Abstract 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.