A Transient Hydraulic Model for Accurate Gas Injection Rate Prediction and Stuck Pipe Mitigation During Gas Drilling of Directional

Abstract

Hole cleaning is a critical operational challenge in gas drilling, particularly in directional and horizontal wellbores, where cuttings accumulate along the low side of the annulus. Ineffective cuttings transport can cause hole packing, excessive torque and drag, and ultimately stuck-pipe incidents, increasing non-productive time (NPT) and operational costs. Traditional predictive models for minimum gas injection rates such as Angel’s kinetic-energy criterion (1957), Guo et al.’s semi-analytical approach (1994), and Chen et al.’s inclined-well extension (2014)—assume steady-state flow and fail to capture the transient dynamics occurring during intermittent drilling, especially after pipe connections when accumulated cuttings beds must be re-entrained. This study develops a physics-based transient hydraulic model to predict the time-dependent gas injection rate required for efficient hole cleaning and stuck-pipe prevention. A mechanistic, first-principles transient model was formulated to describe unsteady flow of a compressible gas-solid mixture in an inclined annulus. The governing equations integrate mass and energy balances while accounting for gravitational forces, frictional losses, transient accumulation effects, and kinetic energy changes. Unlike steady-state approaches, the model explicitly incorporates time-dependent accumulation, enabling simulation of cuttings-bed formation and re-suspension during circulation interruptions. Gas properties were captured using a real-gas equation of state, and particle slip velocity was determined via a modified Gray terminal-velocity correlation, recalibrated for confined annular flow and particle-wall interactions in deviated wellbores. An iterative solution was employed to determine the minimum volumetric gas injection rate required for effective cuttings transport across varying drilling conditions and rates of penetration (ROP). Validation against field data from a deviated well shows that during continuous circulation, the gas injection requirement stabilizes at ~67.76 std m3/min after 1000 minutes. Transient simulations indicate higher early-time demand immediately after restarting circulation, peaking at 82.08 std m3/min around 5 minutes post-circulation, reflecting the hydraulic effort needed to re-suspend accumulated cuttings. The rate gradually declines to 68.94 std m3/min after ~50 minutes as the annulus clears. The peak rate exceeds the field-recommended 76.74 std m3/min by 6.95%, providing a quantifiable transient safety margin. In comparison, existing models underpredict requirements: Chen et al. yields 62.68 std m3/min (18.32% error) and the Modified Angel criterion 42.00 std m3/min (45.27% error). The model captures transient cuttings transport dynamics, linking gas injection to time-dependent accumulation and instantaneous drilling parameters. It enables more accurate gas injection schedules, optimized compressor use, improved safety, and reduced NPT. The framework is suitable for real-time optimization and automated decision-support in complex directional, unconventional, geothermal, and extended-reach drilling operations.