A fundamental wellbore hydraulics model is developed to simulate the pneumatic transport of solid cuttings in the drill-string/wellbore annulus. The model incorporates most of the parameters involved in air and/or mist drilling and forms the basis for a predictive tool for the optimal lifting velocity, an essential ingredient in the optimal design of the air and/or mist drilling program. Extensive parametric analysis of the system is performed to explore the predictability of some of the phenomena associated with air and/or mist drilling. The model is demonstrably capable of predicting pressure drop profile, velocity profiles, concentration distributions in the annulus and the associated phenomena under various simulated drilling conditions. Model prediction shows very good agreement with experimental data.