The problem of wellbore hydraulics in drilling operations poses an intractable problem to ihe drilling engineer anempting to design a drilling program. Intricate interactions between the drill cuttings, the transport fluid (be it drilling mud or air), ihe wellbore and the drill string constitute the source of the difficulties. Lack of understanding of the physics involved coupled with the lack or hind am en Lai descriptive capability, inhibits the development of appropriate predictive capability. This problem is more apparent in the case of air drilling since only a limited amount of data is available on which empirical correlations can be based. A system atic study of this problem especially utilizing a fundamental approach is lacking. This study addresses this important problem using a fundamental hydro-dynamic multiphase flow model. The model incorporates the fundamental phvsics involved in the pneumatic transportation of solid cuttings' in the drill stnng-wellbore annulus. This model forms the basis for a predictive tool for the optimal lifting velocity, an essential ingredient in the optimal design of the air drilling program. Drilling engineers often experience frustration due to lack of models with adequate predictive capability to help generate this basic design parameter. Available correlations are, at best, gross approximation and more importantly, they woefully fail to account for the physical phenomena that are observed in pneumatic conveying involved in air drilling such as choking, dumping, etc. We present a fundamental wellbore hydraulics model based on ihe understanding of the physics involved in ihe pneumatic transport of solid curlings in the the drin-string/wellbore. Annulus. The model accommodates non-uniformity in particle sizes. Extensive paramet-ric analysis of the system is performed ID explore the predictability of same of the phenomena associated with air drilling. The model is demonstrably capable of predicting the pressure drop profile in the annulus under various simulated drilling conditions. In addition, results demonstrate ihe capability of ihe model in being able to predict a number of phenomena that are associated with lifting airruigs out of the bole during air drilling. Model prediction shows very good agreement with experimental data. Finally, the model possesses good scaleup capability.