This study proposes a new mathematical model to overcome the limitations in existing hydraulic models used to predict cuttings transport in coiled tubing horizontal or deviated well drilling. A new three-segment (a horizontal and near horizontal segment, a vertical and near vertical segment, and a transit segment) hydraulic model under two-phase (solid-liquid) flow in annulus was developed to predict and interpret cuttings transport mechanisms. In particular, the model developed in this study advances three-layer (a stationary bed layer of drilled cuttings at the bottom, a moving bed layer above it, and a heterogeneous suspension layer at the top) hydraulic model for the horizontal and near horizontal segment. An existing two-layer model was modified for a transit segment, and a one-layer model was used for the vertical segment. This paper specifically describes model development for each segment, solution, and the simulation results of the integrated segment model. The simulation results show how to obtain a reasonable pumping velocity and optimize the rheology of drilling fluid with the possible lowest pressure gradient that might serve as an operational guideline during drilling. Moreover, the effects of various parameters that affect the efficiency of cuttings transport are discussed. These results were compared with published experimental data. The observed agreement and discrepancies are discussed.