A generalized and consistent pressure drop and flow regime transition model for drilling hydraulics

Generalized laminar and turbulent pressure loss formulations are presented that are suitable for both annular and circular conduits. In so doing, a new rheological parameter is introduced that provides a consistent link between turbulent and laminar flow calculations and flow regime transition criteria. The approach presented is independent of the form of the rheological model of choice, it makes no assumptions about conduit geometry, can include the presence of a laminar plug flow region, accommodates drillpipe rotation effects and accounts for the effects of annular eccentricity. Simple, explicit and general formulations for approximating pressure losses over measurement while drilling tools and positive displacement motors are also presented to augment the suite of expressions required for comprehensive hydraulic calculation over the circulating system. Furthermore, procedures for establishing realistic bounds of confidence for laminar pressure loss functions are presented, enabling computation of the degree of certainty attributable to such a calculation. This procedure for establishing confidence intervals is applicable to any function requiring fitted parameters, hence it has a broader application potential than just drilling hydraulics. The model demonstrates good agreement with measured data from studies involving drilling fluids flowing in both circular and annular conduits.