production. Accurate predictions of fluid displacement in the wellbore are vital to design fluid properties and plan the cementing job. In this work, an analytical model is developed to simulate the displacement of fluids in eccentric annuli. This paper presents an analytical method for the solution of cement/mud displacement and evaluation of interfluid contamination during displacement in vertical eccentric annuli. This new approach starts by addressing the problem of single-fluid flow in eccentric annuli by analytically solving the governing transport equations for a flow inside an unwrapped annulus. The solution is then extended to a system of two fluids in a vertical annulus by adjusting the boundary conditions for displacement. The model is completed by adding the time-dependent calculation of interface between the two fluids, enabling the accurate determination of the amount of interfluid mixing and displacement efficiency. The analytical method proposed is used to simulate single- and multifluid flows and study the effect of fluid properties of cement, spacer, and drilling mud at different flow rates on displacement efficiency for both concentric and eccentric vertical annuli. Noting that the drilling fluids are non-Newtonian, the concept of apparent viscosity is used, accounting for variable apparent viscosity at different annular gaps. 3D computational-fluid-dynamics (CFD) simulations were performed and the results were compared with the analytical solution. Moreover, instability of the interface in all cases was studied, and the analysis offers an understanding of the role of fluid properties and proposes applicable optimized design to enhance the displacements. The amount of interfluid mixing and contamination that occurs during the displacement was calculated for both methods. The analytical solution and CFD produce results within a 13% difference, which sufficiently validates the analytical model. Evidence was gathered to support that the improper design of fluid properties and flow rate along with a highly eccentric annulus can lead to substantial cement contamination. This can lead to underdesigning the amount of fluids to be pumped to provide a complete mud removal and an efficient cement placement. On the other hand, learnings and models developed allow the optimization of fluid properties that can lead to the best outcomes, even for a highly eccentric annulus. The present work aims to take part in addressing the undeniable importance of a complete cement displacement by means of a semianalytical solution for the fluid displacement coupled with the interface-instability analysis, attempting to provide a realistic prediction of the amount of interfluid mixing and cement contamination, along with qualitative judgements on the quality of the cementing job. This methodology is intended to offer improvement techniques for the displacement and provide enhancements for practical industrial applications.

Summary 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 guarantee the zonal isolation and integrity of the cement sheath. Proper cementing jobs ensure safety, whereas poor displacements lead to multiple problems, including environmental aspects such as the contamination of freshwater-bearing zones. There are a number of factors, such as physical properties of fluids, geometrical specifications of the annulus, flow regime, and flow rate, that 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 phenomena, 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 (RT) and Kelvin-Helmholtz (KH) instabilities. Moreover, with the same analyses, optimized designs for the improvement of the displacement process in any specific situation can be 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. The 3D-computational-fluid-dynamics (CFD) simulations are performed with commercially available CFD software to study several displacement cases. To validate the results, numerous experiments were conducted for fluids with various combinations of physical properties and operational conditions. For one of the inefficient displacement cases, an optimized design is provided on the basis of a study of the instability of the interface, and the improvements are validated by CFD simulations. The results present the effect of fluid properties, geometrical configurations, and flow rate on the instability of the interface and displacement efficiency. A reasonably good agreement between the results of all approaches presented in the paper is 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 the displacement process, beneficial guidelines for industrial applications, and compelling evidence of the importance of correct predictions and appropriate designs of the displacement of fluids in cementing operations.

Primary cementing is a crucial task in the completion of oil and gas wells, as it is potentially meant to provide zonal isolation, and prevent uncontrolled flows and environmental hazards. Much research has been conducted to find the key techniques for obtaining the maximum displacement efficiency during cementing operations. Yet, it appears that the industry could benefit from more investigations on the complications involved in displacement processes. In this work, a methodology is proposed in an attempt to obtain qualitative and quantitative predictions of displacement efficiency. This method, which appears to complement previously existing methods, introduces a combined analysis of instability of the interface between the two fluids with an analytical solution of fluid displacement flow in eccentric annuli. The analytical solution enables the time-dependent calculation of interface location and provides a quantitative judgement on the volume fraction of the displaced fluid left in the annular space. On the other hand, the instability models provide an insight on the degree of cement contamination, and guidelines on how to minimize the amount of inter-mixing. The proposed approach was implemented for several displacement cases and the results were evaluated by both Computational Fluid Dynamics (CFD) simulations and experimental tests. Instability of the interface in all the cases was studied and the analysis provided more in-depth understanding of the effect of different parameters on displacement efficiency. Considering that in the existing analytical models, including the one presented in this work, the interface between the two fluids is supposed to be sharp, the calculated volume fraction of displacing fluid can be not necessarily a proper representative of the real displacement efficiency. It was observed that there can exist cases where the volume fraction of the displacing fluid did not necessarily indicate an inefficient displacement, whereas the instability analysis suggested that the corresponding design had to be avoided. This was also validated by CFD simulations. Moreover, the instability model can provide more information about the critical values of design parameters and propose optimized designs for the improvement of displacement efficiency. The present work provides a versatile tool that enables quantitative determination of displacement efficiency, along with an enhanced judgement on the amount of inter-fluid mixing and cement contamination. The novel approach of coupling the instability analysis with displacement flow calculation not only offers improvements on displacement designs, but also assists to avoid any undesirable outcomes caused by ineffective cement placement.