The prediction of accurate drilling fluids behavior inside an annulus is especially important in drilling engineering during hydraulic program design. The flow characteristics of Newtonian and non-Newtonian fluids drastically change in the annuli when the inner pipe is eccentric. In this study, the fluid flow inside concentric, partially eccentric, and fully eccentric annuli are modeled using computational fluid dynamics. Computational fluid dynamics simulations are performed to investigate the effect of pipe eccentricity on frictional pressure loss, tangential velocity, axial velocity, and effective viscosity of water and non-Newtonian fluids for two horizontal wellbore sections (0.074-0.046 m, 0.0185-0.0117 m). Computational fluid dynamic software predictions of pressure losses are verified with experimental data as well as basic theoretical calculations. Predicted and experimental pressure drop values are in good agreement with each other almost for all cases. It emerged that pipe eccentricity drastically decreases frictional pressure loss but significantly increases the tangential velocity and effective viscosity in annuli, if all other parameters are kept constant. Nevertheless, as the fluid viscosity is increased, the pipe eccentricity effect on tangential velocity becomes more severe.