Effective mud removal is a prerequisite to attain the cement coverage necessary for good zonal isolation. Because of this, the oilfield industry has dedicated considerable attention to the topic of mud displacement over the past 60 years. The first 2D annular displacement simulator was introduced in the 1990s and it is now widely available. The results are satisfactory for simpler configurations. However, for deeper wells with complex trajectories such as highly deviated or horizontal wells, the models start to show their limits. This paper discusses the advancements in mud displacement simulation that overcome the limitations of the previous generation simulator and provide a more realistic simulation in highly deviated and horizontal wells. A new generation simulator now provides high-fidelity results via a combination of: 1) a pipe displacement model, accounting for fluid contamination inside the pipe; 2) a high-resolution annular displacement model, accounting for the complex 3D annulus shape with full determination of axial and azimuthal flows; and 3) a stiff-string centralization model based on the finite-element method, predicting casing position in a 3D wellbore. A primary cementing operation for a horizontal well was studied and an unprecedented congruence was witnessed between predicted fluids annular concentration maps and ultrasonic cement log. The simulator was also able to predict complex channeling patterns in the annulus. These results allow a better understanding of the cement placement technique and provide means to optimize the sequence of fluids to achieve effective mud displacement in the well. Enabled by advancements in today’s computing capabilities, the new simulator is able to simulate both simple and highly complex scenarios more realistically. Finally, the new model allows better planning and decision making to achieve zonal isolation and well objectives