Investigating Transitional Flow Regimes in Annular Fluid Flow for Drilling Applications

In drilling operations, accurately predicting pressure along the annular gap, where fluids return to the surface, is of great importance to prevent formation fracturing and maintain well control. Flows in such geometries and typical drilling conditions may be laminar, transitional, or turbulent. While analytical solutions and empirical correlations exist for predicting pressure losses in the laminar and turbulent regimes, the transitional regime, particularly under hole-cleaning conditions with viscoplastic fluids, remains less understood. This uncertainty is aggravated in annular configurations where eccentricity and pipe rotation are present, rendering traditional correlations susceptible to error during transitions between regimes. To investigate the transitional points in such conditions, an experimental setup was designed with an acrylic glass outer pipe (100 mm diameter) and a stainless-steel inner pipe (60 mm diameter) across an 8.5-meter test section. The configuration allows the setting of eccentricity and rotational velocity of the inner pipe. Two measurement methods were employed: (1) pressure loss measurements relative to flow rate or Reynolds number, enabling direct observation of transitional behavior; and (2) particle image velocimetry (PIV), which provides detailed velocity profiles, enhancing insights into flow dynamics and transition. The tests were conducted using a viscoplastic fluid (polyacrylic acid, Carbopol). The experiments included concentric and five eccentric configurations, with each configuration including non-rotational tests and two rotational settings (48 and 156 RPM). Results are presented for pressure loss versus flow rate, friction factor versus effective Reynolds number, and rheological data. In addition, PIV data illustrates flow behavior across regimes. Results were categorized to isolate the effects of rotation and eccentricity. In concentric tests with rotation, pressure losses increased in the laminar and transitional regimes, while turbulent regimes remained unaffected by rotation. Transition onset was more gradual with rotation due to shifted velocity profiles, which displaced peak velocities towards the outer wall and increased wall shear rates, leading to higher pressure losses. In eccentric configurations without rotation, distinct flow behaviors appeared within the same cross-section: while turbulence developed in the wider gap, the narrower gap often retained laminar flow. Greater eccentricity reduced pressure losses in the laminar regime but led to earlier transition, with pressure losses during transition converging across eccentricities. In fully turbulent conditions, higher eccentricity again significantly affected pressure loss. When rotation and eccentricity were combined, rotation-induced velocity shifts persisted, leading to higher pressure losses in laminar regimes. Transition occurred at lower flow rates due to the combined effects of rotation and eccentricity, resulting in overall higher pressure losses. Transition predictions using existing methods were assessed: concentric configurations with low yield-stress fluids aligned well with models by Ryan & Johnson and Erge et al., while Pilehvari & Serth’s method better predicted transitions for eccentric setups and higher yield-stresses.