The domestic drilling industry needs to reduce petroleum drilling costs and improve well productivity. Reducing the bottom-hole-pressure during drilling, increases penetration rates and induces positive flow that protects productive zones from infiltration of cuttings and fluids. Underbalanced drilling reduces the pressure on the drilled formations using low density drilling fluids such as air, mists, foams, or aerated drilling muds. Use of these fluids can increase drilling rate by 50 to 100%. Oil and gas producing rates are routinely increased by 25% to 50% when drill fluid invasion is reduced. Underbalanced drilling is particularly useful for drilling infill wells through depleted zones and for wells with long horizontal sections. Industry has developed simulation codes that are projecting wellbore pressures with increasing accuracy and are attempting to model cuttings transport in compressible drilling fluids and non vertical bores. The DEA 101 MudLite simulator is advancing a PC windows based, steady state simulator and a 3-D simulator is available from Roglands Research in Norway that can perform transient analysis. Neither program simulates downhole motor performance. The Petroleum Engineering Department at the University of Tulsa (UT) has developed a mathematical model of PDM performance for incompressible fluids and is developing a model of PDM performance for compressible fluids. They need performance data for PDM operation with compressible fluids to evaluate and verify their models. Work to be Performed: Simulate multi-phase compressible fluid flow in a coiled-tubing drilling system with emphasis on both rotary and percussive hydraulic/pneumatic power conversion, fluid dynamics in horizontal annuli and in on-reel coiled-tubing, and well design and drilling system optimization. Address specific industry concerns related to the successful application of compressible fluids to coiled tubing, directional, slimhole, and microhole drilling including: motor or hammer performance, cuttings transport, separation and surging of fluids in reeled tubing, and bottom-hole-assembly resonance and vibration in low density, compressible drilling fluids.